17 #define COLL_INT_POLY_DEGREE 8 19 GasTransport::GasTransport(ThermoPhase* thermo) :
39 void GasTransport::update_T()
41 if (m_thermo->nSpecies() != m_nsp) {
43 init(m_thermo, m_mode, m_log_level);
46 double T = m_thermo->temperature();
55 m_sqrt_t = sqrt(m_temp);
56 m_t14 = sqrt(m_sqrt_t);
57 m_t32 = m_temp * m_sqrt_t;
60 m_polytempvec[0] = 1.0;
61 m_polytempvec[1] = m_logt;
62 m_polytempvec[2] = m_logt*m_logt;
63 m_polytempvec[3] = m_logt*m_logt*m_logt;
64 m_polytempvec[4] = m_logt*m_logt*m_logt*m_logt;
73 doublereal GasTransport::viscosity()
82 doublereal vismix = 0.0;
88 multiply(m_phi, m_molefracs.data(), m_spwork.data());
90 for (
size_t k = 0; k < m_nsp; k++) {
91 vismix += m_molefracs[k] * m_visc[k]/m_spwork[k];
97 void GasTransport::updateViscosity_T()
100 updateSpeciesViscosities();
104 for (
size_t j = 0; j < m_nsp; j++) {
105 for (
size_t k = j; k < m_nsp; k++) {
106 double vratiokj = m_visc[k]/m_visc[j];
107 double wratiojk = m_mw[j]/m_mw[k];
110 double factor1 = 1.0 + (m_sqvisc[k]/m_sqvisc[j]) * m_wratjk(k,j);
111 m_phi(k,j) = factor1*factor1 / (sqrt(8.0) * m_wratkj1(j,k));
112 m_phi(j,k) = m_phi(k,j)/(vratiokj * wratiojk);
118 void GasTransport::updateSpeciesViscosities()
121 if (m_mode == CK_Mode) {
122 for (
size_t k = 0; k < m_nsp; k++) {
123 m_visc[k] = exp(
dot4(m_polytempvec, m_visccoeffs[k]));
124 m_sqvisc[k] = sqrt(m_visc[k]);
127 for (
size_t k = 0; k < m_nsp; k++) {
129 m_sqvisc[k] = m_t14 *
dot5(m_polytempvec, m_visccoeffs[k]);
130 m_visc[k] = (m_sqvisc[k] * m_sqvisc[k]);
136 void GasTransport::updateDiff_T()
141 if (m_mode == CK_Mode) {
142 for (
size_t i = 0; i < m_nsp; i++) {
143 for (
size_t j = i; j < m_nsp; j++) {
144 m_bdiff(i,j) = exp(
dot4(m_polytempvec, m_diffcoeffs[ic]));
145 m_bdiff(j,i) = m_bdiff(i,j);
150 for (
size_t i = 0; i < m_nsp; i++) {
151 for (
size_t j = i; j < m_nsp; j++) {
152 m_bdiff(i,j) = m_temp * m_sqrt_t*
dot5(m_polytempvec,
154 m_bdiff(j,i) = m_bdiff(i,j);
162 void GasTransport::getBinaryDiffCoeffs(
const size_t ld, doublereal*
const d)
170 throw CanteraError(
" MixTransport::getBinaryDiffCoeffs()",
"ld is too small");
172 doublereal rp = 1.0/m_thermo->pressure();
173 for (
size_t i = 0; i < m_nsp; i++) {
174 for (
size_t j = 0; j < m_nsp; j++) {
175 d[ld*j + i] = rp * m_bdiff(i,j);
180 void GasTransport::getMixDiffCoeffs(doublereal*
const d)
190 doublereal mmw = m_thermo->meanMolecularWeight();
191 doublereal p = m_thermo->pressure();
193 d[0] = m_bdiff(0,0) / p;
195 for (
size_t k = 0; k < m_nsp; k++) {
197 for (
size_t j = 0; j < m_nsp; j++) {
199 sum2 += m_molefracs[j] / m_bdiff(j,k);
203 d[k] = m_bdiff(k,k) / p;
205 d[k] = (mmw - m_molefracs[k] * m_mw[k])/(p * mmw * sum2);
211 void GasTransport::getMixDiffCoeffsMole(doublereal*
