General integral conservation form of Navier-Stokes equations and numerical application

Gauss theorem for tensor of any order, such as scalar, vector and second order tensor, is presented with a tensor analysis technique. A general integral conservation form of Navier-Stokes equations in any three-dimensional curvilinear coordinate is derived. A time-marching algorithm coupled with finite volume is applied to discretization of the governing equations. A CFD code is developed to simulate a three dimensional rotating viscous flow field inside an NASA low-speed centrifugal compressor (LSCC) impeller with vaneless diffuser. Numerical algorithm and general integral conservation form of N-S equations are validated with experimental data. It provides a study basis for complex physical region.