MixTransport.h

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/**
 *  @file MixTransport.h
 *    Headers for the MixTransport object, which models transport properties
 *    in ideal gas solutions using a mixture averaged approximation
 *    (see \ref tranprops and \link Cantera::MixTransport MixTransport \endlink) .
 */

// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.

#ifndef CT_MIXTRAN_H
#define CT_MIXTRAN_H

#include "GasTransport.h"
#include "cantera/numerics/DenseMatrix.h"

namespace Cantera
{
//! Class MixTransport implements mixture-averaged transport properties for
//! ideal gas mixtures.
/*!
 * The model is based on that described in: R. J. Kee, M. J. Coltrin, and P.
 * Glarborg, "Chemically Reacting Flow: Theory & Practice", John Wiley & Sons,
 * 2003.
 *
 * The viscosity is computed using the Wilke mixture rule (kg /m /s)
 *
 * \f[
 *     \mu = \sum_k \frac{\mu_k X_k}{\sum_j \Phi_{k,j} X_j}.
 * \f]
 *
 * Here \f$ \mu_k \f$ is the viscosity of pure species \e k, and
 *
 * \f[
 *     \Phi_{k,j} = \frac{\left[1
 *                  + \sqrt{\left(\frac{\mu_k}{\mu_j}\sqrt{\frac{M_j}{M_k}}\right)}\right]^2}
 *                  {\sqrt{8}\sqrt{1 + M_k/M_j}}
 * \f]
 *
 * The thermal conductivity is computed from the following mixture rule:
 * \f[
 *     \lambda = 0.5 \left( \sum_k X_k \lambda_k  + \frac{1}{\sum_k X_k/\lambda_k} \right)
 * \f]
 *
 * It's used to compute the flux of energy due to a thermal gradient
 *
 * \f[
 *     j_T =  - \lambda  \nabla T
 * \f]
 *
 * The flux of energy has units of energy (kg m2 /s2) per second per area.
 *
 * The units of lambda are W / m K which is equivalent to kg m / s^3 K.
 * @ingroup tranprops
 */
class MixTransport : public GasTransport
{
public:
    //! Default constructor.
    MixTransport();

    virtual std::string transportType() const {
        return (m_mode == CK_Mode) ? "CK_Mix" : "Mix";
    }

    //! Return the thermal diffusion coefficients
    /*!
     * For this approximation, these are all zero.
     *
     * @param dt  Vector of thermal diffusion coefficients. Units = kg/m/s
     */
    virtual void getThermalDiffCoeffs(doublereal* const dt);

    //! Returns the mixture thermal conductivity (W/m /K)
    /*!
     * The thermal conductivity is computed from the following mixture rule:
     * \f[
     *     \lambda = 0.5 \left( \sum_k X_k \lambda_k  + \frac{1}{\sum_k X_k/\lambda_k} \right)
     * \f]
     *
     * It's used to compute the flux of energy due to a thermal gradient
     *
     * \f[
     *     j_T =  - \lambda  \nabla T
     * \f]
     *
     * The flux of energy has units of energy (kg m2 /s2) per second per area.
     *
     * The units of lambda are W / m K which is equivalent to kg m / s^3 K.
     *
     * @returns the mixture thermal conductivity, with units of W/m/K
     */
    virtual doublereal thermalConductivity();

    //! Get the Electrical mobilities (m^2/V/s).
    /*!
     * This function returns the mobilities. In some formulations this is equal
     * to the normal mobility multiplied by Faraday's constant.
     *
     * Here, the mobility is calculated from the diffusion coefficient using the
     * Einstein relation
     *
     * \f[
     *     \mu^e_k = \frac{F D_k}{R T}
     * \f]
     *
     * @param mobil  Returns the mobilities of the species in array \c mobil.
     *               The array must be dimensioned at least as large as the
     *               number of species.
     */
    virtual void getMobilities(doublereal* const mobil);

    //! Update the internal parameters whenever the temperature has changed
    /*!
     * This is called whenever a transport property is requested if the
     * temperature has changed since the last call to update_T().
     */
    virtual void update_T();

    //! Update the internal parameters whenever the concentrations have changed
    /*!
     * This is called whenever a transport property is requested if the
     * concentrations have changed since the last call to update_C().
     */
    virtual void update_C();

    //! Get the species diffusive mass fluxes wrt to the mass averaged velocity,
    //! given the gradients in mole fraction and temperature
    /*!
     * Units for the returned fluxes are kg m-2 s-1.
     *
     * The diffusive mass flux of species \e k is computed from
     * \f[
     *     \vec{j}_k = -n M_k D_k \nabla X_k.
     * \f]
     *
     * @param ndim      Number of dimensions in the flux expressions
     * @param grad_T    Gradient of the temperature (length = ndim)
     * @param ldx       Leading dimension of the grad_X array
     *                  (usually equal to m_nsp but not always)
     * @param grad_X    Gradients of the mole fraction. Flat vector with the
     *                  m_nsp in the inner loop. length = ldx * ndim
     * @param ldf       Leading dimension of the fluxes array
     *                  (usually equal to m_nsp but not always)
     * @param fluxes    Output of the diffusive mass fluxes. Flat vector with
     *                  the m_nsp in the inner loop. length = ldx * ndim
     */
    virtual void getSpeciesFluxes(size_t ndim, const doublereal* const grad_T,
                                  size_t ldx, const doublereal* const grad_X,
                                  size_t ldf, doublereal* const fluxes);

    virtual void init(thermo_t* thermo, int mode=0, int log_level=0);

protected:
    //! Calculate the pressure from the ideal gas law
    doublereal pressure_ig() const {
        return (m_thermo->molarDensity() * GasConstant *
                m_thermo->temperature());
    }

    //! Update the temperature dependent parts of the species thermal
    //! conductivities
    /*!
     * These are evaluated from the polynomial fits of the temperature and are
     * assumed to be independent of pressure
     */
    void updateCond_T();

    //! vector of species thermal conductivities (W/m /K)
    /*!
     * These are used in wilke's rule to calculate the viscosity of the
     * solution. units = W /m /K = kg m /s^3 /K. length = m_kk.
     */
    vector_fp m_cond;

    //! Internal storage for the calculated mixture thermal conductivity
    /*!
     *  Units = W /m /K
     */
    doublereal m_lambda;

    //! Update boolean for the species thermal conductivities
    bool m_spcond_ok;

    //! Update boolean for the mixture rule for the mixture thermal conductivity
    bool m_condmix_ok;
};
}
#endif