PecosTransport.cpp

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/**
 *  @file PecosTransport.cpp
 *  Mixture-averaged transport properties.
 */

#include "cantera/transport/PecosTransport.h"
#include "cantera/transport/TransportParams.h"
#include "cantera/base/stringUtils.h"
#include "cantera/thermo/IdealGasPhase.h"

#include <sstream>

using namespace std;

namespace Cantera
{

PecosTransport::PecosTransport() :
    m_nsp(0),
    m_temp(-1.0),
    m_logt(0.0)
{
    warn_deprecated("class PecosTransport", "To be removed after Cantera 2.2");
}

bool PecosTransport::initGas(GasTransportParams& tr)
{
    // constant substance attributes
    m_thermo = tr.thermo;
    m_nsp   = static_cast<int>(m_thermo->nSpecies());

    // make a local copy of the molecular weights
    m_mw.resize(m_nsp);
    copy(m_thermo->molecularWeights().begin(),
         m_thermo->molecularWeights().end(), m_mw.begin());

    // copy polynomials and parameters into local storage
    m_poly       = tr.poly;
    m_visccoeffs = tr.visccoeffs;
    m_condcoeffs = tr.condcoeffs;
    m_diffcoeffs = tr.diffcoeffs;

    m_zrot       = tr.zrot;
    m_crot       = tr.crot;
    m_epsilon    = tr.epsilon;
    m_mode       = tr.mode_;
    m_diam       = tr.diam;
    m_eps        = tr.eps;
    m_alpha      = tr.alpha;
    m_dipoleDiag.resize(m_nsp);
    for (int i = 0; i < m_nsp; i++) {
        m_dipoleDiag[i] = tr.dipole(i,i);
    }

    m_phi.resize(m_nsp, m_nsp, 0.0);
    m_wratjk.resize(m_nsp, m_nsp, 0.0);
    m_wratkj1.resize(m_nsp, m_nsp, 0.0);
    int j, k;
    for (j = 0; j < m_nsp; j++)
        for (k = j; k < m_nsp; k++) {
            m_wratjk(j,k) = sqrt(m_mw[j]/m_mw[k]);
            m_wratjk(k,j) = sqrt(m_wratjk(j,k));
            m_wratkj1(j,k) = sqrt(1.0 + m_mw[k]/m_mw[j]);
        }

    m_polytempvec.resize(5);
    m_visc.resize(m_nsp);
    m_sqvisc.resize(m_nsp);
    m_cond.resize(m_nsp);
    m_bdiff.resize(m_nsp, m_nsp);

    m_molefracs.resize(m_nsp);
    m_spwork.resize(m_nsp);

    // set flags all false
    m_viscmix_ok = false;
    m_viscwt_ok = false;
    m_spvisc_ok = false;
    m_spcond_ok = false;
    m_condmix_ok = false;
    m_spcond_ok = false;
    m_diffmix_ok = false;
    m_abc_ok = false;

    // read blottner fit parameters (A,B,C)
    read_blottner_transport_table();

    // set specific heats
    cv_rot.resize(m_nsp);
    cp_R.resize(m_nsp);
    cv_int.resize(m_nsp);

    for (k = 0; k < m_nsp; k++) {
        cv_rot[k] = tr.crot[k];
        cp_R[k] = ((IdealGasPhase*)tr.thermo)->cp_R_ref()[k];
        cv_int[k] = cp_R[k] - 2.5 - cv_rot[k];
    }
    return true;
}

doublereal PecosTransport::viscosity()
{
    update_T();
    update_C();

    if (m_viscmix_ok) {
        return m_viscmix;
    }

    doublereal vismix = 0.0;
    int k;
    // update m_visc and m_phi if necessary
    if (!m_viscwt_ok) {
        updateViscosity_T();
    }

    multiply(m_phi, DATA_PTR(m_molefracs), DATA_PTR(m_spwork));

    for (k = 0; k < m_nsp; k++) {
        vismix += m_molefracs[k] * m_visc[k]/m_spwork[k]; //denom;
    }
    m_viscmix = vismix;
    return vismix;
}

void PecosTransport::getBinaryDiffCoeffs(const size_t ld, doublereal* const d)
{
    int i,j;

    update_T();

