Theoretical Analysis of the Charging Process with Perfectly Mixed Region in Stratified Thermal Storage Tanks

완전혼합영역을 갖는 성층축열조의 충전과정에 대한 이론적인 해석

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.