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Research Papers: Energy Storage/Systems

# Numerical Investigation of Entropy Generation in Stratified Thermal Stores

[+] Author and Article Information
Howard O. Njoku

Applied Renewable and Sustainable
Energy Research Group,
Department of Mechanical Engineering,
University of Nigeria,
Nsukka 410001, Nigeria
e-mail: howard.njoku@unn.edu.ng

Onyemaechi V. Ekechukwu

Professor
Department of Mechanical Engineering,
University of Nigeria,
Nsukka 410001, Nigeria
e-mail: ovekechukwu@yahoo.com

Samuel O. Onyegegbu

Emeritus Professor
Department of Mechanical Engineering,
University of Nigeria,
Nsukka 410001, Nigeria
e-mail: samuel_onyegegbu@yahoo.co.uk

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received April 5, 2016; final manuscript received July 7, 2017; published online August 22, 2017. Assoc. Editor: Mohamed A. Habib.

J. Energy Resour. Technol 140(1), 011901 (Aug 22, 2017) (11 pages) Paper No: JERT-16-1161; doi: 10.1115/1.4037535 History: Received April 05, 2016; Revised July 07, 2017

## Abstract

This paper investigates the nature of entropy generation in stratified sensible thermal energy stores (SSTES) during charging using a dimensionless axisymmetric numerical model of an SSTES. Time-varying dimensionless entropy generation rates and the cumulative entropy generation in SSTES were determined from finite volume computations. The aspect ratios (AR), Peclet numbers (PeD), and Richardson numbers (Ri), for the stores considered were within the ranges $1≤AR≤4, 5×103≤PeD≤100×103$, and $10≤Ri≤104$, respectively. Using the Bejan number (Be), the total entropy generation was shown to be almost entirely due to thermal effects in the SSTES. The Be is practically unity for most of the SSTES' charging duration. The contributions of radial thermal gradients to the thermal entropy generation were further shown to be largely negligible in comparison to the contributions of axial thermal gradients, except at low Ri. Entropy generation numbers, Ns, in the SSTES were also computed and found to increase with decreasing AR and PeD and with increasing Ri. PeD was found to have the most significant influence on Ns. Based on this axisymmetric analyses of time-varying entropy generation in SSTES, estimates have been obtained of (1) the relative significance of radial effects on entropy generation within SSTES and (2) the relative significance of viscous shear entropy generation mechanisms within SSTES.

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Topics: Entropy , Temperature

