Abstract
The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.
Similar content being viewed by others
References
Fox DG, Orszag SA. Pseudospectral approximation to two-dimensional turbulence.J Comput Phys, 1973, 11: 612–619
Herring JR, Orszag SA, Kraichnan RH, Fox DG. Decay of two-dimensional homogeneous turbulence.J Fluid Mech, 1974, 66: 417–444
Fornberg B. A numerical study of 2-D turbulence.J Comput Phys, 1977, 25: 1–31
Hosokawa I, Yamamoto K. Intermittency exponents and generalized dimensions of a directly simulated fully developed turbulence.Phys Fluids A, 1990, 2(6): 889–892
Erlebacher G, Hussaini MY, Speziale CG, Zang TA. Toward the large-eddy simulation of compressible turbulent flows. NASA CR-178273. ICASE report No. 87-20, 1987
Clarke, JF. Small amplitude gasdynamic disturbances in an exploding atmosphere.J Fluid Mech, 1978, 89: 343
Klein R, Peters N. Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder.J Fluid Mech, 1988, 187: 197
Oran ES, Boris JP. Weak ans strong ignition. II. Sensitivity of the hudrogen-oxygen system.Combustion and Flame, 1982, 48: 149
Lutz AE, Kee RJ, Miller JA. The influence of pressure disturbances on spontaneous ignition. Combustion Institute Western States Meeting, 1987
Lutz AE, Kee RJ, Miller JA, Dwyer HA, Oppenheim AK. Dynamic effects of autoignition centers for hydrogen and C1,2-hydrocarbon fuels. In: Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA. 1987, 1683
Tsuge S, Sagara K. Arrhenius' law in turbulent media and an equivalent tunnel effect.Combust Sci Technol, 1978, 18: 179
Sagara K. Exact turbulence correction to Arrhenius' law in the asymptotic limit of high activation energy.Combust Sci Technol, 1980, 21: 191
Maas U, Warnatz J. Modeling of H2−O2 ignition by hot spots. In: Kuhl AL et al, Ed, Dynamics of Deflagrations and Reactive Systems: Flames, Progress in Astronautics and Aeronautics, AIAA, Washington DC, 1991, 131: 3
Ashurst WT, Barr PK. Stochastic calculation of laminar wrinkled flame propagation via vortex dynamics.Combust Sci Technol, 1983, 34: 227–256
Rutland CJ, Ferzieger JH, El Tahry SH. Full numerical simulations and modeling of turbulent premixed flames. In: Twenty-third Symposium (International) on Combustion, The Combustion Institute, 1990. 621–627
Poinsot T, Veynante D, Candel S. Diagrams of premixed turbulent combustion based on direct simulation. In: Twenty-third Symposium (International) on Combustion, The Combustion Institute, 1990. 613–619
Poinsot T, Veynante D, Candel S. Quenching precess and premixed turbulent combustion diagrams.J Fluid Mech, 1991, 228: 561–606
Shepherd IG, Ashurst WT. Flame front geometry in premixed turbulent flames. In: Twenty-fourth Symposium (International) on Combustion, The Combustion Institute, 1992. 485–491
Ashurst WT. Constant-density Markstein flamelet in Navier-Stokes turbulence.Combust Sci Technol, 1993
Haworth DC, Poinsot TJ. Numerical simulations of Lewis number effects in turbulent premixed flames.J Fluid Mech, 1992, 244: 405–436
Meadows KR, Kumar A, Hussaini MY. Computational study on the interaction between a vortex and a shock wave.AIAA J, 1991, 29: 174–179
Guichard L, Vervisch L, Domingo P. Numerical study of the interaction between a mixing zone and a pressure discontinuity. AIAA paper 95-0877, Proceedings of AIAA 33rd Aerospace Science Meeting, 1995
Rotman D. Shock wave effects on a turbulent flow.Physics of Fluids A, 1991, 3: 1792–1806
Lee S, Lele SK, Moin P. Direct numerical simulation of isotropic turbulence interacting with a weak shock wave.J Fluid Mech, 1993, 251: 533–562
Hannappel R, Freidrich R. DNS of aM=2 shock interacting with isotropic turbulence. In: Proceedings of First ERCOFTAC Workshop on DNS and LES, 1994
Canuto C, Hussaini MY, Quarteroni A, Zang TA. Spectral Methods in Fluid Dynamics. Springer-Verlag, 1987
Hussaini MY, Kopriva DA, Salas MD, Zang TA. Spectral methods for the Euler equations: Part I—Fourier methods and shock capturing.AIAA J, 1985, 23: 64–70
Wang JP, Nakamura Y, Yasuhara M. A Chebyshev collocation method for the compressible Navier-Stokes equations in generalized coordinates.Transactions of the Japan Society for Aeronautical and Space Sciences, 1990, 33 (101): 120–134
Wang JP, Nakamura Y, Yasuhara M. Several improvements of spectral method in compressible flow calculation. In: Proc Int Sympo on Computational Fluid Dynamics, Nagoya, 1989. 1210–1215
Wang JP. Non-periodic Fourier transform and finite spectral method. In: Proc 6th Int Sympo on Computational Fluid Dynamics, Lake Tahoe, 1995. 1339–1344
Hasegawa T, Yoshinari H, Wang JP, Jounouchi T, Yamaguchi S. Direct numerical simulations of compressible homogeneous turbulence. In: Proc 4th Sympo on Computational Fluid Dynamics, 1990. 375–378
Hasegawa T, Noguchi S, Nakamura T, Kuchida M, Yamaguchi S. Direct numerical simulation of compressible turbulence and its application. In: Proc 6th Sympo on Computational Fluid Dynamics, 1992. 321–324
Hasegawa T, Arai A, Kadowaki S, Wang JP, Jounouchi T, Yamaguchi S. Direct numerical analysis of autoignition of a turbulent premixed gas. In: Proc 28th Sympo on Combustion, 1990. 284–286
Hasegawa T, Arai A, Kadowaki S, Yamaguchi S. Autoignition of a turbulent premixed gas.Combust Sci and Tech, 1992, 84: 1–13
Arai A, Hasegawa T, Kadowaki S, Wang JP, Jounouchi T, Yamaguchi S. Direct numerical simulation of autoignition process in a turbulent premixed gas. In: Proc 4th Sympo on Computational Fluid Dynamics, 1990. 657–660
Borghi R. On the structure and morphology of turbulent premixed flames. In: Casci C ed. Recent Advances in the Aerospace Sciences. Plenum Publishing Co., 1985. 117–138
Peters N. Length and time scales in turbulent combustion. In: Borghi R and Murthy SBN, eds. Turbulent Reactive Flows. Springer-Verlag, 1989. 242–256
Hasegawa T, Yamaguchi S, Wang JP, Jounouchi T. Propagation of premixed flames in vortical flows. In: Proc 27th Sympo on Combustion, 1989. 49–51
Hasegawa T, Kuchita M, Yamaguchi S. Interaction of premixed flames with high-intensity two-dimensional turbulence.Combust Sci and Tech (Japanese language companion publication), 1994, 2: 77–87
Hasegawa T, Noguchi S. Numerical study on a turbulent flow compressed by a weak shock wave.Int J Comput Fluid Dynamics, 1997, 8: 63–75
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jianping, W., Hasegawa, T. Numerical simulation on compressible turbulence by spectral method. Acta Mech Sinica 14, 193–207 (1998). https://doi.org/10.1007/BF02487754
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487754