The central, wall and corner sub-channels forming the entire domain of interest were modeled individually, duplicated and translated to their respective positions to form the geometry. Spacer grid CAD file made by using CATIA 5 obtained from KAERI was then imported a number of times and the Boolean operation “Subtract parts” applied at each import to subtracts the shape defined by the spacer grid with vanes from the volume of the sub-channel. Upon the Boolean operation, the surfaces of the imported spacer grid were imprinted in the target sub-channel. After identifying the inlet, outlet, and spacer grid boundaries the 3D CAD model was used to create a new geometry part with the named parts forming separate surfaces. The resulting fluid part was then assigned to region with the region mode set to one region per part and the boundary mode to one boundary per part surface. In-place interfaces were automatically formed and correctly defined. The new region has as its boundaries, the part surfaces defining the inlet, outlet, spacer grid and fluid volume. Velocity inlet, pressure outlet and no slip wall boundary types were assigned respectively and a geometry scene created to enable visualization of the final geometry which was used as sub-surface for mesh generation [12] [13].

Surface, polyhedral, prism and extruder meshing models were applied. The initial surface was re-tessellated so as to obtain a finer triangulation for generation of a high-quality volume mesh [5]. In the present study, the surface remesher was employed to re-triangulate and optimize the surface quality for volume meshing and also generate the sub-surface for the prism layer mesher. Table 1 shows the surface mesh parameters used in the present study [12] [13].

The polyhedral mesh type was selected considering such factors as, the turn-around time for building the mesh, the desired solution accuracy and convergence rate, the computational memory available, the quality of the starting surface mesh and quality of solution. The prism layer mesh model was used in conjunction with the core polyhedral mesh to generate orthogonal prismatic cells next to wall boundaries. The thickness of each cell layer was calculated using a geometric progression approach based on a constant size ratio. Table 2 shows the specification used for the prism layer in the present study.

The inlet and outlet boundaries of the completed geometry were extruded using the method of constant rate normal to extend the original domain along the z-axis to the required dimension in Figure 6. After a successful application of the meshing models, the meshed geometry generated is as illustrated in Figure 6. The mesh density and wall y⁺ are 9.5 million and 11 respectively. Table 3 shows the extrusion mesh reference values [12] [13].

The physics continuum for single phase liquid (water) used for the present study consisted of the models shown in Table 4.

1) Material Modeling

Single component water which was the material simulated in the continuum was responsible for managing the various thermodynamic and transport properties and physical processes being modeled in the continuum. Table 5 illustrates the properties of water used in the present study [12] [13].

2) Turbulence Modeling

The three turbulence models employed for this work are the realizable two-layer k-epsilon model, the non-linear standard k-epsilon model and the SST-k-Omega model [5]. Although it is strictly possible to simulate turbulent flow directly by resolving all the scales of the flow (termed direct numerical simulation), the computer resources required are too large for practical flow simulations [5]. Therefore, a suitable turbulence modeling approach which provides closure of the governing equations in turbulent flows must be employed. Most simulations rely on models that provide closure for the Reynolds Average Navier Stokes (RANS) equations. The challenge in turbulence modeling however is the model of the Reynolds stress tensor in terms of the mean flow quantities. The eddy viscosity model and the Reynolds stress transport models are the two basic approaches employed for modeling the stress tensor which is expressed as [5].

T t = ρ u ′ u ′ ¯ = ρ [ u ′ u ′ ¯ u ′ v ′ ¯ u ′ w ′ ¯ u ′ v ′ ¯ v ′ v ′ ¯ v ′ w ′ ¯ u ′ w ′ ¯ v ′ w ′ ¯ w ′ w ′ ¯ ] (1)

For the present study, k-epsilon turbulence model which is a two-equation model that solves transport equations of turbulent kinetic energy k and its dissipation rate ε was employed. The inherent approach employed to model the stress tensor is therefore the eddy viscosity model which is based on the concept of turbulence viscosity. The most common eddy viscosity model is the Boussinesq approximation which is given by Equation (2) [5].

