Convection from multiple jets over a complex moving surface

Flávia Vieira Barbosa novembro de 2021 UMinho | 2021 Convection from Multiple Jets over a Complex Moving Surface Universidade do Minho Escola de Engenharia Flávia Vieira Barbosa Convection from Multiple Jets over a Complex Moving Surface novembro de 2021 Tese de Doutoramento Programa Doutoral em Líderes para Indústrias Tecnológicas Trabalho realizado sob a orientação de Professor Doutor José Carlos Fernandes Teixeira Professora Doutora Senhorinha de Fátima Capela Fortunas Teixeira Flávia Vieira Barbosa Convection from Multiple Jets over a Complex Moving Surface Universidade do Minho Escola de Engenharia ii DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos. Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada. Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho. Licença concedida aos utilizadores deste trabalho Atribuição-NãoComercial CC BY-NC https://creativecommons.org/licenses/by-nc/4.0/ iii ACKNOWLEDGMENTS Este documento reflete muitos anos de trabalho e dedicação, e a sua conclusão não teria sido possível sem o apoio de algumas pessoas e instituições. Antes de mais, quero agradecer ao meu orientador, Professor José Carlos Teixeira, por todo o apoio prestado desde a licenciatura até ao doutoramento. Por confiar no meu trabalho e por estar sempre presente para dar os impulsos necessários para que a investigação fosse conduzida com sucesso. À Professora Senhorinha Teixeira, pelos comentários construtivos, conselhos e partilha de informação relevante para que a tese fosse levada a bom porto. Agradeço ainda ao Professor Pierre Lermusiaux do MIT por me ter acolhido e dado uma oportunidade de viver uma das melhores experiências da minha vida. Um agradecimento especial ao Professor Sérgio Sousa pelo seu apoio incansável no desenvolvimento do DoE. Ao Eng. Carlos Costa, pelo apoio prestado, pelos conhecimentos partilhados, e pelas longas semanas de trabalho em torno da instalação experimental e quantificação de incertezas. Ao Eng. Filipe Marques, por impulsionar o trabalho prático nas oficinas do DEM e pela partilha de experiências que me ajudou na tomada de decisões. Ao Eng. Nuno Pacheco, por estar sempre atento e disponível para ajudar nos trabalhos experimentais. Ao Wael por todo o apoio prestado nos trabalhos desenvolvidos no MSEAS e ao Abhinav pela partilha de conhecimentos do 2.29 FV. Quero ainda agradecer à Fundação para a Ciência e Tecnologia (FCT) pela bolsa de doutoramento que me foi atribuída (PD/BD/128216/2016), sem a qual este trabalho não poderia ter sido realizado, e ao programa MIT Portugal pela oportunidade que me concedeu em realizar o programa doutoral LTI. Assim como ao MEtRICs pelo apoio na investigação e apresentação de trabalhos em conferências nacionais e internacionais e ao Departamento de Engenharia Mecânica da Universidade do Minho por me facultar condições para realizar o trabalho mas também por me ter convidado a lecionar. Finalmente agradeço aos meus fortes pilares, à minha família e amigos pelo apoio ao longo desta caminhada. Começando pelo meu namorado, Orlando, por ser o meu porto seguro e nunca me deixar desanimar por mais ingreme que o caminho fosse. Aos meus amigos e parceiros Vítor e Filipe que estiveram sempre ao meu lado ao longo destes últimos anos, apoiando em tudo o que pudessem, transmitindo sempre boas energias. Ao João que me ajudou com o CFD e à Andreia Faria, minha parceira do PhD, que se tornaram grandes amigos neste percurso. Um agradecimento especial à Professora Cândida Vilarinho pelo carinho e apoio prestado ao longo da minha vida académica. Agradeço à minha irmã, Andréa, pelo carinho e por acreditar sempre em mim, e especialmente aos meus pais e avós, pelos valores que me transmitiram e por me incentivarem a seguir os meus sonhos e nunca desistir. Sem eles não seria quem sou hoje. Muito obrigada a todos. iv STATEMENT OF INTEGRITY I hereby declare having conducted this academic work with integrity. I confirm that I have not used plagiarism or any form of undue use of information or falsification of results along the process leading to its elaboration. I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of Minho. v RESUMO Convecção por jatos múltiplos sobre uma superfície complexa em movimento Os jatos múltiplos de ar são usados como processo de convecção forçada em diversas aplicações de engenharia, uma vez que garantem elevadas taxas de transferência de calor. Porém, a complexidade da física envolvida no impacto dos jatos sobre a superfície alvo em espaços confinados torna esta área de investigação desafiante. Em algumas indústrias, a complexidade do aquecimento e/ou arrefecimento aumenta com o uso de superfícies irregulares e em movimento, tal como no processo de soldadura por refluxo. Por forma a contribuir para a sua melhoria em ambiente industrial, este trabalho tem como objetivo o estudo experimental e numérico do impacto de jatos de ar sobre superfícies complexas em movimento. Uma instalação experimental foi desenvolvida para a medição da velocidade do escoamento usando um sistema 2D-PIV, e a transferência de calor sobre a superfície alvo é medida por um sensor de fluxo. Estas técnicas experimentais permitem a caracterização da dinâmica do escoamento de um e múltiplos jatos. Os resultados provam que a técnica PIV captura com rigor as estruturas complexas do escoamento, geradas em toda a zona de medição, para diferentes números de Reynolds. Para além disso, modelos numéricos foram desenvolvidos usando o software comercial ANSYS FLUENT para a simulação de jatos em diferentes regimes de escoamento, assim como uma ferramenta própria desenvolvida em MATLAB para a análise do escoamento de um jato laminar. A comparação com dados experimentais mostra que o FLUENT prevê com rigor as diferentes regiões do jato, as interações entre jatos, bem como a transferência de calor, sem comprometer a eficiência computacional, ao passo que a ferramenta MATLAB consegue prever os vórtices gerados em todo o domínio. De modo a otimizar o trabalho experimental, os ensaios são definidos usando um planeamento de experiências baseado no método de Taguchi. Este método mostra que o processo de convecção por jatos múltiplos é otimizado para elevados números de Reynolds, um espaçamento entre jatos e uma distância entre a placa de jatos e a superfície alvo igual a 3 e 2 vezes o diâmetro do jato, respetivamente. Por outro lado, os resultados mostram um aumento da transferência de calor em 25% na vizinhança do degrau localizado sobre a superfície, devido ao aumento da turbulência do fluído comparativamente com a superfície plana. Finalmente, os resultados experimentais e numéricos apresentam um aumento da taxa de transferência de calor com o movimento da placa, mesmo quando são aplicadas baixas velocidades. Correlações para a determinação do número de Nusselt médio são propostas para superfícies estáticas e dinâmicas, estando de acordo com a literatura. Palavras-chave: Dinâmica de Fluídos Computacional; Impacto de jatos; Velocimetria por imagem de partículas; Planeamento de experiências; Transferência de calor. vi ABSTRACT Convection from multiple jets over a complex moving surface Multiple air jet impingement is a complex heat transfer process widely used in several engineering applications since it allows high heat transfer rates. However, the complexity of the physics under multiple jets impinging a target surface in a confined space makes this research field highly challenging. In some industrial processes, the complexity of the cooling and/or heating is increased by non-flat and moving surfaces, which is the case of the reflow soldering process. To provide relevant insights for industries that apply multiple jet impingement in their processes, this work focuses on the experimental and numerical study of air jets impinging a complex moving surface. A purpose-built test facility has been commissioned to measure the flow field velocity using a 2D-PIV system, while the heat transfer over the target plate is collected using a heat flux sensor. These experimental techniques are used to characterize the jet flow dynamics of single and multiple air jets. The results demonstrate that the PIV is able to capture the complex flow structure generated all over the measurement region, for different Reynolds numbers. Moreover, numerical models were developed using the commercial software ANSYS FLUENT to simulate jets lying in all flow regimes, and an in-house MATLAB code to analyze a laminar single jet impingement. Comparisons with experimental data show that FLUENT predicts with accuracy the jet flow regions, jets interactions, and heat transfer, at low computational costs, while the MATLAB code is able to capture the large and small scales induced over the domain. To optimize the experimental work, the tests are defined using a Design of Experiments based on Taguchi’s method. This study demonstrated that the multiple jet impingement process is optimized for high Reynolds numbers, a jet-to-jet spacing, and a nozzle-to-plate distance equal to 3 and 2 times the jet diameter, respectively. Furthermore, results show that the heat transfer increases 25 % in the vicinity of the step surface due to the increased flow turbulence induced by the step compared with a flat plate. Finally, both numerical and experimental results highlight an increase of the heat transfer rate with the plate motion, even for low target surface velocities. Correlations for the average Nusselt number are proposed for both static and moving plates and are in good agreement with the literature. Keywords: Computational Fluid Dynamics, Design of Experiments, Heat Transfer, Jet Impingement, Particle Image Velocimetry. vii TABLE OF CONTENTS ACKNOWLEDGMENTS ............................................................................................................................. III RESUMO ............................................................................................................................................ V ABSTRACT ..........................................................................................................................................VI TABLE OF CONTENTS ........................................................................................................................... VII LIST OF FIGURES ................................................................................................................................. IX LIST OF TABLES .................................................................................................................................. XV LIST OF ACRONYMS ........................................................................................................................... XVII LIST OF SYMBOLS ............................................................................................................................... XIX 1. INTRODUCTION ............................................................................................................................. 1 1.1. Motivation ........................................................................................................................... 1 1.2. Scope and Objectives .......................................................................................................... 4 1.3. Research Methodology ........................................................................................................ 5 1.4. Thesis Outline ..................................................................................................................... 7 1.5. Scientific Contribution ......................................................................................................... 9 2. LITERATURE REVIEW .................................................................................................................... 11 2.1. Jet Impingement ............................................................................................................... 11 2.2. Influence of Process Variables ........................................................................................... 15 2.3. Jet Impingement Modeling ................................................................................................ 39 3. EXPERIMENTAL METHODS ............................................................................................................. 45 3.1. Experimental Procedure .................................................................................................... 45 xiv Figure 107. Variation of the Nusselt number in function of the Reynolds number for H/D = 2 and S/D = 3. ................................................................................................................................................ 198 Figure 108. Variation of the Nusselt number in function of the Reynolds number for H/D = 6 and S/D = 6. ............................................................................................................................................. 199 xv LIST OF TABLES Table 1. Correlations for average Nusselt number. ......................................................................... 36 Table 2. Turbulence models applied in jet impingement simulations. ............................................... 43 Table 3. Averaged heat flux and temperature measurements. ......................................................... 52 Table 4. Analytical results of heat flux over the plate. ...................................................................... 53 Table 5. Reynolds number obtained by the total pressure measurements. ........................................ 58 Table 6. Systematic uncertainties. ................................................................................................. 66 Table 7. Systematic uncertainties. ................................................................................................. 67 Table 8. Virgin olive oil properties. ................................................................................................. 79 Table 9. Variation of the mean vaporizer temperature in function of the heater voltage and the flow rate in steady-state conditions. ............................................................................................................ 82 Table 10. Velocity and Reynolds number at the exit of the orifice nozzle measured indirectly using the Pitot tube and directly by PIV. ....................................................................................................... 92 Table 11. Optimized time between pulses for different Reynolds numbers. ....................................... 94 Table 12. Air Properties at 22 °C. ............................................................................................... 110 Table 13. Simulation data information. ........................................................................................ 110 Table 14. Mesh Properties. ........................................................................................................ 113 Table 15. Air Properties at 25 °C. ............................................................................................... 116 Table 16. Properties of the three grids analyzed. .......................................................................... 116 Table 17. Comparison between the experimental heat transfer values and data presented in the literature. ................................................................................................................................................ 127 Table 18. Instantaneous velocity profile at Re = 420 obtained by FLUENT and 2.29 FV. ................. 128 Table 19. Average Nusselt number obtained experimentally and numerically. ................................. 140 Table 20. Selected factors and their levels. .................................................................................. 154 Table 21. Design Orthogonal Array generated using Minitab™. ...................................................... 156 Table 22. Nusselt number obtained from the static and moving plate experiments. ......................... 157 Table 23. ANOVA results for Signal-to-Noise ratios for the static plate case. .................................... 172 xvi Table 24. ANOVA results for Signal-to-Noise ratios for the moving plate case. ................................. 172 Table 25. ANOVA results for Signal-to-Noise ratios for the static plate case. .................................... 174 Table 26. ANOVA results for Signal-to-Noise ratios for the moving plate case. ................................. 174 Table 27. Confirmation test results.............................................................................................. 175 Table 28. Average Nusselt number measurements. ...................................................................... 184 Table 29. Average Nusselt number over the static plate. ............................................................... 186 Table 30. Average Nusselt number over the moving plate. ............................................................ 187 xvii LIST OF ACRONYMS ANOVA Analysis of Variance CAGR Compound Annual Growth Rate CCD Charge Coupled Device CD-SR Convergent-Divergent Ribs CDS Central Difference Scheme CFD Computational Fluid Dynamics CFL Courant-Friedrichs-Lewy DNS Direct Numerical Simulation DoE Design of Experiments DoF Degree of Freedom EDAM Engineering Design and Advanced Manufacturing EVM Eddy Viscosity Models FCT Fundação para a Ciência e Tecnologia FV Finite Volume GCI Grid Convergence Index HFS Heat Flux Sensor IA Interrogation Area LES Large Eddy Simulation LIF Laser-Induced Fluorescent LTI Leaders for Technical Industries MIT Massachusetts Institute of Technology MSEAS Multidisciplinary simulation, Estimation, and Assimilation Systems xviii N-S Navier-Stokes Equations OA Orthogonal Array PCB Printed Circuit Boards PIV Particle Image Velocimetry RNG Re-Normalisation Group RSM Reynolds Stress equation Model SMD Sauter Mean Diameter SMT Surface Mount Technology SST Shear Stress Transport TFO Transitional Flow Option TVD Total Variation Diminishing UW Upwind scheme V-SR V-Shaped Ribs 2D 2-Dimensional 3D 3-Dimensional LIST OF SYMBOLS Latin Symbols Symbol Unit (SI) Description Af - Non-dimensional area A (m) Area B - Systematic uncertainty C - Physical advection speed d (m) Dimple depth di (m) Mean diameter of the size band doff (m) Offset distance D (m) Diameter e (m) Height of rib F - Variance ratio g (m/s2) Gravitational acceleration G (kg/s) Mass flow rate Gk (kg/m·s3) Generation of k Gω (kg/m3·s2) Generation of ω Gr - Grashof number h (W/m2K) Heat transfer coefficient h  (W/m2K) Average heat transfer coefficient xx H (m) Nozzle-to-plate distance I (%) Turbulence intensity k (m2/s2); (W/m·K) Turbulent kinetic energy; Thermal conductivity kp - Expansion factor l (m) Characteristic length L (m) Length Lj (m) Estimated seeding particle diameter Ma - Mach number n - Refractive index; Number of test repetitions N - Samples number Nu - Nusselt number Nu     - Average Nusselt number p (Pa) Pressure pi - Sensitivity coefficient P (Pa) Pseudo-pressure Pr - Prandtl number q (W/m2); - Heat flux; order of the method q (W/m2) Average heat flux Q (W) Heat transfer rate r (m) Radial distance Ra - Rayleigh number Re - Reynolds number Ri - Richardson number xxi S (m) Jet-to-jet spacing SS - Sum of squares SS’ - Pure sum of squares Sc - Scale factor Seff - Seebeck coefficient Sq (μV/W/m2) Sensor sensitivity St (1/s) Modulus of the mean rate-of-strain tensor Sx, Sy (m) Streamwise pitch, Spanwise pitch Sϕ (W/m3) Source term t (s) Time T (°C) Temperature T* (dependent variable) Grand total of all results u (dependent variable) Uncertainty u95 (dependent variable) Uncertainty for 95 % confidence U (m/s) Velocity U’ (m/s) Velocity fluctuation U  (m/s) Average velocity Uτ (m/s) Shear velocity V (m3); - Volume; Variance 𝑉󰇗 (m3/s) Volumetric flow rate Vi (m3) Relative volume Vs - Surface-to-jet velocity y+ - Dimensionless distance of the first node to the wall xxii Yi (dependent variable) Quality characteristic Yk (kg/m·s3) Dissipation of k Yopt (dependent variable) Estimated performance at optimum condition Yω (kg/m3·s2) Dissipation of ω x, y, z - Cartesian coordinates u, v, w (m/s) Velocity according to the cartesian coordinates Greek Symbols Symbol Unit (SI) Description α - Slip correction adjustment factor β - Response phase β* (1/°C) Coefficient of volume expansion 𝛾 - Intermittency factor Γk (kg/m·s) Effective diffusivity of k Γω (kg/m·s) Effective diffusivity of ω ∆t (s) Time between laser pulses ∆ V (V) Output voltage ∆x (m) Absolute distance of the first grid cell to the wall ∆xp (pix) Particle displacement ∆δ (m) Thickness ε (m2/s3) Turbulent dissipation rate η - Amplitude ratio θ (°) Angle with the jet impinging point xxiii κ (m2/s) Thermal diffusivity μ (Pa/s) Dynamic viscosity μt (Pa/s) Turbulent dynamic viscosity υ (m2/s) Kinematic viscosity υt (m2/s) Turbulent kinematic viscosity ξ (dependent variable) Error ρ (kg/m3) Density 𝜎 - Standard deviation σx - Random uncertainty σxR - Resultant random uncertainty σxU,V (m) Displacement random uncertainty σω, σk - Turbulent Prandtl number τij (Pa) Reynolds stress tensor ϕ (dependent variable) Scalar quantity ω (1/s) Specific dissipation rate Ω (1/s) Angular frequency Subscripts ∞ Ambient air cf Crossflow ce Cell d Dimple 6 1. INTRODUCTION behave?” , while numerical simulation focuses on “ How it is possible to predict the behavior of the interaction between impinging jets and a moving non-flat surface in an industrial process?”. Even if these methodologies are complementary, each one can be, in the beginning, conducted separately. After the complete definition of the numerical modeling of the multiple jet impingement system, some experimental results can be introduced in the numerical model to enhance the accuracy of the simulations. The analysis of both numerical and experimental results allows to define the heat transfer of multiple jet impingement over a complex moving surface. In the end, the knowledge acquired throughout the experimental and numerical studies allows to optimize the multiple air jet impingement process, which can be implemented in the reflow soldering, in order to reduce product defect and to increase the process performance. To determine the convective conditions that allow to simulate the multiple air jet impingement process with accuracy, it is necessary, first, to perform experimental tests. Through these experiments, it is possible to characterize all the variables involved in this forced convection process, from the flow characterization to the analysis of the geometrical properties between the jets and the target surface. This laboratory research is conducted on a purpose-built test facility that has been commissioned, using a PIV system. This technique is highly suited to measure the velocity field of flows, providing detailed information about the flow behavior over the target surface, but also to identify the phenomenon that occurs in the vicinity of surface transition (such as back steps and forward steps). To determine the heat transfer coefficients over the target plate, a heat flux sensor and thermocouples are applied on the impinging plate. However, to reduce time and costs related to the experimental tests, it is important to perform a Design of Experiments (DoE), which allows to reduce the number of tests, focusing on the parameters that have a greater influence on the process performance [11]. Taguchi’s method allows the optimization of the process through the selection of the most suitable parameter values. Therefore, this DoE method is applied in this work. The results obtained from these experiments allow to apply more realistic boundary conditions to the numerical simulation and the accuracy of the numerical model is validated by the experimental data. To develop the numerical simulation of the process, several studies such as [12]–[15], use the CFD (Computational Fluid Dynamics) software ANSYS FLUENT, specially designed to predict the flow behavior. This is an important tool to solve engineering problems since there is an increasing demand for precision in the least time possible to reduce production costs. Considering these advantages, numerical simulation has been a tool widely implemented in jet impingement studies. The fast advancement of computational resources and numerical algorithms has led to an improvement in the accuracy of the models used to 1. INTRODUCTION 7 study impinging flows and heat transfer. Most industrial applications that use jet impingement are governed by turbulent flows which is the case of reflow soldering. Nevertheless, these flows represent a great challenge to predict the behavior of jets with accuracy. To validate the turbulence model, proving its reliability, the results obtained numerically need to be compared with the experimental data. However, even if several numerical works have been conducted in multiple jet impingement, a lack of experimental studies that support the numerical modeling of multiple jets impinging on a complex moving surface was identified. This leads to an uncertainty of the results obtained numerically which is not acceptable in an industrial context. In that sense, this PhD thesis pretends to develop a reliable and accurate numerical model of this process which will take into consideration all the variables applied in the process but also the complex geometry of the target surface. 