# UFR 4-18 Best Practice Advice

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# Flow and heat transfer in a pin-fin array

## Confined Flows

### Underlying Flow Regime 4-18

# Best Practice Advice

## Key Physics

Our aim in the present test-case is to predict the following physical parameters:

- The pressure drop across the matrix.
- The average and local Nusselt numbers on the bottom wall.

The temperature is passive (forced convection regime), thus predicting the dynamics of the flow is the critical issue. The two key physical phenomena which have then to be captured here are:

- The vortex shedding around the pins.
- The horseshoe vortices due to the interaction between the pins and the endwall.

## Numerical Modelling

### Numerical scheme

- The convection scheme must be centered for the velocity components but may involve some upwinding for URANS computations, and purely centered in LES. This is mandatory to have the unsteadiness.
- The convection scheme for the turbulent quantities can rely on an upwind scheme for fine meshes.

### Grid refinement

- For a wall resolved LES, the grid must respect the following requirements around the pins and the endwalls: (Δx+<40, Δz+<80,Δy+<2). Delibra et al.'s LES was carried out with 5.5 million meshes for the Reynolds number of 10000 and the present calculation with 76 million computational grid points at the same Reynolds number and with a similar discretization scheme. For High fidelity results, the finer mesh used in the present study is necessary.
- A strict convergence study must be carried out for URANS computations and this will lead to very fine meshes which might be unusual for URANS computations (the number of grid points has not been optimized in the present work, it should be equal to few millions).

## Physical Modelling

### Turbulence Modelling

- Linear eddy viscosity models cannot be used in the present configuration. They give wrong results and do not exhibit unsteadiness at the highest Reynolds number, at least for the four first rows of pins.
- Large Eddy Simulation is in very good agreement with experimental results. With the present fine grid used, the sub-grid scale model seems to play a minor role.
- The Elliptic Blending Reynolds Stress Model (EB-RSM) combined with a Generalized Gradient Diffusion Hypothesis for the turbulent heat fluxes gives very satisfactory results at the highest Reynolds number and this is promising for industrial configurations.

### Boundary conditions

- At the inlet, standard boundary conditions can be used; uniform velocity for LES without any turbulence and a uniform velocity and 5% turbulence intensity for URANS approaches.

### Computing physical quantities

Special care has to be taken to calculate the local Nusselt number on the bottom wall by taking into account the increase in the bulk temperature of the fluid from the heated surface as it flows down the array (see "Test Case Studies" section).

## Recommendations for Future Work

- LES at Re=30000 with more computing power.
- Test more advanced wall-resolved turbulent heat-flux models.
- Extend the computational domain to more pins in the span-wise direction in order to check the effect of this uncertain parameter.

Contributed by: **Sofiane Benhamadouche** — *EDF*

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