Nonperiodic Fluctuations Induced by Stationary Surface Waviness on a Semi-Infinite Plate.

摘要

An analytical/numerical study of flow over an aerodynamic model or vehicle with surface waviness illustrates how surface waviness can generate several families of waves. The classical Kelvin-Hemholtz solution for irrotational flow over a wavy wall is extended to include the effects of the leading edge of a semi-infinite plate. The solution, obtained by conformal mapping and integral transforms, shows that a monochromatic surface waviness can generate a spectrum of standing waves with a continuum of x-wavenumbers, as well as the Kelvin-Helmholtz solution. Downstream of the leading edge, each of those standing waves decays exponentially in the streamwise direction and oscillates sinusoidally in the direction normal to the plate. These standings waves satisfy the usual boundary conditions on a flat plate, although they are initiated by the combined effects of the waviness of the wall and the leading edge. The spectrum depends upon the phase of the surface waviness with respect to the leading edge. Far downstream of the leading edge, only the Kelvin-Helmholtz solution remains. Upstream of the leading edge, the flow field can be represented as a superposition of exponentially-growing standing waves. The theory for flow over a stationary wavy wall is applicable to the case of flow over a traveling wavy wall if the velocity is properly nondimensionalized and the phase of the surface waviness is replaced by the product by frequency and time. (Author)