Question: Compute analysis of the turbulent momentum boundary layer over a flat plate with zero pressure gradient and constant properties: Use a mixinglength turbulence model with the Van Driest damping function to calculate a flat-plate boundary layer flow over the range of Re/5zfrom 2000 to 10,000. Compare the friction coefficient results based on x Reynolds number and momentum thickness Reynolds number with the results in the text. Evaluate the virtual origin concept as described in Prob. Examine the development in the streamwise direction of the momentum thickness and assess the validity of the momentum integral. Feel free to investigate any other attribute of the boundary-layer flow. You can choose how to set up the problem in terms of suitable choice of dimensions and fluid properties (constant). For the initial condition at the specified starting Re/5z' construct a composite velocity using a continuous law-of-the-wall model in the inner region and a power-law model in the outer region.

Problem: Consider constant-property flow along a flat plate with constant u∞: Let the boundary layer starting at the origin of the plate be laminar, but assume that a transition to a turbulent boundary layer takes place abruptly at some prescribed critical Reynolds number. Assuming that at the point of transition the momentum thickness of the turbulent boundary layer is the same as the laminar boundary layer (and this is a point for discussion), calculate the development of the turbulent boundary layer and the friction coefficient for the turbulent boundary layer. Plot the friction coefficient as a function of Reynolds number on log-log paper for transition Reynolds numbers (based on distance from the leading edge) of 300,000 and 1,000,000, and compare with the turbulent flow friction coefficient that would obtain were the boundary layer turbulent from the plate origin. On the basis of these results, determine a "virtual origin" of a turbulent boundary layer preceded by a laminar boundary layer; that is, the turbulent boundary layer will behave as if the boundary layer had been entirely a turbulent one starting at the virtual origin.