Treatment of physical and numerical diffusion in fluid dynamic simulations

Abstract

A computer code is developed to predict the behavior of the hydrogen gas in the containment aftet a loss-ofcoolant accident. The conservation equations for the four components, i.e., air, hydrogen, steam and water, are set up and solved numerically by decoupling the continuity and momentum equations from the energy, mass diffusion and turbulence equations. The homogeneous mixture form is used for the momentum and energy equations and the steam and liquid droplets are assumed to be in the saturation state.

There are two diffusion processes, molecular and turbulent, which should be modelled in different ways. Molecular diffusion is modelled by Wilke's formula for the multi-component gas diffusion, where the diffusion constants are dependent on the relative concentrations. Turbulent diffusion is basically modelled by the k- model with modifications for low Reynolds number flow effects. Numerical diffusion is eliminated by a corrective scheme which is based on accurate prediction of cross-flow diffusion. The corrective scheme in a fully explicit treatment is both conservative and stable, therefore can be used in long transient calculations. The corrective scheme allows relatively large mesh sizes without introducing the false diffusion and the time step size of the same order of magnitude as the Courant limit may be used.