# Energy Analysis of Kalina and Kalina Flash Cycles Driven by Renewable Energy
## 2 Materials and Methods  
The schematic diagrams of the (a) Kalina cycle (KC) and the (b) Kalina flash cycle (KFC) are shown in Figure 1. As these two systems are the same except for the added components of the flash vessel and turbine 2, the same location numbers in KC are allotted to the corresponding locations in the KFC and a pair of dual numbers are used to simply bypass the missing components. KFC consists of a heat-recovery vapor generator (HRVG), separator, flash vessel, turbines 1 and 2, throttle valve, mixer, condenser, pump, and regenerator. The processes in KFC are as follows [15]: the ammonia solution in water with basic mass fraction of \(x_{b}\) and at pressure and temperature of \(P_{H}\) and \(T_{H}\) vaporizes in HRVG. The fluid of two-phase flow (state 1) out of HRVG then enters the separator and is separated into vapor (state 2) and solution (state 3). The solution from separator is delivered to the flash vessel and flashed. After flashing, the fluid is divided into secondary vapor (state 4) and secondary solution (state 5) at pressure \(P_{f}\). The primary vapor from separator enters and leaves turbine 1 after producing power (state 6), and the secondary vapor from flash vessel enters and leaves turbine 2 after producing additional power (state 7), and two exhaust fluids mix together (state 10). The secondary solution from the flash vessel is cooled in regenerator (state 8), throttled (state 9), and mixed with the fluid from two turbines (state 11). In the condenser the fluid completely condenses to a liquid at saturation temperature of \(T_{L}\) (state 12). A cycle is completed when the working fluid is pressurized (state 13) and preheated (state 14), and then enters HRVG. Aside from the working fluid, two fluids are additionally involved in the cycle operation: a source fluid of air and a coolant of water. The source fluid makes the working fluid vaporize at HRVG with its sensible heat corresponding to the difference between temperatures at the inlet of \(T_{s}\) (state 15)and the outlet of \(T_{so}\) (state 16). The temperature of coolant rises from \(T_{c}\) at the inlet (state 17) to \(T_{co}\) at the outlet (state 18) of the condenser. For the convenience of simulation the system is assumed to satisfy the following simplifications:  
1. The cycle operates as a steady process. 2. Pressure drops such as in the pipe lines are negligible. 3. Heat loss at any component is negligible. 4. The pump and turbines operate with constant isentropic efficiencies. 5. The heat exchangers operate with constant pinch point temperature differences. 6. Both vapor and liquid phases of the mixture are saturated at the exits of separator and flash vessel. When the mass flow rate at any location is denoted by subscripted \(m\) and its enthalpy by \(h\), mass flow rates through the HRVG, turbines, flash vessel, and regenerator are determined from the mass and energy conservations as follows:  
\[m_{1}=m_{s}c_{ps}\frac{T_{s}-T_{so}}{h_{1}-h_{14}} \tag{1}\]  
\[m_{2}=m_{1}\frac{h_{1}-h_{3}}{h_{2}-h_{3}} \tag{2}\]  
\[m_{3}=m_{1}-m_{2} \tag{3}\]  
\[m_{4}=m_{3}\frac{h_{3}-h_{5}}{h_{4}-h_{5}} \tag{4}\]  
\[m_{5}=m_{3}-m_{4} \tag{5}\]  
Here, \(m_{s}\) denotes the source's specified mass flow rate and \(c_{ps}\) denotes its isobaric specific heat. The heat transfer rates at HRVG, regenerator, and condenser, denoted by \(Q_{s}\), \(Q_{r}\), and \(Q_{c}\) can be determined from the enthalpy changes of the working fluid and given by:  
\[Q_{s}=m_{1}(h_{1}-h_{14}) \tag{6}\]  
\[Q_{r}=m_{5}(h_{5}-h_{8}) \tag{7}\]  
\[Q_{c}=m_{11}(h_{11}-h_{12}) \tag{8}\]  
Figure 1: Schematic diagrams of the Kalina cycle (**a**) and the Kalina flash cycle (**b**). The powers produced by turbines, \(W_{t1}\) and \(W_{t2}\), and consumed by pump, \(W_{p}\), can be determined in the same way.