ρ u ′ u ′ ¯ = 2 μ t S − 2 3 ( μ ∇ ⋅ v + ρ k ) I (2)

where, k is the turbulent kinetic energy and S is the strain tensor computed from the resolved velocity fields v . Although the k-epsilon model also exists in its standard form, the realizable two-layer model was adopted for the present investigation. The realizable two-layer k-epsilon model combines the realizable k-epsilon model with the two-layer model and hence gains added flexibility of an all-y⁺ wall treatment. An all-y⁺ wall treatment is a hybrid approach designed to give results similar to the low-y⁺ wall treatment as y + → 0 and to the high-y⁺ wall treatment for y + > 30 . It will also give reasonable results for intermediate meshes where the cell centroid falls in the buffer layer [5]. The dimensionless wall distance y⁺ is related to the wall distance y from the first prism layer cell by,

y + = y v τ w ρ (3)

where, τ w is wall shear stress, ρ is density and v is kinematic viscosity.

The realizable k-epsilon model developed by Shih et al. [14] contains a new transport equation for the turbulent dissipation rate ε and also, a critical coefficient of the model C μ , expressed as a function of mean flow and turbulence properties, rather than assumed to be constant as in the standard k-epsilon model. This allows the model to satisfy certain mathematical constraints on the normal stresses consistent with the physics of turbulence. For the realizable k-epsilon model [5], the turbulent viscosity in the transport equation is evaluated by Equation (4).

μ t = ρ C μ k 2 ε (4)

where, the coefficient C μ is no longer constant as with the standard k-epsilon model, but is instead given by Equation (5) [5],

C μ = 1 A o + A s U ( ∗ ) k ε (5)

The coefficients defining the model have the following values [5],

C ε 2 = 1.9 , σ k = 1.0 , σ ε = 1.2

C ε 1 = max ( 0.43 , η 5 + η ) (6)

η = S k ε (7)

where, the turbulent kinetic energy (k) is derived from a specified turbulent intensity (I) and local velocity (v) by the relation,

k = 3 2 ( I v ) 2 (8)

and the modulus of the mean strain rate tensor S and the strain tensor S are expressed as,

S = | S | = 2 S : S (9)

S = 1 2 ( ∇ v + ∇ v T ) (10)

The two-layer approach, first suggested by Rodi [15], is an alternative to the low-Reynolds number approach that allows the k-epsilon model to be applied in the viscous sub-layer. In this approach, the computation is divided into two layers. In the layer adjacent to the wall, the turbulent dissipation rate ε and the turbulent viscosity μ t are specified as functions of wall distance. The values of ε specified in the near-wall layer are blended smoothly with the values computed from solving the transport equation far from the wall. The equation for the turbulent kinetic energy is solved in the entire flow. The realizable models implemented with a two-layer approach, enables resolution of the viscous sublayer when used with fine meshes. The two-layer model is parameterized as a length scale function, l ε = f ( y , Re y ) and a turbulent viscosity ratio function, μ t / μ = f ( Re y ) . The dissipation rate computed from the two-layer model is evaluated as [5],

ε = k 3 / 2 l ε (11)

The two-layer model blends a one-equation model. According to the Wolfstein one equation model [5],

l ε = C 1 y [ 1 − exp ( Re y A ε ) ] (12)

where, A ε = 2 C 1 and C 1 = κ C μ 3 / 2 .

C μ = 0.09 and κ = 0.42

The turbulent viscosity is computed from Equation (13) [5],

μ t μ = Re y C μ 1 / 4 κ [ 1 − exp ( Re y A μ ) ] (13)

where, Re y = k y / v and A μ = 70 .

The model coefficients for the cubic constitutive correlation as described in Baglietto et al. [16] were applied for the non-linear standard k-epsilon (NLS-K-E) model.

