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Ing. Patrick Schwarzbauer Solar thermal organic Rankine cycle (ORC) 5.2 Theoretical foundations There are two different ways to do the thermodynamic calculation on a HEX, the log mean temperature difference method (LMTD) or the NTU-method. If only the inlet temperatures are known, the use of the LMTD method requires a cumbersome iterative procedure [11]. Therefore, the use of the NTU-method would be more efficient. Since all temperatures and pressures are known, the LMTD calculation will be explained in detail. Another important factor of heat exchanger analysis is the overall heat transfer coefficient, see Equation 2. Sometimes it is difficult to predict the overall heat coefficient, especially when there is a change in phase of the fluid. It is highly recommended to check the result for the overall heat exchanger with representative values, therefore see Table 3. To approach realistic values the so-called fouling factor Rf is implemented in the equation. The value of the fouling factor strongly depends on the operating temperature, fluid velocity, and length of service of the heat exchanger [11]. In this calculation, the fouling factor will be neglected to keep the calculation simple, for representative values see Table 4. . = . +#"4,6+ln 9: +#"4,:+ . (2) /0 1202 02 96 0; 1;0; The formulaic character for the overall heat coefficient is U. The formula also contains the Area Ai and Ao, both heat transfer coefficients hi and ho, fouling factors R”f,i and R”f,o as well as the diameters of the cylindrical wall. The calculation is based on cylindrical cross areas, where the subscript i means inside the tube and o means outside the tube. For other geometries it necessary to calculate the hydraulic diameter of the cross-section. Table 3. Representative values of the overall heat coefficient U [11]. 5.2.1 The Log Mean Temperature Difference (LMTD) For heat exchanger analysis, it is essential to define temperatures, pressures as well as mass flow rates. The more values are known the better and easier the calculation is going to be. Another important value to predict the performance of a heat exchanger is enthalpy h. With the mass flow rate, which is constant, and the enthalpy difference at the inlet and outlet, the heat transfer rate Q can be calculated, see Equation 3. The specific heat capacity cp at constant pressure is typically 4,180 [kJ/(kg*K)] for liquid water [11]. The inlet and outlet temperature of the hot fluid are calculated in Kelvin, in order to satisfy the equation. The mass flow rate mh [kg/s] of the solar cycle was defined by previous senior design teams to reach the highest outlet temperature of the solar collectors. 𝑄=𝑚1∗ h2−h; =𝑐𝑝1∗𝑚1∗(𝑇1,2−𝑇1,;) (3) The heat transfer rate is related on the hot fluid, due to the laws of thermodynamics heat can only be transferred from a hot medium to a cold medium and not vice versa. For the ORC system, the hot fluid is the incoming solar water which evaporates and superheats the refrigerant before it enters the turbine. In case of condensing the refrigerant, the hot water is tap water of the City of Portland. The knowledge of the minimum and maximum temperature of the tap water is important for calculating the condenser as well as the overall performance of the ORC itself. Some systems use finned-tube heat exchangers, where the refrigerant is in the tubes and the air is in cross flow, see Figure 26. Due to a low overall heat transfer coefficient of such heat exchangers, the area has to be higher than the area of plate heat exchangers or other types. Fluid Combination Water to water Water to oil Steam condenser (water in tubes) Ammonia condenser (water in tubes) Finned-tube heat exchanger (water in tubes, air in cross flow) U [W/(m2*K)] 850 - 1700 110 – 350 1000 - 6000 800 - 1400 25-50 Table 4. Representative fouling factors [11]. Fluid Seawater and treated boiler feedwater (below 50 °C) Seawater and treated boiler feedwater (above 50 °C) River water (below 50 °C) Fuel oil Refrigerant liquids R”f [(m2*K/W)] 0,0001 0,0002 0,0002 – 0,001 0,0009 0,0002 Figure 26. Fin-tube heat exchanger [9]. -11-PDF Image | Solar thermal organic Rankine cycle (ORC)
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