Cantera 2.6.0

HighPressureGasTransport.cpp
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1/**
2 * @file HighPressureGasTransport.cpp
3 * Implementation file for class HighPressureGasTransport
4 *
5 * Transport parameters are calculated using corresponding states models:
6 * Binary diffusion coefficients use the generalized chart described by
7 * Takahashi, et al. and viscosity calculations use the Lucas method.
8 * All methods are described in Reid, Prausnitz, and Polling, "The Properties
9 * of Gases and Liquids, 4th ed., 1987 (viscosity in Ch. 9, Thermal
10 * conductivity in Ch. 10, and Diffusion coefficients in Ch. 11).
11 **/
12
13// This file is part of Cantera. See License.txt in the top-level directory or
14// at https://cantera.org/license.txt for license and copyright information.
15
16#include "cantera/transport/HighPressureGasTransport.h"
17#include "cantera/numerics/ctlapack.h"
18#include "cantera/base/utilities.h"
19#include "cantera/thermo/IdealGasPhase.h"
20#include "cantera/transport/TransportFactory.h"
21#include "cantera/base/stringUtils.h"
22#include "cantera/transport/MultiTransport.h"
23
24 using namespace std;
25
26 namespace Cantera
27{
28
29 HighPressureGasTransport::HighPressureGasTransport(ThermoPhase* thermo)
30: MultiTransport(thermo)
31{
32}
33
34 double HighPressureGasTransport::thermalConductivity()
35{
36 // Method of Ely and Hanley:
37 update_T();
38 doublereal Lprime_m = 0.0;
39 const doublereal c1 = 1./16.04;
40 size_t nsp = m_thermo->nSpecies();
41 vector_fp molefracs(nsp);
42 m_thermo->getMoleFractions(&molefracs[0]);
43 vector_fp cp_0_R(nsp);
44 m_thermo->getCp_R_ref(&cp_0_R[0]);
45
46 vector_fp L_i(nsp);
47 vector_fp f_i(nsp);
48 vector_fp h_i(nsp);
49 vector_fp V_k(nsp);
50
51 m_thermo -> getPartialMolarVolumes(&V_k[0]);
52 doublereal L_i_min = BigNumber;
53
54 for (size_t i = 0; i < m_nsp; i++) {
55 doublereal Tc_i = Tcrit_i(i);
56 doublereal Vc_i = Vcrit_i(i);
57 doublereal T_r = m_thermo->temperature()/Tc_i;
58 doublereal V_r = V_k[i]/Vc_i;
59 doublereal T_p = std::min(T_r,2.0);
60 doublereal V_p = std::max(0.5,std::min(V_r,2.0));
61
62 // Calculate variables for density-independent component:
63 doublereal theta_p = 1.0 + (m_w_ac[i] - 0.011)*(0.56553
64 - 0.86276*log(T_p) - 0.69852/T_p);
65 doublereal phi_p = (1.0 + (m_w_ac[i] - 0.011)*(0.38560
66 - 1.1617*log(T_p)))*0.288/Zcrit_i(i);
67 doublereal f_fac = Tc_i*theta_p/190.4;
68 doublereal h_fac = 1000*Vc_i*phi_p/99.2;
69 doublereal T_0 = m_temp/f_fac;
70 doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
71 + 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4*pow(T_0,1./3.)
72 - 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0 - 1.44591e1*pow(T_0,4./3.)