## References

Kaizawa, A. , Kamano, H. , Kawai, A. , Jozuka, T. , Senda, T. , Maruoka, N. , and Akiyama, T. , 2008, “ Thermal and Flow Behaviors in Heat Transportation Container Using Phase Change Material,” Energy Convers. Manage., 49(4), pp. 698–706.
Afrin, S. , Kumar, V. , Bharathan, D. , Glatzmaier, G. C. , and Ma, Z. , 2014, “ Computational Analysis of a Pipe Flow Distributor for a Thermocline Based Thermal Energy Storage System,” ASME J. Sol. Energy Eng., 136(2), p. 021010.
Njoku, H. O. , Ekechukwu, O. V. , and Onyegegbu, S. O. , 2014, “ Analysis of Stratified Thermal Storage Systems: An Overview,” Heat Mass Transfer, 50(7), pp. 1017–1030.
Khan, F. , and Savilonis, B. , 2016, “ Plate Diffuser Performance in Spherical Tank Thermocline Storage System,” ASME J. Energy Resour. Technol., 138(5), p. 052006.
Hollands, K. G. T. , and Lightstone, M. F. , 1989, “ A Review of Low-Flow, Stratified-Tank Solar Water Heating Systems,” Sol. Energy, 43(2), pp. 97–105.
Zurigat, Y. H. , and Ghajar, A. J. , 2002, “ Thermal Energy Storage: Systems and Applications,” Heat Transfer and Stratification in Sensible Heat Storage Systems, Wiley, Chichester, UK, Chap. 6.
Han, Y. M. , Wang, R. Z. , and Dai, Y. J. , 2009, “ Thermal Stratification Within the Water Tank,” Renewable Sustainable Energy Rev., 13(5), pp. 1014–1026.
Duffie, J. A. , and Beckman, W. A. , 1991, Solar Engineering of Thermal Processes, 2nd ed., Wiley, New York.
Abu-Hamdan, M. G. , Zurigat, Y. H. , and Ghajar, A. J. , 1992, “ An Experimental Study of a Stratified Thermal Storage Under Variable Inlet Temperature for Different Inlet Designs,” Int. J. Heat Mass Transfer, 35(8), pp. 1927–1934.
Cristofari, C. , Notton, G. , Poggi, P. , and Louche, A. , 2003, “ Influence of the Flow Rate and the Tank Stratification Degree on the Performances of a Solar Flat-Plate Collector,” Int. J. Therm. Sci., 42(5), pp. 455–469.
Rosen, M. A. , Tang, R. , and Dincer, I. , 2004, “ Effect of Stratification on Energy and Exergy Capacities in Thermal Storage Systems,” Int. J. Energy Res., 28(2), pp. 177–193.
Haller, M. Y. , Cruickshank, C. A. , Streicher, W. , Harrison, S. J. , Andersen, E. , and Furbo, S. , 2009, “ Methods to Determine Stratification Efficiency of Thermal Energy Storage Processes—Review and Theoretical Comparison,” Sol. Energy, 83(10), pp. 1847–1860.
Castell, A. , Medrano, M. , Solé, C. , and Cabeza, L. F. , 2010, “ Dimensionless Numbers Used to Characterize Stratification in Water Tanks for Discharging at Low Flow Rates,” Renewable Energy, 35(10), pp. 2192–2199.
Rosen, M. A. , 2001, “ The Exergy of Stratified Thermal Energy Storages,” Sol. Energy, 71(3), pp. 173–185.
Rosen, M. A. , and Dincer, I. , 2003, “ Exergy Methods for Assessing and Comparing Thermal Storage Systems,” Int. J. Energy Res., 27(4), pp. 415–430.
Njoku, H. O. , Ekechukwu, O. V. , and Onyegegbu, S. O. , 2016, “ Comparison of Energy, Exergy and Entropy Generation-Based Criteria for Evaluating Stratified Thermal Store Performances,” Energy Build., 124, pp. 141–152.
Consul, R. , Rodryguez, I. , Perez-Segarra, C. D. , and Soria, M. , 2004, “ Virtual Prototyping of Storage Tanks by Means of Three-Dimensional CFD and Heat Transfer Numerical Simulations,” Sol. Energy, 77(2), pp. 179–191.
Bjurström, H. , and Carlsson, B. , 1985, “ An Exergy Analysis of Sensible and Latent Heat Storage,” Heat Recovery Syst. CHP, 5(3), pp. 233–250.
Solé, C. , Medrano, M. , Castell, A. , Nogués, M. , Mehling, H. , and Cabeza, L. F. , 2008, “ Energetic and Exergetic Analysis of a Domestic Water Tank With Phase Change Material,” Int. J. Energy Res., 32(3), pp. 204–214.
Jack, M. W. , and Wrobel, J. , 2009, “ Thermodynamic Optimization of a Stratified Thermal Storage Device,” Appl. Therm. Eng., 29, pp. 2344–2349.
Martinez-Patino, J. , Serra, L. , Verda, V. , Picon-Nunez, M. , and Rubio-Maya, C. , 2016, “ Thermodynamic Analysis of Simultaneous Heat and Mass Transfer Systems,” ASME J. Energy Resour. Technol., 138(6), p. 062006.
Mira-Hernandez, C. , Flueckiger, S. M. , and Garimella, S. V. , 2015, “ Comparative Analysis of Single- and Dual-Media Thermocline Tanks for Thermal Energy Storage in Concentrating Solar Power Plants,” ASME J. Sol. Energy Eng., 137(3), p. 031012.
AlZahrani, A. A. , and Dincer, I. , 2016, “ Performance Assessment of an Aquifer Thermal Energy Storage System for Heating and Cooling Applications,” ASME J. Energy Resour. Technol., 138(1), p. 011901.
