Effect of liquid preheating on high-velocity airblast atomization: From water to crude rapeseed oil

Effect of liquid preheating on high-velocity airblast atomization: From water to crude rapeseed oil URBÁN, A.; MALÝ, M.; JÓZSA, V.; JEDELSKÝ, J. Experimental Thermal and Fluid Science 2019, vol. 102, April 2019, pp. 137-151 ISSN: 0894-1777 DOI: https://doi.org/10.1016/j.expthermflusci.2018.11.006 Accepted manuscript © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0/), doi: https://doi.org/10.1016/j.expthermflusci.2018.11.006 Final version available from https://www.sciencedirect.com/science/article/pii/S0894177718314377 dspace.vutbr.cz Effect of liquid preheating on high-velocity airblast atomization: from water to crude rapeseed oil András Urbána, Milan Malýb, Viktor Józsaa, Jan Jedelskýb a Budapest, University of Technology and Economics, Faculty of Mechanical Engineering, Department of Energy Engineering, 1111 Budapest, Műegyetem rkp. 3., Hungary b Faculty of Mechanical Engineering, Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic Abstract Airblast atomization is a suitable model platform to understand atomization physics since the atomizer geometry has an insignificant influence on the spray formation. Besides its theoretical relevance, this configuration is used in several practical applications ranging from healthcare to combustion. Presently, a plain-jet airblast atomizer has been investigated experimentally under atmospheric conditions at various atomizing pressures and liquid preheating temperatures. To cover a wide range of liquids by viscosity and surface tension, water, diesel oil, light heating oil, and crude rapeseed oil were atomized to evaluate the droplet size-velocity correlations when the spray is fully developed. Increasing the temperature of high-viscosity liquids prior to atomization improves the spray characteristics until their kinematic viscosity decreases to a certain value that is newly introduced as a limiting viscosity. Further preheating has a marginal effect on droplet size-velocity plots, and the spray becomes more homogeneous. Several SMDestimating formulae were analyzed and improved to consider the effect of liquid preheating and to extend their range of validity. When the kinematic viscosity exceeded the limiting viscosity, the part containing the Weber number was corrected linearly by the preheating temperature. The coefficient of the Ohnesorge number was corrected by the inverse of the kinematic viscosity, without considering the limiting viscosity. The above results help to correct the SMD of atmospheric measurements to elevated liquid temperatures and to contribute to advanced atomization models for numerical software. Keywords: airblast atomizer; SMD; PDA; rapeseed oil; light heating oil; preheating Nomenclature Latin letters a Speed of sound, m/s A, B, C, E, F, G, H, I, J, K, L, M Experimental parameters ALR Air-to-liquid mass flow ratio, – D Droplet diameter, µm d, d0 Characteristic size, mm EFR Energy flux rate, – ISMD meas Measured integral SMD, µm l Dimension of measurement volume, mm m Mass flow rate, kg/s Ma Mach number, – MFR Momentum flux rate, – Oh Ohnesorge number, – p g Atomization gauge pressure, bar R2 Coefficient of determination, – Re Reynolds number, – SMD Sauter mean diameter, µm SMD calc Calculated SMD, µm t p Preheated liquid temperature, °C t r Reference temperature, °C u Velocity, m/s We Weber number, – z Axial distance, mm Greek symbols µ Dynamic viscosity, kg/(m∙s) ρ Density, kg/m 3 σ Surface tension, N/m υ Kinematic viscosity, mm2/s υ l,lim Limiting viscosity of the liquid, mm2/s Abbreviations D Diesel GA Genetic algorithm LHO Light heating oil PDA Phase Doppler Anemometry RO Rapeseed oil ScS Scatter Search W Water Subscripts a Air l Liquid r Relative x, y, z projection in the XYZ coordinate system 1. Introduction Plain-jet airblast atomization, investigated in the present paper, is an excellent model platform to better understand the atomization phenomena. Besides its theoretical relevance, it is widely used in numerous fields from healthcare [1] through heat transfer enhancement [2] to combustion [3]. Our motivation comes from the last example since there is a technological push to replace fossil fuels with renewable ones to achieve a sustainable economy [4]. None of the renewable-based fuels has turned to be dominant in the past decades [5]; nevertheless, utilizing the locally available ones is usually a reasonable choice. Hence, liquid fuel combustion investigations with both long-chained hydrocarbons, like crude