IdealGasPhase.h

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/**
 *  @file IdealGasPhase.h
 *   ThermoPhase object for the ideal gas equation of
 * state - workhorse for %Cantera (see @ref thermoprops
 * and class @link Cantera::IdealGasPhase IdealGasPhase@endlink).
 */
 
// This file is part of Cantera. See License.txt in the top-level directory or
// at https://cantera.org/license.txt for license and copyright information.
 
#ifndef CT_IDEALGASPHASE_H
#define CT_IDEALGASPHASE_H
 
#include "ThermoPhase.h"
 
namespace Cantera
{
 
//! Class IdealGasPhase represents low-density gases that obey the ideal gas
//! equation of state.
/*!
 *
 * IdealGasPhase derives from class ThermoPhase, and overloads the virtual
 * methods defined there with ones that use expressions appropriate for ideal
 * gas mixtures.
 *
 * The independent unknowns are density, mass fraction, and temperature. the
 * #setPressure() function will calculate the density consistent with the
 * current mass fraction vector and temperature and the desired pressure, and
 * then set the density.
 *
 * ## Specification of Species Standard State Properties
 *
 * It is assumed that the reference state thermodynamics may be obtained by a
 * pointer to a populated species thermodynamic property manager class in the
 * base class, ThermoPhase::m_spthermo (see the base class @link
 * Cantera::MultiSpeciesThermo MultiSpeciesThermo @endlink for a description of
 * the specification of reference state species thermodynamics functions). The
 * reference state, where the pressure is fixed at a single pressure, is a key
 * species property calculation for the Ideal Gas Equation of state.
 *
 * This class is optimized for speed of execution. All calls to thermodynamic
 * functions first call internal routines (aka #enthalpy_RT_ref()) which return
 * references the reference state thermodynamics functions. Within these
 * internal reference state functions, the function #updateThermo() is called,
 * that first checks to see whether the temperature has changed. If it has, it
 * updates the internal reference state thermo functions by calling the
 * MultiSpeciesThermo object.
 *
 * Functions for the calculation of standard state properties for species at
 * arbitrary pressure are provided in IdealGasPhase. However, they are all
 * derived from their reference state counterparts.
 *
 * The standard state enthalpy is independent of pressure:
 *
 * @f[
 *      h^o_k(T,P) = h^{ref}_k(T)
 * @f]
 *
 * The standard state constant-pressure heat capacity is independent of pressure:
 *
 * @f[
 *      Cp^o_k(T,P) = Cp^{ref}_k(T)
 * @f]
 *
 * The standard state entropy depends in the following fashion on pressure:
 *
 * @f[
 *      S^o_k(T,P) = S^{ref}_k(T) -  R \ln(\frac{P}{P_{ref}})
 * @f]
 * The standard state Gibbs free energy is obtained from the enthalpy and entropy
 * functions:
 *
 * @f[
 *      \mu^o_k(T,P) =  h^o_k(T,P) - S^o_k(T,P) T
 * @f]
 *
 * @f[
 *      \mu^o_k(T,P) =  \mu^{ref}_k(T) + R T \ln( \frac{P}{P_{ref}})
 * @f]
 *
 * where
 * @f[
 *      \mu^{ref}_k(T) =   h^{ref}_k(T)   - T S^{ref}_k(T)
 * @f]
 *
 * The standard state internal energy is obtained from the enthalpy function also
 *
 * @f[
 *      u^o_k(T,P) = h^o_k(T) - R T
 * @f]
 *
 * The molar volume of a species is given by the ideal gas law
 *
 * @f[
 *      V^o_k(T,P) = \frac{R T}{P}
 * @f]
 *
 * where R is the molar gas constant. For a complete list of physical constants
 * used within %Cantera, see @ref physConstants .
 *
 * ## Specification of Solution Thermodynamic Properties
 *
 * The activity of a species defined in the phase is given by the ideal gas law:
 * @f[
 *      a_k = X_k
 * @f]
 * where @f$ X_k @f$ is the mole fraction of species *k*. The chemical potential
 * for species *k* is equal to
 *
 * @f[
 *      \mu_k(T,P) = \mu^o_k(T, P) + R T \ln X_k
 * @f]
 *
 * In terms of the reference state, the above can be rewritten
 *
 * @f[
 *      \mu_k(T,P) = \mu^{ref}_k(T, P) + R T \ln \frac{P X_k}{P_{ref}}
 * @f]
 *
 * The partial molar entropy for species *k* is given by the following relation,
 *
 * @f[
 *      \tilde{s}_k(T,P) = s^o_k(T,P) - R \ln X_k = s^{ref}_k(T) - R \ln \frac{P X_k}{P_{ref}}
 * @f]
 *
 * The partial molar enthalpy for species *k* is
 *
 * @f[
 *      \tilde{h}_k(T,P) = h^o_k(T,P) = h^{ref}_k(T)
 * @f]
 *
 * The partial molar Internal Energy for species *k* is
 *
 * @f[