Bejan, A. , 1996, Entropy Generation Minimization, CRC Press, Boca Raton, FL.
Dincer, I. , and Rosen, M. A. , 2011, Thermal Energy Storage: Systems and Applications, 2nd ed., Wiley, Chichester, UK.
Bejan, A. , 1979, “ A Study of Entropy Generation in Fundamental Convective Heat Transfer,” ASME J. Heat Transfer, 101(4), pp. 718–725.
Bejan, A. , 1982, Entropy Generation Through Heat and Fluid Flow, Wiley, New York.
Bejan, A. , 1996, “ Entropy Generation Minimization: The New Thermodynamics of Finite-Size Devices and Finite-Time Processes,” J. Appl. Phys., 79(3), pp. 1191–1218.
Bejan, A. , 1996, “ Method of Entropy Generation Minimization, or Modeling and Optimization Based on Combined Heat Transfer and Thermodynamics,” Rev. Gén. Therm., 35, pp. 637–646.
Ting, T. W. , Hung, Y. M. , and Guo, N. , 2016, “ Viscous Dissipation Effect on Streamwise Entropy Generation of Nanofluid Flow in Microchannel Heat Sinks,” ASME J. Energy Resour. Technol., 138(5), p. 052002.
Vasu, B. , RamReddy, C. , Murthy, P. V. S. N. , and Gorla, R. S. R. , 2017, “ Entropy Generation Analysis in Nonlinear Convection Flow of Thermally Stratified Fluid in Saturated Porous Medium With Convective Boundary Condition,” ASME J. Heat Transfer, 139(9), p. 091701.
Homan, K. O. , 2003, “ Internal Entropy Generation Limits for Direct Sensible Thermal Storage,” ASME J. Energy Resour. Technol., 125(2), pp. 85–93.
Ji, Y. , and Homan, K. O. , 2007, “ On Simplified Models for the Rate- and Time-Dependent Performance of Stratified Thermal Storage,” ASME J. Energy Resour. Technol., 129(4), pp. 214–222.
Badescu, V. , 2004, “ Optimal Operation of Thermal Energy Storage Units Based on Stratified and Fully Mixed Water Tanks,” Appl. Therm. Eng., 24, pp. 2101–2116.
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, 34(1), pp. 115–125.
Van Berkel, J. , 1996, “ Mixing in Thermally Stratified Energy Stores,” Sol. Energy, 58(4–6), pp. 203–211.
Van Berkel, J. , Rindt, C. C. M. , and Van Steenhoven, A. A. , 1999, “ Modelling of Two-Layer Stratified Stores,” Sol. Energy, 67(1–3), pp. 65–78.
Shah, L. J. , and Furbo, S. , 2003, “ Entrance Effects in Solar Storage Tanks,” Sol. Energy, 75(4), pp. 337–348.
Shah, L. J. , Andersen, E. , and Furbo, S. , 2005, “ Theoretical and Experimental Investigations of Inlet Stratifiers for Solar Storage Tanks,” Appl. Therm. Eng., 25, pp. 2086–2099.
Hahne, E. , and Chen, Y. , 1998, “ Numerical Study of Flow and Heat Transfer Characteristics in Hot Water Stores,” Sol. Energy, 64(1–3), pp. 9–18.
Farmahini-Farahani, M. , 2012, “ Investigation of Four Geometrical Parameters on Thermal Stratification of Cold Water Tanks by Exergy Analysis,” Int. J. Exergy, 10(3), pp. 332–345.
Njoku, H. O. , Ekechukwu, O. V. , and Onyegegbu, S. O. , 2016, “ Normalized Charging Exergy Performance of Stratified Sensible Thermal Stores,” Sol. Energy, 136, pp. 487–498.
OpenCFD, 2013, “ OpenFOAM—The Open Source CFD Toolbox (User Guide),” OpenFOAM Foundation, London, accessed Aug. 14, 2017,
Yoo, H. , and Pak, E. , 1993, “ Theoretical Model of the Charging Process for Stratified Thermal Storage Tanks,” Sol. Energy, 51(6), pp. 513–519.
Cole, R. L. , and Bellinger, F. O. , 1982, “ Thermally Stratified Tanks,” ASHRAE Trans., 88, pp. 1005–1017.
Chen, S. , and Krafczyk, M. , 2009, “ Entropy Generation in Turbulent Natural Convection Due to Internal Heat Generation,” Int. J. Therm. Sci., 48(10), pp. 1978–1987.
Shanbghazani, M. , Heidarpoor, V. , Rosen, M. A. , and Iraj, M. , 2010, “ Numerical Investigation of Local Entropy Generation for Laminar Flow in Rotating-Disk Systems,” ASME J. Heat Transfer, 132(9), p. 091701.
Li, J. , and Kleinstreuer, C. , 2010, “ Entropy Generation Analysis for Nanofluid Flow in Microchannels,” ASME J. Heat Transfer, 132(12), p. 122401.
Sarkar, S. , Ganguly, S. , and Dalal, A. , 2012, “ Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Square Cylinder in Vertically Upward Flow,” ASME J. Heat Transfer, 134(12), p. 122501.
Sarkar, S. , Ganguly, S. , and Dalal, A. , 2014, “ Analysis of Entropy Generation During Mixed Convective Heat Transfer of Nanofluids Past a Rotating Circular Cylinder,” ASME J. Heat Transfer, 136(6), p. 062501.
Lienhard, J. H. , and Lienhard, J. H. , 2006, A Heat Transfer Textbook, 3rd ed., Phlogiston Press, Cambridge, MA.

