A Study of Incompressible Flow Calculations with Artificial Compressibility

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The three-dimensional Navier-Stokes code with the pseudo-compressibility, the implicit formulation of finite difference, the high accuracy TVD scheme and the Kーe turbulence model has been developed for the Francis water runner as an example of incompressible flow. The authors have already developed the 3-D turbulent flow calculation code for the advanced turboprop (ATP) with compressible flow scheme of the rotating blade, which enables one to predict the performance and the detailed flow including the location of shock successfully.We take the implicit finite difference and approximate factorization method so as to get the comparatively large time step for the time marching. The K-e turbulence model requiring two transporting equations is introduced for simulating the high Reynolds number flow, while the wall function is used to decrease the number of the grid points. The TVD (Total Variations Diminishing) scheme is also available in order to get the converged results adding the minimum artificial viscosity automatically.The results of the code developed here are reasonable comparing with the experimental data, and this simulation can describe the proper influence of the viscosity such as the secondary flow owing to the rotation. In order to decrease the computational time, the implicit scheme and the wall function near the surface are introduced efficiently so that this Navier-Stokes code is acceptable in the small computer like the engineering work station as well as the supercomputer.