Semiempirical prediction of Sauter mean diameter for pressure swirl atomizer based on instability theory
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摘要:
基于液膜雾化的不稳定性理论,同时考虑离心喷嘴锥形液膜气液相互作用过程中开尔文-亥姆霍兹(K-H)不稳定性和瑞利-泰勒(R-T)不稳定性对液膜破碎的影响,建立了离心喷嘴液雾索太尔平均直径(SMD)半理论预测模型,并在燃油温度240~300 K、燃油压力0.5~3 MPa条件下开展了离心喷嘴燃油雾化全息试验和激光多普勒粒子分析仪(PDPA)测试验证试验。研究表明:液膜表面同时存在流向波和周向波,燃油压力和燃油温度的降低,均会抑制液膜表面不稳定性的发展,使得液雾SMD增大,且相较于K-H不稳定性,燃油压力变化对R-T不稳定性的影响更为显著;模型可实现对变物性、结构和工况离心喷嘴液雾SMD的良好预测,最大预测误差在±15%左右,对离心喷嘴的雾化性能预测和结构优化设计具有一定的工程应用价值。
Abstract:Based on the liquid atomization instability theory, a semiempirical model was established to predict the Sauter mean diameter (SMD) of pressure swirl atomizers, considering the Kelvin-Helmholtz (K-H) instability and Rayleigh-Taylor (R-T) instability generated by the interactions between air and liquid film. The experiments were also conducted using phase Doppler particle analyzer (PDPA) technique and digital off-axis holography with liquid temperature ranging from 240—300 K and liquid pressure ranging from 0.5—3 MPa. The results showed that: there were circumferential waves and axial waves on the surface of liquid sheet. With the decrease of liquid pressure and liquid temperature, the instability of liquid film was inhibited, which led to the increase of the SMD. Compared with the K-H instability, the effect of the liquid pressure on R-T instability was more significant; the effects of liquid physical properties, geometrical structures and operating conditions were included in the semiempirical correlation. The predictions showed good agreement with the experimental results, and the maximum uncertainty of the semiempirical correlation to predict the SMD was about ±15% for the available experimental data, making it valuable for the prediction of atomization performance and the optimization of the structure of pressure swirl atomizers.
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表 1 试验工况
Table 1. Operating conditions
工况编号 燃油温度$ T/ $K 燃油压力$ \Delta p/ $MPa 1 300 0.8 2 260 0.8 3 240 0.8 4 250 0.5 5 250 1.5 6 250 3 工况编号 $ {d}_{0}/\mathrm{m}\mathrm{m} $ $ {l}_{0} $/$ {d}_{0} $ $ {d}_{\mathrm{s}}/ $m $ {A}_{\mathrm{p}}/{10}^{-6}\;\mathrm{m}^{2} $ $ K $ $ \Delta p/\mathrm{M}\mathrm{P}\mathrm{a} $ $ \dot{{m}_{\mathrm{l}}}/ (\mathrm{k}\mathrm{g}/\mathrm{s}) $ $ \mathrm{S}\mathrm{M}\mathrm{D}/{\text{μ}}\mathrm{m} $ 数据来源 7 1 1 0.018 12 0.66 0.6 0.014 98 Xiao等[18] 8 2 0.5 0.018 12 0.33 0.6 0.035 106 Xiao等[18] 9 3 0.33 0.018 12 0.22 0.6 0.063 140 Xiao等[18] 10 2 0.5 0.018 8 0.22 0.6 0.032 105 Xiao等[18] 11 2 0.5 0.018 16 0.44 0.6 0.042 130 Xiao等[18] 12 0.4 0.5 0.002 0.59 0.74 0.6 0.003 45 Xiao等[18] 13 0.4 1.25 0.002 0.59 0.74 0.6 0.0029 49 Xiao等[18] 14 0.4 2.5 0.002 0.59 0.74 0.6 0.0034 54 Xiao等[18] 15 1 1 0.003 1.2 0.4 0.3 0.0055 89 Couto等[34] 16 1 1 0.003 1.2 0.4 0.4 0.00613 81 Couto等[34] 17 1 1 0.003 1.2 0.4 0.5 0.0067 75 Couto等[34] 18 1 1 0.003 1.2 0.4 0.6 0.0074 71 Couto等[34] -
[1] LEFEBVRE A H,BALLAL D R. Gas turbine combustion: alternative fuels and emissions[M]. Boca Raton,US: CRC Press,2010. [2] LEFEBVRE A H,MCDONELL V G. Atomization and sprays[M]. Boca Raton,US: CRC Press,2017. [3] KANG Zhongtao,WANG Zhenguo,LI Qinglian,et al. Review on pressure swirl injector in liquid rocket engine[J]. Acta Astronautica,2018,145: 174-198. doi: 10.1016/j.actaastro.2017.12.038 [4] DONJAT D,ESTIVALEZES J L,MICHAU M,et al. Phenomenological study of the pressure swirl atomizer internal flow[R]. Sorrento,Italy: International Conference on Liquid and Spray Systems,2003. [5] RADCLIFFE A. Fuel injection,high speed aerodynamics