Cantera  2.3.0
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 http://www.cantera.org/license.txt for license and copyright information.
15 
18 #include "cantera/base/utilities.h"
24 
25 using namespace std;
26 
27 namespace Cantera
28 {
29 
30 HighPressureGasTransport::HighPressureGasTransport(thermo_t* thermo)
31 : MultiTransport(thermo)
32 {
33 }
34 
36 {
37  // Method of Ely and Hanley:
38  update_T();
39  doublereal Lprime_m = 0.0;
40  const doublereal c1 = 1./16.04;
41  size_t nsp = m_thermo->nSpecies();
42  vector_fp molefracs(nsp);
43  m_thermo->getMoleFractions(&molefracs[0]);
44  vector_fp cp_0_R(nsp);
45  m_thermo->getCp_R_ref(&cp_0_R[0]);
46 
47  vector_fp L_i(nsp);
48  vector_fp f_i(nsp);
49  vector_fp h_i(nsp);
50  vector_fp V_k(nsp);
51 
52  m_thermo -> getPartialMolarVolumes(&V_k[0]);
53  doublereal L_i_min = BigNumber;
54 
55  for (size_t i = 0; i < m_nsp; i++) {
56  doublereal Tc_i = Tcrit_i(i);
57  doublereal Vc_i = Vcrit_i(i);
58  doublereal T_r = m_thermo->temperature()/Tc_i;
59  doublereal V_r = V_k[i]/Vc_i;
60  doublereal T_p = std::min(T_r,2.0);
61  doublereal V_p = std::max(0.5,std::min(V_r,2.0));
62 
63  // Calculate variables for density-independent component:
64  doublereal theta_p = 1.0 + (m_w_ac[i] - 0.011)*(0.56553
65  - 0.86276*log(T_p) - 0.69852/T_p);
66  doublereal phi_p = (1.0 + (m_w_ac[i] - 0.011)*(0.38560
67  - 1.1617*log(T_p)))*0.288/Zcrit_i(i);
68  doublereal f_fac = Tc_i*theta_p/190.4;
69  doublereal h_fac = 1000*Vc_i*phi_p/99.2;
70  doublereal T_0 = m_temp/f_fac;
71  doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
72  + 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4*pow(T_0,1./3.)
73  - 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0 - 1.44591e1*pow(T_0,4./3.)
74  + 2.03712e-1*pow(T_0,5./3.));
75  doublereal H = sqrt(f_fac*16.04/m_mw[i])*pow(h_fac,-2./3.);
76  doublereal mu_i = mu_0*H*m_mw[i]*c1;
77  L_i[i] = mu_i*1.32*GasConstant*(cp_0_R[i] - 2.5)/m_mw[i];
78  L_i_min = min(L_i_min,L_i[i]);
79  // Calculate variables for density-dependent component:
80  doublereal theta_s = 1 + (m_w_ac[i] - 0.011)*(0.09057 - 0.86276*log(T_p)
81  + (0.31664 - 0.46568/T_p)*(V_p - 0.5));
82  doublereal phi_s = (1 + (m_w_ac[i] - 0.011)*(0.39490*(V_p - 1.02355)
83  - 0.93281*(V_p - 0.75464)*log(T_p)))*0.288/Zcrit_i(i);
84  f_i[i] = Tc_i*theta_s/190.4;
85  h_i[i] = 1000*Vc_i*phi_s/99.2;
86  }
87 
88  doublereal h_m = 0;
89  doublereal f_m = 0;
90  doublereal mw_m = 0;
91  for (size_t i = 0; i < m_nsp; i++) {
92  for (size_t j = 0; j < m_nsp; j++) {
93  // Density-independent component:
94  doublereal L_ij = 2*L_i[i]*L_i[j]/(L_i[i] + L_i[j] + Tiny);
95  Lprime_m += molefracs[i]*molefracs[j]*L_ij;
96  // Additional variables for density-dependent component:
97  doublereal f_ij = sqrt(f_i[i]*f_i[j]);
98  doublereal h_ij = 0.125*pow(pow(h_i[i],1./3.) + pow(h_i[j],1./3.),3.);
99  doublereal mw_ij_inv = (m_mw[i] + m_mw[j])/(2*m_mw[i]*m_mw[j]);
100  f_m += molefracs[i]*molefracs[j]*f_ij*h_ij;
101  h_m += molefracs[i]*molefracs[j]*h_ij;
102  mw_m += molefracs[i]*molefracs[j]*sqrt(mw_ij_inv*f_ij)*pow(h_ij,-4./3.);
103  }
104  }
105 
106  f_m = f_m/h_m;
107  mw_m = pow(mw_m,-2.)*f_m*pow(h_m,-8./3.);
108 
109  doublereal rho_0 = 16.04*h_m/(1000*m_thermo->molarVolume());
110  doublereal T_0 = m_temp/f_m;
111  doublereal mu_0 = 1e-7*(2.90774e6/T_0 - 3.31287e6*pow(T_0,-2./3.)