1.4. Thesis Outline This work focuses on the experimental and numerical analysis of multiple air jets impinging on a complex moving surface. Within this general objective, the present thesis is organized into seven chapters. The second chapter presents the literature review under the topic of this PhD thesis. The physical concepts under single and multiple air jet impingement are discussed, followed by the influence of the process variables on both jet flow dynamics and heat transfer performance. The correlation for the average Nusselt number for both single and multiple jet impingement is provided. Finally, the different methods applied for the numerical modeling of single and multiple jet impingement are presented. Although this work focuses on a multiple air jet impingement process, the single jet impingement must be fully understood to be able to interpret the physical concept under multiple jet interactions. Thus, the single jet is also explored in this work. Chapter three discusses the experimental methodology followed in this thesis. The purpose-built experimental setup is presented, and its operation is discussed. Furthermore, the experimental techniques used in this work are detailed. Due to its complexity, the PIV technique has a sub-chapter entirely dedicated to it, in which the study of the seeding particles, which plays an important role in the accuracy of the PIV measurement, is presented. Considering the relevance of the source of errors on the measurement’s accuracy, a section regarding this topic was created, as well as a section for data reduction and uncertainty estimation of the measured variables. Chapter four is dedicated to the numerical methodology implemented in this project. The main concepts are discussed, from the governing equations to the turbulence model applied. Two numerical techniques are explored in this thesis. A Direct Numerical Simulation (DNS) is conducted for the study of 8 1. INTRODUCTION a laminar single jet flow, using a MATLAB framework implemented by the MSEAS group at MIT, followed by RANS (Reynolds Averaged Navier-Stokes Equations) for the study of the jet flow in transition and turbulence regimes, using the ANSYS FLUENT software. All the details regarding the numerical domain, boundary conditions, and mesh sensitivity analysis are presented in this chapter. The results are divided into two chapters, five and six. Chapter 5 concerns the study of a single jet in a laminar and transition regime. This chapter is relevant since it makes the bridge between the relevant physical concepts concerning the jet flow dynamics and the main goal of this work, the study of the convection of multiple jets over a complex moving surface. The flow dynamics analysis of isothermal and non-isothermal jets impinging a flat plate is discussed. The experimental results are used to validate two numerical techniques implemented in Chapter four. Considering that the nozzle-to-plate distance ratio (H/D) is one of the most relevant process variables identified in jet impingement, the study of the effect of H/D on the flow dynamics of a jet in the transition regime is provided. Chapter six is the focus of the research since the experimental and numerical results of the multiple air jet impingement over a complex moving surface are presented. The presentation of the DoE methodology is the starting point of this chapter, from which a matrix of experiments is presented. This matrix sets the pattern to conduct both velocity field and heat transfer measurements. The heat flux measurements allow to define the effect of each control variable on the average heat transfer performance, and the jet’s flow velocity profiles obtained by the PIV measurements analyze the effect of these variables on the jet’s flow dynamics and provide the physical insight of the flow dynamics to understand the cause-effect diagrams and ANOVA (Analysis of Variance) analysis. From this study, an optimized configuration is obtained, and a numerical model is developed. The experimental data are used to validate the optimized numerical modeling of multiple air jets impinging a complex moving surface. At the end of this chapter, correlations for both static and dynamic plates impinged by multiple air jets are proposed. Finally, in chapter seven, the most relevant conclusions of the present work are outlined. Based on the experimental and numerical work, different research lines are proposed for future investigation in this field. 1. INTRODUCTION 9 1.5. Scientific Contribution Jet impingement is widely implemented in a variety of engineering applications and industrial processes, essentially in thermal equipment for heating, cooling, and drying and, as such, this process has been extensively investigated [10]. This technology received considerable attention due to its inherent characteristics of high performance for heat transfer enhancement in thermal equipment, providing very high rates of heat transfer, which lead to rapid cooling and heating in specific heat transfer areas [16] [17]. Even if several works have been published in this area, it is observed a lack of studies in multiple jet impingement that involves target surface motion and the influence of different geometries over the impinging surface, such as electronic components with different sizes and shapes. Until now, no study addresses the average heat transfer in the vicinity of surface transitions (such as back steps and forward steps) coupled with surface motion. In that sense, this PhD thesis focus on the study of the non-isothermal jet interaction with non-flat surfaces moving perpendicularly to the jet axis. This investigation enables the definition of more realistic boundary conditions and turbulence models for the thermal simulation of multiple air jet impingement. To achieve, with success, the objectives previously stated, this project follows an experimental and numerical approach. The results are expected to contribute to the enhancement of scientific knowledge and industrial processes that use multiple air jet impingement, in order to optimize the engineering applications and to reduce the problems and defects related to nonuniform heat transfer. The project thesis involves proficiency in several areas, from the design and construction of a setup and experimentation using a PIV system to the effective learning and application of theoretical concepts in jet impingement, heat transfer, and numerical modeling. The innovation and added values of this thesis are reinforced by the LTI PhD program partnership since the numerical models developed during the project are improved through the collaboration of MIT. This is an ambitious project that intends to provide relevant answers to the reflow soldering process, but which can be extended to other applications that use multiple jet impingement. In that sense, the LTI provided relevant methodologies necessary to combine the research and advanced processes in order to obtain results worthy to be implemented in technically advanced industries. This page was intentionally left in blank. 2. LITERATURE REVIEW 11 2. LITERATURE REVIEW Impinging jets have been extensively studied due to their wide applicability in engineering applications, where high heat transfer rates are required. However, the complexity of this flow continues to encourage researchers to provide scientifically-based solutions to the industry in order to reduce product defects and increase heat transfer performance. Jet impingement can be performed by single or multiple jets. While single jets have a localized high heat transfer rate, multiple jets produce a more uniform cooling and heating, which can be a great advantage in some applications [18]. In a multi-jet configuration, the individual jets can be substantially affected by different interactions that increase the complexity of the flow. In addition, the jet impingement process involves several variables which increase these flow interactions, from the jet flow parameters (velocity and temperature) to the target surface and process geometry (nozzle-to-plate distance, ribs, etc.). To fully characterize the flow field and heat transfer of a jet impingement process, several studies have been conducted. In that sense, this chapter focuses on the flow characterization of single and multiple jet impingement systems as well as the analysis of the influence of the process variables on the heat transfer efficiency over the target plate. Considering the fast advancement of numerical tools and their increasing implementation to predict the fluid flow structure and heat transfer of single and multiple jet impingement, this chapter analyzes different numerical and experimental works that have been conducted in this field and presents the relevant concepts and phenomena. 2.1. Jet Impingement Jet impingement is a complex heat transfer process that involves flow interactions between the jets and the target surface. To be able to analyze accurately all the phenomena that occur during the jet impingement, it is important to understand the underlying physics of single and multiple jets. 12 2. LITERATURE REVIEW 2.1.1. Jet Flow Characterization In jet impingement, fluid passes through a nozzle and flows into a domain with ambient fluid in rest, and progresses in direction to the target plate. Once the flow reaches the surface, strong flow interactions occur over the wall, and high heat transfer rates are obtained, ensuring an effective cooling or heating of the impinging plate. From the nozzle to the target plate, different regions can be identified. This work was first conducted by Martin [19], who presented relevant insights in this field and divided the jet impingement regions into the free jet, the stagnation zone, and the wall jet. Between the free jet and the stagnation regions, Viskanta [20] identified the decaying region and subdivided it into two zones, the initial “developing zone” and the “fully developed zone”. These primary studies are the basis for the development of a jet flow configuration known until then and presented in Figure 4. Figure 4. Flow regions of an impinging jet captured by the PIV system. Right-hand side: Averaged velocity field; Left-hand side: Instantaneous flow field. The free jet region is generated at the nozzle exit, being characterized by its maximum velocity. As the jet flows through the nozzle, it produces a near flat-topped velocity profile, dominated by axial velocity. Once the jet flow starts to mix with the ambient fluid, a shear flow generated at its edges is the primary source of turbulence characterized by entrainment of mass, momentum, and energy [20]. This entrainment generates several effects such as jet expansion, a nonuniform radial velocity profile within the jet, the increase of the overall mass flow rate, and jet temperature change before the impingement over the target surface. As the jet develops in direction of the impinging plate, the shear layer grows. If the jet velocity is high, i.e. Re > 1,000, the destabilizing effects of the shear forces overcome the stabilizing effect of fluid viscosity/momentum diffusion and Kelvin-Helmholtz instabilities are induced [21]. These instabilities increase the flow entrainment and form large-scale eddies along the sides of the jet. The length scale of the large-scale eddies correlates with the jet diameter. This structure is preserved 2. LITERATURE REVIEW 13 until eddies break up into smaller ones or when an interaction with other downstream flows occurs [22]. The strong interactions between the jet flow and the surrounding fluid induce a decrease in velocity as the flow gets closer to the target plate. The point where the maximum velocity decays 5 % defines the end of the potential core [23]. As depicted in Figure 4, the end of the core region represents the beginning of the decaying region, characterized by the decay of the axial velocity caused by large shear stress at the jet boundary [20, 21]. Viskanta [20] subdivided the decaying region into the “developing zone” and the “developed zone”, characterized by a bell-shape that can be described approximately by a Gaussian distribution. As the flow gets closer to the wall, it loses axial velocity and turns, generating a stagnation region in which the velocity is near zero [24]. In the stagnation region, the flow is characterized by higher static pressure on and above the wall, the eddies are stretched and distorted and the flow is gradually reoriented to be roughly parallel with the wall [25], inducing the wall upstream effect [21]. According to Katti & Prabhu [9] the stagnation region occurs at a nozzle-to-plate distance ratio (H/D) below the unity. The last zone, called the wall jet region, occurs once the jet impacts the target surface. After the contact with the plate, the flow is divided into two streams moving in opposite radial directions along the surface, being observed a change of the flow direction from axial (vertical axis y) to radial (longitudinal axis x) direction. As the flow impinges the wall, its kinetic energy decreases rapidly and is converted into a corresponding rise in pressure energy which generates an accelerated streamwise flow in radial direction [26]. A boundary layer is formed, showing a constant thickness, typically lower than 1 % of the jet diameter [19], and grows until maximum levels of turbulence are reached, away from the jet axis [9, 22]. Higher heat transfer coefficients are identified in the vicinity of the stagnation region, where the boundary layer is thinner. As the boundary layer gets thicker, turbulence increases due to turbulent fluctuations in velocity and pressure gradient which produce a reversal of the local flow along the wall and promote the formation of secondary vortices [24]. These vortices cause local rises in heat and mass transfer [22]. The separation of the flow occurs where the boundary layer leaves the surface of the plate [8]. 2.1.2. Multiple Jet Impingement In several applications such as reflow soldering, textile drying, and cooling of turbojet blades, high average heat transfer coefficients and the uniformity of the heat transfer over the impinging surface are required to improve the performance of the process and to avoid local hot (or cold) spots. These applications require large areas, and therefore, a single jet system is not efficient, being the multi-jet configuration more appropriate. 14 2. LITERATURE REVIEW Regarding the flow as arrays of impinging jets, the same three regions identified in single jet impingement are recognized: free jet, stagnation zone, and wall jet [19]. However, as mentioned above, in a multiple jet configuration, the individual jets are substantially affected by three types of interactions that do not occur in a single jet impingement: the jet interference between adjacent jets prior to the impingement over the target surface; the jet-to-jet interaction among the adjacent jets after the impingement over the surface; and the interactions due to jet-induced crossflow [7]. Figure 5 represents the main regions identified in a multiple jet impingement process. Figure 5. Flow regions of a multiple jet impingement for Re = 2,000, S/D = 5.7 and H/D = 3: (a) orifice nozzle; (b) free jet; (c) separation flow; (d) stagnation point; (e) stagnation region; (f) wall jet region; (g) central jet; (h) adjacent jets; (i) fountain flow; (j) collision point; (k) upwash flow; (l) primary vortices; (m) separation point; (n) vortices. The flow exits the orifice nozzles [Figure 5 (a)] with a mostly flat velocity profile at a maximum value [21]. As the flow moves downstream, it progresses through a free jet region [Figure 5 (b)] in which jets and the surrounding air start to mix, leading to some flow separation [Figure 5 (c)] identified at the sides of the jets. Jets transfer momentum and entrain surrounding flow, leading to an increase of the jet’s mass flow and a decrease of their energy and, consequently, a decrease of the velocity magnitude along jets periphery is observed [20] [27]. As the jets approach the target plate, the axil velocity decreases, reaching the stagnation point [Figure 5 (d)], and the flow is diverted radially. This is the stagnation region [Figure 5 (e)], characterized by a constant thin boundary layer [21]. After the impingement, the jets turn and the flow moves parallel to the target wall, entraining surrounding flow, growing in thickness, and decreasing in velocity magnitude. This is the wall jet region [Figure 5 (f)]. In this specific zone, [27] observed that the impinging surface starts to obstruct the flow leading to a deflection of jets into the wall-parallel direction. The remaining part of the spent fluid flows in direction of the outlet, generating a self-induced crossflow. This crossflow interaction can cause an asymmetric jet flow field, disruptions to other wall jets, movement of the stagnation points, thicker boundary layers, and a reduction of the average heat transfer rates [21]. The collision between the wall jets of the central jet [Figure 5 (g)] and adjacent jets [Figure 5 (h)] generate a fountain flow region [Figure 5 (i)], clearly identified on both sides of the central jet. The collision between 2. LITERATURE REVIEW 15 the two wall jets originates a second stagnation region at the collision point [Figure 5 (j)], and the rotation of the flow. Here, upwash flows [Figure 5 (k)] are induced, leading to an increase of the axial velocity in the jets shear layers and to a generation of recirculation regions on both sides of the central jet, identified by Caliskan et al. [28] as primary vortices [Figure 5 (l)]. These large primary vortices interfere with the flow development of the adjacent jets. While in the central jet the vortex ring is closed, the vortex flow of the jets located around it are pushed outwards. The separation of the jet’s flow from the wall occurs where the boundary layer detaches the surface of the target plate. The position of the separation point [Figure 5 (m)] moves away from the centerline of the jet with increasing the Reynolds number [24]. Looking at the vortices generated at the boundaries of the side jets [Figure 5 (n)], it seems that the separation point occurs at a higher distance from the jet axis, minimizing the interference of these vortices with the jet flow. Considering that the behavior of the heat transfer in multiple jet impingement is highly influenced by the geometric variables and flow properties, but also by the roughness of the impinging surface, all these process variables need to be very well understood to enhance the heat transfer performance. In that sense, they will be referred to in the following section. 2.2. Influence of Process Variables Although heat transfer by jet impingement is highly effective and easily controllable by changing the flow rate [29], it is highly heterogeneous and associated with complex interactions between a wide variety of parameters [30]. Therefore, a wrong combination between them can result in a decrease in heat transfer rates over the target plate. In that sense, these process variables are discussed in this section and Figure 6 identifies the terminology used. Figure 6. Basic geometric parameters in jet impingement. 22 2. LITERATURE REVIEW In summary, this analysis shows that the effect of the jet pattern in heat transfer depends mainly on the jet-to-jet spacing and the nozzle-to-plate distance. Comparing the results presented by [7, 39, 43, 44, 50, 51, 53], it seems that for S/D ≥ 3 and H/D = 2, the staggered pattern enhances the heat transfer compared with inline arrays, due to stronger jet’s interactions. While, for S/D < 3 and H/D ≥ 3, the degrading effects of crossflow are intensified, reducing the heat transfer over the surface. Therefore, in this specific case, an inline configuration increases the heat transfer rate due to the protecting effect of upstream jets on downstream jets from crossflow. This means that equilibrium must be found between the effect of the different variables on crossflow, in order to ensure that the turbulence intensity induced inside the confined space promotes the heat transfer and does not degrade it. 2.2.3. Jet-to-Jet Spacing In multiple jet impingement, jet-to-jet spacing is a parameter extremely important since it influences the jet’s interaction upstream the impingement of the target surface. Two jet-to-jet spacing configurations are possible, irregular arrangements, in which the spanwise (Sy) and streamwise (S x ) distances are different and regular arrangements, where Sx = Sy = S. Due to the added complexity of irregular arrangements, regular ones have been studied more frequently [54]. The jet-to-jet interaction is mainly caused by the upwash flows, already presented in Figure 5 (k), resulting from the collision of wall jets. Therefore, the interactions between jets before and after the impingement are intensified at low S/D, as confirmed in several studies [7, 27, 48, 55–60]. At the collision point, midway two jets, Figure 5 (j), a second heat transfer peak arises due to their strong interaction. Buchlin [61] explained that this phenomenon occurs due to the increase of the pressure gradient when two jets approach each other, inducing a thickening of the boundary layer which generates a flow separation, giving rise to a complex three-dimensional vortex. The remaining part of the spent fluid leaves the configuration, generating a self-induced crossflow which can cause an asymmetric jet flow field, disturbs other wall jets, moves stagnation points, thickens boundary layers, reducing the average heat transfer rates over the plate [21]. San & Lai [62] observed that, for small S/D, the interference between two adjacent jets occurs before the impingement due to the shear layer expansion, which weakens the jet strength, minimizing the heat transfer. In addition, Ichikawa et al. [29] verified that a small S/D ratio leads to an intensification of the effect of the interaction between adjacent jets and the velocity dispersion after the vortex roll-up affects the jet directly. Recently, Li et al. [38] and Chen et al. [63] found that higher S/D values reduce the heat transfer mainly due to inadequate surface coverage. These observations are in agreement with [48]. 