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 transport is reduced to the 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.

Grid refinement

LES grid must respect around the pins and the endwalls the following requirements for a wall resolved LES almost everywhere in the matrix region (Δx+<40, Δx+<80,Δx+<2). Delibra et al. meshes with LES contained 5.5 and 15 million cells for the two highest Reynolds number respectively and the present meshes contain 18 and 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
Transition modelling
Near-wall modelling
Other modelling

Turbulence Modelling

Linear eddy viscosity models can't be used in the present configuratio. They give wrong results and don't exhibit unsteadiness at the highest Reynolds number, at least for the four 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.
If one considers the work of Delibra et al., wall modelling using wall fucntions is to be ivoided.

Application Uncertainties

Summarise any aspects of the UFR model set-up which are subject to uncertainty and to which the assessment parameters are particularly sensitive (e.g location and nature of transition to turbulence; specification of turbulence quantities at inlet; flow leakage through gaps etc.)

Recommendations for Future Work

Propose further studies which will improve the quality or scope of the BPA and perhaps bring it up to date. For example, perhaps further calculations of the test-case should be performed employing more recent, highly promising models of turbulence (e.g Spalart and Allmaras, Durbin's v2f, etc.). Or perhaps new experiments should be undertaken for which the values of key parameters (e.g. pressure gradient or streamline curvature) are much closer to those encountered in real application challenges.

Contributed by: Sofiane Benhamadouche — EDF