The Effect of Numerical Diffusion on Oscillatory Flow in Two-Phase Boiling Channel

The purpose of this paper is to study the effect of numerical diffusion on the ill-posedness and the accuracy of the model simulated the thermal-hydraulic instabilities in boiling water reactor channels. The model of the upward flow system in two-phase boiling channel simulating BWR core was developed to investigate the oscillatory flow, which was caused by flow instabilities, by using the drift-flux model. The time step was fixed at 1 millisecond at all time and the mesh size was varied as follows: 400, 200, 100, 50 and 20 mm. Then the numerical diffusion in the conservation equations was analyzed in reference to spatial mesh size. The maximums of the absolute ratios of the first order and the second order approximations of the time derivative terms (A/B) and the convective terms (C/D), including the summations of the second power of the ratios of the second order and the first order approximations of the time derivative terms (Σ(B/A)²) and the convective terms (Σ(D/C)²) were calculated to investigate the ill-posedness and the accuracy of numerical calculation of this model. The results from the model showed that the numerical diffusion in the time derivative term and the convective term play the important role in the drift-flux model for the small mesh size and may cause the ill-posedness and degrade the accuracy of the model. It was found that the A/B, the C/D, the Σ(B/A)² and the Σ(D/C)² in the drift-flux model highly fluctuated at the small mesh size of 50 and 20 mm. More importantly, the numerical diffusion due to the oscillation flow and the mesh size variation may have an effect on the amplitude of the pressure drop of the oscillatory flow at the small mesh size.