Orthogonal arrays: An introduction and their application in optimizing underrelaxation factors in ‘simple’‐based algorithm

Abstract

AbstractThe primary aim of this paper is to demonstrate how the ‘design‐of‐experiments’ techniques which are successful in physical experiments could also be adapted to a numerical simulation code.As an example this technique is applied to a general finite difference code used for predicting three‐dimensional turbulent recirculating flows. Here the equations for velocities and continuity are solved using the algorithm called SIMPLE, which stands for semi‐implicit method for pressure‐linked equations. Physical modelling of turbulence is taken care of by means of kinetic energy and turbulence dissipation rate equations.The objective is to optimize the underrelaxation factors of primary and secondary flow variables so that the number of iterations required for convergence is minimum. This is done by the orthogonal array technique (a particular type of design‐of‐experiment technique).The geometry considered for this purpose is that of a simple gas turbine can combustor and the study is restricted to the isothermal non‐reacting condition.Tests are carried out on three different grid configurations. In each case the underrelaxation factor for velocities contributed most to speed up the rate of convergence. Also, for each grid configuration the underrelaxation factor settings for minimum iterations for convergence was found to be same. Hence it is proposed that when doing grid independence tests for any similar flow situation, all the underrelaxation factors could be optimized on coarse grids.