411 lines
14 KiB
C
411 lines
14 KiB
C
#include "therm.h"
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#include <math.h>
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#include "Detail.h"
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void Therm_Init(Therm *therm) {
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therm->CAL_TH = 4.1840;
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therm->coefA = 0;
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therm->coefB = 1;
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therm->coefC = 2;
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therm->coefD = 3;
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therm->coefE = 4;
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therm->coefF = 5;
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therm->coefG = 6;
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therm->coefH = 7;
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therm->coefI = 8;
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therm->coefJ = 9;
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therm->coefK = 10;
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therm->dPdD = 0.0;
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therm->dPdT = 0.0;
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therm->dSi = 0.0;
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therm->dTold = 0.0;
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therm->dMrxold = 0.0;
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therm->GK_points = 5;
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therm->GK_root[0] = 0.14887433898163121088;
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therm->GK_root[1] = 0.43339539412924719080;
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therm->GK_root[2] = 0.67940956829902440263;
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therm->GK_root[3] = 0.86506336668898451073;
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therm->GK_root[4] = 0.97390652851717172008;
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therm->GK_weight[0] = 0.29552422471475286217;
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therm->GK_weight[1] = 0.26926671930999634918;
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therm->GK_weight[2] = 0.21908636251598204295;
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therm->GK_weight[3] = 0.14945134915058059038;
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therm->GK_weight[4] = 0.066671344308688137179;
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double thermConstants[21][11] = {
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{-29776.4, 7.95454, 43.9417, 1037.09, 1.56373, 813.205, -24.9027, 1019.98, -10.1601, 1070.14, -20.0615},
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{-3495.34, 6.95587, 0.272892, 662.738, -0.291318, -680.562, 1.78980, 1740.06, 0.0, 100.0, 4.49823},
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{20.7307, 6.96237, 2.68645, 500.371, -2.56429, -530.443, 3.91921, 500.198, 2.13290, 2197.22, 5.81381},
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{-37524.4, 7.98139, 24.3668, 752.320, 3.53990, 272.846, 8.44724, 1020.13, -13.2732, 869.510, -22.4010},
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{-56072.1, 8.14319, 37.0629, 735.402, 9.38159, 247.190, 13.4556, 1454.78, -11.7342, 984.518, -24.0426},
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{-13773.1, 7.97183, 6.27078, 2572.63, 2.05010, 1156.72, 0.0, 100.0, 0.0, 100.0, -3.24989},
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{-10085.4, 7.94680, -0.08380, 433.801, 2.85539, 843.792, 6.31595, 1481.43, -2.88457, 1102.23, -0.51551},
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{-5565.60, 6.66789, 2.33458, 2584.98, 0.749019, 559.656, 0.0, 100.0, 0.0, 100.0, -7.94821},
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{-2753.49, 6.95854, 2.02441, 1541.22, 0.096774, 3674.81, 0.0, 100.0, 0.0, 100.0, 6.23387},
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{-3497.45, 6.96302, 2.40013, 2522.05, 2.21752, 1154.15, 0.0, 100.0, 0.0, 100.0, 9.19749},
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{-72387.0, 17.8143, 58.2062, 1787.39, 40.7621, 808.645, 0.0, 100.0, 0.0, 100.0, -44.1341},
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{-72674.8, 18.6383, 57.4178, 1792.73, 38.6599, 814.151, 0.0, 100.0, 0.0, 100.0, -46.1938},
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{-91505.5, 21.3861, 74.3410, 1701.58, 47.0587, 775.899, 0.0, 100.0, 0.0, 100.0, -60.2474},
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{-83845.2, 22.5012, 69.5789, 1719.58, 46.2164, 802.174, 0.0, 100.0, 0.0, 100.0, -62.2197},
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{-94982.5, 26.6225, 80.3819, 1718.49, 55.6598, 802.069, 0.0, 100.0, 0.0, 100.0, -77.5366},
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{-103353.0, 30.4029, 90.6941, 1669.32, 63.2028, 786.001, 0.0, 100.0, 0.0, 100.0, -92.0164},
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{-109674.0, 34.0847, 100.253, 1611.55, 69.7675, 768.847, 0.0, 100.0, 0.0, 100.0, -106.149},
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{-122599.0, 38.5014, 111.446, 1646.48, 80.5015, 781.588, 0.0, 100.0, 0.0, 100.0, -122.444},
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{-133564.0, 42.7143, 122.173, 1654.85, 90.2255, 785.564, 0.0, 100.0, 0.0, 100.0, -138.006},
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{0.0, 4.9680, 0.0, 100.0, 0.0, 100.0, 0.0, 100.0, 0.0, 100.0, 0.0},
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{0.0, 4.9680, 0.0, 100.0, 0.0, 100.0, 0.0, 100.0, 0.0, 100.0, 0.0}
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};
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for (int i = 0; i < 21; i++) {
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for (int j = 0; j < 11; j++) {
