Weighted Least Squares Kinetic Upwind Method (WLSKUM) for computation of flow through blade passage with Kinetic Periodic Boundary Condition (KPBC)

摘要

This paper deals with the deveopment of the Kinetic Periodic Boundary Conditon (KPBC) for the computation of the flow through the turbine cascade. The problem of the flow through the turbine cascade has been approached via the grid-free method route. The main advantage of the grid free method is its ability to work effectively on any distribution of points. However this method is limited by the requirement of a good connectivity around a node. Here, a very robust form of the grid free method called Weighted Least Squares Kinetic Upwind Method (WLSKUM) has been used to avoid the problem of code divergence due to the bad connectivity.In WLSKUM, the weights are calculated to diagonalize the least squares matrix A(w) such that the x and y directions become the eigen directions along which the higher dimensional least squares formulae reduce to the corresponding one dimensional formulae. The KPBC for the Single passage (SP) computation of the flow through the cascade has been developed based on the Moment Method Strategy. The advantage of the KPBC to do the SP computations in place of the Multi passage (MP) computations has been clearly brought out in the paper. This helps not only in reducing the computational time and effort, but the grid refinement studies can be easily and effectively performed using the SP flow computations in place of the MP flow computations.