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Ing. Patrick Schwarzbauer Solar thermal organic Rankine cycle (ORC) to calculate the generated heat capacity Q_solar [W] of the solar collectors, see Equation 8. Q_solar=mdot_solar*cp_w*(T2_solarT- 1_solar)(8) With the knowledge of the generated heat capacity from Equation 8 it is possible to start the calculation of the refrigerant cycle. Like before it is necessary to define all known information of the heat exchanger, in this case the outlet temperature of the evaporator T2_ev and the evaporation pressure p_ev. The next step is to implement a code to interpolate the values for enthalpy which are generated with EES and exported to an excel sheet called “PropertiesR134a.xlsx”. To import the data from excel we can use the Matlab command: >>Table_h = xlsread('PropertiesR134a.xlsx') To realize an Organic-Rankine cycle several steps are necessary: • 1-2: real expansion in turbine, ηT = 0,80 [3, page 26] • 2-3: isobaric heat dissipation in condenser, p=const. • 3-4: isobaric condensation, p=const. • 4-5: real compression in pump, ηP = 0,75 [3, page 26] • 5-6: isobaric heat supply, p=const. • 6-7: isobaric evaporation, p=const. • 7-1: isobaric heat supply, p=const. To find the enthalpy of condition 1, which represents the superheated gas (R134a) following code can be used: >>T2_ev_deg=65; >>T2_ev=T2_ev_deg+273.15; >>p_ev=17*10.^5; %Import excel data for Enthalpy >>Table_h = xlsread('PropertiesR134a.xlsx') >>find p_ev=17 >>T_find=65; %temperature of superheated gas >>r=(p- repmat(p_find,1,length(p))).^2+(trepmat(T_find,1,length( t))).^2); % Find the smallest residual >> [m,i] = min(r); %the index, i, now represents the point closest to the value we are trying to look up. >>h1 = interp1([p(i) p(i+1)],[h(i) h(i+1)],p_find,'linear') This procedure can be done for every condition of the ORC cycle, see Table 7. Table 7. Key thermodynamic states during evaporation. Within all the values for enthalpy, all three heat capacities for all phases of the HEX can be calculated. The command repmat has following definition: “B = repmat(A,n) returns an array containing n copies of A in the row and column dimensions. The size of B is size(A)*n when A is a matrix” [13]. For interpolating between values, the command interp1 can be used with following description: “vq = interp1(x,v,xq) returns interpolated values of a 1-D function at specific query points using linear interpolation. Vector x contains the sample points, and v contains the corresponding values, v(x). Vector xq contains the coordinates of the query points. If you have multiple sets of data that are sampled at the same point coordinates, then you can pass v as an array. Each column of array v contains a different set of 1-D sample values” [13]. Now it is possible to calculate the dimensions, numbers of gaps, areas of each phase as well as the Reynold numbers, Nusselt numbers and the overall convection coefficients U for each phase, see Appendix B for thermodynamic calculation. To simplify the code, an assumption for the overall convection coefficient of the boiling phase is made. During this phase change a lot of knowledge of heat transfer is necessary. To make sure the area is big enough to evaporate the refrigerant the convection coefficient is defined very low (U2 = 2000 [W/(m2*K)]). As a design decision, the exterior dimensions are quadratic (L = 0.2 m). This results in several solutions for number of gaps as well as the gap width “a” for each phase, see Appendix B. For superheating the gas, laminar flow is assumed. This assumption is true for water but not for the superheated refrigerant. Therefore, it is necessary to calculate a new Nusselt number for turbulent flow, see Equation 9 [11, page 485]. >>find T2_ev_deg=65 >>sl = 2; >>t1 = Table_h(:,2); >>t = t1(1:length(t1)); >>t = repmat(t,1,sl-1); repeats %size of the square input matrix %Capture the table headers %fix the first NaN value %make the headers a matrix that %creates a vector out of matrix %Capture the labels for each row >>t = t(:)'; >>p1 = Table_h(:,1); >>p = p1(1:length(p1))';%fix the first NaN value >>p = repmat(p,1,sl-1); repeats >>h = Table_h(:,3); %turn the matrix of h values into a long vector >>h= h(:)'; %creates a vector out of matrix %make the headers a matrix that %Just the enthalpy values % Now we have 3 long vectors that contain pressure, temperature and enthalpy. to find the closest point to our target values we can use minimization of residuals. >>p_find=17; %pressure of superheated gas -13-PDF Image | Solar thermal organic Rankine cycle (ORC)
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