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therm->ThermConstants[i][j] = thermConstants[i][j];
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}
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}
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}
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void Therm_Run(Therm *therm, NGParSTRUCT *ptNGPar, Detail *detail) {
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double c, x, y, z;
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Detail_Run(detail, ptNGPar);
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Detail_dZdD(detail, ptNGPar->dDf);
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Therm_CprCvrHS(therm, ptNGPar, detail);
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ptNGPar->dk = ptNGPar->dCp / ptNGPar->dCv;
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x = ptNGPar->dk * RGAS * 1000.0 * ptNGPar->dTf;
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y = ptNGPar->dMrx;
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z = ptNGPar->dZf + ptNGPar->dDf * detail->ddZdD;
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c = (x / y) * z;
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ptNGPar->dSOS = sqrt(c);
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ptNGPar->dKappa = (c * ptNGPar->dRhof) / ptNGPar->dPf;
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}
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double Therm_CpiMolar(Therm *therm, NGParSTRUCT *ptNGPar) {
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double cp = 0.0;
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double Cpx;
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double DT, FT, HT, JT;
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double Dx, Fx, Hx, Jx;
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double T;
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T = ptNGPar->dTf;
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for (int i = 0; i < NUMBEROFCOMPONENTS; i++) {
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if (ptNGPar->adMixture[i] > 0) {
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Cpx = 0.0;
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DT = therm->ThermConstants[i][therm->coefD] / T;
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FT = therm->ThermConstants[i][therm->coefF] / T;
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HT = therm->ThermConstants[i][therm->coefH] / T;
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JT = therm->ThermConstants[i][therm->coefJ] / T;
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Dx = DT / sinh(DT);
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Fx = FT / cosh(FT);
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Hx = HT / sinh(HT);
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Jx = JT / cosh(JT);
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Cpx += therm->ThermConstants[i][therm->coefB];
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Cpx += therm->ThermConstants[i][therm->coefC] * Dx * Dx;
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Cpx += therm->ThermConstants[i][therm->coefE] * Fx * Fx;
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Cpx += therm->ThermConstants[i][therm->coefG] * Hx * Hx;
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Cpx += therm->ThermConstants[i][therm->coefI] * Jx * Jx;
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Cpx *= ptNGPar->adMixture[i];
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cp += Cpx;
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}
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}
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cp *= therm->CAL_TH;
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return cp;
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}
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double Therm_coth(double x) {
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return 1.0 / tanh(x);
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}
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double Therm_Ho(Therm *therm, NGParSTRUCT *ptNGPar) {
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double H = 0.0;
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double Hx;
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double DT, FT, HT, JT;
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double cothDT, tanhFT, cothHT, tanhJT;
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double T = ptNGPar->dTf;
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for (int i = 0; i < NUMBEROFCOMPONENTS; i++) {
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if (ptNGPar->adMixture[i] <= 0.0) continue;
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Hx = 0.0;
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DT = therm->ThermConstants[i][therm->coefD] / T;
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FT = therm->ThermConstants[i][therm->coefF] / T;
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HT = therm->ThermConstants[i][therm->coefH] / T;
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JT = therm->ThermConstants[i][therm->coefJ] / T;
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cothDT = Therm_coth(DT);
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tanhFT = tanh(FT);
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cothHT = Therm_coth(HT);
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tanhJT = tanh(JT);
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Hx += therm->ThermConstants[i][therm->coefA];
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Hx += therm->ThermConstants[i][therm->coefB] * T;
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Hx += therm->ThermConstants[i][therm->coefC] * therm->ThermConstants[i][therm->coefD] * cothDT;
