| Citation: | ZENG Shuhua, ZHAO Wenwen, JIANG Zhongzheng, et al. Numerical investigation and experimental validation of nonlinear constitutive models with solving algorithms in continuum flows[J]. Journal of Aerospace Power, 2024, 39（3）：20220256 doi: 10.13224/j.cnki.jasp.20220256
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Combined with numerical simulation and wind tunnel test technology, the nonlinear coupled constitutive relations (NCCR) model and the simplified generalized hydrodynamic (SGH) model derived by dimensional analysis in hypersonic continuum flows were studied. Based on the hypersonic wind tunnel test system, the aerodynamic force and surface pressure of the type hypervelocity Ballistic 2 (HB2) standard model and the blunt cone were measured under different flow conditions. Meanwhile, under the three-dimensional finite volume framework, the NCCR model with decomposed and undecomposed algorithm and SGH model were used for numerical investigation of the flight models under the test conditions. Result showed that, the aerodynamic force and surface pressure obtained by NCCR model and SGH model were consistent with the solutions of Navier-Stokes (NS) equations as well as the data measured in the wind tunnel. However, the friction/heat flux coefficients predicted by NCCR model with decomposed algorithm at the expansion corner of head of type HB2 were lower than those of NS equations, while the NCCR model with undecomposed algorithm was consistent with NS solver. The computational results and experimental data showed that the accuracy of NCCR model and SGH model in hypersonic continuous flow was validated, and the applicability of decomposed algorithm of NCCR model in three-dimensional high-speed flows shall be further improved.
| [1] |
ANDERSON J D. Hypersonic and high-temperature gas dynamics[M]. 2nd ed. Reston, US: American Institute of Aeronautics and Astronautics, 2006
|
| [2] |
吴其芬, 陈伟芳, 黄琳, 等. 稀薄气体动力学[M]. 长沙: 国防科技大学出版社, 2004.
|
| [3] |
沈青. 稀薄气体动力学[M]. 北京: 国防工业出版社, 2003.
|
| [4] |
BIRD G A. Molecular gas dynamics and the direct simulation of gas flows[M]. Oxford, UK: Clarendon Press, 1994
|
| [5] |
BHATNAGAR P L,GROSS E P,KROOK M. A model for collision processes in gases. Ⅰ. small amplitude processes in charged and neutral one-component systems[J]. Physical Review,1954,94(3): 511-525. doi: 10.1103/PhysRev.94.511
|
| [6] |
XU Kun,HUANG Juanchen. 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
|
| [7] |
LI Zhihui,ZHANG Hanxin. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J]. Journal of Computational Physics,2004,193(2): 708-738. doi: 10.1016/j.jcp.2003.08.022
|
| [8] |
刘沙,王勇,袁瑞峰,等. 统一气体动理学方法研究进展[J]. 气体物理,2019,4(4): 1-13. doi: 10.19527/j.cnki.2096-1642.0809
LIU Sha,WANG Yong,YUAN Ruifeng,et al. Advance in unified methods based on gas-kinetic theory[J]. Physics of Gases,2019,4(4): 1-13. (in Chinese) doi: 10.19527/j.cnki.2096-1642.0809
|
| [9] |
陈伟芳,赵文文,江中正,等. 稀薄气体动力学矩方法研究综述[J]. 气体物理,2016,1(5): 9-24. doi: 10.19527/j.cnki.2096-1642.2016.05.002
CHEN Weifang,ZHAO Wenwen,JIANG Zhongzheng,et al. A review of moment equations for rarefied gas dynamics[J]. Physics of Gases,2016,1(5): 9-24. (in Chinese) doi: 10.19527/j.cnki.2096-1642.2016.05.002
|
| [10] |
蔡振宁. 气体动理学中数值矩方法的算法研究与应用[D]. 北京: 北京大学, 2013.
CAI Zhenning. Investigations and applications of the numerical moment method in the kinetic theory of gases[D]. Beijing: Peking University, 2013. (in Chinese)
|
| [11] |
CHAPMAN S, COWLING T. The mathematical theory of non-uniform gases[M]. 2nd ed. London: Cambridge University Press, 1953
|
| [12] |
BURNETT D. The distribution of molecular velocities and the mean motion in a non-uniform gas[J]. Proceedings of the London Mathematical Society,1936(1): 382-435.
|
| [13] |
GRAD H. On the kinetic theory of rarefied gases[J]. Communications on Pure and Applied Mathematics,1949,2(4): 331-407. doi: 10.1002/cpa.3160020403
|
| [14] |
TORRILHON M,STRUCHTRUP H. Regularized 13-moment equations: shock structure calculations and comparison to Burnett models[J]. Journal of Fluid Mechanics,2004,513: 171-198. doi: 10.1017/S0022112004009917
|
| [15] |
赵文文. 高超声速流动Burnett方程稳定性与数值计算方法研究[D]. 杭州: 浙江大学, 2014.
