Introduction into Boundary Layer Theory

In Chapter 19 we have shown that using the computational fluid dynamics (CFD), flow details in and around complex geometries can be predicted with an acceptable degree of accuracy. The flow field calculation includes details very close to the wall, where the viscosity plays a significant role. In the absence of random fluctuations the (laminar) flow can be calculated with high accuracy. For predicting turbulent flows, however, turbulence models were required to be implemented into the Navier-Stokes equations to account for turbulence fluctuations. One of the more important tasks in turbomachinery fluid mechanics is to predict the drag forces acting on the surfaces such as turbine and compressor blade surfaces, endwalls, inlet nozzles and exit diffusers. As seen in Chapter 6, the drag forces are produced by the fluid viscosity which causes the shear stress acting on the surface. The question that arises is how far from the surface the viscosity dominates the flow field. Prandtl [1] was the first to answer this question. Combining his physical intuition with experiments, he developed the concept of the boundary layer theory. This theory in its differential or integral forms can be applied to a turbomachinery flow to determine the blade profile loss. It delivers accurate results as long as the boundary layer is not separated.