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Numerical and physical experiments in viscous separated flows

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Progress in Numerical Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 41))

Abstract

From this study of three quite different viscous separated flow problems using the same numerical techniques, it is apparent that experimentation is as important in the numerical sense as it is in the physical sense. The time-depen dent conservative equations with upwind differencing for advection terms produced stable solutions over a wide range of Reynolds numbers. The actual accuracy of the numerical solutions varied with the flow problem and mesh geometry. A variable mesh, concentrating mesh points in regions of steepest gradients, appears to be a convenient method of reducing the, ever present, artificial viscosity effect. Numerical solutions with engineering accuracy can be obtained if great care is taken to control this artificial viscosity effect. Furthermore, they allow the study of basic flow phenomena which would be more difficult to produce and study in physical experiments. These methods, however, are still in the developmental stages and are not available in foolproof form for use by design engineers.

There should be no doubt that, at present and for the foreseeable future, the computer and wind tunnel are and will be dependent upon each other for the practical solution of complex separated flow problems.

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Abbreviations

C:

Courant number

D:

diameter or channel half width

f:

arbitrary function

h:

base height or step height

L:

length of separated region behind disc or characteristic length

P:

pressure

ReD :

Reynolds number based upon D

Reh :

Reynolds number based upon h

ReL :

Reynolds number based upon L

r:

radial direction t time

v:

velocity

x,y:

cartesian coordinates

z:

axial direction

α:

kinematic viscosity

α e :

effective or artificial viscosity

Δ:

increment

Ï‘:

increment or boundary layer thisckess

δ:

streamline angle or cylindrical coordinate

μ:

absolute viscosity

ξ:

vorticity

ϱ:

density

Ï„:

shear stress

ψ:

stream function

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, 46556, Indiana

    Thomas J. Mueller

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  1. Thomas J. Mueller
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H. J. Wirz

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© 1975 Springer-Verlag

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Mueller, T.J. (1975). Numerical and physical experiments in viscous separated flows. In: Wirz, H.J. (eds) Progress in Numerical Fluid Dynamics. Lecture Notes in Physics, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07408-2_6

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  • DOI: https://doi.org/10.1007/3-540-07408-2_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07408-3

  • Online ISBN: 978-3-540-37926-3

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