DustyGasTransport.h

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/**
 *  @file DustyGasTransport.h
 *    Headers for the DustyGasTransport object, which models transport properties
 *    in porous media using the dusty gas approximation
 *    (see \ref tranprops and \link Cantera::DustyGasTransport DustyGasTransport \endlink) .
 */

// Copyright 2003  California Institute of Technology


#ifndef CT_DUSTYGASTRAN_H
#define CT_DUSTYGASTRAN_H

// Cantera includes
#include "TransportBase.h"
#include "cantera/numerics/DenseMatrix.h"


namespace Cantera
{

//! Class DustyGasTransport implements the Dusty Gas model for transport in porous media.
/*!
 *    As implemented here, only species transport is handled. The viscosity, thermal conductivity, and thermal
 *    diffusion coefficients are not implemented.
 *
 *   The dusty gas model includes the effects of Darcy's law. There is a net flux of species due to a pressure gradient
 *   that is part of Darcy's law.
 *
 *   The dusty gas model expresses the value of the molar flux of species \f$ k \f$, \f$ J_k \f$ by the following formula.
 *
 *   \f[
 *       \sum_{j \ne k}{\frac{X_j J_k - X_k J_j}{D^e_{kj}}} + \frac{J_k}{\mathcal{D}^{e}_{k,knud}} =
 *               - \nabla C_k  - \frac{C_k}{\mathcal{D}^{e}_{k,knud}} \frac{\kappa}{\mu} \nabla p
 *   \f]
 *
 *  \f$ j \f$ is a sum over all species in the gas.
 *
 *  The effective Knudsen diffusion coefficients are given by the following form
 *
 *     \f[
 *        \mathcal{D}^e_{k,knud} =  \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k}  \right)^{1/2}
 *     \f]
 *
 *  The effective knudsen diffusion coefficients take into account the effects of collisions of gas-phase
 *  molecules with the wall.
 *
 *  References for the Dusty Gas Model
 *
 * (1)    H. Zhu, R. J. Kee, "Modeling Electrochemical Impedance Spectra in SOFC Button Cells with
 *       Internal Methane Reforming," J. Electrochem. Soc., 153(9) A1765-1772 (2006).
 *
 * (2)    H. Zhu, R. J. Kee, V. M. Janardhanan, O. Deutschmann, D. G. Goodwin, J. Electrochem. Soc., 152, A2427 (2005).
 *
 * (3)    E. A. Mason, A. P. Malinauskas," Gas Transport in Porous Media: the Dusty-Gas Model",
 *        American Elsevier, New York (1983).
 *
 *  (4)   J. W. Veldsink, R. M. J. van Damme, G. F. Versteeg, W. P. M. van Swaaij,
 *        "The use of the dusty gas model for the description of mass transport with chemical reaction in porous media,"
 *        Chemical Engineering Journal, 57, 115 - 125 (1995).
 */
class DustyGasTransport : public Transport
{

public:

    //! default constructor
    /*!
     *  @param thermo   Pointer to the %ThermoPhase object for this phase. Defaults to zero.
     */
    DustyGasTransport(thermo_t* thermo=0);

    //!   Copy Constructor for the %DustyGasTransport object.
    /*!
     *    @param right  %LiquidTransport to be copied
     */
    DustyGasTransport(const DustyGasTransport& right);

    //! Assignment operator
    /*!
     *
     *    Warning -> Shallow pointer copies are made of m_thermo and m_gastran.. gastran may not point to the correct
     *               object after this copy. The routine initialize() must be called after this
     *               routine to complete the copy.
     *
     * @param right    Reference to %DustyGasTransport object to be copied
     *                 into the current one.
     */
    DustyGasTransport& operator=(const  DustyGasTransport& right);

    //! Destructor.
    virtual ~DustyGasTransport();

    //! Duplication routine for objects which inherit from %Transport
    /*!
     *  This virtual routine can be used to duplicate %Transport objects
     *  inherited from %Transport even if the application only has
     *  a pointer to %Transport to work with.
     *
     *  These routines are basically wrappers around the derived copy
     *  constructor.
     */
    virtual Transport* duplMyselfAsTransport() const;