 *      \tilde{u}_k(T,P) = u^o_k(T,P) = u^{ref}_k(T)
 * @f]
 *
 * The partial molar Heat Capacity for species *k* is
 *
 * @f[
 *      \tilde{Cp}_k(T,P) = Cp^o_k(T,P) = Cp^{ref}_k(T)
 * @f]
 *
 * ## Application within Kinetics Managers
 *
 * @f$ C^a_k @f$ are defined such that @f$ a_k = C^a_k / C^s_k, @f$ where @f$
 * C^s_k @f$ is a standard concentration defined below and @f$ a_k @f$ are
 * activities used in the thermodynamic functions.  These activity (or
 * generalized) concentrations are used by kinetics manager classes to compute
 * the forward and reverse rates of elementary reactions. The activity
 * concentration,@f$  C^a_k @f$,is given by the following expression.
 *
 * @f[
 *      C^a_k = C^s_k  X_k  = \frac{P}{R T} X_k
 * @f]
 *
 * The standard concentration for species *k* is independent of *k* and equal to
 *
 * @f[
 *     C^s_k =  C^s = \frac{P}{R T}
 * @f]
 *
 * For example, a bulk-phase binary gas reaction between species j and k,
 * producing a new gas species l would have the following equation for its rate
 * of progress variable, @f$ R^1 @f$, which has units of kmol m-3 s-1.
 *
 * @f[
 *    R^1 = k^1 C_j^a C_k^a =  k^1 (C^s a_j) (C^s a_k)
 * @f]
 * where
 * @f[
 *    C_j^a = C^s a_j \quad \mbox{and} \quad C_k^a = C^s a_k
 * @f]
 *
 * @f$ C_j^a @f$ is the activity concentration of species j, and
 * @f$ C_k^a @f$ is the activity concentration of species k. @f$ C^s @f$ is the
 * standard concentration. @f$ a_j @f$ is the activity of species j which is
 * equal to the mole fraction of j.
 *
 * The reverse rate constant can then be obtained from the law of microscopic
 * reversibility and the equilibrium expression for the system.
 *
 * @f[
 *     \frac{a_j a_k}{ a_l} = K_a^{o,1} = \exp(\frac{\mu^o_l - \mu^o_j - \mu^o_k}{R T} )
 * @f]
 *
 * @f$  K_a^{o,1} @f$ is the dimensionless form of the equilibrium constant,
 * associated with the pressure dependent standard states @f$ \mu^o_l(T,P) @f$
 * and their associated activities, @f$ a_l @f$, repeated here:
 *
 * @f[
 *      \mu_l(T,P) = \mu^o_l(T, P) + R T \ln a_l
 * @f]
 *
 * We can switch over to expressing the equilibrium constant in terms of the
 * reference state chemical potentials
 *
 * @f[
 *     K_a^{o,1} = \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{P}
 * @f]
 *
 * The concentration equilibrium constant, @f$ K_c @f$, may be obtained by
 * changing over to activity concentrations. When this is done:
 *
 * @f[
 *       \frac{C^a_j C^a_k}{ C^a_l} = C^o K_a^{o,1} = K_c^1 =
 *           \exp(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} ) * \frac{P_{ref}}{RT}
 * @f]
 *
 * %Kinetics managers will calculate the concentration equilibrium constant,
 * @f$ K_c @f$, using the second and third part of the above expression as a
 * definition for the concentration equilibrium constant.
 *
 * For completeness, the pressure equilibrium constant may be obtained as well
 *
 * @f[
 *       \frac{P_j P_k}{ P_l P_{ref}} = K_p^1 =
 *           \exp\left(\frac{\mu^{ref}_l - \mu^{ref}_j - \mu^{ref}_k}{R T} \right)
 * @f]
 *
 * @f$ K_p @f$ is the simplest form of the equilibrium constant for ideal gases.
 * However, it isn't necessarily the simplest form of the equilibrium constant
 * for other types of phases; @f$ K_c @f$ is used instead because it is
 * completely general.
 *
 * The reverse rate of progress may be written down as
 * @f[
 *    R^{-1} = k^{-1} C_l^a =  k^{-1} (C^o a_l)
 * @f]
 *
 * where we can use the concept of microscopic reversibility to write the
 * reverse rate constant in terms of the forward rate constant and the
 * concentration equilibrium constant, @f$ K_c @f$.
 *
 * @f[
 *    k^{-1} =  k^1 K^1_c
 * @f]
 *
 * @f$ k^{-1} @f$ has units of s-1.
 *
 * ## YAML Example
 *
 * An example ideal gas phase definition is given in the
 * [YAML API Reference](../yaml/phases.html#ideal-gas).
 *
 * @ingroup thermoprops
 */
class IdealGasPhase: public ThermoPhase
{
public:
    //! Construct and initialize an IdealGasPhase ThermoPhase object
    //! directly from an input file
    /*!
     * @param inputFile Name of the input file containing the phase definition
     *                  to set up the object. If blank, an empty phase will be
     *                  created.
     * @param id        ID of the phase in the input file. Defaults to the
     *                  empty string.
     */
    explicit IdealGasPhase(const string& inputFile="", const string& id="");
 
