Enhanced characteristic equation method for single-stage absorption heat pumps

Abstract

The method of characteristic equations aims to describe the part-load behavior of sorption heat pumps and chillers as well as heat transformers as simply as possible but yet still accurately. Based on an approach by T. Furukawa for heat transformers, the method was further developed by F. Ziegler and others for absorption heat pumps and generalized for application in multistage processes. Clever simplifications were made, to represent the cooling capacity ${\dot{Q}}_E$ of absorption chillers with a characteristic temperature difference $\Delta \Delta t$ as a simple linear equation ${\dot{Q}}_E=s_E·(\Delta \Delta t-\Delta \Delta t_{\min ,E})$. In $\Delta \Delta t$, the average hot, cooling, and chilled water temperatures are combined, and the slope and loss parameters, $s_E$ and $\Delta \Delta t_{\min ,E}$ are constant. However, in practical applications of this established method, inconsistencies arise. For example, the calculated slope parameter $s_E$ does not match the slope when plotting simulated or measured cooling capacities against $\Delta \Delta t$. Furthermore, the loss parameter $\Delta \Delta t_{\min ,E}$ is actually not constant.

In this work a more precise formulation of the characteristic equation is derived which takes into account that the solution entering the absorber and desorber is generally superheated or subcooled. By means of a domain-wise heat transfer calculation, these effects can be implemented into the method and explain the above mentioned inconsistencies. The new formulation allows for explicit consideration of different heat exchanger designs and cooling water configurations. No iterations or regression analyses are required. Thus, the calculation method can be easily implemented into industrial controllers e.g. for the model predictive control of absorption chillers and heat pumps.