73 + 2.03712e-1*pow(T_0,5./3.));
74 doublereal H = sqrt(f_fac*16.04/m_mw[i])*pow(h_fac,-2./3.);
75 doublereal mu_i = mu_0*H*m_mw[i]*c1;
76 L_i[i] = mu_i*1.32*GasConstant*(cp_0_R[i] - 2.5)/m_mw[i];
77 L_i_min = min(L_i_min,L_i[i]);
78 // Calculate variables for density-dependent component:
79 doublereal theta_s = 1 + (m_w_ac[i] - 0.011)*(0.09057 - 0.86276*log(T_p)
80 + (0.31664 - 0.46568/T_p)*(V_p - 0.5));
81 doublereal phi_s = (1 + (m_w_ac[i] - 0.011)*(0.39490*(V_p - 1.02355)
82 - 0.93281*(V_p - 0.75464)*log(T_p)))*0.288/Zcrit_i(i);
83 f_i[i] = Tc_i*theta_s/190.4;
84 h_i[i] = 1000*Vc_i*phi_s/99.2;
85 }
86
87 doublereal h_m = 0;
88 doublereal f_m = 0;
89 doublereal mw_m = 0;
90 for (size_t i = 0; i < m_nsp; i++) {
91 for (size_t j = 0; j < m_nsp; j++) {
92 // Density-independent component:
93 doublereal L_ij = 2*L_i[i]*L_i[j]/(L_i[i] + L_i[j] + Tiny);
94 Lprime_m += molefracs[i]*molefracs[j]*L_ij;
95 // Additional variables for density-dependent component:
96 doublereal f_ij = sqrt(f_i[i]*f_i[j]);
97 doublereal h_ij = 0.125*pow(pow(h_i[i],1./3.) + pow(h_i[j],1./3.),3.);
98 doublereal mw_ij_inv = (m_mw[i] + m_mw[j])/(2*m_mw[i]*m_mw[j]);
99 f_m += molefracs[i]*molefracs[j]*f_ij*h_ij;
100 h_m += molefracs[i]*molefracs[j]*h_ij;
101 mw_m += molefracs[i]*molefracs[j]*sqrt(mw_ij_inv*f_ij)*pow(h_ij,-4./3.);
102 }
103 }
104
105 f_m = f_m/h_m;
106 mw_m = pow(mw_m,-2.)*f_m*pow(h_m,-8./3.);
107
108 doublereal rho_0 = 16.04*h_m/(1000*m_thermo->molarVolume());
109 doublereal T_0 = m_temp/f_m;
110 doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
111 + 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4
112 *pow(T_0,1./3.) - 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0
113 - 1.44591e1*pow(T_0,4./3.) + 2.03712e-1*pow(T_0,5./3.));
114 doublereal L_1m = 1944*mu_0;
115 doublereal L_2m = (-2.5276e-4 + 3.3433e-4*pow(1.12 - log(T_0/1.680e2),2))*rho_0;
116 doublereal L_3m = exp(-7.19771 + 85.67822/T_0)*(exp((12.47183
117 - 984.6252*pow(T_0,-1.5))*pow(rho_0,0.1) + (rho_0/0.1617 - 1)
118 *sqrt(rho_0)*(0.3594685 + 69.79841/T_0 - 872.8833*pow(T_0,-2))) - 1.)*1e-3;
119 doublereal H_m = sqrt(f_m*16.04/mw_m)*pow(h_m,-2./3.);
120 doublereal Lstar_m = H_m*(L_1m + L_2m + L_3m);
121 return Lprime_m + Lstar_m;
122}
123
124 void HighPressureGasTransport::getThermalDiffCoeffs(doublereal* const dt)
125{
126 // Method for MultiTransport class:
127 // solveLMatrixEquation();
128 // const doublereal c = 1.6/GasConstant;
129 // for (size_t k = 0; k < m_nsp; k++) {
130 // dt[k] = c * m_mw[k] * m_molefracs[k] * m_a[k];
131 // }
132 throw NotImplementedError("HighPressureGasTransport::getThermalDiffCoeffs");
133}
134
135 void HighPressureGasTransport::getBinaryDiffCoeffs(const size_t ld, doublereal* const d)
136{
137 vector_fp PcP(5);
138 size_t nsp = m_thermo->nSpecies();
139 vector_fp molefracs(nsp);
140 m_thermo->getMoleFractions(&molefracs[0]);
141
142 update_T();
143 // Evaluate the binary diffusion coefficients from the polynomial fits.
144 // This should perhaps be preceded by a check to see whether any of T, P, or
145 // C have changed.
