SimpleTransport.h

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/**
 *  @file SimpleTransport.h
 *   Header file for the class SimpleTransport which provides simple
 *   transport properties for liquids and solids
 *   (see \ref tranprops and \link Cantera::SimpleTransport SimpleTransport \endlink) .
 */
#ifndef CT_SIMPLETRAN_H
#define CT_SIMPLETRAN_H

#include "LiquidTransportParams.h"

namespace Cantera
{
//! Class SimpleTransport implements mixture-averaged transport
//! properties for liquid phases.
/*!
 *  The model is based on that described by Newman, Electrochemical Systems
 *
 *  The velocity of species i may be described by the
 *  following equation p. 297 (12.1)
 *
 *   \f[
 *     c_i \nabla \mu_i = R T \sum_j \frac{c_i c_j}{c_T D_{ij}}
 *         (\mathbf{v}_j - \mathbf{v}_i)
 *   \f]
 *
 * This as written is degenerate by 1 dof.
 *
 * To fix this we must add in the definition of the mass averaged
 * velocity of the solution. We will call the simple bold-faced
 *  \f$\mathbf{v} \f$
 * symbol the mass-averaged velocity. Then, the relation
 * between \f$\mathbf{v}\f$ and the individual species velocities is
 * \f$\mathbf{v}_i\f$
 *
 *  \f[
 *      \rho_i \mathbf{v}_i =  \rho_i \mathbf{v} + \mathbf{j}_i
 *  \f]
 *   where \f$\mathbf{j}_i\f$ are the diffusional fluxes of species i
 *   with respect to the mass averaged velocity and
 *
 *  \f[
 *       \sum_i \mathbf{j}_i = 0
 *  \f]
 *
 *  and
 *
 *  \f[
 *     \sum_i \rho_i \mathbf{v}_i =  \rho \mathbf{v}
 *  \f]
 *
 * Using these definitions, we can write
 *
 *  \f[
 *      \mathbf{v}_i =  \mathbf{v} + \frac{\mathbf{j}_i}{\rho_i}
 *  \f]
 *
 *  \f[
 *     c_i \nabla \mu_i = R T \sum_j \frac{c_i c_j}{c_T D_{ij}}
 *         (\frac{\mathbf{j}_j}{\rho_j} - \frac{\mathbf{j}_i}{\rho_i})
 *         =  R T \sum_j \frac{1}{D_{ij}}
 *         (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i})
 *  \f]
 *
 * The equations that we actually solve are
 *
 *  \f[
 *     c_i \nabla \mu_i =
 *         =  R T \sum_j \frac{1}{D_{ij}}
 *         (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i})
 *  \f]
 *  and we replace the 0th equation with the following:
 *
 *  \f[
 *       \sum_i \mathbf{j}_i = 0
 *  \f]
 *
 *  When there are charged species, we replace the RHS with the
 *  gradient of the electrochemical potential to obtain the
 *  modified equation
 *
 *  \f[
 *     c_i \nabla \mu_i + c_i F z_i \nabla \Phi
 *         =  R T \sum_j \frac{1}{D_{ij}}
 *         (\frac{x_i \mathbf{j}_j}{M_j} - \frac{x_j \mathbf{j}_i}{M_i})
 *  \f]
 *
 * With this formulation we may solve for the diffusion velocities,
 * without having to worry about what the mass averaged velocity
 * is.
 *
 *  <H2> Viscosity Calculation  </H2>
 *
 *  The viscosity calculation may be broken down into two parts.
 *  In the first part, the viscosity of the pure species are calculated
 *  In the second part, a mixing rule is applied. There are two mixing rules.
 *  Solvent-only and mixture-averaged.
 *
 *  For the solvent-only mixing rule, we use the pure species viscosity calculated for
 *  the solvent as the viscosity of the entire mixture. For the mixture averaged rule
 *  we do a mole fraction based average of the pure species viscosities:
 *
 *  Solvent-only:
 *    \f[
 *         \mu = \mu_0
 *    \f]
 *  Mixture-average:
 *    \f[
 *         \mu = \sum_k {\mu_k X_k}
 *    \f]
 *
 *  <H2> Calculate of the Binary Diffusion Coefficients </H2>
 *
 *  The binary diffusion coefficients are obtained from the pure species diffusion coefficients
 *  using an additive process
 *
 *    \f[
 *        D_{i,j} = \frac{1}{2} \left( D^0_i(T) +  D^0_j(T) \right)
 *    \f]
 *
 *  <H2> Electrical Mobilities </H2>
 *
 *   The mobility \f$  \mu^e_k \f$  is calculated from the diffusion coefficient using the Einstein relation.
 *
 *     \f[
 *          \mu^e_k = \frac{F D_k}{R T}
 *     \f]
 *
 *   The diffusion coefficients,  \f$  D_k \f$ , is calculated from a call to the mixture diffusion
 *   coefficient routine.
 *
 *  <H2> Species Diffusive Fluxes </H2>
 *
 *  The diffusive mass flux of species \e k is computed from the following
 *  formula
 *
 *  Usually the specified solution average velocity is the mass averaged velocity.
 *  This is changed in some subclasses, however.
 *
 *    \f[
 *         j_k = - c^T M_k D_k \nabla X_k - \rho Y_k V_c
 *    \f]
 *
 *    where V_c is the correction velocity
 *
 *    \f[
 *         \rho V_c =  - \sum_j {c^T M_j D_j \nabla X_j}
 *    \f]
 *
 *  In the above equation, \f$ D_k \f$ is the mixture diffusivity for species k calculated for the current
 *  conditions, which may depend on T, P, and X_k. \f$ C^T \f$ is the total concentration of the phase.
 *
 *  When this is electrical migration, the formulas above are enhanced to
 *
 *    \f[
 *         j_k = - C^T M_k D_k \nabla X_k  + F C^T M_k \frac{D_k}{ R T } X_k z_k   \nabla V   - \rho Y_k V_c
 *    \f]
 *
 *   where V_c is the correction velocity
 *
 *    \f[
 *         \rho V_c =  - \sum_j {c^T M_j D_j \nabla X_j} + \sum_j  F C^T M_j \frac{D_j}{ R T } X_j z_j  \nabla V
 *    \f]
 *
 *  <H2> Species Diffusional Velocities </H2>
 *
 *  Species diffusional velocities are calculated from the species diffusional fluxes, within this object,
 *  using the following formula for the diffusional velocity of the kth species, \f$  V_k^d \f$
 *
 *     \f[
 *         j_k = \rho Y_k V_k^d
 *     \f]
 *
 *         TODO
 *   This object has to be made compatible with different types of reference velocities. Right now, elements
 *   of the formulas are only compatible with the mass-averaged velocity.
 *
 *  @ingroup tranprops
 */
class SimpleTransport : public Transport
{
public:
    //! Default constructor.
    /*!
     * This requires call to initLiquid(LiquidTransportParams& tr)
     * after filling LiquidTransportParams to complete instantiation.
     * The filling of LiquidTransportParams is currently carried out
     * in the TransportFactory class, but might be moved at some point.
     *
     * @param thermo  ThermoPhase object holding species information.
     * @param ndim    Number of spatial dimensions.
     */
    SimpleTransport(thermo_t* thermo = 0, int ndim = 1);

