Research on the Correlation of the Fluctuating Density Gradient of the Compressible Flows

Authors: Yasuo Obikane

Abstract:

This work is to study a roll of the fluctuating density gradient in the compressible flows for the computational fluid dynamics (CFD). A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups: group proportional to the mean velocity, and that proportional to the mean strain rate, and that proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vorticity in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.

Keywords: Turbulence Modeling , Density Gradient Correlation, Compressible

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081077

References:

[1] SPEZIALE,C.G.1991 "Analytical Methods for the development of Reynolds stress closure in Turbulence Annual Review of Fluid MechanicsVOL. 23.pp107-57.
[2] LIGHTHILL,M.J 1952 On Sound Generated Aerodynamically Proc.Roy.Soc(London) VOL.A 211.
[3] COLEMAN,B.D., AND NOLL, W. 1960 Arch. Rat. Mech. and Anal. VOL.6 pp355
[4] OBIKANE, Y.1984 A numerical Computation of the Reynolds Stress in Supersonic Inlet Flows AIAA Paper,AIAA-84-1364
[5] OBIKANE, Y.1983 Numerical Computation of turbulent flow Around the spinner of a Turbofan Engine 13th International Symposium on air breathing engine,paris.
[6] OBIKANE, Y.1979 Turbulence Modeling in Homogeneous Flows: Determination of the Rapid Terms Ph.D.Dessertation,Cornell University
[7] MARGNAT, F & FORTUNE, V & JORDAN, P. & GERVAIS, Y2008 Analysis of free-shear flow noise through a decomposition of the Lighthill source term,5TH INTERNATIONAL CONFERENCE OF CFDSeul,Koria
[8] POPE, S. B.2000 Turbulent Flows,Cambridge University Press, Appendix B
[9] Obikane,Y. Kuwahara,K. Direct Simulation for Acoustic near Fields Using the Compressible Navier-Stokes Equation", ICCDF5(2008)-181, Splinger Verlag(2009.7 published)
[10] Obikane,Y."Aeroacoustic Simulation in Automobile Muffler by using the Exact Compressible Navier-Stokes Equation " ,ICCDF5(2008)-182 Splinger Verlag(2009.7 published)