Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T12:47:18.178Z Has data issue: false hasContentIssue false
  • English
  • Français

A Pdf Description of Momentum Fluctuation Correlations of a Rarefied Free Shear Layer

Published online by Cambridge University Press:  05 May 2011

Z.-C. Hong ,
C.-E. Zhen  and
C.-Y. Yang
Z.-C. Hong*
Affiliation:
Department of Mechanical and Electro-Mechanical Engineering, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
C.-E. Zhen*
Affiliation:
Department of Mechanical Engineering, National Central University, Chungli, Taiwan 32054, R.O.C.
C.-Y. Yang*
Affiliation:
Department of Mechanical Engineering, National Central University, Chungli, Taiwan 32054, R.O.C.
*
*Professor
**Graduate student
*Professor
Get access

Abstract

The mixing properties of various orders of fluctuation correlations are investigated in the present paper for a rarefied gas free shear layer at hypersonic speed. The molecular kinetic theory and the direct simulation Monte Carlo (DSMC) method are employed for the present calculations. The Reynolds average process is assumed in obtaining the correlation functions. The results show that flow field structure was very similar to that of continuum flow ones at high Reynolds numbers. The probability density functions (pdf) in velocity space f(u′),f(v′), and f(u′, v′) are also calculated to counter explain the distributions of the correlation functions in the mixing layer. From the calculated distributions of the fluctuation correlation functions, <u′v′>, <u′2v′>, and <v′2u′>, one can find that the distributions behave similar to the turbulent transport phenomena in that of a continuum flow one. The distributions of the fluctuation correlation functions, <u′, v′> is described via the joint probability density function, f(u′, v′). The behavior of the higher-order fluctuation correlation functions, <u′2v′>, <u′3> and <u′4 >, are also explained via the probability density function.