    SimpleTransport(const SimpleTransport& right);
    SimpleTransport& operator=(const  SimpleTransport& right);
    virtual Transport* duplMyselfAsTransport() const;
    virtual ~SimpleTransport();

    //! Initialize the transport object
    /*!
     * Here we change all of the internal dimensions to be sufficient.
     * We get the object ready to do property evaluations.
     *
     * @param tr  Transport parameters for all of the species in the phase.
     */
    virtual bool initLiquid(LiquidTransportParams& tr);

    virtual int model() const {
        return cSimpleTransport;
    }

    //! Returns the mixture viscosity of the solution
    /*!
     * The viscosity is computed using the general mixture rules
     * specified in the variable compositionDepType_.
     *
     * Solvent-only:
     *    \f[
     *         \mu = \mu_0
     *    \f]
     * Mixture-average:
     *    \f[
     *         \mu = \sum_k {\mu_k X_k}
     *    \f]
     *
     * Here \f$ \mu_k \f$ is the viscosity of pure species \e k.
     *
     * units are Pa s  or kg/m/s
     *
     * @see updateViscosity_T();
     */
    virtual doublereal viscosity();

    //! Returns the pure species viscosities
    /*!
     *  The pure species viscosities are to be given in an Arrhenius
     *  form in accordance with activated-jump-process dominated transport.
     *
     * units are Pa s  or kg/m/s
     *
     *  @param visc Return the species viscosities as a vector of length m_nsp
     */
    virtual void getSpeciesViscosities(doublereal* const visc);

    //! Returns the binary diffusion coefficients
    /*!
     *   @param ld
     *   @param d
     */
    virtual void getBinaryDiffCoeffs(const size_t ld, doublereal* const d);

    //! Get the Mixture diffusion coefficients
    /*!
     *  @param d vector of mixture diffusion coefficients
     *          units = m2 s-1. length = number of species
     */
    virtual void getMixDiffCoeffs(doublereal* const d);

