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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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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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