Boundary Layer Flow

Recall our discussion in the very first chapter of the Thought Experiment where we had two parallel plates. One of the plates was stationary (the lower one) and the other one moving. We said that there was a No Slip condition, which meant that the fluid does not slip past the solid in contact. Needless to say that this is a typical effect of viscosity.

Figure 6.1: Formation of a Boundary Layer

Let us now follow the effects as a flow approaches a solid body, to make it simple, a flat plate, Fig.6.1 . Consider a uniform (inviscid) flow in front of a flat plate at a speed $U_\infty$. As soon as the flow 'hits' the plate No Slip Conditions gets into action. As a result, the velocity on the body becomes zero. Since the effect of viscosity is to resist fluid motion, the velocity close to the solid surface continuously decreases towards downstream. But away from the flat plate the speed is equal to the freestream value of $U_\infty$. Consequently a velocity gradient is set up in the fluid in a direction normal to flow. Thus a layer establishes itself close to the wall with a velocity gradient. This is what we call the Boundary Layer. We will find out later that this is a high Reynolds Number concept and is due to Prandtl(), a leading German Aerodynamicist. The boundary layer is not a static phenomenon. It is dynamic. The thickness of boundary layer (the height from the solid surface where we first encounter 99% of free stream speed) continuously increases. A shear stress develops on the solid wall. It is this shear stress that causes drag on the plate.

Boundary layer has a pronounced effect upon any object which is immersed and moving in a fluid. Drag on an aeroplane or a ship and friction in a pipe are some of the common manifestations of boundary layer. Understandably, boundary layer has become a very important branch of fluid dynamic research.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney