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RESEARCH PAPERS

Natural Convective Flow and Heat Transfer in a Collector Storage with an Immersed Heat Exchanger: Numerical Study

[+] Author and Article Information
Yan Su

Department of Mechanical Engineering,  University of Minnesota, 111 Church Street, S.E., Minneapolis, MN 55455

Jane H. Davidson1

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

1

To whom all correspondence should be addressed.

J. Sol. Energy Eng 127(3), 324-332 (Mar 04, 2005) (9 pages) doi:10.1115/1.1934735 History: Received February 18, 2005; Revised March 04, 2005

A three-dimensional model and dimensionless scale analysis of the transient fluid dynamics and heat transfer in an inclined adiabatic water-filled enclosure with an immersed cylindrical cold sink is presented. The geometry represents an integral collector storage system with an immersed heat exchanger. The modeled enclosure has an aspect ratio of 6:1 and is inclined at 30deg to the horizontal. The heat exchanger is represented by a constant surface temperature horizontal cylinder positioned near the top of the enclosure. A scale analysis of the transient heat transfer process identifies four temporal periods: conduction, quasi-steady, fluctuating, and decay. It also provides general formulations for the transient Nusselt number, and volume-averaged water temperature in the enclosure. Insight to the transient fluid and thermal processes is provided by presentation of instantaneous flow streamlines and isotherm contours during each transient period. The flow field consists of two distinct zones. The zone above the cold sink is nearly stagnant. The larger zone below the sink is one of strong mixing and recirculation initiated by the cold plume formed in the boundary layer of the cylindrical sink. Correlations for the transient Nusselt number and the dimensionless volume-averaged tank temperature predicted from the model compare favorably to prior measured data. Fluid motion in the enclosure enhances heat transfer compared to that of a cylinder in an unbounded fluid.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Conceptual drawing of an integral solar collector storage (ICS) system with an immersed tube bundle, or heat exchanger, for domestic water heating

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Figure 2

Sketches of the laboratory ICS and the numerical domain. (a) The laboratory ICS has overall dimensions of H=121.9cm, L=94.0cm, and W=10.2cm. A 2.86cm diameter heat exchanger tube is located 11.5cm from the top of the enclosure at the mid x-z plane. The computational domain is shown by dashed lines. (b) The computational domain has dimensions H′=60cm, L′=10cm, and W=10cm. Periodical boundary conditions are applied at z=±L′∕2.

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Figure 3

Multi-zone mesh used to simulate the boundary layer at the tube and enclosure walls as well as the far field flow and temperature fields

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Figure 4

Three-dimensional streamlines for the four temporal periods for ΔT=∣Tw−T0∣=20K (T0=353K) and Tw=333K) corresponding to RaD*=2.345×107: (a) conduction (τ=0.029, t=0.014s); (b) conduction (τ=1.953, t=0.955s); (c) quasi-steady (τ=11.778, t=5.76s); (d) fluctuating (τ=111.78, t=54.66s); (e) decay (τ=2441, t=1194s); (f) decay (τ=65710, t=32315s)

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Figure 5

Three-dimensional isotherms for the four temporal periods for ΔT=∣Tw−T0∣=20K (T0=353K and Tw=333K) corresponding to RaD*=2.345×107: (a) conduction (τ=0.029, t=0.014s); (b) conduction (τ=1.953, t=0.955s); (c) quasi-steady (τ=11.778, t=5.76s); (d) fluctuating (τ=111.78, t=54.66s); (e) decay (τ=2441, t=1194s); (f) decay (τ=65710, t=32315s)

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Figure 6

Predicted NuD*¯ versus dimensionless time for initial Rayleigh numbers of RaD*=1.1726×105, 1.1726×106, 5.8628×106, 1.1726×107, and 2.345×107 corresponding to ΔT=∣Tw−T0∣ equal to 0.1, 1, 5, 10, and 20K. Numerical results are shown for 2-D and 3-D simulations. The long dashed lines indicate the analytical results for pure conduction. The four temporal periods are indicated by short dashed vertical lines along the time axis.

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Figure 7

Predicted dimensionless temperature difference ϴ¯ versus dimensionless time for initial Rayleigh numbers of RaD*=1.1726×105, 1.1726×106, 5.8628×106, 1.1726×107, and 2.345×107 corresponding to ΔT=∣Tw−T0∣ equal to 0.1, 1, 5, 10, and 20K

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Figure 8

Comparison of the predicted quasi-steady NuD*¯ with empirical correlation of Morgan (22)

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Figure 9

Comparison of the predicted Nusselt number and experiment (8) for the decay period. The experiment was conducted with T0=353K and water flowing through the tube at 0.03kg∕s with a constant inlet temperature equal to 298K (run no. 2 in (8)).

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Figure 10

Comparison of the correlation suggested by the scale analysis ( Eq. 33) to experiment (8)

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