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摘要:
为研究气体分子转动非平衡效应对喷管内流动的影响，在气体动理论统一算法(GKUA)计算框架下，发展了分子速度分布函数层次下考虑转动能影响的喷管流动边界条件数学模型，构造了直接求解分子速度分布函数的气体动理论数值格式，数值求解了考虑转动能影响的Boltzmann-Rykov模型方程。通过对一维非定常激波管内流动、一维定常正激波结构及二维型面喷管内流动问题进行模拟研究，计算结果与理论解、文献值及实验数据相吻合，验证了统一算法对内流动问题的可行性与计算精度。分析了考虑转动能影响的喷管内流动流场，结果表明：可使用克努森数作为喷管流动特性和性能的表征。
Abstract:The kinetic Boltzmann-Rykov model is used to explore the influence of rotating non-equilibrium on the inner flow of the nozzle, based on the computing principle of the gas-kinetic unified algorithm (GKUA). Mathematical models for the boundary conditions of nozzle flows were developed under the level of molecular velocity distribution function, and a numerical scheme of gas-kinetic was constructed to solve the molecular velocity distribution function directly. The Boltzmann-Rykov model equation considering the effect of rotational energy was numerically solved. The inner flow problems including the one-dimensional unsteady shock tube, one-dimensional steady positive shock structure, and two-dimensional planar nozzle flow were numerically simulated. The computed results match the theoretical solution, simulation value, and experimental data. It verifies the feasibility and accuracy of the unified algorithm for the inner flow problems. Lastly, an analysis was conducted on the nozzle’s inner flow field while taking rotational energy into account. The results show that the Knudsen number can be used as the characterization of nozzle flow characteristics and performance.
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图 1 激波管内流动宏观流动参数分布
Figure 1. Distribution of macroscopic flow parameters for flow in a shock tube
图 2 不同流域下激波管内流动温度分布
Figure 2. Temperature profiles of flow in the shock tube in different regimes
图 5 不同入口压力下喷管出口马赫数分布
Figure 5. Mach number profile at the exit plane under different inlet pressure
图 6 不同入口压力下喷管轴线温度分布
Figure 6. Temperature profile along the centerline under different inlet pressure
图 7 不同入口压力下当地克努森数分布
Figure 7. The local Knudsen number contours under different inlet pressure
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[1] BRYKOV N A, EMELYANOV V N, KARPENKO A G, et al. Flows of real gas in nozzles with unsteady local energy supply[J]. Computers & Mathematics with Applications, 2021, 81: 702-724. [2] GOMEZ J, GROLL R. Pressure drop and thrust predictions for transonic micronozzle flows[J]. Physics of Fluids, 2016, 28(2): 022008. doi: 10.1063/1.4942238 [3] LI Z H, LI Z H, WU J L, et al. Coupled Navier-Stokes/direct simulation Monte Carlo simulation of multicomponent mixture plume flows[J]. Journal of Propulsion and Power, 2014, 30(3): 672-689. doi: 10.2514/1.B34971 [4] HAN Z, LI Z H, BAI Z Y, et al. Study on numerical algorithm of the N-S equation for multi-body flows around irregular disintegrations in near space[J]. Aerospace, 2022, 9(7): 347. doi: 10.3390/aerospace9070347 [5] CONSTANTIN P, FOIAS C. Navier-Stokes equations [M]. Chicago: University of Chicago Press, 2020. [6] BIRD G A. Molecular gas dynamics and the direct simulation of gas flows[M]. Oxford: Oxford University Press, 1994: 148-182. [7] FANG M, LI Z H, LI Z H, et al. DSMC approach for rarefied air ionization during spacecraft reentry[J]. Communications in Computational Physics, 2018, 23(4): 1167-1190. doi: 10.4208/cicp.OA-2016-0186 [8] GU K, WATKINS C B, KOPLIK J. Atomistic hybrid DSMC/NEMD method for nonequilibrium multiscale simulations[J]. Journal of Computational Physics, 2010, 229(5): 1381-1400. doi: 10.1016/j.jcp.2009.10.035 [9] BURT J M, BOYD I D. A hybrid particle approach for continuum and rarefied flow simulation[J]. Journal of Computational Physics, 2009, 228(2): 460-475. doi: 10.1016/j.jcp.2008.09.022 [10] CARLSON H, ROVEDA R, BOYD I, et al. A hybrid CFD-DSMC method of modeling continuum-rarefied flows[C]//Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit. Reston: AIAA, 2004: 1180. [11] LI Z H, HU W Q, WU J L, et al. Improved gas-kinetic unified algorithm for high rarefied to continuum flows by computable modeling of the Boltzmann equation[J]. Physics of Fluids, 2021, 33(12): 126114. [12] LI Z H, PENG A P, ZHANG H X, et al. Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations[J]. Progress in Aerospace Sciences, 2015, 74: 81-113. doi: 10.1016/j.paerosci.2014.12.002 [13] LI Z H, ZHANG H X. Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry[J]. Journal of Computational Physics, 2009, 228(4): 1116-1138. doi: 10.1016/j.jcp.2008.10.013 [14] 李志辉, 张涵信. 