Research Papers

Analysis of Numerical Error in One-Dimensional Storage Tank Models for Solar Energy System Simulations

[+] Author and Article Information
C. M. Unrau

Department of Mechanical Engineering,
McMaster University,
Hamilton, ON L8S 4L8, Canada
e-mail: unraucm@mcmaster.ca

M. F. Lightstone

Department of Mechanical Engineering,
McMaster University,
Hamilton, ON L8S 4L8, Canada
e-mail: lightsm@mcmaster.ca

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received September 8, 2017; final manuscript received April 2, 2018; published online May 7, 2018. Assoc. Editor: Gerardo Diaz.

J. Sol. Energy Eng 140(5), 051004 (May 07, 2018) (11 pages) Paper No: SOL-17-1375; doi: 10.1115/1.4039985 History: Received September 08, 2017; Revised April 02, 2018

This study investigates the temperature profiles predicted by trnsys one-dimensional (1D) thermal storage tank models for typical charging conditions. Simulation parameters, such as grid spacing and time-step size, were varied to observe the changes in the numerical error when compared with an exact analytical solution. A Taylor series expansion was also performed on the discretized, 1D, advection–diffusion equation to obtain an expression for this numerical error. A numerical diffusion term was found which could be used to improve the prediction of the temperature profile in a storage tank simulation. Finally, the influence of this error on predictions of the annual solar fraction for a domestic hot water system was explored.

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Minister of Natural Resources, 2016, “Energy Efficiency Trends in Canada—1990 to 2013,” Natural Resources Canada, Ottawa, ON, Canada, Technical Report. https://www.nrcan.gc.ca/energy/publications/19030
Sibbitt, B. , McClenahan, D. , Djebbar, R. , Thornton, J. , Wong, B. , Carriere, J. , and Kokko, J. , 2012, “The Performance of a High Solar Fraction Seasonal Storage District Heating System—Five Years of Operation,” Energy Procedia, 30, pp. 856–865. [CrossRef]
Mavros, P. , Belessiotis, V. , and Haralambopoulos, D. , 1994, “Stratified Energy Storage Vessels Characterization of Performance and Modelling of Mixing Behaviour,” Sol. Energy, 52(4), pp. 327–336. [CrossRef]
Wuestling, M. D. , Klein, S. A. , and Duffie, J. A. , 1985, “Promising Control Alternatives for Solar Water Heating Systems,” ASME J. Sol. Energy Eng., 107(3), pp. 215–221. [CrossRef]
Lavan, Z. , and Thompson, J. , 1977, “Experimental Study of Thermally Stratified Hot Water Storage Tanks,” Sol. Energy, 19(5), pp. 519–524. [CrossRef]
Lightstone, M. , 1987, “A Numerical Study of Thermal Stratification in Solar Energy Storage Tanks,” M.S. thesis, University of Waterloo, Waterloo, ON, Canada. https://uwaterloo.ca/solar-thermal-research-laboratory/people-profiles/marilyn-lightstone
Csordas, G. F. , Brunger, A. P. , Hollands, K. G. T. , and Lightstone, M. F. , 1992, “Plume Entrainment Effects in Solar Domestic Hot Water Systems Employing Variable-Flow-Rate Control Strategies,” Sol. Energy, 49(6), pp. 497–505. [CrossRef]
Aviv, A. , Morad, S. , Ratzon, Y. , Ziskind, G. , and Letan, R. , 2009, “Experimental and Numerical Study of Mixing in a Horizontal Hot Water Storage Tank,” ASME J. Sol. Energy Eng., 131(3), p. 031004. [CrossRef]
Shah, L. J. , and Furbo, S. , 2003, “Entrance Effects in Solar Storage Tanks,” Sol. Energy, 75(4), pp. 337–348. [CrossRef]
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, 33(10), pp. 2236–2245. [CrossRef]
Shaarawy, M. , and Lightstone, M. , 2016, “Numerical Analysis of Thermal Stratification in Large Horizontal Thermal Energy Storage Tanks,” ASME J. Sol. Energy Eng., 138(2), p. 021009. [CrossRef]
Oliveski, R. C. , Krenzinger, A. , and Vielmo, H. A. , 2003, “Comparison Between Models for the Simulation of Hot Water Storage Tanks,” Sol. Energy, 75(2), pp. 121–134. [CrossRef]
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, 111(3), pp. 204–210.
Newton, B. J. , 1995, “Modelling of Solar Storage Tanks,” M.S. thesis, University of Wisconsin-Madison, Madison, WI. https://minds.wisconsin.edu/handle/1793/7803
Klein, S. A. , Beckman, W. A. , Mitchell, J. W. , Duffie, J. A. , Duffie, N. A. , Freeman, T. L. , Mitchell, J. C. , Braun, J. E. , Evans, B. L. , Kummer, J. E. , Urban, R. E. , Fiksel, A. , Thornton, J. W. , Blair, N. J. , Williams, P. M. , Bradley, D. E. , McDowell, T. P. , Kummert, M. , Arias, D. A. , and Duffy, M. J. , 2010, TRNSYS User's Manual, 17th ed., University of Wisconsin-Madison, Madison, WI.
TESSLibs, 2014, Storage Tank Library Mathematical Reference, 11th ed., TRNSYS 17, University of Wisconsin-Madison, Madison, WI.
Baldwin, C. , and Cruickshank, C. A. , 2016, “Using TRNSYS Types 4, 60, and 534 to Model Residential Cold Thermal Storage Using Water and Water/Glycol Solutions,” IBPSA-Canada's eSim Conference, Hamilton, ON, Canada, May 3–6, pp. 1–11. http://www.ibpsa.org/proceedings/eSimPapers/2016/52-77-eSim2016.pdf
Chu, J. , 2014, “Evaluation of a Dual Tank Indirect Solar-Assisted Heat Pump System for a High Performance House,” M.S. thesis, Carleton University, Ottawa, ON, Canada. https://curve.carleton.ca/system/files/etd/164e656c-b5c1-4422-8d23-cf18e06355de/etd_pdf/99cece07c445fa9f7d19b59f1ed473f2/chu-evaluationofadualtankindirectsolarassisted.pdf
Allard, Y. , Kummert, M. , Bernier, M. , and Moreau, A. , 2011, “Intermodel Comparison and Experimental Validation of Electrical Water Heater Models in TRNSYS,” Building Simulation 2011: 12th Conference of International Building Performance Simulation Association, Sydney, Australia, Nov. 14–16, pp. 688–695. https://pdfs.semanticscholar.org/98eb/a83c9065053f2dd6a98da1ca84c649a197e3.pdf
Kleinbach, E. M. , Beckman, W. A. , and Klein, S. A. , 1993, “Performance Study of One-Dimensional Models for Stratified Thermal Storage Tanks,” Sol. Energy, 50(2), pp. 155–166. [CrossRef]
Powell, K. M. , and Edgar, T. F. , 2013, “An Adaptive-Grid Model for Dynamic Simulation of Thermocline Thermal Energy Storage Systems,” Energy Conservation Manage., 76, pp. 865–873. [CrossRef]
Nizami, D. J. , Lightstone, M. F. , Harrison, S. J. , and Cruickshank, C. A. , 2013, “Negative Buoyant Plume Model for Solar Domestic Hot Water Tank Systems Incorporating a Vertical Inlet,” Sol. Energy, 87, pp. 53–63. [CrossRef]
Zurigat, Y. H. , Ghajar, A. J. , and Moretti, P. M. , 1988, “Stratified Thermal Storage Tank Inlet Mixing Characterization,” Appl. Energy, 30(2), pp. 99–111. [CrossRef]