and jet propulsion[M]. Princeton,US: Princeton University Press,1960. [6] JASUJA A K. Atomization of crude and residual fuel oils[J]. Journal of Engineering for Power,1979,101(2): 250-258. doi: 10.1115/1.3446480 [7] DOPAZO C,BALLESTER J. Drop size measurements in heavy oil sprays from pressure-swirl nozzles[J]. Atomization and Sprays,1996,6(4): 377-408. doi: 10.1615/AtomizSpr.v6.i4.10 [8] LEFEBVRE A H,WANG X F. Mean drop sizes from pressure-swirl nozzles[J]. Journal of Propulsion and Power,1987,3(1): 11-18. doi: 10.2514/3.22946 [9] WANG Pengfei,TIAN Chang,LIU Ronghua,et al. Mathematical model for multivariate nonlinear prediction of SMD of X-type swirl pressure nozzles[J]. Process Safety and Environmental Protection,2019,125: 228-237. doi: 10.1016/j.psep.2019.03.023 [10] REZAEI S,VASHAHI F,DAFSARI R A,et al. A correlation of aviation fuel temperature effect on mean drop size in pressure swirl spray[J]. Atomization and Sprays,2021,31(4): 81-97. doi: 10.1615/AtomizSpr.2021034393 [11] LI Shilin,WU Gaogao,WANG Pengfei,et al. A mathematical model for predicting the sauter mean diameter of liquid-medium ultrasonic atomizing nozzle based on orthogonal design[J]. Applied Sciences,2021,11(24): 11628. doi: 10.3390/app112411628 [12] SQUIRE H B. Investigation of the instability of a moving liquid film[J]. British Journal of Applied Physics,1953,4(6): 167-169. doi: 10.1088/0508-3443/4/6/302 [13] DOMBROWSKI N,JOHNS W R. The aerodynamic instability and disintegration of viscous liquid sheets[J]. Chemical Engineering Science,1963,18(3): 203-214. doi: 10.1016/0009-2509(63)85005-8 [14] SENECAL P K,SCHMIDT D P,NOUAR I,et al. Modeling high-speed viscous liquid sheet atomization[J]. International Journal of Multiphase Flow,1999,25(6/7): 1073-1097. [15] COUTO H S,CARVALHO J A,BASTOS-NETTO D. Theoretical formulation for sauter mean diameter of pressure-swirl atomizers[J]. Journal of Propulsion and Power,1997,13(5): 691-696. doi: 10.2514/2.5221 [16] RIVAS J R R,PIMENTA A P,LESSA J S,et al. An improved theoretical formulation for Sauter mean diameter of pressure-swirl atomizers using geometrical parameters of atomization[J]. Propulsion and Power Research,2022,11(2): 240-252. doi: 10.1016/j.jppr.2022.02.007 [17] 杨建辉,樊未军,杨茂林. 离心式喷嘴雾化参数的计算[J]. 航空动力学报,2003,18(6): 799-802. YANG Jianhui,FAN Weijun,YANG Maolin. A calculation of spray parameters of pressure-swirl atomizer[J]. Journal of Aerospace Power,2003,18(6): 799-802. (in ChineseYANG Jianhui, FAN Weijun, YANG Maolin. A calculation of spray parameters of pressure-swirl atomizer[J]. Journal of Aerospace Power, 2003, 18(6): 799-802. (in Chinese) [18] XIAO Wei,HUANG Yong. Improved semiempirical correlation to predict sauter mean diameter for pressure-swirl atomizers[J]. Journal of Propulsion and Power,2014,30(6): 1628-1635. doi: 10.2514/1.B35238 [19] CHU C C,CHOU S F,LIN H I,et al. Theoretical analysis of heat and mass transfer in swirl atomizers[J]. Heat and Mass Transfer,2007,43(11): 1213-1224. doi: 10.1007/s00231-006-0206-7 [20] REITZ R D,BEALE J C. Modeling spray atomization with the kelvin-helmholtz/rayleigh-taylor hybrid model[J]. Atomization and Sprays,1999,9(6): 623-650. doi: 10.1615/AtomizSpr.v9.i6.40 [21] BOUKRA M,CARTELLIER A,DUCASSE,et al. Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers[J]. Comptes Rendus Mecanique,2009,337(6): 492-503. [22] VARGA C M,LASHERAS J C,HOPFINGER E J. Initial breakup of a small-diameter liquid jet by a high-speed gas stream[J]. Journal of Fluid Mechanics,2003,497: 405-434. doi: 10.1017/S0022112003006724 [23] 邵长孝,罗坤,樊建人. 旋转射流雾化的直接数值模拟研究[J]. 