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The Initial Stage of Wake Development in Linearized Incompressible and Compressible Flow.

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Interim rept. May-Aug 86,

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This report investigates the initial stage of the wake formation in linearized incompressible or compressible subsonic flows after a change of the upwash at the wing in the form of a step function in time. By a superposition of solutions of this kind all other changes of the upwash at the wing can be treated. The potential due to the above perturbation can be expressed by a circulation-free flow that satisfies the boundary condition imposed by the sudden change of upwash and the potential due to the wake vortices which leaves the boundary conditions unchanged. The latter is expressed by a superposition of the potentials due to individual vortices emanating form the trailing edge at different times and traveling downstream with the free stream velocity. The intensity of these vortices is determined by the Kutta condition, namely that at the trailing edge and at all times the upwash in the wake obtained by the combination of circulation-free flow and wake vortices be finite. In the incomprehensible flow case the analysis can be carried out in all details. In the comprehensible case the flow fields needed can be described by similarity solutions, but of a rather complex character. The feature essential for the present problem, namely the upwash singularity at the trailing edge can, however, be gleaned b a discussion in general terms so that one can determine the vortex distribution within the wake except for one constant factor. Keywords Linearized subsonic time-dependent flow and Unsteady aerodynamics.

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  • Fluid Mechanics

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