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Compressible turbulent channel and pipe flow: similarities and differences

Published online by Cambridge University Press:  07 April 2010

SOMNATH GHOSH ,
HOLGER FOYSI  and
RAINER FRIEDRICH
SOMNATH GHOSH
Affiliation:
Lehrstuhl für Aerodynamik, TU München, Boltzmannstrasse 15, D-85748, Garching, Germany
HOLGER FOYSI
Affiliation:
Aerodynamisches Institut, RWTH Aachen, Wuellnerstrasse 5a, D-52062, Aachen, Germany
RAINER FRIEDRICH*
Affiliation:
Lehrstuhl für Aerodynamik, TU München, Boltzmannstrasse 15, D-85748, Garching, Germany
*
†Email address for correspondence: r.friedrich@lrz.tum.de
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Abstract

Direct numerical simulation (DNS) is used to explore similarities and differences between fully developed supersonic turbulent plane channel and axisymmetric non-swirling pipe flow bounded by isothermal walls. The comparison is based on equal friction Mach number, friction Reynolds number, Prandtl number, ratio of specific heats and viscosity exponent. The channel half-width and pipe radius are chosen to define the Reynolds numbers. To what extent and why mean flow quantities, second-order turbulence statistics and terms in the Reynolds stress equations coincide or diverge in both flows are investigated. The role of the fluctuating pressure in causing characteristic differences among correlations involving pressure fluctuations is identified via a Green-function-based analysis of the pressure field.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 648 , 10 April 2010 , pp. 155 - 181
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Abe, H., Kawamura, H. & Choi, H. 2004 Very large-scale structures and their effects on the wall shear-stress fluctuations in turbulent channel flow upto Re τ = 640. ASME J. Fluids Engng 126, 835–843.CrossRefGoogle Scholar
Adams, N. A. & Shariff, K. 1996 A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comput. Phys. 127, 27–51.CrossRefGoogle Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. J. Wiley and Sons.Google Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–52.CrossRefGoogle Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, F. & Sarkar, S. 2002 Variable Density Fluid Turbulence. Kluwer Academic Press.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1976 A critical compilation of compressible turbulent boundary layer data. AGARDograph 223.Google Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207–216.CrossRefGoogle Scholar
Gatski, T. B. & Bonnet, J. P. 2009 Compressibility, Turbulence and High Speed Flow. Elsevier.Google Scholar
Ghosh, S., Sesterhenn, J. & Friedrich, R. 2008 Large-eddy simulation of supersonic turbulent flow in axisymmetric nozzles and diffusers. Intl J. Heat Fluid Flow 29, 579–590.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521–542.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.CrossRefGoogle ScholarPubMed
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.CrossRefGoogle Scholar
Kline, S. J., Cantwell, B. J. & Lilley, G. M. 1982 Proceedings of the 1980–81 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flows, vol. 1. Department of Mechanical Engineering, Stanford University.Google Scholar
Lechner, R., Sesterhenn, J. & Friedrich, R. 2001 Turbulent supersonic channel flow. J. Turbul. 2, 1–25.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Lele, S. K. 1994 Compressibiliy effects on turbulence. Annu. Rev. Fluid Mech. 26, 211–254.CrossRefGoogle Scholar
Mohseni, K. & Colonius, T. 2000 Numerical treatment of polar coordinate singularities. J. Comput. Phys. 157, 787–795.CrossRefGoogle Scholar
Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.CrossRefGoogle Scholar
Nickels, T. B. 2004 Inner scaling of wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217–239.CrossRefGoogle Scholar
Nieuwstadt, F. T. M. & Bradshaw, P. 1997 Similarities and differences of turbulent boundary layer, pipe and channel flow. In Boundary Layer Separation in Aircraft Aerodynamics (ed. Henkes, R. A. W. M. & Bakker, P. G.), pp. 15–22. Delft University Press.Google Scholar
Schlichting, H. 1968 Boundary-Layer Theory, 6th edn. McGraw-Hill.Google Scholar
Sesterhenn, J. 2001 A characteristic-type formulation of the Navier–Stokes equations for high order upwind schemes. Comput. Fluids 30, 37–67.CrossRefGoogle Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow, 2nd edn. Springer.Google Scholar
Stakgold, I. 1979 Green's Functions and Boundary Value Problems. Wiley Interscience.Google Scholar
Williamson, J. K. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.CrossRefGoogle Scholar
Wosnik, M., Castillo, L. & George, W. K. 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115–145.CrossRefGoogle Scholar
Wu, X. & Moin, P. 2008 A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112.CrossRefGoogle Scholar