112  + 1.60810e6*pow(T_0,-1./3.) - 4.33190e5 + 7.06248e4
113  *pow(T_0,1./3.) - 7.11662e3*pow(T_0,2./3.) + 4.32517e2*T_0
114  - 1.44591e1*pow(T_0,4./3.) + 2.03712e-1*pow(T_0,5./3.));
115  doublereal L_1m = 1944*mu_0;
116  doublereal L_2m = (-2.5276e-4 + 3.3433e-4*pow(1.12 - log(T_0/1.680e2),2))*rho_0;
117  doublereal L_3m = exp(-7.19771 + 85.67822/T_0)*(exp((12.47183
118  - 984.6252*pow(T_0,-1.5))*pow(rho_0,0.1) + (rho_0/0.1617 - 1)
119  *sqrt(rho_0)*(0.3594685 + 69.79841/T_0 - 872.8833*pow(T_0,-2))) - 1.)*1e-3;
120  doublereal H_m = sqrt(f_m*16.04/mw_m)*pow(h_m,-2./3.);
121  doublereal Lstar_m = H_m*(L_1m + L_2m + L_3m);
122  return Lprime_m + Lstar_m;
123 }
124 
126 {
127  // Method for MultiTransport class:
128  // solveLMatrixEquation();
129  // const doublereal c = 1.6/GasConstant;
130  // for (size_t k = 0; k < m_nsp; k++) {
131  // dt[k] = c * m_mw[k] * m_molefracs[k] * m_a[k];
132  // }
133  throw CanteraError("HighPressureGasTransport::getThermalDiffCoeffs",
134  "Not yet implemented.");
135 }
136 
137 void HighPressureGasTransport::getBinaryDiffCoeffs(const size_t ld, doublereal* const d)
138 {
139  vector_fp PcP(5);
140  size_t nsp = m_thermo->nSpecies();
141  vector_fp molefracs(nsp);
142  m_thermo->getMoleFractions(&molefracs[0]);
143 
144  update_T();
145  // Evaluate the binary diffusion coefficients from the polynomial fits.
146  // This should perhaps be preceded by a check to see whether any of T, P, or
147  // C have changed.
148  //if (!m_bindiff_ok) {
149  updateDiff_T();
150  //}
151  if (ld < nsp) {
152  throw CanteraError("HighPressureTransport::getBinaryDiffCoeffs()", "ld is too small");
153  }
154  doublereal rp = 1.0/m_thermo->pressure();
155  for (size_t i = 0; i < nsp; i++) {
156  for (size_t j = 0; j < nsp; j++) {
157  // Add an offset to avoid a condition where x_i and x_j both equal
158  // zero (this would lead to Pr_ij = Inf):
159  doublereal x_i = std::max(Tiny, molefracs[i]);
160  doublereal x_j = std::max(Tiny, molefracs[j]);
161 
162  // Weight mole fractions of i and j so that X_i + X_j = 1.0:
163  x_i = x_i/(x_i + x_j);
164  x_j = x_j/(x_i + x_j);
165 
166  //Calculate Tr and Pr based on mole-fraction-weighted crit constants:
167  double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
168  double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
169 
170  double P_corr_ij;
171  if (Pr_ij < 0.1) {
172  // If pressure is low enough, no correction is needed:
173  P_corr_ij = 1;
174  }else {
175  // Otherwise, calculate the parameters for Takahashi correlation
176  // by interpolating on Pr_ij:
177  P_corr_ij = setPcorr(Pr_ij, Tr_ij);
178 
179  // If the reduced temperature is too low, the correction factor
180  // P_corr_ij will be < 0:
181  if (P_corr_ij<0) {
182  P_corr_ij = Tiny;
183  }
184  }
185 
186  // Multiply the standard low-pressure binary diffusion coefficient
187  // (m_bdiff) by the Takahashi correction factor P_corr_ij:
188  d[ld*j + i] = P_corr_ij*rp * m_bdiff(i,j);
189  }
190  }
191 }
192 
193 void HighPressureGasTransport::getMultiDiffCoeffs(const size_t ld, doublereal* const d)
194 {
195  // Not currently implemented. m_Lmatrix inversion returns NaN. Needs to be
196  // fixed. --SCD - 2-28-2014
197  throw CanteraError("HighPressureTransport:getMultiDiffCoeffs()",
198  "Routine not yet implemented");
199  // Calculate the multi-component Stefan-Maxwell diffusion coefficients,
200  // based on the Takahashi-correlation-corrected binary diffusion coefficients.
