Fluid model equations system geometry

The modeling is based on adaptation of the equations in the previous section to the coupled loops case. The model equations developed herein will be written for the case of single-phase flow in the primary and secondary loops. Both steady-state and off-normal transient conditions in the Gen IV nuclear reactor case involve two-phase fluid states. Safety-grade analyses of design and off-normal states will generally be handled by systems-analysis models and codes that easily accommodate generalized geometry, fluid states, and flow directions. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

An even more drastic simplification of the dynamics is made in lattice-gas automaton models for fluid flow [127,128]. Here particles are placed on a suitable regular lattice so that particle positions are discrete variables. Particle velocities are also made discrete. Simple rules move particles from site to site and change discrete velocities in a manner that satisfies the basic conservation laws. Because the lattice geometry destroys isotropy, artifacts appear in the hydrodynamics equations that have limited the utility of this method. Lattice-gas automaton models have been extended to treat reaction-diffusion systems [129]. 

The governing equations, along with the appropriate constitutive relations, completely describe the fluid flow within a given geometry. However, the mathematical model forms a system of partial differential equations obeying mixed elliptic-parabolic behaviour which cannot be solved unless we specify the boundary conditions for the problem. Mathematically they fix the integration constants yielded upon integration. From a physical point of... 

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