146 //if (!m_bindiff_ok) {
147 updateDiff_T();
148 //}
149 if (ld < nsp) {
150 throw CanteraError("HighPressureGasTransport::getBinaryDiffCoeffs",
151 "ld is too small");
152 }
153 doublereal rp = 1.0/m_thermo->pressure();
154 for (size_t i = 0; i < nsp; i++) {
155 for (size_t j = 0; j < nsp; j++) {
156 // Add an offset to avoid a condition where x_i and x_j both equal
157 // zero (this would lead to Pr_ij = Inf):
158 doublereal x_i = std::max(Tiny, molefracs[i]);
159 doublereal x_j = std::max(Tiny, molefracs[j]);
160
161 // Weight mole fractions of i and j so that X_i + X_j = 1.0:
162 x_i = x_i/(x_i + x_j);
163 x_j = x_j/(x_i + x_j);
164
165 //Calculate Tr and Pr based on mole-fraction-weighted crit constants:
166 double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
167 double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
168
169 double P_corr_ij;
170 if (Pr_ij < 0.1) {
171 // If pressure is low enough, no correction is needed:
172 P_corr_ij = 1;
173 }else {
174 // Otherwise, calculate the parameters for Takahashi correlation
175 // by interpolating on Pr_ij:
176 P_corr_ij = setPcorr(Pr_ij, Tr_ij);
177
178 // If the reduced temperature is too low, the correction factor
179 // P_corr_ij will be < 0:
180 if (P_corr_ij<0) {
181 P_corr_ij = Tiny;
182 }
183 }
184
185 // Multiply the standard low-pressure binary diffusion coefficient
186 // (m_bdiff) by the Takahashi correction factor P_corr_ij:
187 d[ld*j + i] = P_corr_ij*rp * m_bdiff(i,j);
188 }
189 }
190}
191
192 void HighPressureGasTransport::getMultiDiffCoeffs(const size_t ld, doublereal* const d)
193{
194 // Not currently implemented. m_Lmatrix inversion returns NaN. Needs to be
195 // fixed. --SCD - 2-28-2014
196 throw NotImplementedError("HighPressureGasTransport:getMultiDiffCoeffs");
197 // Calculate the multi-component Stefan-Maxwell diffusion coefficients,
198 // based on the Takahashi-correlation-corrected binary diffusion coefficients.
199
200 // update the mole fractions
201 update_C();
202
203 // update the binary diffusion coefficients
204 update_T();
205 updateThermal_T();
206
207 // Correct the binary diffusion coefficients for high-pressure effects; this
208 // is basically the same routine used in 'getBinaryDiffCoeffs,' above:
209 size_t nsp = m_thermo->nSpecies();
210 vector_fp molefracs(nsp);
211 m_thermo->getMoleFractions(&molefracs[0]);
212 update_T();
213 // Evaluate the binary diffusion coefficients from the polynomial fits -
214 // this should perhaps be preceded by a check for changes in T, P, or C.
215 updateDiff_T();
216
217 if (ld < m_nsp) {
218 throw CanteraError("HighPressureGasTransport::getMultiDiffCoeffs",
219 "ld is too small");
220 }
221 for (size_t i = 0; i < m_nsp; i++) {
222 for (size_t j = 0; j < m_nsp; j++) {
223 // Add an offset to avoid a condition where x_i and x_j both equal
224 // zero (this would lead to Pr_ij = Inf):
225 doublereal x_i = std::max(Tiny, molefracs[i]);
226 doublereal x_j = std::max(Tiny, molefracs[j]);
227 x_i = x_i/(x_i+x_j);
228 x_j = x_j/(x_i+x_j);
229 double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
230 double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
231
232 double P_corr_ij;
233 if (Pr_ij < 0.1) {
234 P_corr_ij = 1;
235 }else {
236 P_corr_ij = setPcorr(Pr_ij, Tr_ij);
237 if (P_corr_ij<0) {
238 P_corr_ij = Tiny;
239 }
240 }
241
242 m_bdiff(i,j) *= P_corr_ij;
243 }
244 }
245 m_bindiff_ok = false; // m_bdiff is overwritten by the above routine.
246
247 // Having corrected m_bdiff for pressure and concentration effects, the
248 // routine now proceeds the same as in the low-pressure case:
249
250 // evaluate L0000 if the temperature or concentrations have
251 // changed since it was last evaluated.