工程热物理学报,2017,38(3): 553-556. SHAO Changxiao,LUO Kun,FAN Jianren. Direct numerical simulation of swirling liquid atomization[J]. Journal of Engineering Thermophysics,2017,38(3): 553-556. (in ChineseSHAO Changxiao, LUO Kun, FAN Jianren. Direct numerical simulation of swirling liquid atomization[J]. Journal of Engineering Thermophysics, 2017, 38(3): 553-556. (in Chinese) [24] 王雷,方斌,王光彩. 基于大涡模拟的离心式喷嘴雾化过程研究[J]. 推进技术,2021,42(8): 1855-1864. WANG Lei,FANG Bin,WANG Guangcai. Process of pressure swirl nozzle atomization based on large eddy simulation[J]. Journal of Propulsion Technology,2021,42(8): 1855-1864. (in ChineseWANG Lei, FANG Bin, WANG Guangcai. Process of pressure swirl nozzle atomization based on large eddy simulation[J]. Journal of Propulsion Technology, 2021, 42(8): 1855-1864. (in Chinese) [25] RAYNAL L. Instabilité et entraînement á l’interface d’une couche de mélange liquide-gaz[D]. Grenoble,Français: Laboratoire des écoulements géophysiques et industriels,1997. [26] INAMURA T,SHIROTA M,TSUSHIMA M,et al. Spray characteristics of prefilming type of airblast atomizer[R]. Heidelberg,Germany: International Conference on Liquid and Spray Systems,2012. [27] CHAUSSONNET G,VERMOREL O,RIBER E,et al. A new phenomenological model to predict drop size distribution in Large-Eddy Simulations of airblast atomizers[J]. International Journal of Multiphase Flow,2016,80: 29-42. doi: 10.1016/j.ijmultiphaseflow.2015.10.014 [28] HOLZ S,CHAUSSONNET G,GEPPERTH S,et al. Comparison of the primary atomization model PAMELA with drop size distributions of an industrial prefilming airblast nozzle[R]. Brighton,UK: 27th Annual Conference on Liquid Atomization and Spray Systems,2016. [29] SCHMIDT D P,NOUAR I,SENECAL P K,et al. Pressure-swirl atomization in the near field[R]. Warrendale,US: SAE International Congress & Exhibition,1999. [30] HAN Zhiyu,PARRISH S,FARRELL P V,et al. Modeling atomization processes of pressure-swirl hollow-cone fuel sprays[J]. Atomization and Sprays,1997,7(6): 663-684. doi: 10.1615/AtomizSpr.v7.i6.70 [31] RIZK N K,LEFEBVRE A H. Prediction of velocity coefficient and spray cone angle for simplex swirl atomizers[J]. International Journal of Turbo and Jet Engines,1987,4(1/2): 65-74. [32] HONG M,Atomisation et mélange dans les jets coaxiaux liquide-gaz[D]. Grenoble,Français: Laboratoire des écoulements géophysiques et industriels,2003. [33] KIM S,KHIL T,KIM D,et al. Effect of geometric parameters on the liquid film thickness and air core formation in a swirl injector[J]. Measurement Science and Technology,2009,20(1): 015403. doi: 10.1088/0957-0233/20/1/015403 [34] COUTO H D S,LACAVA P T,BASTOS-NETTO D,et al. Experimental evaluation of a low pressure-swirl atomizer applied engineering design procedure[J]. Journal of Propulsion and Power,2009,25(2): 358-364. doi: 10.2514/1.37018 [35] FU Qingfei,YANG Lijun,QU Yuanyuan,et al. Linear stability analysis of a conical liquid sheet[J]. Journal of Propulsion and Power,2010,26(5): 955-968. doi: 10.2514/1.48346 [36] 富庆飞. 液体火箭发动机同轴喷嘴稳/动态特性研究[D]. 北京: 北京航空航天大学,2012. FU Qingfei. Investigation of the steady/dynamic characteristics of the coaxial injectors in liquid rocket engine[D]. Beijing: Beihang University,2012. (in ChineseFU Qingfei. Investigation of the steady/dynamic characteristics of the coaxial injectors in liquid rocket engine[D]. Beijing: Beihang University, 2012. (in Chinese) [37] LIU Zhilin,HUANG Yong,SUN Lei. Studies on air core size in a simplex pressure-swirl atomizer[J]. International Journal of Hydrogen Energy,2017,42(29): 18649-18657. doi: 10.1016/j.ijhydene.2017.04.188 -