Implemented the viscosity correlation for n-Heptane of Assael, JPCRD, 2014 (http://scitation.aip.org/content/aip/journal/jpcrd/43/2/10.1063/1.4875930) and testing data

Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
2026-04-01 03:00:13 -04:00 · 2014-06-10 15:21:24 +02:00
parent e34cd9bd9f
commit b4791ed33a
7 changed files with 96 additions and 19 deletions
--- a/dev/fluids/n-Heptane.json
+++ b/dev/fluids/n-Heptane.json
@@ -394,6 +394,57 @@
        ], 
        "type": "polynomial"
      }
+    },
+    "viscosity": {
+      "BibTeX": "Assael-JPCRD-2014-Heptane", 
+      "dilute": {
+        "C": 2.1357e-08, 
+        "a": [
+          0.33974, 
+          -0.49396, 
+          0.08050
+        ], 
+        "molar_mass": 0.100202, 
+        "molar_mass_units": "kg/mol", 
+        "t": [
+          0, 
+          1, 
+          3
+        ], 
+        "type": "collision_integral"
+      }, 
+      "epsilon_over_k": 426.118, 
+      "epsilon_over_k_units": "K", 
+      "higher_order": {
+        "hardcoded": "n-Heptane"
+      }, 
+      "initial_density": {
+        "b": [
+          -19.572881, 
+          219.73999, 
+          -1015.3226, 
+          2471.01251, 
+          -3375.1717, 
+          2491.6597, 
+          -787.26086, 
+          14.085455, 
+          -0.34664158
+        ], 
+        "t": [
+          0, 
+          -0.25, 
+          -0.5, 
+          -0.75, 
+          -1.0, 
+          -1.25, 
+          -1.5, 
+          -2.5, 
+          -5.5
+        ], 
+        "type": "Rainwater-Friend"
+      }, 
+      "sigma_eta": 0.61362e-9, 
+      "sigma_eta_units": "m"
    }
  }
 }
--- a/include/CoolPropFluid.h
+++ b/include/CoolPropFluid.h
@@ -188,6 +188,7 @@ struct ViscosityHigherOrderVariables
    enum ViscosityDiluteEnum {VISCOSITY_HIGHER_ORDER_BATSCHINKI_HILDEBRAND,
                              VISCOSITY_HIGHER_ORDER_HYDROGEN,
                              VISCOSITY_HIGHER_ORDER_HEXANE,
+                              VISCOSITY_HIGHER_ORDER_HEPTANE,
                              VISCOSITY_HIGHER_ORDER_ETHANE,
                              VISCOSITY_HIGHER_ORDER_FRICTION_THEORY,
                              VISCOSITY_HIGHER_ORDER_NOT_SET
--- a/src/Backends/Helmholtz/Fluids/FluidLibrary.h
+++ b/src/Backends/Helmholtz/Fluids/FluidLibrary.h
@@ -427,6 +427,9 @@ protected:
            else if (!target.compare("n-Hexane")){
                fluid.transport.viscosity_higher_order.type = CoolProp::ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HEXANE; return;
            }
+            else if (!target.compare("n-Heptane")){
+                fluid.transport.viscosity_higher_order.type = CoolProp::ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HEPTANE; return;
+            }
            else if (!target.compare("Ethane")){
                fluid.transport.viscosity_higher_order.type = CoolProp::ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_ETHANE; return;
            }
--- a/src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
+++ b/src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
@@ -189,6 +189,8 @@ long double HelmholtzEOSMixtureBackend::calc_viscosity_background(long double et
        delta_eta_h = TransportRoutines::viscosity_hydrogen_higher_order_hardcoded(*this); break;
    case ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HEXANE:
        delta_eta_h = TransportRoutines::viscosity_hexane_higher_order_hardcoded(*this); break;
+    case ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HEPTANE:
+        delta_eta_h = TransportRoutines::viscosity_heptane_higher_order_hardcoded(*this); break;
    case ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_ETHANE:
        delta_eta_h = TransportRoutines::viscosity_ethane_higher_order_hardcoded(*this); break;
    default:
--- a/src/Backends/Helmholtz/TransportRoutines.cpp
+++ b/src/Backends/Helmholtz/TransportRoutines.cpp
@@ -280,6 +280,7 @@ long double TransportRoutines::viscosity_hydrogen_higher_order_hardcoded(Helmhol

 long double TransportRoutines::viscosity_hexane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS)
 {
+
    long double Tr = HEOS.T()/507.82, rhor = HEOS.keyed_output(CoolProp::iDmass)/233.182;