    //! Return the thermal diffusion coefficients
    /*!
     *  These are all zero for this simple implementation
     *
     *  @param dt thermal diffusion coefficients
     */
    virtual void getThermalDiffCoeffs(doublereal* const dt);

    //! Returns the mixture thermal conductivity of the solution
    /*!
     * The thermal is computed using the general mixture rules
     * specified in the variable compositionDepType_.
     *
     *  Controlling update boolean = m_condmix_ok
     *
     *  Units are in W/m/K  or equivalently kg m / s3 / K
     *
     * Solvent-only:
     *    \f[
     *         \lambda = \lambda_0
     *
     *    \f]
     * Mixture-average:
     *    \f[
     *         \lambda = \sum_k {\lambda_k X_k}
     *    \f]
     *
     * Here \f$ \lambda_k \f$ is the thermal conductivity of pure species \e k.
     *
     * @see updateCond_T();
     */
    virtual doublereal thermalConductivity();

    virtual void getMobilities(doublereal* const mobil_e);

    virtual void getFluidMobilities(doublereal* const mobil_f);

    //! Specify the value of the gradient of the voltage
    /*!
     * @param grad_V Gradient of the voltage (length num dimensions);
     */
    virtual void set_Grad_V(const doublereal* const grad_V);

    //! Specify the value of the gradient of the temperature
    /*!
     * @param grad_T Gradient of the temperature (length num dimensions);
     */
    virtual void set_Grad_T(const doublereal* const grad_T);

    //! Specify the value of the gradient of the MoleFractions
    /*!
     * @param grad_X Gradient of the mole fractions(length nsp * num dimensions);
     */
    virtual void set_Grad_X(const doublereal* const grad_X);

    //! Get the species diffusive velocities wrt to the averaged velocity,
    //! given the gradients in mole fraction and temperature
    /*!
     * The average velocity can be computed on a mole-weighted
     * or mass-weighted basis, or the diffusion velocities may
     * be specified as relative to a specific species (i.e. a
     * solvent) all according to the velocityBasis input parameter.
     *
     *  Units for the returned velocities are m s-1.
     *
     *  @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 Vdiff  Output of the diffusive velocities.
     *             Flat vector with the m_nsp in the inner loop.
     *             length = ldx * ndim
     */
    virtual void getSpeciesVdiff(size_t ndim,
                                 const doublereal* grad_T,
                                 int ldx,
                                 const doublereal* grad_X,
                                 int ldf,
                                 doublereal* Vdiff);

    //! Get the species diffusive velocities wrt to the averaged velocity,
    //! given the gradients in mole fraction, temperature and electrostatic potential.
    /*!
     * The average velocity can be computed on a mole-weighted
     * or mass-weighted basis, or the diffusion velocities may
     * be specified as relative to a specific species (i.e. a
     * solvent) all according to the velocityBasis input parameter.
     *
     *  Units for the returned velocities are m s-1.
     *
     *  @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 grad_Phi   Gradients of the electrostatic potential
     *                        (length = ndim)
     * @param Vdiff      Output of the species diffusion velocities
     *                   Flat vector with the m_nsp in the inner loop.
     *                     length = ldx * ndim
     */
    virtual void getSpeciesVdiffES(size_t ndim, const doublereal* grad_T,
                                   int ldx,  const doublereal* grad_X,
                                   int ldf,  const doublereal* grad_Phi,
                                   doublereal* Vdiff);

    //! Get the species diffusive mass fluxes wrt to the specified solution averaged velocity,
    //! given the gradients in mole fraction and temperature
    /*!
     *  units = kg/m2/s
     *
     *  The diffusive mass flux of species \e k is computed from the following
     *  formula
     *
     *  Usually the specified solution average velocity is the mass averaged velocity.
     *  This is changed in some subclasses, however.
     *
     *    \f[
     *         j_k = - \rho M_k D_k \nabla X_k - Y_k V_c
     *    \f]
     *
     *    where V_c is the correction velocity
     *
     *    \f[
     *         V_c =  - \sum_j {\rho M_j D_j \nabla X_j}
     *    \f]
     *
     * @param ndim     The number of spatial dimensions (1, 2, or 3).
     * @param grad_T   The temperature gradient (ignored in this model).
     * @param ldx      Leading dimension of the grad_X array.
     * @param grad_X   Gradient of the mole fractions(length nsp * num dimensions);
     * @param ldf      Leading dimension of the fluxes array.
     * @param fluxes   Output fluxes of species.
     */
    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);

