Comprehensive optimization of centrifugal pump performance through the integration of the Taguchi method and polynomial regression models

 Corresponding author: M. Eng, B. Eng Enemugha Emmanuel Ebikabowei. Copyright © 2025 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0. Comprehensive optimization of centrifugal pump performance through the integration of the Taguchi method and polynomial regression models Enemugha Emmanuel Ebikabowei *, Mohd Sayuti Ab Karim and Nik Nazri Nik Ghazali Department of Mechanical, Faculty of Engineering, Universiti Malaya (UM). 50603, Kuala Lumpur, Malaysia. Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 Publication history: Received on 26 December 2024; revised on 02 February 2025; accepted on 05 February 2025 Article DOI: https://doi.org/10.30574/gjeta.2025.22.2.0026 Abstract This study aims to optimize the performance of centrifugal pumps by integrating the Taguchi Method with polynomial regression models, and the objective is to enhance pump efficiency and reduce energy consumption by optimizing multiple design parameters concurrently; the methodology uses Design Expert 360 software and ANSYS 2024R1 to conduct experiments based on the Taguchi Method and Simulation, focusing on five factors: number of blades, impeller blade angle, flow rate, Head, and rotational speed. Computational Fluid Dynamics (CFD) simulations validated the optimization results. The optimal combination of parameters rotational speed of 1500 rpm, Head of 20 m, impeller blade angle of 36°, number of blades 6, and flow rate of 400 m³/h achieved a maximum pump efficiency of 86.2%. The regression models developed for predicting total efficiency, Head, and shaft power showed high predictive accuracy, with R² values of 0.9469 for total efficiency and shaft power 0.9986 and 0.9812 for Head. CFD simulations confirmed the consistency of the optimization process with an efficiency of 84.1% and a difference of 2.1%, showing a high correlation with the optimized value. This study extends existing knowledge by employing polynomial regression models to predict pump efficiency and the Head and shaft power, providing a robust background for future design improvements in centrifugal pump performance. The findings offer valuable insights for enhancing the efficiency and performance of centrifugal pumps in various industrial applications. Keywords: Centrifugal pump; Optimization; Taguchi Method; Polynomial regression 1. Introduction Centrifugal pumps are indispensable in many industrial applications, such as chemical processing and water treatment, because of their dependability and efficiency. Their design factors significantly impact their performance, including Head, flow rate, rotational speed, impeller blade angle, and number of blades. Reducing energy consumption, increasing pump efficiency, and cutting operating expenses depend on parameter optimization. Low-fidelity surrogate models have been employed to reduce computational expenses and get the best answers [1]. In conjunction with particle swarm optimization, entropy generation theory has been used to reduce energy losses and boost efficiency [2]. It has been demonstrated that adaptive single-objective algorithms combined with computational fluid dynamics can automatically optimize pump shape, resulting in better internal flow fields and higher efficiency [3]. The optimization of centrifugal pump performance has been extensively researched utilizing various methods. The Taguchi strategy substantially enhances pump efficiency and overall performance when combined with numerical techniques and CFD analysis [4-6]. Impeller diameter has the most noticeable impact on pump performance, with blade angle, volute tongue angle, and impeller diameter being crucial design elements [5]). Efficiency may be increased, low-pressure areas can be reduced, and better pressure distribution can be obtained by adjusting these parameters [4]. Regression and correlation analysis have also been used to improve impeller design based on real-time data, offering an economical way to alter machinery [7]. Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 16 Extensive geometric parameter adjustment has been shown to improve centrifugal pump performance significantly, aid in a more comprehensive effective range, and raise the optimal efficiency point [4-5]. Response surface methodology (RSM) has been used to improve guide vane centrifugal pumps, considering several geometric characteristics that affect pump performance [8]. In a different work, [9] used RSM with computational fluid dynamics to forecast and maximize hydraulic efficiency for high-specific-speed centrifugal pumps. Genetic algorithms and radial basis function neural networks are two examples of multi-objective optimization approaches with concurrently enhanced centrifugal pump volutes' hydraulic and acoustic performance [10-11]) used the Taguchi approach to optimize the inlet blade and wrap angles, which improved the cavitation performance of a centrifugal pump impeller. Similarly, [12] sought to optimize design parameters such as blade outlet setting and wrap angles to increase the cavitation performance and energy conversion efficiency of ultra-low specific-speed centrifugal pumps. Using a parametric design, [13]) performed a multiobjective optimization of an ultra-high-head pump-turbine runner, highlighting the value of multi-objective optimization in attaining balanced performance gains. By optimizing the impeller design of a centrifugal pump using the Taguchi approach, [6] discovered that this might significantly increase pump efficiency and consistency; using the Taguchi approach, [14] optimized parameters like input diameter and output breadth to increase a centrifugal pump's hydrodynamic performance. Despite their substantial contributions to the discipline, these studies frequently concentrate on optimizing individual parameters. The optimization of centrifugal pump performance using a variety of approaches has been well-studied in the past. Entropy generation theory and particle swarm optimization have improved impeller design, which has reduced entropy generation and raised efficiency [2]. A more thorough method that considers several design factors at once is required. This study combines the Taguchi Method with polynomial regression models to fill this gap and optimize a centrifugal pump's design parameters. It focuses on five factors: the number of blades, the impeller blade angle, the flow rate, the Head, and the rotating speed. This method increases the accuracy of predictions and offers a solid foundation for design enhancements. 2. Methodology This study conducted a detailed optimization and simulation, investigating the factors affecting centrifugal pump performance, efficiency, Head, and power. The thoroughness of our methodology, from creating precise 3D geometric designs to applying realistic boundary conditions, instils confidence in the accuracy of the predictions. 2.1. Design of Experiment This study conducted trials based on the Taguchi Method, a tried-and-true method for optimizing design components and procedures to improve quality, using the Design Expert 360 software. For the experiment design, four levels and five variables were selected. The impeller blade's operating specifications were its number of blades, angle, flow rate, Head, and rotating speed (4-7, 27-360, 100-400 m3/h, 20-50 m, 1500-4500 rpm). As indicated in Table 1, the experimental design used a Taguchi orthogonal array, namely L16(45), with five factors and sixteen runs. 2.2. Numerical Simulation This section uses the CFD method to design, mesh, and numerically simulate an original model of a centrifugal pump based on the ANSYS 2024R1 Workbench platform Student version. This process involves creating an input-output channel. Additionally, ANSYS Computational Fluid Dynamics (CFD) was employed to model the impeller through Vista Centrifugal Pump Design (CPD), which was used to design the impeller blade. 