Low-Fidelity Approach for Contoured Nozzle Design

Creating a supersonic jet in the laboratory is both a challenging and an expensive task. The supersonic flow is sensitive to the shape of the wall bounding it because a shock could be developed at the sharp edges. Moreover, the growth of boundary layer, within and outside the nozzle, makes the design of a convergent–divergent nozzle a sophisticated work. The present work proposes an optimization algorithm that is believed to be efficient in constructing a nozzle contour to deliver a shock-free radially uniform flow at the exit plane. The steepest descent optimization technique is employed to obtain the shape with minimum radial velocity at the outlet, along with restriction on the inlet angle, i.e., the angle of divergence immediately downstream the throat. Three different ways of implementing the constraints are discussed and compared with the experimental results after fabricating the nozzle. The optimized nozzle shows a potential core of 7 throat diameters height at the nozzle exit and an axial extent of 28 throat diameters downstream the exit plane. Further, the nozzle appears to operate efficiently even after increasing the nominal total temperature by 25% or decreasing it by 50%.