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Asymptotic analysis of plane turbulent Couette-Poiseuille flows

Published online by Cambridge University Press:  19 April 2006

Kurt O. Lund  and
William B. Bush
Kurt O. Lund
Affiliation:
University of California, San Diego, California
William B. Bush
Affiliation:
University of California, San Diego, California
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Abstract

Matched asymptotic expansions, are used to describe turbulent Couette–Poiseuille flow (plane duct flow with a pressure gradient and a moving wall). A special modification of conventional eddy-diffusivity closure accounts for the experimentally observed non-coincidence of the locations of zero shear stress and maximum velocity. An asymptotic solution is presented which is valid as the Reynolds number tends to infinity for the whole family of Couette–Poiseuille flows (adverse, favourable, and zero pressure gradients in combination with a moving wall). It is shown that plane Poiseuille flow is a limiting case of Couette–Poiseuille flow. The solution agrees with experimental data for plane Couette flow, for the limiting plane Poiseuille flow, and for a special case having zero net flow and an adverse pressure gradient. The asymptotic analysis shows that conventional eddy diffusivity closures are inadequate for general Couette–Poiseuille flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 1 , 16 January 1980 , pp. 81 - 104
Copyright
© 1980 Cambridge University Press

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References

Bush, W. B. & Fendell, F. E. 1972 Asymptotic analysis of turbulent channel and boundary-layer flow. J. Fluid Mech. 56, 657–681.Google Scholar
Bush, W. B. & Fendell, F. E. 1973 Asymptotic analysis of turbulent channel flow for mean turbulent energy closures. Phys. Fluids 16, 1189–1197.Google Scholar
Bush, W. B. & Fendell, F. E. 1974 Asymptotic analysis of turbulent channel flow for mixing length theory. SIAM J. Appl. Math. 26, 413–427.Google Scholar
Burgers, J. M. 1922 Ein Versuch zur Abschätzung des turbulenten Strömungswiderstandes. In Vorträge aus dem Gebiete der Hydro- und Aerodynamic (ed. T. von Kármán & T. Levi-Civita), pp. 143–145. Springer.
Chue, S. H. 1969 An experimental investigation on turbulent plane Couette flow in dilute polymer solutions. MS thesis, Purdue University.
Chue, S. H. & McDonald, A. T. 1970 Application of a new effective viscosity model to turbulent plane Couette flow. A.I.A.A. J. 8, 2076–2078.Google Scholar
Cole, J. D. 1968 Perturbation Methods in Applied Mathematics. Watham, Massachusetts: Blaisdell.
Constantinescu, V. N. 1959 On turbulence lubrication. Proc. Inst. Mech. Eng. 173, 881–900d.Google Scholar
Couette, M. 1890 Etudes sur le frottement des liquides. Ann. Chem. Phys. 21, (6) 433–510.Google Scholar
Elrod, H. G. & Ng, C. W. 1967 A theory for turbulent fluid films and its application to bearings. J. Lubr. Tech. 89, 346–362.Google Scholar
Fendell, F. E. 1972 Singular perturbation and turbulent shear layers near walls. J. Astro. Sci. 20, 129–165.Google Scholar
Hanjali, K. & Launder, B. E. 1972 Fully developed asymmetric flow in a plane channel. J. Fluid Mech. 51, 301–335.Google Scholar
Heisenberg, W. 1922 Nichtlaminare Lösungen der Differentialgleichungen für reibende Flüssigkeiten. In Vorträge aus dem Gebiete der Hydro- und Aerodynamic (ed. T. von Kármán & T. Levi-Civita), pp. 139–142. Springer.
Hofmeister, M. 1976 Über eine lokale Abschlussbedingung für turbulente Scherströmungen. Z. angew. Math. Mech. 56, 415–419.Google Scholar
Ho, M. K. & Vohr, J. H. 1974 Application of energy model of turbulence to calculation of lubricant flows. J. Lubr. Tech. 96, 95–102.Google Scholar
Huey, L. J. & Williamson, J. W. 1974 Plane turbulent Couette flow with zero net flow. J. Appl. Mech. 41, 885–890.Google Scholar
Hussain, A. K. M. F. & Reynolds, W. C. 1975 Measurements in fully developed turbulent channel flow. J. Fluids Engng 97, 568–580.Google Scholar
Kármán, T. von 1937 The fundamentals of the statistical theory of turbulence. J. Aero. Sci. 4, 131–138.Google Scholar
Korkegi, R. H. & Briggs, R. A. 1968 On compressible turbulent plane Couette flow. A.I.A.A. J. 6, 742–744.Google Scholar
Korkegi, R. H. & Briggs, R. A. 1970 Compressible turbulent plane Couette flow with variable heat transfer based on von Kármán model. A.I.A.A. J. 8, 817–819.Google Scholar
Leutheusser, H. J. & Chu, V. H. 1971 Experiments on plane Couette flow. Proc. A.S.C.E. J. Hydraul. Div. 97, 1269–1284.Google Scholar
Ng, C. W. 1964 Fluid dynamic foundation of turbulent lubrication theory. Trans. A.S.L.E. 7, 311–321.Google Scholar
Rehme, K. 1974 Turbulent flow in smooth concentric annuli with small radius ratios. J. Fluid Mech. 64, 263–287.Google Scholar
Reichardt, H. 1956 Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung. Z. angew. Math. Mech. Sonderheft 36, S26–29.Google Scholar
Reichardt, H. 1959 Gesetzmässigkeiten der geradlinigen turbulenten Couetteströmung. Mitt. Max-Planck-Inst. fur Strömungsforschung, no. 22, Göttingen.
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Robertson, J. M. 1959 On turbulent plane Couette flow. Proc. 6th Midwestern Conf. on Fluid Mech., pp. 169–182. University of Texas, Austin.
Robertson, J. M. & Johnson, H. F. 1970 Turbulence structure in plane Couette flow. Proc. A.S.C.E., J. Eng. Mech. Div. 96, 1171–1182.Google Scholar
Szablewski, W. 1968 Turbulente Parallelströmungen. Z. angew. Math. Mech. 48, 35–50.Google Scholar
White, F. M. 1974 Viscous Fluid Flow. McGraw-Hill.
Yajnik, K. S. 1970 Asymptotic theory of turbulent shear flows. J. Fluid Mech. 42, 411–427.Google Scholar