稀薄流到连续流的气体运动论模型方程算法研究[J]. 力学学报, 2002, 34(2): 145-155.LI Z H, ZHANG H X. Study on gas kinetic algorithm for flows from rarefied transition to continuum using Boltzmann model equation[J]. Acta Mechanica Sinica, 2002, 34(2): 145-155 (in Chinese). [15] SHAKHOV E M. Generalization of the Krook kinetic relaxation equation[J]. Fluid Dynamics, 1968, 3(5): 95-96. [16] YANG J Y, HUANG J C. Rarefied flow computations using nonlinear model Boltzmann equations[J]. Journal of Computational Physics, 1995, 120(2): 323-339. doi: 10.1006/jcph.1995.1168 [17] TITAREV V A, SHAKHOV E M. Computational study of a rarefied gas flow through a long circular pipe into vacuum[J]. Vacuum, 2012, 86(11): 1709-1716. doi: 10.1016/j.vacuum.2012.02.026 [18] HOLWAY L H. New statistical models for kinetic theory: Methods of construction[J]. Physics of Fluids, 1966, 9(9): 1658-1673. doi: 10.1063/1.1761920 [19] SEGAL B M, FERZIGER J H. Shock-wave structure using nonlinear model Boltzmann equations[J]. Physics of Fluids, 1972, 15(7): 1233-1247. [20] MORSE T F. Kinetic model for gases with internal degrees of freedom[J]. Physics of Fluids, 1964, 7(2): 159-169. [21] RYKOV V A. A model kinetic equation for a gas with rotational degrees of freedom[J]. Fluid Dynamics, 1975, 10(6): 959-966. [22] RYKOV V A, TITAREV V A, SHAKHOV E M. Shock wave structure in a diatomic gas based on a kinetic model[J]. Fluid Dynamics, 2008, 43(2): 316-326. doi: 10.1134/S0015462808020178 [23] LI Z H, ZHANG H X. Numerical investigation from rarefied flow to continuum by solving the Boltzmann model equation[J]. International Journal for Numerical Methods in Fluids, 2003, 42(4): 361-382. doi: 10.1002/fld.517 [24] LI Z H, HU W Q, PENG A P, et al. Gas-kinetic unified algorithm for plane external force-driven flows covering all flow regimes by modeling of Boltzmann equation[J]. International Journal for Numerical Methods in Fluids, 2020, 92(8): 922-949. doi: 10.1002/fld.4812 [25] LI Z H, PENG A P, MA Q, et al. Gas-kinetic unified algorithm for computable modeling of Boltzmann equation and application to aerothermodynamics for falling disintegration of uncontrolled Tiangong-No.1 spacecraft[J]. Advances in Aerodynamics, 2019, 1(1): 1-21. doi: 10.1186/s42774-019-0001-z [26] BHATHNAGOR P, GROSS E, KROOK M. A model for collision processes in gases[J]. Physical Review, 1954, 94(3): 511. doi: 10.1103/PhysRev.94.511 [27] XIONG S W, ZHONG C W, ZHUO C S, et al. Numerical simulation of compressible turbulent flow via improved gas-kinetic BGK scheme[J]. International Journal for Numerical Methods in Fluids, 2011, 67(12): 1833-1847. doi: 10.1002/fld.2449 [28] LIU C, XU K, SUN Q H, et al. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations[J]. Journal of Computational Physics, 2016, 314: 305-340. doi: 10.1016/j.jcp.2016.03.014 [29] ZHU Y J, ZHONG C W, XU K. An implicit unified gas-kinetic scheme for unsteady flow in all Knudsen regimes[J]. Journal of Computational Physics, 2019, 386: 190-217. doi: 10.1016/j.jcp.2019.01.033 [30] XU K, HUANG J C. A unified gas-kinetic scheme for continuum and rarefied flows[J]. Journal of Computational Physics, 2010, 229(20): 7747-7764. doi: 10.1016/j.jcp.2010.06.032 [31] XU X C, CHEN Y P, LIU C, et al. Unified gas-kinetic wave-particle methods V: Diatomic molecular flow[J]. Journal of Computational Physics, 2021, 442: 110496. doi: 10.1016/j.jcp.2021.110496 [32] LIU S, YU P B, XU K, et al. Unified gas-kinetic scheme for diatomic molecular simulations in all flow regimes[J]. Journal of Computational Physics, 2014, 259: 96-113. doi: 10.1016/j.jcp.2013.11.030 [33] 江松, 徐昆, 孙文俊, 等. 辐射输运方程的统一气体动理学格式[J]. 中国科学: 数学, 2021, 51(6): 799-832. doi: 10.1360/SSM-2020-0278JIANG S, XU K, SUN W J, et al. Unified gas kinetic schemes for the radiation transfer equations[J]. Scientia Sinica (Mathematica), 2021, 51(6): 799-832 (in Chinese). doi: 10.1360/SSM-2020-0278 [34] 曾嘉楠, 李琪, 吴雷. 分子气体稀薄效应的动理学建模[J]. 空气动力学学报, 2022, 40(2): 1-30.ZENG J N, LI Q, WU L. Kinetic modeling of rarefied molecular gas dynamics[J]. Acta Aerodynamica Sinica, 2022, 40(2): 1-30(in Chinese). [35] ROBBEN F, TALBOT L. Experimental study of the rotational distribution function of nitrogen in a shock wave[J]. Physics of Fluids, 1966, 9(4): 653-662. doi: 10.1063/1.1761730 [36] LIU M H, ZHANG X F, ZHANG G X, et al. Study on micronozzle flow and propulsion performance using DSMC and continuum methods[J]. Acta Mechanica Sinica, 2006, 22(5): 409-416. doi: 10.1007/s10409-006-0020-y -
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