    string type() const override {
        return "ideal-gas";
    }
 
    bool isIdeal() const override {
        return true;
    }
 
    //! String indicating the mechanical phase of the matter in this Phase.
    /*!
     * For the `IdealGasPhase`, this string is always `gas`.
     */
    string phaseOfMatter() const override {
        return "gas";
    }
 
    //! @name Molar Thermodynamic Properties of the Solution
    //! @{
 
    //! Return the Molar enthalpy. Units: J/kmol.
    /*!
     * For an ideal gas mixture,
     * @f[
     * \hat h(T) = \sum_k X_k \hat h^0_k(T),
     * @f]
     * and is a function only of temperature. The standard-state pure-species
     * enthalpies @f$ \hat h^0_k(T) @f$ are computed by the species
     * thermodynamic property manager.
     *
     * @see MultiSpeciesThermo
     */
    double enthalpy_mole() const override {
        return RT() * mean_X(enthalpy_RT_ref());
    }
 
    /**
     * Molar entropy. Units: J/kmol/K.
     * For an ideal gas mixture,
     * @f[
     * \hat s(T, P) = \sum_k X_k \hat s^0_k(T) - \hat R \ln \frac{P}{P^0}.
     * @f]
     * The reference-state pure-species entropies @f$ \hat s^0_k(T) @f$ are
     * computed by the species thermodynamic property manager.
     * @see MultiSpeciesThermo
     */
    double entropy_mole() const override;
 
    /**
     * Molar heat capacity at constant pressure and composition [J/kmol/K].
     * For an ideal gas mixture,
     * @f[
     * \hat c_p(t) = \sum_k \hat c^0_{p,k}(T).
     * @f]
     * The reference-state pure-species heat capacities @f$ \hat c^0_{p,k}(T) @f$
     * are computed by the species thermodynamic property manager.
     * @see MultiSpeciesThermo
     */
    double cp_mole() const override;
 
    /**
     * Molar heat capacity at constant volume and composition [J/kmol/K].
     * For an ideal gas mixture,
     * @f[ \hat c_v = \hat c_p - \hat R. @f]
     */
    double cv_mole() const override;
 
    //! @}
    //! @name Mechanical Equation of State
    //! @{
 
    /**
     * Pressure. Units: Pa.
     * For an ideal gas mixture,
     * @f[ P = n \hat R T. @f]
     */
    double pressure() const override {
        return GasConstant * molarDensity() * temperature();
    }
 
    //! Set the pressure at constant temperature and composition.
    /*!
     * Units: Pa.
     * This method is implemented by setting the mass density to
     * @f[
     * \rho = \frac{P \overline W}{\hat R T }.
     * @f]
     *
     * @param p Pressure (Pa)
     */
    void setPressure(double p) override {
        setDensity(p * meanMolecularWeight() / RT());
    }
 
