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SPECIAL SECTION ON RANS/LES/DES/DNS: THE FUTURE PROSPECTS OF TURBULENCE MODELING

# Detached Eddy Simulation of Turbulent Flow and Heat Transfer in a Ribbed Duct

[+] Author and Article Information
Aroon K. Viswanathan

Mechanical Engineering Department,  Virginia Polytechnic Institute and State University, Blacksburg, VA 24060

Danesh K. Tafti

Mechanical Engineering Department,  Virginia Polytechnic Institute and State University, Blacksburg, VA 24060dtafti@vt.edu

J. Fluids Eng 127(5), 888-896 (Jul 13, 2005) (9 pages) doi:10.1115/1.2033010 History: Received July 29, 2004; Revised July 13, 2005

## Abstract

Detached Eddy Simulation (DES) of a hydrodynamic and thermally developed turbulent flow is presented for a stationary duct with square ribs aligned normal to the main flow direction. The rib height to channel hydraulic diameter $(e∕Dh)$ is 0.1, the rib pitch to rib height $(P∕e)$ is 10 and the calculations have been carried out for a bulk Reynolds number of 20,000. DES calculations are carried out on a $963$ grid, a $643$ grid, and a $483$ grid to study the effect of grid resolution. Based on the agreement with earlier LES computations, the $643$ grid is observed to be suitable for the DES computation. DES and RANS calculations carried out on the $643$ grid are compared to LES calculations on $963∕1283$ grids and experimental measurements. The flow and heat transfer characteristics for the DES cases compare well with the LES results and the experiments. The average friction and the augmentation ratios are consistent with experimental results, predicting values within 10% of the measured quantities, at a cost lower than the LES calculations. RANS fails to capture some key features of the flow.

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## Figures

Figure 1

The computational model. A pair of ribs placed at the center of the duct. Flow in the duct is periodic in streamwise direction. A 643 mesh (baseline grid) is used to grid the domain. The dark lines represent the 8 blocks into which the domain is divided.

Figure 2

Comparison of the streamwise velocities in a plane through the ribs (Y∕e=0.25) for the (a) 483 grid, (b) 643 grid, (c) 963 grid, and (d) LES 1283 case. 643 and the 963 case show the best agreement. 483 grid underpredits the velocities.

Figure 3

Plot of the LES and RANS region in the DES computation for the 643 grid in a Z plane. A value of 1 represents a complete LES region and a value of 0 a complete RANS region.

Figure 4

Streamline plots at the center of the duct for the (a) k-ω and (b) Menter’s SST DES calculations showing flow separation and reattachment

Figure 5

Streamwise velocity distributions at the center of the duct at Y∕e=0.1

Figure 6

Comparison of streamwise velocity distributions at Y∕e=0.25 for the (a) k-ω DES case, (b) SST DES case, (c) k-ω RANS case, and (d) LES case

Figure 7

Comparison of the secondary flow distribution at Y∕e=1.5 and Z∕Dh=0.45

Figure 8

Comparison of the secondary flow (a) predicted by DES k-ω model, (b) DES SST model, (c) k-ω RANS model, (d) experiment (10-11)

Figure 9

Streamlines showing the recirculation region in front of the rib and primary and secondary circulations behind the rib and their effect on heat transfer on the walls. Red regions represent high heat transfer, while blue regions represent low heat transfer.

Figure 10

Comparison of augmentation ratios on the ribbed floor for the (a) k-ω DES case, (b) Menter’s SST DES case, (c) k-ω RANS case, and (d) LES case

Figure 11

Comparison of the augmentation ratios (a) at the center of the ribbed floor and (b) side walls upstream of the rib

Figure 12

Comparison of the heat transfer augmentation ratios on the side walls (a) k-ω DES, (b) Menter’s SST DES, (c) k-ω RANS, and (d) LES

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