4. Models and methods

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64

4. Models and methods

The general purpose code ANSYS CFX 15 [43] was used for all the numerical simulations presented here. The code employs a coupled technique, which simultaneously solves all the transport equations in the whole domain through a false time-step algorithm. The linearized system of equations is reconditioned in order to reduce all the eigenvalues to the same order of magnitude. The multi-grid approach reduces the low frequency error, converting it to a high frequency error at the finest grid level; this results in a great acceleration of convergence.

Although, with this method, a single iteration is slower than a single iteration in the classical decoupled (segregated) SIMPLE approach, the number of iterations necessary for a full convergence to a steady state is generally of the order of 10

, against typical values of 10

for decoupled algorithms.

The SST (Shear Stress Transport) k-ω model by Menter [44] is extensively used in this paper.

It is formulated to solve the viscous sub-layer explicitly, and requires several computational grid points inside this latter. The model applies the k-ω model close to the wall, and the k-ε model (in a k-ω formulation) in the core region, with a blending function in between. It was originally designed to provide accurate predictions of flow separation under adverse pressure gradients, but it has since been applied to a large variety of turbulent flows and it is now the default and most commonly used model in CFX-15 and other CFD codes.

The SST model adopts the eddy diffusivity approach for momentum transport. Regarding heat transfer, the k-ω family turbulence model adopted in this context, uses, coherently with the classical turbulence theory, the well-known analogy between turbulent transport of momentum and energy, i.e. a Reynolds analogy re-proposed at a turbulence level; for the turbulent thermal diffusivity Γ

:

= (4.1) where Pr

is the turbulent Prandtl number, which is of the order of 1 for liquid metals and it has been kept constant and fixed to 1.5 for LBE in this case, according to the literature [47].

The ratio of this choice was more extensively discussed in the context of the presentation of results in section 6.1.2.

4.1 The CFD model of the FPS

A full 3D CFD computation of the Fuel Pins Simulator (FPS) has been performed in order to assess the local and global effect of the wire spacer, better understanding the velocity field and its development in this complex geometry and assess heat transfer phenomena between heated pins and LBE.

The model is geometrically built on the nominal sizing of the pin and the wire. A collapsed

model [17] was adopted for wires and pins simulation, avoiding the contact point issue

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involved in heat transfer phenomena between this two bodies. A nominal interference of 0.05 mm was imposed on wire-pin centre-to-centre distance.

4.1.1. The preliminary model (only fluid) The model developed can be seen in Figure 4-1. It includes:

 A 20 mm horizontal inlet region for imposing a more realistic inlet boundary condition and investigate the whole length of the pin bundle;

 A 753 mm vertical developing region (in blue), non-heated, lower sliced at the horizontal inlet pipe, with a wire wrap bundle geometry and a sudden contraction passing from circular to hexagonal external shape (Figure 3-4).

 A 600 mm vertical active region (in red), for investigating the thermal field inside the LBE and heat transfer phenomena involved.

 A 120 mm vertical follower region (in orange), including the last unheated part (100 mm) of the pin bundle, the pins support grid (for investigating its hydraulic effect) and 10 mm upper region for future comparisons with NACIE-UP experimental data.

According to ANSYS Meshing best practice, the CAD model was sliced in 100 mm length pieces.

As we can see from Figure 4-3, unstructured tetrahedral mesh elements were adopted and the number of mesh elements is inflated on fluid-solid boundary surfaces for a better resolution of the viscous sub-layer; the y

obtained ranges from 1 to 4 .

The working fluid simulated is LBE with constant properties fixed at 250 °C [45] and resumed

OUTLET

INLET

BOTTOM

Figure 4-1 Layout of the preliminary CFD model developed.

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66

in Table 4-1. Every buoyancy effect into the sub-channels is neglected (Ri

≪ 1).

LBE (250°C)

ρ [kg / m

] 10403.5

C

[J / kg / K] 146.72

μ [Pa s] 2.088∙10

k [W / m / K] 11.336

Pr 2.7∙10

Table 4-1 The LBE properties implemented in the CFD simulation.

A fixed mass flow rate, a constant temperature of 200 °C and a 5 % turbulence intensity is imposed on the inlet section (INLET). A free slip condition is imposed on the lower surface of the model called BOTTOM (being a virtual surface into the LBE). A constant heat flux condition is imposed on pins surfaces of the active region. A constant zero pressure condition is imposed at the outlet section (OUTLET). All the other surfaces, included the external pipe surfaces in the active region, are adiabatic.

4.1.2. The solid structures issue

Including solid structures as pins, wires and the hexagonal pipe of the active region into the CFD model has benefit and drawbacks. The most important advantage is the conjugate heat transfer effect inclusion in the CFD study, especially the large hexagonal pipe’s one. The principal drawbacks are mesh generation problem for linking the mesh of the fluid body with the new ones and higher computational efforts for the CFX Solver unit given from the increased number of nodes.

4.1.3. The complete model with solid structures

All the solid structures of the active region (pins, wires and hexagonal pipe) are included into the preliminary model. The solid structure of the pins includes only the external steel clad,

Figure 4-2 A detailed view of the generated mesh.

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while the copper electrical wires and the electrical insulation are neglected. A sketch of the final result is given in Figure 4-3, with the hexagonal pipe in green and the heated elements (pins and wires) in orange. For a more realistic simulation of the heat transfer phenomena involved between pin and wire, the actual steel thickness of the pin is implemented.

The mesh of the solid structures is generated with a semi-structured method adopting tetrahedral and hexahedral elements both, as we can see from the mesh elements of the hexagonal pipe in Figure 4-3.

The boundary conditions on INLET, OUTLET and BOTTOM surfaces are the same of the previous model. This heat flux condition is now imposed on the inner surface of the pins (while the total thermal power is the same), a fluid-solid interface condition is imposed between the surfaces of the heated fluid and the corresponding solid ones. All the other surfaces, included the external surface of the hexagonal pipe, are adiabatic.

Figure 4-3 Layout of the complete CFD model developed.

OUTLET

INLET

BOTTOM