    // if necessary, evaluate the binary diffusion coefficents
    if (!m_bindiff_ok) {
        updateDiff_T();
    }

    doublereal rp = 1.0/pressure_ig();
    for (i = 0; i < m_nsp; i++)
        for (j = 0; j < m_nsp; j++) {
            d[ld*j + i] = rp * m_bdiff(i,j);
        }
}

void PecosTransport::getMobilities(doublereal* const mobil)
{
    int k;
    getMixDiffCoeffs(DATA_PTR(m_spwork));
    doublereal c1 = ElectronCharge / (Boltzmann * m_temp);
    for (k = 0; k < m_nsp; k++) {
        mobil[k] = c1 * m_spwork[k] * m_thermo->charge(k);
    }
}

doublereal PecosTransport::thermalConductivity()
{
    int k;
    doublereal lambda = 0.0;

    update_T();
    update_C();

    // update m_cond and m_phi if necessary
    if (!m_spcond_ok) {
        updateCond_T();
    }
    if (!m_condmix_ok) {

        multiply(m_phi, DATA_PTR(m_molefracs), DATA_PTR(m_spwork));

        for (k = 0; k < m_nsp; k++) {
            lambda += m_molefracs[k] * m_cond[k]/m_spwork[k]; //denom;
        }

    }
    m_lambda = lambda;
    return m_lambda;

}

void PecosTransport::getThermalDiffCoeffs(doublereal* const dt)
{
    int k;
    for (k = 0; k < m_nsp; k++) {
        dt[k] = 0.0;
    }
}

void PecosTransport::getSpeciesFluxes(size_t ndim,
                                      const doublereal* const grad_T,
                                      size_t ldx, const doublereal* const grad_X,
                                      size_t ldf, doublereal* const fluxes)
{
    size_t n = 0;
    int k;

    update_T();
    update_C();

    getMixDiffCoeffs(DATA_PTR(m_spwork));

    const vector_fp& mw = m_thermo->molecularWeights();
    const doublereal* y  = m_thermo->massFractions();
    doublereal rhon = m_thermo->molarDensity();

    vector_fp sum(ndim,0.0);

    doublereal correction=0.0;
    // grab 2nd (summation) term -- still need to multiply by mass fraction (\rho_s / \rho)
    for (k = 0; k < m_nsp; k++) {
        correction += rhon * mw[k] * m_spwork[k] * grad_X[n*ldx + k];
    }

    for (n = 0; n < ndim; n++) {
        for (k = 0; k < m_nsp; k++) {
            fluxes[n*ldf + k] = -rhon * mw[k] * m_spwork[k] * grad_X[n*ldx + k] + y[k]*correction;
            sum[n] += fluxes[n*ldf + k];
        }
    }
    // add correction flux to enforce sum to zero
    for (n = 0; n < ndim; n++) {
        for (k = 0; k < m_nsp; k++) {
            fluxes[n*ldf + k] -= y[k]*sum[n];
        }
    }
}

void PecosTransport::getMixDiffCoeffs(doublereal* const d)
{
    update_T();
    update_C();

    // update the binary diffusion coefficients if necessary
    if (!m_bindiff_ok) {
        updateDiff_T();
    }

    int k, j;
    doublereal mmw = m_thermo->meanMolecularWeight();
    doublereal sumxw = 0.0, sum2;
    doublereal p = pressure_ig();
    if (m_nsp == 1) {
        d[0] = m_bdiff(0,0) / p;
    } else {
        for (k = 0; k < m_nsp; k++) {
            sumxw += m_molefracs[k] * m_mw[k];
        }
        for (k = 0; k < m_nsp; k++) {
            sum2 = 0.0;
            for (j = 0; j < m_nsp; j++) {
                if (j != k) {
                    sum2 += m_molefracs[j] / m_bdiff(j,k);
                }
            }
            if (sum2 <= 0.0) {
                d[k] = m_bdiff(k,k) / p;
            } else {
                d[k] = (sumxw - m_molefracs[k] * m_mw[k])/(p * mmw * sum2);
            }
        }
    }
}

void PecosTransport::getMixDiffCoeffsMole(doublereal* const d)
{
    update_T();
    update_C();

    // update the binary diffusion coefficients if necessary
    if (!m_bindiff_ok) {
        updateDiff_T();
    }

    doublereal p = m_thermo->pressure();
    if (m_nsp == 1) {
        d[0] = m_bdiff(0,0) / p;
    } else {
        for (int k = 0; k < m_nsp; k++) {
            double sum2 = 0.0;
            for (int j = 0; j < m_nsp; j++) {
                if (j != k) {
                    sum2 += m_molefracs[j] / m_bdiff(j,k);
                }
            }
            if (sum2 <= 0.0) {
                d[k] = m_bdiff(k,k) / p;
            } else {
                d[k] = (1 - m_molefracs[k]) / (p * sum2);
            }
        }
    }
}

void PecosTransport::getMixDiffCoeffsMass(doublereal* const d)
{
    update_T();
    update_C();

