Duct Design in Subsonic and Supersonic Flow Regimes with and without Normal Shock Waves Using Flexible String Algorithm

In this investigation, the Flexible String Algorithm (FSA) used before for the inverse design of 2D subsonic ducts is developed and applied for the inverse design of subsonic and supersonic ducts with and without normal shock waves. In this method, the duct wall shape is changed under a novel algorithm based on the deformation of a virtual exible string in a ow. Deformation of the string due to the local ow conditions resulting from changes in the wall geometry is performed until the target shape satisfying the prescribed walls pressure distribution is achieved. The ow eld at each shape modi cation step is analyzed using an Euler equation solution by the AUSM method. Some validation test cases and design examples in subsonic and supersonic regimes are presented here, which show the robustness and exibility of the method in handling the complex geometries in various ow regimes. In the case of unsymmetrical ducts with two unknown walls, the FSA is modi ed to increase the convergence rate signi cantly. Also, the e ect of duct inlet and outlet boundary conditions on the convergence of the FSA is investigated. The FSA is a physical and quick converging approach and can eciently utilize ow analysis codes as a black box.