Spatiotemporal Growth of Laminar Boundary Layers in a Concentric Annulus

Vortex rings are fascinating fluid flow phenomena occurring in nature. To accurately predict the dynamic behavior of such rings, researchers have been postulating analytical models and carrying out a huge number of experiments over the last couple of decades. It is an established fact that the most important feature of the flow that dictates the generation, and hence propagation, of vortex rings is in fact the growth of the boundary layer. As far as the generation process of these rings is concerned, Rayleigh’s analytical solution to the Navier-Stokes equations for impulsive motion of fluid over a flat plate is considered as a benchmark for the development of dynamic models. The limitation of using Rayleigh’s solution is that it is valid only at the edge of the boundary layer where the velocity of the boundary layer flow is nearly equal to the potential flow velocity. There is a need to develop a solution for the Navier-Stokes equations inside the boundary layer. Based on Computational Fluid Dynamics, an empirical model for the solution of the Navier-Stokes equations inside the boundary layer is presented here. The flow under consideration is Laminar in a concentric annular pipe. It has been concluded that the Rayleigh’s solution is applicable to the flow in annuls as well.