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TECHNICAL PAPERS: Forced Convection

# Investigation of Detached Eddy Simulations in Capturing the Effects of Coriolis Forces and Centrifugal Buoyancy in Ribbed Ducts

[+] Author and Article Information
Aroon K. Viswanathan

High Performance Computational Fluids-Thermal Sciences and Engineering Group, Mechanical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

Danesh K. Tafti

High Performance Computational Fluids-Thermal Sciences and Engineering Group, Mechanical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061dtafti@vt.edu

Although the whole domain is considered in the computations, because of the two-way symmetry in the $y$ and $z$ directions, only a quadrant of the domain is presented in the results.

J. Heat Transfer 129(7), 778-789 (Jan 05, 2007) (12 pages) doi:10.1115/1.2717944 History: Received September 04, 2006; Revised January 05, 2007

## Abstract

The predictive capability of Detached Eddy Simulations (DES) is investigated in stationary as well as rotating ribbed ducts with relevance to the internal cooling of turbine blades. A number of calculations are presented at $Re=20,000$ and rotation numbers ranging from 0.18 to 0.67 with buoyancy parameters up to 0.29 in a ribbed duct with ribs normal to the main flow direction. The results show that DES by admitting a LES solution in critical regions transcends some of the limitations of the base RANS model on which it is based. This feature of DES is exemplified by its sensitivity to turbulence driven secondary flows at the rib side-wall junction, to the effect of Coriolis forces, and centrifugal buoyancy effects. It is shown that DES responds consistently to these non-canonical effects when RANS and URANS with the same model cannot, at a cost which is about a tenth of that of LES for the geometry and Reynolds number considered in this study.

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## Figures

Figure 1

Computational domain considered for the fully developed ribbed channel with normal ribs. Flow is in the positive x direction and is periodic in this direction.

Figure 2

Separation and reattachment of the shear layer due to the presence of the rib. The arrow shows the direction of the flow.

Figure 3

Comparison of the secondary velocities predicted at y∕Dh=0.15, z∕Dh=0.5

Figure 4

Heat transfer distribution in one quadrant of the duct with normal ribs. Direction of the flow is indicated by the arrows.

Figure 5

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

Figure 6

Geometry of a rotating sudden expansion duct used to study the effect of Coriolis forces (top). Variation of the reattachment length with rotation as predicted by DES and RANS studies (bottom).

Figure 7

Streamlines showing the flow in a fully developed duct rotating at Ro=0.35 at Z=0.5 as predicted by (a) LES and (b) DES. Y=0 represents the trailing wall, while Y=1 represents the leading wall. Flow direction is from left to right.

Figure 8

Heat transfer augmentation (Nu∕Nu0) predicted at the leading (upper half of the plot) and the trailing walls (lower half of the plot) for the Ro=0.35 case by (a) LES and (b) DES. Flow direction is from left to right.

Figure 9

Heat transfer augmentation (Nu∕Nu0) predicted at the side wall for the Ro=0.35 case by (a) LES and (b) DES. Flow direction is from left to right.

Figure 10

Side wall heat transfer predicted by LES and DES for the various rotation cases

Figure 11

Comparison of pitch averaged Nusselt number augmentation ratios at the leading and trailing sides with experiments

Figure 12

Comparison of the temperature variation in the cavity predicted by DES in comparison with experimental measurements by Grand (53)

Figure 13

Comparison of the recirculation regions at the leading edge for the three different buoyancy cases with Ro=0.35

Figure 14

Heat transfer distribution at the ribbed walls for varying buoyancy parameters for a constant Ro=0.35

Figure 15

Effect of the variation of rotation and buoyancy on the heat transfer at the side walls, plotted at a distance of 0.5e upstream of the ribs

Figure 16

Comparison of the ribbed (top) and side wall (bottom) heat transfer predicted by DES and LES for Ro=0.35 and Bo=0.29

Figure 17

Comparison of the surface averaged ribbed wall heat transfer augmentation

Figure 18

Comparison of the side wall heat transfer augmentations

## Errata

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