# Dynamic Performance Analysis for an Absorption Chiller under Different Working Conditions
## 3 Modelling
### Energy Conservation  
#### 3.3.1 Generator  
In the generator, outside heat source (point 13, 14) transfers the driving heat to the inside working fluids, as shown in Figure 2. Since there are thermal storages like the heat exchanger, the container and the solution storage, the machine needs some relaxation time to achieve a new steady-state. Thus, the thermal capacities are taken into consideration in the model.  
(1) External heat exchange occurs between the driving heat source (hot water) and the heat exchanger, which is assumed to have a uniform temperature [26]. Thus, the energy balance equations are:  
\[Q_{g,ext}=Vol_{g}\cdot\rho_{uu,g}\cdot Cp_{uu}\cdot(T_{13}-T_{14}) \tag{14}\]  
\[Q_{g,ext}=UA_{ext,g}\cdot LMTD_{ext,g} \tag{15}\]  
\[LMTD_{ext,g}=\frac{(T_{13}-T_{hx,g})-(T_{14}-T_{hx,g})}{\ln(\frac{T_{13}-T_{hx,g}}{T_{14}-T_{hx,g}})} \tag{16}\]  
where \(Q_{g,ext}\) is the external heat exchange rate in the generator, kW; \(Vol_{g}\) is the volumetric flow rate of the hot water in point 13, m\({}^{3}\)/h; \(\rho_{uu,g}\). is the density of the hot water at its inlet temperature \(T_{13}\), kg/m\({}^{3}\); \(Cp_{uu}\) is the specific heat of the hot water, kJ/(kg\(\cdot\)K); \(T_{13}\) is the generator inlet temperature, \({}^{\circ}\)C; \(T_{14}\) is the generator outlet temperature, \({}^{\circ}\)C; \(UA_{ext,g}\) is the product of the external heat transfer coefficient and external heat transfer area for the generator, kW/K; \(LMTD_{ext,g}\) is the external logarithmic mean temperature difference, \({}^{\circ}\)C; and \(T_{hx,g}\) is the uniform temperature of the heat exchanger in the generator, \({}^{\circ}\)C.  
(2) Internal heat exchange between the heat exchanger and the working fluids is:  
\[Q_{g,int}=UA_{int,g}\cdot LMTD_{int,g} \tag{17}\]  
\[LMTD_{int,g}=\frac{(T_{hx,g}-T_{9})-(T_{hx,g}-T_{10})}{\ln(\frac{T_{hx,g}-T_{9 }}{T_{hx,g}-T_{10}})} \tag{18}\]  
where \(Q_{g,int}\) is the internal heat exchange rate in the generator, kW; \(UA_{int,g}\) is the product of the internal heat transfer coefficient and internal heat transfer area of the generator, kW/K; \(LMTD_{int,gi}\) is the internal logarithmic mean temperature difference in the generator, \({}^{\circ}\)C.  
(3) The difference between \(Q_{g,ext}\) and \(Q_{g,int}\) represents the thermal energy stored in the body of the heat exchanger.  
\[Q_{g,ext}-Q_{g,int}=MCp_{hx,g}\cdot\frac{dT_{hx,g}}{dt} \tag{19}\]  
where \(MCp_{hx,g}\) is the product of the heat exchanger mass and its specific heat in the generator, kJ/K.  
Figure 2: The energy flow diagram in the generator; \(LMTD_{ext,g}\): external logarithmic mean temperature difference in the generator.  
(4) All the internal heat \(Q_{g,int}\) is not used for the generation process; part of it is applied to raise the temperatures of the solution storage and container in the generator:  
\[Q_{g,int}=m_{v,des}\cdot h_{1}+m_{s}\cdot h_{10}-m_{w}\cdot h_{9}+MCp_{g}\cdot \frac{dT_{10}}{dt} \tag{20}\]  
\[MCp_{g}=M_{s,g}\cdot Cp_{10}+MCp_{g,con} \tag{21}\]  
where \(MCp_{g}\) is the thermal capacities of the solution storage and the container in the generator, kJ/K, \(MCp_{g,con}\) is the product of the container mass and its specific heat in the generator, kJ/K.  
The desorbed vapor temperature \(T_{1}\) equals to the saturation temperature associated with the weak solution entering the generator. It is between the weak solution temperature and the strong solution temperature, meaning the temperature that the refrigerant begins to be desorbed from the weak solution. The temperature of the container is set to be same with that of the solution storage [26].