const d)
221 doublereal p = m_thermo->pressure();
223 d[0] = m_bdiff(0,0) / p;
225 for (
size_t k = 0; k < m_nsp; k++) {
227 for (
size_t j = 0; j < m_nsp; j++) {
229 sum2 += m_molefracs[j] / m_bdiff(j,k);
233 d[k] = m_bdiff(k,k) / p;
235 d[k] = (1 - m_molefracs[k]) / (p * sum2);
241 void GasTransport::getMixDiffCoeffsMass(doublereal*
const d)
251 doublereal mmw = m_thermo->meanMolecularWeight();
252 doublereal p = m_thermo->pressure();
255 d[0] = m_bdiff(0,0) / p;
257 for (
size_t k=0; k<m_nsp; k++) {
260 for (
size_t i=0; i<m_nsp; i++) {
264 sum1 += m_molefracs[i] / m_bdiff(k,i);
265 sum2 += m_molefracs[i] * m_mw[i] / m_bdiff(k,i);
268 sum2 *= p * m_molefracs[k] / (mmw - m_mw[k]*m_molefracs[k]);
269 d[k] = 1.0 / (sum1 + sum2);
274 void GasTransport::init(
thermo_t* thermo,
int mode,
int log_level)
279 m_log_level = log_level;
282 setupCollisionParameters();
283 setupCollisionIntegral();
285 m_molefracs.resize(m_nsp);
286 m_spwork.resize(m_nsp);
287 m_visc.resize(m_nsp);
288 m_sqvisc.resize(m_nsp);
289 m_phi.resize(m_nsp, m_nsp, 0.0);
290 m_bdiff.resize(m_nsp, m_nsp);
293 m_mw = m_thermo->molecularWeights();
295 m_wratjk.resize(m_nsp, m_nsp, 0.0);
296 m_wratkj1.resize(m_nsp, m_nsp, 0.0);
297 for (
size_t j = 0; j < m_nsp; j++) {
298 for (
size_t k = j; k < m_nsp; k++) {
299 m_wratjk(j,k) = sqrt(m_mw[j]/m_mw[k]);
300 m_wratjk(k,j) = sqrt(m_wratjk(j,k));
301 m_wratkj1(j,k) = sqrt(1.0 + m_mw[k]/m_mw[j]);
306 void GasTransport::setupCollisionParameters()
308 m_epsilon.resize(m_nsp, m_nsp, 0.0);
309 m_delta.resize(m_nsp, m_nsp, 0.0);
310 m_reducedMass.resize(m_nsp, m_nsp, 0.0);
311 m_dipole.resize(m_nsp, m_nsp, 0.0);
312 m_diam.resize(m_nsp, m_nsp, 0.0);
313 m_crot.resize(m_nsp);
314 m_zrot.resize(m_nsp);
315 m_polar.resize(m_nsp,
false);
316 m_alpha.resize(m_nsp, 0.0);
317 m_poly.resize(m_nsp);
318 m_sigma.resize(m_nsp);
320 m_w_ac.resize(m_nsp);
321 m_disp.resize(m_nsp, 0.0);
322 m_quad_polar.resize(m_nsp, 0.0);
324 const vector_fp& mw = m_thermo->molecularWeights();
327 for (
size_t i = 0; i < m_nsp; i++) {
328 m_poly[i].resize(m_nsp);
331 double f_eps, f_sigma;
333 for (
size_t i = 0; i < m_nsp; i++) {
334 for (
size_t j = i; j < m_nsp; j++) {
336 m_reducedMass(i,j) = mw[i] * mw[j] / (
Avogadro * (mw[i] + mw[j]));
339 m_diam(i,j) = 0.5*(m_sigma[i] + m_sigma[j]);
342 m_epsilon(i,j) = sqrt(m_eps[i]*m_eps[j]);
345 m_dipole(i,j) = sqrt(m_dipole(i,i)*m_dipole(j,j));
348 double d = m_diam(i,j);
349 m_delta(i,j) = 0.5 * m_dipole(i,j)*m_dipole(i,j)
350 / (4 *
Pi *
epsilon_0 * m_epsilon(i,j) * d * d * d);
351 makePolarCorrections(i, j, f_eps, f_sigma);
352 m_diam(i,j) *= f_sigma;
353 m_epsilon(i,j) *= f_eps;
356 m_reducedMass(j,i) = m_reducedMass(i,j);
357 m_diam(j,i) = m_diam(i,j);