rapeseed oil [6] and light fuels, like aqueous ethanol [7], were performed earlier. The cited papers use an atomizer similar to the currently investigated one. During the evaluation of crop-originated fuels, their impact on food security should firstly be taken into account [8]. Comparing various renewable fuels and technologies is crucial for decision making to select the best candidate and utilize it most efficiently. For this purpose, the ethanol equivalent is a reasonable basis since the production, and hence the energy balance of ethanol is well-known [9]. Atomization was intensively investigated around the 1980s [10], principally investigating water, kerosene, diesel oil, and various oil sprays at ambient temperature [11]. At that time, the effects of atomizing air temperature and operating pressure were in focus due to the market pull by the gas turbine industry [12]. Due to the available measurement technology at that time, the semi-empirical estimations of the average droplet size were limited to 100 m/s air discharge velocity in the case of airblast atomizers [13]. In combustion applications, the droplets have to evaporate prior to the flame front. Hence, the volume-to-surface diameter (D32) or Sauter Mean Diameter (SMD) is determined instead of other average diameter types. This is defined as follows: 𝑆𝑆𝑆𝑆𝑆𝑆=∑𝑆𝑆𝑖𝑖3 𝑖𝑖/∑𝑆𝑆𝑖𝑖2 𝑖𝑖, (1) where Di is the diameter of a single droplet at a single measurement point. It was discussed in our previous work [14] that the suggested formula of Lefebvre [10], detailed at first in Section 2, estimated the SMD most accurately. Nevertheless, the investigated air discharge velocity range was 200–500 m/s in our case, which far exceeds the original validity range of 10–120 m/s. Injection of light fuels at ambient temperature is usually adequate for efficient combustion. However, various long-chained oils – which have an emerging relevance as renewable fuels – need preheating [15]. Wang and Lefebvre [16] discussed the effect of fuel preheating, emphasizing that it reduces the SMD and its effect seems independent of the ambient pressure. The researchers published plain measurement results and performed no statistical evaluation or comparison with the estimated SMD. More recently, Shah and Ganesh [17] measured the relevant temperature-dependent properties of karanj oil, which is a straight vegetable oil type. The researchers directly put the measurement data into an SMD-estimating equation, but the experimental validation of the results was not discussed. Hanna and Zoughaib [18] experienced a temperature change of the atomized compressor lubricant oil. However, they did not control the injection temperature systematically, and the measurements were limited to the range of 11–27 °C. Fuel preheating in internal combustion engine was performed by Park et al. [19], leading to a similar result as that of Wang and Lefebvre. The present paper focuses on the atmospheric temperature-dependent spray characteristics of the following model liquids to cover a relatively wide range of viscosity, which is one of the novelties of the present paper. Atomization of distilled water (W), standard diesel oil (D, EN 590:2014), light heating oil (LHO), and crude rapeseed oil (RO) were investigated in the liquid preheating temperature range of 25– 100 °C which partially covers, e.g., the thermal stability range of the pyrolysis oils as well [20– 22]. These temperature limits for the four liquids allows the investigation of a wide physical parameter range. I.e., for liquid viscosity, it covers more than two magnitudes. The corresponding measured liquid properties are summarized in Appendix A. A key issue in many of the empirical correlations published to date is that they are generally only tested on simple fuels over a very narrow range of physical properties, therefore making correlations to date of limited use. Hence, the resulting wide non-dimensional space allows the re-assessment of the existing empirical correlations, which is the principal goal of the present paper. The scientific relevance of atmospheric measurements is often questioned by researchers since the operating pressure of e.g. gas turbines is several tens of bars [23]. It was shown by Zheng et al. [24] that SMD varies slightly up to 12 bar in a gas turbine combustion chamber. Chigier [3] highlighted that the engine startup – when atomization occurs at reduced pressure – is the most critical phase. Then, operation characteristics, including flammability limits and fuelair mixture quality at the flame front, start to