Research Papers: Micro/Nanoscale Heat Transfer

Numerical Investigation of Flow Structure and Heat Transfer Produced by a Single Highly Confined Bubble in a Pressure-Driven Channel Flow

[+] Author and Article Information
John R. Willard

Department of Mechanical
and Aerospace Engineering,
University of Alabama in Huntsville,
301 Sparkman Drive 35899,
Huntsville, AL 35899
e-mail: jrw0030@uah.edu

D. Keith Hollingsworth

Department of Mechanical
and Aerospace Engineering,
University of Alabama in Huntsville,
301 Sparkman Drive 35899,
Huntsville, AL 35899
e-mail: keith.hollingsworth@uah.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 3, 2017; final manuscript received August 17, 2017; published online January 10, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(4), 042402 (Jan 10, 2018) (10 pages) Paper No: HT-17-1321; doi: 10.1115/1.4038233 History: Received June 03, 2017; Revised August 17, 2017

A numerical investigation of a single highly confined bubble moving through a millimeter-scale channel in the absence of phase change is presented. The simulation includes thermal boundary conditions designed to match those of completed experiments involving bubbly flows with large numbers of bubbles. The channel is horizontal with a uniform-heat-generation upper wall and an adiabatic lower boundary condition. The use of a Lagrangian framework allows for the simulation of a channel of arbitrary length using a limited computational domain. The liquid phase is a low-Reynolds-number laminar flow, and the phase interactions are modeled using the volume-of-fluid (VOF) method with full geometric reconstruction of the liquid/gas interface. Results are presented for three bubble diameters, which include two levels of confinement within the channel and two liquid flow rates. Bubble shape and speed closely match experimental observations for each bubble size and liquid flow rate. Nusselt numbers in the bubble wake for all configurations follow a power law relationship with distance behind the bubble. Important dynamical structures include a pair of vortical structures at the rear of the bubble associated with the primary heat transfer enhancement and a pair of prominent liquid jets oriented in the transverse direction on either side of the bubble.

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Fig. 1

Schematic (not to scale) of the domain use for the simulation

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Fig. 2

Illustration of the Lagrangian framework of the simulation domain

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Fig. 3

Illustration of the leading and following boundaries and the (a) velocity and (b) temperature profiles at those boundaries

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Fig. 4

Rendering of the phase interface surface for the VOF initialization of the simulation

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Fig. 5

Renderings of (a) Db/H = 3.3, (b) Db/H = 2.0 and (c) Db/H = 1.1 from the simulation and (lower) from in-situ images by Albahloul and Hollingsworth [7]

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Fig. 6

Top view of simulation domain, illustrating the regions used for validation

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Fig. 7

Nu plotted along centerline of channel showing convergence in time

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Fig. 8

Eulerian bubble speed showing convergence in grid density. Correlation for bubble speed from Albahloul [9].

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Fig. 9

Plot of cell-averaged Nusselt number for both a one-square and three-square region behind the bubble. A convergence trend can be seen in the three-square region plot.

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Fig. 10

Comparison of simulated undisturbed channel values at the center of the domain and theoretical values at t = 1 s

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Fig. 11

Plot of experimental data from Albahloul [9] correlating bubble speed and diameter simulated bubbles are called out

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Fig. 12

Two-dimensional renderings of (a) Nusselt number and (b) plate temperature. The Nu shading is scaled logarithmically to highlight secondary areas of lesser but significant Nu increase. For (b), the white transition is set at the temperature of the following edge of the plate in an undisturbed channel. Note the temperature minimum occurs about 2Db behind the trailing edge of the bubble.

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Fig. 13

Illustration of the spatial averaging and dimensions used for data reduction

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Fig. 14

Convection coefficient versus distance behind bubble

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Fig. 15

Nu versus x* plotted with log–log axes

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Fig. 16

Isometric rendering of invariant-Q iso-zero surfaces near a Db/H = 2.0 bubble

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Fig. 17

Temperature in the fluid phases at planes located at 0.75H (top row) and 0.5H (bottom row) for (a) Db/H = 3.3, (b) Db/H = 2.0, and (c) Db/H = 1.1. The bubble surface is also shown in gray, the diameter of the bubble at the location of the section plane as well as the contact line where the bubble meets the plate are also shown. The images do not share the same scale so that flow structures are more easily seen. Overlaid on the temperature field are representations of prevailing velocity vectors at that location.




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