# UFR 4-18 Description

# Flow and heat transfer in a pin-fin array

## Confined Flows

### Underlying Flow Regime 4-18

# Description

## Introduction

The present case consists of the flow through a wall bounded pin matrix in a staggered arrangement with a heated bottom wall. In addition to its interest for the complex underlying physics, this case is close to several industrial configurations found in internal cooling of gas-turbine blades, electronic devices and also in the nuclear field.

The pin fins accelerate the flow in the reduced passages and produce wake regions behind the pins caracterized by strong vortex shedding. This leads to high turbulence levels which enhance heat transfer. The presence of endwalls leads to the apparition of horseshoe vortices which also enhance heat transfer.

The available heat transfer measurements by Ames et al. (2004, 2005, 2006, 2007), which will be used all along this UFR, are rare and valuable for CFD validation. The present case can be qualified as a semi-industrial test-case as it involves complex physics but its geomhetry is simple enough to allow a deep and precise analysis.

## Review of UFR studies and choice of test case

### Relevent studies

#### Experimental investigations

Several experimenal studies exist in the literature on the use of pin fin arrays to increase the turbulence level which leads to enhanced heat transfer.

Jacob (1938) provides correlations for the pressure drop coefficient as a function of the pitch to diameter ratio and the Reynolds numbers. Metzger et al. (1982) and Van Fossen (1982) studied experimentally several configurations with heat transfer and provided correlations for the global Nusselt number.

Ames et al. (2004, 2005, 2006, 2007), from the University of North Dakota, carried out a fairly extensive and comprehensive experimental study for a particular configuration: the incompressible flow through a confined staggered pin-fin array with a pitch-to-diameter ratio of 2.5, at three Reynolds numbers (3000, 10000, 30000) and with a heated bottom wall in the forced convection regime. Note that there are also data with heated pins. All the detailed experimental data (mean-velocity, turbulence quantities, local Nusselt numbers) which will be used to confront CFD computations are from this team.

The experiments and computations which are related to the present configuration are recalled hereafter. The reader can refer to the two following articles to have additional references: Lawson et al. (2011) and Rao et al. (2012).

#### Numerical investigations

The configuration examined experimentally by Ames et al has already been studied numerically by Delibra et al. (2008, 2009, 2010) using the Unsteady Reynolds Averaged Navier Stokes (URANS) approach with the ζ-f model (Hanjalic et al. (2004)) and a hybrid RANS/LES method for the two highest Reynolds numbers. They also performed a LES but it seemed to be under-resolved. They concluded that the URANS approach revealed several discrepancies, among them, its inability to reproduce the unsteadiness of the flow around the first three arrays of the matrix. They also suggested that the small structures unresolved by URANS need to be predicted. This brought them to conduct hybrid RANS/LES calculations (LES using a dynamic Smagorinsky model with RANS wall-treatment based on the ζ-f model). They found that hybrid RANS/LES gave more acceptable accuracy than URANS, in particular for capturing the large convective structures. Note that the computational domain of the URANS and hybrid RANS/LES approaches consisted of 8 by 2 and 8 by 1 pins, respectively, and that the wall temperature and not the heat flux was fixed at the bottom wall.

Ames and Dvorak (2006a) also conducted RANS computations with the Realizable k-&epsilon and RNG k-&epsilon models. They concluded that their approach underpredicted heat transfer and pressure drop. This discrepancy was attributed to the fact that unsteadiness was not possible to predict with this approach(no vortex shedding).

### Choice of test case

The configuration studied by Ames et al. was chosen as a test case for the 15th ERCOFTAC-SIG15/IAHR Workshop on Refined Turbulence Modelling which took place in 2011 at EDF Lab Chatou, France (EDF = Electricité de France). Since the calculations were carried out for this workshop, the present test case has been chosen for the UFR. The computations which will be shown have been partly published by Benhamadouche et al. (2012) and are to be published soon in a journal paper.

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