From 7bb80f7b9fb953da15c1f3abd1ab19d21e2194e5 Mon Sep 17 00:00:00 2001
From: Benjamin Faigle <benjamin.faigle@posteo.de>
Date: Wed, 12 Feb 2014 10:14:29 +0000
Subject: [PATCH] Add functions for the heat capacity to the components air and
co2, that will be required by the decoupled NI-model. Enabled acess to these
methods in the co2-brine-fluidsystem (only pure-phase heat capacities are
used). reviewed by Klaus
git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@12462 2fb0f335-1f38-0410-981e-8018bf24f1b0
---
dumux/material/components/air.hh | 38 +++++++++++++++++++
dumux/material/components/co2.hh | 25 ++++++++++++
dumux/material/components/h2o.hh | 2 +-
.../fluidsystems/brineco2fluidsystem.hh | 17 +++++++--
4 files changed, 78 insertions(+), 4 deletions(-)
diff --git a/dumux/material/components/air.hh b/dumux/material/components/air.hh
index 23600c5f03..90da3c6575 100644
--- a/dumux/material/components/air.hh
+++ b/dumux/material/components/air.hh
@@ -203,6 +203,44 @@ public:
/ molarMass(); // conversion from [J/(mol K)] to [J/(kg K)]
}
+ /*!
+ * \brief Specific isobaric heat capacity \f$[J/(kg K)]\f$ of pure
+ * air.
+ *
+ * This methods uses the formula for "zero-pressure" heat capacity that
+ * is only dependent on temperature, because the pressure dependence is rather small.
+ * This one should be accurate for a pressure of 1 atm.
+ * Values taken from NASA Contractor Report 4755, Real-Gas Flow Properties for NASA
+ * Langley Research Center Aerothermodynamic Facilities Complex Wind Tunnels
+ * using data from
+ * Hilsenrath et al 1955, "Tables of Thermal Properties of Gases"
+ * \param temperature temperature of component in \f$\mathrm{[K]}\f$
+ * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
+ */
+ static const Scalar gasHeatCapacity(Scalar temperature,
+ Scalar pressure)
+ {
+ // scale temperature with referenence temp of 100K
+ Scalar phi = temperature/100;
+
+ Scalar c_p = 0.661738E+01
+ -0.105885E+01 * phi
+ +0.201650E+00 * pow(phi,2.)
+ -0.196930E-01 * pow(phi,3.)
+ +0.106460E-02 * pow(phi,4.)
+ -0.303284E-04 * pow(phi,5.)
+ +0.355861E-06 * pow(phi,6.);
+ c_p += -0.549169E+01 * pow(phi,-1.)
+ +0.585171E+01* pow(phi,-2.)
+ -0.372865E+01* pow(phi,-3.)
+ +0.133981E+01* pow(phi,-4.)
+ -0.233758E+00* pow(phi,-5.)
+ +0.125718E-01* pow(phi,-6.);
+ c_p *= IdealGas::R / (molarMass() * 1000); // in J/mol/K * mol / kg / 1000 = kJ/kg/K
+
+
+ return c_p;
+ }
};
} // end namespace
diff --git a/dumux/material/components/co2.hh b/dumux/material/components/co2.hh
index b13a72a955..6813e41919 100644
--- a/dumux/material/components/co2.hh
+++ b/dumux/material/components/co2.hh
@@ -249,11 +249,36 @@ public:
DUNE_THROW(NumericalProblem, "CO2::liquidPressure()");
}
+ /*!
+ * \brief Specific isobaric heat capacity of the component [J/kg] as a liquid.
+ * USE WITH CAUTION! Exploits enthalpy function with artificial increment
+ * of the temperature!
+ * Equation with which the specific heat capacity is calculated : \f$ c_p = \frac{dh}{dT}\f$
+ * \param temperature temperature of component in \f$\mathrm{[K]}\f$
+ * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
+ */
+ static Scalar liquidHeatCapacity(Scalar temperature, Scalar pressure)
+ {
+ //temperature difference :
+ Scalar dT = 1.; // 1K temperature increment
+ Scalar temperature2 = temperature+dT;
+
+ // enthalpy difference
+ Scalar hold = liquidEnthalpy(temperature, pressure);
+ Scalar hnew = liquidEnthalpy(temperature2, pressure);
+ Scalar dh = hold-hnew;
+
+ //specific heat capacity
+ return dh/dT ;
+ }
+
/*!
* \brief The dynamic viscosity [N/m^3*s] of CO2.
* Equations given in: - Vesovic et al., 1990
* - Fenhour et al., 1998
+ * \param temperature temperature of component in \f$\mathrm{[K]}\f$
+ * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
*/
static Scalar gasViscosity(Scalar temperature, Scalar pressure)
{
diff --git a/dumux/material/components/h2o.hh b/dumux/material/components/h2o.hh
index 83fe5cdfd3..29ea091236 100644
--- a/dumux/material/components/h2o.hh
+++ b/dumux/material/components/h2o.hh
@@ -449,7 +449,7 @@ public:
}
/*!
- * \brief Specific isochoric heat capacity of liquid water \f$\mathrm{[J/kg]}\f$.
+ * \brief Specific isochoric heat capacity of liquid water \f$\mathrm{[J/m^3]}\f$.
*
* \param temperature temperature of component in \f$\mathrm{[K]}\f$
* \param pressure pressure of component in \f$\mathrm{[Pa]}\f$
diff --git a/dumux/material/fluidsystems/brineco2fluidsystem.hh b/dumux/material/fluidsystems/brineco2fluidsystem.hh
index 63f528dbe3..3fe4b8f163 100644
--- a/dumux/material/fluidsystems/brineco2fluidsystem.hh
+++ b/dumux/material/fluidsystems/brineco2fluidsystem.hh
@@ -560,14 +560,25 @@ public:
/*!
* \copydoc BaseFluidSystem::heatCapacity
+ *
+ * We employ the heat capacity of the pure phases.
+ * Todo: Include compositional effects.
+ *
+ * \param fluidState An arbitrary fluid state
+ * \param phaseIdx The index of the fluid phase to consider
+ * \tparam FluidState the fluid state class
*/
+ using Base::heatCapacity;
template <class FluidState>
static Scalar heatCapacity(const FluidState &fluidState,
- const ParameterCache ¶mCache,
int phaseIdx)
{
- // TODO!
- DUNE_THROW(Dune::NotImplemented, "Heat capacities");
+ if(phaseIdx == wPhaseIdx)
+ return H2O::liquidHeatCapacity(fluidState.temperature(phaseIdx),
+ fluidState.pressure(phaseIdx));
+ else
+ return CO2::liquidHeatCapacity(fluidState.temperature(phaseIdx),
+ fluidState.pressure(phaseIdx));
}
private:
--
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