    // update the binary diffusion coefficients if necessary
    if (!m_bindiff_ok) {
        updateDiff_T();
    }

    doublereal mmw = m_thermo->meanMolecularWeight();
    doublereal p = m_thermo->pressure();

    if (m_nsp == 1) {
        d[0] = m_bdiff(0,0) / p;
    } else {
        for (int k=0; k<m_nsp; k++) {
            double sum1 = 0.0;
            double sum2 = 0.0;
            for (int i=0; i<m_nsp; i++) {
                if (i==k) {
                    continue;
                }
                sum1 += m_molefracs[i] / m_bdiff(k,i);
                sum2 += m_molefracs[i] * m_mw[i] / m_bdiff(k,i);
            }
            sum1 *= p;
            sum2 *= p * m_molefracs[k] / (mmw - m_mw[k]*m_molefracs[k]);
            d[k] = 1.0 / (sum1 +  sum2);
        }
    }
}

/**
 *  @internal This is called whenever a transport property is
 *  requested from ThermoSubstance if the temperature has changed
 *  since the last call to update_T.
 */
void PecosTransport::update_T()
{
    doublereal t = m_thermo->temperature();
    if (t == m_temp) {
        return;
    }
    if (t <= 0.0) {
        throw CanteraError("PecosTransport::update_T",
                           "negative temperature "+fp2str(t));
    }
    m_temp = t;
    m_logt = log(m_temp);
    m_kbt = Boltzmann * m_temp;
    m_sqrt_t = sqrt(m_temp);
    m_t14 = sqrt(m_sqrt_t);
    m_t32 = m_temp * m_sqrt_t;
    m_sqrt_kbt = sqrt(Boltzmann*m_temp);

    // compute powers of log(T)
    m_polytempvec[0] = 1.0;
    m_polytempvec[1] = m_logt;
    m_polytempvec[2] = m_logt*m_logt;
    m_polytempvec[3] = m_logt*m_logt*m_logt;
    m_polytempvec[4] = m_logt*m_logt*m_logt*m_logt;

    // temperature has changed, so polynomial fits will need to be redone.
    m_viscmix_ok = false;
    m_spvisc_ok = false;
    m_viscwt_ok = false;
    m_spcond_ok = false;
    m_diffmix_ok = false;
    m_bindiff_ok = false;
    m_abc_ok  = false;
    m_condmix_ok = false;
}

void PecosTransport::update_C()
{
    // signal that concentration-dependent quantities will need to
    // be recomputed before use, and update the local mole
    // fractions.

    m_viscmix_ok = false;
    m_diffmix_ok = false;
    m_condmix_ok = false;

    m_thermo->getMoleFractions(DATA_PTR(m_molefracs));

    // add an offset to avoid a pure species condition
    int k;
    for (k = 0; k < m_nsp; k++) {
        m_molefracs[k] = std::max(Tiny, m_molefracs[k]);
    }
}

void PecosTransport::updateCond_T()
{
    int k;
    doublereal fivehalves = 5/2;
    for (k = 0; k < m_nsp; k++) {
        // need to add cv_elec in the future
        m_cond[k] = m_visc[k] * (fivehalves * cv_int[k]  + cv_rot[k] + m_thermo->cv_vib(k,m_temp));
    }
    m_spcond_ok = true;
    m_condmix_ok = false;
}

void PecosTransport::updateDiff_T()
{
    // evaluate binary diffusion coefficients at unit pressure
    int i,j;
    int ic = 0;
    if (m_mode == CK_Mode) {
        for (i = 0; i < m_nsp; i++) {
            for (j = i; j < m_nsp; j++) {
                m_bdiff(i,j) = exp(dot4(m_polytempvec, m_diffcoeffs[ic]));
                m_bdiff(j,i) = m_bdiff(i,j);
                ic++;
            }
        }
    } else {
        for (i = 0; i < m_nsp; i++) {
            for (j = i; j < m_nsp; j++) {
                m_bdiff(i,j) = m_temp * m_sqrt_t*dot5(m_polytempvec,
                                                      m_diffcoeffs[ic]);
                m_bdiff(j,i) = m_bdiff(i,j);
                ic++;
            }
        }
    }

    m_bindiff_ok = true;
    m_diffmix_ok = false;
}

void PecosTransport::updateSpeciesViscosities()
{
    int k;
    // iterate over species, update pure-species viscosity
    for (k = 0; k < m_nsp; k++) {
        m_visc[k] = 0.10*std::exp(a[k]*(m_logt*m_logt) + b[k]*m_logt + c[k]);
        m_sqvisc[k] = sqrt(m_visc[k]);
    }

