For inverse problems in complex flow passages, a calculation procedure based on a multizone Navier-Stokes method was developed. A heuristic approach was employed to derive wall shape corrections from the wall pressure error. Only two subdomains sharing a row of control volumes were used. The grid work in the common region was identical for both subdomains. The flow solver, inverse calculation procedure, multizone Navier-Stokes method and subdomain inverse calculation procedure were validated independently against experimental data or numerical predictions. Then, the subdomain inverse calculation method was used to determine the wall shape of the main duct of a branching flow passage. A slightly adverse pressure gradient was prescribed downstream of the sidebranch. Inverse calculations resulted in a curved wall diffuser for which the wall pressure distribution matched the design (prescribed) wall pressure distribution. The present method was illustrated for laminar, incompressible flows in branching passages. However, the method presented is flexible and can be extended for turbulent flows in multiply connected domains.
A primitive variable, strongly implicit calculation procedure for two and three-dimensional unsteady viscous flows: applications to compressible and incompressible flows including flows with free surfaces
