Boundary layer flows over rough surfaces #

Jason Ferguson

14:50 Monday in 4Q08.

Part of the Boundary layer flows and stability session.

Abstract #

We consider high Reynolds number boundary layer flows over rough surfaces. We restrict our attention to the study of boundary layer flows of fluids over a rough plate which is infinite in length. The effect of a sinusoidal surface is considered as a model for roughness and a range of different amplitudes and frequencies are considered. The purpose of the research is to investigate whether such a surface can be used as a drag reduction technique. For many boundary layer flows such as the Blasius boundary layer over a smooth flat plate and the Falkner boundary layer flow which examines flow over a wedge, self-similar solutions exist. The challenge when modelling a rough surface is that self-similar solutions do not exist. We correctly reformulate the problem by appropriately transforming the Navier stokes equations to account for the roughness and solve the governing equations utilising the TDMA algorithm. We examine the velocity profiles for a range of amplitudes and frequencies. Care is taken when considering the amplitude, to large an amplitude leads to boundary layer separation. We also investigate the effect the wavy surface has on the shear. As expected, both the velocity profile and the shear vary in streamwise direction. This method for solving such equations has been considered Moving forward we plan to consider the bi-global linear stability characteristics of such flows. Thus far, only a wavy surface has been considered. We would like to examine a surface profile that more closely matches physical roughness profiles. One method is to consider a surface that exhibits a randomized surface profile where the amplitude and shape of the profile varies in the streamwise direction.
References
Boundary layer flow and heat transfer on a continuous moving wavy surface D.A.S Rees and I. Pop Laminar Boundary layer flow of power-law fluids over wavy surfaces. I.Pop and S.Nakamura