improve. Nukiyama and Tanasawa [25], the first systematic investigators of airblast atomization, pointed out that the mean droplet diameter depends on surface tension, density, fluid viscosity, volume flow rates of air and liquid, and the relative velocity between the two phases. The governing dimensionless numbers of airblast atomization are Reynolds number (Re), Weber number (We), Ohnesorge number (Oh), and air-to-liquid mass flow ratio (ALR), defined by Eqs. (2)–(5): 𝑅𝑅𝑅𝑅=𝑢𝑢𝑟𝑟∙𝑑𝑑∙𝜌𝜌/𝜇𝜇, (2) 𝑊𝑊𝑅𝑅=𝑢𝑢𝑟𝑟2∙𝑑𝑑∙𝜌𝜌/𝜎𝜎, (3) 𝑂𝑂ℎ=𝑊𝑊𝑅𝑅0.5/𝑅𝑅𝑅𝑅=𝜇𝜇/(𝜎𝜎∙𝑑𝑑∙𝜌𝜌)0.5, (4) 𝐴𝐴𝐴𝐴𝑅𝑅=𝑚𝑚𝑎𝑎/𝑚𝑚𝑙𝑙, (5) where ur is the relative velocity between the air and the liquid, d is a characteristic size, ρ is the density, µ is the dynamic viscosity, σ is the surface tension, and m is the mass flow rate. a and l subscripts refer to air and liquid, respectively. Later on, if Re or We receive an A or L subscript, the equations refer to the fluid used for the density and dynamic viscosity calculation. Non-intrusive spray measurements can be performed by both imaging and non-imaging optical techniques [11]. For size characterization, the Phase Doppler technique is used most widely. In parallel, high-speed imaging is usually applied for qualitative analysis [26,27]. The present study is primarily focused on the results of Phase Doppler Anemometry (PDA) measurements. Full simulation of atomization in a practical combustion chamber is unfeasible at the present time since the control volume of one liter would require ~1020 cells. Such a detailed mesh is necessary for tracking liquid fractions down to one µm by the Eulerian approach. However, there are spectacular results achieved recently by the PAMELA software code [28] for prefilming airblast atomizers; its application in engineering practice requires the additional refinement and development to be extended for other atomizer types. Nevertheless, the primary liquid breakup in three dimensions can be modeled with the present computational capabilities [29–31]. Atomization simulation in a mixed Eulerian-Lagrangian space is common in computational fluid dynamics software codes [32]. This approach is characterized by several magnitudes lower computational time as the mesh size can be significantly smaller. However, the corresponding models strongly rely on empirical formulae [32]. Hence, improving these models through analyzing the results of systematic measurements has a notable importance even today. Consequently, the present paper provides the analysis of measurement data in a wide parameter range to enhance these atomizer models and provide a more realistic performance in engineering applications. I.e., the present results facilitate the atomization modeling of e.g. typical liquid fuels from crude vegetable oil to light fuels. Concluding from the above findings, the effect of liquid preheating on atomization characteristics has both theoretical and practical relevance. Therefore, the principal aim of this work is to analyze quantitatively the global and local spray characteristics of various liquids atomized by an atmospheric plain-jet airblast atomizer. The high air discharge velocities with the preheating temperature range of 25–100 °C for four liquids (W, D, LHO, and RO) incorporate a wide non-dimensional parameter range, summarized in a tabular form in the end of Section 3. Therefore, re-assessment of the existing SMD-estimating formulae – reviewed in Section 2 – is discussed with the inclusion of the effect of liquid preheating. 2. Review of SMD-estimating formulae of airblast atomization This section reviews six different empirical and semi-empirical formulae for estimating SMD, which were derived from optical measurements. Each contains at least one empirical parameter to be determined by a fitting method, which is lastly discussed. 2.1. SMD-estimating formulae Previous empirical regression analyses lead to the conclusion that SMD is primarily governed by We, Oh, and ALR, for plain-jet airblast atomizers which were discussed by several researchers [11,13,23]. Equation (6) shows the most widely used equation for airblast atomization, principally derived for the prefilming type [10]: 𝑆𝑆𝑆𝑆𝑆𝑆=𝑑𝑑0(1 + 1/𝐴𝐴𝐴𝐴𝑅𝑅)(𝐴𝐴∙𝑊𝑊𝑅𝑅𝑎𝑎𝐶𝐶+𝐵𝐵∙𝑂𝑂ℎ𝑙𝑙𝐸𝐸),(6Chyba! Záložka není used with a lens of 112 mm diameter. The focal length was 310 and 500 mm for the transmitting and the receiving optics, respectively. The half-intersection angle between the laser beams was set to 6.92°. Dimensions of the measurement volume were lx = 0.60 mm, ly = 0.072 mm, lz = 0.073 mm, according to the coordinate system in Fig. 