    //!  Return the species diffusive mass fluxes wrt to
    //!  the mass averaged velocity,
    /*!
     *  units = kg/m2/s
     *
     * Internally, gradients in the in mole fraction, temperature
     * and electrostatic potential contribute to the diffusive flux
     *
     * The diffusive mass flux of species \e k is computed from the following
     * formula
     *
     *    \f[
     *         j_k = - \rho M_k D_k \nabla X_k - Y_k V_c
     *    \f]
     *
     *    where V_c is the correction velocity
     *
     *    \f[
     *         V_c =  - \sum_j {\rho M_j D_j \nabla X_j}
     *    \f]
     *
     *  @param ldf     stride of the fluxes array. Must be equal to
     *                 or greater than the number of species.
     *  @param fluxes  Vector of calculated fluxes
     */
    virtual void getSpeciesFluxesExt(size_t ldf, doublereal* fluxes);

protected:
    //! Handles the effects of changes in the Temperature, internally
    //! within the object.
    /*!
     *  This is called whenever a transport property is requested.
     *  The first task is to check whether the temperature has changed
     *  since the last call to update_T().
     *  If it hasn't then an immediate return is carried out.
     *
     * @return  Returns true if the temperature has changed, and false otherwise
     */
    virtual bool update_T();

    //! Handles the effects of changes in the mixture concentration
    /*!
     *   This is called for every interface call to check whether
     *   the concentrations have changed. Concentrations change
     *   whenever the pressure or the mole fraction has changed.
     *   If it has changed, the recalculations should be done.
     *
     *   Note this should be a lightweight function since it's
     *   part of all of the interfaces.
     */
    virtual bool update_C();

    //!  Update the temperature-dependent viscosity terms.
    //!  Updates the array of pure species viscosities, and the
    //!  weighting functions in the viscosity mixture rule.
    /*!
     * The flag m_visc_temp_ok is set to true.
     */
    void updateViscosity_T();

    //! Update the temperature-dependent parts of the mixture-averaged
    //! thermal conductivity.
    void updateCond_T();

    //! Update the concentration parts of the viscosities
    /*!
     *  Internal routine is run whenever the update_boolean is false. This
     *  routine will calculate internal values for the species viscosities.
     */
    void updateViscosities_C();

    //! Update the binary diffusion coefficients wrt T.
    /*!
     *   These are evaluated from the polynomial fits at unit pressure (1 Pa).
     */
    void updateDiff_T();

private:
    //! Temperature dependence type
    /*!
     *     The following coefficients are allowed to have simple
     *     temperature dependencies:
     *         mixture viscosity
     *         mixture thermal conductivity
     *         diffusitivy
     *
     *  Types of temperature dependencies:
     *     0  - Independent of temperature (only one implemented so far)
     *     1  - extended arrhenius form
     *     2  - polynomial in temperature form
     */
    int tempDepType_;

    //! Composition dependence of the transport properties
    /*!
     *   The following coefficients are allowed to have simple composition dependencies
     *
     *       mixture viscosity
     *       mixture thermal conductivity
     *
     *   Permissible types of composition dependencies
     *    0 - Solvent values (i.e., species 0) contributes only
     *    1 - linear combination of mole fractions;
     */
    enum LiquidTranMixingModel compositionDepType_;

    //! Boolean indicating whether to use the hydrodynamic radius formulation
    /*!
     * If true, then the diffusion coefficient is calculated from the
     * hydrodynamic radius.
     */
    bool useHydroRadius_;

    //! Boolean indicating whether electro-migration term should be added
    bool doMigration_;

    //! Local Copy of the molecular weights of the species
    /*!
     *  Length is Equal to the number of species in the mechanism.
     */
    vector_fp  m_mw;

    //! Pure species viscosities in Arrhenius temperature-dependent form.
    std::vector<LTPspecies*>  m_coeffVisc_Ns;

    //! Pure species thermal conductivities in Arrhenius temperature-dependent form.
    std::vector<LTPspecies*>  m_coeffLambda_Ns;

    //! Pure species viscosities in Arrhenius temperature-dependent form.
    std::vector<LTPspecies*>  m_coeffDiff_Ns;

    //! Hydrodynamic radius in LTPspecies form
    std::vector<LTPspecies*>  m_coeffHydroRadius_Ns;

    //! Internal value of the gradient of the mole fraction vector
    /*!
     *  Note, this is the only gradient value that can and perhaps
     *  should reflect the true state of the mole fractions in the
     *  application solution vector. In other words no cropping or
     *  massaging of the values to make sure they are above zero
     *  should occur. - developing ....
     *
     *  m_nsp is the number of species in the fluid
     *  k is the species index
     *  n is the dimensional index (x, y, or z). It has a length
     *    equal to m_nDim
     *
     *    m_Grad_X[n*m_nsp + k]
     */
    vector_fp m_Grad_X;

