Fig. 7-5 Motion of the fluid in a two-dimensional rectangular vessel is calculated under the boundary condition that the fluid at the top boundary moves with a given speed (the cavity flow problem). The rotating flow of the fluid is reproduced by the CA method.

Fig. 7-6 Time evolution of the cavity flow of the two-phase fluid with the initial condition that the two phases are separated vertically. With the progress of the simulation run a large cluster of the mixed fluid appears, consisting of many small phase-separated parts.

Fig. 7-7 Dependence of the interfacial area concentration on the boundary speed and the fluid density for the steady state cavity flow. The horizontal axis denotes the speed of the fluid at the top boundary and the vertical axis is the interfacial area concentration normalized so that it is equal to unity when the speed is zero.

For the safety analyses of a nuclear power reactor it is necessary to carry out a simulation of a two-phase flow as bubbles may form in a cooling pipe. In such a case, when two immiscible fluids, water and vapor, are mixed with each other, the boundary surfaces between the phases become gradually larger with increasing mixing rate. It is rather difficult, therefore, to understand the behavior of such a system by solving partial differential equations. Quantitatively the scale of the boundary surface is defined as the "area of the boundary surfaces in a unit volume," i.e., the "interfacial area concentration." As the transport between two phases always occurs through this surface, one can evaluate the transport of various physical quantities between the two phases if the interfacial area concentration is known. To know the interfacial area concentration we usually depend on experimentally obtained scaling laws as we cannot rely on the solution of the partial differential equations. We demonstrated that the cellular automata (CA) method is effectively applied to calculate the interfacial area concentration of the two-phase flow. As an example we solved the "cavity flow problem" where the fluid motion in a two-dimensional rectangular vessel is calculated by giving a finite speed at the top boundary (Fig. 7-5) for immiscible fluids by using a kind of CA method, the "immiscible lattice gas model." It is shown in Fig. 7-6 that from the initial condition when the two phases are separated vertically they become mixed with time, and finally a large cluster of the fluids composed of two mixed phases appears. Figure 7-7 shows the dependence of the interfacial area concentration on the boundary speed and the fluid density.

Reference T. Watanabe et al., Numerical Evaluation of Interfacial Area Concentration Using the Immiscible Lattice Gas, Nucl. Eng. Des., 188, 111 (1999).

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