2. A spatial filter with a slit size of 0.1 mm was used to reduce the lx dimension of the measurement volume. The scattering angle was set to Brewster’s angle, 68° [53]. The measured signals were processed by the BSA P80 flow and the particle processor and visualized by BSA Flow Software v5.2. The modular instrument was configured for the measurement in the dense spray containing small droplets. The droplet velocities notably varied in space and were sensitive to the inlet conditions. Hence, the system parameters were set individually for different inlet pressures and axial distances from the atomizer nozzle. The maximum droplet size to measure was set to 64.1 μm with a size resolution of ±0.05 μm and uncertainty of ±0.5 μm. The particle refractive index was set to 1.45 for all oils and 1.33 for water. The axial and radial velocity range was set from 0–64 m/s to 0–144 m/s and 0–46 m/s to 0–98 m/s, respectively, considering the effects of axial distance from the atomizer nozzle and the atomizing pressure on the maximum droplet velocity. For this reason, the velocity span was set from 128 m/s to 192 m/s. The velocity resolution was 0.002%, and the uncertainty was less than 1% of the selected range. The PDA system was set to acquire 40,000 individual particles or measure for 15 seconds in the low-density regions. According to the preliminary results (not shown here), the spray was found to be axisymmetric. The experimental atmospheric test rig is shown in Fig. 3. The atomizing air was taken from the central compressed air system through a pressure regulator followed by a mass flow meter towards the atomizer. The following atomizing gauge pressures, pg, were investigated: 0.3, 0.6, 0.9, 1.2, 1.8, and 2.4 bar. The lowest value was selected based on the criteria of stable combustion in the hot test cases – without spray measurement – [50,54]. A pressurized tank was used to feed the liquids into the atomizer without fluctuation. A control valve and a Coriolis mass flow meter Mass 2100 Di3 fitted with the Mass 6000 transmitter (Siemens AG, GE) were applied to set a constant 0.35 g/s liquid mass flow rate with an accuracy of ±0.1% of the actual flow rate. A rotameter was also installed into the feed pipe for visual checking. Both liquid and atomizing air lines were equipped with piezo-resistive pressure transducers DMP 331i (BD SENSORS s.r.o., CZ) and B class Pt100 resistance thermometers. The uncertainty was 2 kPa and 0.3 °C in the pressure and temperature sensing, respectively. The resulting ALR range of all measurements was 0.78–2.07. Fig. 3. Liquid and atomizing air supply lines and their instrumentation of the experimental test rig. The liquid preheater was controlled by a PID unit made by HAGA Kft. using a temperature control signal of a Pt100 resistance temperature detector. A toroidal transformer was used to set the heating power of the PID control to avoid outlet temperature oscillations. The following preheating temperatures, tp, were investigated for D, LHO, and RO: 25, 40, 55, 70 and 100 °C. W is an exception from this series since the maximum temperature was 90 °C to avoid boiling, but the lower tps were the same. The relevant physical properties of the liquids and their measurement methods were presented in Appendix A. The PDA measurements were carried out at three axial distances downstream of the nozzle, z = 20, 40 and 60 mm, with fifteen equally spaced radial points along X and Y axes at z = 60 mm, thirteen at z = 40 mm and seventeen at z = 20 mm. At z = 20 mm, the step was 1 mm between the points and 2 mm at z = 40 and 60 mm. Based on the analysis of the previous measurement results, the z < 20 mm regime was later rejected [14] as droplet velocities close to the nozzle exceed the limitations of PDA (~300 m/s). Based on the results of our previous studies, z = 60 mm was found to be a sufficient downstream distance to ensure a fully developed, stable spray that was suitable for ISMD calculation. Besides the mentioned dimensionless numbers, defined by Eqs. (2) – (5), the momentum flux rate, MFR, energy flux rate, EFR, and Mach number, Ma, are also key parameters of airblast atomization. They are defined by Eqs. (13) – (15): 𝑆𝑆𝐹𝐹𝑅𝑅=𝜌𝜌𝑎𝑎∙𝑢𝑢𝑎𝑎 2/(𝜌𝜌𝑙𝑙∙𝑢𝑢𝑙𝑙2), (13) 𝐸𝐸𝐹𝐹𝑅𝑅=𝜌𝜌𝑎𝑎∙𝑢𝑢𝑎𝑎 3/(𝜌𝜌𝑙𝑙∙𝑢𝑢𝑙𝑙3), (14) 𝑆𝑆𝑀𝑀=𝑢𝑢𝑎𝑎/𝑀𝑀, (15) where a is the speed of sound. All the mentioned dimensionless numbers, including Re and We for both air and liquid phases are summarized in Table 3 to show the range of investigated cases. Table 3. Intervals of the investigation ranges of the liquids. D LHO RO W pg [bar] min. 