201 
202  // update the mole fractions
203  update_C();
204 
205  // update the binary diffusion coefficients
206  update_T();
207  updateThermal_T();
208 
209  // Correct the binary diffusion coefficients for high-pressure effects; this
210  // is basically the same routine used in 'getBinaryDiffCoeffs,' above:
211  size_t nsp = m_thermo->nSpecies();
212  vector_fp molefracs(nsp);
213  m_thermo->getMoleFractions(&molefracs[0]);
214  update_T();
215  // Evaluate the binary diffusion coefficients from the polynomial fits -
216  // this should perhaps be preceded by a check for changes in T, P, or C.
217  updateDiff_T();
218 
219  if (ld < m_nsp) {
220  throw CanteraError("HighPressureTransport::getMultiDiffCoeffs()",
221  "ld is too small");
222  }
223  for (size_t i = 0; i < m_nsp; i++) {
224  for (size_t j = 0; j < m_nsp; j++) {
225  // Add an offset to avoid a condition where x_i and x_j both equal
226  // zero (this would lead to Pr_ij = Inf):
227  doublereal x_i = std::max(Tiny, molefracs[i]);
228  doublereal x_j = std::max(Tiny, molefracs[j]);
229  x_i = x_i/(x_i+x_j);
230  x_j = x_j/(x_i+x_j);
231  double Tr_ij = m_temp/(x_i*Tcrit_i(i) + x_j*Tcrit_i(j));
232  double Pr_ij = m_thermo->pressure()/(x_i*Pcrit_i(i) + x_j*Pcrit_i(j));
233 
234  double P_corr_ij;
235  if (Pr_ij < 0.1) {
236  P_corr_ij = 1;
237  }else {
238  P_corr_ij = setPcorr(Pr_ij, Tr_ij);
239  if (P_corr_ij<0) {
240  P_corr_ij = Tiny;
241  }
242  }
243 
244  m_bdiff(i,j) *= P_corr_ij;
245  }
246  }
247  m_bindiff_ok = false; // m_bdiff is overwritten by the above routine.
248 
249  // Having corrected m_bdiff for pressure and concentration effects, the
250  // routine now proceeds the same as in the low-pressure case:
251 
252  // evaluate L0000 if the temperature or concentrations have
253  // changed since it was last evaluated.
254  if (!m_l0000_ok) {
255  eval_L0000(molefracs.data());
256  }
257 
258  // invert L00,00
259  int ierr = invert(m_Lmatrix, m_nsp);
260  if (ierr != 0) {
261  throw CanteraError("HighPressureGasTransport::getMultiDiffCoeffs",
262  "invert returned ierr = {}", ierr);
263  }
264  m_l0000_ok = false; // matrix is overwritten by inverse
265  m_lmatrix_soln_ok = false;
266 
267  doublereal prefactor = 16.0 * m_temp
269 
270  for (size_t i = 0; i < m_nsp; i++) {
271  for (size_t j = 0; j < m_nsp; j++) {
272  double c = prefactor/m_mw[j];
273  d[ld*j + i] = c*molefracs[i]*(m_Lmatrix(i,j) - m_Lmatrix(i,i));
274  }
275  }
276 }
277 
279 {
280  // Calculate the high-pressure mixture viscosity, based on the Lucas method.