    //---------------------------------------------------------
    // overloaded base class methods

    virtual int model() const {
        return cDustyGasTransport;
    }


    //! Set the Parameters in the model
    /*!
     *    @param type     Type of the parameter to set
     *                     0 - porosity
     *                     1 - tortuosity
     *                     2 - mean pore radius
     *                     3 - mean particle radius
     *                     4 - permeability
     *    @param k        Unused int
     *    @param p         pointer to double for the input list of parameters
     *
     */
    virtual void setParameters(const int type, const int k, const doublereal* const p);


    //! Return the Multicomponent diffusion coefficients. Units: [m^2/s].
    /*!
     * Returns the array of multicomponent diffusion coefficients.
     *
     *  @param ld  The dimension of the inner loop of d (usually equal to m_nsp)
     *  @param d  flat vector of diffusion coefficients, fortran ordering.
     *            d[ld*j+i] is the D_ij diffusion coefficient (the diffusion
     *            coefficient for species i due to species j).
     */
    virtual void getMultiDiffCoeffs(const size_t ld, doublereal* const d);

    //! Get the molar fluxes [kmol/m^2/s], given the thermodynamic state at two nearby points.
    /*!
     *
     *   \f[
     *       J_k = - \sum_{j = 1, N} \left[D^{multi}_{kj}\right]^{-1} \left( \nabla C_j  + \frac{C_j}{\mathcal{D}^{knud}_j} \frac{\kappa}{\mu} \nabla p \right)
     *   \f]
     *
     * @param  state1  Array of temperature, density, and mass fractions for state 1.
     * @param  state2  Array of temperature, density, and mass  fractions for state 2.
     * @param  delta   Distance from state 1 to state 2 (m).
     *
     * @param fluxes   Vector of species molar fluxes due to diffusional driving force
     */
    virtual void getMolarFluxes(const doublereal* const state1,
                                const doublereal* const state2, const doublereal delta,
                                doublereal* const fluxes);

    //-----------------------------------------------------------
    // new methods added in this class

    //! Set the porosity (dimensionless)
    /*!
     *  @param   porosity       Set the value of the porosity
     */
    void setPorosity(doublereal porosity);

    //! Set the tortuosity (dimensionless)
    /*!
     *  Tortuosity is considered to be constant within the object
     *
     *   @param    tort   Value of the tortuosity
     */
    void setTortuosity(doublereal tort);

    //! Set the mean pore radius (m)
    /*!
     *     @param   rbar    Value of the pore radius ( m)
     */
    void setMeanPoreRadius(doublereal rbar);

    //! Set the mean particle diameter
    /*!
     *   @param dbar   Set the mean particle diameter (m)
     */
    void setMeanParticleDiameter(doublereal dbar);

    //! Set the permeability of the media
    /*!
     * If not set, the value for close-packed spheres will be used by default.
     *
     *  The value for close-packed spheres is given below, where p is the porosity,
     *  t is the tortuosity, and d is the diameter of the sphere
     *
     *  \f[
     *      \kappa = \frac{p^3 d^2}{72 t (1 - p)^2}
     *  \f]
     *
     * @param B  set the permeability of the media (units = m^2)
     */
    void setPermeability(doublereal B);

    //! Return a reference to the transport manager used to compute the gas
    //! binary diffusion coefficients and the viscosity.
    /*!
     *   @return  Returns a reference to the gas transport object
     */
    Transport& gasTransport();


    //! Make the TransportFactory object a friend, because this object has restricted its
    //! instantiation to classes which are friends.
    friend class TransportFactory;


protected:

    //!  Initialization routine called by TransportFactory
    /*!
     *  The DustyGas model is a subordinate model to the gas phase transport model. Here we
     *  set the gas phase models.
     *
     *  This is a protected routine, so that initialization of the Model must occur within Cantera's setup
     *
     *   @param  phase           Pointer to the underlying ThermoPhase model for the gas phase
     *   @param  gastr           Pointer to the underlying Transport model for transport in the gas phase.
     */
    void initialize(ThermoPhase* phase, Transport* gastr);


private:

    //! Update temperature-dependent quantities within the object
    /*!
     *  The object keeps a value m_temp, which is the temperature at which quantities were last evaluated
     *  at. If the temperature is changed, update Booleans are set false, triggering recomputation.
     */
    void updateTransport_T();

