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Far Field Conditions in Steady Flows with a Free Stream Mach Number One

Report Number: AFWAL TR 81-3064
Author(s): K. G. Guderly
Corporate Author: University of Dayton Research institute
Date of Publication: 1981-06-01
Pages: 66
Contract: AFOSR 78-3524
Project: 2304
Task: 2304N1
AD Number: ADA102174

Abstract:
The far field in a steady flow with a free stream Mach number one is governed by the potential equation simplified by the assumption that the deviations from a sonic parallel flow are small. In a suitable system of coordinates the dominant expression has the form of a similarity solution. To formulate far field conditions (conditions imposed by far field to the computed part of the flow field at its outer edge) one considers perturbations to the dominant part of the distant field. The particular solutions of the linear partial differential equation so obtained have also similarity form. The far field conditions express the requirement that only such perturbations are admitted which die out more quickly than the basic flow as one moves toward infinity. The derivation uses a Laplace form technique; the absence of nonadmissible particular solutions expresses itself by the absence of certain poles of the Laplace transform. These conditions are ultimately formulated in terms of quantities available in the physical plane. One obtains integrals extended over the outer contour of the computed flow field which contain the potential and its gradient.

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