    // time to update mixing
    m_spvisc_ok = true;
}

void PecosTransport::read_blottner_transport_table()
{
    // from: AIAA-1997-2474 and Sandia Report SC-RR-70-754
    //
    //   # Air  -- Identical to N2 fit
    //   # N    -- Sandia Report SC-RR-70-754
    //   # N2   -- Sandia Report SC-RR-70-754
    //   # CPN2 -- Identical to N2 fit
    //   # NO   -- Sandia Report SC-RR-70-754
    //   # O    -- Sandia Report SC-RR-70-754
    //   # O2   -- Sandia Report SC-RR-70-754
    //   # C    -- AIAA-1997-2474
    //   # C2   -- AIAA-1997-2474
    //   # C3   -- AIAA-1997-2474
    //   # C2H  -- wild-ass guess: identical to HCN fit
    //   # CN   -- AIAA-1997-2474
    //   # CO   -- AIAA-1997-2474
    //   # CO2  -- AIAA-1997-2474
    //   # HCN  -- AIAA-1997-2474
    //   # H    -- AIAA-1997-2474
    //   # H2   -- AIAA-1997-2474
    //   # e    -- Sandia Report SC-RR-70-754

    istringstream blot
    ("Air 2.68142000000e-02 3.17783800000e-01 -1.13155513000e+01\n"
     "CPAir 2.68142000000e-02 3.17783800000e-01 -1.13155513000e+01\n"
     "N 1.15572000000e-02 6.03167900000e-01 -1.24327495000e+01\n"
     "N2 2.68142000000e-02 3.17783800000e-01 -1.13155513000e+01\n"
     "CPN2 2.68142000000e-02 3.17783800000e-01 -1.13155513000e+01\n"
     "NO 4.36378000000e-02 -3.35511000000e-02 -9.57674300000e+00\n"
     "O 2.03144000000e-02 4.29440400000e-01 -1.16031403000e+01\n"
     "O2 4.49290000000e-02 -8.26158000000e-02 -9.20194750000e+00\n"
     "C -8.3285e-3 0.7703240 -12.7378000\n"
     "C2 -8.4311e-3 0.7876060 -13.0268000\n"
     "C3 -8.4312e-3 0.7876090 -12.8240000\n"
     "C2H -2.4241e-2 1.0946550 -14.5835500\n"
     "CN -8.3811e-3 0.7860330 -12.9406000\n"
     "CO -0.019527394 1.013295 -13.97873\n"
     "CO2 -0.019527387 1.047818 -14.32212\n"
     "HCN -2.4241e-2 1.0946550 -14.5835500\n"
     "H -8.3912e-3 0.7743270 -13.6653000\n"
     "H2 -8.3346e-3 0.7815380 -13.5351000\n"
     "e 0.00000000000e+00 0.00000000000e+00 -1.16031403000e+01\n");

    string line;
    string name;
    string ss1,ss2,ss3,ss4,sss;
    int k;
    int i = 0;

    while (std::getline(blot, line)) {

        istringstream ss(line);
        std::getline(ss, ss1, ' ');
        std::getline(ss, ss2, ' ');
        std::getline(ss, ss3, ' ');
        std::getline(ss, ss4, ' ');
        name = ss1;

        // now put coefficients in correct species
        for (k = 0; k < m_nsp; k++) {
            string sss = m_thermo->speciesName(k);

            // this is the right species index
            if (sss.compare(ss1) == 0) {
                a[k] = fpValue(ss2);
                b[k] = fpValue(ss3);
                c[k] = fpValue(ss4);

                // index
                i++;
            } else { // default to air

                a[k] = 0.026;
                b[k] = 0.3;
                c[k] = -11.3;
            }

        } // done with for loop
    }
}

void PecosTransport::updateViscosity_T()
{
    doublereal vratiokj, wratiojk, factor1;

    if (!m_spvisc_ok) {
        updateSpeciesViscosities();
    }

    // see Eq. (9-5.15) of Reid, Prausnitz, and Poling
    int j, k;
    for (j = 0; j < m_nsp; j++) {
        for (k = j; k < m_nsp; k++) {
            vratiokj = m_visc[k]/m_visc[j];
            wratiojk = m_mw[j]/m_mw[k];

            // Note that m_wratjk(k,j) holds the square root of
            // m_wratjk(j,k)!
            factor1 = 1.0 + (m_sqvisc[k]/m_sqvisc[j]) * m_wratjk(k,j);
            m_phi(k,j) = factor1*factor1 /
                         (sqrt(8.0) * m_wratkj1(j,k));
            m_phi(j,k) = m_phi(k,j)/(vratiokj * wratiojk);
        }
    }
    m_viscwt_ok = true;
}

}