281  double Tc_mix = 0.;
282  double Pc_mix_n = 0.;
283  double Pc_mix_d = 0.;
284  double MW_mix = m_thermo->meanMolecularWeight();
285  double MW_H = m_mw[0];
286  double MW_L = m_mw[0];
287  doublereal FP_mix_o = 0;
288  doublereal FQ_mix_o = 0;
289  doublereal tKelvin = m_thermo->temperature();
290  double Pvp_mix = m_thermo->satPressure(tKelvin);
291  size_t nsp = m_thermo->nSpecies();
292  vector_fp molefracs(nsp);
293  m_thermo->getMoleFractions(&molefracs[0]);
294 
295  double x_H = molefracs[0];
296  for (size_t i = 0; i < m_nsp; i++) {
297  // Calculate pure-species critical constants and add their contribution
298  // to the mole-fraction-weighted mixture averages:
299  double Tc = Tcrit_i(i);
300  double Tr = tKelvin/Tc;
301  double Zc = Zcrit_i(i);
302  Tc_mix += Tc*molefracs[i];
303  Pc_mix_n += molefracs[i]*Zc; //numerator
304  Pc_mix_d += molefracs[i]*Vcrit_i(i); //denominator
305 
306  // Need to calculate ratio of heaviest to lightest species:
307  if (m_mw[i] > MW_H) {
308  MW_H = m_mw[i];
309  x_H = molefracs[i];
310  } else if (m_mw[i] < MW_L) {
311  MW_L = m_mw[i]; }
312 
313  // Calculate reduced dipole moment for polar correction term:
314  doublereal mu_ri = 52.46*100000*m_dipole(i,i)*m_dipole(i,i)
315  *Pcrit_i(i)/(Tc*Tc);
316  if (mu_ri < 0.022) {
317  FP_mix_o += molefracs[i];
318  } else if (mu_ri < 0.075) {
319  FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72));
320  } else { FP_mix_o += molefracs[i]*(1. + 30.55*pow(0.292 - Zc, 1.72)
321  *fabs(0.96 + 0.1*(Tr - 0.7)));
322  }
323 
324  // Calculate contribution to quantum correction term.
325  // SCD Note: This assumes the species of interest (He, H2, and D2) have
326  // been named in this specific way. They are perhaps the most obvious
327  // names, but it would of course be preferred to have a more general
328  // approach, here.
329  std::vector<std::string> spnames = m_thermo->speciesNames();
330  if (spnames[i] == "He") {
331  FQ_mix_o += molefracs[i]*FQ_i(1.38,Tr,m_mw[i]);
332  } else if (spnames[i] == "H2") {
333  FQ_mix_o += molefracs[i]*(FQ_i(0.76,Tr,m_mw[i]));
334  } else if (spnames[i] == "D2") {
335  FQ_mix_o += molefracs[i]*(FQ_i(0.52,Tr,m_mw[i]));
336  } else {
337  FQ_mix_o += molefracs[i];
338  }
339  }
340 
341  double Tr_mix = tKelvin/Tc_mix;
342  double Pc_mix = GasConstant*Tc_mix*Pc_mix_n/Pc_mix_d;
343  double Pr_mix = m_thermo->pressure()/Pc_mix;
344  double ratio = MW_H/MW_L;
345  double ksi = pow(GasConstant*Tc_mix*3.6277*pow(10.0,53.0)/(pow(MW_mix,3)
346  *pow(Pc_mix,4)),1.0/6.0);
347 
348  if (ratio > 9 && x_H > 0.05 && x_H < 0.7) {
349  FQ_mix_o *= 1 - 0.01*pow(ratio,0.87);
350  }
351 
352  // Calculate Z1m
353  double Z1m = (0.807*pow(Tr_mix,0.618) - 0.357*exp(-0.449*Tr_mix)
354  + 0.340*exp(-4.058*Tr_mix)+0.018)*FP_mix_o*FQ_mix_o;
355 
356  // Calculate Z2m:
357  double Z2m;
358  if (Tr_mix <= 1.0) {
359  if (Pr_mix < Pvp_mix/Pc_mix) {