2.3. Design Parameters The centrifugal pump used in this study has the following operational parameters for the impeller blade: the number of blades, impeller blade angle, flow rate, Head, and rotational speed of the impeller (4-7, 27-360, 100-400 m3/h, 20-50m, 1500-4500 rpm). Table 3 lists the significant elements and design parameters for the pump. 2.4. Mesh Generation ANSYS Turbo-grid receives the model once it has been developed in Blade-Gen. This software's primary goals are complete automation and unmatched mesh quality for extremely complex blade geometries. All of the following processes are carried out automatically, and the final mesh dimensions required to produce an exceptionally highquality mesh are specified, as shown in Figure 1 and Table 1. Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 17 Table 1 Mesh Analysis Domain Nodes Elements Statistics R1 502250 473518 1754.85 Figure 1 Mesh generation of the Optimize Impeller Blade 2.5. Boundary Conditions The boundary conditions for the CFD simulations were set as follows: Table 2 Boundary conditions of different blade counts Inflow boundary condition Mass flow inlet Type of Fluid Water Turbulence Model Used Shear Stress Transport (SST) Flow Direction Normal to Boundary Reference Pressure 0 [atm] 0 [atm] Static Pressure 1 [atm] Mass flow rate 77.8 kg/s Rotational Speed 1500 rpm, Wall roughness Smooth Wall Wall influence on the flow No Slip Turbulence intensity 5% The centrifugal pumps' CFD simulations' boundary conditions centre on varying impeller blade counts, with a mass flow rate of 77.8 kg/s; water serves as the working fluid. Using the Shear Stress Transport (SST) turbulence model, the simulations average the flow direction at the boundary. One bar is the static pressure, while zero is the reference pressure. 1500 rpm is the impeller's rotational speed. Smooth surface roughness and a no-slip condition are imposed on the walls. As seen in Table 2, the turbulence intensity is set at 5%. 2.6. Governing Equations The efficiency of the pump (η) Furthermore, one crucial aim function for immediate optimization in the specified pumps was the Net Positive Suction Head (NPSH) [15], which outlines the optimal centrifugal pump's efficiency. Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 18 𝐻 = 𝑃𝑑− 𝑃 𝑠 𝜌𝑔 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 1, 𝜂 = 𝑃𝑖𝑛 𝑃𝑜𝑢𝑡 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − −2, 𝑃𝑜𝑢𝑡 =  × 𝑔 × 𝐻 × 𝑄 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − 3, The inlet pressure is denoted as Pin, while specifically unsolidified mass and charge velocity are denoted as Y and vin, respectively. Q represents the flow rate. 2.7. Orthogonal Optimization Table 3 presents the design of the orthogonal array. Table 3 Design of Orthogonal Array Run Rotational Speed (rpm) Head (m) Impeller blade angle (0) Number of blades Flow rate (m3/h) 1 4500 50 27 6 200 2 3500 40 27 5 400 3 2500 50 33 5 100 4 1500 50 36 7 400 5 1500 20 27 4 100 6 3500 50 30 4 300 7 1500 40 33 6 300 8 4500 20 36 5 300 9 3500 30 36 6 100 10 2500 40 36 4 200 11 4500 40 30 7 100 12 1500 30 30 5 200 13 3500 20 33 7 200 14 4500 30 33 4 400 15 2500 30 27 7 300 16 2500 20 30 6 400 Table 4 represents the pump efficiency, shaft power, and Head of the numerical simulation results of the orthogonal design. Table 4 Numerical Results of the orthogonal design. Run Pump Efficiency (%) Shaft Power (Kw) Head (m) 1 88 33.9 39 2 73.9 48.8 47 3 36.5 7.8 3.7 4 91 3.5 41 Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 19 5 68 4.3 4 6 80.5 53 56 7 87.5 1.8 21 8 89.7 35.1 41 9 77.5 10.2 10 10 87.6 25.5 29 11 60.5 10.4 8 12 85 10.6 12 13 88.7 16.1 19 14 80.3 46 48 15 81.3 26.4 28 16 82.8 32 34 3. Results 3.1. Optimization Results The optimization focused on five key parameters: rotational speed, head, impeller blade angle, number of blades, and flow rate. Tables 5 and 6 summarize the optimal values for these parameters. Table 5 Presents the optimization results for the impeller blade parameters and the solution for the four-factor levels of the optimization results. Number Rotational Speed Head Impeller blade angle Number of blades Flow rate Pump efficiency Power (Kw) Desirability 1 1,500 20 36 6 400 86.202 22.837 0.518 Selected 2 3,500 20 36 6 400 83.474 22.837 0.508 3 4,500 20 36 6 400 82.949 22.837 0.506 4 2,500 20 36 6 400 75.374 22.837 0.477 The optimal combination of parameters for maximum pump efficiency was selected at a rotational speed of 1500 rpm, Head of 20 m, impeller blade angle of 36°, number of blades 6, and flow rate of 400 m³/h, achieving an efficiency of 86.2% of the optimized parameters. 