TURBULENT BOUNDARY LAYER OVER FLEXIBLE SURFACES

Abstract

Turbulent flow over flexibile surfaces deals with the flow over rubber - like surfaces which possess both elasticity and damping and thereby have the inherent property of interacting with the flow system. In fluid mechanics investigations, boundary surfaces are usually rigid which in theoretical work leads to clearly defined boundary conditions. In nature,however,flow boun ding surfaces are not rigid but show some sort of flexibility e.g. dolphin swimming in water,blood flow in arteries etc. It , is evident that flow along a flexible surface shall not be the same as flow along a rigid surface. Research on flows over flexible surfaces is primarily moti vated by the possibility of drag reduction by their use.Studies in this area began from the observed remarkable speed of dolphin (25). Kramer (36,37,38,40) initiated experiments on under water streamlined cylindrical bodies, partly covered with flexible surface and reported considerable drag reduction upto to 60% possibly due to stabilization of boundary layer.Benjamin (5,7) and others (12,13,28,42) investigated stability ofiboundary layer over flexible,surfaces. Some studies on turbulent flow over flexible surface were also conducted (9,23,68,69). While some information, about drag reduction on flexible surfaces is available, information on characteristics of turbulent boundary layer over flexible surfaces is rather scanty. Even the information on drag reduction does not fulfill the basic requirement of reproducibility and so the problem of drag reduction due to flexibility of surface has to be regarded as being in an uncertain state. This thesis presents an experimental as well as numerical study concerning turbulent boundary layer over flexible surfaces. Experiments were carried out in a wind tunnel for various models,viz.,flat plate,two-dimensional symmetrical aerofoil and three-dimensional axisymmetric body with rigid and flexible sur faces and detailed measurements of pressure distribution,mean velocity profiles and drag force were taken. Detailed comparison of characteristics of turbulent boundary layer over rigid and flexible models,namely, velocity profiles, various boundary layer thicknesses, friction coefficients and drag force,were made. For numerical prediction of turbulent boundary layer characteristics, thin shear layer equations were solved numerically by finite difference technique.In the case of rigid surfaces, the computer program originally developed by Cebeci and Carr (15) was used while for the case of the flexible surfaces this program was suitably modified. The flexible surface was modelled as a spring-mass-dashpot system. Wall properties of Ill each flexible surface, namely,stiffness and damping were measured by vibration test. The computer program was modified by introducing a flexibility coefficient for optimally adjusting the values of mixing length and inner eddy viscosity in the turbulence model so as to minimize the percentage absolute error between the predicted and observed velocity profiles.A relation between the flexibility coefficient and the damping factor has been developed. Using this modification,the characteristics of turbulent boundary layer for flexible surfaces were satisfactorily predicted in the present study. ' Results indicate a number of important differences between the flow characteristics for rigid and flexible surfaces.The mean velocity in the case of flexible surfaces is smaller than the corresponding velocity in the case of rigid surface for major part of the boundary layer. The boundary layer thicknesses are consistently higher on flexible surfaces than that on the corresponding rigid surfaces. Finally on account of flexibility of surface, drag reduction has generally been observed. IV