252 if (!m_l0000_ok) {
253 eval_L0000(molefracs.data());
254 }
255
256 // invert L00,00
257 int ierr = invert(m_Lmatrix, m_nsp);
258 if (ierr != 0) {
259 throw CanteraError("HighPressureGasTransport::getMultiDiffCoeffs",
260 "invert returned ierr = {}", ierr);
261 }
262 m_l0000_ok = false; // matrix is overwritten by inverse
263 m_lmatrix_soln_ok = false;
264
265 doublereal prefactor = 16.0 * m_temp
266 *m_thermo->meanMolecularWeight()/(25.0*m_thermo->pressure());
267
268 for (size_t i = 0; i < m_nsp; i++) {
269 for (size_t j = 0; j < m_nsp; j++) {
270 double c = prefactor/m_mw[j];
271 d[ld*j + i] = c*molefracs[i]*(m_Lmatrix(i,j) - m_Lmatrix(i,i));
272 }
273 }
274}
275
276doublereal HighPressureGasTransport::viscosity()
277{
278 // Calculate the high-pressure mixture viscosity, based on the Lucas method.
279 double Tc_mix = 0.;
280 double Pc_mix_n = 0.;
281 double Pc_mix_d = 0.;
282 double MW_mix = m_thermo->meanMolecularWeight();
283 double MW_H = m_mw[0];
284 double MW_L = m_mw[0];
285 doublereal FP_mix_o = 0;
286 doublereal FQ_mix_o = 0;
287 doublereal tKelvin = m_thermo->temperature();
288 double Pvp_mix = m_thermo->satPressure(tKelvin);
289 size_t nsp = m_thermo->nSpecies();
290 vector_fp molefracs(nsp);
291 m_thermo->getMoleFractions(&molefracs[0]);
292
293 double x_H = molefracs[0];
294 for (size_t i = 0; i < m_nsp; i++) {
295 // Calculate pure-species critical constants and add their contribution
296 // to the mole-fraction-weighted mixture averages:
297 double Tc = Tcrit_i(i);
298 double Tr = tKelvin/Tc;
299 double Zc = Zcrit_i(i);
300 Tc_mix += Tc*molefracs[i];
301 Pc_mix_n += molefracs[i]*Zc; //numerator
302 Pc_mix_d += molefracs[i]*Vcrit_i(i); //denominator
303
304 // Need to calculate ratio of heaviest to lightest species:
305 if (m_mw[i] > MW_H) {
306 MW_H = m_mw[i];
307 x_H = molefracs[i];
308 } else if (m_mw[i] < MW_L) {
309 MW_L = m_mw[i]; }
310
311 // Calculate reduced dipole moment for polar correction term:
312 doublereal mu_ri = 52.46*100000*m_dipole(i,i)*m_dipole(i,i)
313 *Pcrit_i(i)/(Tc*Tc);
314 if (mu_ri < 0.022) {
315 FP_mix_o += molefracs[i];
316 } else if (mu_ri < 0.075) {
317 FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72));
318 } else { FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72)
319 *fabs(0.96 + 0.1*(Tr - 0.7)));
320 }
321
322 // Calculate contribution to quantum correction term.
323 // SCD Note: This assumes the species of interest (He, H2, and D2) have
324 // been named in this specific way. They are perhaps the most obvious
325 // names, but it would of course be preferred to have a more general
326 // approach, here.