2. LITERATURE REVIEW 23 Considering the complex flow dynamics induced by jet interactions in multiple jet impingement, several studies focused on the analysis of the jet-to-jet spacing that enhances the average heat transfer rates. Metzger et al. [64] determined that the heat transfer is higher for configurations with S/D < 10 in both streamwise and spanwise directions. Buchlin [61] observed that increasing the distance from the jet axis, the velocity dispersion increases at S/D = 4 and S/D = 6 due to the influence of vortex breakdown which induces large velocity dispersions [65]. From their analysis, San & Lai [62] concluded that the optimum jet-to jet-spacing, considering a Reynolds number between 10,000 and 30,000, is 8 for a nozzleto-plate distance equal to 2, 12 if H/D is equal to 3, and 6 for H/D equal to 5. Goodro et al. [66] observed that for a streamwise and spanwise distance equal to 12 D, the jets show the behavior of an individual jet. However, decreasing the distance to 8 D, the influence of the adjacent jets is strong, inducing crossflow and interactions. In that sense, the averaged Nusselt number is higher for a jet spacing of 8 D than for 12 D at the same conditions, as it can be observed in Figure 11. In its turn, Yong et al. [7] mentioned that for S/D = 3 the highest heat transfer is observed at the same Reynolds number (16,130). However, considering the same mass flow rate of coolant per unit area of cooled surface, it seems that S/D = 5 increases the heat transfer performance (Re = 19,540), which is in agreement with [67]. Comparing S/D = 3 with S/D = 2, the authors mentioned that at S = 2 D , due to the strong interactions between adjacent jets, the jet impingement behaves like a channel flow. This effect induces the jet’s flow deflection prior to the impingement that weakens the normal penetration of the jets and decreases the jet’s momentum, reducing the heat transfer. At S = 3 D, the increase of the Nusselt number shows that the interaction between jets prior to the impingement is weaker when compared with S = 2 D, allowing the wall jet to develop over the surface, leading to an increase of the local heat transfer. Overall, higher jet-to-jet spacing values (S/D > 3) result in less effective surface coverage, leading to a decrease in local heat transfer. 24 2. LITERATURE REVIEW Figure 11. Averaged Nusselt number in function of the streamwise direction at different Re numbers, S/D and H/D spacing. Based on numerical results, Badra et al. [55] concluded that the interaction between jets occurs at S/D < 10. Jet’s interference is intensified at S/D = 2, resulting in heat transfer enhancement. However, for S/D > 10, this interaction disappears, and the two adjacent jets behave as a single jet with a symmetric profile is observed in both jets. Through a LES simulation, Draksler et al. [27] mentioned that S/D = 2 allows that the individual jet of a multiple jet array preserves some of the typical characteristics of a single jet, enabling at the same time the development of jets interactions. Barbosa et al. [56] found through RANS simulation that the size of recirculation flow between two jets increases with the separation (S/D > 4), leading to a deviation of the secondary stagnation point. This is not observed for S/D = 2 and 3 and so, higher heat transfer rates are obtained for these two cases. Recently, Otero-Pérez et al. [34] perform a parametric study on turbulent multi-jet impingement cooling using LES for H/D = 4.5, Re = 10,000, Ma = 0.3, and different jet-to-jet distances (S/D = 5, 10, and 15). Their results demonstrate that as S/D increases the Nusselt number decreases. In addition, at the midpoint between two adjacent jets, they observed that the heat transfer is dominated by the interaction of two developing boundary layers induced by the wall jets. Regarding the central jet, the Nusselt number peak decreases with the increasing the S/D ratio. Compared with a single jet, the results show that the cooling effect is slightly reduced due to flow recirculation induced by the wall jets collision which increases the temperature in the vicinity of the central jet. However, the surface coverage is increased, leading to an increase of the averga heat transfer over the surface. Regarding a moving target plate, results obtained by [68] and [69] demonstrate that the Nusselt number decreases with the increase of S/D, as for the static plate case. 0 10 20 30 40 50 60 70 80 0.0 1.0 2.0 3.0 4.0 5.0 Nu x/D Re = 10,000; S/D = 4; H/D = 2 (San & Lai, 2001) Re = 20,000; S/D = 4; H/D = 2 (San & Lai, 2001) Re = 30,000; S/D = 4; H/D = 2 (San & Lai, 2001) Re = 10,980; S/D = 2; H/D =4 (Yong et al., 2015) Re = 10,000; S/D = 8; H/D = 2; Ma = 0.11 (Ichikawa, 2016) Re = 10,000; S/D = 15; H/D = 4.5; Ma = 0.3 (Otero-Pérez et al., 2021) Re = 10,000; S/D = 10; H/D = 4.5; Ma = 0.3 (Otero-Pérez et al., 2021) Re = 10,000; S/D = 5; H/D = 4.5; Ma = 0.3 (Otero-Pérez et al., 2021) 2. LITERATURE REVIEW 25 Through the analysis of the literature, summarized in Figure 11, it seems that experimental and numerical results agree that the higher the S the less effective the surface coverage, leading to a decrease in local heat transfer. A large distance between jets reduces the interaction between the wall jets and weakens the jets induced crossflow, reducing the turbulence and consequently the local and average Nusselt number. This is clearly observed in Figure 11, comparing the results obtained by Yong et al. [7] for S/D = 2 with those presented by San & Lai [62] and Otero-Perez et al. [34], for a Reynolds number close to 10,000. In addition, Figure 11 shows that higher Reynolds and Mach numbers increase the heat transfer for the same S/D conditions and that the H/D is another parameter that plays an important role in the heat transfer efficiency. Therefore, H/D is analyzed in detail in the next section. 2.2.4. Nozzle-to-Plate Distance Amongst the different process variables, nozzle-to-plate distance (H) is considered one of the most important geometrical parameters in jet impingement due to its strong influence on heat transfer performance. As stated by [45], the effect of H/D is the result of the interaction between jet momentum and locally generated crossflow. In that sense, for both single and multiple jets, confined jets (low H/D values) induce higher heat transfer rates, as mentioned by several authors [9, 48, 64, 70, 71]. Garimella & Schroeder [72] demonstrated experimentally that a decrease in H/D leads to an increase of the heat transfer coefficients, due to higher levels of turbulence intensity induced in the confined space, increasing this effect at higher Reynolds numbers. Reodikar et al. [73] observed that the Nusselt number distribution is more uniform for lower H/D values, due to the uniform velocity profile in the potential core region of the jet. This is valid for both single and multiple jet impingement as recently demonstrated by [37]. The jet’s flow structure obtained by PIV analysis shows a thicker wall jet for lower H/D induced by stronger interactions between jets and the surrounding air in a confined space. Increasing the H/D value, larger primary vortices are generated. These large but weak vortices interfere with the flow development of the adjacent jets and reduce the heat transfer in the vicinity of the target surface. These observations are supported by Ichikawa et al. [29], who determined, through PIV, that a small impinging distance increases the jet’s momentum around the impingement, leading to a bigger and stronger roll-up structure of the vortex. Ozmen & Ipek [74] found a significant increase of the pressure near the stagnation points at low H/D followed by a pressure decrease as the flow accelerates along the target surface. Furthermore, they identified that the primary stagnation Nusselt numbers and heat transfer ratios increase with the decrease of H/D and the pressure’s peak at the jet’s stagnation point decreases with increasing this distance. Shariatmadar et al. [75] stated that large H/D decreases the heat transfer performance due to 26 2. LITERATURE REVIEW a decrease of jet’s momentum before the contact with the surface. Considering a target surface with roughness (in this case micro pin fins), the study performed by Brakmann et al. [43] showed that the Nusselt number decreases with increasing the nozzle-to-plate distance, being more pronounced in this target surface than in flat plate. These observations are supported both experimentally and numerically by Tepe et al. [76]. Even when inclined nozzles are applied, the trend is still the same: smaller H/ D increases the averaged Nusselt number over the wall. However, studies conducted by [39, 44, 45] show that at 0 ≤ H/D ≤ 1.2 the heat transfer is lower than at H/D = 2. According to [45], as the flow accelerates in direction to the outlet, the pattern of the Nusselt number is shifted from a circular shape to a horseshoe vortex shape distribution. A large discrepancy is observed between the local jet momentum of the upstream jets and downstream jets, being the first ones lower than the second ones. This induces lower average heat transfer rates, and it is called crossflow-dominated impingement flow. To determine the value of the nozzle-to-plate distance, that enhances the heat transfer, several studies were conducted. Xing & Weigand [44] analyzed experimentally multiple jets impinging on a flat and dimpled surface with different crossflow schemes and Reynolds numbers ranging between 15,000 and 35,000. They observed that heat transfer performance is enhanced at H/D = 3 and minimum crossflow, on both flat and dimpled plates [77]. Caliskan et al. [28] studied experimentally and numerically the effect of H/D over a flat and non-flat surface and found that the heat transfer performance at Re = 10,000 is higher for H/D = 2. Yong et al. [7] analyzed the convective heat transfer for multiple air jets in a semiconfined channel for a Reynolds number between 5,000 and 25,000 and observed that the strong interference between adjacent jets at H/D = 2 increases the heat transfer over the target surface. Li et al. [45] determined the effect of H/D on the cooling performance of a jet array (5,000 < Re < 25,000) and showed that the Nusselt number is increased by the increase of the H/D, reaching a peak value at around H/D = 2. These results are in agreement with several numerical and experimental studies [28, 29, 45, 60, 78–80]. This enhanced efficiency is enlightened by the generation of strong vortices in a confined space, while larger distances reduce both crossflow and jet’s momentum, decreasing the heat transfer over the target surface [51]. These studies demonstrated that the heat transfer over an impinging surface is enhanced when H/D = 2. As it can be observed in Figure 12, regardless of the experimental conditions, such as jet pattern, S/D spacing, Reynolds number, and surface roughness, the Nusselt number decreases with the increase of H/D in multi-jet configurations. This decrease seems to be more pronounced for higher Reynolds numbers and complex surfaces. 2. LITERATURE REVIEW 27 Figure 12. Average Nusselt number in function of the H/D spacing. 2.2.5. Jet Velocity The jet velocity, as defined by the Reynolds number, is crucial in jet impingement processes since it strongly influences the local, line-averaged, and area-averaged Nusselt number [66]. Each study uses a specific range of Reynolds numbers, some authors decided to perform their studies on laminar flows others in turbulent ones. Air jets exhibit a typical laminar flow at Re < 1,000, becoming fully turbulent at Re > 3,000. In that sense, the transition region occurs at 1000 < Re < 3,000 [21]. Through the analysis of the research performed in jet impingement, most of the studies focus on turbulent flows since turbulence induces higher heat and mass transfer rates. Due to this fact, a typical gas jet installation for heat transfer works at a Reynolds number ranging between 4,000 and 80,000 [21]. According to the researches conducted for a single and multiple jet impingement, a higher Reynolds number increases the local heat transfer coefficient throughout the target surface [38, 53, 77, 79, 81– 85]. High Reynolds number increases the flow turbulence which promotes the mixing between the jet’s flow and the surrounding air, increasing the heat transfer. According to Jensen & Walther [82], high turbulence levels are generated near the stagnation point for high jet Reynolds numbers, increasing the heat transfer rates. Shariatmadar et al. [75] mentioned that at lower Reynolds numbers a decrease of the local Nusselt number over the target plate is observed since the strength of the jet momentum is not enough to reach the surface uniformly. Chandramohan et al. [79] complemented the idea stating that at a particular Reynolds number, as the nozzle-to-plate distance increases, the jet flow can mix and becomes wavier leading to a decrease of the heat transfer coefficient. Li et al. [38] detected that the flow structure is qualitatively similar at different Reynolds numbers and by increasing this parameter five times (5,000 28 2. LITERATURE REVIEW to 25,000) an increase of the Nusselt number by a factor of 3.5 is observed. This is in agreement with Park et al. [81] who mentioned that regardless of the Reynolds number used, the qualitative distribution of the local Nusselt number induced by each jet is similar. In terms of cooling efficiency optimization, it seems that it is more efficient to increase the Nusselt number through the increase of the Reynolds number and the non-dimensional area (Af = total nozzle exit area/total target area). These results are in agreement with several studies which perform an analysis of the effect of different process variables on heat transfer [59, 60, 79, 86]. Figure 13 summarizes the results obtained by several authors, showing clearly that the average Nusselt number increases with increasing the Reynolds number regardless of the nozzle-to-plate and jetto-jet distances, supporting the discussion previously presented. Figure 13. Average Nusselt number variation in function of the Reynolds number for different jet-to-plate and jet-to-jet distances. 2.2.6. Target Plate Geometry One of the biggest challenges of the multiple jet impingement is the difficulty to obtain uniform temperatures over the impinging surface. If the complexity of the surface is increased, more hot/cold spots can appear, leading to product defects. In order to understand the influence of the target plate geometry on heat transfer performance, several studies have been conducted. Different geometries can 2. LITERATURE REVIEW 29 be considered, from ribs and pin fins to dimples. Since their effect on heat transfer is different, they are presented separately. a) Ribs Ribs, depicted in Figure 14, are applied over impinging surfaces to increase the turbulence and the effective surface area [21]. In order to understand the effect of ribs on heat transfer performance, several studies have been conducted. Spring et al. [87] combined experimental and numerical investigation of turbulent flows (Re = 35,000) and determined that ribs did not improve the heat transfer coefficients in inline arrays configurations, while for staggered jet pattern, an enhancement is observed. This is explained by the fact that ribs help to minimize the strong degrading effects of the crossflow. The analysis of the pressure loss shows that ribs do not increase the pressure drop, since a reduction of the mixing and turbulence induced by the interaction between the crossflow and the jet flow is observed. This is in accordance with Andrews et al. [88]. The last authors added that ribs do not contribute to an improvement of the surface average heat transfer compared with a flat plate. The main effect of ribs is to change the axial dependence of the heat transfer on the crossflow. In the absence of crossflow, ribs reduce turbulence over the surface, removing the aerodynamics interactions between jets on the target surface. As concluded by Andrews et al. [88], smooth ribs with co-flow improve the heat transfer compared with slotted ribs configuration since secondary flows in the channels between the ribs are induced. Regarding ribs shape, Annerfeldt et al. [89] mentioned that triangle-shaped, wing-shaped, cylindrical, and rectangular elements enhance the Nusselt number by a factor from 1 to 1.3 for cooling application and recommended the use of rectangular ribs or cylinders. Further, Caliskan & Baskaya [90] investigated the heat transfer in an inline impingement jet array on smooth and rib-roughened surfaces according to two configurations: V-shaped ribs (V-SR) and convergent-divergent ribs (CD-SR). Through their analysis, they concluded that both configurations increase the heat transfer coefficient over the surface from 4 % to 26.6 % when compared with a flat plate. Their results show that V-SR configuration presents a higher average heat transfer than CD-SR since this structure generates vortices that increase the mixing of the flow, enhancing the heat transfer. V-SR disturbs the boundary layer induced by jet impingement inside the rib cavity, which creates a higher turbulence, especially at H/D = 2. Alenezi et al. [91] and Tepe et al. [76] highlight the importance of the rib height since too height rib can induce lower heat transfer rate compared with flat plates. In height ribs, the flow must travel a longer distance between the wall and the upper edge of the rib before the re-attachment. In that sense, it seems that a rib height that matches with the boundary layer thickness, and located between the stagnation region and 30 2. LITERATURE REVIEW the wall jet region, enhances the local heat transfer mainly due to the increased turbulence induced by the flow recirculation upstream and downstream the rib [91]. Shukla [92] analyzed the effect of ribs using different RANS models and found that a detached rib configuration enhances the heat transfer rates compared to attached ribs due to flow acceleration in the space between the plate and the rib. Figure 14. Ribs structure (a) Longitudinal ribs; (b) V ribs. b) Small-scale pin fins roughness Brakmann et al. [43] analyzed the influence of micro cube-shaped pins (Figure 15) on the target surface (15,000 < Re < 35,000) and concluded that pin fins increase the target area by 150 % in comparison with a flat plate. This increases the convective heat transfer between 135 % and 142 %. In terms of the flow field, the airflow that goes through a pin is separated, creating a vortex on the downstream side of the pin. This leads to a decrease in heat transfer and an increase in pressure loss in this zone. Furthermore, Ligrani et al. [93] studied the influence of small-scale cylinders in the target plate and observed that the increase of the height of small cylinders leads to an increase of the local mixing, vorticity, turbulent thermal transport, and thermal resistance, generating a substantial thermal insulation barrier. These elements increase the target area by 47 % for a height of 0.125 D, 71 % for 0.188 D and 94 % in the case of 0.250 D. Buzzard et al. [84] proved that, for Re ranging between 900 and 11,000, the average Nusselt number is increased by small rectangle roughness height, since the increase of the height leads to an increase of the local vorticity and larger amounts of mixing. In addition, for laminar flows, plates with small roughness alone present higher Nusselt numbers than plates with a combination of small and large roughness. However, the inverse situation is observed when the flow is turbulent. According to Ren et al. [94], this is due to two reasons: firstly, in turbulent flows, the combination of large and small pins increases the mixing of the flow, increasing the convective heat transfer at the surface; secondly, in laminar flows, the extra material provided by large rectangles generates an insulating effect. Regarding the effective surface area, Ren et al. [94] registered that small rectangle roughness alone increases this area by 60 % and 120 % compared with the smooth target surface. However, for the combination between large and small rectangles, this increase varies between 105 % and 160 %. In (a) (b) 2. LITERATURE REVIEW 31 addition, these authors mentioned that the combination of large and small triangle roughness presents little advantages compared with small triangle roughness alone. This is explained by the fact that small triangle roughness arises the Nusselt number due to their sharper corners that generate a more turbulent mixing, increasing the vorticity within the flow. This configuration induces a higher averaged Nusselt number and higher surface convective heat transfer rates compared with small rectangle roughness elements (at the same height and Reynolds number). The combination of large rectangles and small triangles roughness induces higher average Nusselt numbers than small triangle or rectangle roughness alone, leading to an increase of the effective surface area between 92 % and 132 % compared with a smooth target surface. Figure 15. Micro pins structure. c) Dimples, grooves, and protrusions Xing & Weigand [77] proved that the application of dimples (Figure 16) over the target plate leads to an increase of 26.4 % of the effective surface area compared with a flat plate. Regarding the crossflow scheme, an increase of 6.2 % of the heat transfer coefficient is recorded for a maximum crossflow. This phenomenon is explained by the fact that dimples enhance the heat transfer of the channel flow. For medium crossflow, dimples worsen the heat transfer coefficient by 10 % since the recirculation flow generated inside the dimples cannot escape fast from them. This value is improved by the minimum crossflow scheme (for H/D = 3 and Re = 35,000) in 12.3 %, essentially due to the full usage of the dimple edge to make the boundary layer thinner and to increase the crossflow velocity. Kanokjaruvijit & Martinez-Botas [95] observed that at H/D ≤ 2, the dimples did not improve the heat transfer compared with the flat plate due to the occurrence of strong recirculation. Nevertheless, considering a higher H/D value, dimples lead to an improvement of the heat transfer. They also concluded that a small dimple curvature (D/Dd = 0.25, where D is the jet diameter and Dd the dimple diameter) leads to a lower heat transfer value when compared with a flat plate while higher values (0.50 and 1.15) improve the heat transfer. Moreover, a shallow dimple (d/Dd = 0.15, where d is the dimple depth measured from edge to 38 2. LITERATURE REVIEW Garimella & Schroeder [72] 0.693 0.4 0.105 Nu 0.127Re Pr ( / )HD − = 5,000 ≤ Re ≤ 20,000. Regular inline array; Minimum crossflow. Meola [120] 0.68 0.42 0.3 0.15 0.56 0.3Re Pr ( / ) Nu F f D C AH − − = Flow coefficient, CF , is defined in the paper. 200 ≤ Re ≤ 100,000; 1.6 ≤ H/D ≤ 20 ; 0.0008 ≤ Af ≤ 0.02 General correlation flow. Kanokjaruvijit & Martinez-Botas [95] 0.69 0.49 |flat Nu 0.1543Re ( / ) DHD − = 0.61 0.23 0.60 0.85 |on dimple Nu 0.1770Re ( / ) ( / ) ( / ) D d d H D d D D D −− = 0.50 0.16 0.64 0.31 |on flat Nu 0.3472Re ( / ) ( / ) ( / ) D d d H D d D D D −− = 5,000 ≤ Re ≤ 11,500; 1 ≤ H/D ≤ 12; d/Dd = 0.15, 0.25, 0.29. Round nozzles inline array. Caliskan & Baskaya [90] 0.697 0.11 0.069 Nu 0.0687Re ( / ) ( / )H D e D − = 2,000 ≤ Re ≤ 10,000; 2 ≤ H/D ≤ 12; 0.6 ≤ e/D ≤ 1.2. Round nozzles inline array impinging on a V-shaped ribs (V-SR) plate. Chitsazan & Glasmacher [111] 0.54 0.73 0.85 /Nu 1.09Re ( / ) (1 )jsS D U U −− =+ 0.54 0.49 0.5 Nu 0.78Re ( / ) (sin )SD  − = 0.49 0.46 Nu 0.85Re ( / ) sinSD  − = H/D ≥ 2; Single row; H/D < 2; Single row; Multiple rows. Moving plate; Equidistant jets. Pachpute & Premachandran. [53] 0.1 0.6 0.7 |inNu ( / ) ( / ) ( / ) Repic b a H D D d S d − = 5,000 ≤ Re ≤ 20,000; 5.5 ≤ D/d ≤ 17; 1.4 ≤ S/dpic ≤ 2.9; 2 ≤ H/D ≤ 12. a = 0.25 and b = -0.14 5,000 ≤ Re ≤ 15,000; a = 0.27 and b = -0.14 15,000 ≤ Re ≤ 20,000. pic 0.1 0.6 0.02 0.7 |stagNu ( / ) ( / ) ( / ) ( / ) Repic boffa H D D d S d d d −− = a = 0.25 and b = -0.13 5,000 ≤ Re ≤ 15,000; a = 0.3 and b = -0.2 15,000 ≤ Re ≤ 20,000. 