• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.9 no.1
• /
• pp.43-54
• /
• 1997

This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.7 no.2
• /
• pp.184-195
• /
• 1995

A theoretical one-dimensional model for the charging process in stratified thermal storage tanks is established presuming that the fluid ensuing from the tank inlet creates a perfectly mixed, layer above the thermocline. Both the generic and asymptotic closed-form solutions are obtained via the Laplace transformation. The asymptotic solution describes the nature of the charging pertaining to the case of no thermal diffusion, whereas the generic solution is of practical importance to understand the role of operating parameters on the stratification. The present model is validated through comparison with available experimental data, where they agree well with each other within a reasonable limit. An interpretation of the exact solution entails two important features associated with the charging process. The first is that an in-crease in the mixing depth $h_m$ causes a relatively slow temperature rise in the perfectly mixed region, but on the other hand it results in a faster decay of the overall temperature gradient across the thermocline. Next is the predominance of the mixing depth in the presence of the prefectly mixed region. In such a case the effect of the Peclet number is marginal and there-fore the thermal characteristics are solely dependent on the mixing depth paticularly for large $h_m$. The Peclet number affects significantly only for the case without mixing. Variation of the storage efficiency in response to the change in the mass flow rate agrees favorably with the published experimental results, which confirms the utility of the present study.

• Solar Energy
• /
• v.11 no.3
• /
• pp.44-52
• /
• 1991

The benefits of thermal stratification in sensible heat storage systems has been considered and studying by several investigators. In this paper, the basic data which is hard to obtain normally through the experiment were obtainable through the computer simulation. The major objectives of the study were to assess the benefits of stratified storage in residential solar water heating application and to suggest the optimum design parameters. From the computer simulation, following results were obtained. 1. The solar load fraction increases with increasing the number of tank segments. In these simulation, the magnitude of the improvement was about 10%. 2. The solar load fraction increases when the ratio of diameter to height of the tank(H/D) increases to 3, but H/D exceed 3 then, the solar load fraction decreases. In these simulation, the magnitude of the improvement was about 3%. 3. Increasing the collector flow rate slightly improved the performance of the mixed storage system(Node=1). But, for the stratified storage system(Node=N), the solar load fraction increases with decreasing flow rate until the point is reached at which the collector outlet temperature reaches the boiloff limit of $100^{\circ}C$ over some portion of the simulation period.