0.3 0.3 0.3 0.3 max. 2.4 2.4 2.4 2.4 ALR [-] min. 0.78 0.78 0.78 0.78 max. 2.07 2.07 2.07 2.07 Rea [-] min. 8969 8974 8979 8994 max. 30037 30047 30058 30075 Rel [-] min. 22749452 5035776 1565911 91217176 max. 115408537 51798814 21023241 380150588 Wea [-] min. 988.4 792.5 730.6 289.7 max. 9549 4640 5014 1982 Wea [-] min. 655242 550332 531391 228328 max. 4638184 2346382 2626442 1157407 Oh [-] min. 0.019 0.029 0.077 0.0028 max. 0.036 0.147 0.465 0.0052 Ma [-] min. 0.62 0.62 0.62 0.62 max. 1.45 1.45 1.45 1.45 MFR [-] min. 5.68 5.91 6.13 6.83 max. 31.7 33.23 34.8 37.7 EFR [-] min. 342.2 370.9 398 494.7 max. 4011 4401 4828 5667 ISMD/d0 [-] min. 0.0216 0.0218 0.0278 0.0244 max. 0.0652 0.0656 0.0671 0.0691 4. Results and discussion Firstly, this section focuses on the droplet size-velocity correlation at various pg and tp to evaluate single measurement points for all four liquids. Secondly, the temperature-dependent characteristics of SMD estimating formulae are discussed and adjusted to fit the effects of preheating temperature. Hence, the governing parameters were identified and included in the experimentally determined constant parameters. 4.1. Droplet size-velocity correlations The liquid jet is disrupted by the shear effect of the flowing gas, and the newly created liquid fractions are further accelerated, which leads to the formation of ligaments; these then break up into smaller droplets. The larger droplets, accelerated by the atomizing air near the nozzle, typically lose their momentum slower than the surrounding gas jet. Hence, it leads to a reverse momentum exchange between the gas and liquid phases downstream, which is called overshooting [14,55]. Figures 4–7 show typical radial-axial velocity scatter plots at selected atomization gauge pressures and liquid temperatures for all four liquids at the center, and z = 60 mm of the fully developed spray. The results of the near field can be found in our previous work [14] and are not discussed here since the results were quite similar. Now the focus is on the effects of liquid preheating on the spray at only three tp and pg. The rest of the cases followed the same trend. Note that the logarithm of the droplet diameter gives the base of coloring to help distinguishing various sizes and hence characteristics. A droplet velocity has a dominant axial component while the radial component remains relatively low with decreasing atomizing pressure. The swirl component was below 10 m/s even at high atomizing pressures. Since the used PDA measures two perpendicular velocity components simultaneously, the swirl velocity was omitted in the systematic analysis. As for the axial velocity distribution, the results follow a similar trend; in general, the larger droplets have a higher velocity. However, the radial components tend to increase evenly with the atomizing pressure of all droplets. At tp = 100 °C and pg = 1.8 bar, the majority of droplets in the spray are smaller than 20 µm, and the droplet size range is narrow. As the spray develops, the smaller droplets lose their momentum faster, clearly showing the phenomenon of overshooting. Fig. 4. Size-velocity correlation at x = y = 0 mm and z = 60 mm in the case of diesel oil (D) at various tp and pg. Fig. 5. Size-velocity correlation at x = y = 0 mm and z = 60 mm in the case of light heating oil (LHO) at various tp and pg. Fig. 6. Size-velocity correlation at x = y = 0 mm and z = 60 mm in the case of rapeseed oil (RO) at various tp and pg. Fig. 7. Size-velocity correlation at x = y = 0 mm and z = 60 mm in the case of water (W) at various tp and pg. The droplet velocity variation, including both uz and uy components, is principally governed by pg; liquid type and tp have a smaller effect on it. However, in the case of the high- viscosity LHO and RO, the plots significantly differ from D and W. This effect is further supported by the fact that only small droplets feature the same velocity scatter as it is in the D and W cases. The medium-sized droplets are concentrated on the horizontal axis while the large droplets are characterized by a similar scatter compared to D and W. The scatter of LHO at temperature of 100 °C becomes similar to that of the low viscosity liquids. Nevertheless, RO did not achieve this state since its viscosity at 100 °C is 2.4 times higher than that of D at 25 °C. Consequently, preheating of LHO up to 70 °C and above, discussed in subsection 4.2., leads to similar atomization characteristics as D. The poor atomization characteristics of RO were indirectly identified during the combustion