2. LITERATURE REVIEW 39 2.3. Jet Impingement Modeling Numerical simulation has been a tool widely implemented in jet impingement studies, essentially due to cost savings resulting from the minimization of the experimental tests required to study and improve the process. The fast advancement of computational resources and numerical algorithms has led to an improvement in the accuracy of the models used to study impinging flow dynamics and heat transfer. Numerical modeling has been essentially used for device design, prediction, sensitivity analysis, and validation/verification. Most of the industrial applications that use jet impingement involve turbulent flows, however, they represent a great challenge to predict the behavior of jets with accuracy and rapidity. Different numerical methods can be implemented to study turbulent single and multiple jets, such as Large Eddy Simulation (LES), Reynolds Averaged Navier-Stokes (RANS), or Direct Numerical Simulation (DNS), and the selection of the most appropriate method depends on the aim of the research work. If time-averaged quantities are suitable to characterize the flow, RANS must be applied since it is less expensive and therefore, widely used in practice. However, if fundamental research is required, DNS is the obvious choice, since Navier-Stokes (N-S) equations are fully solved. The use of LES in jet flow modeling has been an astute choice for fundamental investigation at higher Reynolds numbers since filtered N-S equations are solved, leading to lower computational costs compared to DNS. 2.3.1. DNS DNS is the most physical exact approach since the N-S, continuity, and energy equations are fully solved using discrete units of time and space [21]. However, to fully resolve all the turbulent flow properties, an extremely small grid must be implemented in order to capture the microscopic turbulent length scale. This involves high computational costs and time which limits the applicability of DNS, special for the study of turbulent flows, and therefore, it is mainly applied for the study of flows with a low Reynolds number. Focusing on the numerical modeling of laminar air jet impingement, Chung & Luo [121] applied DNS to study the unsteady heat transfer caused by a confined impinging jet at Reynolds numbers between 300 and 1,000. Their results show that the vortices generated over the target plate induce an increase of the heat transfer and that higher Reynolds numbers promote the generation of secondary maximum Nusselt number. Chung et al. [122] performed DNS of unsteady jet impingement at low Reynolds number (Re = 300, 500, and 1,000) and analyzed the momentum and heat transfer. They used a high-order time-accurate finite differences method with non-reflecting boundary conditions to solve the N-S and energy equations. Numerical results show that primary vortices generated from the jet nozzle cause, 40 2. LITERATURE REVIEW together with the wall shear layer, the unsteadiness of the impingement heat transfer over the target plate. Chattopadhyay [123] used an axisymmetric formulation with the SIMPLE algorithm to solve the governing equations used for the prediction of an annular impinging jet (250 < Re < 1,000). Their predictions demonstrate that the heat transfer performance of annular jets is 20 % lower compared to circular jets. Jiang et al. [124] analyzed the unsteady flow and temperature of an impinging hot jet, at Re = 1,000 and H/D = 6, using a spatial DNS based on high order finite difference numerical scheme and high-fidelity boundary-conditions. They concluded that external perturbations strongly affect the jet flow structures. However, the re-laminarization effect of the wall reduces these perturbations on the wall stresses and heat transfer characteristics of the jet. Lee et al. [125] applied a central differences scheme with second-order accuracy based on the finite volume (FV) method to investigate the unsteady 2D fluid flow and heat transfer of confined jets for Reynolds numbers between 50 and 500. Their results show that different characteristics in terms of pressure coefficient, skin friction coefficient, and Nusselt number are observed compared with the steady region. 2.3.2. LES As a way to solve the limited applicability of the DNS method, LES simulation was developed. This method tracks flow properties with the full equations down to some user defined length scale, which is usually the grid spacing and uses additional sub-grid-scale equations to describe the flow structure at smaller scales [21]. Therefore, LES is applied for the analysis of complex physical phenomena which occur during the impingement, such as the flow dynamics and development of vortical structures. In this context, Hadžiabdić and Hanjalić [126] performed an interesting work using LES in order to analyze in the detail the vortical and turbulence structures induced by a round impinging jet (Re = 20,000 and H = 2 D). They concluded that LES data provided explanations of some phenomena detected experimentally in statistically averaged flow features, such as double peaks Nusselt numbers and the negative production of turbulence energy in the stagnation region. These observations are also supported by Uddin et al. [127] who added that LES is very sensitive to the quality of the grid in different regions of the jet impingement. Dairay et al. [128] analyzed a turbulent single jet (Re = 10,000 and H = 2 D) and found that LES leads to acceptable velocity statistics in comparison with DNS and experimental data. In addition, Dutta et al. [129] found that LES with the vortex method activated increases the efficiency of the jet impingement simulation. A study performed by Draksler et al. [27] demonstrated that LES generates accurate results, in good agreement with experimental data, allowing to understand the complex flow interaction between multiple jets and the target surface. However, LES is limited to a small 2. LITERATURE REVIEW 41 Re number for wall-bounded flows, which can be an important limitation in some applications. Penumadu & Rao [130] compared RANS and LES to model the heat transfer and pressure drop characteristics in multiple jet impingement systems (5,000 < Re < 90,000) and found that LES provides deeper insight into the flow physics of multiple jet impingement. Recently, Otero-Pérez et al. [34] performed a parametric study on multiple jet impingement cooling (Re = 10,000; H = 4.5 D) using LES, validated by both experimental data and DNS, and found that the jet-to-jet spacing and crossflow highly affect the heat transfer. 2.3.3. RANS As mentioned previously, even if DNS and LES provide deeper insights into the physics of single and multiple jet impingement flows, RANS has been widely implemented in industrial and academic research, since it provides fairly accurate results at low computational costs. However, the selection of the most appropriate RANS model to simulate numerically, with accuracy, this enhanced heat transfer process, has been the topic of several research projects. Hofmann et al. [131] analyzed 13 turbulence models to determine which one better predicts the jet impingement process of a turbulent round jet (Re = 34,000 and 124,000; H/D = 2.5 and 10): standard k-ε model, RNG (Re-Normalisation Group) k-ε model, realizable k-ε model, Reynolds stress model, LowReynolds k-ε model (Launder-Sharma), Low-Reynolds k-ε model (Abid) Low-Reynolds k-ε model (AbeKondoh-Nagano), Standard k-ω model, Shear Stress Transport (SST) k-ω model and transitional flow option. To analyze and compare each model, the authors modeled a single jet impingement. Through this study, they concluded that nearly all the models predict well the wall jet heat transfer. However, they almost all fail in predicting the local heat transfer near the stagnation region. The SST k-ω model, developed by Menter [132], with activated transitional flow option seems to be the model which ensures more accurate results. Ortega-Casanova & Granados-Ortiz [96] compared the efficiency of three turbulence models for the simulation of a single jet (7,000 < Re < 19,000 and H/D = 5, 10, 30): the SST k-ω model, the Standard k-ω and the Enhanced k-ε models. The authors agreed that SST kω model is more accurate in single jet impingement modeling since it predicts the secondary maximum Nusselt number with accuracy. Zhou et al. [133] investigated the accuracy of the v2-f, SST, RSM (Reynolds Stress equation Model), and RNG turbulence models for the modeling of a turbulent round jet (4,000 < Re < 12,000) and concluded that v2-f presents good predictions for the local Nu number, especially of the secondary Nusselt number peak, even if it over-predicts the Nusselt number in the stagnation region. The other models present a higher difference between their predictions and the 42 2. LITERATURE REVIEW experimental data: 70 % in the stagnation region by RSM model, 10 % by RNG model, and 6 % by SST kω model. Hatami et al. [134] also observed a higher deviation between the numerical and experimental results in the case of the SST k-ω model (10 %) compared with the v2-f model (2 %). These deviations were observed near the center of the heated surface for the prediction of the stagnation Nusselt number. These results are in agreement with [135]. Regarding the numerical analysis of multiple jet impingement, Zu et al. [136] compared different turbulence models with experimental data (standard k-ε model, realizable k-ε model, the standard k-ω model, and the SST k-ω model) and determined their accuracy for the modeling of two-line staggered and inline round jets. From the analysis, they found that the SST k-ω model presents a better compromise between computational costs and accuracy. Wen et al. [137] modeled multiple round jets (Re = 35,000) impinging on a flat plat and compared the SST k-ω model with the Standard k-ω model, the Realizable k-ε model, and the v2-f. From the results, they concluded that comparing the prediction with experimental data, the SST k-ω model presents a higher accuracy than the k-ω and k-ε models. Additionally, even if v2-f presents a good accuracy in predicting the stagnation zone, it requires a higher computational cost, making the SST k-ω model a better choice. Badra et al. [138] compared the SST k-ω model with v2-f to determine the accuracy of the predictions obtained for the case of multiple jets impinging on a moving flat plate. The results show that both models are comparable in performance, although, SST k-ω predictions of the stagnation Nusselt number are more accurate. Penumadu et Rao [35] analyzed a jet array (5,000 < Re < 90,000) and compared the SST k-ω with the standard k-ε. From the data analysis, they found that the heat transfer characteristics are better predicted by the SST k-ω model essentially due to its ability to predict with accuracy regions with high pressure gradients. However, the simulation of the pressure drop is critical, the prediction deviations from the experimental data are around 50 %. The main characteristics of the different numerical methods applied in jet impingement studies are summarized in Table 2. The literature review regarding the turbulence models applied for the numerical simulation of jet impingement shows that, according to several authors, the SST k-ω model was revealed both accurate and computing time-saving in engineering applications. These advantages make this model a good choice for the numerical modeling of single and multiple jets impinging on static [15, 52, 76, 85, 139–141] and moving [109, 111, 138] plates. 2. LITERATURE REVIEW 43 Table 2. Turbulence models applied in jet impingement simulations. Model DNS LES RANS Classical k-ε k -ω models Standard k-ε , RNG k-ε, realizable k-ε, RSM Standard k-ω SST k-ω Transitional flow option (TFO) Equations Original N-S equations Filtered N-S equations Time-averaged N-S equations Velocity field Three-dimensional and unsteady Three-dimensional and unsteady Steady/Unsteady Modeling No modeling Only small scales are modeled All scales are modeled Cost of computation Most expensive Between DNS and RANS Least expensive Low (RSM is moderate) Moderate Accuracy Excellent Poor Poor except SST k-ω which is good Application Simple geometries at low Reynolds number High potential for practical as well as fundamental use Widely used in practice Studies [121]–[125], [142]–[146] [27], [34], [35], [126]–[129], [147], [148] [107], [131], [135], [149]–[152] [15], [21], [52], [76], [85], [87], [111], [131], [135]–[137], [139]–[141], [153]– [155] Performance in jet impingement simulation Notable outcome on the local heat transfer upon changing the boundary condition at the impingement wall from a constant heat flux to a constant temperature. Good prediction of the flow physics. However, the design of a practical impinging system at a small cost requires modeling of the near-wall region since LES is limited to a small Re number for wall-bounded flows. Good prediction in the wall jet region but is not able to predict heat transfer in the low-turbulence region near the stagnation point. Only the SST k-ω with TFO can predict correctly the laminar-turbulent transition and the local heat transfer coefficients at small H/D spacing. At large H/D distances, the standard k-ω model with TFO is most appropriate, however, it fails for small radial distances. This page was intentionally left in blank. 3. EXPERIMENTAL METHODS 45 3. EXPERIMENTAL METHODS 3.1. Experimental Procedure The experimental procedure concerns the presentation of the experimental setup which was specially designed and constructed to conduct the heat transfer and PIV measurements. Each component was built to ensure the highest accuracy of the measurements, in that sense, the correct operation of the facility is crucial. Therefore, all the steps followed to conduct, with success, the experiments are detailed in this section. 3.1.1. Experimental Setup The experimental setup was specially built to perform the PIV and heat transfer measurements of multiple air jets impinging on static and moving hot flat plates. As it can be observed, the test rig presented in Figure 17 (a) can be divided into three main sections: the setup structure, shown in Figure 17 (b), the target plate, Figure 17 (c), and the system control, Figure 17 (d). Starting with the setup structure, it consists of a centrifugal fan that blows the air into an acrylic plenum, which is an acrylic box with a section with larger dimensions compared with the exit of the fan, in order to stabilize the flow and to reduce the turbulence. The seeding particles are introduced inside this box, to ensure a uniform mixing with the air flow. The length of the acrylic plenum allows the flow to develop uniformly, upstream of the nozzle plate. A honeycomb structure is placed at the beginning of the tube, to promote the uniformization of the flow. At the bottom of this tube, a nozzle plate with a pattern of circular orifices is placed to generate the air jets. The number of nozzles was fixed according to the nozzle plate with the larger jet-to-jet spacing (S = 6 D) to ensure a constant open area in all nozzle plates applied in this study. The seeded air flow goes through the circular nozzles, 5 mm in diameter, spaced by a jet-to-jet spacing normalized by the jet diameter (S/D), which varies between 2 and 6, depending on the nozzle plate applied in the experiment. A normalized jet-to-plate distance (H/D) is also defined in each experiment and can vary between 2 and 7. The measurement zone consists of the area between the nozzle plate and the target surface, which is surrounded by an acrylic box to minimize the interference 46 3. EXPERIMENTAL METHODS of the surrounding air. The transparency of this box is crucial to ensure the correct operation of the PIV measurement technique. Figure 17. Experimental setup: (a) Test rig; (b) Setup structure; (c) Target plate; (d) System control. The jets generated by the air flowing through the nozzle plate impinge an aluminum alloy target plate. This material was selected to ensure a uniform temperature distribution over the surface, Figure 17 (c). Since aluminum alloy presents a high thermal conductivity, k ≈ 170 W/m·K [156], the contribution of the plate to the overall thermal resistance is expected to be reduced. To ensure the uniform heating of this plate, a 1000 W, 200× 200 mm mica heater is fixed between two support plates also made of aluminum alloy, as it can be observed in detail in Figure 18. The control of the target plate temperature is ensured by a thermocouple connected to a Selec TC544 temperature controller, as explained in more detail in the next section. To measure the convective heat transfer, an OMEGA® HFS-4 thin film heat flux sensor, rated at a maximum of 94,500 W/m2, is mounted at the center of the target surface. Thermocouples are also placed over the impinging plate to measure the local surface temperature, as depicted in Figure 18. Besides the representation of the thermocouples and the heat flux sensor positions over the target plate, the schematic shows the configuration of the plate with the mica heater inserted between the support plates; the plate motion, from the left to the right; and the air motion from the inlets to the outlets. 3. EXPERIMENTAL METHODS 47 Figure 18. Position of the heat flux and thermocouples over the target surface. T1, T2, and T3 represent the thermocouples; TC is the thermocouple connected to the temperature controller. The heat flux, located at the center of the plate, has an integrated thermocouple, Theat flux, to measure the local temperature. The target surface has two configurations possible, flat and non-flat, as represented in Figure 19. The second one consists of a step surface with a high equal to 2 D. The plate is fixed to a motion mechanism, Figure 17 (b), which comprises a worm gear connected to a 24 V motor. The system allows the motion and variation of the target plate velocity and consists of two end course sensors, a speed controller, and an on-off switch. As presented in Figure 18, besides the plate motion, the variation of the angle of inclination of the target plate can also be controlled, using a screw and nuts system. The system control table allows the control of all the sub-systems of the experimental setup. From the right to the left of Figure 17 (d), it is possible to identify: the computer which controls the 2D PIV system from Dantec™, through the Dynamic Studio software; the frequency regulator, which adjusts the air blown by the fan; the switch that allows to move the target plate from the right to the left and vice-versa; and the seeding generator Aerotech Concept™, through which it is possible to control the seeding concentration inside the test rig. 54 3. EXPERIMENTAL METHODS requirements of the experiments since the temperatures vary between 20 °C and 120 °C. These thermocouples are connected to a NI 9213 data acquisition system, Figure 23 (c), with a measurement sensibility < 0.02 °C and a sample rate of 75 s-1. The thermocouple which controls the reference temperature is coupled to a temperature controller TC544A with a resolution of 0.1 °C (for thermocouples), Figure 24. However, due to the thermal inertia of the target plate, the plate takes time to achieve a uniform temperature. From experiments, the target plate takes 10 min to achieve an average temperature of 120 °C. Figure 23. (a) Mica heater; (b) Type K thermocouple (c) Acquisition system NI 9213. From the measurements of the temperatures over the target plate, it was observed a standard deviation of 120 ± 1 °C between the thermocouples placed on the flat plate and 120 ± 2.5 °C over the step plate. This higher difference is due to the temperature measured over the step plate. Considering that the step thickness is equal to 2 D, the losses due to conduction are twice higher. However, since all the heat transfer measurements are conducted at the bottom of the step, this temperature difference will not interfere with the accuracy of the measurements performed by the heat flux sensor. Figure 24. Temperature controller TC544A. Besides the control of the plate temperature, it is also important to control the temperature of the jets, to ensure the reproducibility of the experiments. Since the jet flow corresponds to the air which is blown 3. EXPERIMENTAL METHODS 55 by the fan from the ambient to the setup, the jet temperature corresponds to the ambient air temperature. To control the temperature, an air conditioning system installed in the laboratory is used, ensuring that the temperature variation does not exceed 1 °C throughout the experiments. Besides the thermocouple located in the stabilization chamber, a weather station (W.155 Weather station from Ventus, Denmark) with a resolution of 0.1 °C records the temperature variation of the ambient air. 3.2.3. Flow Rate The precise control of the flow parameters throughout the experiments is crucial to ensure the accuracy of the measurements. In that sense, the flow rate is measured both at the inlet of the experimental setup and at the exit. The monitorization of the flow rate is also important to ensure that no leaks or air intakes interfere with the results. To conduct this analysis, a bell mouth of elliptical shape (Ø = 125 mm) followed by a straight section for flow development, is mounted upstream of the air inlet of the ventilator, as presented in Figure 25. Figure 25. Velocity measurement at the inlet and outlet of the experimental setup. A pressure tapping, located at the throat of the bell mouth, enables the static pressure measurement using the digital micromanometer Love Controls HM28 with a resolution of 1 Pa and a range of measurement from 0 to 7,000 Pa. To determine the dynamic pressure at the exit of the acrylic duct with a rectangular section (200 × 200 mm), a Pitot tube is used. Subtracting the value measured by both static and dynamic pressures to the atmospheric pressure, it is possible to obtain the theoretical average 56 3. EXPERIMENTAL METHODS velocity of the flow at the entrance and exit using a simplified Bernoulli equation (Eq. 10), in which ρ is assumed to be 1.204 kg/m3 (air density at 20 °C [156]). 2 =p U   (10) The apparatus used to perform the measurements is presented in Figure 26 and consists of a Pitot tube fixed to a support instrument that ensures its correct positioning according. Figure 26. Apparatus to measure the total pressure at the setup exit. The flow rate which supplies the experimental setup is controlled by a Mitsubishi S500 fan frequency regulator, presented in Figure 27, which allows the variation of the frequency from 0 to 50 Hz with a resolution equal to 0.1 Hz. Furthermore, to determine the flow rate, the velocity obtained by Eq. (10) is multiplied by the section area. Figure 27. Fan frequency regulator Mitsubishi S500. 3. EXPERIMENTAL METHODS 57 The variation of the flow rate at the exit and the entry of the experimental setup, without the nozzle plate, for different fan frequencies, was analyzed. The results show that within the operating flow rate (up to 15 Hz) the difference was below 7 %, which is acceptable. To determine the flow rate at the nozzle’s inlet, the same procedure is followed. First, the mean total pressure at the nozzle’s inlet is measured at the nozzle of the central jet, and the adjacent jets, in a total of five measurement points. The analysis focuses on the center of the nozzle plate, due to the location of the heat flux sensor. However, as expected, the velocity decreases from the center to the tube walls, therefore the focus of the study is on the central region of the nozzle plate. Although the Pitot tube is a sensitive measurement device, to ensure accurate velocity values at the nozzle’s inlet, some considerations must be taken into account. According to Klopfenstein [162], it is recommended to allocate the sensing tip of the Pitot tube at least one diameter downstream of the air exit of the measurement zone and point straight to the moving air stream, ensuring that the Pitot tube is parallel to the direction of the flow since its radial placement influences the accuracy of the flow calculations. Considering these recommendations, the Pitot tube is placed as presented schematically in Figure 28. Figure 28. Measurement of the total pressure at the nozzle’s inlet (a) Photograph of the Pitot tube position in the setup; (b) Schematic position of the Pitot tube in relation to the nozzle. As the maximum velocity is recorded at the exit of the nozzle, this is the selected reference velocity. The control of the velocity is performed using the fan frequency regulator and the frequency range analyzed varies between 2.5 to 50 Hz. The direct measurement of the total mean pressure by the Pitot tube, expressed by the digital manometer, allows to determine the mean velocity using Eq. (10). From these measurements, the volumetric flow rate, V 󰇗, and Reynolds number are obtained by Eq. (11) and Eq. (12), respectively. The results are expressed in Table 5. 