壓力旋流噴嘴(pressure swirl injector)因為優秀的霧化能力被廣泛應用在火箭引擎上，因此有許多對於壓力旋流噴嘴霧化性能方面的研究。然而，以實驗量測影響霧化性能的物理現象以特徵尺度來說十分困難，且建立實驗場和準備材料需要耗費大量的時間和金錢，因此使用計算流體力學進行數值計算是很好解決上述問題的方法。本研究的目的為建立一個可提供給不同噴嘴幾何與工作流體使用的計算方法，使用OpenFOAM的interFoam配合多相流之流體體積法(Volume of fluid, VoF)描述兩相間介面，並考慮表面張力之作用，採用大渦模型(Large eddy simulation)模擬紊流流場，並透過自適應網格法(Adaptive mesh refinement, AMR)節省網格數量，模擬旋流噴嘴內空氣柱的形成和液體因不穩定性而破裂成水滴之現象。測試了在不同區域加密網格對於空氣柱成型的影響，並將模擬的噴霧角度與實驗進行比對，以驗證模擬的準確性。從模擬結果發現將噴嘴中心網格加密更容易使空氣柱形成，原因是在噴嘴中心不受黏性影響，流場為無旋流動，因此流體在噴嘴中心有較高的速度，進而導致紊流擾動較強。分析液體噴出噴嘴後的破裂過程，發現液膜的表面波動與外部空氣交互作用後呈現蜿蜒狀(Sinuous wave)，因此認為導致液膜分解成韌帶的主要原因為Kelvin-Helmholtz instability，其中韌帶在擴張的過程中，併吞了許多周圍細小的孔洞，導致表面上的鋸齒狀分布，而這些鋸齒狀分布造成Plateau-Rayleigh instability和Rayleigh-Taylor instabilit的現象而加速韌帶破裂成液滴。

The pressure swirl injector, due to its excellent atomization capability, is extensively employed in rocket propulsion systems, prompting numerous studies on its atomization performance. The aim of this research is to establish a computational methodology applicable to various nozzle geometries and working fluids. The approach employs OpenFOAM's interFoam solver in conjunction with the Volume of Fluid (VoF) method for multiphase flow, considering surface tension effects. Large Eddy Simulation (LES) is employed to model turbulent flow, and Adaptive Mesh Refinement (AMR) is used to reduce grid requirements. The simulation focuses on the formation of an air column within the swirling injector and the instability-driven breakup of liquid into droplets. The influence of grid refinement in different regions on air column formation is examined, and the simulated spray angle is compared to experimental data to validate accuracy.

From the simulation results, it is observed that enhancing grid refinement near the nozzle center facilitates air column formation. This is attributed to the absence of viscosity effects and non-swirling flow at the nozzle center, resulting in higher fluid velocities and stronger turbulent disturbances. Analyzing the post-nozzle liquid breakup process reveals that surface waves on the liquid sheet interact with external air, exhibiting a sinuous pattern. The primary cause of liquid sheet breakup into ligaments is attributed to Kelvin-Helmholtz instability. During the extension process of these ligaments, they assimilate numerous small surrounding voids, leading to serrated patterns on the surface. These serrated patterns trigger Plateau-Rayleigh instability and Rayleigh-Taylor instability, accelerating the breakup of ligaments into droplets.

[1] Z. Kang, Z.-g. Wang, Q. Li, and P. Cheng, "Review on pressure swirl injector in liquid rocket engine," Acta Astronautica, vol. 145, pp. 174-198, 2018, doi: 10.1016/j.actaastro.2017.12.038.
[2] Q.-f. Fu, L.-j. Yang, and X.-d. Wang, "Theoretical and experimental study of the dynamics of a liquid swirl injector," J. Propul. Power, vol. 26, no. 1, pp. 94-101, 2010.
[3] V. Natarajan, U. Unnikrishnan, W.-S. Hwang, J.-Y. Choi, and V. Yang, "Numerical study of two-phase flow dynamics and atomization in an open-type liquid swirl injector," Int. J. Multiphase Flow, vol. 143, 2021, doi: 10.1016/j.ijmultiphaseflow.2021.103702.
[4] M. L. Dranovsky, Combustion instabilities in liquid rocket engines: testing and development practices in Russia. American Institute of Aeronautics and Astronautics, 2007.
[5] A. Datta and S. Som, "Numerical prediction of air core diameter, coefficient of discharge and spray cone angle of a swirl spray pressure nozzle," Int. J. Heat Fluid Flow, vol. 21, no. 4, pp. 412-419, 2000.
