Aerodynamics of bodies in shear flow.

Abstract

This dissertation investigates spanwise periodic shear flow past two-dimensional bodies. The flow is assumed to be inviscid and incompressible. Using singular perturbation techniques, the solution is developed for ε = L/ℓ ≪ 1, where L represents body cross-sectional size, and ℓ the period of the oncoming flow U(z). The singular perturbation analysis involves three regions: the inner, wake and outer regions. The leading order solutions are developed in all regions, and in the inner region higher order terms are obtained. In the inner region near the body, the primary flow (U₀, V₀, P₀) corresponds to potential flow past the body with a local free stream value of U(z). The spanwise variation in U(z) produces a weak O(ε) secondary flow W₁ in the spanwise direction. As the vortex lines of the upstream flow are convected downstream, they wrap around the body, producing significant streamwise vorticity in a wake region of thickness O(L) directly behind the body. This streamwise vorticity induces a net volume flux into the wake. In the outer region far from the body, a nonlifting body appears as a distribution of three-dimensional dipoles, and the wake appears as a sheet of mass sinks. Both singularity structures must be included in describing the leading outer flow. For lifting bodies, the body appears as a lifting line, and the wake appears as a sheet of shed vorticity. The trailing vorticity is found to be equal to the spanwise derivative of the product of the circulation and the oncoming flow. For lifting bodies the first higher order correction to the inner flow is the response of the body to the downwash produced by the trailing vorticity. At large distances from the body, the flow takes on remarkably simple form.