tests [6]. The liquid from the same shipment – which was used for atomization measurements – was required to be preheated up to 150 °C to eliminate the presence of the burning droplets in the flame. Overall, the increasing liquid temperature slightly reduces the SMDs, as shown in Fig. 8a. The increased atomizing pressure smoothens the droplet size distribution and makes it more monodisperse, as shown in Fig. 8b. It can be concluded from the two plots that atomizing pressure has a greater effect on the spray size distribution than the liquid preheating, as inertial forces govern the spray formation over viscous forces under the presently investigated conditions. Note that a rich statistical analysis of the present data on the size distribution in the spray will be published in a successor work. Fig. 8. Effect of a) tp and b) pg on droplet size distribution of W at pg = 2.4 bar and tp = 25 °C, respectively. The applied bin size was uniformly 1 µm. 4.2. The temperature dependence of the SMD-estimating formulae Figure 9 shows ISMD of the measured data at tp = 25 °C and z = 60 mm for D and RO. While Fig. 9a suggests that all the formulae provide a reasonably good estimation for SMD, Fig. 9b shows that the effect of viscosity is poorly treated in Eqs. (8) and (11). These are the two extreme examples where the liquid viscosity was low (D) and high (RO) while the rest of the measurement parameters were matched. Nevertheless, this outcome was evident only in the latter case since Oh is absent in Eq. (11). Concluding from the results, it was a general observation that, when the liquid viscosity was below ~4.3 mm2/s, all the formulae provided a fair estimation of ISMD, even Eq. (11), where the term containing Oh is missing. This finding and the modern PDA system provide the answer why Kulkarni and Deshmukh [56] achieved the best estimation of SMD in the case of airblast atomization of water by using Eq. (11). Fig. 9. Fitted SMD-estimating formulae at tp = 25 °C and z = 60 mm in the case of a) D and b) RO. Note the loglog scales. To evaluate the fit quality quantitatively, R2 values were summarized in Table 4. Equations (6a) – (7) represent a single type of SMD-estimating formulae. The exponents in Eq. (6a) were not limited. However, their typical values were in the [-5, 5] range. To achieve faster convergence and more accurate results, the exponents in Eq. (6b) were limited to this range. Note that the equations were fitted to the six measured pressure points for a given liquid and tp. Hence, 4 8 16 32 64 0,25 0,5 124 SMD [µm] p g [bar] a) Meas. [D] Eq. 6a Eq. 6b Eq. 6c Eq. 6d Eq. 7 Eq. 8 Eq. 9 Eq. 10 Eq. 11 4 8 16 32 64 0,25 0,5 124 SMD [µm] p g [bar] b) Meas. [RO] Eq. 6a Eq. 6b Eq. 6c Eq. 6d Eq. 7 Eq. 8 Eq. 9 Eq. 10 Eq. 11 590:2014 standard allows for the viscosity of D as υl = 2–4.5 mm2/s, implying that even D should be preheated if it has a slightly higher viscosity but within the allowed range. This outcome is against the practice since no commonly used diesel engine contains a fuel preheater to achieve better atomization. Thirdly, the estimation of I for RO failed. However, this equation was originally derived for low-viscosity liquids, and the estimations work nearly fine for the remaining three liquids. The parameter J could be excellently corrected by the viscosity; hence, Fig. 12b shows a satisfying result. Fig. 13. Temperature dependence of K and L parameters of Eq. (10) for all liquids. Equation (10) was derived for high-viscosity liquids. Therefore, parameter K is estimated excellently even for RO as shown in Fig. 13a. υl,lim = 4.85 mm2/s, which is similar to that of Eq. 0 0,002 0,004 0,006 0,008 0,01 0,012 20 40 60 80 100 K[m0.55] t p [°C] a) DLHO RO W D est. LHO est. RO est. W est. 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 20 40 60 80 100 L[m0.6] tp[°C] b) DLHO RO W D est. LHO est. RO est. W est. (7) and slightly higher than that of Eq. (6d). Figure 13b shows a good estimation for D and W while parameter L is underestimated in the case of LHO and RO. It might be addressed to the slightly different exponents of Eq. (10) compared to Eq. (6d). Overall, in the dynamic term, Eq. (10) provides excellent fits; however, the material property term is less accurately estimated. As for a summary, Eq. (6d) turned out to be the most accurate equation for SMD estimation which is followed by Eqs. (7) and (10). Even though the present analysis contained various formulae, it seems that the equation structure, suggested by Lefebvre in 1980 [10], seems to be the best one to date. Namely, SMD is