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Fig. 1

Schematic diagram of the experimental tank used by Chu [18]

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Fig. 2

Simulation and experimental temperature versus time results at nine different tank locations during the charging of a thermal storage tank. Experimental data are from Chu [18].

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Fig. 3

Illustration of how numerical diffusion in 1D models is created due to the assumption of fully mixed control volumes

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Fig. 4

Temperature versus tank depth results for the analytical model and the trnsys type 60 model after 1 h with varying numbers of nodes and 1 s time steps

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Fig. 5

Temperature versus tank depth results for the analytical model and the trnsys type 60 model after 1 h with varying time-step sizes and 50 tank nodes

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Fig. 6

Temperature versus tank depth results for tank charging after 1 h using 1 s time steps. The trnsys type 60 results arecompared with the analytical solution and the analytical solution with the additional diffusion: (a) 100, (b) 50, and (c) 10 nodes.

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Fig. 7

Energy balance surrounding the entire SDHW system showing the energy inputs, outputs, and losses

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Fig. 8

trnsys setups of the SDHW system cases: (a) idealized system and (b) realistic system

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Fig. 9

Solar radiation profiles used for the idealized case (constant radiation) and the realistic case

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Fig. 11

RMS temperature errors for (a) tank charging with varying grid spacing (after 1 h) and (b) tank charging with varying time-step sizes (after 1 h)

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Fig. 10

Solar fraction versus tank volume results with 10, 20, 50, and 100 nodes for the three tested cases using weather data from Toronto, Canada: (a) idealized system—24 h, (b) realistic system—24 h, and (c) realistic system—1 year



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