360  doublereal alpha = 3.262 + 14.98*pow(Pr_mix,5.508);
361  doublereal beta = 1.390 + 5.746*Pr_mix;
362  Z2m = 0.600 + 0.760*pow(Pr_mix,alpha) + (0.6990*pow(Pr_mix,beta) -
363  0.60)*(1- Tr_mix);
364  } else {
365  throw CanteraError("HighPressureGasTransport::viscosity",
366  "State is outside the limits of the Lucas model, Tr <= 1");
367  }
368  } else if ((Tr_mix > 1.0) && (Tr_mix < 40.0)) {
369  if ((Pr_mix > 0.0) && (Pr_mix <= 100.0)) {
370  doublereal a_fac = 0.001245*exp(5.1726*pow(Tr_mix,-0.3286))/Tr_mix;
371  doublereal b_fac = a_fac*(1.6553*Tr_mix - 1.2723);
372  doublereal c_fac = 0.4489*exp(3.0578*pow(Tr_mix,-37.7332))/Tr_mix;
373  doublereal d_fac = 1.7368*exp(2.2310*pow(Tr_mix,-7.6351))/Tr_mix;
374  doublereal f_fac = 0.9425*exp(-0.1853*pow(Tr_mix,0.4489));
375 
376  Z2m = Z1m*(1 + a_fac*pow(Pr_mix,1.3088)/(b_fac*pow(Pr_mix,f_fac)
377  + pow(1+c_fac*pow(Pr_mix,d_fac),-1)));
378  } else {
379  throw CanteraError("HighPressureGasTransport::viscosity",
380  "State is outside the limits of the Lucas model, 1.0 < Tr < 40");
381  }
382  } else {
383  throw CanteraError("HighPressureGasTransport::viscosity",
384  "State is outside the limits of the Lucas model, Tr > 40");
385  }
386 
387  // Calculate Y:
388  doublereal Y = Z2m/Z1m;
389 
390  // Return the viscosity:
391  return Z2m*(1 + (FP_mix_o - 1)*pow(Y,-3))*(1 + (FQ_mix_o - 1)
392  *(1/Y - 0.007*pow(log(Y),4)))/(ksi*FP_mix_o*FQ_mix_o);
393 }
394 
395 // Pure species critical properties - Tc, Pc, Vc, Zc:
396 doublereal HighPressureGasTransport::Tcrit_i(size_t i)
397 {
398  // Store current molefracs and set temp molefrac of species i to 1.0:
399  vector_fp molefracs = store(i, m_thermo->nSpecies());
400 
401  double tc = m_thermo->critTemperature();
402  // Restore actual molefracs:
403  m_thermo->setMoleFractions(&molefracs[0]);
404  return tc;
405 }
406 
407 doublereal HighPressureGasTransport::Pcrit_i(size_t i)
408 {
409  // Store current molefracs and set temp molefrac of species i to 1.0:
410  vector_fp molefracs = store(i, m_thermo->nSpecies());
411 
412  double pc = m_thermo->critPressure();
413  // Restore actual molefracs:
414  m_thermo->setMoleFractions(&molefracs[0]);
415  return pc;
416 }
417 
418 doublereal HighPressureGasTransport::Vcrit_i(size_t i)
419 {
420  // Store current molefracs and set temp molefrac of species i to 1.0:
421  vector_fp molefracs = store(i, m_thermo->nSpecies());
422 
423  double vc = m_thermo->critVolume();
424  // Restore actual molefracs:
425  m_thermo->setMoleFractions(&molefracs[0]);
426  return vc;
427 }
428 
429 doublereal HighPressureGasTransport::Zcrit_i(size_t i)
430 {
431  // Store current molefracs and set temp molefrac of species i to 1.0:
432  vector_fp molefracs = store(i, m_thermo->nSpecies());
433 
434  double zc = m_thermo->critCompressibility();
435  // Restore actual molefracs:
436  m_thermo->setMoleFractions(&molefracs[0]);
437  return zc;
438 }
439 
