Analysis of Leaks Through Microchannel Cracks Using RELAP5-3D

The purpose of the present work is to study the flow leakage through postulated microchannels. In the framework of the leak before break, it is reasonable to assume that a detectable leak develops before a large break occurs. A large pressure difference may exist between the crack inlet and outlet; the fluid residence time is so brief that thermodynamic equilibrium conditions cannot be reached within the crack. Using RELAP5-3D system code, the modified Henry's homogeneous nonequilibrium model was adopted to simulate the fluid condition at the choked point. In channels with large L/D_H, mechanical equilibrium between the phases is usually reached. On the other hand, because of the small residence time, thermal equilibrium may not be achieved. Thus, the critical flow through the crack is kinematically homogeneous, but thermodynamically in nonequilibrium conditions. In this investigation, various channel cross-flow areas were considered, each having a sensitivity study performed in reference to the wall roughness. In this approach it was possible to analyze the dependence of channel pressure drop as a function of the Reynolds number and wall roughness. For high values of the Reynolds number, the pressure drop showed very little influence of the Reynolds number over the fluid conditions inside the microchannel. On the other hand, the wall roughness strongly influences the channel pressure drop and, consequently, the critical mass flow rate through the crack. The RELAP5-3D wall friction correlation was compared with various available models in the literature, such as John et al. (1987), modified Karman, Nikuradse (1933), and Button et al. (1978). These correlations predict similar values for the friction factor.

The RELAP5-3D model was also in agreement with modified Karman correlation for the studied wall roughness values. However, it underestimated the friction factor with respect to John's formula. This indicates that the crack critical mass flow rate predicted by RELAP5-3D is larger than that calculated using John's correlation.