Towards boiling crisis simulation : the level set method.

The accurate prediction of the so-called Departure from Nucleate Boiling is a crucial point in the safety analysis of nuclear reactor cores. Nowadays, the DNB evaluation is based on experimental correlations using numerical results of averaged two-phase flo w models. A natural goal is therefore to replace this rough procedure by a direct numerical simulation of the boiling crisis. The physical model now involves the motion of two phases separated by an interface and the main difficulty is to simulate this interface. Although there are many unresolved issues concerning the modelling of the entire boiling crisis phenomenon (such as triple points, nucleation, etc.), we focus merely on the numerical aspects of solving its hydrodynamics. Our goal is to devise a numerical algorithm for computing the motion of two compressible phases separated by an interface (with surface tension effects) through which mass, momentum, and energy exchanges occur. It is based on the level set method introduced by Osher and Sethian (1988) which views the interface as the zero level set of a so-called “level set function”. Contrary to other methods, e.g. front tracking, the point is not to follow precisely the interface but rather to “capture” it on a fix ed Eulerian mesh. The level set function is evolved by a new equation of Hamilton-Jacobi type. The main advantages of this method are its ability to deal with complex interface topologies and its versatility even for three-dimensional computations. With the evolution of computer power new challenges emerge in the numerical simulation of two-phase flo ws with applications to the safety analysis of nuclear reactors. Nowadays, almost all computer codes in this area are based on averaged models of two-phase flo ws. These models deliver satisfactory macroscopic results but are unable to predict fine microscopic phenomena that still may be pertinent for safety analysis. This is the case, for example, for the prediction of the onset of the boiling crisis in a the reactor core. Industrial computer codes use instead experimental correlations to check that nominal operating conditions stay away, with a safe margin, from the departure of nucleate boiling. The steady progress in computer speed now allows to overcome these averaged modelizations and to propose a direct simulation of the two phases separated by an interface. Many recent works