Nozzle Shape Optimization to Achieve the Maximum Gain in the GDLs

The geometry of a divergent nozzle of the gas dynamic laser is optimized to achieve the maximum possible gain in an optical cavity. The problem is numerically studied using two-dimensional computation of the governing equations beside the conjugate gradient method for the shape optimization. The system of governing equations is solved with a finite volume approach using a structured grid in which the advection upstream splitting method is used to calculate the convective numerical fluxes. The finite difference approximation approach is used to calculate the sensitivity matrix coefficient of the optimization procedure. The results show that the optimum geometry of the considered problem can improve the maximum small signal gain as much as about 9 percent in comparison with the simple linear nozzle. The steady state solution of the equations is considered here.