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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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References

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Figures

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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. 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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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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