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Interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows

Published online by Cambridge University Press:  14 February 2011

LIANG WEI  and
ANDREW POLLARD
LIANG WEI
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, ON K7L 3N6, Canada
ANDREW POLLARD*
Affiliation:
Department of Mechanical and Materials Engineering, Queen's University, Kingston, ON K7L 3N6, Canada
*
†Email address for correspondence: pollard@me.queensu.ca
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Abstract

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The interactions among pressure, density, vorticity and their gradients in compressible turbulent channel flows (TCF) are studied using direct numerical simulations (DNS). DNS of three isothermal-wall TCF for Mach number Ma = 0.2, 0.7, and 1.5, respectively are performed using a discontinuous Galerkin method (DGM). The Reynolds numbers of these three cases are ≈2800, based on the bulk velocity, bulk density, half channel width and dynamic viscosity at the wall. A high cross-correlation between density and spanwise vorticity occurs at y+≈4, which is coincident with the peak mean spanwise baroclinicity. The relationship between the spanwise baroclinicity and the correlation is analysed. The difference between the evolution of density and spanwise vorticity very near the wall is discussed. The transport equation for the mean product of density and vorticity fluctuations 〈ρ′ω′i〉 is presented and the distributions of terms in the 〈ρ′ω′z〉 transport equation indicate that the minima and maxima of the profiles are located around y+≈5. The connection between pressure gradients and vorticity fluxes for compressible turbulent flows with variable viscosity has been formulated and verified. High correlations (0.7–1.0) between pressure gradient and vorticity flux are found very close to the wall (y+<5). The correlation coefficients are significantly influenced by Ma and viscosity in this region. Turbulence advection plays an important role in destroying the high correlations between pressure gradient and vorticity flux in the region away from the wall (y+ > 5).

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent boundary layers Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 673 , 25 April 2011 , pp. 1 - 18
Copyright
Copyright © Cambridge University Press 2011. The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution-NonCommercial-ShareAlike licence <http://creativecommons.org/licenses/by-nc-sa/2.5/>. The written permission of Cambridge University Press must be obtained for commercial re-use.

References

REFERENCES

Andreopoulos, J. & Agui, J. H. 1996 Wall-vorticity flux dynamics in a two-dimensional turbulent boundary layer. J. Fluid Mech. 309, 45–84.CrossRefGoogle Scholar
Cockburn, B., Karniadakis, G. E. & Shu, C.-W. 2000 Discontinuous Galerkin Methods – Theory, Computation and Applications. Springer.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
Gad-El-Hak, M. 1990 Control of low-speed airfoil aerodynamics. AIAA J. 28 (9), 1537–1552.CrossRefGoogle Scholar
Karniadakis, G. E. & Sherwin, S. 2005 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford Science Publications.CrossRefGoogle Scholar
Koumoutsakos, P. 1999 Vorticity flux control for a turbulent channel flow. Phys. Fluids 11 (2), 248–250.CrossRefGoogle Scholar
Lee, C. & Kim, J. 2002 Control of viscous sublayer for drag reduction. Phys. Fluids 14 (7), 2523–2529.CrossRefGoogle Scholar
Lighthill, M. J. 1963 Introduction. Boundary Layer Theory. In Laminar Boundary Layers, chap. II Oxford University Press.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ ≈ 590. Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
Panton, R. L. 1984 Incompressible Flows. Wiley Interscience.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill Book Company.Google Scholar
Wei, L. 2009 Direct numerical simulation of compressible and incompressible wall bounded turbulent flows with pressure gradients. PhD thesis, Queen's University, Kingston, ON, Canada.Google Scholar
Wei, L. & Pollard, A. 2010 Direct numerical simulation of compressible turbulent channel flows using discontinuous Galerkin method. Comput. Fluids (Tentatively accepted).CrossRefGoogle Scholar
Wu, J. Z. & Wu, J. M. 1998 Boundary vorticity dynamics since Lighthill's 1963 article: review and development. Theor. Comput. Fluid Dyn. 10, 459–474.CrossRefGoogle Scholar
Wu, J. Z., Wu, J. M. & Wu, C. J. 1988 A viscous compressible flow theory on the interaction between moving bodies and flow field in the (ω, ϑ) framework. Fluid Dyn. Res. 3, 203–208.CrossRefGoogle Scholar
Wu, J. Z., Wu, X. H. & Wu, J. M. 1993 Streaming vorticity flux from oscillating walls with finite amplitude. Phys. Fluids A 5, 1933–1938.CrossRefGoogle Scholar