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Hx -= therm->ThermConstants[i][therm->coefE] * therm->ThermConstants[i][therm->coefF] * tanhFT;
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Hx += therm->ThermConstants[i][therm->coefG] * therm->ThermConstants[i][therm->coefH] * cothHT;
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Hx -= therm->ThermConstants[i][therm->coefI] * therm->ThermConstants[i][therm->coefJ] * tanhJT;
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Hx *= ptNGPar->adMixture[i];
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H += Hx;
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}
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H *= therm->CAL_TH;
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H /= ptNGPar->dMrx;
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return H * 1000.0;
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}
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double Therm_So(Therm *therm, NGParSTRUCT *ptNGPar) {
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double S = 0.0;
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double Sx;
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double DT, FT, HT, JT;
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double cothDT, tanhFT, cothHT, tanhJT;
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double sinhDT, coshFT, sinhHT, coshJT;
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double T = ptNGPar->dTf;
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for (int i = 0; i < NUMBEROFCOMPONENTS; i++) {
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if (ptNGPar->adMixture[i] <= 0.0) continue;
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Sx = 0.0;
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DT = therm->ThermConstants[i][therm->coefD] / T;
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FT = therm->ThermConstants[i][therm->coefF] / T;
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HT = therm->ThermConstants[i][therm->coefH] / T;
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JT = therm->ThermConstants[i][therm->coefJ] / T;
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cothDT = Therm_coth(DT);
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tanhFT = tanh(FT);
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cothHT = Therm_coth(HT);
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tanhJT = tanh(JT);
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sinhDT = sinh(DT);
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coshFT = cosh(FT);
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sinhHT = sinh(HT);
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coshJT = cosh(JT);
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Sx += therm->ThermConstants[i][therm->coefK];
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Sx += therm->ThermConstants[i][therm->coefB] * log(T);
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Sx += therm->ThermConstants[i][therm->coefC] * (DT * cothDT - log(sinhDT));
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Sx -= therm->ThermConstants[i][therm->coefE] * (FT * tanhFT - log(coshFT));
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Sx += therm->ThermConstants[i][therm->coefG] * (HT * cothHT - log(sinhHT));
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Sx -= therm->ThermConstants[i][therm->coefI] * (JT * tanhJT - log(coshJT));
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Sx *= ptNGPar->adMixture[i];
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S += Sx;
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}
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S *= therm->CAL_TH;
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S /= ptNGPar->dMrx;
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return S * 1000.0;
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}
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void Therm_CprCvrHS(Therm *therm, NGParSTRUCT *ptNGPar, Detail *detail) {
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double Cvinc = 0.0;
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double Cvr, Cpr;
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double Hinc = 0.0;
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double Sinc = 0.0;
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double Smixing = 0.0;
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double Si;
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double Cp = Therm_CpiMolar(therm, ptNGPar);
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ptNGPar->dHo = Therm_Ho(therm, ptNGPar);
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Si = Therm_So(therm, ptNGPar);
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ptNGPar->dCpi = (Cp * 1000.0) / ptNGPar->dMrx;
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for (int i = 0; i < therm->GK_points; i++) {
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double x = ptNGPar->dDf * (1.0 + therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Hinc += therm->GK_weight[i] * detail->ddZdT / x;
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Cvinc += therm->GK_weight[i] * (2.0 * detail->ddZdT + ptNGPar->dTf * detail->dd2ZdT2) / x;
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Sinc += therm->GK_weight[i] * (detail->dZ + ptNGPar->dTf * detail->ddZdT - 1.0) / x;
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x = ptNGPar->dDf * (1.0 - therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Hinc += therm->GK_weight[i] * detail->ddZdT / x;
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Cvinc += therm->GK_weight[i] * (2.0 * detail->ddZdT + ptNGPar->dTf * detail->dd2ZdT2) / x;