    //! Set the density and pressure at constant composition.
    /*!
     * Units: kg/m^3, Pa.
     * This method is implemented by setting the density to the input value and
     * setting the temperature to
     * @f[
     * T = \frac{P \overline W}{\hat R \rho}.
     * @f]
     *
     * @param rho Density (kg/m^3)
     * @param p Pressure (Pa)
     * @since New in %Cantera 3.0.
     */
    void setState_DP(double rho, double p) override {
        if (p <= 0) {
            throw CanteraError("IdealGasPhase::setState_DP",
                               "pressure must be positive");
        }
        setDensity(rho);
        setTemperature(p * meanMolecularWeight() / (GasConstant * rho));
    }
 
    //! Returns the isothermal compressibility. Units: 1/Pa.
    /**
     * The isothermal compressibility is defined as
     * @f[
     * \kappa_T = -\frac{1}{v}\left(\frac{\partial v}{\partial P}\right)_T
     * @f]
     *  For ideal gases it's equal to the inverse of the pressure
     */
    double isothermalCompressibility() const override {
        return 1.0 / pressure();
    }
 
    //! Return the volumetric thermal expansion coefficient. Units: 1/K.
    /*!
     * The thermal expansion coefficient is defined as
     * @f[
     * \beta = \frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_P
     * @f]
     * For ideal gases, it's equal to the inverse of the temperature.
     */
    double thermalExpansionCoeff() const override {
        return 1.0 / temperature();
    }
 
    //! Return the internal pressure. Units: Pa.
    /*!
     * For ideal gases, @f$ (\partial P/\partial T)_V = P/T @f$, so
     * @f$ \pi_T = T(P/T) - P = 0 @f$.
     */
    double internalPressure() const override {
        return 0.0;
    }
 
    double soundSpeed() const override;
 
    //! @}
    //! @name Chemical Potentials and Activities
    //!
    //! The activity @f$ a_k @f$ of a species in solution is
    //! related to the chemical potential by
    //! @f[
    //!  \mu_k(T,P,X_k) = \mu_k^0(T,P) + \hat R T \ln a_k.
    //!  @f]
    //! The quantity @f$ \mu_k^0(T,P) @f$ is the standard state chemical potential
    //! at unit activity. It may depend on the pressure and the temperature.
    //! However, it may not depend on the mole fractions of the species in the
    //! solution.
    //!
    //! The activities are related to the generalized concentrations, @f$ \tilde
    //! C_k @f$, and standard concentrations, @f$ C^0_k @f$, by the following
    //! formula:
    //!
    //!  @f[
    //!  a_k = \frac{\tilde C_k}{C^0_k}
    //!  @f]
    //! The generalized concentrations are used in the kinetics classes to
    //! describe the rates of progress of reactions involving the species. Their
    //! formulation depends upon the specification of the rate constants for
    //! reaction, especially the units used in specifying the rate constants. The
    //! bridge between the thermodynamic equilibrium expressions that use a_k and
    //! the kinetics expressions which use the generalized concentrations is
    //! provided by the multiplicative factor of the standard concentrations.
    //! @{
 
    //! This method returns the array of generalized concentrations.
    /*!
     *  For an ideal gas mixture, these are simply the actual concentrations.
     *
     * @param c Output array of generalized concentrations. The units depend
     *           upon the implementation of the reaction rate expressions within
     *           the phase.
     */
    void getActivityConcentrations(span<double> c) const override {
        getConcentrations(c);
    }
 
    //! Returns the standard concentration @f$ C^0_k @f$, which is used to
    //! normalize the generalized concentration.
    /*!
     * This is defined as the concentration by which the generalized
     * concentration is normalized to produce the activity. In many cases, this
     * quantity will be the same for all species in a phase. Since the activity
     * for an ideal gas mixture is simply the mole fraction, for an ideal gas
     * @f$ C^0_k = P/\hat R T @f$.
     *
     * @param k Optional parameter indicating the species. The default
     *          is to assume this refers to species 0.
     * @return
     *   Returns the standard Concentration in units of m3 kmol-1.
     */
    double standardConcentration(size_t k=0) const override;
 
    //! Get the array of non-dimensional activity coefficients at the current
    //! solution temperature, pressure, and solution concentration.
    /*!
     *  For ideal gases, the activity coefficients are all equal to one.
     *
     * @param ac Output vector of activity coefficients. Length: m_kk.
     */
    void getActivityCoefficients(span<double> ac) const override;
 
