Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer

CHEN Chongpei; LIANG Jianhan; GUAN Qingdi; GAO Tianyun

doi:10.7527/S1000-6893.2021.26364

ACTA AERONAUTICAET ASTRONAUTICA SINICA >

2021 , Vol. 42 >Issue S1: 726364 - 726364

DOI: https://doi.org/10.7527/S1000-6893.2021.26364

Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer

CHEN Chongpei ,
LIANG Jianhan ,
GUAN Qingdi ,
GAO Tianyun

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1. Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
2. International Studies College, National University of Defense Technology, Nanjing 210039, China

Received date: 2021-09-01

Revised date: 2021-09-14

Online published: 2021-10-09

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Abstract

The One-Dimensional Turbulence (ODT) method is a turbulence modeling method that follows the basic physical laws of turbulence in the one-dimensional computational domain. The statistical laws of turbulence can be accurately captured in the one-dimensional computational domain by combining deterministic and stochastic solving methods, and modeling in the reduced dimension can significantly reduce the amount of computation. The ODT method is widely used in the study of incompressible turbulence and turbulent combustion, but needs to be further improved to simulate high-speed compressible turbulent flows. Different from the incompressible ODT method, in this paper, the dependent variables are changed from the original variables to the conservative fluxes based on the Euler reference frame, which is beneficial to reducing the error of compressible turbulence simulation. A component solution module is also proposed in this research. A conservative compressible ODT method capable of simulating scalar mixing is developed by further improving both deterministic and stochastic solving modules in a corresponding manner. In the deterministic module, the one-dimensional truncated governing equations solved are adjusted as the ones with conservative fluxes as dependent variables, and the triplet mapped object is correspondingly changed from the original variables to the conservative fluxes, and simultaneously the kernel transformation with two kernels is selected to ensure momentum conservation for variable density when one-dimensional eddies are constructed in the stochastic module. The accuracy of the method for capturing scalar mixing in the compressible shear turbulent field was verified by simulating the spatially developing supersonic plane turbulent mixing layer and comparing the results of the self-similar stage with the experimental results. The mean profile and the fluctuation intensity profile of velocity field and component field captured by the method proposed are in excellent agreement with experimental results. The accuracy of the proposed method is obviously better than that of the Large Eddy Simulation with the Gradient Diffusion sub-grid closure (LES-GRAD.DIFF.) and that of the Large Eddy Simulation coupled with the Linear Eddy Mixing (LEM) model (LES-LEM), and the dimensionality reduction of the method proposed gives it a significant advantage in reducing computational cost.

Key words： One-Dimensional Turbulence (ODT); compressible turbulent flow; numerical simulation; conservative; mixing layer; scalar mixing

Cite this article

CHEN Chongpei , LIANG Jianhan , GUAN Qingdi , GAO Tianyun . Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021 , 42(S1) : 726364 -726364 . DOI: 10.7527/S1000-6893.2021.26364