327 std::vector<std::string> spnames = m_thermo->speciesNames();
328 if (spnames[i] == "He") {
329 FQ_mix_o += molefracs[i]*FQ_i(1.38,Tr,m_mw[i]);
330 } else if (spnames[i] == "H2") {
331 FQ_mix_o += molefracs[i]*(FQ_i(0.76,Tr,m_mw[i]));
332 } else if (spnames[i] == "D2") {
333 FQ_mix_o += molefracs[i]*(FQ_i(0.52,Tr,m_mw[i]));
334 } else {
335 FQ_mix_o += molefracs[i];
336 }
337 }
338
339 double Tr_mix = tKelvin/Tc_mix;
340 double Pc_mix = GasConstant*Tc_mix*Pc_mix_n/Pc_mix_d;
341 double Pr_mix = m_thermo->pressure()/Pc_mix;
342 double ratio = MW_H/MW_L;
343 double ksi = pow(GasConstant*Tc_mix*3.6277*pow(10.0,53.0)/(pow(MW_mix,3)
344 *pow(Pc_mix,4)),1.0/6.0);
345
346 if (ratio > 9 && x_H > 0.05 && x_H < 0.7) {
347 FQ_mix_o *= 1 - 0.01*pow(ratio,0.87);
348 }
349
350 // Calculate Z1m
351 double Z1m = (0.807*pow(Tr_mix,0.618) - 0.357*exp(-0.449*Tr_mix)
352 + 0.340*exp(-4.058*Tr_mix)+0.018)*FP_mix_o*FQ_mix_o;
353
354 // Calculate Z2m:
355 double Z2m;
356 if (Tr_mix <= 1.0) {
357 if (Pr_mix < Pvp_mix/Pc_mix) {
358 doublereal alpha = 3.262 + 14.98*pow(Pr_mix,5.508);
359 doublereal beta = 1.390 + 5.746*Pr_mix;
360 Z2m = 0.600 + 0.760*pow(Pr_mix,alpha) + (0.6990*pow(Pr_mix,beta) -
361 0.60)*(1- Tr_mix);
362 } else {
363 throw CanteraError("HighPressureGasTransport::viscosity",
364 "State is outside the limits of the Lucas model, Tr <= 1");
365 }
366 } else if ((Tr_mix > 1.0) && (Tr_mix < 40.0)) {
367 if ((Pr_mix > 0.0) && (Pr_mix <= 100.0)) {
368 doublereal a_fac = 0.001245*exp(5.1726*pow(Tr_mix,-0.3286))/Tr_mix;
369 doublereal b_fac = a_fac*(1.6553*Tr_mix - 1.2723);
370 doublereal c_fac = 0.4489*exp(3.0578*pow(Tr_mix,-37.7332))/Tr_mix;
371 doublereal d_fac = 1.7368*exp(2.2310*pow(Tr_mix,-7.6351))/Tr_mix;
372 doublereal f_fac = 0.9425*exp(-0.1853*pow(Tr_mix,0.4489));
373
374 Z2m = Z1m*(1 + a_fac*pow(Pr_mix,1.3088)/(b_fac*pow(Pr_mix,f_fac)
375 + pow(1+c_fac*pow(Pr_mix,d_fac),-1)));
376 } else {
377 throw CanteraError("HighPressureGasTransport::viscosity",
378 "State is outside the limits of the Lucas model, 1.0 < Tr < 40");
379 }
380 } else {
381 throw CanteraError("HighPressureGasTransport::viscosity",
382 "State is outside the limits of the Lucas model, Tr > 40");
383 }
384
385 // Calculate Y:
386 doublereal Y = Z2m/Z1m;
387
388 // Return the viscosity:
389 return Z2m*(1 + (FP_mix_o - 1)*pow(Y,-3))*(1 + (FQ_mix_o - 1)
390 *(1/Y - 0.007*pow(log(Y),4)))/(ksi*FP_mix_o*FQ_mix_o);
391}
392
393// Pure species critical properties - Tc, Pc, Vc, Zc:
394doublereal HighPressureGasTransport::Tcrit_i(size_t i)
395{
396 // Store current molefracs and set temp molefrac of species i to 1.0:
397 vector_fp molefracs = store(i, m_thermo->nSpecies());
398
399 double tc = m_thermo->critTemperature();
400 // Restore actual molefracs:
401 m_thermo->setMoleFractions(&molefracs[0]);
402 return tc;
403}
404
405doublereal HighPressureGasTransport::Pcrit_i(size_t i)
406{
407 // Store current molefracs and set temp molefrac of species i to 1.0:
408 vector_fp molefracs = store(i, m_thermo->nSpecies());
409
410 double pc = m_thermo->critPressure();
411 // Restore actual molefracs:
412 m_thermo->setMoleFractions(&molefracs[0]);
413 return pc;
414}
415
416doublereal HighPressureGasTransport::Vcrit_i(size_t i)
417{
418 // Store current molefracs and set temp molefrac of species i to 1.0:
419 vector_fp molefracs = store(i, m_thermo->nSpecies());