3.2. Confirmation Test The optimal impeller blade parameters were confirmed through additional tests. The results are presented in Table 6. Table 6 Confirmation of the Optimal Impeller Blade. 3.3. CFD Simulation Validation CFD simulations were conducted to validate the optimization results. The optimal blade's Head, 26.3 m, total efficiency, 84.05%, and shaft power, 23.8 KW, were calculated by varying the mass flow rates. The results are summarized in Table 7. Rotational Speed(rpm) Head(m) Impeller blade angle (0) Number of blades Flow rate(m3/h) 1,500 20 36 6 400 Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 20 Table 7 CFD Calculation of the Head, Total efficiency, and Shaft power of the Optimal blade by varying mass flow rates. Mass flow rate (kg/s) Head (m) Efficiency (%) Shaft Power (KW) 77.8 26.2566 84.0514 23.834 80 26.0805 84.1995 24.301 90 25.1503 85.2545 26.037 100 23.8471 85.8339 27.247 110 23.7713 89.7573 28.571 120 22.7436 91.4167 29.279 130 21.7318 91.9182 30.141 The velocity vectors at the impeller blade's 20%, 50%, and 80% span are displayed. Near the leading edge of the impeller blade, at 20% span, the lowest velocity is shown, signifying the fluid's first acceleration. At this span, where the fluid gathers momentum from the impeller's spin, Figure 2 displays the most incredible velocity close to the trailing edge. The velocity distribution gets more complicated around 50% span, with greater velocities localized close to the blade surfaces. While the maximum velocity dramatically rises, suggesting effective energy transfer, the lowest velocity stays close to the leading edge. With the most considerable velocity occurring close to the blade tips, the velocity vectors at 80% span demonstrate a well-distributed flow pattern, indicating efficient fluid management across the blade span. The total pressure (Ptr), static pressure (Ps), and total pressure (Pt) contour plots at 50% span are shown in Figure 3. Effective energy transmission is shown by the lowest total pressure (Ptr) at the intake and the highest total pressure close to the blade surfaces. With the lowest static pressure at the intake and the highest at the outlet, the pressure (Ps) contour ensures a constant flow rate by gradually increasing from the inlet to the exit. The locations of maximum pressure, which correspond to those with the best energy conversion efficiency, are highlighted by the total pressure (Pt) contour. The outcomes confirm how well the revised impeller design provides consistent pressure distribution, lowers hydraulic losses, and boosts pump efficiency. Figure 2 Velocity Vectors at 20%, 50% Span and at 80% Span Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 21 Figure 3 The contour of P tr, Pt and Ps at 50% span 3.4. Regression Models The regression polynomial equations for total efficiency, shaft power, and Head with mass flow rate are as follows: Table 8 Coefficient of ṁ2, ṁ, 𝑹² and the Predicted values Regression Model of Total Efficiency ṁ (kg/s) Coefficient of ṁ2 Coefficient of ṁ Predicted Efficiency (%) Constant 77.8 3.63 3.11 83.65 76.911 80.0 3.84 3.20 83.95 76.911 90.0 4.86 3.60 86.37 76.911 100.0 6.0 4.00 86.91 76.911 110.0 7.26 4.40 88.57 76.911 120.0 8.64 4.80 90.35 76.911 130.0 10.14 5.2 92.25 76.911 (𝜼)𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 = 𝟎. 𝟎𝟎𝟎𝟔ṁ𝟐+ 𝟎. 𝟎𝟒ṁ + 𝟕𝟔.𝟗𝟏𝟏, 𝑹² = 𝟎. 𝟗𝟒𝟔𝟗 Table 9 Coefficient of ṁ2, ṁ, 𝑹, ²Predicted values, Head's regression model. Mas flow rate ṁ (kg/s) Coefficient of ṁ2 Coefficient of ṁ Predicted Head (m) Constant 77.8 1.211 -9.033 26.49 34.322 80.0 1.280 -9.288 26.31 34.322 90.0 1.620 -10.449 25.49 34.322 100.0 2.000 -11.61 24.71 34.322 110.0 2.420 -12.771 23.97 34.322 120.0 2.880 13.932 23.27 34.322 130.0 3.380 -15.093 22.61 34.322 𝑯𝒆𝒂𝒅 = 𝟎. 𝟎𝟎𝟎𝟐ṁ𝟐− 𝟎. 𝟏𝟏𝟔𝟏ṁ + 𝟑𝟒.𝟑𝟐𝟐, 𝑹𝟐= 𝟎. 