Research Papers: Conduction

Convective Heat Transfer in an Impinging Synthetic Jet: A Numerical Investigation of a Canonical Geometry

[+] Author and Article Information
Luis A. Silva

e-mail: luis.silva@villanova.edu

Alfonso Ortega

e-mail: alfonso.ortega@villanova.edu
Laboratory for Advanced Thermal and Fluid Systems,
Villanova University,
800 East Lancaster Avenue, Villanova, PA 19085

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received May 18, 2012; final manuscript received April 8, 2013; published online July 11, 2013. Assoc. Editor: Phillip M. Ligrani.

J. Heat Transfer 135(8), 082201 (Jul 11, 2013) (11 pages) Paper No: HT-12-1232; doi: 10.1115/1.4024262 History: Received May 18, 2012; Revised April 08, 2013

Synthetic jets are generated by an equivalent inflow and outflow of fluid into a system. Even though such a jet creates no net mass flux, net positive momentum can be produced because the outflow momentum during the first half of the cycle is contained primarily in a vigorous vortex pair created at the orifice edges; whereas in the backstroke, the backflow momentum is weaker, despite the fact that mass is conserved. As a consequence of this, the approach can be potentially utilized for the impingement of a cooling fluid onto a heated surface. In previous studies, little attention has been given to the influence of the jet's origins; hence it has been difficult to find reproducible results that are independent of the jet apparatus or actuators utilized to create the jet. Furthermore, because of restrictions of the resonators used in typical actuators, previous investigations have not been able to independently isolate effects of jet frequency, amplitude, and Reynolds number. In the present study, a canonical geometry is presented, in order to study the flow and heat transfer of a purely oscillatory jet that is not influenced by the manner in which it is produced. The unsteady Navier–Stokes equations and the convection–diffusion equation were solved using a fully unsteady, two-dimensional finite volume approach in order to capture the complex time dependent flow field. A detailed analysis was performed on the correlation between the complex velocity field and the observed wall heat transfer. Scaling analysis of the governing equations was utilized to identify nondimensional groups and propose a correlation for the space-averaged and time-averaged Nusselt number. A fundamental frequency, in addition to the jet forcing frequency, was found, and was attributed to the coalescence of consecutive vortex pairs. In terms of time-averaged data, the merging of vortices led to lower heat transfer. Point to point correlations showed that the instantaneous local Nusselt number strongly correlates with the vertical velocity v although the spatial-temporal dependencies are not yet fully understood.

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Fig. 1

Schematic of the physical domain that represents the canonical geometry

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Fig. 2

Computational domain and boundary conditions for the hybrid structured-unstructured grid. Upper and lower zoomed boxes enclose large gradient zones and high mesh sensitivity at the jet exit and stagnation zone, respectively.

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Fig. 6

Time- and space-averaged Nusselt number as a function of H/w for Re = 203 (○), 305 (♦), 406 (Δ), 508 (□). White symbols represent data calculated using Eq. (10).

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Fig. 7

Time- and space-averaged Nusselt number as a function of Re for H/w = 5 (▽), 7.5 (□), 10 (▹), 12.5 (♦), 15 (○), 17.5 (◃), and 20 (Δ)

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Fig. 3

(a) Time-averaged Nusselt number distribution over the heated wall and (b) net mass flux at the pressure inlet–outlet boundary compared to inlet condition (dotted line) for H/w = 10, Re = 508, and f = 400 Hz

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Fig. 4

Time-averaged Nusselt number distribution over the heated wall for three different time steps for H/w = 10, Re = 508, and f = 400 Hz

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Fig. 8

Schematic of a vorticity line source and the velocity induced by it near a solid surface

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Fig. 5

Velocity vectors in the vicinity of the jet and heat transfer at the wall for Re = 508, H/w = 5, f = 400 Hz (a)–(d) and Re = 305, H/w = 10, f = 1200 Hz (e)–(h). Solid lines enclose zones of high vorticity, |ω| 5000 s−1.

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Fig. 10

Nusselt number comparison between correlation data and measured data from the present work (numerical) and Gillespie et al. [5]

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Fig. 11

Nusselt number evolution, spectral decomposition, and phase portrait at x/w = 0, H/w = 15, Re = 508, f = 400 (a)(c) and 1200 Hz (d)–(f)

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Fig. 12

Velocity vectors colored by velocity magnitude for Re = 508, H/w = 15, and f = 1200 Hz. Solid lines enclose zones of high vorticity, |ω| ≥ 5000 s−1.

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Fig. 9

Normalized and averaged Nusselt number in space and time versus Womersley number for (a) H/w = 5 (□), 7.5 (Δ) and (b) H/w = 10 (○), 15 (∇), and 20 (♦)

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Fig. 15

Contour plots as a function of H/w and x/w for three different frequencies: (a) Nu0, (b) Nu1, (c) Nu2, and (d) ratio Nu1/Nu2 (Re = 508)

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Fig. 16

Correlation coefficient between Nu and (a) u, (b) v

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Fig. 13

Nu and Rev for H/w = 10, f = 1200 Hz, Re = 508, and x/w = 1. Symbols represent numerical data, dashed lines their respective fitted curve, and the solid line is the phase shifted Rev.

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Fig. 14

Mean deviation of the fitted Nu (%) with respect to the numerical data, as a function of H/w and x/w for three different frequencies (Re = 508)



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