58 3. EXPERIMENTAL METHODS 𝑉󰇗= U Aj (11) Re = ρUD μ (12) where U is the jet velocity measured at the nozzle inlet, Aj is the cross-section area of the jet and D the jet’s diameter, and ρ and μ are the density and dynamic viscosity of the air flow. Table 5. Reynolds number obtained by the total pressure measurements. Fan Frequency (Hz) Mean Dynamic Pressure (Pa) Mean Jets Velocity (m/s) Mean Flow rate (m³/s) Mean Re 2.5(0) ± 0.06 2.(0) ± 0.3 1.(8) ± 0.2 3.(3)E-05 ± 8.2E-07 601.(2) ± 5.9 5.0(0) ± 0.06 15.(6) ± 3.1 5.(1) ± 0.6 1.(0)E-04 ± 3.8E-06 1,679.(2) ± 172.5 10.0(0) ± 0.06 70.(2) ± 6.5 10.(8) ± 1.0 2.(1)E-04 ± 7.5E-06 3,562.(1) ± 322.2 15.0(0) ± 0.06 150.(4) ± 8.6 15.(8) ± 1.0 3.(1)E-04 ± 9.2E-06 5,213.(9) ± 328.0 20.0(0) ± 0.06 256.(6) ± 7.0 20.(6) ± 0.6 4.(1)E-04 ± 9.9E-06 6,810.(3) ± 197.8 25.0(0) ± 0.06 373.(0) ± 8.5 24.(9) ± 0.6 4.(9)E-04 ± 1.2E-05 8,210.(9) ± 218.1 30.0(0) ± 0.06 490.(6) ± 10.3 28.(6) ± 0.7 5.(6)E-04 ± 1.4E-05 9,416.(7) ± 243.8 35.0(0) ± 0.06 601.(2) ± 24.5 31.(6) ± 1.7 6.(2)E-04 ± 1.7E-05 10,424.(3) ± 561.8 40.0(0) ± 0.06 687.(4) ± 22.0 33.(8) ± 1.4 6.(6)E-04 ± 1.7E-05 11,146.(5) ± 471.4 45.0(0) ± 0.06 757.(4) ± 25.5 35.(5) ± 1.6 6.(7)E-04 ± 1.9E-05 11,700.(3) ± 526.2 50.0(0) ±0.06 800.(4) ± 38.0 36.(5) ± 2.3 7.(2)E-04 ± 2.1E-05 12,027.(9) ± 773.6 () – uncertain digit The methodology followed to determine the uncertainty of the measurements is detailed in the next section. Looking at the results, it seems that for a frequency equal to 2.5 Hz, the flow is laminar, at 10 Hz is in a transition regime, while for a frequency above 10 Hz, the flow is turbulent. In this study, the focus is on flow which lies in the transition and turbulent regimes, therefore a Reynolds number near to 2,000 and 5,000 are selected. However, to fully understand the flow dynamics of the jet impingement a case study for a single laminar air jet is also considered. From the analysis of the experimental setup, it is observed that the nozzle plate highly increases the head losses. To determine the effect of the head losses upstream of the nozzle plate, PIV measurements were conducted. The velocity field obtained is presented in Figure 29 for a fan frequency varying between 5 Hz and 15 Hz and shows that the head losses increase with the increase of the air flow velocity, as observed in Figure 29. Moreover, it is clear that as the fan frequency rises, the complexity of the flow highly increases upstream of the nozzle plate. However, the results demonstrate that the air flow is, in general, uniform at the center of the acrylic tube, and near to zero at the edges of the wall, as expected. 3. EXPERIMENTAL METHODS 59 Figure 29. Velocity field measured at the bottom of the acrylic tube, upstream of the nozzle plate: (a) 5 Hz; (b) 15 Hz. To understand the effect of the nozzle plate on the flow rate, this property was measured at the outlet of the setup with and without the nozzle plate. As shown in Figure 30, as the flow velocity increases, a slight difference is observed between the two cases. This difference can be explained by the fact that the Pitot tube is an intrusive method and considering the slight difference between the Pitot’s head (3 mm) and the nozzle’s diameter (5 mm), it is expected that high flow velocities induce higher measurement errors. Figure 30. Inlet and outlet flow rate in function of the fan frequency. 0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0 5 10 15 20 25 30 Flow rate (m³/s) Fan frequency (Hz) Inlet with nozzle plate Jets exit 60 3. EXPERIMENTAL METHODS 3.2.4. Source of Errors Several factors influence the measurements performed, inducing errors that can have two different components, random and systematic errors [163]. Therefore, every measurement is a combination of the true value and the total measurement error (random and systematic), being necessary to express the uncertainty in every measured value, i.e. the range within which lies the true value [164, 165]. To be able to estimate the uncertainties associated with the measurements, it is necessary to identify the contribution of each factor. The sources of error identified in the experimental apparatus are expressed by the Causeand-Effect Diagram (or Ishikawa Diagram), illustrated in Figure 31. Through this diagram, it is possible to identify the causes for the uncertainty associated with the velocity fields, measured through the PIV technique and heat transfer, measured by the heat flux sensor. The causes of the problem are divided into four main categories: Experimental setup, Ambient, Seeding, and PIV system. Each main category has specific causes that are expressed as branches in the Causeand-Effect Diagram. Sub-causes are added in order to understand why a particular event occurred. To understand how the different causes, interfere with the problem statement, each category is discussed in detail below. However, the source of errors and uncertainty quantification related to the Seeding and PIV system is explored in the next section. Even if it is difficult to quantify the influence of each quantity, Figure 31. Factors that influence the uncertainty of the heat transfer and velocity field measurements. 3. EXPERIMENTAL METHODS 61 i.e. the quantity that affects the relationship between the value provided by the measuring instrument and the result but does not affect the measured quantity directly [163], it is important to identify them and to act in order to minimize their effects on the measurements. Therefore, while the effect of some influence quantities is only discussed in this section, others must be considered on the uncertainty estimation of heat transfer and velocity measurements, thus, they are quantified in the following section: “3.2.5. Data Reduction and Uncertainty Estimation”. a) Flow uniformization The uniformization of the flow through the setup is important to ensure the reliability of the results. The same quantity of seeded flow must go through the different orifice nozzles. Furthermore, the same velocity must be recorded at the exit of the orifices. For that, it is necessary to minimize the turbulence of the flow at the exit of the fan as well as to ensure uniform distribution, upstream the nozzle plate. Through experimental analysis, it is observed that a large distance between the fan and the orifice nozzles must be ensured for proper flow development. In that sense, the full height of the laboratory is used for the setup design. To minimize the turbulence and increase the flow uniformity, a diffuser is placed at the exit of the fan, followed by a stabilization chamber with a larger cross section compared with the diffuser. The air enters into the acrylic tube, inside which a honeycomb structure is placed, to straighten the air flow. To validate that the uniformization of the flow is performed with success, the velocity vectors obtained by PIV at the exit of the nozzles are analyzed. The experiments are conducted in a confined space at Re = 2,000. The jet-to-jet spacing (S/D) is fixed at 5.7 while the nozzle-to-plate distance (H/D) is equal to 7. The results presented in Figure 32 show a good uniformity of the flow through the different orifice nozzles, with the maximum velocity recorded at the exit of the orifice and decreasing with the decrease of the distance to the target plate. The symmetry of the vortices generated on both sides of the central jet, as well as on each side of the adjacent jets (in direction to the exhaust), also supports the idea of a proper uniformization of the flow. Figure 32. Time-averaged velocity profile for H/D = 7 distances at Re = 2,000 and S/D = 5.7. 62 3. EXPERIMENTAL METHODS b) Alignment, perpendicularity, and parallelism As previously mentioned, the alignment between the CCD (Charge Coupled Device) camera and the laser is crucial to minimize particle lag and out-of-plane velocity components. In that sense, a pivot point Bushnell® laser level is used for the perfect alignment between the laser and the experimental setup as well as the experimental setup, laser sheet, and the CCD camera, as observed in Figure 33. Figure 33. PIV system alignment using the Bushnell® laser. After the definition of the correct setting of the camera and the laser, their position must be fixed before starting the calibration. As mentioned by [166], to minimize errors, it is important to ensure that the calibration conditions are the same as the measurement conditions. Other important aspects are identified during the preparation of the experiments. First, it is verified that the nozzle plate and the target plate must be perfectly parallel to minimize flow deviation and asymmetry. To ensure this requirement, a torpedo level is used. This condition cannot be verified if the perpendicularity of the acrylic tube is not ensured. Furthermore, the perpendicularity between the setup and the laser must be verified, otherwise, undesired shadows can appear over the measurement region. Problems related to the alignment between the laser, the camera, and the acrylic tube for jet impingement visualization are very common and difficult to be fully controlled. In that sense, they must be considered in the design of the setup and accurate measurement instruments must be used to minimize the effect of these factors on both jet flow profile and PIV images. 3. EXPERIMENTAL METHODS 63 d) Transparency and reflectivity As mentioned previously, to minimize the interference of the ambient on the measurement, an acrylic box is placed around the measurement region. The transparency of this box is of paramount importance since it must allow a clear passage of the laser beam to ensure an accurate illumination of the measurement region. However, it is necessary to account for the refraction of the light, since it can induce errors during the measurement of the seeding particles displacement [167]. In that sense, it is important to ensure that the materials used for flow visualization, i.e., test section walls and seeding particles, have closely matched refractive indices. According to [167] and considering that the laser emits light of a wavelength of 532 nm, the refractive index (n) of the acrylic material is approximately 1.49. The refractive index of the seeding particles is addressed in section 3.3.3. In addition, the images captured by the camera must be as clear as possible to reduce image distortion noise. However, transparency is not required in the background captured by the camera, i.e., behind the measurement zone, or in any wall that can induce reflections of the laser beam. That means that the acrylic box must have two transparent walls and the opposite walls must be painted in black (opaque). In addition, any part of the experimental setup which induces reflections that interfere negatively with the results is removed or painted in black [166]. e) Roughness The orifice nozzles plate is manufactured by laser cutting. However, looking at preliminary results, it is observed that problems with jet symmetry occurred due to orifice roughness. To reduce the effect of the roughness on the air flow, the swarf around the orifice nozzles was removed. After this process, the mean roughness value is estimated to be equal to 0.900 ± 0.015 µm throughout the nozzle orifice, which seems to be satisfactory to ensure the flow symmetry. This parameter represents the arithmetical average of surface heights measured over the surface. The heights are averaged across microscopic peaks and valleys. Further studies must be conducted to analyze quantitatively the effect of orifice nozzle roughness on the jet impingement performance. Regarding the target plate roughness, several studies are conducted [84, 93, 94, 98, 168] showing the influence of this parameter on the heat transfer performance of impinging jets. This parameter will be explored in future works. 70 3. EXPERIMENTAL METHODS necessary [175]. Gas flows are seeded with liquid droplets or with solid particles. For droplets, the techniques of atomization and condensation are feasible, whereas for solid particles atomization (solutions or suspensions of particles) and fluidization can be considered. Considering the accuracy of this technique, PIV is highly suited to measure the flow velocity field, providing detailed information about the jet’s flow dynamics. Therefore, it has been used in several jet impingement studies [8, 29, 176–180]. Using this method, it is intended to see, on a macro scale, the flow behavior over the target surface, but also to identify, on a micro-scale, the phenomenon that occurs in the vicinity of surface transition (such as back steps and forward steps). The PIV method also allows the measurement of the velocity distribution of the impinging jet flow, being possible to identify the jet’s regions – the shear layer of the free jet, the stagnation zone, and the wall jet region – and the disturbances of its normal behavior when the fluid flows through the various surface irregularities, considering also the plate motion. 3.3.2. 2D-PIV System The 2D-PIV system, presented in Figure 35 (a), used for the experimental measurements consists of a 145 mJ double-pulse Nd:YAG laser which generates a light sheet firing on the second harmonic, i.e. green 532 nm. A two-dimensional laser sheet is obtained by the two beams previously recombined on the same optical path by a polarized dichroic filter and expanded in one direction through a combination of spherical and cylindrical lenses [8]. This laser sheet illuminates the measurement region, shown in Figure 35 (b), from the exit of the nozzles to the target plate over the length of the test chamber. The light scattered by the seeding particles is captured by the HiSense Zyla CCD camera, positioned perpendicularly to the laser sheet. This camera is equipped with a 50 mm Zeiss lens with a pixel size of 6.5 µm and a pixel resolution of 2560 × 2160 (5.5 Megapixel). The instantaneous motion of the air is obtained by the analysis of the two consecutive images, spaced by a short Δt, defined by the user as a function of the flow velocity. It is clear that, for seeded flows with a low velocity, the Δt must be large enough to capture the motion of the particle, while for high flow velocity, Δt should be small enough to be able to capture on time the required number of particles per interrogation area. Therefore, studies must be conducted to define the best compromise between Δt and the flow velocity. The data acquisition and processing of the images are performed by the software Dynamic Studio. The adaptive correlation method is used to process the data. According to [181–183], this method achieves higher accuracy supplemented with high sub-pixel accuracy and adaptive deforming window 3. EXPERIMENTAL METHODS 71 algorithm. This method applies a certain number of refinement steps to iteratively adjust the size and shape of the interrogation area (IA) and uses the information of the intermediary results between a larger and a smaller IA until the final IA is reached [181]. To achieve higher spatial resolution, a small IA size and a high overlap ratio are required. However, a compromise between higher quality images and computing time must be ensured. In this case, the interrogation area size is varied from 128 × 128 pixels to 32 × 32 pixels with 3 refinement steps and an overlap of 50 % in both horizontal and vertical directions. According to Cao et al. [182], these values lie between the typical values implemented for indoor airflow PIV applications. Figure 35. (a) PIV system; (b) measurement region. To conduct the measurements, three inputs can be introduced by the user to improve the accuracy of the measurements: the time between two laser pulses, i.e., the time difference between the two particle images, Δt; the trigger rate, i.e., the sampling frequency of the PIV setup; and the number of images required for acquisition. The measurements are performed using a double frame mode through which the camera acquires one single frame for each trigger pulse. Considering that the time between each pulse defines the exposure time, the camera is triggered twice in double frame mode giving the double exposure [184]. Since the trigger rate is defined by the properties of the laser, it is kept constant and equal to the maximum frequency allowed by the system, i.e. 15 Hz. Regarding the time between pulses, the definition of the appropriate value is more difficult to determine. According to Cao et al. [185], the pulse delay is defined by the separation of the particle images on the CCD camera which means that for cross-correlation, the separation of the particle images, in pixels, must be smaller than a quarter of the interrogation area (in pixels) and larger than the accuracy of the peak detection. The analysis of the most appropriate time between pulses for the measurements is presented in detail in section 3.3.4. (a) (b) 72 3. EXPERIMENTAL METHODS 3.3.3. Seeding Particles As mentioned previously, the seeding particles play an important role in the accuracy of the PIV measurement. According to [175], the tracer particles should not affect the dynamic of the flow neither changing their properties during the measurement nor interact with each other. Furthermore, they must be randomly and uniformly distributed across all the flow with a specific concentration in order to increase the accuracy of the measurements. However, achieving an optimum flow seeding is the most difficult part of the PIV experiments. According to [186], if the working fluid is air, the seeding needs to be entrained into the air upstream of the measurement region. However, the correct concentration of tracer particles is challenging, since besides ensuring a uniform distribution of the seeding across the test chamber, the deposition of the particles on walls is another factor difficult to overcome. Two problems arise from this deposition: first, the seeding system must insert more particles to compensate those adhering to the walls; second, window deposition is also a limiting factor, since the transparency is reduced, leading to a deformation of the image captured that generates measurement errors. This implies a continuous cleaning of the experimental setup walls. In addition to the precise distribution of the seeding throughout the measurement region, the selection of the seeding particles for the accurate tracking of the working flow is crucial to obtain accurate measurements. According to [187], a compromise between reduced particle size and low inertia, to improve the flow tracking, and large particle size to improve the light scattering, ensuring its detection by the camera, must be ensured. Melling [175] mentioned that a particle’s diameter between 2 µm and 3 µm is acceptable to track gas flows with a frequency response close to 1 kHz, while particles with 1 µm are suitable for turbulent flows. Another aspect is related to the concentration of the particles since a reduced concentration leads to inaccurate measurements while too many particles induce medium opacity [186]. In that sense, a compromise between the dimension of the seeding particles and their concentration must be ensured to obtain accurate velocity fields. Due to the importance of the selection of tracer particles that are suitable for the tracking of the flow in the study and the entire test facility, a seeding characterization is performed and presented in this section. a) Particles motion in air flow The interaction between particles in a continuous flow can be expressed by Eq. (24), assuming that the particles are small compared with the length scale of the motion and that the Stokes regime is valid. This equation is known as the equation for the unsteady motion of a suspended sphere [188]. 3. EXPERIMENTAL METHODS 73 3 3 3 2 0 1 3 ' 3 6 6 2 6 2 ' ' t pf RR p p p f p f p f f p R f dU dU dU dU dt d d U d d d dt dt dt dt tt          = + + + −  (24) where dp is the particle diameter, ρf and ρ p represent the fluid and particle density, respectively. Uf and Up are the fluid and particle velocity, respectively, while UR is the relative velocity (Uf – Up) and µf the fluid viscosity. The first two terms represent the acceleration force and the viscous resistance according to Stokes’ law which can be applied if the particle Reynolds number is lower than unity. That can be simplified using Eq. (25). 1 1 2 3 0 '' ' ' fp t pf pf dU dU dU dU dt dt aU aU a a dt dt dt tt − + = + + −  (25) where a1, a2 , and a3 can be obtained by equation expressed in (26): 1 2 3 2 3 36 18 ;; (2 ) (2 ) (2 ) f fff p f p f p p f p a a a d d           = = = ++ + (26) For particle response in turbulent flows, the equation of motion can be expressed by the amplitude ratio, η, and the response phase β of the instantaneous particle and fluid motions or as the ratio of the fluctuation energies of the time-averaged particle and fluid motion 2 p u / 2 f u . In this section, the first method is approached. According to [189], the flow and particle velocities can be expressed using Fourier integrals, as presented by Eq. (27) and Eq. (28). ( ) 0'cos sin f U t t d   =  +    (27) ( ) ( ) 0'cos sin p U t t d      =  + +  +     (28) where  is the angular frequency of the fluid motion. The second equation shows that the response of the particle to the fluid turbulence is lagged by β , given by Eq. (29), with an amplitude corrected by a factor η (Eq. 30), that is below the unit. ( ) ( ) 2 1 1 tan 1ff  −      =+ (29)   1/2 22 12 1 ( ) ( )ff   = +  +   (30) where f1 and f2 are obtained by Eq. (31) and Eq. (32), respectively. 74 3. EXPERIMENTAL METHODS ( ) ( ) ( ) ( ) ( ) 32 122 1 3 3 21 22 aa fa a a    +  − = +  + +  (31) ( ) ( ) ( ) ( ) ( ) 1 3 2 222 1 3 3 21 22 a a a fa a a    +  − = +  + +  (32) β and η are values that vary in function of the fluid oscillation frequencies, the fluid physical properties, and the dimension of the particles. If ρp/ρf = 1, the particles track the flow regardless of their size. In this study, the seeding particles that will be used are olive oil with a density of 908.7 kg/m3 at ambient temperature [190] and the flow is air which density and dynamic viscosity at ambient temperature is 1.204 kg/m3 and 1.825×10-5 kg/m·s, respectively. In order to analyze the behavior of the olive oil droplets in air, in amplitude and phase, with the variation of the oscillation frequency, two graphs are plotted and presented in Figure 36 and Figure 37. Figure 36. Response in amplitude of olive oil droplets in air for different particles diameter. 3. EXPERIMENTAL METHODS 75 Figure 37. Response in phase of olive oils in air at different particles diameter. From the concepts presented above, the olive oil droplet only can be considered an ideal seeding particle if η is close to the unit. As presented by Figure 36 and Figure 37, highly turbulent flows require tracking particles with small diameters. If the oscillation frequency of the flow is less than 10,000 Hz, olive oil particle with a diameter in the order of 5 μm can be applied, however, the efficiency of the tracking is increased if the diameter lies between 1 and 2.5 μm. However, if  > 10,000 Hz, a diameter of 1 μm must be ensured. To determine the range of the flow frequency, PIV measurements are conducted and the vorticity magnitude is determined. Vorticity is defined as the curl of the velocity field, given by Eq. (33). 