A characteristic based method for the calculation of three-dimensional incompressible, turbulent and steady flows in hydraulic turbomachines and installations

Abstract

The present algorithm is developed to calculate three-dimensional incompressible, turbulent and steady flows in hydraulic turbomachines and installations. The code is based on a characteristic based method for the solution of the incompressible Navier–Stokes equations, coupling the continuity and momentum equations after the introduction of the artificial compressibility formulation. The primitive variables, pressure and velocity components are defined as functions of their values on the characteristics. The primitive variables on the characteristics are calculated by an upwind differencing scheme based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. The upwind scheme uses interpolation formulas of third-order accuracy. The standard k–ε model is applied for the description of turbulence effects. The time discretization is obtained by the explicit Runge–Kutta method. For faster convergences to the steady state solution, a local time stepping and a mesh-sequencing scheme are used. Validation of the algorithm is performed on many two- and three-dimensional laminar and turbulent flow cases, while in the present work, the three-dimensional flow (laminar and turbulent) through a square duct with a 90° bend is presented. Finally, the code is applied for the prediction of the relative flow through the impeller of the Societe Hydrotechnique de France (SHF) water pump. The numerical results are compared with the corresponding experimental measurements. Copyright © 2000 John Wiley & Sons, Ltd.