Two and three-dimensional incompressible and compressible viscous fluctuations

Abstract

Small unsteady disturbances of boundary-layer flow fields are often encountered in engineering applications, as for example, in the aerodynamics of a helicopter rotor or a turbine cascade or in a fluttering airfoil as well as in a variety of bioengineering problems. The present dissertation is a unified attempt to study some special classes of unsteady two- and three-dimensional incompressible and compressible . boundary-layer flows. The general character of the mathematical problem is investigated first for each particular area. Asymptotic solutions are then provided based on the assumption of small amplitude and small frequency of oscillation. Systems of general differential equations in a single variable are obtained and solved numerically by the shooting technique. A straightforward fourth order Runge-Kutta integration scheme is employed and the values of the functions at the edge of the boundary-layer are checked against the outer flow boundary conditions. In the first chapter we study simultaneously the effects of three dimensionality coupled with the response to outer flow oscillations. It is believed that the coupling will have significant implications in cascade flows where the finite span blocks the development of cross flows. Some interesting features of oscillatory three-dimensional flows are disclosed. In particular it is found that the coupling of the momentum equations permits the transfer of momentum from the chordwise to the spanwise direction. In this way it is possible to excite a fluctuating boundary layer flow in the spanwise direction even though there is no outer flow fluctuations. In the second chapter the response of laminar compressible boundary layers to fluctuations of the skin of the body or the outer flow are studied in the special case of a wall at the adiabatic temperature. Unsteady outer pressure fluctuations are considered for the first time and their effects to the energy equation and heat transfer is estimated. The analysis holds both for two-dimensional and axisymmetric configurations.