implemented inverse function of vapor pressure to get the temperature at vapor pressure.

Verified as 0.1Mpa: 372.755918611338; 1Mpa: 453.035632391467; 10Mpa: 584.149487998528; reviewed Phil

git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@8863 2fb0f335-1f38-0410-981e-8018bf24f1b0

dumux/material/components/h2o.hh

@@ -139,6 +139,27 @@ public:
 
         return Region4::saturationPressure(T);
     }
+    /*!
+     * \brief The vapor temperature in \f$\mathrm{[Ka]}\f$ of pure water
+     *        at a given pressure.
+     *
+     *\param pressure pressure in \f$\mathrm{[Pa]}\f$
+     *
+     * See:
+     *
+     * IAPWS: "Revised Release on the IAPWS Industrial Formulation
+     * 1997 for the Thermodynamic Properties of Water and Steam",
+     * http://www.iapws.org/relguide/IF97-Rev.pdf
+     */
+    static Scalar vaporTemperature(Scalar pressure)
+    {
+        if (pressure > criticalPressure())
+            pressure = criticalPressure();
+        if (pressure < triplePressure())
+            pressure = triplePressure();
+
+        return Region4::vaporTemperature(pressure);
+    }
 
     /*!
      * \brief Specific enthalpy of water steam \f$\mathrm{[J/kg]}\f$.

dumux/material/components/iapws/region4.hh

@@ -89,6 +89,35 @@ public:
 
         return 1e6*tmp;
     }
+
+    /*!
+     * \brief Returns the saturation temperature in \f$\mathrm{[K]}\f$ of pure water at a given
+     *        pressure.
+     *
+     *\param pressure pressure of component in \f$\mathrm{[Pa]}\f$
+     *
+     * The saturation pressure is often also called vapor pressure.
+     */
+    static Scalar vaporTemperature(Scalar pressure)
+    {
+        static const Scalar n[10] = {
+            0.11670521452767e4, -0.72421316703206e6, -0.17073846940092e2,
+            0.12020824702470e5, -0.32325550322333e7, 0.14915108613530e2,
+            -0.48232657361591e4, 0.40511340542057e6, -0.23855557567849,
+            0.65017534844798e3
+        };
+        Scalar beta = pow((pressure/1e6 /*from Pa to MPa*/), (1./4.));
+        Scalar beta2 = pow(beta, 2.);
+        Scalar E = beta2 + n[2] * beta + n[5];
+        Scalar F = n[0]*beta2 + n[3]*beta + n[6];
+        Scalar G = n[1]*beta2 + n[4]*beta + n[7];
+
+        Scalar D = ( 2.*G)/(-F -std::sqrt(pow(F,2.) - 4.*E*G));
+
+        Scalar temperature = (n[9] + D - std::sqrt(pow(n[9]+D , 2.) - 4.* (n[8] + n[9]*D)) ) * 0.5;
+
+        return temperature;
+    }
 };
 
 } // end namepace IAPWS