358 m_epsilon(j,i) = m_epsilon(i,j);
359 m_dipole(j,i) = m_dipole(i,j);
360 m_delta(j,i) = m_delta(i,j);
365 void GasTransport::setupCollisionIntegral()
367 double tstar_min = 1.e8, tstar_max = 0.0;
368 for (
size_t i = 0; i < m_nsp; i++) {
369 for (
size_t j = i; j < m_nsp; j++) {
372 tstar_min = std::min(tstar_min,
Boltzmann * m_thermo->minTemp()/m_epsilon(i,j));
373 tstar_max = std::max(tstar_max,
Boltzmann * m_thermo->maxTemp()/m_epsilon(i,j));
378 if (m_mode == CK_Mode) {
384 debuglog(
"*** collision_integrals ***\n", m_log_level);
386 integrals.
init(tstar_min, tstar_max, m_log_level);
387 fitCollisionIntegrals(integrals);
388 debuglog(
"*** end of collision_integrals ***\n", m_log_level);
390 debuglog(
"*** property fits ***\n", m_log_level);
391 fitProperties(integrals);
392 debuglog(
"*** end of property fits ***\n", m_log_level);
395 void GasTransport::getTransportData()
397 for (
size_t k = 0; k < m_thermo->nSpecies(); k++) {
398 shared_ptr<Species> s = m_thermo->species(m_thermo->speciesName(k));
403 "Missing gas-phase transport data for species '{}'.", s->name);
408 }
else if (sptran->
geometry ==
"linear") {
410 }
else if (sptran->
geometry ==
"nonlinear") {
416 m_dipole(k,k) = sptran->
dipole;
417 m_polar[k] = (sptran->
dipole > 0);
426 void GasTransport::makePolarCorrections(
size_t i,
size_t j,
427 doublereal& f_eps, doublereal& f_sigma)
430 if (m_polar[i] == m_polar[j]) {
438 size_t kp = (m_polar[i] ? i : j);
439 size_t knp = (i == kp ? j : i);
440 double d3np, d3p, alpha_star, mu_p_star, xi;
441 d3np = pow(m_sigma[knp],3);
442 d3p = pow(m_sigma[kp],3);
443 alpha_star = m_alpha[knp]/d3np;
444 mu_p_star = m_dipole(kp,kp)/sqrt(4 *
Pi *
epsilon_0 * d3p * m_eps[kp]);
445 xi = 1.0 + 0.25 * alpha_star * mu_p_star * mu_p_star *
446 sqrt(m_eps[kp]/m_eps[knp]);
447 f_sigma = pow(xi, -1.0/6.0);
457 "fits to A*, B*, and C* vs. log(T*).\n" 458 "These are done only for the required dstar(j,k) values.\n\n");
459 if (m_log_level < 3) {
460 writelog(
"*** polynomial coefficients not printed (log_level < 3) ***\n");
464 m_omega22_poly.clear();
465 m_astar_poly.clear();
466 m_bstar_poly.clear();
467 m_cstar_poly.clear();
468 for (
size_t i = 0; i < m_nsp; i++) {
469 for (
size_t j = i; j < m_nsp; j++) {
471 double dstar = (m_mode != CK_Mode) ? m_delta(i,j) : 0.0;
478 auto dptr = find(fitlist.begin(), fitlist.end(), dstar);
479 if (dptr == fitlist.end()) {
480 vector_fp ca(degree+1), cb(degree+1), cc(degree+1);
482 integrals.fit(degree, dstar, ca.data(), cb.data(), cc.data());
483 integrals.fit_omega22(degree, dstar, co22.data());
484 m_omega22_poly.push_back(co22);
485 m_astar_poly.push_back(ca);
486 m_bstar_poly.push_back(cb);
487 m_cstar_poly.push_back(cc);
488 m_poly[i][j] =