Keywords

DSMCFree shear layerPDFFluctuation correlation function.
Type
Articles
Information
Journal of Mechanics , Volume 22 , Issue 2 , June 2006 , pp. 85 - 92
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Tollmien, W., “Berechnung Turbulenter Ausbreitungsvorgange,” Zeitschrigt Fur Angewandte Mathematik Und Mechanik, 6, pp.468–478 (1926).CrossRefGoogle Scholar
2.Gortier, H., “Brechnung Von Aufgaben Der Freien Turbulenz Auf Grund Eines Neuen Naherungsansatzes,” Zeitschrigt Fur Angewandte Mathematik Und Mechanik, 22, pp. 244–254 (1942).CrossRefGoogle Scholar
3.Lee, S. C. and Harsha, P. T., “Use of Turbulent Kinetic Energy in Free Mixing Studies,” AIAA J., 8, pp. 1026–1032 (1970).CrossRefGoogle Scholar
4.Spencer, B. W. and Jones, B. C., “Statistical Investigation of Pressure and Velocity Fields in the Turbulent Two-Stream Mixing Layer,” AIAA Paper 71–613 (1971).Google Scholar
5.Hong, Z. C., “Turbulent Reacting Flows According to a Kinetic Theory,” Ph.D. Dissertation, Dept. of Mechanical Engineering, The University of, Illinois U.S.A. (1975).Google Scholar
6.Jones, I. S. F., “The Maintenance of Turbulent Shear Stress in a Mxing Layer,” J. Fluid Mech., 74, pp. 269–295 (1976).CrossRefGoogle Scholar
7.Mohammadian, S., Saiy, M. and Peorless, S. J., “Fluid Mixing with Unequal Free-Stream Turbulence Intensities,” J. Fluids Eng.-Trans. ASME, 98, pp. 229–242 (1976).CrossRefGoogle Scholar
8.Batt, R. G., “Turbulent Mixing of Passive and Chemically Reacting Species in a Low-speed Shear Layer,” J. Fluid Mech., 82, pp. 53–95 (1977).CrossRefGoogle Scholar
9.Bywater, R. J., “Velocity Space Description of Certain Turbulent Free Shear Flow Characteristics,” AIAA J., 19, pp. 969–975 (1981).CrossRefGoogle Scholar
10.Hong, Z. C. and Lai, Z. C., “On the Mixing Analysis of a Free Turbulence Shear Layer,” The Chinese Journal of Mechanics, 1, pp. 25–33 (1983).Google Scholar
11.Haworth, D. C. and Pope, S. B., “A Generalized Langevin Model for Turbulent Free Shear Flows,” Phys. Fluids, 29, pp. 387–405 (1986).CrossRefGoogle Scholar
12.Hong, Z. C. and Chen, M. H., “Statistical Model of a Self-Similar Turbulent Plane Shear Layer,” J. Fluids Eng.-Trans. ASME, 120, pp. 263–273 (1998).CrossRefGoogle Scholar
13.Sandham, N. D. and Reynold, W. C., “Compressible Mixing Layer: Linear Theory and Direct Simulation,” AIAA J., 28, pp. 618–624 (1990).CrossRefGoogle Scholar
14.Tang, W., Komerath, N. M. and Sankar, L. N., “Numerical Simulation of the Growth of Instabilities in Supersonic Free Shear Layers,” J. Propulsion Power, 6, pp. 455–460 (1990).CrossRefGoogle Scholar
15.Drummond, J. P., Carpenter, M. H. and Riggins, D. W., “Mixing and Mixing Enhancement in Supersonic Reacting Flowfields,” Proc. in Astronautics and Aeronautics, High-Speed Flight Propulsion Systems, Murthy, S. N. B. and Curran, E. T., eds., 125137, pp. 383–455 (1991).Google Scholar
16.Chinzei, N., Masuya, G., Komuro, T., Murakami, A. and Kudou, K., “Spreading of Two-Stream Supersonic Turbulent Mixing Layers,” Phys. Fluids, 29, pp. 1345–1347 (1986).CrossRefGoogle Scholar
17.Papamoschou, D. and Roshko, A., “The Compressible Turbulent Shear Layer: An Experimental Study,” J. Fluid Mech., 197, pp. 453–477 (1988).CrossRefGoogle Scholar
18.Goebel, S. G. and Dutton, J. C., “Experimental Study of Compressible Turbulent Mixing Layers,” AIAA J, 29, pp. 538–546 (1991).CrossRefGoogle Scholar
19.Elliott, G. S., Samimy, M. and Arnette, S. A., “Study of Compressible Mixing Layers Using Filtered Raylaigh Scattering Based Visualizations,” AIAA J., 30, pp. 2567–2569 (1992).CrossRefGoogle Scholar
20.Clemens, N. T. and Mungal, M. G., “Large-Scale Structure and Entrainment in the Supersonic Mixing Layer,” J. Fluid Mech., 284, pp. 171–216 (1995).CrossRefGoogle Scholar
21.Buttsworth, D. R., Morgan, R. G. and Jones, T. V., “A Gun Tunnel Investigation of Hypersonic Free Shear Layers in a Planar Duct,” J. Fluid Mech., 299, pp. 133–152 (1995).CrossRefGoogle Scholar
22.Bird, G. A., Molecular Gas Dynamics and the Direct Simulation of Gas Flow, Clarenden Press, Oxford, UK (1994).CrossRefGoogle Scholar
23.Bird, G. A., “Approach to Translational Equilibrium in a Rigid Sphere Gas,” Phys. Fluids, 6, pp. 1518–1519 (1963).CrossRefGoogle Scholar
24.Bird, G. A., Molecular Gas Dynamics, Clarenden Press, Oxford, UK (1976).Google Scholar
25.Bird, G. A., “Monte Carlo Simulation of Gas Flows,” Ann. Rev. Fluid Mech., 10, pp. 11–31 (1978).CrossRefGoogle Scholar
26.Muntz, E. P., “Rarefied Gas Dynamics,” Ann. Rev. Fluid Mech., 21, pp. 387–417 (1989).CrossRefGoogle Scholar
27.Cheng, H. K., “Perspectives on Hypersonic Viscous Flow Research,” Ann. Rev. Fluid Mech., 25, pp. 455–484 (1993).CrossRefGoogle Scholar
28.Cheng, H. K. and Emmanuel, G., “Perspectives on Hypersonic Nonequilibrium Flow,” AIAA J., 33, pp. 385–400 (1995).CrossRefGoogle Scholar
29.Bird, G. A., “Recent Advances and Current Challenges for DSMC,” Comput. Math. Appl., 35, pp. 1–14 (1998).CrossRefGoogle Scholar
30.Oran, E. S., Oh, C. K. and Cybyk, B. Z., “Direct Simulation Monte Carlo: Recent Advances and Applications,” Ann. Rev. Fluid Mech., 30, pp. 403–441 (1998).CrossRefGoogle Scholar
31.Nance, R. P., Hash, D. B. and Hassan, H. A., “Role of Boundary Conditions in Monte Carlo Simulation of Microelectromechanical Systems,” Journal of Thermophysics and Heat Transfer, 12, pp. 447–449 (1997).CrossRefGoogle Scholar
32.Fan, J. and Shen, C., “Statistical Simulation of Low-Speed Unidirectional Flows in Transitional Region,” Proc. 21st Int. Symp. on Rarefied Gas Dynamics, Marseilles, France (1998).Google Scholar
33.Cai, C. P., Boyd, I. D., Fan, J. and Candler, G. V., “Direct Simulation Methods for Low-Speed Microchannel Flows,” Journal of Thermophysics and Heat Transfer, 14, pp. 368–378 (2000).CrossRefGoogle Scholar
34.Bird, G. A., “The Velocity Distribution Function within a Shock Wave,” J. Fluid Mech., 30, pp. 479–487 (1967).CrossRefGoogle Scholar
35.Pham-Van-Diep, G., Erwin, D. and Muntz, E. P., “Nonequilibrium Molecular Motion in a Hypersonic Shock Wave,” Science, 245, pp. 624–626 (1989).CrossRefGoogle Scholar
36.Stefanov, S. K., Boyd, L. D. and Cai, C. P., “Monte Carlo Analysis of Macroscopic Fluctuations in Rarefied Hypersonic Flow Around a Cylinder,” Phys. Fluids, 12, pp. 1226–1239 (2000).CrossRefGoogle Scholar
37.Hong, Z. C., Fu, W. A. and Duh, W. C., “The Momentum Fluctuation Correlations in Rarefied Free Shear Layer,” Transactions of the Aeronautical Society of the Republic of China, 30, pp. 77–86 (1998).Google Scholar
38.Borgnakke, C. and Larsen, P. S., “Statistical Collision Model for Monte Carlo Simulation of Polyatomic Gas Mixture,” J. Comput. Phys., 18, pp. 405–420 (1975).CrossRefGoogle Scholar