ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Probability density function method in general curvilinear coordinate system and its application in supersonic combustion
Received date: 2021-11-19
Revised date: 2021-12-10
Accepted date: 2022-01-19
Online published: 2022-01-26
Supported by
National Natural Science Foundation of China(91641201)
The transported Probability Density Function （PDF） method can accurately solve turbulence/chemical reaction interactions， and can be used as a reliable computational model for complex supersonic turbulent combustion simulations in scramjet engines. At present， research on the PDF method for the supersonic flow is mostly confined to simple configuration， which seriously limits its application in practical supersonic combustion. The objective of this paper is to develop a curvilinear PDF method based on multi-block structured grids， which is applicable to the simulation of real supersonic combustion problems with complex configurations. The PDF equations and stochastic differential equations in curvilinear coordinates are derived， and the PDF method in a general curvilinear coordinate system and its numerical solution framework are established. A method for particle tracking in curvilinear coordinates on the multi-block structural grid is proposed. The topological information between multiple grid blocks is used for particle local coordinate transformation and communication， which solves the problem of inconsistency between particle local coordinates and global coordinates in curvilinear coordinates. Continuous tracking of particles on the global grid is successfully achieved. The accuracy of the curvilinear coordinate method and model is verified by comparing the results with the exact solution and direct numerical simulations in the one-dimensional shock tube and two-dimensional temporal mixing layer. The ability of the method to handle complex configurations is further tested in the simulations of the flow around a two-dimensional cylinder and a three-dimensional spherical blunt. Finally， numerical simulation of a typical supersonic coaxial jet flame is carried out， and the numerical results are quantitatively compared with the experimental results. The comparison results show that the predicted reaction components are in good agreement with those obtained in the experiment， which comprehensively verifies the applicability and accuracy of the PDF method in the general curvilinear coordinate system in actual supersonic combustion problems.
Qingdi GUAN , Jianhan LIANG , Lin ZHANG , Wenwu CHEN , Yuqiao CHEN . Probability density function method in general curvilinear coordinate system and its application in supersonic combustion[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(4) : 126677 -126677 . DOI: 10.7527/S1000-6893.2022.26677
| 1 | 杨越， 游加平， 孙明波. 超声速燃烧数值模拟中的湍流与化学反应相互作用模型［J］. 航空学报， 2015， 36（1）： 261-273. |
| YANG Y， YOU J P， SUN M B. Modeling of turbulence-chemistry interactions in numerical simulations of supersonic combustion［J］. Acta Aeronautica et Astronautica Sinica， 2015， 36（1）： 261-273 （in Chinese）. | |
| 2 | 许爱国， 单奕铭， 陈锋， 等. 燃烧多相流的介尺度动理学建模研究进展［J］. 航空学报， 2021， 42（12）： 625842. |
| XU A G， SHAN Y M， CHEN F， et al. Progress of mesoscale modeling and investigation of combustion multiphase flow［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（12）： 625842 （in Chinese）. | |
| 3 | PIERCE C D， MOIN P. Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion［J］. Journal of Fluid Mechanics， 2004， 504： 73-97. |
| 4 | BERGLUND M， FEDINA E， FUREBY C， et al. Finite rate chemistry large-eddy simulation of self-ignition in supersonic combustion ramjet［J］. AIAA Journal， 2010， 48（3）： 540-550. |
| 5 | KERSTEIN A R. A linear-eddy model of turbulent scalar transport and mixing［J］. Combustion Science and Technology， 1988， 60（4-6）： 391-421. |
| 6 | 陈崇沛， 梁剑寒， 关清帝， 等. 守恒型可压缩一维湍流方法及其在超声速标量混合层中的应用［J］. 航空学报， 2021， 42（S1）： 726364. |
| CHEN C P， LIANG J H， GUAN Q D， et al. Conservative compressible one-dimensional turbulence method and its application in supersonic scalar mixing layer［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（S1）： 726364 （in Chinese）. | |
| 7 | POPE S B. PDF methods for turbulent reactive flows［J］. Progress in Energy and Combustion Science， 1985， 11（2）： 119-192. |
