UFR 4-18 Description

Flow and heat transfer in a pin-fin array

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Description

Test Case Studies

Evaluation

Best Practice Advice

References

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 for internal cooling of gas-turbine blades, electronic devices and can be also found 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 a complex physics but its geomhetry in enough simple to allow deep and precise analysis.

Review of UFR studies and choice of test case

Relevent studies

Experimental investigations

Several experiment exist in the literature around the use of pin fin arrays to increase the turbulence levels which leads to enhance heat transfer.

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

Ames et al. (2004, 2005, 2006, 2007), from 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 fine experimental data (mean-velocity, turbulence quantities, local Nusselt numbers) which will be used to confront CFD computations are from this team.

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

Numerical investigations

This configuration has already been studied numerically by Delibra et al. (2008, 2009, 2010) using Unsteady Reynolds Average Navier Stokes (URANS) with the ζ-f model (Hanjalic et al. (2004)) and a hybrid RANS/LES for the two highest Reynolds numbers. They also performed a LES but it seemed to be under-resolved. They concluded that the URANS approach presented 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 (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.

Ames and Dvorak (2006a) also conducted RANS computations with the Realizable and RNG k-ε. They concluded that their approach was underpredicting heat transfer and pressure drop. This discrepancy was attributed to the fact that unsteadiness was not possible to predict(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. 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 should be published soon in a journal paper.

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