static_cast<int>(m_astar_poly.size()) - 1;
489 fitlist.push_back(dstar);
492 m_poly[i][j] =
static_cast<int>((dptr - fitlist.begin()));
494 m_poly[j][i] = m_poly[i][j];
502 const size_t np = 50;
503 int degree = (m_mode == CK_Mode ? 3 : 4);
504 double dt = (m_thermo->maxTemp() - m_thermo->minTemp())/(np-1);
505 vector_fp tlog(np), spvisc(np), spcond(np);
508 m_visccoeffs.clear();
509 m_condcoeffs.clear();
512 for (
size_t n = 0; n < np; n++) {
513 double t = m_thermo->minTemp() + dt*n;
521 if (m_log_level && m_log_level < 2) {
522 writelog(
"*** polynomial coefficients not printed (log_level < 2) ***\n");
524 double visc, err, relerr,
525 mxerr = 0.0, mxrelerr = 0.0, mxerr_cond = 0.0, mxrelerr_cond = 0.0;
528 writelog(
"Polynomial fits for viscosity:\n");
529 if (m_mode == CK_Mode) {
530 writelog(
"log(viscosity) fit to cubic polynomial in log(T)\n");
532 writelogf(
"viscosity/sqrt(T) fit to polynomial of degree " 533 "%d in log(T)", degree);
537 double T_save = m_thermo->temperature();
538 const vector_fp& mw = m_thermo->molecularWeights();
539 for (
size_t k = 0; k < m_nsp; k++) {
540 double tstar =
Boltzmann * 298.0 / m_eps[k];
543 double fz_298 = 1.0 + pow(
Pi, 1.5) / sqrt(tstar) * (0.5 + 1.0 / tstar) +
544 (0.25 *
Pi *
Pi + 2) / tstar;
546 for (
size_t n = 0; n < np; n++) {
547 double t = m_thermo->minTemp() + dt*n;
548 m_thermo->setTemperature(t);
549 vector_fp cp_R_all(m_thermo->nSpecies());
550 m_thermo->getCp_R_ref(&cp_R_all[0]);
551 double cp_R = cp_R_all[k];
553 double sqrt_T = sqrt(t);
554 double om22 = integrals.omega22(tstar, m_delta(k,k));
555 double om11 = integrals.omega11(tstar, m_delta(k,k));
558 double diffcoeff = 3.0/16.0 * sqrt(2.0 *
Pi/m_reducedMass(k,k)) *
560 (
Pi * m_sigma[k] * m_sigma[k] * om11);
564 (om22 *
Pi * m_sigma[k]*m_sigma[k]);
567 double f_int = mw[k]/(
GasConstant * t) * diffcoeff/visc;
568 double cv_rot = m_crot[k];
569 double A_factor = 2.5 - f_int;
570 double fz_tstar = 1.0 + pow(
Pi, 1.5) / sqrt(tstar) * (0.5 + 1.0 / tstar) +
571 (0.25 *
Pi *
Pi + 2) / tstar;
572 double B_factor = m_zrot[k] * fz_298 / fz_tstar + 2.0/
Pi * (5.0/3.0 * cv_rot + f_int);
573 double c1 = 2.0/
Pi * A_factor/B_factor;
574 double cv_int = cp_R - 2.5 - cv_rot;
575 double f_rot = f_int * (1.0 + c1);
576 double f_trans = 2.5 * (1.0 - c1 * cv_rot/1.5);
577 double cond = (visc/mw[k])*
GasConstant*(f_trans * 1.5
578 + f_rot * cv_rot + f_int * cv_int);
580 if (m_mode == CK_Mode) {
581 spvisc[n] = log(visc);
582 spcond[n] = log(cond);
592 spvisc[n] = sqrt(visc/sqrt_T);
597 spcond[n] = cond/sqrt_T;
598 w[n] = 1.0/(spvisc[n]*spvisc[n]);
599 w2[n] = 1.0/(spcond[n]*spcond[n]);
602 polyfit(np, degree, tlog.data(), spvisc.data(), w.data(), c.data());
603 polyfit(np, degree, tlog.data(), spcond.data(), w2.data(), c2.data());