440 vector_fp HighPressureGasTransport::store(size_t i, size_t nsp)
441 {
442  vector_fp molefracs(nsp);
443  m_thermo->getMoleFractions(&molefracs[0]);
444  vector_fp mf_temp(nsp, 0.0);
445  mf_temp[i] = 1;
446  m_thermo->setMoleFractions(&mf_temp[0]);
447  return molefracs;
448 }
449 
450 // Calculates quantum correction term for a species based on Tr and MW, used in
451 // viscosity calculation:
452 doublereal HighPressureGasTransport::FQ_i(doublereal Q, doublereal Tr, doublereal MW)
453 {
454  return 1.22*pow(Q,0.15)*(1 + 0.00385*pow(pow(Tr - 12.,2.),1./MW)
455  *fabs(Tr-12)/(Tr-12));
456 }
457 
458 // Set value of parameter values for Takahashi correlation, by interpolating
459 // table of constants vs. Pr:
460 doublereal HighPressureGasTransport::setPcorr(doublereal Pr, doublereal Tr)
461 {
462  const static double Pr_lookup[17] = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0,
463  1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 4.0, 5.0};
464  const static double DP_Rt_lookup[17] = {1.01, 1.01, 1.01, 1.01, 1.01, 1.01,
465  1.01, 1.02, 1.02, 1.02, 1.02, 1.03, 1.03, 1.04, 1.05, 1.06, 1.07};
466  const static double A_ij_lookup[17] = {0.038042, 0.067433, 0.098317,
467  0.137610, 0.175081, 0.216376, 0.314051, 0.385736, 0.514553, 0.599184,
468  0.557725, 0.593007, 0.696001, 0.790770, 0.502100, 0.837452, 0.890390};
469  const static double B_ij_lookup[17] = {1.52267, 2.16794, 2.42910, 2.77605,
470  2.98256, 3.11384, 3.50264, 3.07773, 3.54744, 3.61216, 3.41882, 3.18415,
471  3.37660, 3.27984, 3.39031, 3.23513, 3.13001};
472  const static double C_ij_lookup[17] = {0., 0., 0., 0., 0., 0., 0., 0.141211,
473  0.278407, 0.372683, 0.504894, 0.678469, 0.665702, 0., 0.602907, 0., 0.};
474  const static double E_ij_lookup[17] = {1., 1., 1., 1., 1., 1., 1., 13.45454,
475  14., 10.00900, 8.57519, 10.37483, 11.21674, 1., 6.19043, 1., 1.};
476 
477  // Interpolate Pr vs. those used in Takahashi table:
478  int Pr_i = 0;
479  double frac = 0.;
480 
481  if (Pr < 0.1) {
482  frac = (Pr - Pr_lookup[0])/(Pr_lookup[1] - Pr_lookup[0]);
483  } else {
484  for (int j = 1; j < 17; j++) {
485  if (Pr_lookup[j] > Pr) {
486  frac = (Pr - Pr_lookup[j-1])/(Pr_lookup[j] - Pr_lookup[j-1]);
487  break;
488  }
489  Pr_i++;
490  }
491  }
492  // If Pr is greater than the greatest value used by Takahashi (5.0), use the
493  // final table value. Should eventually add in an extrapolation:
494  if (Pr_i == 17) {
495  frac = 1.0;
496  }
497 
498  doublereal P_corr_1 = DP_Rt_lookup[Pr_i]*(1.0 - A_ij_lookup[Pr_i]
499  *pow(Tr,-B_ij_lookup[Pr_i]))*(1-C_ij_lookup[Pr_i]
500  *pow(Tr,-E_ij_lookup[Pr_i]));
501  doublereal P_corr_2 = DP_Rt_lookup[Pr_i+1]*(1.0 - A_ij_lookup[Pr_i+1]
502  *pow(Tr,-B_ij_lookup[Pr_i+1]))*(1-C_ij_lookup[Pr_i+1]
503  *pow(Tr,-E_ij_lookup[Pr_i+1]));
504  return P_corr_1*(1.0-frac) + P_corr_2*frac;
505 }
506 
507 }
doublereal molarVolume() const
Molar volume (m^3/kmol).
