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The interaction between vortex-array representations of free-stream turbulence and semi-infinite flat plates

Published online by Cambridge University Press:  12 April 2006

H. Rogler
H. Rogler
Affiliation:
Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, Ohio Present address: Department of Aerospace Engineering, University of Southern California, Los Angeles.
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Abstract

Free-stream turbulence is modelled by a low-intensity array of vortices where the vorticity is distributed continuously throughout the flow. This vorticity approaches and convects along a semi-infinite flat plate and the structure of the free-stream disturbances is altered by the impermeability condition at the plate. The analysis consists of tracking the vorticity as it convects with the uniform mean flow, determining the stream function induced by that vorticity field without imposing the impermeability condition, and finally superimposing an irrotational flow field which effects impermeability. The bisecting of a vortex as it encounters the plate yields a pair of vortices which rotate in the same direction. The combined heights of these vortices are less than the height of the original vortex. Small segments of a vortex which has been cut by the plate, but not through its centre, are completely absorbed by neighbouring vortices. Far from the leading edge in any direction, the disturbance pressure is O(ρq2), where q is the characteristic disturbance speed, and the streamline patterns convect with the mean flow. Near the leading edge, the fluctuating pressure is O(ρqU∞) because of unsteady vortex distortion and the velocity correlations reveal that Taylor's hypothesis is not valid. These correlations are based on averages over time and over all possible orientations of the vortex array. Vortex structures based on iso-vorticity contours are sometimes quite different from the structures based on disturbance streamlines.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 3 , 15 August 1978 , pp. 583 - 606
Copyright
© 1978 Cambridge University Press

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