𝜔 󰇍 󰇍 =∇× 𝑢 󰇍 (33) From the results, the flow frequency varies between 3,000 Hz and 13,000 Hz. From this analysis and considering the conclusions presented in the above paragraph, to ensure the success of the measurements, a seeding particle with a diameter between 2.5 μm and 1 μm must be ensured. In that sense, a study is conducted in order to determine if the diameter of the tracking particles produced by the seeding generator is within this range. b) Seeding generator The seeding particles generator is from Aerotech Concept and consists of a reservoir filled with liquid olive oil which flows through a probe with a vaporizer at its extremity, as shown in Figure 38. The vaporizer is similar to a tubular heating element used in ovens and comprises a stainless-steel enclosure inside which a fine coil of nichrome (NiCr) alloy wire heater is located, insulated by a ceramic material. The vaporizer heats the olive oil at a temperature above the smoke point and after the contact with the 76 3. EXPERIMENTAL METHODS surrounding air, the smoke condenses into fine droplets, generating the seeding particles that are introduced in the flow. The smoke generator allows the variation of two parameters, the flow rate, and the heater voltage. These two parameters are related to the quantity of oil that flows through the probe and the temperature at which the olive oil is vaporized, generating the seeding. Therefore, their combination influences the diameter and concentration of the seeding particles. In that sense, it is important to understand the relationship between the flow rate and vaporizer temperature on the diameter of the seeding particles. This study is fundamental since, to ensure an accurate PIV measurement, a compromise between a reduced particle size to improve the flow tracking and a large particle size to improve the light scattering must be ensured [187]. Figure 38. Concept Smoke Aerotech System. c) Experimental setup for the measurement of the seeding particles diameter To measure the particle’s diameter a Laser Diffraction Technique is applied using a Malvern 2600. This method, depicted in Figure 39, uses a low-power He-Ne laser that forms a collimated beam of light. If the beam strikes a particle, light is scattered and it is subsequently collected by a receiver lens which operates as a Fourier transform lens forming the far field diffraction pattern of the scattered light at its focal plane. This scattered light is later gathered over a range of solid angles of scattering, by a detector that consists of 31 concentric annular sectors. The unscattered light passes through a small aperture in the detector and out of the optical system, being monitored in order to determine the volume concentration of the sample. The diffraction angle increases with decreasing particle size and the number of particles can be obtained through the intensity of the diffracted beam at any angle [191]. The measured size range depends on the lens focal length. Using the available lens, the size range can be extended from 0.5 μm up to 2 mm diameters with a dynamic range (dmax/dmi n ) of approximately 100. To obtain 3. EXPERIMENTAL METHODS 77 an accurate measurement, it is recommended that the number of particles in an experiment varies between 100 and 10,000. The measurement is performed in two steps due to the influence of the external light sources that can also be reflected by the particle. In that sense, the measurement of the background light is performed before the introduction of the particles, and its contribution is subtracted from the sample measurement. To ensure accurate results, both background and sample measurements are performed close in time to each other, to reduce the possibility of stray light conditions changes. Figure 39. Experimental setup scheme for the measurement of the particle’s diameter. Regarding the sample, its concentration is of paramount importance to ensure accurate results. The Malvern 2600 data processing system allows the monitorization of the particle’s concentration, showing if it is in the range of acceptability for an accurate measurement. The measurement is performed after the system indicates that the concentration is close to “ideal”. To ensure a suitable distribution of the particles, the vaporizer is introduced inside an acrylic tube in order to minimize the interference of external factors such as air currents. To ensure the appropriate measurement conditions, the particles are introduced at a distance of 200 mm from the laser beam. According to Malvern 2600 manual, at this distance, the system should ensure a beam length active of 100 mm for a measurement volume of 8 mm diameter× 100 mm, represented in Figure 40 as V. Due to the irregularity of the flow that is expelled from the vaporizer, even if the 200 mm condition is maintained, it is difficult to ensure this specific measurement volume throughout all the experiments. 78 3. EXPERIMENTAL METHODS Figure 40. Geometry of the experiment. For the temperature measurement, two type K thermocouples are used, one to record the ambient temperature (Thermocouple 1 in Figure 39) and another connected to the vaporizer (Thermocouple 2 in Figure 39). The data acquisition system NI 9213 allows the continuous measurement of the temperatures from the ambient until the maximum ensuring an error below 0.02 °C. The experimental setup is depicted in Figure 41. Figure 41. Photograph of the experimental setup. With the measurement of the vaporizer temperature, it is possible to determine the relationship between the vaporizer temperature and the diameter of the particle generated by the seeding generator. To control the vaporizer heating, the seeding generator allows the variation of the heater voltage from 5 V to 30 V. However, from previous experience, the study was restricted between 5 V and 20 V, since higher voltage leads to vaporizer overheating. In that sense, different heater voltage are tested for each flow rate, and a specific vaporizer temperature is recorded. An important information that must be known before the discussion of the results is related to the properties of the olive oil. In this case, the one used for the 3. EXPERIMENTAL METHODS 79 experiments is a mixture of refined and virgin olive oil. According to Detwiler & Markley [192], virgin olive oil presents the thermal properties presented in Table 8. Table 8. Virgin olive oil properties. Property Definition Temperature (°C) Smoke point Temperature at which the oil starts to produce a continuous and visible smoke 199 - 243 Flash point Lowest temperature at which vapors of the material will ignite 321 Fire point Lowest temperature at which vapor will keep burning after the ignition source is removed 361 d) Analysis method for the measurement of the seeding particles diameter In terms of analysis mode used by Malvern 2600, the Model Independent Analysis is selected. This mode estimates a volume distribution based on the measured light energy data, assuming a 15 degree polynomial, and new light energy distribution is calculated using the equation (34) while the residual difference is calculated by equation (35): Dj = Ui,jVi (34) Log D = Log10 (∑(Dj−Lj) 2) (35) where i is the index of size band, j the index of detector elements, Ui,j describes how particles in size band i scatter light to detector element j. Dj is the measured data, Vi the relative volume of material contained in the particles in size band i and Lj the data calculated from the estimated volume distribution. A new set of values of Lj is calculated from the difference between Dj and Lj. This is an iterative process that stops when the residual reaches a minimum. The result of the measurement corresponds to a volume distribution of the material in the 32 bands. Since the main interest of the measurement is to obtain a particle diameter, the volume distribution must be converted to diameter. The derived diameters are calculated using equation (36): Dm,n =[∑Vidim-3 ∑Vidin-3 ]1 m-n (36) where di represents the mean diameter of size band i , m and n are subscripts that can take the value 3, if a representation of the diameter in terms of volume is desired, a value of 2 for surface, 1 for length, and 0 for number. The derived diameter usually used in this type of measurement is the Sauter Mean 86 3. EXPERIMENTAL METHODS A last comment related to the seeding particles concerns the refractive index. As previously mentioned, it is important to ensure that the materials used for flow visualization, i.e. test section walls and seeding particles, have closely matched refractive indices [167]. Considering that olive oil has a refractive index varying between 1.44 and 1.47 and this value for the acrylic walls is equal to 1.49, it can be concluded that the olive oil particles are a good choice to conduct the PIV measurements. 3.3.4. Source of Errors Considering all the aspects previously explored, the two main factors that influence the uncertainty quantification in PIV are the experimental setup and the seeding particles. These factors induce influence quantities that affect the relationship between the indication and the measurement results [163]. Before addressing these factors, attention is given to the calibration process and the time between pulses, since they are directly dependent on the user. a) Calibration The calibration of the PIV system is performed using a ruler (Figure 48). It has been demonstrated by [197] that the error resulting from calibration, applying as a comparison the scaling factors obtained in each measurement, is insignificant using a ruler or a calibration plate. The ruler is aligned with the laser sheet which passes through the center of the central nozzle. A minimum sheet thickness of 2 mm is ensured to reduce errors induced by the out-of-plane motion of the seeding particles [166]. Figure 48. PIV system calibration b) Time between pulses The definition of a correct time between pulses is fundamental to minimize measurement errors. This parameter must be set according to the flow velocity and must be long enough to determine, with 3. EXPERIMENTAL METHODS 87 accuracy, the displacement between particles but short enough to minimize out-of-plane particle’s displacement [196]. To analyze the influence of the time between pulses on the velocity magnitude measured by the PIV system, this parameter is varied, and the velocity profile obtained at the exit of the nozzle plate and over the target plate are plotted and presented in Figure 49 and Figure 50, respectively for a Reynolds number equal to 420. While the velocity magnitude normalized by the maximum nozzle exit velocity (U/Umax) is plotted over all the nozzle orifice diameter, the variation of U/Umax over the target plate is plotted from the jet axis (x/D = 0) to one side of the plate since the jet is symmetric. To conduct this analysis the normalized distance from the jet axis to the target plate is considered as x/D, the ratio between the distance in x direction and the jet diameter, D. Looking at Figure 49, where the maximum velocity is recorded, it appears that too high (600 µs) and too low (100 µs) time between pulses lead to higher measurement errors, as mentioned previously. Between 200 µs and 500 µs the difference between the maximum normalized velocity recorded is lower than 1 %. Focusing on the velocity profile over the target plate, Figure 50, a larger time between pulses (1300 µs to 600 µs) seems to underestimate the maximum velocity when compared to lower Δt. The maximum normalized velocity of 0.55 is recorded at Δt = 500 µs. For Δt = 300 µs, a maximum value close to 0.55 is observed but higher velocities are recorded over the target plate compared with Δt = 500 µs. In addition, the velocity profile seems to be more uniform at Δt = 300 µs. Figure 49. Variation of the normalized velocity magnitude at the exit of the nozzle throughout all its diameter for different time between pulses. 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0 1 2 3 4 5 U/Umax Nozzle orifice (mm) 100 µs 200 µs 300 µs 400 µs 500 µs 600 µs 88 3. EXPERIMENTAL METHODS (a) (b) Figure 50. Normalized velocity magnitude over the target plate at a different time between pulses (a) 800 µs to 1300 µs (b) 200 µs to 700 µs. As it can be observed, the maximum value is recorded at the exit of the nozzle orifice and decreases when approaching the target plate, until the stagnation point is reached. From this region, the jet flow is divided, increasing its velocity magnitude near the jet axis. In this specific case of a Reynolds number of 420, the experiments show a velocity decrease of approximately 45 % from the nozzle plate to the maximum velocity recorded over the target plate, if a correct time between pulses is applied. Looking at the data presented in Figure 49 and Figure 50, a Δt between 300 µs and 600 µs seems to be appropriate for the study of an air jet impingement flow for Re = 420. More details regarding the selection of the appropriate time between pulses are presented in the next section, based on the uncertainty estimation. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0 1 2 3 4 5 6 7 8 9 10 U/Umax x/Dj 700 µs 600 µs 500 µs 400 µs 300 µs 200 µs 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 1 2 3 4 5 6 7 8 9 10 U/Umax x/Dj 1300 µs 1200 µs 1100 µs 1000 µs 900 µs 800 µs 3. EXPERIMENTAL METHODS 89 3.3.5. Uncertainty Estimation in PIV Measurements An analysis of different variables, identified in a purpose-built experimental setup, that affects the velocity field of multiple jet impingement, was presented in the previous section. Four main categories were identified in the Ishikawa Diagram (Figure 31): PIV, Seeding, Experimental and Ambient conditions. As mentioned above, the different quantities identified have a great influence on the flow field velocity [169]. However, some of them are difficult to quantify. In that sense, they are not all accounted for in the uncertainty quantification of the velocity measurement. In the case of the PIV and Seeding, they are accounted by the Sciacchitano et al. method [198], which is presented in this section. As previously stated, the total uncertainty of a measurement is composed of the uncertainty arising from systematic and random effects [169]. The systematic errors are typically constant and mainly related to incorrect calibration and/or incorrect operation of the measurement system. However, these errors are difficult to determine in complex measurement systems such as PIV. Several works have been dedicated to quantify the total uncertainty of PIV systems [198–201]. In this work, the methodology presented by [198] is applied. Regarding the random errors, they are characterized by their nonpredictable nature and can change in magnitude and sign for every single measurement [166]. In the PIV technique, the velocity field of the flow is obtained indirectly as a displacement of the tracer particles in a finite time interval as presented in Eq.(38) [202]: D(X;t', t'')=∫U [X(t), t] dt t'' t' (38) where, D (X; t', t'') is the tracer particle displacement and U [X(t), t] its velocity. For ideal particles, U must be equal to the velocity of the flow in study. The PIV system analyzes this displacement by image analysis, and so, the instantaneous velocity of the particle (U) given by the system is such as Eq. (39): U = Sc ∆xp ∆t (39) where Sc is the scale factor, Δxp is the displacement in pixels, and ∆t the time between the two consecutive images recorded by the camera [203]. The scale factor is used to convert pixel coordinates to an object-space position (in mm) [197]. The scale factor value, obtained by image calibration, is used to reconstruct each image obtained by the PIV [204]. The connection between the physical distance, provided by a normalized measurement scale, and the pixel grid is obtained by the image captured by the camera. 90 3. EXPERIMENTAL METHODS The velocity obtained by PIV through Eq. (39), even if determined automatically, is a quantity that depends upon Δxp and ∆t. In that sense, an uncertainty estimation can be obtained by Eq. (40), which results from the development of the Taylor series for the uncertainty of a dependent quantity [169]: u2=∑pi2 u2(xi) N i=1 (40) where u is the combined standard uncertainty, while u(xi) is a standard uncertainty for a specific quantity xi and pi, expressed by Eq. (41), is the sensitivity coefficient given in terms of each quantity xi. pi 2= (∂f ∂xi)2 (41) The velocity measured, U, is composed by two components, in x direction and y direction, being the uncertainty related to both components expressed by uUx and uVy, respectively. In this specific case, uUx = uVy = uU and pi depends on the time between pulses, Δt, the scalar factor variation, ΔSc, and the particle’s displacement, Δxp. Replacing these variables in Eq. (40), one obtains Eq. (42): uU=√(∂U ∂(∆𝑆𝑐)u𝑆𝑐)2 +(∂U ∂(∆𝑥𝑝)u𝑥𝑝)2 +(∂U ∂tut)2 (42) Since the time between pulses Δt, can be considered infinitely small, for a certain range of flow turbulence, its contribution to the velocity uncertainty can be neglected, simplifying the equation in Eq. (43): uU=√(∂U ∂(∆Sc)uSc)2 +(∂U ∂(∆𝑥𝑝)u∆𝑥𝑝)2 (43) Sciacchitano et al. [198] presented a methodology for uncertainty quantification of PIV systems, known as the discrete window offset technique. This method consists of the statistical analysis of the matched particle image disparity, which is the residual distance between two consecutive particle images obtained after the matching. The displacement between two particles in an image is obtained by cross-correlation analysis [174]. The interrogation window obtained in the second image will be shifted toward the first window using the closest integer approximation, from which pairs of particles will overlap. Even if this 3. EXPERIMENTAL METHODS 91 measurement procedure is capable, some pairs of particles are expected not to correspond exactly. This mismatch can be related to several factors, namely: the displacement of particle image that can be related to sub-pixel particle image movement, laser power fluctuation, and camera viewing angle; the measurement position coming from the origin correlation and particles distribution; the time between pulses that must be defined in function of the particles velocity gradient; the calibration errors, due to lens image distortion, misalignment between the calibration plate and the laser sheet, image and physical distance of calibration plate dots, but also due to lens aberration and magnification [203]. The uncertainty quantification through discrete windows offset technique follows a sequence presented by Sciacchitano et al. [198]: First, the shift between the first and second interrogation windows is approximated to the closest integer number of pixels, being obtained the best velocity estimator. The particle images identified close to each other are considered as a pair and the distance between each pair is measured from their centroids. In the end, the velocity vector error is estimated by the statistical analysis of the dispersion (i.e. the variability of the observed values about their mean [169]) and the mean value of the disparity vectors of each particle pairs identified in a specific window. The dispersion of the disparity vector returns the estimate of the random error, while the mean value of the disparity indicates the occurrence of systematic errors [198]. In that sense, the accuracy of the error estimation depends on particle image density. a) Random uncertainty in PIV The random errors in PIV measurements are due to horizontal and vertical displacement, σxU, and σxV, respectively. These errors are assumed to be independent and normally distributed with zero mean and standard deviation σ . The resultant random error, σxR, follows a Rayleigh distribution, being given by the square root of the squared random errors, σxU, and σxV, as expressed in Eq. (44) [184]. For this analysis,σxR is determined considering the level of confidence of 95 % and is obtained by the square root of the squared σxU and σxV. A total sample number, N, equal to 100 is considered, being the 95 % confidence achieved with a factor equal to kp = 1.96 [165] according to Eq. (45). This equation is used for 𝜎𝑥𝑈 and σxV considering σU and σV, respectively. σxR=√σxU2+σxV2∙ (44) σxU, V=kp σU, V √N (45) 92 3. EXPERIMENTAL METHODS b) Comparing PIV with Pitot tube Because of the sensitiveness of the PIV technique, it is fundamental to ensure that all the test conditions are accurately controlled, minimizing the uncertainty associated with random and systematic errors. The Pitot tube is used to confirm if the velocities measured by the PIV lies within the expected range of values, following the methodology presented in section 3.2.3. The test conditions are performed with air at ambient temperature (≈ 22 °C), impinging a flat plate at the same temperature. As the maximum velocity occurs at the nozzle inlet, this velocity is analyzed to compare both measurement systems. The control of the air velocity is performed using the fan frequency drive Mitsubishi S500. The results presented in Table 10 show the velocity obtained at the nozzle exit recorded by the Pitot tube and PIV. A total of 5 dynamic pressures per fan frequency are considered to estimate the uncertainty associated with the velocity measured by the Pitot tube. These velocities are compared with those measured by the PIV system, being the uncertainty obtained by the statics analysis of 100 images using the methodology presented above. The results demonstrate that the velocities obtained through PIV lie in the range of values measured by the Pitot tube. In addition, the deviation between the velocity values recorded by the two techniques varies between 1 % and 5 %, and between 1 % and 10 % for the Reynolds number, except for the lower velocity, which is expected since the value measured by the Pitot tube is close to the uncertainty value of the measurement system. This study shows a good agreement between both measurement techniques. Table 10. Velocity and Reynolds number at the exit of the orifice nozzle measured indirectly using the Pitot tube and directly by PIV. Fan Frequency (Hz) Mean Velocity Pitot (m/s) Mean Velocity PIV (m/s) Re Pitot Re PIV 2.5 1.(8) ± 0.2 2.7(2) ± 0.20 601.(2) ± 5.9 897.2(3) ± 37.52 5 5.(1) ± 0.6 5.6(3) ± 0.40 1,679.(1) ± 172.5 1,857.1(3) ± 77.66 10 10.(8) ± 1.0 10.9(8) ± 0.80 3,562.(1) ± 322.2 3,621.9(0) ± 151.46 15 15.(8) ± 1.0 15.9(5) ± 1.05 5,213.(7) ± 328.0 5,261.3(2) ± 220.02 20 20.(7) ± 0.6 20.3(9) ± 1.20 6,810.(3) ± 197.8 6,725.9(1) ± 281.26 30 28.(6) ± 0.6 27.3(8) ± 1.45 9,416.(2) ± 243.8 9,031.6(5) ± 377.69 3. EXPERIMENTAL METHODS 93 Regarding measurement uncertainties for both Pitot tube and PIV, the uncertainty increases with higher velocity values, as expected, however, this value decreases in percentage. Regarding the PIV system, the velocity at the nozzle inlet and Reynolds number uncertainties are close to 7 % and 4 %, respectively. While with Pitot tube, the uncertainty decreases from 10 % to 2 %, for both velocity and Reynolds number measurements. These results are in agreement with several studies [73, 205–207]. c) Optimization of the time between pulses based on random uncertainty To optimize the time between pulses, the random errors for different Δt are estimated in order to confirm the statements presented in the previous section. Furthermore, the previous analysis shows that the results obtained by the PIV measurements are in agreement with the Pitot tube measurements, and the analysis of the random and systematic errors, obtained for the maximum velocity values, demonstrate that the random errors have a greater influence on uncertainty compared with systematic errors. In that sense, random errors are considered to analyze the accuracy of the velocity measurement using PIV at a different time between pulses. The study is conducted for the case of an isothermal air jet, at a Reynolds number of 420, impinging a flat plate. Figure 51 shows the variation of the random errors over the target plate for a different time between pulses. The results demonstrated that even if a Δt = 300 µs and 400 µs allow to obtain a good profile over the target plate, the random error is higher compared with Δt = 500 µs and 600 µs. The results also demonstrated that the random errors are higher near the jet axis, showing that it is difficult to predict with precision the stagnation region and that this precision is higher for the case of Δt = 500 µs and 600 µs. The higher random errors are estimated at the position where the jet flow is maximum in all cases. They decrease from this maximum with the increase of the distance from the jet axis, where velocity near zero is observed. Looking at the random errors profile in the wall jet region, the results indicate that a low time between pulses (Δt = 200 µs and 300 µs) presents higher random errors, showing that they are not reliable to predict the jet flow behavior in these conditions. This analysis highlights the fact that the uncertainty related to measurements is highly influenced by the time between pulses, being necessary to select a value that minimizes errors. 