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RESEARCH PAPERS

# On Simplified Models for the Rate- and Time-Dependent Performance of Stratified Thermal Storage

[+] Author and Article Information
Ying Ji

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65409–0050khoman@umr.edu

K. O. Homan1

Department of Mechanical and Aerospace Engineering, University of Missouri-Rolla, Rolla, MO 65409–0050khoman@umr.edu

1

Corresponding author.

J. Energy Resour. Technol 129(3), 214-222 (Feb 15, 2007) (9 pages) doi:10.1115/1.2748814 History: Received April 22, 2004; Revised February 15, 2007

## Abstract

In direct sensible thermal storage systems, both the energy discharging and charging processes are inherently time-dependent as well as rate-dependent. Simplified models which depict the characteristics of this transient process are therefore crucial to the sizing and rating of the storage devices. In this paper, existing models which represent three distinct classes of models for thermal storage behavior are recast into a common formulation and used to predict the variations of discharge volume fraction, thermal mixing factor, and entropy generation. For each of the models considered, the parametric dependence of key performance measures is shown to be expressible in terms of a Peclet number and a Froude number or temperature difference ratio. The thermal mixing factor for each of the models is reasonably well described by a power law fit with $Fr2Pe$ for the convection-dominated portion of the operating range. For the uniform and nonuniform diffusivity models examined, there is shown to be a Peclet number which maximizes the discharge volume fraction. In addition, the cumulative entropy generation from the simplified models is compared with the ideally-stratified and the fully-mixed limits. Of the models considered, only the nonuniform diffusivity model exhibits an optimal Peclet number at which the cumulative entropy generation is minimized. For each of the other models examined, the cumulative entropy generation varies monotonically with Peclet number.

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## Figures

Figure 1

Simplified schematic of a direct sensible storage vessel and a representative vertical temperature profile

Figure 2

Variation of discharge volume fraction with Peclet number for thermocline thickness model of Lavan and Thompson (29). The dimensionless edge temperature is Te=0.1.

Figure 3

Thermal mixing factor for thermocline thickness model of Lavan and Thomson (29). Curve 1 is κd=6.0×10−7(Fr2Pe)1.6581 and curve 2 is κd=2.2×10−3(Fr2Pe)0.7768.

Figure 4

Cumulative entropy generation over the duration of the discharge process for thermocline thickness model of Lavan and Thompson (29). The dimensionless edge temperature is Te=0.1. Curve 1 represents the fully-mixed limit and curve 2 the ideally-stratified limit.

Figure 5

Variation of discharge volume fraction with Peclet number for thermocline thickness model of Bahnfleth and Musser (28). The dimensionless edge temperature is Te=0.1.

Figure 6

Thermal mixing factor for thermocline thickness model of Bahnfleth and Musser (28). The curve fit equation is κd=5.47×10−2(Fr2Pe)0.6025.

Figure 7

Cumulative entropy generation over the duration of the discharge process for thermocline thickness model of Bahnfleth and Musser (28). The dimensionless edge temperature is Te=0.1.

Figure 8

Variation of discharge volume fraction with Peclet number for uniform diffusivity model of Cole and Bellinger (9)

Figure 9

Thermal mixing factor for uniform diffusivity model of Cole and Bellinger (9). The curve fit equation is κd=8.76×10−2(Fr2Pe)0.4572 for Fr2Pe>3×102.

Figure 10

Time variation of entropy generation rate for uniform diffusivity model of Cole and Bellinger (9) with τl=0.04

Figure 11

Cumulative entropy generation over the duration of the discharge process for uniform diffusivity model of Cole and Bellinger (9). The dimensionless edge temperature is Te=0.15. Curve 1 represents the fully-mixed limit and curve 2 the ideally-stratified limit.

Figure 12

Variation of discharge volume fraction with Peclet number for nonuniform diffusivity model of Zurigat (14)

Figure 13

Thermal mixing factor for the nonuniform diffusivity model of Zurigat (14). The dimensionless edge temperature is Te=0.15. Curve 1 is κd=9.656×10−1(Fr2Pe)0.0166 and curve 2 is κd=2.0×10−3(Fr2Pe)0.731.

Figure 14

Time variation of entropy generation rate for nonuniform diffusivity model of Zurigate (14)

Figure 15

Cumulative entropy generation over the duration of the discharge process for nonuniform diffusivity model of Zurigate (14). The dimensionless edge temperature is Te=0.15.

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