[6] S. Moon, E. Abo-Serie, and C. Bae, "Air flow and pressure inside a pressure-swirl spray and their effects on spray development," Exp. Therm Fluid Sci., vol. 33, no. 2, pp. 222-231, 2009, doi: 10.1016/j.expthermflusci.2008.08.005.
[7] M. Halder, S. Dash, and S. Som, "Initiation of air core in a simplex nozzle and the effects of operating and geometrical parameters on its shape and size," Exp. Therm Fluid Sci., vol. 26, no. 8, pp. 871-878, 2002.
[8] E. J. Lee, S. Y. Oh, H. Y. Kim, S. C. James, and S. S. Yoon, "Measuring air core characteristics of a pressure-swirl atomizer via a transparent acrylic nozzle at various Reynolds numbers," Exp. Therm Fluid Sci., vol. 34, no. 8, pp. 1475-1483, 2010.
[9] G. Amini, "Liquid flow in a simplex swirl nozzle," Int. J. Multiphase Flow, vol. 79, pp. 225-235, 2016, doi: 10.1016/j.ijmultiphaseflow.2015.09.004.
[10] K. Hansen, J. Madsen, C. Trinh, C. Ibsen, T. Solberg, and B. Hjertager, "A computational and experimental study of the internal flow in a scaled pressure-swirl atomizer," Zaragoza, vol. 9, p. 11, 2002.
[11] Z. Liu, Y. Huang, and L. Sun, "Studies on air core size in a simplex pressure-swirl atomizer," Int. J. Hydrogen Energy, vol. 42, no. 29, pp. 18649-18657, 2017.
[12] J. Jedelsky, M. Maly, N. Pinto del Corral, G. Wigley, L. Janackova, and M. Jicha, "Air–liquid interactions in a pressure-swirl spray," Int. J. Heat Mass Transfer, vol. 121, pp. 788-804, 2018, doi: 10.1016/j.ijheatmasstransfer.2018.01.003.
[13] J. Jedelsky and M. Jicha, "Energy considerations in spraying process of a spill-return pressure-swirl atomizer," Applied Energy, vol. 132, pp. 485-495, 2014, doi: 10.1016/j.apenergy.2014.07.042.
[14] C. Dumouchel, "On the experimental investigation on primary atomization of liquid streams," Exp. Fluids, vol. 45, no. 3, pp. 371-422, 2008, doi: 10.1007/s00348-008-0526-0.
[15] A. H. Lefebvre and V. G. McDonell, Atomization and sprays. CRC press, 2017.
[16] W. V. Ohnesorge, "Die bildung von tropfen an düsen und die auflösung flüssiger strahlen," ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol. 16, no. 6, pp. 355-358, 1936.
[17] R. D. Reitz, Atomization and other breakup regimes of a liquid jet. Princeton University, 1978.
[18] R. Surya Prakash, H. Gadgil, and B. N. Raghunandan, "Breakup processes of pressure swirl spray in gaseous cross-flow," Int. J. Multiphase Flow, vol. 66, pp. 79-91, 2014, doi: 10.1016/j.ijmultiphaseflow.2014.07.002.
[19] M. Yue, H. Xu, M.-l. Yang, H.-j. Yuan, and S.-z. Sheng, "Study on Breakup of Conical Liquid Sheet under Varying Flow Conditions," Chinese Journal of Aeronautics, vol. 16, no. 1, pp. 12-14, 2003, doi: 10.1016/s1000-9361(11)60164-7.
[20] Y. Moon, D. Kim, and Y. Yoon, "Improved Spray Model for Viscous Annular Sheets in a Swirl Injector," J. Propul. Power, vol. 26, no. 2, pp. 267-279, 2010, doi: 10.2514/1.45010.
[21] P. Senecal, D. P. Schmidt, I. Nouar, C. J. Rutland, R. D. Reitz, and M. Corradini, "Modeling high-speed viscous liquid sheet atomization," Int. J. Multiphase Flow, vol. 25, no. 6-7, pp. 1073-1097, 1999.
[22] B.-H. Bang, C.-S. Ahn, S. S. Yoon, and A. L. Yarin, "Breakup of swirling films issued from a pressure-swirl atomizer," Fuel, vol. 332, 2023, doi: 10.1016/j.fuel.2022.125847.
[23] D. H. Sharp, "An overview of Rayleigh-Taylor instability," Physica D: Nonlinear Phenomena, vol. 12, no. 1-3, pp. 3-18, 1984.
[24] J.-W. Ding, G.-X. Li, Y.-S. Yu, and H.-M. Li, "Numerical investigation on primary atomization mechanism of hollow cone swirling sprays," International Journal of Rotating Machinery, vol. 2016, 2016.