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Sinc += therm->GK_weight[i] * (detail->dZ + ptNGPar->dTf * detail->ddZdT - 1.0) / x;
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}
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Detail_zdetail(detail, ptNGPar->dDf);
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Detail_dZdT(detail, ptNGPar->dDf);
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Detail_d2ZdT2(detail, ptNGPar->dDf);
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Cvr = Cp - RGAS * (1.0 + ptNGPar->dTf * Cvinc * 0.5 * ptNGPar->dDf);
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double a = (ptNGPar->dZf + ptNGPar->dTf * detail->ddZdT);
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double b = (ptNGPar->dZf + ptNGPar->dDf * detail->ddZdD);
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double dPdT = RGAS * ptNGPar->dDf * a;
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double dPdD = RGAS * ptNGPar->dTf * b;
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Cpr = Cvr + RGAS * ((a * a) / b);
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Cpr /= ptNGPar->dMrx;
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Cvr /= ptNGPar->dMrx;
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ptNGPar->dCv = Cvr * 1000.0;
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ptNGPar->dCp = Cpr * 1000.0;
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ptNGPar->dH = ptNGPar->dHo + 1000.0 * RGAS * ptNGPar->dTf * (
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ptNGPar->dZf - 1.0 - ptNGPar->dTf * Hinc * 0.5 * ptNGPar->dDf) / ptNGPar->dMrx;
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for (int i = 0; i < NUMBEROFCOMPONENTS; i++) {
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if (ptNGPar->adMixture[i] != 0) Smixing += ptNGPar->adMixture[i] * log(ptNGPar->adMixture[i]);
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}
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Smixing *= RGAS;
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ptNGPar->dS = Si - Smixing - 1000.0 * RGAS * (
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log(ptNGPar->dPf / 101325.0) - log(ptNGPar->dZf) + Sinc * 0.5 * ptNGPar->dDf) / ptNGPar->dMrx;
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}
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void Therm_HS_Mode(Therm *therm, NGParSTRUCT *ptNGPar, Detail *detail, double H, double S, bool bGuess) {
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double s0 = S;
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double h0 = H;
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double t1, t2, tmin, tmax;
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double p1, p2, px, pmin, pmax;
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double delta1, delta2;
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double tolerance = 0.001;
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if (bGuess) {
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t1 = ptNGPar->dTf;
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px = ptNGPar->dPf;
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pmax = px * 2.0;
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pmin = px * 0.1;
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tmax = t1 * 1.5;
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tmin = t1 * 0.67;
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} else {
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t1 = 273.15;
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px = 1013250.0;
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pmax = P_MAX;
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pmin = 10000.0;
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tmax = T_MAX;
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tmin = T_MIN;
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}
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t2 = t1 + 10.0;
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Detail_Run(detail, ptNGPar);
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double h1 = Therm_H(therm, ptNGPar, detail) - h0;
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for (int i = 0; i < MAX_NUM_OF_ITERATIONS; i++) {
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ptNGPar->dTf = t2;
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p1 = px;
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p2 = px * 0.1;
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ptNGPar->dPf = p1;
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Detail_Run(detail, ptNGPar);
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double s1 = Therm_S(therm, ptNGPar, detail) - s0;
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for (int j = 0; j < MAX_NUM_OF_ITERATIONS; j++) {
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ptNGPar->dPf = p2;
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Detail_Run(detail, ptNGPar);
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double s2 = Therm_S(therm, ptNGPar, detail) - s0;
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delta2 = fabs(s1 - s2) / s0;
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if (delta2 < tolerance) break;
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double p0 = p2;
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p2 = (p1 * s2 - p2 * s1) / (s2 - s1);
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if (p2 <= pmin) p2 = pmin;
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if (p2 >= pmax) p2 = pmax;
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p1 = p0;
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s1 = s2;
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}
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if (ptNGPar->lStatus == MAX_NUM_OF_ITERATIONS_EXCEEDED) break;
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double h2 = Therm_H(therm, ptNGPar, detail) - h0;