420
421 double vc = m_thermo->critVolume();
422 // Restore actual molefracs:
423 m_thermo->setMoleFractions(&molefracs[0]);
424 return vc;
425}
426
427doublereal HighPressureGasTransport::Zcrit_i(size_t i)
428{
429 // Store current molefracs and set temp molefrac of species i to 1.0:
430 vector_fp molefracs = store(i, m_thermo->nSpecies());
431
432 double zc = m_thermo->critCompressibility();
433 // Restore actual molefracs:
434 m_thermo->setMoleFractions(&molefracs[0]);
435 return zc;
436}
437
438 vector_fp HighPressureGasTransport::store(size_t i, size_t nsp)
439{
440 vector_fp molefracs(nsp);
441 m_thermo->getMoleFractions(&molefracs[0]);
442 vector_fp mf_temp(nsp, 0.0);
443 mf_temp[i] = 1;
444 m_thermo->setMoleFractions(&mf_temp[0]);
445 return molefracs;
446}
447
448// Calculates quantum correction term for a species based on Tr and MW, used in
449// viscosity calculation:
450doublereal HighPressureGasTransport::FQ_i(doublereal Q, doublereal Tr, doublereal MW)
451{
452 return 1.22*pow(Q,0.15)*(1 + 0.00385*pow(pow(Tr - 12.,2.),1./MW)
453 *fabs(Tr-12)/(Tr-12));
454}
455
456// Set value of parameter values for Takahashi correlation, by interpolating
457// table of constants vs. Pr:
458doublereal HighPressureGasTransport::setPcorr(doublereal Pr, doublereal Tr)
459{
460 const static double Pr_lookup[17] = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0,
461 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 4.0, 5.0};
462 const static double DP_Rt_lookup[17] = {1.01, 1.01, 1.01, 1.01, 1.01, 1.01,
463 1.01, 1.02, 1.02, 1.02, 1.02, 1.03, 1.03, 1.04, 1.05, 1.06, 1.07};
464 const static double A_ij_lookup[17] = {0.038042, 0.067433, 0.098317,
465 0.137610, 0.175081, 0.216376, 0.314051, 0.385736, 0.514553, 0.599184,
466 0.557725, 0.593007, 0.696001, 0.790770, 0.502100, 0.837452, 0.890390};
467 const static double B_ij_lookup[17] = {1.52267, 2.16794, 2.42910, 2.77605,
468 2.98256, 3.11384, 3.50264, 3.07773, 3.54744, 3.61216, 3.41882, 3.18415,
469 3.37660, 3.27984, 3.39031, 3.23513, 3.13001};
470 const static double C_ij_lookup[17] = {0., 0., 0., 0., 0., 0., 0., 0.141211,
471 0.278407, 0.372683, 0.504894, 0.678469, 0.665702, 0., 0.602907, 0., 0.};
472 const static double E_ij_lookup[17] = {1., 1., 1., 1., 1., 1., 1., 13.45454,
473 14., 10.00900, 8.57519, 10.37483, 11.21674, 1., 6.19043, 1., 1.};
474
475 // Interpolate Pr vs. those used in Takahashi table:
476 int Pr_i = 0;
477 double frac = 0.;
478
479 if (Pr < 0.1) {
480 frac = (Pr - Pr_lookup[0])/(Pr_lookup[1] - Pr_lookup[0]);
481 } else {
482 for (int j = 1; j < 17; j++) {
483 if (Pr_lookup[j] > Pr) {
484 frac = (Pr - Pr_lookup[j-1])/(Pr_lookup[j] - Pr_lookup[j-1]);
485 break;
486 }
487 Pr_i++;
488 }
489 }
490 // If Pr is greater than the greatest value used by Takahashi (5.0), use the
491 // final table value. Should eventually add in an extrapolation:
492 if (Pr_i == 17) {
493 frac = 1.0;
494 }
495
496 doublereal P_corr_1 = DP_Rt_lookup[Pr_i]*(1.0 - A_ij_lookup[Pr_i]
497 *pow(Tr,-B_ij_lookup[Pr_i]))*(1-C_ij_lookup[Pr_i]
498 *pow(Tr,-E_ij_lookup[Pr_i]));
499 doublereal P_corr_2 = DP_Rt_lookup[Pr_i+1]*(1.0 - A_ij_lookup[Pr_i+1]
500 *pow(Tr,-B_ij_lookup[Pr_i+1]))*(1-C_ij_lookup[Pr_i+1]
501 *pow(Tr,-E_ij_lookup[Pr_i+1]));
502 return P_corr_1*(1.0-frac) + P_corr_2*frac;
503}
504
505}
HighPressureGasTransport.h
Interface for class HighPressureGasTransport.