94 3. EXPERIMENTAL METHODS Figure 51. Normalized random error estimation for a different time between pulses at Re = 420 and H/D = 7. This procedure is conducted for different Reynolds numbers and Table 11 shows the optimized Δt for different Reynolds numbers. In this work, the focus is on Re = 420, Re = 1,857, and Re = 5,261, which corresponds to laminar, transition, and turbulent flow regimes, respectively. Table 11. Optimized time between pulses for different Reynolds numbers. Re Δt (μs) 897.2(3) ± 37.52 250 1,857.1(3) ± 77.66 250 3,621.9(0) ± 151.46 50 5,261.3(2) ± 220.02 40 6,725.9(1) ± 281.26 30 9,031.6(5) ± 377.69 10 d) Variation of the random error in function of the Reynolds number As mentioned throughout this work, the Reynolds number is one of the most important parameters that characterize the flow. To analyze if the behavior of the random errors is the same during the impingement process for different Reynolds numbers, the graph presented in Figure 52 is plotted. A H/D = 7 is preserved and the variation of the Reynolds number is performed by changing the air velocity using the Mitsubishi S500 fan frequency drive. 0 0.01 0.02 0.03 0.04 0.05 0.06 0 1 2 3 4 5 6 7 8 9 10 Random error (m/s) x/D 600 µs 500 µs 400 µs 300 µs 200 µs 3. EXPERIMENTAL METHODS 95 Figure 52. Normalized random error estimation for different Reynolds numbers for H/D = 7. The results show that by increasing the Reynolds number, the error estimated in the stagnation point increases. This is a critical point that must be correctly defined in jet impingement studies. In that sense, these results confirm that applying jets with high Reynolds number, the PIV setup parameters must be improved, such as the time between pulses and the accuracy of the focus of the images captured by the CCD camera in this specific region, to be able to decrease the measurement errors. As in the previous study, higher measurement errors are detected at the point where the flow velocity is maximum. The higher the velocity the greater the random errors, as expected. In addition, these results demonstrate that the accurate estimative of the velocity field at the stagnation region is difficult to obtain. Proceeding to a global analysis of the random errors profile over the target plate, it seems that the velocity measurements recorded at Re = 5,261 are more accurate than Re between 897 and 1,857. This specific case breaks the tendency observed in Figure 52, in which the higher the Reynolds number the higher the random errors measured over the wall jet region. These results suggested that by improving the PIV parameters, it is possible to enhance the measurements regardless of the level of turbulence of the flow. 102 4. NUMERICAL METHODS First, according to Eq. (64), the coefficient α* softens the turbulent viscosity causing a low-Reynolds number correction. Since the range of Reynolds numbers analyzed in this work is low, the low-Re correction option is activated. In the jet flow stagnation region, excess of turbulence kinetic energy, Gk, can occur. To avoid this problem, the generation of turbulence energy can be limited through production limiters. Two methods are available in FLUENT solver. One is based on the application of a coefficient of limitation, which takes the value of 10, and the second one considers the vorticity rate of the flow. As the deformation in the stagnation zone is nearly irrotational, vorticity is close to zero, which leads to a reduction of Gk [216]. While the first approach is known as Production Limiter, the second one is named Kato-Launder Production Limiter. To determine the effect of these parameters on the accuracy of the numerical prediction, the SST kω model with different functions activated is tested and compared with experimental data. The numerical domain consists of a row of ten jets (Re = 2,000) spaced 2 D impinging a flat plate, spaced 7 D from the nozzle plate. These conditions are selected since multiple jets in a confined space and close to each other increase the turbulence and the complexity of the flow. The boundary conditions and solution methods are maintained constant in all simulations. To compare the different approaches, the velocity profiles over the target plate and at the central jet axis are plotted and presented in Figure 54 and Figure 55, respectively. From the results, it appears that at the central jet axis, there is little influence of the turbulence parameter as the data follows the same profile from the nozzle inlet to the target plate. The higher difference is observed near the stagnation point, in which the SST k-ω model with the production limiter activated seems to perform better compared with the others. However, this difference is intensified in the velocity profile over the target plate. From the results, the SST k-ω model with the production limiter activated continues to be the one whose predictions are closer to the experimental data, while the SST k-ω model with the Kato-Launder production limiter presents the worst results. Considering this analysis, the SST k-ω model with low Reynolds number correction and production limiter activated is implemented. 4. NUMERICAL METHODS 103 Figure 54. Velocity profile over the target plate, at y/D = 0.2, for different SST k-ω model approaches. Figure 55. Velocity profile over the central jet axis (x/D = 0) for different SST k-ω model approaches. Another parameter that is not accounted for by the SST k-ω model is the streamline curvature. This effect, generated in the vicinity of the target surface, can affect the jet flow dynamics, mainly if the target is a curved surface, as stated by [217]. In that sense, it is important to analyze if this parameter has a strong effect on the numerical prediction of multiple jets impinging a flat plate. The model with sensitivity to streamline curvature and system rotation available in FLUENT solver is known as curvature correction, which is presented in detail by [212]. To study the effect of this parameter on the prediction’s accuracy, the numerical model was changed in order to intensify the effect of the streamline curvature and system rotation on the jet’s flow dynamics. Therefore, a line of five jet with the following conditions is modeled: S/D = 4, to be able to analyze the effect of the model on the vortices induces between jets, H/D = 2 to increase the overall flow turbulence 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 U/Umax x (mm) Experimental SST + Production Limiter SST + Kato Launder Limiter 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 y/D U/Umax Experimental SST + Production limiter SST + Kato-Launder Limiter 104 4. NUMERICAL METHODS intensity due to strong confinement and Re = 5,000 to ensure that the flow is fully turbulent. The SST kω model with the low Reynolds number correction and production limiter activated is tested with and without curvature correction option, and the predicted results are compared. The velocity field over the domain, Figure 56, shows that the magnitude of the vortices developed over the surface and between the jets is approximately the same and no significant differences are observed with or without the activation of the curvature correction. In terms of the normalized velocity magnitude in the vicinity of the target plate, presented in Figure 57, the results demonstrate that a slight difference is observed near the stagnation region. However, globally, this difference is insignificant. Since the curvature correction model does not present significant improvements to the model, it will not be considered. Figure 56. Velocity field for S/D = 4, H/D = 2, and Re = 5,000: (a) without curvature correction; (b) with curvature correction. Figure 57. Velocity profile over the target plate, at y/D = 0.02, for S/D = 4, H/D = 2, and Re = 5,000. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 -80.00 -60.00 -40.00 -20.00 0.00 20.00 40.00 60.00 80.00 U/Umax x (mm) without curvature correction with curvature correction 4. NUMERICAL METHODS 105 4.2. Numerical Softwares 4.2.1. ANSYS FLUENT ANSYS FLUENT solves the governing equations for the conservation of mass, momentum, and energy through a Finite Volume method and the discrete values of any variable ϕ are stored at the cell centers. The discretization on a given cell, solved by ANSYS FLUENT, is expressed by Eq. (68) [209]: ∂ρϕ ∂t dVc e + ∑ρf v f ϕf∙Af 󰇍 󰇍 󰇍 =∑Γϕ ∇ ϕf∙Af 󰇍 󰇍 󰇍 + SϕVce Nfa f Nfa f (68) where Nfa is the number of faces enclosing cell, ϕf represents the value of ϕ convected through face f, the term ρf v f ϕf Af 󰇍 󰇍 󰇍 is the mass flux through the face, in which Af 󰇍 󰇍 󰇍 is the area of face f, ∇ϕf the gradient of ϕ at face f , Sϕ the source term, and Vce the cell volume. ∂ρϕ ∂t dVce is defined in temporal discretization. However, for the convection terms, face values ϕf are required and they are interpolated from the cell center values using a second-order upwind scheme which derived ϕf from quantities in the cell upstream relative to the direction of the normal velocity [209]. To compute the face values of pressure from the cell values, a second order interpolation scheme is implemented using a central differencing scheme. The spatial discretization of the convection and diffusion terms is ensured by computing the gradients ∇ϕ of a scalar ϕ through a Least Squares Cell-Based gradient evaluation. Pressure-velocity coupling is applied to derive an additional condition for pressure and a procedure similar to that outlined by Rhie and Chow [218] is used to prevent checkboarding [210]. The pressure-based solver applies a SIMPLE method, which uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field [210]. To be able to analyze the flow development from the nozzle exit to the target plate, the simulations are transient, so the governing equations are discretized in time through a first-order implicit integration. To perform the transient calculations, an adaptative time step is used. This method adjusts the time step size in function of the truncation error. If the truncation error is smaller than 0.01, the size of the time step is increased, while if the truncation error is greater, the time step size is decreased. The truncation error-based method was selected instead of the CFL method since it presents a suitable accuracy and lower computational time. Moreover, the constant truncation error value was defined based on preliminary 106 4. NUMERICAL METHODS studies which compare different values and the simulation time, being found that an error equal to 0.01 presents good predictions at a lower simulation time. As previously mentioned, the numerical simulations are conducted for different flow regimes, laminar, transition, and turbulent. While for the jet’s flow in the transition and turbulence regime, the SST k-ω model is implemented, for the laminar flow, FLUENT has a “Laminar model” option. This is not a DNS method, instead and since is based on Reynolds-averaged Navier-Stokes equations, this model neglected the fluctuating quantity and solves the Navier-Stokes equations considering the time-averaged velocity The development of numerical simulations using the Laminar model is important in this work since the results obtained will be compared with a DNS formulation, based on a MATLAB framework, to validate the accuracy of FLUENT to model an air jet impingement process. 4.2.2. MATLAB 2.29 Finite Volume framework 2.29 MATLAB Finite Volume framework (2.29 FV) is an in-house code developed by the MSEAS group at MIT. To solve the Navier-Stokes equations, a Boussinesq buoyancy approximation by a Finite Volume discretization on a uniform cartesian mesh using an incremental Pressure Correction in a rotational form projection method is applied. A second-order backward difference-time marching scheme is implemented, and a LU factorization is used to solve the linear systems. The advection uses a Total Variation Diminishing (TVD) advection scheme which is a mixture between the central difference scheme (CDS) and the upwind scheme (UW). TVD limits the slope to ensure that the maximum value of the function is never exceeded, and its minimum value is never undershot. The projection method implemented by 2.29 FV to solve the Stokes problem is based on a rotational form of the Incremental Pressure correction scheme. In that sense, the time integration is conducted in the following steps, Eq. (69) – (72) [219]: [I ∆tυ ∇ 2]u t +1=u t ∆t- ∇P t+F t +1 (69) ∇ 2(q t +1)= 1 ∆t∇∙u t +1 (70) u t+1 = u t +1- ∆t ∇q t +1 (71) P t +1= q t +1+P tυ ∇ ∙u t +1 (72) 4. NUMERICAL METHODS 107 where P is the “Pseudo-pressure”, t is the time step, t + 1 is the next time step, υ is the kinetic viscosity, and q the effective order of the method. The nonlinear terms are treated explicitly, i.e., to solve the Navier Stokes equation F n+1≈ -u n∙∇u n. The Navier-Stokes solvers implemented in the 2.29 framework require three inputs: the DriverScript, the SetupScript, and the PlotScript. The DriverScript is a structure where all the variables are defined as well as the fields app.Nx, app.Ny and app.dt, which represents the number of interior points in the xdirection and y-direction, the time of the simulation, and the time step size respectively. The SetupScript allows to set up the problem from the determination of the mesh to the definition of the boundary conditions and initial conditions. Regarding PlotScript, it allows to plot the solution. To compare FLUENT and 2.29 FV in the same conditions, the plotscript was adapted. 4.3. Jet Impingement Models The numerical models developed in this thesis consist of single and multiple jet impingement. The main focus of the first approach is the development of a numerical model that accurately predicts the flow dynamics of a single jet impinging on a flat plate, considering a Reynolds number in the laminar regime, Re = 420, and in the transition regime, Re =2,000. To conduct this analysis, two different approaches are followed, being presented in detail in section 4.3.1 as “Laminar single jet impingement” and “Single jet impingement in the transition regime”. Regarding the multiple jet impingement, a numerical model is developed to accurately predict the jet’s flow dynamics and heat transfer performance of turbulent multiple air jets (Re = 5,000) impinging a moving and static flat plate. Details regarding this model are presented in section 4.3.2. 4.3.1. Single Jet Impingement The physical problem considered in this study is a 2D single air jet impinging a flat plate in a confined space. The configuration of the jet impingement flow is presented in Figure 58. The jet flows through a circular nozzle of diameter D, with a velocity, v , and impinges perpendicularly on a flat plate at a distance H from the nozzle plate. Since the Mach number is below 0.3 in all numerical models, the air jet flow is considered incompressible. The jet impingement flow is characterized by three main regions: free jet, stagnation, and wall jet [19]. The free jet region starts at the nozzle exit, where the dominant velocity component is axial and maximum values are recorded. As the jet flow interacts with the ambient air, a shear layer is generated which induces high lateral velocity gradients. As the flow gets closer to the wall, 108 4. NUMERICAL METHODS it loses axial velocity and turns, generating a stagnation region in which the overall velocity is near zero. The last region is the wall jet, identified once the air jet impacts the target surface. The flow is divided into two streams moving in opposite radial directions along the surface, in which the boundary layer thickens as it moves outward due to the entrainment of the surrounding fluid. To conduct the numerical simulation, L is established considering the statement presented by [92], i.e. the outlet must be located at a distance from the jet center, at both sides of the jet, equal to 60 jet diameters, to avoid flow reversal. Considering that D = 5 mm, L is assumed to be equal to 600 mm. Figure 58. Problem statement of a single jet impingement. Two studies are conducted involving a 2D single jet impingement. While the first study focuses on a Laminar jet, using the Laminar model of FLUENT and the 2.29 FV, the second one consists of a single jet in a transition regime, using the SST k-ω model. The great advantage of the first approach is mainly related to the use of a DNS formulation to validate the accuracy of a commercial software to model a laminar single air jet impingement process. In addition, the accurate description and prediction of the jet impingement, at low Reynolds numbers (Re < 1,000), helps to understand the jet flow dynamics and physical phenomena for high Reynolds numbers impinging jets. Regarding the second study, it focuses on the validation of the SST k-ω model for the numerical modeling of a single air jet in a transition regime. Since several industrial processes, such as drying and reflow soldering, applies jet flows with a Reynolds number between 1,000 and 3,000, it is important to understand if the SST k-ω model, whose accuracy has already been validated for the numerical modeling of turbulent flows (as presented in section 2.3), also performs well at low Reynolds numbers (Re = 2,000). a) Numerical domain and boundary conditions Laminar single jet impingement The modeling domain consists of a confined single air jet impinging on a flat plate surface, based on the problem statement presented in Figure 58. The air flows through a circular nozzle, spaced 6 D from the target plate, at a specific velocity that ensures a Re = 420. In this study, two case studies are 4. NUMERICAL METHODS 109 considered, an isothermal and non-isothermal jet impingement, in order to analyze the effect of the target plate temperature on the jet flow dynamics. For the isothermal case, a constant ambient temperature of 22 °C is applied throughout the domain, at the jet inlet, and over the target plate. While for the nonisothermal case, a constant temperature of 120 °C is considered on the impinging surface. Regarding the boundary conditions applied at the nozzle plate, which consists of a wall with a circular nozzle located in its center, two different conditions are considered. The circular nozzle, the air flow inlet, consists of the Dirichlet boundary condition. At the exit of the nozzle, a uniform velocity profile (top hat) of the jet flow is considered as well as a constant velocity in the y-direction (v ≠ 0 m/s) and a constant ambient temperature (T = 22 °C). The nozzle plate walls are defined by no-slip and adiabatic conditions, meaning that Neuman boundary condition is applied in terms of temperature (∂T/∂x = 0) and Dirichlet for velocity (u = v = 0 m/s). Regarding the target plate, a constant temperature, T = 22 °C for the isothermal case and T = 120 °C for the non-isothermal case, and no-slip conditions are implemented. The side walls are set as outlets. In 2.29 FV, the pressure is defined automatically through the implementation of an open boundary condition. The Open boundary condition sets: ∂u ∂n = 0, ∂v ∂n = 0, ∂2p ∂n2 = 0, where p is pressure and n is in the normal direction [219]. In FLUENT a pressure outlet boundary condition is implemented. For more details regarding pressure outlet refer to [209]. Single jet impingement in the transition regime The numerical conditions set for the single jet impingement in the transition regime, are the same as the ones presented in the previous study for the isothermal case. However, in this case, the nozzle-to-plate distance (H/D) is varied between 2 and 6, in order to determine the effect of this important process variable on the jet flow dynamics. In that sense, the uniform velocity distribution is applied at the inlet while no-slip conditions are implemented at both nozzle and target plates. A constant temperature of 22 °C is specified to the inlet and target surface and the adiabatic wall is defined at the nozzle plate. Pressure outlet boundary condition with zero initial gauge pressure is applied to the open sides of the domain. b) Air flow properties The air flow properties are the same for both laminar and transition single jet impingement. To investigate the effect of the density, thermal conductivity, dynamic viscosity, and specific heat capacity on impingement heat transfer, Zhou et al. [133] analyzed the variation of these four variables considering three cases at different temperatures differences (200 K, 400 K, and 600 K) and three Reynolds numbers 110 4. NUMERICAL METHODS (4,000, 8,000 and 12,000) and compared the results with the heat transfer coefficient predicted by changing density and thermal properties, i.e. real gas. Their results show a slight variation between the real heat transfer coefficient and the heat transfer coefficient obtained with constant thermal properties. The maximum difference is obtained for the higher temperature difference, 600 K, and it is not more than 5 %. This study justifies the use of constant thermal properties in the majority of the numerical work performed in jet impingement research [19, 96, 144, 149, 220–222]. The air thermal properties are defined at an ambient temperature according to [156] and presented in Table 12. For the case of density, incompressible ideal gas law [209] is selected instead of a constant value, since previous studies reveal a higher accuracy of the predicted values compared with constant density. Table 12. Air Properties at 22 °C. Properties Values Density [kg/m3] Incompressible ideal gas Specific Heat [J/kg·K] 1006 Thermal Conductivity [W/m·K] 0.0242 Dynamic Viscosity [kg/m·s] 1.789 × 10-5 c) Grid Discretization Laminar single jet impingement A structured grid with square elements is applied in both numerical models using FLUENT Laminar model and 2.29 FV framework. Considering that 2.29 FV requires the implementation of a uniform grid, no wall refinement must be applied. The two meshes implemented in this study are presented in Table 13, and the information regarding the mesh size and the simulation parameters are mentioned. Table 13. Simulation data information. Simulation Tool Mesh Reynolds number Simulation time Time step Computational time Laminar modelFLUENT 5050 × 300 420 1 s Adaptive mode starting on 1E-5 s ≈ 20h 2.29 FV 2000 × 250 Fixed mode 1E-5 s ≈ 1 day and 5 h 4. NUMERICAL METHODS 111 As it can be observed, while 2.29 FV performs the numerical calculations with a fixed time step, FLUENT allows both fixed and adaptive time step methods. Using the adaptive time step, the calculation starts with a pre-defined time step, which can be changed automatically throughout the simulation, based on the estimation of the truncation error associated with the time integration scheme [209]. If the truncation error is smaller than 0.01, the size of the time step is increased, while if the truncation error is greater, the time step size is decreased. Preliminary analysis shows that the adaptive time step is accurate to model a single jet impingement, therefore, it is used in this study since it decreases the simulation time. However, since the time step size is not a fixed low value kept during all the simulations, to ensure accurate results, a higher number of cells is needed. In that sense, the velocity profiles obtained numerically using different mesh sizes (250,000 to 2,000,000) were analyzed and compared with experimental data. From the preliminary study, a mesh size with a total of 1.5 million elements is used, allowing a good compromise between the solution accuracy and the computational time. Regarding 2.29 FV mesh size, preliminary studies were conducted, varying the mesh size (from 250,000 to 750,000 elements) and the time step size (from 1E-4 s to 1E-6 s). The velocity profiles obtained numerically were compared with experimental data and the analysis shows that the flow profile predicted by a mesh with 500,000 cells is accurate enough to predict the jet flow profile while decreasing the computational time by 25 %. The time step is also defined by preliminary analysis, based on the Courant-Friedrichs-Lewy (CFL) condition, expressed in Eq (73). 