1.1 Overview of ACE-3D

ACE-3D has been developed by the Japan Atomic Energy Agency (JAEA) to simulate water- vapor or water-air two-phase flows at subcritical pressures. The basic equations of ACE-3D are shown below.

Mass conservation for vapor and liquid phases:

dt (agpg> + dx. iagpgUg, j> Г

Here, t represents time; x, a spatial coordinate; U, velocity; P, pressure; g, acceleration due to gravity; e, internal energy; and p, density. Subscripts g and l indicate vapor and liquid phases, respectively. Subscripts i and j indicate spatial coordinate components. If the subscripts of the spatial coordinate components are duplicative, the summation convention is applied to the term. The terms qw and qint indicate wall heat flux and interfacial heat flux, respectively, and hsat represents saturation enthalpy. Summation of volume ratios ag and al is equal to one. Г+, Г -, and Г represent vapor generation rates. Г+ in Eq. (3) is equal to Г if Г is positive and is zero if Г is negative. On the other hand, Г — is equal to Г if Г is negative and is zero if Г is positive. T &ij and Tl/ij in Eqs. (3) and (4), respectively, are shear stress tensors. The liquid shear stress tensor, Tl/ij, is a summation of shear induced turbulence obtained and bubble induced turbulence (Bertodano, 1994).

Summation of interface stress, Mint, of the vapor and liquid phases is equal to zero. The interface stress is determined by correlations between turbulent diffusion force (Lehey,
1991), lift force (Tomiyama, 1995), interface friction force, and bubble diameter (Lilies, 1988). The lift force is calculated as follows.

= — cliftagpg (g — Ul )X rotUl

Clift Clift0 + Cwake

c = 0288 ! — exp (-0242Rebubble) Clift 0 — U.288 —

f 1 + exp (-0.242 Rebubble)

0 (Et < 4)

-0.096Et + 0.384 (4 < Et < 10) -0.576 (Et > 10)

where

In Eq. (7), a is the surface tension coefficient; Et, Eotvos number; Rebubble, the bubble Reynolds number; and Db, bubble diameter. clift0 in Eq. (7) describes the effect of shear flow and is a positive value. Cwake describes the effect of bubble deformation and significantly depends on Eotvos number of bubble diameter. The coefficient of lift force clift is estimated by the summation of clift0 and cwake. If the Eotvos number of bubble diameter is small, clift is positive. However, if the Eotvos number of bubble diameter increases, clift is negative. Therefore, the lift force corresponding to a small bubble diameter acts in a direction opposite to that corresponding to a large bubble diameter.

Bubble diameter is evaluated by the following equations.

Db ( Xslug jDbubble + XslugDslug

Xslug — 3XS2 — 2X3, Xs — 4 ( — 0.25)

where a is the surface tension coefficient; We, a critical Weber number of 5.0; and Dbmax, the maximum bubble diameter, which is an input parameter. Bubble diameter, Db, is estimated by linear interpolation of small bubble diameter, Dbubble, and slug diameter, Dslug, with a coefficient, Xslug, which is dependent on the void fraction. Therefore, Db increases with an increase in the void fraction.

In ACE-3D, the two-phase flow turbulent model based on the standard k-£ model (Bertodano, 1994) is introduced below.

Turbulent energy conservation for vapor and liquid phases:

Turbulent energy dissipation rate conservation for vapor and liquid phases:

The basic equations represented in Eqs. (1) to (12) are expanded to a boundary fitted coordinate system (Yang, 1994). ACE-3D adopts the finite difference method using constructed grids, although it is difficult to construct fuel assembly geometry by using only constructed grids. Therefore, a computational domain, which consists of constructed grids, is regarded as one block, and complex geometry such as that of a fuel assembly is divided into more than one block. An analysis of complex geometry can be performed by a calculation that takes the interaction between blocks into consideration. Parallelization based on the Message Passing Interface (MPI) was also introduced to ACE-3D to enable the analysis of large-scale domains.

From a previous experiment in which the three-dimensional distribution of the void fraction (vapor volume ratio) in a tight-lattice fuel assembly was measured (Kureta, 1994), it is known that the vapor void (void fraction) is concentrated in the narrowest region between adjacent fuel rods near the starting point of boiling and as the elevation of the flow channel increases, the vapor void spreads over a wide region surrounding the fuel rods. This tendency of the vapor void to redistribute has been described by a past analysis using ACE — 3D (Misawa, et al., 2008). Therefore, it is confirmed that the boiling two-phase flow analysis can be carried out using ACE-3D under steady-state conditions and with no oscillation.