References

[1] SANKARAN V, MENON S. LES of scalar mixing in supersonic mixing layers[J]. Proceedings of the Combustion Institute, 2005, 30(2): 2835-2842.
[2] KERSTEIN A R. One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows[J]. Journal of Fluid Mechanics, 1999, 392: 277-334.
[3] KERSTEIN A R, ASHURST W T, WUNSCH S, et al. One-dimensional turbulence: Vector formulation and application to free shear flows[J]. Journal of Fluid Mechanics, 2001, 447: 85-109.
[4] ASHURST W T, KERSTEIN A R. One-dimensional turbulence: Variable-density formulation and application to mixing layers[J]. Physics of Fluids, 2005, 17(2): 025107.
[5] RAKHI, KLEIN M, MEDINA M J A, et al. One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS[J]. Journal of Turbulence, 2019, 20(8): 506-543.
[6] RAKHI, SCHMIDT H. One-dimensional turbulence: Application to incompressible spatially developing turbulent boundary layers[J]. International Journal of Heat and Fluid Flow, 2020, 85: 108626.
[7] ECHEKKI T, KERSTEIN A R, DREEBEN T D, et al. ‘One-dimensional turbulence’ simulation of turbulent jet diffusion flames: model formulation and illustrative applications[J]. Combustion and Flame, 2001, 125(3): 1083-1105.
[8] RANGANATH B, ECHEKKI T. One-dimensional turbulence-based closure with extinction and reignition[J]. Combustion and Flame, 2008, 154(1-2): 23-46.
[9] ECHEKKI T, GUPTA K G. Hydrogen autoignition in a turbulent jet with preheated co-flow air[J]. International Journal of Hydrogen Energy, 2009, 34(19): 8352-8377.
[10] AN J T, JIANG Y, YE M J, et al. One-dimensional turbulence simulations and chemical explosive mode analysis for flame suppression mechanism of hydrogen/air flames[J]. International Journal of Hydrogen Energy, 2013, 38(18): 7528-7538.
[11] MOVAGHAR A, LINNE M, OEVERMANN M, et al. Numerical investigation of turbulent-jet primary breakup using one-dimensional turbulence[J]. International Journal of Multiphase Flow, 2017, 89: 241-254.
[12] FISTLER M, KERSTEIN A, LIGNELL D O, et al. Turbulence modulation in particle-laden stationary homogeneous isotropic turbulence using one-dimensional turbulence[J]. Physical Review Fluids, 2020, 5(4): 044308.
[13] ECHEKKI T, GUPTA K G. Hydrogen autoignition in a turbulent jet with preheated co-flow air[J]. International Journal of Hydrogen Energy, 2009, 34(19): 8352-8377.
[14] GUPTA K G, ECHEKKI T. One-dimensional turbulence model simulations of autoignition of hydrogen/carbon monoxide fuel mixtures in a turbulent jet[J]. Combustion and Flame, 2011, 158(2): 327-344.
[15] GOWDA B D, ECHEKKI T. One-dimensional turbulence simulations of hydrogen-fueled HCCI combustion[J]. International Journal of Hydrogen Energy, 2012, 37(9): 7912-7924.
[16] LIGNELL D O, RAPPLEYE D S. One-dimensional-turbulence simulation of flame extinction and reignition in planar ethylene jet flames[J]. Combustion and Flame, 2012, 159(9): 2930-2943.
[17] 蒋勇, 邱榕, 董刚, 等. 基于一维全尺度湍流模型的氢气射流扩散火焰结构数值模拟[J]. 燃烧科学与技术, 2006, 12(5): 401-407. JIANG Y, QIU R, DONG G, et al. One-dimensional turbulence simulation of diffusion flame in a hydrogen-air jet with detailed chemistry[J]. Journal of Combustion Science and Technology, 2006, 12(5): 401-407(in Chinese).
[18] WU S H, QIU R, JIANG Y. Local extinction and reignition in non-premixed turbulent jet H₂/N₂ diffusion flames[J]. 燃烧科学与技术, 2007, 13(4): 347-354. WU S H, QIU R, JIANG Y. Local extinction and reignition in non-premixed turbulent jet H₂/N₂ diffusion flames[J]. Journal of Combustion Science and Technology, 2007, 13(4): 347-354(in Chinese).
[19] 卓丽颖, 蒋勇, 徐武, 等. 湍流射流C₃H₈/H₂/air扩散火焰中的局部熄火和再燃现象[J]. 火灾科学, 2014, 23(2): 85-91. ZHUO L Y, JIANG Y, XU W, et al. Local extinction and reignition in nonpremixed turbulent jet C₃H₈/H₂/air diffusion flames[J]. Fire Safety Science, 2014, 23(2): 85-91(in Chinese).
