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 even with 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. meshes for LES contained 5.5 for the Reynolds number equal to 10000 and the present meshes contain 76 million computational grid points at the same Reynolds number and with a similar discretization scheme.
- 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).
Physical Modelling
Turbulence Modelling
- Linear eddy viscosity models can't be used in the present configuration. They give wrong results and don't exhibit unsteadiness at the highest Reynolds number, at least for the four first rows of pins.
- Large Eddy Simulation is in very good agreemnt with experimental results. With the present refinements, the sub-grid scale model seems to play a minor role.
- The Elliptic Blending Reynolds Stress Model (EB-RSM) combined to a Generalized Gradient Diffusion Hypothesis for the turbulent heat fluxes gives very satisfactory results at the highest Reynolds number and this is promizing for industrial configurations. There is no point of using a Simple Gradient Diffusion Hypothesis if one consideres the results obtained with this combination on a simple 1D turbulent channel flow.
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 advance turbulent wall resolved turbulence 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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