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Statistical Characteristics of the Velocity Incidence in a Decelerated Boundary Layer

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Turbulent Shear Flows 6

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Abstract

The probability distributions of the velocity incidence are presented. The analysis is performed in one or two points and the duration of the greatest events is taken into account. The length scaling is given by various positions and the spacings of the probes in a cross section. The flow investigated is a boundary layer submitted to a positive pressure gradient and with self-preserved profiles for mean and conventional turbulent properties.

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Abbreviations

A(t) or A t :

instantaneous incidence: tan−1(V(t)/U(t)) ≡ A + a(t)

a :

coefficient of the relation

a :

coefficient of the relation U 0 = (X − X 0 )a

C f :

friction factor: τ p /0.5 ϱU 2 0

G :

clauser factor:

G :

clauser factor: (H 12 −1)H 12 (C f /2)1/2

H 12 :

form factor: δ 1 /δ 2

L :

threshold for A(t)

N :

probability to observe one event by the two probes (def in the paper)

P :

probability to observe one event by one probe

pdf :

probability density function

R :

Reynolds number basedon δ = U 0 δ/v

S :

skewness factor (for \(g: g^3/{(g^2)^{3/2}})\)

T :

flatness factor (for g: \(g: g^4/{(g^2)^{2}})\)

X :

longitudinal coordinate

Y:

transverse coordinate

U :

longitudinal mean velocity

U 0 :

longitudinal free stream mean velocity

V :

transverse mean velocity

U(t), V(t):

instantaneous velocities, U(t)=U + u(t), V(t)= V+ v(t)

β :

−(δ 1 /τ p )/U 0 (dU 0 /dX)

δ :

boundary layer thickness

δ 1 :

displacement thickness:\(\int^{\delta}_{0}(1-U/U_o)\text dy\)

δ 2 :

momentum thickness:\(\int^{\delta}_{0}(1-U/U_o)(U/U_o)\text dy\)

Δy :

distance between two X-wire probes in a cross section

v :

kinematic viscosity

τ p :

wall friction

ψ(t):

pseudo fluctuating incidence: tan−1(v(t)/u(t))

´:

R.M.S. value

—:

time average

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Author information

Authors and Affiliations

  1. Laboratoire de Mécanique des Fluides, UA CNRS 263, Ecole Centrale de Lyon, Ecully, France

    H. Zougari

  2. Institut de Mécanique des Fluides de Toulouse, UA CNRS 005, ENSEEIHT, Toulouse, France

    G. Charnay

Authors
  1. H. Zougari
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  2. G. Charnay
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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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Zougari, H., Charnay, G. (1989). Statistical Characteristics of the Velocity Incidence in a Decelerated 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_15

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  • DOI: https://doi.org/10.1007/978-3-642-73948-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73950-7

  • Online ISBN: 978-3-642-73948-4

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