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Research Papers: Forced Convection

# Large Eddy Simulation of Turbulent Heat Transfer in Curved-Pipe Flow

[+] Author and Article Information
Changwoo Kang

Department of Mechanical Engineering,
Inha University,
Incheon 402-751, Korea
e-mail: cwkang@inha.edu

Kyung-Soo Yang

Professor
Department of Mechanical Engineering,
Inha University,
Incheon 402-751, Korea
e-mail: ksyang@inha.ac.kr

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 19, 2014; final manuscript received April 29, 2015; published online August 11, 2015. Assoc. Editor: Danesh / D. K. Tafti.

J. Heat Transfer 138(1), 011704 (Aug 11, 2015) (11 pages) Paper No: HT-14-1629; doi: 10.1115/1.4030968 History: Received September 19, 2014

## Abstract

In the present investigation, turbulent heat transfer in fully developed curved-pipe flow has been studied by using large eddy simulation (LES). We consider a fully developed turbulent curved-pipe flow with axially uniform wall heat flux. The friction Reynolds number under consideration is $Reτ$  = 1000 based on the mean friction velocity and the pipe radius, and the Prandtl number (Pr) is 0.71. To investigate the effects of wall curvature on turbulent flow and heat transfer, we varied the nondimensionalized curvature (δ) from 0.01 to 0.1. Dynamic subgrid-scale models for turbulent subgrid-scale stresses and heat fluxes were employed to close the governing equations. To elucidate the secondary flow structures due to the pipe curvature and their effect on the heat transfer, the mean quantities and various turbulence statistics of the flow and temperature fields are presented, and compared with those of the straight-pipe flow. The friction factor and the mean Nusselt number computed in the present study are in good agreement with the experimental results currently available in the literature. We also present turbulence intensities, skewness and flatness factors of temperature fluctuations, and cross-correlations of velocity and temperature fluctuations. In addition, we report the results of an octant analysis to clarify the correlation between near-wall turbulence structures and temperature fluctuation in the vicinity of the pipe wall. Based on our results, we attempt to clarify the effects of the pipe curvature on turbulent heat transfer. Our LES provides researchers and engineers with useful data to understand the heat-transfer mechanisms in turbulent curved-pipe flow, which has numerous applications in engineering.

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## Figures

Fig. 1

Flow configuration and grid system (every other grid point is plotted in each direction for clarity): (a) coordinate system, (b) r-θ plane, (c) r-s plane, a central portion of the curved pipe

Fig. 2

Mean axial-velocity profiles along the horizontal line (A–A) for Reb  = 5480 and δ = 1/18.2

Fig. 3

Streamlines on the r–θ plane, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01, (b) δ = 0.05, and (c) δ = 0.1

Fig. 4

Contours of the mean axial-velocity component on the r–θ plane, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 5

Profiles of the mean axial-velocity component, Reτ  = 1000, Pr  = 0.71: (a) along the horizontal line (A–A) and (b) along the vertical line (B–B)

Fig. 6

Profiles of the mean-axial-velocity component in wall units, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 7

Local friction coefficient, Reτ  = 1000, Pr  = 0.71

Fig. 8

Mean friction factor

Fig. 9

Contours of the nondimensionalized mean temperature on the r–θ plane, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 10

Profiles of the nondimensionalized mean temperature, Reτ  = 1000, Pr  = 0.71: (a) on the horizontal line (A–A) and (b) on the vertical line (B–B)

Fig. 11

Local mean Nusselt number averaged both in the axial direction and in time, Reτ  = 1000, Pr  = 0.71

Fig. 12

Mean Nusselt number

Fig. 13

Rms of fluctuation along the horizontal wall-normal radial line (A–A), Reτ  = 1000, Pr  = 0.71: (a) axial-velocity component and (b) temperature

Fig. 14

Profiles of rms of temperature fluctuation, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 15

Skewness factor of temperature fluctuation, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 16

Flatness factor of temperature fluctuation, Reτ  = 1000, Pr  = 0.71: (a) δ = 0.01 and (b) δ = 0.1

Fig. 17

Cross-correlation coefficients along the horizontal line for δ = 0.1, Reτ  = 1000, Pr  = 0.71: (a) at the outer wall (θ = 0) and (b) at the inner wall (θ = π)

Fig. 18

Definition of octants

Fig. 19

Octant contributions for the straight-pipe flow ((a)–(c)), δ = 0.1 at the outer wall (θ = 0) ((d)–(f)), and δ = 0.1 at the inner wall (θ = π) ((g)–(i)), Reτ  = 1000, Pr  = 0.71; (a), (d), (g): axial turbulent heat flux; (b), (e), (h): radial turbulent heat flux; and (c), (f), (i): probability of octant events

Fig. 20

Contours of instantaneous resolvable temperature fluctuation at y+≅5.3. White and black colors represent positive and negative values, respectively, (a) δ = 0.01 and (b) δ = 0.1.

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