The under relaxation factors for the turbulence solver that controls the solution of the k-epsilon models (k and ε ) and the turbulent viscosity solver that controls the update of turbulent viscosity were under-relaxed for the flow solution to be stable and hence converged. The algebraic multigrid parameters were kept at default conditions for the present simulation [12] [13].

Figure 14 and Figure 15 show a comparison of curves of axial velocity at a lateral position of Y1 as shown in Figure 5 for the case of flow of water through a square duct that encloses a 5 × 5 rod bundle arrangement and a spacer grid without mixing vanes. For each graph, simulation data were compared for the

case that involved the imposition of periodic boundary condition (NV-SIM-CPBC) and the other with no imposed periodic boundary condition (NV-SIM) at the inlet-outlet boundaries at axial positions of 0.5 hydraulic diameters Before Spacer Grid (BSG) and 1.0 hydraulic diameter After Spacer Grid (ASG).

Large variations in the trend of axial velocity are noticed between the two interface topology types Before Spacer Grid (BSG) as observed in Figure 14. The deviation has however narrowed after flow through the spacer grid as seen in Figure 15. The upstream effect on flow due to differences in interface topology are however still prominent downstream of the spacer grid without mixing vane, as observed in Figure 15. Thus, much longer segment of the domain is required in order to nullify the entrance effect on the downstream of flow parameters.

The comparison of the interface topology effect on turbulent intensity in the presence and absence of mixing vanes is as shown in Figure 16 and Figure 17. As in Figure 16, large deviations in turbulent intensity profile of the two different topology types is observed at entry of flow to the spacer grid which is depicted by Figure 16. At exit of the spacer grid, although the variation in trend reduced drastically, an appreciable difference is profile especially at the maxima is noticeable in Figure 17. This observation indicates that in the absence of mixing vanes, the effect of the imposed inlet-outlet interface topology type on mean and turbulent flow parameters cannot be neglected immediately downstream of the spacer grid.

As observed for the case of spacer grid without attached mixing vanes, the inlet-outlet interface topology effect was evident even after flow through the spacer grid. In the presence of mixing vanes however, the deviations observed in the curves upstream were almost completely cancelled downstream of the spacer grid as shown in Figure 18 and Figure 19. Thus shorter segment of the domain than required for the case of flow through a spacer grid without vane is needed

to conceal the effect of the inlet-outlet interface topology on flow development downstream of a spacer grid with attached split mixing vanes. The computational resource demand when modeling flow through a spacer grid with split mixing vanes would therefore be appreciably lower than in the absence of mixing vanes.

Comparison of Figure 20 and Figure 21 also show a complete nullification of the interface topology effect on the turbulent parameter in the presence of mixing vanes at exit of the spacer grid.

The independence of the mean and turbulent flow parameter distribution at 1.0 hydraulic diameter downstream of the spacer grid on interface topology for the case of flow of water through a spacer grid with split mixing vanes is attributed to the additional pressure drop at this location due to the mixing vanes. Table 7 shows line averaged pressure drop values across the spacer grid obtained over line probes positioned at spacer inlet and at 1.0 hydraulic diameter from the exit face of the spacer grid. The split vane effects (ratio of pressured drop in the presence of split vane to pressure drop in the absence of split vane) at lateral

positions Y1, Y2 and Y3 as in Figure 5 for the four Reynolds numbers employed in the present study are also tabulated.

At the lateral position Y1, Table 7 shows an increase in pressure drop due to the mixing vane by 40% at Re1, 44% at Re2, 48% at Re3 and 50% at Re4. These large increases in pressure drops that are also observed at lateral positions Y2 and Y3 led to a reduction in momentum and subsequent deceleration in the flow such that much time was available to attain a more developed redistribution just behind the mixing vanes than for the case of spacer grid without vanes for which no deceleration in the axial flow due to mixing vanes is present.