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delta1 = fabs(h1 - h2) / h0;
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if (delta1 < tolerance && i > 0) break;
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double t0 = t2;
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t2 = (t1 * h2 - t2 * h1) / (h2 - h1);
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if (t2 >= tmax) t2 = tmax;
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if (t2 <= tmin) {
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t2 = t0 + 10.0;
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ptNGPar->dTf = t2;
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Detail_Run(detail, ptNGPar);
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h2 = Therm_H(therm, ptNGPar, detail) - h0;
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}
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t1 = t0;
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h1 = h2;
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}
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if (ptNGPar->lStatus == MAX_NUM_OF_ITERATIONS_EXCEEDED) {
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ptNGPar->lStatus = MAX_NUM_OF_ITERATIONS_EXCEEDED;
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}
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}
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double Therm_H(Therm *therm, NGParSTRUCT *ptNGPar, Detail *detail) {
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double Hinc = 0.0;
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ptNGPar->dHo = Therm_Ho(therm, ptNGPar);
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for (int i = 0; i < therm->GK_points; i++) {
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double x = ptNGPar->dDf * (1.0 + therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Hinc += therm->GK_weight[i] * detail->ddZdT / x;
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if (i == 10) break;
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x = ptNGPar->dDf * (1.0 - therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Hinc += therm->GK_weight[i] * detail->ddZdT / x;
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}
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Detail_zdetail(detail, ptNGPar->dDf);
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Detail_dZdT(detail, ptNGPar->dDf);
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Detail_d2ZdT2(detail, ptNGPar->dDf);
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ptNGPar->dH = ptNGPar->dHo + 1000.0 * RGAS * ptNGPar->dTf * (
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ptNGPar->dZf - 1.0 - ptNGPar->dTf * Hinc * 0.5 * ptNGPar->dDf) / ptNGPar->dMrx;
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return ptNGPar->dH;
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}
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double Therm_S(Therm *therm, NGParSTRUCT *ptNGPar, Detail *detail) {
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double Sinc;
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double Smixing;
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double x;
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int i;
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Sinc = 0.0;
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Smixing = 0.0;
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for (i = 0; i < therm->GK_points; i++) {
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x = ptNGPar->dDf * (1.0 + therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Sinc += therm->GK_weight[i] * (detail->dZ + ptNGPar->dTf * detail->ddZdT - 1.0) / x;
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if (i == 10) break;
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x = ptNGPar->dDf * (1.0 - therm->GK_root[i]) / 2.0;
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Detail_zdetail(detail, x);
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Detail_dZdT(detail, x);
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Detail_d2ZdT2(detail, x);
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Sinc += therm->GK_weight[i] * (detail->dZ + ptNGPar->dTf * detail->ddZdT - 1.0) / x;
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}
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Detail_zdetail(detail, ptNGPar->dDf);
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Detail_dZdT(detail, ptNGPar->dDf);
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Detail_d2ZdT2(detail, ptNGPar->dDf);
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if (ptNGPar->dTf != therm->dTold || ptNGPar->dMrx != therm->dMrxold) {
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therm->dSi = Therm_So(therm, ptNGPar);
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therm->dTold = ptNGPar->dTf;
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therm->dMrxold = ptNGPar->dMrx;
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}
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for (i = 0; i < NUMBEROFCOMPONENTS; i++) {
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if (ptNGPar->adMixture[i] != 0) Smixing += ptNGPar->adMixture[i] * log(ptNGPar->adMixture[i]);
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}
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Smixing *= RGAS;
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ptNGPar->dS = therm->dSi - Smixing - 1000.0 * RGAS * (
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log(ptNGPar->dPf / 101325.0) - log(ptNGPar->dZf) + Sinc * 0.5 * ptNGPar->dDf) / ptNGPar->dMrx;
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return (ptNGPar->dS);
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}
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