IdealGasPhase.h
ThermoPhase object for the ideal gas equation of state - workhorse for Cantera (see Thermodynamic Pro...
MultiTransport.h
Interface for class MultiTransport.
TransportFactory.h
Header file defining class TransportFactory (see TransportFactory)
Cantera::CanteraError
Base class for exceptions thrown by Cantera classes.
Definition: ctexceptions.h:61
Cantera::GasTransport::m_mw
vector_fp m_mw
Local copy of the species molecular weights.
Definition: GasTransport.h:333
Cantera::GasTransport::updateDiff_T
virtual void updateDiff_T()
Update the binary diffusion coefficients.
Definition: GasTransport.cpp:140
Cantera::GasTransport::m_bindiff_ok
bool m_bindiff_ok
Update boolean for the binary diffusivities at unit pressure.
Definition: GasTransport.h:311
Cantera::GasTransport::m_temp
doublereal m_temp
Current value of the temperature at which the properties in this object are calculated (Kelvin).
Definition: GasTransport.h:360
Cantera::GasTransport::m_bdiff
DenseMatrix m_bdiff
Matrix of binary diffusion coefficients at the reference pressure and the current temperature Size is...
Definition: GasTransport.h:398
Cantera::GasTransport::m_dipole
DenseMatrix m_dipole
The effective dipole moment for (i,j) collisions.
Definition: GasTransport.h:527
Cantera::GasTransport::m_w_ac
vector_fp m_w_ac
Pitzer acentric factor.
Definition: GasTransport.h:542
Cantera::HighPressureGasTransport::getThermalDiffCoeffs
virtual void getThermalDiffCoeffs(doublereal *const dt)
Return the thermal diffusion coefficients (kg/m/s)
Definition: HighPressureGasTransport.cpp:124
Cantera::HighPressureGasTransport::getMultiDiffCoeffs
virtual void getMultiDiffCoeffs(const size_t ld, doublereal *const d)
Return the Multicomponent diffusion coefficients. Units: [m^2/s].
Definition: HighPressureGasTransport.cpp:192
Cantera::HighPressureGasTransport::getBinaryDiffCoeffs
virtual void getBinaryDiffCoeffs(const size_t ld, doublereal *const d)
Definition: HighPressureGasTransport.cpp:135
Cantera::HighPressureGasTransport::HighPressureGasTransport
HighPressureGasTransport(ThermoPhase *thermo=0)
default constructor
Definition: HighPressureGasTransport.cpp:29
Cantera::HighPressureGasTransport::thermalConductivity
virtual double thermalConductivity()
Returns the mixture thermal conductivity in W/m/K.
Definition: HighPressureGasTransport.cpp:34
Cantera::HighPressureGasTransport::viscosity
virtual doublereal viscosity()
Viscosity of the mixture (kg /m /s)
Definition: HighPressureGasTransport.cpp:276
Cantera::MultiTransport
Class MultiTransport implements multicomponent transport properties for ideal gas mixtures.
Definition: MultiTransport.h:27
Cantera::MultiTransport::eval_L0000
void eval_L0000(const doublereal *const x)
Evaluate the L0000 matrices.
Definition: MultiTransport.cpp:491
Cantera::MultiTransport::update_T
void update_T()
Update basic temperature-dependent quantities if the temperature has changed.