Definition: Phase.cpp:676
int invert(DenseMatrix &A, size_t nn)
invert A. A is overwritten with A^-1.
virtual void getThermalDiffCoeffs(doublereal *const dt)
Return the thermal diffusion coefficients (kg/m/s)
DenseMatrix m_dipole
The effective dipole moment for (i,j) collisions.
Definition: GasTransport.h:467
doublereal temperature() const
Temperature (K).
Definition: Phase.h:601
Various templated functions that carry out common vector operations (see Templated Utility Functions)...
Interface for class MultiTransport.
bool m_bindiff_ok
Update boolean for the binary diffusivities at unit pressure.
Definition: GasTransport.h:255
thermo_t * m_thermo
pointer to the object representing the phase
size_t nSpecies() const
Returns the number of species in the phase.
Definition: Phase.h:262
STL namespace.
void update_T()
Update basic temperature-dependent quantities if the temperature has changed.
DenseMatrix m_bdiff
Matrix of binary diffusion coefficients at the reference pressure and the current temperature Size is...
Definition: GasTransport.h:342
virtual doublereal satPressure(doublereal t)
Return the saturation pressure given the temperature.
Definition: ThermoPhase.h:1376
doublereal m_temp
Current value of the temperature at which the properties in this object are calculated (Kelvin)...
Definition: GasTransport.h:304
const std::vector< std::string > & speciesNames() const
Return a const reference to the vector of species names.
Definition: Phase.cpp:273
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:724
Header file defining class TransportFactory (see TransportFactory)
Base class for a phase with thermodynamic properties.
Definition: ThermoPhase.h:93
virtual doublereal critPressure() const
Critical pressure (Pa).
Definition: ThermoPhase.h:1336
ThermoPhase object for the ideal gas equation of state - workhorse for Cantera (see Thermodynamic Pro...
virtual void updateDiff_T()
Update the binary diffusion coefficients.
const doublereal BigNumber
largest number to compare to inf.
Definition: ct_defs.h:128
void eval_L0000(const doublereal *const x)
Evaluate the L0000 matrices.
virtual doublereal critCompressibility() const
Critical compressibility (unitless).
Definition: ThermoPhase.h:1346
virtual void getBinaryDiffCoeffs(const size_t ld, doublereal *const d)
virtual double thermalConductivity()
Returns the mixture thermal conductivity in W/m/K.
Base class for exceptions thrown by Cantera classes.
Definition: ctexceptions.h:65
virtual doublereal critVolume() const
Critical volume (m3/kmol).
Definition: ThermoPhase.h:1341
virtual void setMoleFractions(const doublereal *const x)
Set the mole fractions to the specified values.
Definition: Phase.cpp:327
void updateThermal_T()
Update the temperature-dependent terms needed to compute the thermal conductivity and thermal diffusi...
Interface for class HighPressureGasTransport.
void getMoleFractions(doublereal *const x) const
Get the species mole fraction vector.
Definition: Phase.cpp:542
virtual doublereal pressure() const
Return the thermodynamic pressure (Pa).
Definition: ThermoPhase.h:278
virtual void getMultiDiffCoeffs(const size_t ld, doublereal *const d)
Return the Multicomponent diffusion coefficients. Units: [m^2/s].
Class MultiTransport implements multicomponent transport properties for ideal gas mixtures...
virtual doublereal critTemperature() const
Critical temperature (K).
Definition: ThermoPhase.h:1331
virtual doublereal viscosity()
Viscosity of the mixture (kg /m /s)
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:157
doublereal meanMolecularWeight() const
The mean molecular weight. Units: (kg/kmol)
Definition: Phase.h:661
vector_fp m_w_ac
Pitzer acentric factor.
Definition: GasTransport.h:482
const doublereal Tiny
Small number to compare differences of mole fractions against.
Definition: ct_defs.h:143
const doublereal GasConstant
Universal Gas Constant. [J/kmol/K].
Definition: ct_defs.h:64
Contains declarations for string manipulation functions within Cantera.
size_t m_nsp
Number of species.
Namespace for the Cantera kernel.
Definition: application.cpp:29
Class that holds the data that is read in from the XML file, and which is used for processing of the ...
void update_C()
Update basic concentration-dependent quantities if the concentrations have changed.
vector_fp m_mw
Local copy of the species molecular weights.
Definition: GasTransport.h:277