## Figures

Fig. 1

Typical temperature profile in a stratified thermal storage tank [3]

Fig. 2

Simplified axisymmetric representation of stratified sensible thermal storage tank

Fig. 3

Block-structured SSTES mesh showing (a) the inlet pipe, tank, and outlet pipe blocks and (b) the assembled wedge-shaped SSTES mesh

Fig. 4

Temperature profiles and velocity fields in a typical stratified thermal store (AR = 3, Ri = 102, and PeD = 40 × 103) after tank volume change fractions φ = (a) 0.20, (b) 0.42, (c) 0.65, and (d) 0.87

Fig. 5

Comparison of the CFD results with the 1D analytical results of Yoo and Pak [44] and Cole and Bellinger [45], for different numbers of grid cells

Fig. 6

Time-varying entropy generation rates in stratified stores under different Peclet number regimes for two representative Richardson numbers and aspect ratio, AR = 3: (a) Ri = 102max = 9.51) and (b) Ri = 103max = 7.62)

Fig. 7

Time-varying cumulative entropy generation in stratified stores as influenced by Peclet numbers for two representative Richardson numbers and aspect ratio, AR = 3: (a) Ri = 102max = 9.51) and (b) Ri = 103max = 7.62)

Fig. 8

Effect of Peclet numbers on time-varying Bejan numbers in stratified stores for two representative Richardson numbers and AR = 3: (a) Ri = 102max = 9.51) and (b) Ri = 103max = 7.62)

Fig. 9

Eckert number as a function of Peclet number and the maximum dimensionless temperature difference ratio, ϑmax, within stratified stores

Fig. 10

Time-varying entropy generation rates in stratified stores due to radial thermal gradients, σ˙T,r, and due to axial thermal gradients, σ˙T,z, under different Peclet number regimes for three representative Richardson numbers and AR = 3: (a) Ri = 10 (ϑmax = 12.92), (b) Ri = 102max = 9.51), and (c) Ri = 103max = 7.62)

Fig. 11

Time-varying entropy generation numbers in stratified stores under different Peclet number regimes for two representative Richardson numbers and AR = 3: (a) Ri = 102max = 9.51) and (b) Ri = 103max = 7.62)

Fig. 12

Effect of Richardson numbers and Peclet numbers on entropy generation numbers, Ns, in stratified stores

Fig. 13

Effect of AR and Peclet numbers on entropy generation numbers, Ns, in stratified stores

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