Mechanical Engineering - Research Publications

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Author: PERRY, ANTHONY × Type: Journal (Paginated) × Subject: Turbulent boundary layers ×

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    Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis
    Perry, A. E. ; Marusic, I. ; Li, J. D. ( 1994)
    A new look at the closure problem of turbulent boundary layers is taken here using recently derived analytical expressions for the shear stress distributions. These expressions are based on logarithmic law of the wall and law of the wake formulation of Coles [J. Fluid Mech. 1, 191 (1956)] with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser [Adv. Mech. 4, 1 (1956)] is extended and using similar ideas as Rotta [Prog. Aeronaut. Sci. 2, 1(1962)] for self-similarity, a closure scheme is proposed for layers developing in arbitrary pressure gradients for the case where the streamwise derivative of the Coles wake factor is not too large. For a given flow case, this Coles wake condition can be tested with internal consistency checks. The mathematical framework is most suitable for incorporating Townsend’s attached eddy hypothesis as recently developed by Perry, Li, and Marusic [Phils. Trans. R. Soc. London. Ser. A 336, 67 (1991)] for closure. This gives an opportunity to incorporate coherent structure concepts into closure schemes. Possible ways of handling the difficult case where the streamwise derivative of the Coles wake factor is significant are discussed.
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    On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients
    Perry, A. E. ; Marusic, I. ; Jones, M. B. (Cambridge University Press, 2002)
    A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such asthe log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.