Research Papers

Two-Phase Flow With Phase Change in Porous Channels

[+] Author and Article Information
Gaurav Tomar

Assistant Professor
Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: gtom@mecheng.iisc.ernet.in

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received July 27, 2014; final manuscript received December 15, 2014; published online January 21, 2015. Assoc. Editor: Ranganathan Kumar.

J. Thermal Sci. Eng. Appl 7(2), 021006 (Jun 01, 2015) (8 pages) Paper No: TSEA-14-1172; doi: 10.1115/1.4029458 History: Received July 27, 2014; Revised December 15, 2014; Online January 21, 2015

Phase change heat transfer in porous media finds applications in various geological flows and modern heat pipes. We present a study to show the effect of phase change on heat transfer in a porous channel. We show that the ratio of Jakob numbers based on wall superheat and inlet fluid subcooling governs the liquid–vapor interface location in the porous channel and below a critical value of the ratio, the liquid penetrates all the way to the extent of the channel in the flow direction. In such cases, the Nusselt number is higher due to the proximity of the liquid–vapor interface to the heat loads. For higher heat loads or lower subcooling of the liquid, the liquid–vapor interface is pushed toward the inlet, and heat transfer occurs through a wider vapor region thus resulting in a lower Nusselt number. This study is relevant in the designing of efficient two-phase heat exchangers such as capillary suction based heat pipes where a prior estimation of the interface location for the maximum heat load is required to ensure that the liquid–vapor interface is always inside the porous block for its operation.

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Fig. 1

Schematic showing a porous channel with liquid being imbibed from the left and vapor exiting from the right end. Heating elements, shown by two rectangular blocks at the top and bottom walls of the channel, cause evaporation of the liquid.

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Fig. 2

Typical curves for the fractional flow fw as a function of saturation of the wetting phase. The dashed line is the tangent on the curve for M = 1/4 which passes through origin. The slope, dxs/dt, is the shock speed for an imbibition flow with M = 1/4. The remaining portion of the curve shows the behavior of the expansion wave.

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Fig. 3

Comparison of the numerical results with the solution obtained from Buckley–Leverett analysis for M = 1/4 for two grid-sizes

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Fig. 4

Saturation profiles for different viscosity ratios obtained using the IMPES method

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Fig. 5

Comparison of the analytical profiles (Eq. (39)) with the numerical results at different times

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Fig. 6

Saturation profiles corresponding to the temperature field at different times shown in Fig. 5

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Fig. 7

Steady-state saturation field for Jaw/Jaf = 0.025. Region on the right from the interface represents vapor whereas the region on the left of the interface marks the saturated liquid. The gray rectangular blocks represent the location of the heating elements at temperature Tw. The length of the heating elements is one-third of the channel length, which are placed at the center of the top and bottom walls.

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Fig. 8

Steady-state temperature field (θ = (T-Tsat)/(Tw-Tsat)) for Jaw/Jaf = 0.025

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Fig. 9

Steady-state saturation field for Jaw/Jaf = 0.00525. Region on the right of the interface represents vapor whereas on the left of the interface marks the imbibed liquid.

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Fig. 10

Steady-state temperature field (θ = (T-Tsat)/(Tw-Tsat)) for Jaw/Jaf = 0.00525

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Fig. 11

Variation in the maximum penetration of the liquid in the porous channel with the ratio Jaw/Jaf

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Fig. 12

Variation in the space averaged Nusselt number at the heating elements with the ratio Jaw/Jaf




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