606 for (
size_t n = 0; n < np; n++) {
608 if (m_mode == CK_Mode) {
609 val = exp(spvisc[n]);
610 fit = exp(
poly3(tlog[n], c.data()));
612 double sqrt_T = exp(0.5*tlog[n]);
613 val = sqrt_T * pow(spvisc[n],2);
614 fit = sqrt_T * pow(
poly4(tlog[n], c.data()),2);
618 mxerr = std::max(mxerr, fabs(err));
619 mxrelerr = std::max(mxrelerr, fabs(relerr));
623 for (
size_t n = 0; n < np; n++) {
625 if (m_mode == CK_Mode) {
626 val = exp(spcond[n]);
627 fit = exp(
poly3(tlog[n], c2.data()));
629 double sqrt_T = exp(0.5*tlog[n]);
630 val = sqrt_T * spcond[n];
631 fit = sqrt_T *
poly4(tlog[n], c2.data());
635 mxerr_cond = std::max(mxerr_cond, fabs(err));
636 mxrelerr_cond = std::max(mxrelerr_cond, fabs(relerr));
638 m_visccoeffs.push_back(c);
639 m_condcoeffs.push_back(c2);
641 if (m_log_level >= 2) {
645 m_thermo->setTemperature(T_save);
648 writelogf(
"Maximum viscosity absolute error: %12.6g\n", mxerr);
649 writelogf(
"Maximum viscosity relative error: %12.6g\n", mxrelerr);
650 writelog(
"\nPolynomial fits for conductivity:\n");
651 if (m_mode == CK_Mode) {
652 writelog(
"log(conductivity) fit to cubic polynomial in log(T)");
655 "polynomial of degree %d in log(T)", degree);
657 if (m_log_level >= 2) {
658 for (
size_t k = 0; k < m_nsp; k++) {
659 writelog(m_thermo->speciesName(k) +
": [" +
660 vec2str(m_condcoeffs[k]) +
"]\n");
663 writelogf(
"Maximum conductivity absolute error: %12.6g\n", mxerr_cond);
664 writelogf(
"Maximum conductivity relative error: %12.6g\n", mxrelerr_cond);
667 writelogf(
"\nbinary diffusion coefficients:\n");
668 if (m_mode == CK_Mode) {
669 writelog(
"log(D) fit to cubic polynomial in log(T)");
671 writelogf(
"D/T**(3/2) fit to polynomial of degree %d in log(T)",degree);
675 fitDiffCoeffs(integrals);
681 const size_t np = 50;
682 int degree = (m_mode == CK_Mode ? 3 : 4);
683 double dt = (m_thermo->maxTemp() - m_thermo->minTemp())/(np-1);
688 for (
size_t n = 0; n < np; n++) {
689 double t = m_thermo->minTemp() + dt*n;
696 mxerr = 0.0, mxrelerr = 0.0;
699 m_diffcoeffs.clear();
700 for (
size_t k = 0; k < m_nsp; k++) {
701 for (
size_t j = k; j < m_nsp; j++) {
702 for (
size_t n = 0; n < np; n++) {
703 double t = m_thermo->minTemp() + dt*n;
704 double eps = m_epsilon(j,k);
706 double sigma = m_diam(j,k);
707 double om11 = integrals.omega11(tstar, m_delta(j,k));
708 double diffcoeff = 3.0/16.0 * sqrt(2.0 *
Pi/m_reducedMass(k,j))
709 * pow(
Boltzmann * t, 1.5) / (
Pi * sigma * sigma * om11);
714 getBinDiffCorrection(t, integrals, k, j, 1.0, 1.0, fkj, fjk);
716 if (m_mode == CK_Mode) {
717 diff[n] = log(diffcoeff);
720 diff[n] = diffcoeff/pow(t, 1.5);
721 w[n] = 1.0/(diff[n]*diff[n]);
724 polyfit(np, degree, tlog.data(), diff.data(), w.data(), c.data());