𝟗𝟖𝟏𝟐 Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 22 Table 10 Coefficient of ṁ2, ṁ, 𝑹² and the Predicted values Regression Model of Shaft Power Mass flow rate ṁ (kg/s) Coefficient of ṁ2 Coefficient of ṁ Predicted Shaft Power P (KW) Constant 77.8 -7.26 28.76 23.94 24437 80.0 -7.68 29.58 24.34 24437 90.0 -9.72 33.27 25.99 24437 100.0 -12.0 36.97 27.41 24437 110.0 -14-52 40.67 28.59 24437 120.0 -17.28 44.36 28.76 24437 130.0 -20.28 48.06 30.22 24437 𝑷𝒔𝒉𝒂𝒇𝒕 = −𝟎. 𝟎𝟎𝟏𝟐ṁ𝟐+ 𝟎. 𝟑𝟔𝟗𝟕ṁ + 𝟐𝟒𝟒𝟑𝟕, 𝑹² = 𝟎. 𝟗𝟗𝟖𝟔 Tables 8, 9, and 10 show the regression models forecasting the centrifugal pump shaft power, Head, and overall efficiency. With an R2 value of 0.9469, the overall efficiency model (Table 8) exhibits great prediction accuracy and matches the data well. Although significantly lower, the head model, as shown in Table 19, still reflects a perfect match with an R2 value of 0.9812. A high R2 value of 0.9986 was also validated by the shaft power model, described in Table 10, demonstrating its predictive solid abilities. The shaft power and overall efficiency models are the best of the three since they have the greatest and identical R2 values, indicating a more fantastic ability to predict the respective precise centrifugal pump performance measuring system. The overall efficiency equation is displayed in Figure 4 and has a high predicted accuracy and a great fit, as indicated by its R2 value of 0.9986. As the graph shows, efficiency rises with mass flow rate, reaching an ultimate at higher flow rates. The shaft power equation is shown in Figure 5 and has a high connection with an R2 value of 0.9986. Because more energy is needed to sustain more excellent flow rates, the graphic shows that shaft power rises with mass flow rate. The head equation is shown in Figure 6, where a perfect fit is shown by an R2 value of 0.9812. The graph shows the trade-off between flow rate and pressure head by showing that the Head marginally lowers as the mass flow rate increases. Figure 4 Regression polynomial equation for efficiency for the optimal blade (𝜼)𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒄𝒚 = 𝟎. 𝟎𝟎𝟎𝟔ṁ𝟐+ 𝟎. 𝟎𝟒ṁ + 𝟕𝟔.𝟗𝟏𝟏, 𝑹𝟐= 𝟎. 𝟗𝟒𝟔𝟗 − − − − − − − − 𝟒, Global Journal of Engineering and Technology Advances, 2025, 22(02), 015–026 23 Figure 5 The regression equation for shaft power for the optimal blades 𝑷𝒔𝒉𝒂𝒇𝒕 = −𝟎. 𝟎𝟎𝟏𝟐ṁ𝟐+ 𝟎. 𝟑𝟔𝟗𝟕ṁ + 𝟐. 𝟒𝟒𝟑𝟕 − − − − − − − − − − − − − − − 𝟓, Figure 6 Regression polynomial equation for the Head for the Optimal blades 𝐻𝑒𝑎𝑑 = 0.0002ṁ2− 0.1161ṁ + 34.322 − − − − − − − − − − − − − − − 6, Evaluate the effectiveness of the ideal impeller blade at different mass flow rates by contrasting the regression model's predictions with the CFD simulation results. A high degree of accuracy in the regression model is indicated by Figure 7, which displays a close alignment between the CFD results and the regression model predictions. As the mass flow rate rises, the efficiency peaks and modestly decreases at the most significant flow rates. According to this tendency, an improved impeller blade design may efficiently increase efficiency up to a point beyond which the gains in efficiency start to decline. The strong correlation between the CFD and regression model findings confirms the polynomial regression model's accuracy in predicting pump efficiency, demonstrating its resilience and usefulness in maximizing centrifugal pump performance. The graph indicates that both approaches forecast a declining trend in the Head when the mass flow rate rises. Especially at higher flow rates, the regression model somewhat overestimates the Head compared to the CFD findings. According to this, the regression model may need to adequately represent the intricacies of fluid dynamics at more excellent flow rates, even though it is typically accurate, as shown in Figure 8. Figure 9 contrasts the shaft power of the ideal blade over a range of mass flow rates as predicted by CFD simulations and regression models; with increased mass flow rates, both approaches exhibit a rising trend in shaft power. A small quantity of the regression model underestimates the shaft power compared to the CFD results, particularly at higher flow rates.