Fluid Dynamics

, Volume 1, Issue 2, pp 11–15 | Cite as

Separation of a three-dimensional boundary layer

  • V. S. Avduevskii
  • K. I. Medvedev
Article

Abstract

The line of separation of the three-dimensional boundary layer on an arbitrary curvilinear surface is a singular streamline on the body surface which separates the detachment region and which is a line of confluence for the limiting streamlines. Expressions are derived for the three-dimensional separation criteria on the basis of the condition of zero frictional force in the projection on the normal to the line of separation. The position of the line of separation is determined from the solution of an ordinary differential equation. An analysis is made of various cases of separation on the surface of a yawed cylinder and on the surface of sharp cones at an angle of attack in a supersonic stream. The position of the lines of separation is determined experimentally from the confluence of thin liquid films applied to the surface. It is shown that separation occurs on the sharp cone on the line z=π for values of the parameter K=−0.85.

Keywords

Differential Equation Boundary Layer Ordinary Differential Equation Body Surface Liquid Film 

Notation

x, z

orthogonal curvilinear coordinates on surface

h1, h2

Lamé coefficients

y

coordinate along normal to surface

α, β

coordinates associated with streamlines of ideal fluid

h1, h2

corresponding (to α, β) Lamé coefficients

U

total velocity

u, w

velocity components along x and z axes

p

static pressure

ρ

density

T

temperature

μ

viscosity coefficient

τ

friction stress

δ

boundary layer thickness

θ

cone half-angle

γ

angle between limiting streamline on surface and ideal fluid streamline

K

transverse curvature parameter on cone at angle of attack

R

Reynolds number

Γ0

separation criterion

Subscripts

w

conditions at body surface

1

conditions at edge of boundary layer.

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References

  1. 1.
    E. Eichelbrenner and A. Oudart, “Observations sur un critere de decollement laminare dans la couche limite tridimensionelle,” Rech., aéronaut, no. 40, 1954.Google Scholar
  2. 2.
    H. Schlichting, Boundary Layer Theory [Russian translation], Izd. inostr. lit., 1956.Google Scholar
  3. 3.
    K. I. Babenko, G. P. Voskresenskii, A. N. Lyubimov, and V. V. Rusanov, Three-Dimensional Ideal Gas Flow About Smooth Bodies [in Russian], Izd-vo Nauka, 1964.Google Scholar

Copyright information

© The Faraday Press, Inc. 1968

Authors and Affiliations

  • V. S. Avduevskii
    • 1
  • K. I. Medvedev
    • 1
  1. 1.Moscow

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