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Direct Simulation of a Turbulent Oscillating Boundary Layer

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Turbulent Shear Flows 6

Abstract

The turbulent boundary layer under a freestream velocity that varies sinusoidally in time around a zero mean is considered. The flow has a rich variety of behaviors including strong pressure gradients, inflection points in the velocity profile, and reversal of the shear stress. A theory for the velocity- and stress profiles at high Reynolds number is formulated. Well-resolved direct Navier-Stokes simulations are conducted over a narrow range of Reynolds numbers. The flow is also computed over a wider range of Reynolds numbers using a new algebraic turbulence model. The results produced by the three approaches and by experiments are compared. Detailed phase-averaged statistical results from the direct simulations are provided to assist turbulence-model development.

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Abbreviations

a 1 :

structure parameter in algebraic turbulence model

f 1 , f 2 …:

unknown nondimensional functions, see (3), (4)… k ≡ 〈u ´2 + v ´2 + w´2〉/2 turbulent kinetic energy

l :

local length scale in algebraic turbulence model

L ≡ U 0 /ω :

length scale (1/2 the total travel of the freestream fluid)

Re ≡ U 0 δ l /v :

Reynolds number

S ≡ U y :

strain rate, see (17)

t :

time

u, v, w :

velocity components

U ≡ 〈u〉:

mean velocity component

u´ ≡ u−U :

fluctuating velocity component

U l :

laminar mean velocity component, see (2)

U ∞ :

instantaneous freestream velocity, see (1)

U 0 :

peak freestream velocity, see (1)

u τ :

instantaneous friction velocity (can be negative)

u* :

peak friction velocity, see (5)

U + ≡ U/u τ :

wall units

x, y, z :

streamwise, normal, spanwise coordinates

y + ≡ y|u τ |/v :

wall units

y r :

roughness height, see (15)

\(\delta_1\equiv \sqrt 2 v/\omega\) :

laminar boundary-layer thickness, see (2)

δ :

turbulent boundary-layer thickness, see (5)

ε :

turbulent dissipation rate

κ :

Karman constant, enters (13) and (14)

Λ x , Λ z :

periods in x and z directions, for the direct simulations

v :

kinematic viscosity

v t :

eddy viscosity, see (17)

φ ≡ ωt :

phase angle

φ 0 :

phase shift, a function of Re, see (7)

ω :

frequency, see (1)

\(\tau \equiv v{U_y} - < u'v' > \) :

total shear stress

\(\bar \tau \equiv-\langle u'v'\rangle\) :

Reynolds shear stress, see (17)

〈 〉:

average in x, z and/or ensemble

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Authors and Affiliations

  1. NASA Ames Research Center, USA

    Philippe R. Spalart & Barrett S. Baldwin

Authors
  1. Philippe R. Spalart
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  2. Barrett S. Baldwin
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Editor information

Editors and Affiliations

  1. Centre National de Recherches Météorologiques, 42, Avenue Coriolis, 31057, Toulouse Cedex, France

    Jean-Claude André

  2. O.N.E.R.A./C.E.R.T., 2, Avenue Edouard Belin, 31055, Toulouse Cedex, France

    Jean Cousteix

  3. Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Egerlandstraße 13, 8520, Erlangen, Fed. Rep. of Germany

    Franz Durst

  4. Department of Mechanical Engineering, University of Manchester, Institute of Science and Technology, PO Box 88, Manchester, M60 1QD, England

    Brian E. Launder

  5. Mechanical Engineering Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Frank W. Schmidt

  6. Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, SW7 2BX, England

    James H. Whitelaw

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© 1989 Springer-Verlag Berlin Heidelberg

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Spalart, P.R., Baldwin, B.S. (1989). Direct Simulation of a Turbulent Oscillating Boundary Layer. In: André, JC., Cousteix, J., Durst, F., Launder, B.E., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73948-4_32

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  • DOI: https://doi.org/10.1007/978-3-642-73948-4_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73950-7

  • Online ISBN: 978-3-642-73948-4

  • eBook Packages: Springer Book Archive

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