[25] E. Laurila, J. Roenby, V. Maakala, P. Peltonen, H. Kahila, and V. Vuorinen, "Analysis of viscous fluid flow in a pressure-swirl atomizer using large-eddy simulation," Int. J. Multiphase Flow, vol. 113, pp. 371-388, 2019, doi: 10.1016/j.ijmultiphaseflow.2018.10.008.
[26] A. Wehrfritz, V. Vuorinen, O. Kaario, and M. Larmi, "Large eddy simulation of high-velocity fuel sprays: studying mesh resolution and breakup model effects for spray A," Atomization Sprays, vol. 23, no. 5, 2013.
[27] M. Yousefifard, P. Ghadimi, and M. Mirsalim, "Numerical simulation of biodiesel spray under ultra-high injection pressure using OpenFOAM," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 37, pp. 737-746, 2015.
[28] H. Yu, Y.-C. Jin, W. Cheng, X. Yang, X. Peng, and Y. Xie, "Multiscale simulation of atomization process and droplet particles diffusion of pressure-swirl nozzle," Powder Technol., vol. 379, pp. 127-143, 2021.
[29] M. Di Martino, D. Ahirwal, and P. L. Maffettone, "Computational fluid dynamics characterization of the hollow-cone atomization: Newtonian and non-Newtonian spray comparison," Phys. Fluids, vol. 34, no. 9, 2022.
[30] M. Heinrich and R. Schwarze, "3D-coupling of Volume-of-Fluid and Lagrangian particle tracking for spray atomization simulation in OpenFOAM," SoftwareX, vol. 11, p. 100483, 2020.
[31] J. U. Brackbill, D. B. Kothe, and C. Zemach, "A continuum method for modeling surface tension," J. Comput. Phys., vol. 100, no. 2, pp. 335-354, 1992.
[32] A. Yoshizawa, "Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling," The Physics of fluids, vol. 29, no. 7, pp. 2152-2164, 1986.
[33] K. Inagaki and H. Kobayashi, "Transport and modeling of subgrid-scale turbulent kinetic energy in channel flows," AIP Advances, vol. 12, no. 4, 2022.
[34] F. Liu, "A thorough description of how wall functions are implemented in OpenFOAM," Proceedings of CFD with OpenSource Software, vol. 34, 2016.
[35] C. Lapointe et al., "Efficient simulation of turbulent diffusion flames in OpenFOAM using adaptive mesh refinement," Fire Safety Journal, vol. 111, p. 102934, 2020.
[36] Z. Wang, L. Li, H. Cheng, and B. Ji, "Numerical investigation of unsteady cloud cavitating flow around the Clark-Y hydrofoil with adaptive mesh refinement using OpenFOAM," Ocean Engineering, vol. 206, p. 107349, 2020.
[37] A. Aniello et al., "Experimental and numerical investigation of two flame stabilization regimes observed in a dual swirl H2-air coaxial injector," Combust. Flame, vol. 249, p. 112595, 2023.
[38] H. Sitaraman et al., "Adaptive mesh based combustion simulations of direct fuel injection effects in a supersonic cavity flame-holder," Combust. Flame, vol. 232, p. 111531, 2021.
[39] W. Edelbauer, "Numerical simulation of cavitating injector flow and liquid spray break-up by combination of Eulerian–Eulerian and Volume-of-Fluid methods," Computers & Fluids, vol. 144, pp. 19-33, 2017.
[40] C. Segatori, A. Piano, B. P. Paradisi, F. Millo, and A. Bianco, "Ensemble average method for runtime saving in Large Eddy Simulation of free and Ducted Fuel Injection (DFI) sprays," Fuel, vol. 344, p. 128110, 2023.
[41] C. Galbiati, M. Ertl, S. Tonini, G. E. Cossali, and B. Weigand, "DNS Investigation of the Primary Breakup in a Conical Swirled Jet," in High Performance Computing in Science and Engineering ´15, 2016, ch. Chapter 22, pp. 333-347.
[42] N. Kerr and D. Fraser, "Swirl part 1: Effect on axisymmetrical turbulent jets," J. Inst. Fuel, vol. 38, no. 299, p. 519, 1965.
[43] J. C. Hunt, A. A. Wray, and P. Moin, "Eddies, streams, and convergence zones in turbulent flows," Studying turbulence using numerical simulation databases, 2. Proceedings of the 1988 summer program, 1988.
[44] A. Banko and J. Eaton, "A frame-invariant definition of the Q-criterion," Center for Turbulence Research Annual Research Briefs, pp. 181-194, 2019.