726 for (
size_t n = 0; n < np; n++) {
728 if (m_mode == CK_Mode) {
730 fit = exp(
poly3(tlog[n], c.data()));
732 double t = exp(tlog[n]);
733 double pre = pow(t, 1.5);
735 fit = pre *
poly4(tlog[n], c.data());
739 mxerr = std::max(mxerr, fabs(err));
740 mxrelerr = std::max(mxrelerr, fabs(relerr));
742 m_diffcoeffs.push_back(c);
743 if (m_log_level >= 2) {
744 writelog(m_thermo->speciesName(k) +
"__" +
745 m_thermo->speciesName(j) +
": [" +
vec2str(c) +
"]\n");
750 writelogf(
"Maximum binary diffusion coefficient absolute error:" 752 writelogf(
"Maximum binary diffusion coefficient relative error:" 758 size_t k,
size_t j,
double xk,
double xj,
double& fkj,
double& fjk)
760 double w1 = m_thermo->molecularWeight(k);
761 double w2 = m_thermo->molecularWeight(j);
762 double wsum = w1 + w2;
763 double wmwp = (w1 - w2)/wsum;
764 double sqw12 = sqrt(w1*w2);
765 double sig1 = m_sigma[k];
766 double sig2 = m_sigma[j];
767 double sig12 = 0.5*(m_sigma[k] + m_sigma[j]);
768 double sigratio = sig1*sig1/(sig2*sig2);
769 double sigratio2 = sig1*sig1/(sig12*sig12);
770 double sigratio3 = sig2*sig2/(sig12*sig12);
771 double tstar1 =
Boltzmann * t / m_eps[k];
772 double tstar2 =
Boltzmann * t / m_eps[j];
773 double tstar12 =
Boltzmann * t / sqrt(m_eps[k] * m_eps[j]);
774 double om22_1 = integrals.omega22(tstar1, m_delta(k,k));
775 double om22_2 = integrals.omega22(tstar2, m_delta(j,j));
776 double om11_12 = integrals.omega11(tstar12, m_delta(k,j));
777 double astar_12 = integrals.astar(tstar12, m_delta(k,j));
778 double bstar_12 = integrals.bstar(tstar12, m_delta(k,j));
779 double cstar_12 = integrals.cstar(tstar12, m_delta(k,j));
781 double cnst = sigratio * sqrt(2.0*w2/wsum) * 2.0 * w1*w1/(wsum * w2);
782 double p1 = cnst * om22_1 / om11_12;
784 cnst = (1.0/sigratio) * sqrt(2.0*w1/wsum) * 2.0*w2*w2/(wsum*w1);
785 double p2 = cnst * om22_2 / om11_12;
786 double p12 = 15.0 * wmwp*wmwp + 8.0*w1*w2*astar_12/(wsum*wsum);
788 cnst = (2.0/(w2*wsum))*sqrt(2.0*w2/wsum)*sigratio2;
789 double q1 = cnst*((2.5 - 1.2*bstar_12)*w1*w1 + 3.0*w2*w2
790 + 1.6*w1*w2*astar_12);
792 cnst = (2.0/(w1*wsum))*sqrt(2.0*w1/wsum)*sigratio3;
793 double q2 = cnst*((2.5 - 1.2*bstar_12)*w2*w2 + 3.0*w1*w1
794 + 1.6*w1*w2*astar_12);
795 double q12 = wmwp*wmwp*15.0*(2.5 - 1.2*bstar_12)
796 + 4.0*w1*w2*astar_12*(11.0 - 2.4*bstar_12)/(wsum*wsum)
797 + 1.6*wsum*om22_1*om22_2/(om11_12*om11_12*sqw12)
798 * sigratio2 * sigratio3;
800 cnst = 6.0*cstar_12 - 5.0;
801 fkj = 1.0 + 0.1*cnst*cnst *
802 (p1*xk*xk + p2*xj*xj + p12*xk*xj)/
803 (q1*xk*xk + q2*xj*xj + q12*xk*xj);
804 fjk = 1.0 + 0.1*cnst*cnst *
805 (p2*xk*xk + p1*xj*xj + p12*xk*xj)/
806 (q2*xk*xk + q1*xj*xj + q12*xk*xj);
