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TECHNICAL PAPERS: Forced Convection

# Direct Numerical Simulation of Heat Transfer in Converging–Diverging Wavy Channels

[+] Author and Article Information
E. Stalio1

Dipartimento di Ingegneria Meccanica e Civile, Università degli Studi di Modena e Reggio Emilia, via Vignolese 905/b, 41100 Modena, Italyenrico.stalio@unimore.it

M. Piller

Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Trieste, Sezione Georisorse e Ambiente, via A. Valerio 10, 34127 Trieste, Italypiller@units.it

In order to avoid clumsy turns of phrases, expressions like “turbulent mixing,” “turbulent fluxes,” “turbulent stress” will be used in the present discussion, even though the cases considered belong to the transitional regime and the use of the term “turbulent” in this context may not be appropriate.

1

Corresponding author.

J. Heat Transfer 129(7), 769-777 (Aug 05, 2006) (9 pages) doi:10.1115/1.2717235 History: Received March 25, 2006; Revised August 05, 2006

## Abstract

Corrugated walls are widely used as passive devices for heat and mass transfer enhancement; they are most effective when operated at transitional and turbulent Reynolds numbers. In the present study, direct numerical simulation is used to investigate the unsteady forced convection in sinusoidal, symmetric wavy channels. A novel numerical method is employed for the simulations; it is meant for fully developed flows in periodic ducts of prescribed wall temperature. The algorithm is free of iterative procedures; it accounts for the effects of streamwise diffusion and can be used for unsteady problems. Results of two simulations in the transitional regime for Reynolds numbers based on average duct height and average velocity of $Re=481$ and $Re=872$ are reported. Time averaged and instantaneous velocity and temperature fields together with second-order statistics are interpreted in order to describe the mechanism associated with heat transfer augmentation. Heat flux distributions locate the most active areas in heat transfer and reveal the effects of convective mixing. Slanted traveling waves of high temperature are identified; peak values of Nusselt number are attained when the high-temperature fluid of the waves reaches the converging walls.

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## Figures

Figure 1

Geometry of the problem, longitudinal view

Figure 2

Detail of the orthogonal grid

Figure 3

Time traces of the streamwise component of the velocity vector in the center of the computational domain (x=L∕2,y=Hmax∕2) for Re=481 and Re=872

Figure 4

Instantaneous plots of the velocity and temperature fields for Re=872: (a) trajectories of virtual particles and contours of the velocity module on three spanwise planes; and (b) isosurfaces of temperature fluctuations at level T′=12Tmax′ and T′ contours

Figure 5

Time averaged velocity and temperature fields of the Re=872 case: (a) streamlines; and (b) temperature contours

Figure 6

Mean temperature profiles and intensity of temperature fluctuations T′T′¯: (a) mean temperature profiles in seven x positions; dashed lines identify profiles for Re=481, solid lines for Re=872; and (b) T′T′¯ profiles; dashed lines for the Re=481 case, solid lines for Re=872

Figure 7

Mean advective term v¯T¯ in the y direction: (a) laminar, Re=71 case; and (b) transitional, Re=872 case. Dashed lines show negative contours and solid lines show positive contours.

Figure 8

Advective fluxes in the y direction, dashdot lines show profiles for the laminar Re=71 case, dashed lines for the Re=481 case, and solid lines for Re=872: (a) mean heat fluxes v¯T¯; and (b) turbulent heat fluxes v′T′¯

Figure 9

Temperature fluctuations T′ in instants of relative maximum Nusselt for Re=872: (a) t=147.9 and Nu=39.9; (b) t=151.3 and Nu=41.1; (c) t=160.9 and Nu=34.8; and (d) t=163.7 and Nu=40.8. Dashed lines are negative contours and solid lines are zero and positive contours.

Figure 10

Temperature fluctuations T′ in instants of relative minimum Nusselt number for Re=872: (a) t=149.1 and Nu=24.3; (b) t=153.1 and Nu=19.4; (c) t=159.9 and Nu=20.7; and (d) t=163.3 and Nu=22.6. Dashed lines are negative contours and solid lines are zero and positive contours.

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