governed by two terms, which should be summarized: the first depends on the reciprocal of square root We, while the other on Oh. 5. Conclusions The present paper discussed a high-velocity atmospheric atomization of four liquids: water (W), standard diesel oil (D), light heating oil (LHO), and crude rapeseed oil (RO) at various liquid preheating temperatures. The spray of the plain-jet airblast atomizer was non-intrusively investigated by a two-component Phase Doppler Anemometer. The velocity components, along with droplet sizes, were evaluated at a downstream distance, z = 60 mm from the atomizer nozzle. Then, nine empirical formulae were fitted to the measurement data to estimate the Sauter Mean Diameter, SMD, of the spray with liquid preheating. Since there is no known analytic way to estimate the SMD of the spray of an airblast atomizer in the presently investigated conditions, the given empirical formulae were analyzed to better understand the background physics. Based on the results, the following conclusions were derived: 1. There is a limiting viscosity which significantly affects spray characteristics. It is supported by both the droplet size-velocity scatter plots and the fitted empirical formulae for estimating SMD. The viscosity limit in the current setup is estimated as υl,lim = 4.21 mm2/s based on Eq. (6d). Below this value, further preheating has no additional effect on the spray quality. This finding is in line with the facts that D can be excellently atomized without preheating while RO has to be introduced well above 100 °C into the combustion chamber to have a sufficiently fine spray for liquid fuel combustion. Among the investigated liquids, the limiting viscosity was found only in the case of LHO since only this liquid passes υl,lim from the investigated ones. Such a transitional characteristic was expected based on the results of D and W compared to RO. 2. The overshooting phenomenon was shown at the center of the spray and z = 60 mm; namely, when the large droplets possess a higher velocity than the smaller ones and hence they accelerate the surrounding medium, the y velocity component, uy of the larger droplets was negligible while uz was high. As the droplet size decreases, uz is reduced and uy increases. Since uy originates from the presence of turbulence, its mean value is zero. 3. SMD-estimating Eqs. (6d), (7), (9), and (10) showed the best fit by adjusting their experimental parameters via the Scatter Search MATLAB algorithm. However, the coefficient of the dynamic term of Eq. (9) started from a negative value, which is physically invalid. Since Eqs. (7) and (10) contain adjusted exponents, Eq. (6d) is the most widely applicable SMD-estimating equation to date for airblast atomization. 4. To estimate SMD at elevated liquid temperatures, the parameters measured at ambient temperature have to be adjusted as follows. The coefficient of the Weber number should be multiplied by the desired temperature and divided by the reference temperature if the limiting viscosity is not reached. If reached, then the coefficient does not change any further and remains constant as a function of liquid preheating temperature. However, the Ohnesorge number should be multiplied by the square root of the ratio of the liquid viscosity at the reference temperature divided by the actual viscosity at the desired liquid preheating temperature. The viability of the above findings is supported by the fact that the investigated formulae were developed for various atomizer designs and liquids; moreover, the present conditions regarding the atomizing air discharge velocity far exceeded the validity of the cited literature data. Liquid preheating was not examined by the researchers who experimentally derived the respective equations. However, the present research highlighted which SMD-estimating formulae are valid under the presently applied extreme conditions. In numbers, they are summarized in Table 3. The present researchers suggest modelers using Eq. (16) for estimating SMD of an airblast atomizer while supporting or debating the experimental results are highly welcome to further develop the models. Acknowledgments This work has been supported by the project №. GA18-15839S funded by the Czech Science Foundation and the project LO1202 NETME CENTRE PLUS with the financial support from the Ministry of Education, Youth and Sports of the Czech Republic under the "National Sustainability Program I" (funding of the Czech researchers), National Research, Development and Innovation Fund of Hungary, project №. FIEK 16-1-2016-0007 and OTKA-FK 124704, New National Excellence Program of the Ministry of Human Capacities project № ÚNKP-18-4-BME195, and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences (funding of the Hungarian researchers). Conflict of interest The authors declare that there is no conflict of interest. Appendix A. Measurement of temperature-dependent physical properties of liquids The following temperature-dependent physical properties were required to determine the atomization characteristics of the liquids: ρ, σ, and υ. As for W and D, they are well known in the literature. Besides the density, the other two parameters are rarely discussed for LHO and RO. It is known that the fatty acid composition of RO varies by the climate and the weather, besides cultivation methods [57–59]. Consequently, it was mandatory to measure the mentioned properties of the currently used samples. The investigation temperatures followed the tp: 25, 40, 55, 70, and 100 °C while the highest temperature for W was 90 °C to avoid boiling. Only σ was measured at 75 °C instead of 70 °C. It is well-known that W and D are Newtonian liquids. Fasina and Colley [60] concluded that crude vegetable oils also exhibit Newtonian behavior, including RO. As for a light crude oil – which is more complex than LHO – it was proven by Ariffin et al. [61] that above 200 1/s shear rate it behaves as a Newtonian liquid in the temperature range of 20-90 °C. The shear rate in the present case is estimated as O (100.000) 1/s. Temperature-dependent densities were determined using a 10-ml 3.3 borosilicate glass pycnometer, which was put on a Sartorius L610 D type scale. The device was calibrated with known weights. The measurement results for all liquids were shown in Fig A.1. The combined expanded uncertainty at 95% level of significance was uniformly 4.8 kg/m3. The results of W differ by 0.7% from the literature data at 90 °C while the measurement error was undetectable at 25 °C. This indirect way of measurement error estimation provides an independent basis of the accuracy of density measurements. All the measurements were repeated five times, and the density calculation was performed by their arithmetic average. Fig. A.1. The measured density of the investigated liquids. An Ostwald-type viscometer was used for determining the kinematic viscosities of the liquids. A large tempered tank filled with silicone oil hosted the viscometers. To have a homogeneous temperature distribution, a small pump continuously circulated the liquid. Since the instrument has a calibration constant which is valid at 25 °C, the measurement data of W was used to adjust the calibration constant for the other temperatures. Therefore, W has no error bars in Fig A.2, and its values follow the literature data. The error bars show the combined expanded uncertainties at a 95% level of significance for the three other liquids. These measurements were repeated three times, and the viscosity calculation was performed by their arithmetic average. 800 850 900 950 1000 20 40 60 80 100 ρl[kg/m3] t p [°C] DLHO RO W Fig A.2. The measured kinematic viscosity of the investigated liquids. Note the logarithmic scale on the ordinate. As for surface tension measurement, the Wilhelmy plate method was used in the open atmosphere at various tp by using a double walled tempered pot. The heating medium was silicone oil to enable measurements at 100 °C for D, LHO, and RO. Calibration of the load cell was performed with known weights prior to installing the plate on the hook. The measurements were performed five times at each point, and their arithmetic average was presented in Fig. A.3. After heating the pot up from 25 °C to 100 °C, a check was performed at 75 °C with three individual measurements for all liquids. The estimated uncertainty of the surface tension measurement at 95% level of significance was uniformly 0.2 mN/m. Fig. A.3. The measured surface tension of the investigated liquids. 0,25 0,5 1 2 4 8 16 32 64 20 40 60 80 100 υl[mm2/s] t p [°C] DLHO RO W 0 20 40 60 80 20 40 60 80 100 σ[mN/m] t p [°C] DLHO RO W Temperature measurements had < 1 °C uncertainty. All the measurement data was in good agreement with the literature data where a comparison was possible [15,62–64]. In the case of W, IAPWS-IF97 was used as an internationally accepted reference for the properties of H2O. Nevertheless, none of the required temperature-dependent data for LHO was found in the public literature. References [1] S. Poozesh, K. Lu, P.J. 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