[20] WANG L, JIANG Y, PAN L W, et al. Lagrangian investigation and chemical explosive mode analysis of extinction and re-ignition in H₂/CO/N₂ syngas non-premixed flame[J]. International Journal of Hydrogen Energy, 2016, 41(8): 4820-4830.
[21] 蒋勇, 邱榕, 张和平. 融合湍流燃烧信息实现燃料反应机理简化的方法: 中国, CN101900349A[P]. 2010-12-01. JIANG Y, QIU R, ZHANG H P. A method for simplify-ing fuel reaction mechanism by integrating turbulent combustion information: China, CN101900349A[P]. 2010-12-01(in Chinese).
[22] 吴玉新, 仇晓龙, 张大龙, 等. 采用一维湍流模型对瞬态煤粉气化火焰的数值模拟[J]. 工程热物理学报, 2012, 33(9): 1619-1622. WU Y X, QIU X L, ZHANG D L, et al. Numerical simulation of instantaneous coal gasification flames with one dimension turbulence model[J]. Journal of Engineering Thermophysics, 2012, 33(9): 1619-1622(in Chinese).
[23] 仇晓龙, 吴玉新, 张海, 等. 一维湍流模型对He平面羽流和CH₄/H₂/N₂射流火焰的数值模拟[J]. 工程热物理学报, 2012, 33(6): 1073-1076. QIU X L, WU Y X, ZHANG H, et al. Simulation of He plumes and CH₄/H₂/N₂ flames with one dimensional turbulence model[J]. Journal of Engineering Thermophysics, 2012, 33(6): 1073-1076(in Chinese).
[24] JOZEFIK Z, KERSTEIN A R, SCHMIDT H. Simulation of shock-turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence[J]. Combustion and Flame, 2016, 164: 53-67.
[25] ANDERSON J D .计算流体力学入门[M].姚朝晖, 周强, 译. 北京: 清华大学出版社, 2010: 65-72. ANDERSON J D. Computational fluid dynamics: The basics with applications[M].YAO Z H, ZHOU Q, translated. Beijing: Tsinghua University Press, 2010: 65-72(in Chinese).
[26] SCHMIDT R C, KERSTEIN A R, WUNSCH S, et al. Near-wall LES closure based on one-dimensional turbulence modeling[J]. Journal of Computational Physics, 2003, 186(1): 317-355.
[27] MCDERMOTT R. Toward one-dimensional turbulence subgrid closure for large-eddy simulation[D].Salt lake City: The University of Utah, 2005: 55-66.
[28] HOFFIE A F, ECHEKKI T. A coupled LES-ODT model for spatially-developing turbulent reacting shear layers[J]. International Journal of Heat and Mass Transfer, 2018, 127: 458-473.
[29] CAO S F. A novel hybrid scheme for large-eddy simulation of turbulent combustion based on the one-dimensional turbulence model[D].Raleigh: North Carolina State University, 2006
[30] CAO S F, ECHEKKI T. A low-dimensional stochastic closure model for combustion large-eddy simulation[J]. Journal of Turbulence, 2008, 9: N2.
[31] RANGANATH B, ECHEKKI T. One-dimensional turbulence-based closure with extinction and reignition[J]. Combustion and Flame, 2008, 154(1-2): 23-46.
[32] ECHEKKI T, PARK J. The LES-ODT model for turbulent premixed flames[C]//48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston: AIAA, 2010.
[33] PARK J, ECHEKKI T. LES-ODT study of turbulent premixed interacting flames[J]. Combustion and Flame, 2012, 159(2): 609-620.
[34] 高天运. 基于ODT模型的可压缩湍流建模与数值模拟方法研究[D].长沙: 国防科技大学, 2019: 72-118. GAO T Y. A study of modeling and simulation methods for compressible turbulent flows based on one-dimensional turbulence[D].Changsha: National University of Defense Technology, 2019: 72-118(in Chinese).
[35] 张兆顺, 崔桂香, 许春晓. 湍流理论与模拟[M].北京:清华大学出版社, 2005: 116-118. ZHANG Z S, CUI G X, XU C X. Theory and Modeling of Turbulence[M].Beijing: Tsinghua University Press, 2005: 116-118(in Chinese).
[36] CLEMENS N T, MUNGAL M G. Large-scale structure and entrainment in the supersonic mixing layer[J]. Journal of Fluid Mechanics, 1995, 284: 171-216.
[37] HILL D J, PANTANO C, PULLIN D I. Large-eddy simulation and multiscale modelling of a Richtmyer-Meshkov instability with reshock[J]. Journal of Fluid Mechanics, 2006, 557: 29-61.

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