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An Asymptotic Solution for the Flow About an Ellipsoid Near a Plane Wall

Eisenberg, Phillip (1948) An Asymptotic Solution for the Flow About an Ellipsoid Near a Plane Wall. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20150625-164256043

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Abstract

The inherent difficulties in obtaining the solution for the flow about arbitrary bodies of revolution near a wall usually precludes on exact evaluation of the effect of wall proximity on the pressure distributions However, many bodies of revolution may be replaced with good approximation by an ovary ellipsoid. For this purpose, an approximate solution for the velocity potential is obtained for the flow about an ellipsoid near a plane wall which approaches the exact solution in an infinite stream as the ellipsoid recedes from the wall. The evaluation of the image potentials and rectifying images is accomplished by an expansion in associated Legendre polynomials. A first approximation, which results in a symmetric distribution on the ellipsoid, is essentially an expansion in associated Legendre polynomials of zero order. A second approximation, which correctly predicts differences of pressure on opposite sides of the ellipsoid, is carried out by an exact evaluation of the effects of the image potentials while evaluating the rectifying images by the same method as followed for the first approximation. The solutions ore obtained in closed form with resulting expressions for the velocity and pressure distributions that are especially convenient for application to specific cases. The solutions are compared with pressure distributions measured on two ellipsoid models placed near a plate, simulating a wall, in the free surface flume of the Hydrodynamics Laboratory. The first approximation shows good agreement along the meridian parallel to the wall but rather large deviations at other points of the ellipsoids. This approximation is probably most useful only for estimates of the change in pressure distribution for varying separations; and where a high degree of precision in actual values is not required. The second approximation, on the other hand, shows very good agreement for distances even as small as one diameter from the center of the ellipsoid to the wall. For smaller distances this approximation shows large point of the half meridian accuracy for points on the wall.


Item Type:Report or Paper (Technical Report)
Additional Information:U.S. Navy Bureau of Ordnance Contract NORD 9612. Report No. N-57.
Group:Hydrodynamics Laboratory
Funders:
Funding AgencyGrant Number
Department of the Navy Bureau of OrdnanceNOrd 9612
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Hydrodynamics Laboratory69
Hydrodynamics LaboratoryN-57
Record Number:CaltechAUTHORS:20150625-164256043
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150625-164256043
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58628
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:26 Jun 2015 04:11
Last Modified:26 Jun 2015 04:11

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