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The transverse curvature effect on the incompressible laminar boundary layer for longitudinal flow over a cylinder

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Abstract

A solution to the partial differential equations governing incompressible laminar flow in the axial direction over a circular cylinder is presented. A method is employed which reduces the partial differential equations to a set of ordinary differential equations which are then solved consecutively. The solution is initiated at a leading edge and proceeds far downstream. Velocity profiles and values for the coefficient of skin friction, displacement thickness and momentum thickness are obtained. The results are compared to previously obtained solutions valid near the leading edge and asymptotic solutions valid far downstream.

Zusammenfassung

Die Wirkung der transversalen Krümmung auf die axiale Strömung über einen Zylinder wird untersucht. Eine numerische Methode zur Lösung der zugrundeliegenden partiellen Differentialgleichungen wurde verwendet, um eine Lösung zu erhalten, die an der Vorderkante beginnt, weit stromabwärts anwendbar bleibt und sich daher über einen grossen Bereich erstreckt, für welchen frühere approximative Lösungen nicht gültig sind. Geschwindigkeitsprofile und Werte für die Oberflächenreibungskoeffizienten, Verdrängungsdicke und Impulsverlustdicke werden angegeben. Die Ergebnisse werden mit anderen Lösungen verglichen, die an der Vorderkante gültig sind, und auch mit asymptotischen Lösungen weit stromabwärts.

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Abbreviations

f :

dimensionless stream function (Equation (7))

r :

distance measured from axis of cylinder in radial direction

r 0 :

radius of cylinder

u :

velocity in axial direction

u e :

velocity in axial direction at edge of the boundary layer

v :

velocity in radial direction

x :

distance measured from origin of boundary layer in axial direction

ν:

kinematic viscosity

ϱ:

density

τw :

shear stress at wall

μ:

viscosity

ψ:

stream function

w :

evaluated at wall conditions

∞:

evaluated outside of boundary layer

References

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Authors and Affiliations

  1. McDonnell Douglas Corp., Douglas Aircraft Co., Long Beach, Calif., USA

    N. A. Jaffe (Senior Scientist) & T. T. Okamura

Authors
  1. N. A. Jaffe
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  2. T. T. Okamura
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Jaffe, N.A., Okamura, T.T. The transverse curvature effect on the incompressible laminar boundary layer for longitudinal flow over a cylinder. Journal of Applied Mathematics and Physics (ZAMP) 19, 564–574 (1968). https://doi.org/10.1007/BF01594964

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  • DOI: https://doi.org/10.1007/BF01594964

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