| 8 | PANT T， JAIN U， WANG H F. Transported PDF modeling of compressible turbulent reactive flows by using the Eulerian Monte Carlo fields method［J］. Journal of Computational Physics， 2021， 425： 109899. |
| 9 | GIVI P. Model-free simulations of turbulent reactive flows［J］. Progress in Energy and Combustion Science， 1989， 15（1）： 1-107. |
| 10 | POPE S B. Computations of turbulent combustion： progress and challenges［J］. Symposium （International） on Combustion， 1991， 23（1）： 591-612. |
| 11 | GAO F， O'BRIEN E E. A large-eddy simulation scheme for turbulent reacting flows［J］. Physics of Fluids A： Fluid Dynamics， 1993， 5（6）： 1282-1284. |
| 12 | JAISHREE J. Lagrangian and Eulerian probability density function methods for turbulent reacting flows ［D］. State College： Pennsylvania State University， 2011. |
| 13 | YANG Y， WANG H F， POPE S B， et al. Large-eddy simulation/probability density function modeling of a non-premixed CO/H2 temporally evolving jet flame［J］. Proceedings of the Combustion Institute， 2013， 34（1）： 1241-1249. |
| 14 | JABERI F A， COLUCCI P J， JAMES S， et al. Filtered mass density function for large-eddy simulation of turbulent reacting flows ［J］. Journal of Fluid Mechanics， 1999， 401： 85-121. |
| 15 | BANAEIZADEH A， LI Z R， JABERI F A. Compressible scalar filtered mass density function model for high-speed turbulent flows［J］. AIAA Journal， 2011， 49（10）： 2130-2143. |
| 16 | KOMPERDA J， GHIASI Z， LI D R， et al. Simulation of the cold flow in a ramp-cavity combustor using a DSEM-LES/FMDF hybrid scheme［C］∥54th AIAA Aerospace Sciences Meeting. Reston： AIAA， 2016. |
| 17 | ZHANG L， LIANG J H， SUN M B， et al. An energy-consistency-preserving large eddy simulation-scalar filtered mass density function （LES-SFMDF） method for high-speed flows［J］. Combustion Theory and Modelling， 2018， 22（1）： 1-37. |
| 18 | ZHANG L， LIANG J H， SUN M B， et al. A conservative and consistent scalar filtered mass density function method for supersonic flows［J］. Physics of Fluids， 2021， 33（2）： 026101. |
| 19 | VALIDI A， SCHOCK H， JABERI F. Turbulent jet ignition assisted combustion in a rapid compression machine［J］. Combustion and Flame， 2017， 186： 65-82. |
| 20 | RANADIVE H D. High-order compressible formulation for LES/PDF simulations of turbulent reacting flows［D］. Sydney： University of New South Wales， 2019. |
| 21 | CHENG T S， WEHRMEYER J A， PITZ R W， et al. Raman measurement of mixing and finite-rate chemistry in a supersonic hydrogen-air diffusion flame［J］. Combustion and Flame， 1994， 99（1）： 157-173. |
| 22 | ABDULRAHMAN H， VALIDI A， JABERI F. Large-eddy simulation/filtered mass density function of non-premixed and premixed colorless distributed combustion［J］. Physics of Fluids， 2021， 33（5）： 055118. |
| 23 | YOSHIZAWA A， HORIUTI K. A statistically-derived subgrid-scale kinetic energy model for the large-eddy simulation of turbulent flows［J］. Journal of the Physical Society of Japan， 1985， 54（8）： 2834-2839. |
| 24 | LI P B， LI C Y， WANG H B， et al. Distribution characteristics and mixing mechanism of a liquid jet injected into a cavity-based supersonic combustor［J］. Aerospace Science and Technology， 2019， 94： 105401. |
| 25 | LIU C Y， SUN M B， WANG H B， et al. Ignition and flame stabilization characteristics in an ethylene-fueled scramjet combustor［J］. Aerospace Science and Technology， 2020， 106： 106186. |
| 26 | SHU C W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws： NASA/CR-97-206253［R］. Washington， D.C.： NASA， 1997. |
| 27 | GIKHMAN I I， SKOROKHOD A V. The theory of stochastic processes III［M］. Berlin， Heidelberg： Springer， 2007. |
| 28 | WANG H F， POPOV P P， POPE S B. Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations［J］. Journal of Computational Physics， 2010， 229（5）： 1852-1878. |
| 29 | EVANS J， SCHEXNAYDER C J， BEACH H. Application of a two-dimensional parabolic computer program to prediction of turbulent reacting flows： NASA-TP-1169［R］. Washington， D.C.： NASA， 1978. |
| 30 | LIU C Y， WANG N， YANG K， et al. Large eddy simulation of a supersonic lifted jet flame in the high-enthalpy coflows［J］. Acta Astronautica， 2021， 183： 233-243. |
| 31 | CONAIRE M ó， CURRAN H J， SIMMIE J M， et al. A comprehensive modeling study of hydrogen oxidation［J］. International Journal of Chemical Kinetics， 2004， 36（11）： 603-622. |
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