Transport data for a single gas-phase species which can be used in mixture-averaged or multicomponent...
R poly3(D x, R *c)
Templated evaluation of a polynomial of order 3.
void init(doublereal tsmin, doublereal tsmax, int loglevel=0)
Initialize the object for calculation.
double quadrupole_polarizability
quadrupole. Default 0.0.
std::string vec2str(const vector_fp &v, const std::string &fmt, const std::string &sep)
Convert a vector to a string (separated by commas)
doublereal dot4(const V &x, const V &y)
Templated Inner product of two vectors of length 4.
void writelog(const std::string &fmt, const Args &... args)
Write a formatted message to the screen.
size_t nSpecies() const
Returns the number of species in the phase.
#define COLL_INT_POLY_DEGREE
polynomial degree used for fitting collision integrals except in CK mode, where the degree is 6...
double rotational_relaxation
The rotational relaxation number (the number of collisions it takes to equilibrate the rotational deg...
double well_depth
The Lennard-Jones well depth [J].
Monk and Monchick collision integrals.
R poly4(D x, R *c)
Evaluates a polynomial of order 4.
Base class for a phase with thermodynamic properties.
double diameter
The Lennard-Jones collision diameter [m].
double dispersion_coefficient
dispersion normalized by e^2. [m^5] Default 0.0.
void multiply(const DenseMatrix &A, const double *const b, double *const prod)
Multiply A*b and return the result in prod. Uses BLAS routine DGEMV.
Base class for exceptions thrown by Cantera classes.
double dipole
The permanent dipole moment of the molecule [Coulomb-m]. Default 0.0.
void debuglog(const std::string &msg, int loglevel)
Write a message to the log only if loglevel > 0.
void writelogf(const char *fmt, const Args &... args)
Write a formatted message to the screen.
const doublereal Avogadro
Avogadro's Number [number/kmol].
doublereal dot5(const V &x, const V &y)
Templated Inner product of two vectors of length 5.
std::vector< double > vector_fp
Turn on the use of stl vectors for the basic array type within cantera Vector of doubles.
const doublereal GasConstant
Universal Gas Constant. [J/kmol/K].
Contains declarations for string manipulation functions within Cantera.
std::string geometry
A string specifying the molecular geometry.
const doublereal epsilon_0
Permittivity of free space in F/m.
double polarizability
The polarizability of the molecule [m^3]. Default 0.0.
Calculation of Collision integrals.
double acentric_factor
Pitzer's acentric factor [dimensionless]. Default 0.0.
Namespace for the Cantera kernel.
double polyfit(size_t n, size_t deg, const double *xp, const double *yp, const double *wp, double *pp)
Fits a polynomial function to a set of data points.
const doublereal Boltzmann
Boltzmann's constant [J/K].