    //! @}
    //! @name Partial Molar Properties of the Solution
    //! @{
 
    void getChemPotentials(span<double> mu) const override;
    void getPartialMolarEnthalpies(span<double> hbar) const override;
    void getPartialMolarEntropies(span<double> sbar) const override;
    void getPartialMolarIntEnergies(span<double> ubar) const override;
    void getPartialMolarIntEnergies_TV(span<double> utilde) const override;
    void getPartialMolarCp(span<double> cpbar) const override;
    void getPartialMolarCv_TV(span<double> cvtilde) const override;
    void getPartialMolarVolumes(span<double> vbar) const override;
 
    //! @}
    //! @name  Properties of the Standard State of the Species in the Solution
    //! @{
 
    void getStandardChemPotentials(span<double> mu) const override;
    void getEnthalpy_RT(span<double> hrt) const override;
    void getEntropy_R(span<double> sr) const override;
    void getGibbs_RT(span<double> grt) const override;
    void getIntEnergy_RT(span<double> urt) const override;
    void getCp_R(span<double> cpr) const override;
    void getStandardVolumes(span<double> vol) const override;
 
    //! @}
    //! @name Thermodynamic Values for the Species Reference States
    //! @{
 
    void getEnthalpy_RT_ref(span<double> hrt) const override;
    void getGibbs_RT_ref(span<double> grt) const override;
    void getGibbs_ref(span<double> g) const override;
    void getEntropy_R_ref(span<double> er) const override;
    void getIntEnergy_RT_ref(span<double> urt) const override;
    void getCp_R_ref(span<double> cprt) const override;
    void getStandardVolumes_ref(span<double> vol) const override;
 
    //! @}
 
    bool addSpecies(shared_ptr<Species> spec) override;
    void setToEquilState(span<const double> mu_RT) override;
 
protected:
    //! @name NonVirtual Internal methods to Return References to Reference State Thermo
    //! @{
 
    //! Returns a reference to the dimensionless reference state enthalpy vector.
    /*!
     * This function is part of the layer that checks/recalculates the reference
     * state thermo functions.
     */
    span<const double> enthalpy_RT_ref() const {
        updateThermo();
        return m_h0_RT;
    }
 
    //! Returns a reference to the dimensionless reference state Gibbs free energy vector.
    /*!
     * This function is part of the layer that checks/recalculates the reference
     * state thermo functions.
     */
    span<const double> gibbs_RT_ref() const {
        updateThermo();
        return m_g0_RT;
    }
 
    //! Returns a reference to the dimensionless reference state Entropy vector.
    /*!
     * This function is part of the layer that checks/recalculates the reference
     * state thermo functions.
     */
    span<const double> entropy_R_ref() const {
        updateThermo();
        return m_s0_R;
    }
 
    //! Returns a reference to the dimensionless reference state Heat Capacity vector.
    /*!
     * This function is part of the layer that checks/recalculates the reference
     * state thermo functions.
     */
    span<const double> cp_R_ref() const {
        updateThermo();
        return m_cp0_R;
    }
 
    //! @}
 
    //! Reference state pressure
    /*!
     *  Value of the reference state pressure in Pascals.
     *  All species must have the same reference state pressure.
     */
    double m_p0 = -1.0;
 
    //! Temporary storage for dimensionless reference state enthalpies
    mutable vector<double> m_h0_RT;
 
    //! Temporary storage for dimensionless reference state heat capacities
    mutable vector<double> m_cp0_R;
 
    //! Temporary storage for dimensionless reference state Gibbs energies
    mutable vector<double> m_g0_RT;
 
    //! Temporary storage for dimensionless reference state entropies
    mutable vector<double> m_s0_R;
 
    mutable vector<double> m_expg0_RT;
 
    //! Temporary array containing internally calculated partial pressures
    mutable vector<double> m_pp;
 
    //! Update the species reference state thermodynamic functions
    /*!
     *  This method is called each time a thermodynamic property is requested,
     *  to check whether the internal species properties within the object
     *  need to be updated. Currently, this updates the species thermo
     *  polynomial values for the current value of the temperature. A check is
     *  made to see if the temperature has changed since the last evaluation.
     *  This object does not contain any persistent data that depends on the
     *  concentration, that needs to be updated. The state object modifies its
     *  concentration dependent information at the time the setMoleFractions()
     *  (or equivalent) call is made.
     */
    virtual void updateThermo() const;
};
 
}
 
#endif