Optimum suction distribution for transition control

The optimum suction distribution which gives the longest laminar region for a given total suction is computed. The goal here is to provide the designer with a method of finding the best suction distribution subject to some overall constraints applied to the suction. We formulate the problem using the Lagrangian multiplier method with constraints. The resulting nonlinear system of equations is solved using the Newton-Raphson technique. The computations are performed for a Blasius boundary layer on flat-plate and crossflow cases. For the Blasius boundary layer, the optimum suction distribution peaks upstream of the maximum growth rate region and remains hat in the middle before it decreases to zero at the end of the transition point. For the stationary and travelling crossflow instability, the optimum suction peaks upstream of the maximum growth rate region and decreases gradually to zero.