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Numerical model for the thermal behavior of thermocline storage tanks

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Abstract

Energy storage is a critical factor in the advancement of solar thermal power systems for the sustained delivery of electricity. In addition, the incorporation of thermal energy storage into the operation of concentrated solar power systems (CSPs) offers the potential of delivering electricity without fossil-fuel backup even during peak demand, independent of weather conditions and daylight. Despite this potential, some areas of the design and performance of thermocline systems still require further attention for future incorporation in commercial CSPs, particularly, their operation and control. Therefore, the present study aims to develop a simple but efficient numerical model to allow the comprehensive analysis of thermocline storage systems aiming better understanding of their dynamic temperature response. The validation results, despite the simplifying assumptions of the numerical model, agree well with the experiments for the time evolution of the thermocline region. Three different cases are considered to test the versatility of the numerical model; for the particular type of a storage tank with top round impingement inlet, a simple analytical model was developed to take into consideration the increased turbulence level in the mixing region. The numerical predictions for the three cases are in general good agreement against the experimental results.

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Abbreviations

a:

Fitting constant [m−1]

aw :

Ratio between thermal losses area and tank volume [m−1]

C:

Specific heat capacity [J/kg-K]

d:

Exit diameter [m]

D:

Diameter [m]

hw :

Coefficient of thermal losses to the surrounding [W/m2-K]

hv :

Volumetric interstitial heat transfer coefficient [W/m-K]

k:

Thermal conductance [W/m-K]

lmix :

Mixing length [m]

L:

Height of the tank [m]

\( \dot{m} \) :

Mass flow rate [m3/s]

Prt :

Turbulent Prandtl number

r:

Radius [m]

t:

Time [s]

T:

Temperature [K]

u:

Velocity [m/s]

U:

Average exit velocity [m/s]

V:

Volume [m3]

x:

Downstream distance [m]

α:

Thermal diffusivity [m2/s]

ε:

Porosity of the storage medium (void fraction)

νf :

Kinematic viscosity [m2/s]

νt :

Kinematic eddy viscosity [m2/s]

νtotal :

Effective viscosity [m2/s]

Ө:

Dimensionless temperature

ρ:

Density [kg/m3]

σ :

Standard deviation related to the spread of the profile across the centerline

δ:

Distance from the centerline to the edge of the spreading [m]

*:

Subscript indicating dimensionless quantities

eff:

Subscript refering to the effective storage medium

f:

Fluid

m:

Momentum

s:

Solid

t:

Turbulent

w:

Water

ZEF:

Zone of flow establishment

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Acknowledgements

The present work was sponsored by the State of Libya, under grant n° 469-2009.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Centre for Mechanical Technology and Automation, University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    Ismael A. S. Ehtiwesh & Antonio C. M. Sousa

  2. Department of Mechanical Engineering, Faculty of Engineering, Sabratha University, Sabratha, Libya

    Ismael A. S. Ehtiwesh

Authors
  1. Ismael A. S. Ehtiwesh
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  2. Antonio C. M. Sousa
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Corresponding author

Correspondence to Ismael A. S. Ehtiwesh.

Additional information

Highlights

• Predictions and experiments present similar trend for the time evolution.

• Inlet region deviations are most likely due to the high-level of turbulence.

• The ad-hoc proposed turbulence model leads to improved predictions.

• Predictions in relation to the experiments, have a maximum deviation of less than 12%.

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Ehtiwesh, I.A.S., Sousa, A.C.M. Numerical model for the thermal behavior of thermocline storage tanks. Heat Mass Transfer 54, 831–839 (2018). https://doi.org/10.1007/s00231-017-2181-6

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  • DOI: https://doi.org/10.1007/s00231-017-2181-6

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