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


1 Department of Mechanical Engineering,Sharif University of Technology

2 Department of Aerospace Engineering,I.P.M.


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
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.