    //! Internal value of the gradient of the Temperature vector
    /*!
     *  Generally, if a transport property needs this in its evaluation it
     *  will look to this place to get it.
     *
     *  No internal property is precalculated based on gradients. Gradients
     *  are assumed to be freshly updated before every property call.
     */
    vector_fp m_Grad_T;

    //! Internal value of the gradient of the Pressure vector
    /*!
     *  Generally, if a transport property needs this in its evaluation it
     *  will look to this place to get it.
     *
     *  No internal property is precalculated based on gradients. Gradients
     *  are assumed to be freshly updated before every property call.
     */
    vector_fp m_Grad_P;

    //! Internal value of the gradient of the Electric Voltage
    /*!
     *  Generally, if a transport property needs this in its evaluation it
     *  will look to this place to get it.
     *
     *  No internal property is precalculated based on gradients. Gradients
     *  are assumed to be freshly updated before every property call.
     */
    vector_fp m_Grad_V;

    // property values

    //! Vector of Species Diffusivities
    /*!
     *   Depends on the temperature. We have set the pressure dependence
     *   to zero for this liquid phase constituitve model
     *
     *   units m2/s
     */
    vector_fp m_diffSpecies;

    //! Species viscosities
    /*!
     *   Viscosity of the species
     *   Length = number of species
     *
     *   Depends on the temperature. We have set the pressure dependence
     *   to zero for this model
     *
     * controlling update boolean -> m_visc_temp_ok
     */
    vector_fp m_viscSpecies;

    //! Internal value of the species individual thermal conductivities
    /*!
     * Then a mixture rule is applied to get the solution conductivities
     *
     * Depends on the temperature and perhaps pressure, but
     * not the species concentrations
     *
     * controlling update boolean -> m_cond_temp_ok
     */
    vector_fp  m_condSpecies;

    //! State of the mole fraction vector.
    int m_iStateMF;

    //! Local copy of the mole fractions of the species in the phase
    /*!
     *  The mole fractions here are assumed to be bounded by 0.0 and 1.0
     *  and they are assumed to add up to one exactly. This mole
     *  fraction vector comes from the ThermoPhase object. Derivative
     *  quantities from this are referred to as bounded.
     *
     * Update info?
     * length = m_nsp
     */
    vector_fp m_molefracs;

    //! Local copy of the concentrations of the species in the phase
    /*!
     *  The concentrations are consistent with the m_molefracs
     *  vector which is bounded and sums to one.
     *
     * Update info?
     * length = m_nsp
     */
    vector_fp m_concentrations;

    //! Local copy of the total concentration.
    /*!
     * This is consistent with the m_concentrations[] and
     *  m_molefracs[] vector.
     */
    doublereal concTot_;

    //! Mean molecular weight
    doublereal meanMolecularWeight_;

    //! Density
    doublereal dens_;

    //! Local copy of the charge of each species
    /*!
     *  Contains the charge of each species (length m_nsp)
     */
    vector_fp m_chargeSpecies;

    //! Current Temperature -> locally stored
    /*!
     * This is used to test whether new temperature computations
     * should be performed.
     */
    doublereal m_temp;

    //! Current value of the pressure
    doublereal m_press;

    //! Saved value of the mixture thermal conductivity
    doublereal m_lambda;

    //! Saved value of the mixture viscosity
    doublereal m_viscmix;

    //! work space
    /*!
     *   Length is equal to m_nsp
     */
    vector_fp  m_spwork;

    vector_fp m_fluxes;

private:
    //! Boolean indicating that the top-level mixture viscosity is current
    /*!
     *  This is turned false for every change in T, P, or C.
     */
    bool m_visc_mix_ok;

    //! Boolean indicating that weight factors wrt viscosity is current
    bool m_visc_temp_ok;

    //! Boolean indicating that mixture diffusion coeffs are current
    bool m_diff_mix_ok;

    //! Boolean indicating that binary diffusion coeffs are current
    bool m_diff_temp_ok;

    //! Flag to indicate that the pure species conductivities
    //! are current wrt the temperature
    bool m_cond_temp_ok;

    //! Boolean indicating that mixture conductivity is current
    bool m_cond_mix_ok;

    //! Number of dimensions
    /*!
     * Either 1, 2, or 3
     */
    size_t m_nDim;

    //! Temporary variable that stores the rho Vc value
    double rhoVc[3];
};
}
#endif