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# Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of Large Eddy Simulations and Unsteady Reynolds-Averaged Navier-Stokes Simulations

[+] Author and Article Information
A. K. Saha, Sumanta Acharya

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803

J. Turbomach 127(2), 306-320 (Dec 07, 2004) (15 pages) doi:10.1115/1.1861917 History: Received September 19, 2003; Revised December 07, 2004

## Abstract

Large eddy simulations (LES) and unsteady Reynolds averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation $k-ε$ model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number $(Re=12,500–100,000)$, rotation number $(Ro=0–0.5)$ and density ratio $(Δρ∕ρ=0–0.5)$, while LES results are reported for a single Reynolds number of 12,500 without and with rotation $(Ro=0.12,Δρ∕ρ=0.13)$. Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio $(Nu∕Nu0)$ is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and sidewalls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till $Ro=0.12$) due to the stabilizing effect of rotation on the leading wall. However, beyond $Ro=0.12$, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.

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## Figures

Figure 8

Isosurface of spanwise vorticity (ωy=±20.0) for (a) Ro=0.0 and (b) R=0.12 and Δρ∕ρ=0.13

Figure 9

Isosurface of temperature (θ=0.6) for (a) Ro=0.0 and (b) R=0.12 and Δρ∕ρ=0.13 for LES (top: trailing wall; bottom: leading wall)

Figure 10

Time-averaged velocity vectors and temperature contours at y=0.0 for Ro=0.12 and Δρ∕ρ=0.13, Re=12,500 (a) URANS and (b) LES (top: trailing wall; bottom: leading wall)

Figure 11

Time-averaged temperature contours at x=0.5 for Ro=0.12 and Δρ∕ρ=0.13, Re=12,500 (a) URANS and (b) LES (top: trailing wall; bottom: leading wall)

Figure 12

Time-averaged Nusselt number contours on the trailing wall for Ro=0.12 and Δρ∕ρ=0.13, Re=12,500 (a) URANS and (b) LES

Figure 1

Geometric model of the problem

Figure 2

Comparison of secondary flow structures and streamwise velocity

Figure 3

Comparison of streamwise velocity at (a) station 1 and (b) station 2 and cross-stream velocity at (c) station 1 and (d) station 2

Figure 4

Instantaneous velocity vectors and temperature contours at y=0.0 for (a) Ro=0.0 and (b) Ro=0.12 and Δρ∕ρ=0.13, Re=12,500 (top: trailing wall; bottom: leading wall)

Figure 5

Instantaneous secondary flow structures superimposed on temperature contours at x=0.5 for (a) Ro=0.0 and (b) Ro=0.12 and Δρ∕ρ=0.13, Re=12,500 (top: trailing wall; bottom: leading wall)

Figure 6

Instantaneous Nusselt number contours of the stationary case for Δρ∕ρ=0.13, Re=12,500 (a) leading wall and (b) trailing wall

Figure 7

Instantaneous Nusselt number contours of the rotating case for Δρ∕ρ=0.13, Re=12,500 (a) leading wall and (b) trailing wall

Figure 13

Secondary flow structures superimposed on temperature contours at x=0.5 for (a) Re=25,000 and (b) Re=100,000, Ro=0.12 and Δρ∕ρ=0.13 (top: trailing wall; bottom: leading wall)

Figure 14

Nusselt number contours on the trailing wall at (a) Re=25,000 and (b) Re=100,000 for Ro=0.12 and Δρ∕ρ=0.13

Figure 15

Effect of Reynolds number on Nusselt number ratio for Ro=0.12 and (Δρ∕ρ)=0.13

Figure 16

Secondary flow structures superimposed on temperature contours (x=0.5) at (a) (Δρ∕ρ)=0.13 and (b) (Δρ∕ρ)=0.5 for Ro=0.12 and Re=25,000 (top: trailing wall; bottom: leading wall)

Figure 17

Nusselt number contours on the leading wall at (a) (Δρ∕ρ)=0.13 and (b) (Δρ∕ρ)=0.5 for Ro=0.12 and Re=25,000

Figure 18

Effect of density ratio (Δρ∕ρ) on Nusselt number ratio for Ro=0.12 and Re=25,000

Figure 19

(a) Signal traces of the vertical velocity at x=0.5, y=0, z=0, (b)–(d) secondary flow structures superimposed on temperature contours (x=0.5) at (b) time=14.53, (c) 25.88, and (d) 32.90 for Re=25,000, (Δρ∕ρ)=0.13 and Ro=0.5 (URANS) (top: trailing wall; bottom: leading wall)

Figure 20

Time averaged (a) secondary flow and temperature contours at x=0.5, (top: trailing wall); bottom: leading wall. (b) Trailing wall Nusselt number distribution for Re=25,000, (Δρ∕ρ)=0.13 and Ro=0.5

Figure 22

Effect of rotation number on Nusselt number ratio for Re=25,000, (Δρ∕ρ)=0.13

Figure 21

Time averaged vectors on temperature contours at y=0.0 for Re=25,000, (Δρρ)=0.13 and Ro=0.5. (top: trailing wall; bottom: leading wall)

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