Korean Journal of Air-Conditioning and Refrigeration Engineering (설비공학논문집)

The Society of Air-Conditioning and Refrigerating Engineers of Korea (대한설비공학회)
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Integral Approximate Solutions to a One-Dimensional Model for Stratified Thermal Storage Tanks

성층화된 축열조의 1차원모델에 대한 적분 근사해

  • Received : 2010.02.22
  • Published : 2010.07.10
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Abstract

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

Keywords

References

  1. Dincer, I. and Rosen, M. A., 2002, Thermal Energy Storage, John Wiley and Sons, England.
  2. Musser, A. and Bahnfleth, W. P., 1998, Evolution of temperature distributions in a full-scale stratified chilled-water storage tank with radial diffusers, ASHRAE Transactions : Research, Vol. 104, pp. 55-67.
  3. Zurigat, Y. H., Liche, P. R., and Ghajar, A. J., 1991, Influence of inlet geometry on mixing in thermocline thermal energy storage, Int. J. Heat Mass Transfer, Vol. 34, pp. 115-125. https://doi.org/10.1016/0017-9310(91)90179-I
  4. Hollands, K. G. T. and Lightstone, M. F., 1989, A review of low-flow, stratified-tank solar water heating systems, Solar Energy, Vol. 43, pp. 97-105. https://doi.org/10.1016/0038-092X(89)90151-5
  5. Chung, J. D., Park, J., and Cho, S. H., 2004, Effect of diffuser shape on the performance of water-chilled heat storage, Korean J. Air-Conditioning and Refrigeration Eng., Vol. 16, pp. 1077-1083.
  6. Chung, J. D., Cho, S. H., Tae, C. S., and Yoo. H., 2008, The effect of diffuser configuration on thermal stratification in a rectangular storage tank, Renewable Energy, Vol. 33, pp. 2236-2245. https://doi.org/10.1016/j.renene.2007.12.013
  7. Musser, A. and Bahnfleth, W. P., 2001, Parametric study of charging inlet diffuser performance in stratified chilled water storage tanks with radial diffusers : Part 2-Dimensional analysis, parametric simulations and simplified model development, ASHRAE Transactions : Research, Vol. 107, pp. 41-58.
  8. Zurigat, Y. H., Maloney, K. J., and Ghajar, A. J., 1989, A comparison study of one-dimensional models for stratified thermal storage tanks, Trans. ASME, J. f Solar Energy Engineering, Vol. 111, pp. 204-210. https://doi.org/10.1115/1.3268308
  9. Yoo, H. and Pak, E.-T., 1996, Analytical solutions to a one-dimensional finite-domain model for stratified thermal storage tanks, Solar Energy, Vol. 56, pp. 315-322. https://doi.org/10.1016/0038-092X(96)89365-0
  10. Yoo, H., Pak, E. T., 1995, Theoretical analysis of the charging process with perfectly mixed region in stratified thermal storage tanks, Korean J. Air-Conditioning and Refrigeration Eng, Vol. 7, pp. 184-195.
  11. Yoo, H., Kim, C.-J., and Kim, C. W., 1999, Approximate analytical solutions for stratified thermal storage under variable inlet temperature, Solar Energy, Vol. 66, pp. 47-56. https://doi.org/10.1016/S0038-092X(99)00008-0