Definition: MultiTransport.cpp:394
Cantera::MultiTransport::updateThermal_T
void updateThermal_T()
Update the temperature-dependent terms needed to compute the thermal conductivity and thermal diffusi...
Definition: MultiTransport.cpp:424
Cantera::MultiTransport::update_C
void update_C()
Update basic concentration-dependent quantities if the concentrations have changed.
Definition: MultiTransport.cpp:407
Cantera::NotImplementedError
An error indicating that an unimplemented function has been called.
Definition: ctexceptions.h:187
Cantera::Phase::setMoleFractions
virtual void setMoleFractions(const double *const x)
Set the mole fractions to the specified values.
Definition: Phase.cpp:339
Cantera::Phase::nSpecies
size_t nSpecies() const
Returns the number of species in the phase.
Definition: Phase.h:273
Cantera::Phase::meanMolecularWeight
doublereal meanMolecularWeight() const
The mean molecular weight. Units: (kg/kmol)
Definition: Phase.h:751
Cantera::Phase::getMoleFractions
void getMoleFractions(double *const x) const
Get the species mole fraction vector.
Definition: Phase.cpp:543
Cantera::Phase::temperature
doublereal temperature() const
Temperature (K).
Definition: Phase.h:654
Cantera::Phase::speciesNames
const std::vector< std::string > & speciesNames() const
Return a const reference to the vector of species names.
Definition: Phase.cpp:206
Cantera::Phase::molarVolume
double molarVolume() const
Molar volume (m^3/kmol).
Definition: Phase.cpp:682
Cantera::Phase::pressure
virtual double pressure() const
Return the thermodynamic pressure (Pa).
Definition: Phase.h:672
Cantera::ThermoPhase
Base class for a phase with thermodynamic properties.
Definition: ThermoPhase.h:102
Cantera::ThermoPhase::critPressure
virtual doublereal critPressure() const
Critical pressure (Pa).
Definition: ThermoPhase.h:1489
Cantera::ThermoPhase::critTemperature
virtual doublereal critTemperature() const
Critical temperature (K).
Definition: ThermoPhase.h:1484
Cantera::ThermoPhase::satPressure
virtual doublereal satPressure(doublereal t)
Return the saturation pressure given the temperature.
Definition: ThermoPhase.h:1529
Cantera::ThermoPhase::critVolume
virtual doublereal critVolume() const
Critical volume (m3/kmol).
Definition: ThermoPhase.h:1494
Cantera::ThermoPhase::getCp_R_ref
virtual void getCp_R_ref(doublereal *cprt) const
Returns the vector of nondimensional constant pressure heat capacities of the reference state at the ...
Definition: ThermoPhase.h:725
Cantera::ThermoPhase::critCompressibility
virtual doublereal critCompressibility() const
Critical compressibility (unitless).
Definition: ThermoPhase.h:1499
Cantera::Transport::m_thermo
ThermoPhase * m_thermo
pointer to the object representing the phase
Definition: TransportBase.h:773
Cantera::Transport::m_nsp
size_t m_nsp
Number of species.
Definition: TransportBase.h:779
ctlapack.h
Cantera
Namespace for the Cantera kernel.
Definition: AnyMap.cpp:557
Cantera::Tiny
const double Tiny
Small number to compare differences of mole fractions against.
Definition: ct_defs.h:170
Cantera::invert
int invert(DenseMatrix &A, size_t nn)
invert A. A is overwritten with A^-1.
Definition: DenseMatrix.cpp:236
Cantera::vector_fp
std::vector< double > vector_fp
Turn on the use of stl vectors for the basic array type within cantera Vector of doubles.
Definition: ct_defs.h:184
Cantera::GasConstant
const double GasConstant
Universal Gas Constant [J/kmol/K].
Definition: ct_defs.h:113
Cantera::BigNumber
const double BigNumber
largest number to compare to inf.
Definition: ct_defs.h:155
stringUtils.h
Contains declarations for string manipulation functions within Cantera.
utilities.h
Various templated functions that carry out common vector operations (see Templated Utility Functions)...