Investigation of Small Numerical Instabilities Generated by the Lagrangian Tracking Scheme

We have undertaken simulations of steady-state multiphase flows using the Lagrangian technique. It was noted that in previous studies, we found simulations for certain numerical parameters, flow conditions and problems, that it was not possible to achieve a high-order convergence for the residuals. In this paper we discuss some of these problems and attempt to solve them by various techniques. The investigations have found that there exists a relationship between several characteristics of the model and its convergence behaviour. These characteristics include the void fraction of particles, the number of particle streams and the interval ratio of flow to particle calculations. The problem of high order convergence for all these problems is demonstrated by first selecting a ‘standard configuration’ flow problem of a backward facing step and then varying selected parameters. In order to avoid problems associated with physical modeling of the problem or with turbulence modeling, it was decided to use a laminar flow case. Laminar flow also has the advantage that it appears to be more affected by the presence of particles than turbulent flow. Simulations were undertaken using an in-house CFD code which is designed to solve dilute particulate flow problems. The results of this study show that there is a good correlation between some of the numerical parameters and the magnitude of the order of convergence that can be achieved. We propose that it is possible to use these results to develop procedures whereby the problem of high-order convergence can be achieved. One example of this might be to slowly increase the mass flow rate of particles over a number of iterations. The results from this study should also be of interest to commercial CFD users since they can implement changes without having to directly manipulate the code. Anthony J. Morgan and Iain E. Barton