ZHAO Wenwen. Linearized stability analysis and numerical computation of Burnett equations in hypersonic flow[D]. Hangzhou: Zhejiang University, 2014. (in Chinese)
|
| [16] |
LOCKERBY D A,REESE J M,GALLIS M A. The usefulness of higher-order constitutive relations for describing the Knudsen layer[J]. Physics of Fluids,2005,17(10): 100609.1-100609.6.
|
| [17] |
EU B C. Kinetic theory of nonequilibrium ensembles, irreversible thermodynamics, and generalized hydrodynamics[M]. Cham, Germany: Springer International Publishing, 2016.
|
| [18] |
EU B C. Nonequilibrium statistical mechanics: ensemble method[M]. Dordrecht, the Netherlands: Kluwer Academic, 1998.
|
| [19] |
EU B C. A modified moment method and irreversible thermodynamics[J]. The Journal of Chemical Physics,1980,73(6): 2958-2969. doi: 10.1063/1.440469
|
| [20] |
MYONG R S. Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows[J]. Physics of Fluids,1999,11(9): 2788-2802. doi: 10.1063/1.870137
|
| [21] |
MYONG R S. A generalized hydrodynamic computational model for rarefied and microscale diatomic gas flows[J]. Journal of Computational Physics,2004,195(2): 655-676. doi: 10.1016/j.jcp.2003.10.015
|
| [22] |
江中正. 稀薄气体流动非线性耦合本构关系模型理论与数值研究[D]. 杭州: 浙江大学, 2019.
JIANG Zhongzheng. Theoretical and numerical investigations of nonlinear coupled constitutive relation model in rarefied gas flows[D]. Hangzhou: Zhejiang University, 2019. (in Chinese)
|
| [23] |
何志强. NCCR稀薄气体动力学方程的非结构网格数值模拟研究[D]. 杭州: 浙江大学, 2021.
HE Zhiqiang. Numerical investigations for NCCR based rarefied gas dynamics on unstructured grids[D]. Hangzhou: Zhejiang University, 2021. (in Chinese)
|
| [24] |
袁震宇. 高超声速双原子气体非线性耦合本构关系及计算方法[D]. 杭州: 浙江大学, 2020.
YUAN Zhenyu. Nonlinear coupled constitutive relations and simulation method for hypersonic diatomic gas[D]. Hangzhou: Zhejiang University, 2020. (in Chinese)
|
| [25] |
LIU Sha,YANG Yuehan,ZHONG Chengwen. An extended gas-kinetic scheme for shock structure calculations[J]. Journal of Computational Physics,2019,390: 1-24. doi: 10.1016/j.jcp.2019.04.016
|
| [26] |
JIANG Z,ZHAO W,CHEN W,et al. Computation of shock wave structure using a simpler set of generalized hydrodynamic equations based on nonlinear coupled constitutive relations[J]. Shock Waves,2019,29(8): 1227-1239. doi: 10.1007/s00193-018-0876-3
|
| [27] |
JIANG Zhongzheng,CHEN Weifang,ZHAO Wenwen. Numerical analysis of the micro-Couette flow using a non-Newton-Fourier model with enhanced wall boundary conditions[J]. Microfluidics and Nanofluidics,2017,22(1): 1-20.
|
| [28] |
JIANG Zhongzheng,ZHAO Wenwen,YUAN Zhenyu,et al. Computation of hypersonic flows over flying configurations using a nonlinear constitutive model[J]. AIAA Journal,2019,57(12): 5252-5268. doi: 10.2514/1.J057688
|
| [29] |
JIN Shi. Asymptotic-preserving schemes for multiscale physical problems[EB/OL]. [2021-12-04]. https://arxiv.org/abs/2112.05920
|
| [30] |
CURTISS C F. The classical Boltzmann equation of a gas of diatomic molecules[J]. The Journal of Chemical Physics,1981,75(1): 376-378. doi: 10.1063/1.441792
|
| [31] |
KUBO R. Generalized cumulant expansion method[J]. Journal of the Physical Society of Japan,1962,17(7): 1100-1120. doi: 10.1143/JPSJ.17.1100
|
| [32] |
MYONG R S. On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules[J]. Physics of Fluids,2014,26(5): 056102.1-056102.18.
|
| [33] |
YUAN Zhenyu,ZHAO Wenwen,JIANG Zhongzheng,et al. Modified nonlinear coupled constitutive relations model for hypersonic nonequilibrium flows[J]. Journal of Thermophysics and Heat Transfer,2020,34(4): 848-859. doi: 10.2514/1.T5761
|
| [34] |
江中正, 陈伟芳. 基于非线性本构模型的耦合求解算法研究[C]//中国力学大会暨庆祝中国力学学会成立60周年大会论文集. 北京: 中国力学学会, 2017: 816-831.
|
| [35] |
JIANG Zhongzheng. An undecomposed hybrid algorithm for nonlinear coupled constitutive relations of rarefied gas dynamics[J]. Communications in Computational Physics,2019,26(3): 880-912. doi: 10.4208/cicp.OA-2018-0056
|
| [36] |
KODERA M, TANNO H, TAKAHASHI M, et al. Comparison of re-entry flow computations with high enthalpy shock tunnel experiments[R]. AIAA-2009-7305, 2009.
|
| [37] |
BOYD I D,CHEN Gang,CANDLER G V. Predicting failure of the continuum fluid equations in transitional hypersonic flows[J]. Physics of Fluids,1995,7(1): 210-219. doi: 10.1063/1.868720
|
| [38] |
HOLMAN T, BOYD I. Numerical investigation of the effects of continuum breakdown on hypersonic vehicle surface properties[R]. AIAA-2008-3928, 2008.
|
| [39] |
HE Zhiqiang,JIANG Zhongzheng,ZHANG Huangwei,et al. Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows[J]. Chinese Journal of Aeronautics,2021,34(2): 136-153. doi: 10.1016/j.cja.2020.06.023
|
| [40] |
YUAN Zhenyu,JIANG Zhongzheng,ZHAO Wenwen,et al. Analysis of gas flow over a cylinder at all Knudsen numbers based on non-newtonian constitutive models[J]. International Journal of Modern Physics: B,2020,34(14/15/16): 2040076.1-2040076.5.
|
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