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RESEARCH PAPERS

# Multizone Porous Medium Model of Thermal/Fluid Processes During Discharge of an Inclined Rectangular Storage Vessel Via an Immersed Heat Exchanger

[+] Author and Article Information
Yan Su

Department of Mechanical Engineering, University of Minnesota, 111 Church Street Southeast, Minneapolis, Minnesota 55455

Jane H. Davidson1

Department of Mechanical Engineering, University of Minnesota, 111 Church Street Southeast, Minneapolis, Minnesota 55455jhd@me.umn.edu

1

Corresponding author.

J. Sol. Energy Eng 129(4), 449-457 (May 02, 2007) (9 pages) doi:10.1115/1.2772640 History: Received August 03, 2006; Revised May 02, 2007

## Abstract

The transient natural convective thermal/fluid processes during discharge of an inclined rectangular solar storage tank via an immersed heat exchanger are modeled and compared to prior experimental data. The model treats the heat exchanger as a porous medium within the storage fluid and is applicable to a wide range of tank/heat exchanger configurations. In the present study, a two-dimensional model is applied to discharge of a $126l$ storage tank inclined at $30deg$ with respect to the horizontal and with a height to width ratio of 9:1. The heat exchanger has 240 tubes arranged in parallel and is located near the top of the tank. Transient temperature distributions and flow streamlines demonstrate the complexity of the flow field and the extent of mixing during discharge. The predicted results compare favorably to prior measurements of heat transfer and temperature distribution.

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## Figures

Figure 1

Multizone enclosure model of a thermal storage tank with an immersed heat exchanger: (a) inclined rectangular storage tank with an immersed tube bundle for discharge; (b) multizone porous media model of the inclined rectangular tank in which the heat exchanger is treated as a porous medium. The inclination of the simulated tank is 30deg.

Figure 2

Comparison of the predicted and measured values of dimensionless average tank temperature and fraction of energy discharged. The numerical results are represented by a solid line, and the prior experimental data (9) are represented by open diamonds.

Figure 3

Temporal variation of the predicted average Darcy velocities in the porous and pure fluid zones

Figure 4

Temporal variation of the Nusselt number. The top plot shows mixed convection Nusselt numbers calculated using published correlations for natural and forced convection with input of the predicted mean Darcy velocities and temperatures in the porous zone. This comparison proves the importance of the bounded flow field in the overall heat transfer. The bottom plot compares Nusselt numbers predicted by the model (solid line) with the calculated mixed convection Nusselt numbers (dashed line) and prior measured values (open diamonds) (9).

Figure 5

Predicted temperature distribution (top) and dimensionless flow streamlines (bottom) for selected times during discharge. The stream function is plotted in the range −0.4<ψ<0.4 in increments of 0.05. (a) τ=3, t=7s; (b) τ=10, t=24s; (c) τ=14, t=33s; (d) τ=19, t=45s; (e) τ=30, t=71s; (f) τ=45, t=107s; (g) τ=63, t=150s; (h) τ=100, t=238s; (i) τ=117, t=279s; (j) τ=160, t=381s; (k) τ=170, t=405s; (l) τ=190, t=452s; (m) τ=200, t=476s.

Figure 6

Temporal variation of the average water temperature (top) and stratification factor (bottom)

Figure 7

Predicted temperature distribution selected to demonstrate the level of thermal stratification during discharge: (a) τ=200, t=476s; (b) τ=300, t=714s; (c) τ=600, t=1428s; (d) τ=900, t=2142s; (e) τ=1200, t=2857s; (f) τ=1500, t=3571s. Temperature scales are shown for each time.

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