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3 Numerical methods In this section, the numerical methods used in this thesis are presented. First, the methods and equations used in the process design and in the thermodynamic analysis are presented. Second, the turbine design method is described. Third, the numerical methods used in the computational fluid dynamics (CFD) are described. 3.1 Thermodynamic analysis and process design methods The ORC process modelling and the thermodynamic analysis was based on the well- known calculation principles of a Rankine cycle. The thermodynamic and transport prop- erties database Refprop (Lemmon et al., 2010) was used for determining the working fluid thermodynamic properties. The solved properties were temperature T , pressure p, spe- cific enthalpy h, specific entropy s, density ρ, specific volume v, and speed of sound a. The process condensing temperature, heat source values, and the degree of superheating, as well as the process component efficiencies were used as an input for the computation. The evaporation pressure was used either as an input parameter or was optimized based on the heat source values. The saturated liquid and the saturated vapour thermodynamic state in the condenser and in the evaporator were determined based on the evaporation pressure and the condensing temperature. The parameters given as the input values in the process design are presented in Table 3.1. The unknown thermodynamic states were solved by using the equations of states implemented in Refprop in which two input prop- erties are used to determine other thermodynamic properties in the same process node. The cycle power output, efficiency, thermodynamic states of the working fluid at the in- let and outlet of each component, and the saturated states inside process components, as well as the working fluid mass flow rate were obtained as a result of the simulation by solving the continuity and energy equation for each process component. The calculation procedure for solving the unknown thermodynamic properties in different process nodes is presented in Table 3.2. Processes having subcritical evaporation pressures were studied, and thus, a limit for the evaporation pressure compared to the fluids critical pressure pev/pcrit was used in the ther- modynamic analysis. Another constraint used for optimizing the evaporation pressure was based on the minimum pinch-point temperature difference in the evaporator, ∆Tpp, which is the smallest temperature difference between the heat source and the working fluid. An example of the evaporator temperature diagram, presenting the definition and the location of a typical pinch-point temperature difference in the evaporator, is presented in Figure 3.1. In some of the simulations, the minimum temperature difference between the heat source and the working fluid occurred at the cold end of the evaporator, where the heat source exits the evaporator. A feature was added to the process design tool by using a simple linear search algorithm to optimize the evaporation pressure to reach the target minimum temperature difference in the evaporator with the given heat source values and given working fluid. A small degree of superheating was used in the simulations because a flow-through type evaporator was considered which requires superheating in the process 31PDF Image | WORKING FLUID SELECTION AND DESIGN OF SMALL-SCALE WASTE HEAT RECOVERY SYSTEMS BASED ON ORGANIC RANKINE CYCLES
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