    //! Update concentration-dependent quantities within the object
    /*!
     *  The object keeps a value m_temp, which is the temperature at which quantities were last evaluated
     *  at. If the temperature is changed, update Booleans are set false, triggering recomputation.
     */
    void updateTransport_C();

    //! Private routine to update the dusty gas binary diffusion coefficients
    /*!
     *  The dusty gas binary diffusion coefficients \f$  D^{dg}_{i,j} \f$ are evaluated from the binary
     *  gas-phase diffusion coefficients \f$  D^{bin}_{i,j} \f$  using the following formula
     *
     *     \f[
     *         D^{dg}_{i,j} =  \frac{\phi}{\tau} D^{bin}_{i,j}
     *     \f]
     *
     *  where \f$ \phi \f$ is the porosity of the media and \f$ \tau \f$ is the tortuosity of the media.
     *
     */
    void updateBinaryDiffCoeffs();

    //! Private routine to update the Multicomponent diffusion coefficients that are used in the approximation
    /*!
     *  This routine updates the H matrix and then inverts it.
     */
    void updateMultiDiffCoeffs();

    //! Private routine to update the Knudsen diffusion coefficients
    /*!
     *  The Knudsen diffusion coefficients are given by the following form
     *
     *     \f[
     *        \mathcal{D}^{knud}_k =  \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k}  \right)^{1/2}
     *     \f]
     *
     */
    void updateKnudsenDiffCoeffs();

    //! Private routine to calculate the H matrix
    /*!
     *  The multicomponent diffusion H matrix \f$  H_{k,l} \f$ is given by the following form
     *
     *     \f[
     *        H_{k,l} = - \frac{X_k}{D_{k,l}}
     *     \f]
     *     \f[
     *        H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }
     *     \f]
     */
    void eval_H_matrix();

    //! Local copy of the species molecular weights
    /*!
     *  units kg /kmol
     *  length = m_nsp;
     */
    vector_fp  m_mw;

    //! binary diffusion coefficients
    DenseMatrix m_d;

    //! mole fractions
    vector_fp m_x;

    //! Knudsen diffusion coefficients
    /*!
     *  The Knudsen diffusion coefficients are given by the following form
     *
     *     \f[
     *        \mathcal{D}^{knud}_k =  \frac{2}{3} \frac{r_{pore} \phi}{\tau} \left( \frac{8 R T}{\pi W_k}  \right)^{1/2}
     *     \f]
     *
     */
    vector_fp m_dk;

    //! temperature
    doublereal m_temp;

    //! Multicomponent diffusion coefficients
    /*!
     *  The multicomponent diffusion matrix \f$  H_{k,l} \f$ is given by the following form
     *
     *     \f[
     *        H_{k,l} = - \frac{X_k}{D_{k,l}}
     *     \f]
     *     \f[
     *        H_{k,k} = \frac{1}{\mathcal(D)^{knud}_{k}} + \sum_{j \ne k}^N{ \frac{X_j}{D_{k,j}} }
     *     \f]
     */
    DenseMatrix  m_multidiff;

    //!  work space of size m_nsp;
    vector_fp  m_spwork;

    //!  work space of size m_nsp;
    vector_fp  m_spwork2;

    //! Pressure Gradient
    doublereal m_gradP;

    //! Update-to-date variable for Knudsen diffusion coefficients
    bool m_knudsen_ok;

    //! Update-to-date variable for Binary diffusion coefficients
    bool m_bulk_ok;

    //! Porosity
    doublereal m_porosity;

    //! Tortuosity
    doublereal m_tortuosity;

    //! Pore radius (meter)
    doublereal m_pore_radius;

    //! Particle diameter
    /*!
     *   The medium is assumed to consist of particles of size m_diam
     *   units =  m
     */
    doublereal m_diam;

    //! Permeability of the media
    /*!
     *  The permeability is the proportionality constant for Darcy's
     *  law which relates discharge rate and viscosity to the applied
     *  pressure gradient.
     *
     *   Below is Darcy's law, where \f$ \kappa \f$ is the permeability
     *
     *     \f[
     *         v = \frac{\kappa}{\mu} \frac{\delta P}{\delta x}
     *     \f]
     *
     *  units are m2
     */
    doublereal m_perm;

    //! Pointer to the transport object for the gas phase
    /*!
     * Note, this object owns the gastran object
     */
    Transport* m_gastran;

};
}
#endif