2.29 FV follows the CFL stability criterion on the numerical solution of the advection equations, which means that the maximum allowable information propagation speed in a numerical scheme must exceed the physical advection speed [219]. If this condition is violated, the numerical simulation may become unstable and crash. ∆t ∆xC ≤ 1 (73) where C is the physical advection speed, ∆t represents the time step and ∆x is the length between mesh cells. From this study, it is verified that 1E-5 s is the higher suitable value that allows to run of the numerical simulations without violating the CFL condition. Considering that the interest of this study is to analyze the flow development from the jet inlet to the target plate, a simulation time of 1 s is considered to highlight the transient dynamics of the impingement process. Single jet impingement in the transition regime The spatial discretization of the domain is performed using a block-structured grid with square elements, using the ANSYS 19.1 version. While in the previous study a structured and uniform grid with 118 4. NUMERICAL METHODS d) Mesh Motion The difference between the grid implemented in the static and the moving cases is only related to the target plate since the length implemented is slightly higher (Figure 63) in order to analyze the flow without the interference of the boundary layer generated in front of the plate during its motion. As mentioned by [104], this strong boundary layer induces an increase of the flow velocity in the vicinity of the plate and the downstream jets are highly deflected. To ensure accurate predictions, an interface between the flow and the surface is implemented to be able to visualize the motion of the surface with time. In this study, the plate motion is considered from the left to the right. Several methods can be implemented to perform the numerical simulations of the moving plate. ANSYS FLUENT allows the implementation of three different methodologies, dynamic mesh, sliding mesh, and frame motion [209]. The first method is applied to simulate problems that involve boundary motion and grid deformation, while the sliding mesh allows the motion of domain without grid deformation. In this second method, a non-conformal interface is applied to the junction of cell zones that have relative motion. Figure 63. Numerical domain to conduct the dynamic simulations. Finally, frame motion does not involve the motion of the cell zones since the motion is given to the reference frame, so the cell zones have zero relative motion concerning their reference frame. This leads to the same conservation equations as those without motion with force terms added. Since the interest of this study is the prediction of the heat transfer across the interface flow/surface without grid deformation, the sliding mesh is implemented in this work. This method was also implemented by [138]. 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 119 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 5.1. Test Conditions For the study of single jet impingement, the experimental setup and procedures presented in chapter 3 are applied. The jet flows through a circular nozzle, 5 mm in diameter, with a velocity, v , and impinges perpendicularly on a flat plate at a distance H from the nozzle plate. To measure the velocity field, the PIV technique is applied, as it can be observed in the schematic presented in Figure 64. Figure 64. Experimental setup for the study of a single jet impingement. Two cases are considered in this analysis, an isothermal and non-isothermal single jet impingement. In both case studies, the jet flows through the circular nozzle at a constant ambient temperature, Tj = 22 °C. Two temperatures are applied to the target plate: Tw = 22 °C for the isothermal case, and Tw = 120 °C for the non-isothermal case. Regarding the jet velocity, a Reynolds number close to 420 and 2,000 are used, meaning that the jet flow is laminar and in the transition regime, respectively. For the non-isothermal analysis, to guarantee a correct study of the heat transfer, the heat flux sensor is positioned over the target plate and aligned with the jet axis, ensuring that the jet impinges all the sensor area. Both heat flux and temperatures are recorded over a time span of 30 min. The results used for the data analysis are the heat flux, air jets, and plate temperatures recorded over the stabilization period. The plate temperature is considered constant and equal to 120 °C and the temperature of the jets is recorded at the stabilization chamber to ensure that the target surface temperature does not 120 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT interfere with the air jets temperature. The data reduction and uncertainty estimation of the heat transfer was presented in section 3.2.5. The uncertainty related to the PIV measurements is obtained through a statistical analysis of the data for 300 images. Following the concepts presented in section 3.3.5, the uncertainty obtained for the maximum velocity recorded by the system is close to 10 %. 5.2. Laminar Single Jet Impingement The jet impingement involves several variables that increase the flow interactions, from the jet flow parameters (velocity and temperature) to the target surface and process geometry (nozzle-to-plate distance, ribs, etc.). In that sense, several studies have been conducted in order to fully characterize the flow field of a jet impingement process [19, 21, 54, 225, 226]. However, few works characterize the flow of laminar jets. Even if the applicability of laminar flow is reduced in industrial processes, they are very important to fully characterize the jet impingement flow. Experimental studies, enable the identification of complex structures under impinging jets and to understand their propagation throughout the target plate, which leads to increased flow turbulence and consequently to heat transfer enhancement. The accurate description and prediction of the process, at low Reynolds numbers, helps to understand the phenomena for high Reynolds numbers impinging jets. This first analysis focuses on the effect of the plate temperature on the jet flow development over the target plate, therefore, two cases are considered, an isothermal and non-isothermal single jet impingement. Experiments are conducted, followed by a numerical validation using both 2.29 FV and FLUENT. The results obtained by the numerical simulations are compared with the data collected from the experiments and they allow to determine the accuracy of the numerical predictions. 5.2.1. Experimental Results The measurements collected by the PIV system are presented in this section. The flow structure and velocity profiles obtained experimentally over the target plate and along the jet axis are discussed. a) Flow dynamics of a laminar single jet Regarding the PIV measurements, non-dimensional distances are used to discuss the data, in which H/D represents the normalized nozzle-to-plate distance, x/D the normalized radial distance from the jet axis (x/D = 0), and y/D the normalized axial distance, in which y/D = 0 represents the location of the target plate and y/D = 6 is the location of the nozzle plate. One image of the instantaneous flow profile 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 121 captured by the CCD camera, and presented in Figure 65, reveals that, even for low Reynolds numbers, the jet is unstable and no steadiness is reached after several minutes of the experiment. At the nozzle exit, in which a uniform profile at a maximum velocity occurs [21], the flow seems to be stable. However, at approximately y/D = 1 downstream of the nozzle orifice, flow perturbations are identified. This phenomenon occurs due to the shear layer induced when the jet flow interacts with the low momentum ambient flow. This velocity discontinuity induces Kelvin-Helmholtz instabilities, resulting finally in a vortex structure [227] that dominates the flow. As the jet flow approaches the target plate, the axial velocity component decreases, and, at the moment the plate is reached, the jet spreads radially over the target plate, this is the stagnation region. In this region, the kinetic energy of the flow decreases rapidly and is transformed into a rise in pressure energy which induces an acceleration in the radial component of velocity [26]. After the stagnation zone, the jet flow passes through the acceleration zone, where strongly favorable pressure gradients are induced over the impinging surface, essentially due to the impact of the vortices on the wall which causes a thin boundary layer [126, 228]. From Figure 65, it is possible to identify a decrease of the boundary layer thickness at 1 < x/D < 2, growing again at x/D > 2. At x/D = 2.75, it is possible to observe the presence of vortical structures that propagate over the wall and seems to increase in magnitude as the flow develops along the surface. As mentioned by [26], these vortices entrained surrounding fluid, compress the fluid layer, and cause the penetration of the wall jet flow into the boundary layer, leading to fluctuations in wall pressure. The strength of these large-scale structures leads to increased stress into the boundary layer and consequently, an enhancement of the heat transfer is expected [126]. The axisymmetry of the vortices pattern throughout the impingement wall is clear, being also identified by [8]. The motion of the wall jet over the surface continues until the jet flow has enough kinetic energy. Looking at Figure 65, the exact location where the jet flow detaches from the wall occurs at x/D close to 8.5. At this specific point, it is observed that the boundary layer detaches the wall, the flow deflects upwards until the nozzle plate is reached and rolls up, originating two large and symmetric vortices. The development of these two large vortices is limited by the confinement and induces flow interactions at the edges of the jet. This interaction can interfere with the velocity profile observed at the jet axis. The axisymmetry of the flow is clearly identified, with identical vortical structures detected at both sides of the jet axis. Since Figure 65 represents an instantaneous velocity field, the correct definition of the different regions of the jet is possible through the statistical analysis of the 300 images which is presented in the next section. 122 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT Figure 65. Instantaneous flow profile of an isothermal air jet impinging a flat plate at Re = 420 and H/D = 6. b) Jet velocity profiles The jet velocity profiles obtained for both isothermal and non-isothermal jets are discussed in this section. Isothermal Jet The jet velocity profiles, for the isothermal case, are plotted in Figure 66. As presented in the previous section, the experimental data are obtained by statistical analysis of time-averaged velocity fields of 300 images captured and post-processed by the PIV system. A contour plot, Figure 66 (a), allows to analyze the variation of the velocity magnitude normalized by the maximum nozzle exit velocity (U/Umax) throughout the domain. Higher velocities are recorded at the jet inlet, immediately followed by a decrease in velocity just downstream of the nozzle orifice. As mentioned previously, this decrease is due to the shear layer induced by the interaction between the flow and the surrounding air. However, this decrease throughout the jet axis (x/D = 0) is not uniform. This seems to be in agreement with the observations stated in the previous section. Even if the flow is laminar, the vortices generated interfere with the jet flow, decreasing its velocity, as observed with more detail in Figure 66 (b). A similar profile is also detected by [8]. The maximum velocity is recorded at the exit of the orifice nozzle, followed by a decrease due to the generation of the shear layer, inducing high lateral velocity gradients. As presented in Figure 66 (b), the higher the distance from the jet axis, the stronger the influence of the shear layer on the velocity profile. After this region with strong perturbations, 5.9 < y/D < 4.2, the maximum velocity is recovered at the jet axis. The potential core, defined by Livingood & Hrycak [23] as the distance from the nozzle exit to the position where the jet velocity reaches 95 % of its original value, starts from the jet inlet and ends at y/D = 2.4, which is in accordance with [8]. From the end of the potential core, a deceleration region is identified, followed by an acceleration region, essentially due to the growth of the vortices generated in 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 123 the free-jet shear layer. Finally, below y/D = 1, a stagnation region is reached, and the stagnation point is identified over the target plate at the jet axis, as expected. After impinging the target plate, the wall jet develops radially, increasing in velocity, as expressed in detail in Figure 66 (c). Even if the velocity profile is not totally axisymmetric, the velocity over the target plate increases from the stagnation point, reaching its maximum at x/D = 1.4. This acceleration zone 0 < x/D < 1.4 is mainly related to the growing boundary layer, which induces a fast acceleration of the flow due to larger pressure gradients [24]. The location of this zone varies as a function of the Reynolds number and the nozzle-to-plate distance. Increasing the distance from x/D = 1.4, a uniform decrease in velocity is observed until the flow detaches the wall. As presented in Figure 66 (c), this moment seems to occur near x/D = 8.5. The velocity field develops radially over the wall and, at this specific point, the results presented in Figure 66 (a) demonstrated that the velocity vectors move upward, showing the complete detachment from the wall. Figure 66. Normalized time-averaged velocity magnitude at Re = 420 (a) all the domain; (b) throughout and near the jet axis; (c) over the target plate. Non-isothermal Jet The velocity profiles for a non-isothermal jet are expressed in Figure 67. The contour plot presented in Figure 67 (a) indicates that the effect of the natural convective heat transfer plays an important role in the jet flow structure. 124 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT Figure 67. Normalized time-averaged velocity magnitude at Re = 420 (a) all the domain; (b) throughout and near the jet axis; (c) over the target plate. Compared with the isothermal jet case, a stronger complexity of the jet flow due to the increased temperature of the target plate is clearly demonstrated by the higher magnitude of the velocity vectors expressed in Figure 67 (a) compared with Figure 66 (a). The mixing between the ambient air and the hot air that comes from the target plate is increased by the temperature difference, increasing the jet flow velocity over the surface as well as between the nozzle and the target plates. This effect promotes the heat transfer over the impinging surface and can be explained by the increase of flow driving forces in the vertical direction due to stronger buoyancy forces. While in turbulent flows the buoyancy effect can be neglected, in laminar flows the impinging regime may fall in natural, forced, or mixed convection, depending on the relative strengths of the inertia/viscous forces and the buoyancy forces involved [229]. To support these conclusions, it is important to determine the convection regime of the laminar jet flow analyzed in this work. Therefore, the Richardson number must be determined, Eq. (75). If Ri << 1 the forced convection regime is dominant, while Ri >> 1, natural convection prevails, and if Ri ≈ 1, the flow is in a mixed convection regime. Ri = Gr Re2 (75) According to [229], the Grashof number (Gr) can be determined by Eq. (76): Gr = g (Tw-T∞) H 3 υ 2 (76) *  5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 125 where H is the nozzle-to-plate distance (H = 0.03 m), g is the acceleration of gravity (9.81 m/s2), β* is the coefficient of volumetric expansion (1/T ), and υ the air kinematic viscosity. In this case, the air properties are considered at film temperature, T, given by Eq. (77): T = Tw + T∞ 2 (77) Considering that the average temperature of the target plate (Tw) is 120 °C and the air jet temperature at the exit of the nozzle (T∞) is 22 °C, T is equal to 71 °C, therefore β* = 0.014 and υ = 1.995×10-5 m2/s. These values lead to a Gr = 912,132, and considering that Re = 420, Ri takes a value of 5.17. This analysis demonstrates that natural convection is dominant, and it supports the statements presented above since the strength of the buoyancy forces affects the inertia/viscous forces. The buoyancy force tends to move the air upwards, promoting the mixing between the surrounding air and the jet flow, increasing the heat transfer over the target plate. In that sense, it seems that both natural and forced convection affects the total heat transfer rate, meaning that the heat transfer falls in a mixed convection mode. In addition, looking at the two vortices generated on each side of the jet axis, it seems that their development is different from those induced in the isothermal case. This shows once again the effect of natural convection on jet flow development. As the heated air from the target plate moves upwards, cold air coming from the outlets is entrained and constrains the development of the recirculating vortices, increasing the global turbulence intensity of the flow. Furthermore, looking in detail at the velocity magnitude over the jet axis, Figure 67 (b), the velocity profile presents no significant variations over the jet axis, with maximum velocities recorded over the potential core length, followed by a decrease until the stagnation region is reached. Compared with the isothermal jet, this profile is substantially different. As expressed in Figure 66 (b), without temperature variation, the flow is mainly affected by inertia/viscous forces, therefore, small variations in the shear layer affect the jet velocity profile, inducing acceleration and deceleration zones. Whereas, with temperature gradients induced by the heated plate, the effect of buoyancy forces increases the flow driving forces in the vertical direction, increasing the flow intensity and therefore, affects the inertia/viscous flow. In that sense, it seems that the effect of the shear layer variation on the jet axis velocity profile is negligible when the flow turbulence is increased. The increased complexity of the flow in the vicinity of the wall leads to a reduction of the accuracy of the velocity at the stagnation point, as observed in Figure 67 (a), showing the limitation of PIV in resolving near-wall measurements [230]. As previously mentioned, to enhance the accuracy of the measurements a macro lens must be used to zoom this region combined with a higher time between pulses. 126 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT c) Heat transfer measurements To conduct the heat flux measurements, the OMEGA® HFS-4 thin film heat flux sensor is mounted at the center of the target surface, just below the nozzle, and data is collected over a time span of 30 min, as previously presented in chapter 3, section 3.2.1. The average heat flux is measured, and the heat transfer coefficient is determined considering the temperature difference between the target plate and the air jet, as presented by Eq. (18). From the heat transfer coefficient, the flow properties (ρ and μ), and the jet diameter, the Nusselt number is calculated and a value equal to 5.52 ± 0.80 is obtained. The uncertainty analysis applied in this study for 95 % of confidence follows the methodology presented by [165]. These results are in agreement with those obtained by [83, 231] and the correlation presented by [112]. Even if the heat flux sensor provides an average value, it is expected that the maximum heat transfer is recorded at the stagnation region and decreases with the increased distance from the jet axis. This behavior is in agreement with the jet flow development over the surface. As previously mentioned, higher flow velocities are recorded at the vicinity of the stagnation region, in which a growing boundary layer is generated, leading to a fast acceleration of the flow. This region promotes the mixing between the jet flow and the surrounding air increasing the average heat transfer. To determine if the average Nusselt number determined experimentally is within the range of other studies presented in the literature, it is compared with correlations, experimental and numerical results. From the results presented in Table 17, it seems that a maximum difference of approximately 30 % is observed. This discrepancy can be explained by the fact that the laminar jet is highly influenced by small variations of the flow and the geometrical variables. Even if the correlation and experimental data selected present parameters close to those implemented in this experiment, there are some variations that interfere with the average Nusselt number. While in turbulent jets momentum governs the jet’s flow, in laminar jets the temperature difference between the plate and the jet plays an important role in the jet flow dynamics, influencing the heat transfer performance. However, no published correlation has this aspect into consideration since it is very difficult to quantify. Regarding the two studies presented in Table 17, the implemented temperature difference is not mentioned. 5. RESULTS AND DISCUSSION OF A SINGLE JET IMPINGEMENT 127 Table 17. Comparison between the experimental heat transfer values and data presented in the literature. Nu     Measured Huang Correlation [112] (750 < Re < 27,000 and 3 < H/D < 16) Chattopadhyay (Re = 500) [123] Sparrow & Wrong (Re = 450 and H/D = 5) [232] 5.5(2) ± 0.80 3.85 6.88 8.21 5.2.2. Numerical Validation The jet flow structure and velocity profiles obtained numerically by FLUENT Laminar Model and 2.29 FV MATLAB Framework are presented and discussed in this section. The jet flow velocity profiles at different simulation times are analyzed and compared. From the numerical results, it is intended to determine the accuracy of both numerical tools to capture the jet flow dynamics from the nozzle to the impinging plate. In that sense, the analysis was conducted from 0 to 1 s, which gives enough time for the jet flow to develop from the jet exit to the target plate. Furthermore, the heat transfer over the plate is analyzed for the non-isothermal case and compared with the experimental results. a) Jet flow The development of the jet flow profile over time was predicted using both 2.29 FV MATLAB Framework and FLUENT software and the results are presented in Table 18. The interaction between the ambient fluid and the jet flow is clearly observed at 0.02 s, resulting in the formation of an initial jet shear layer and the generation of a primary vortex due to Kelvin-Helmholtz instabilities. As the jet moves downstream, the vortex grows, entraining more fluid and decreasing the jet axial velocity. Due to the low Reynolds number, the structure of the vortex is preserved further downstream of the nozzle orifice exit. A longer potential core is predicted by FLUENT, being defined by Livingood & Hrycak [23] as the distance from the nozzle exit to the position where the jet velocity reaches 95 % of its original value. The end of the potential core region is identified near y/D = 2 in FLUENT results at 0.2 s, 0.6 s, and 1 s, while 2.29 FV predictions show that this region does not exceed y/D = 3. The end of the core region is followed by the decaying region, characterized by the linear variation of the axial velocity [21]. As the flow approaches the target, it loses axial velocity and turns. This is the stagnation region, where velocities near 0 m/s are detected, being predicted by both 2.29 FV and FLUENT at an extent between 0 < y/D < 1. The stagnation point was clearly identified over the target plate at the jet axis (x/D = 0) as expected.