    // Output is in Pa-s
@@ -287,6 +288,16 @@ long double TransportRoutines::viscosity_hexane_higher_order_hardcoded(Helmholtz
 	return pow(rhor,static_cast<long double>(2.0/3.0))*sqrt(Tr)*(c[0]/Tr+c[1]/(c[2]+Tr+c[3]*rhor*rhor)+c[4]*(1+rhor)/(c[5]+c[6]*Tr+c[7]*rhor+rhor*rhor+c[8]*rhor*Tr));
 }

+long double TransportRoutines::viscosity_heptane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS)
+{
+    /// From Assael, JPCRD, 2014
+    long double Tr = HEOS.T()/540.13, rhor = HEOS.rhomass()/232;
+
+    // Output is in Pa-s
+    double c[] = {0, 22.15000/1e6, -15.00870/1e6, 3.71791/1e6, 77.72818/1e6, 9.73449, 9.51900, -6.34076, -2.51909};
+	return pow(rhor,2.0L/3.0L)*sqrt(Tr)*(c[1]*rhor+c[2]*pow(rhor,2)+c[3]*pow(rhor,3)+c[4]*rhor/(c[5]+c[6]*Tr+c[7]*rhor+rhor*rhor+c[8]*rhor*Tr));
+}
+
 long double TransportRoutines::viscosity_higher_order_friction_theory(HelmholtzEOSMixtureBackend &HEOS)
 {
    if (HEOS.is_pure_or_pseudopure)
--- a/src/Backends/Helmholtz/TransportRoutines.h
+++ b/src/Backends/Helmholtz/TransportRoutines.h
@@ -20,7 +20,7 @@ public:
    with \f$T^* = \frac{T}{\varepsilon/k}\f$ and \f$\sigma\f$ in nm, M is in kg/kmol. Yields viscosity in Pa-s.
    */
    static long double viscosity_dilute_kinetic_theory(HelmholtzEOSMixtureBackend &HEOS);
-    
+
    /**
    \brief The dilute gas viscosity term that is based on collision integral or effective cross section

@@ -34,7 +34,7 @@ public:
    */
    static long double viscosity_dilute_collision_integral(HelmholtzEOSMixtureBackend &HEOS);

-    /** 
+    /**
    \brief A dilute gas viscosity term formed of summation of power terms

    \f[
@@ -46,7 +46,7 @@ public:

    static long double viscosity_dilute_collision_integral_powers_of_T(HelmholtzEOSMixtureBackend &HEOS);

-    /** 
+    /**
    \brief The initial density dependence term \f$B_{\eta}\f$ from Rainwater-Friend theory

    The total contribution from this term is given by
@@ -68,17 +68,17 @@ public:
    */
    static long double viscosity_initial_density_dependence_Rainwater_Friend(HelmholtzEOSMixtureBackend &HEOS);

-    /** 
+    /**
    \brief The modified Batschinski-Hildebrand contribution to the viscosity

    \f[
    \Delta\eta = \displaystyle\sum_{i}a_{i}\delta^{d1_i}\tau^{t1_j}+\left(\displaystyle\sum_{i}f_i\delta^{d2_i}\tau^{t2_i}\right)\left(\frac{1}{\delta_0(\tau)-\delta}-\frac{1}{\delta_0(\tau)}\right)
    \f]
-    where \f$\tau = T_c/T\f$ and \f$\delta = \rho/\rho_c\f$ 
+    where \f$\tau = T_c/T\f$ and \f$\delta = \rho/\rho_c\f$
    \f[
    \delta_0(\tau) = \displaystyle\frac{\displaystyle\sum_{i}g_i\tau^{h_i}}{\displaystyle\sum_{i}p_i\tau^{q_i}}
    \f]
-    The more general form of \f$\delta_0(\tau)\f$ is selected in order to be able to handle all the forms in the literature 
+    The more general form of \f$\delta_0(\tau)\f$ is selected in order to be able to handle all the forms in the literature
    */
    static long double viscosity_higher_order_modified_Batschinski_Hildebrand(HelmholtzEOSMixtureBackend &HEOS);

@@ -91,6 +91,7 @@ public:
    static long double viscosity_ethane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
    static long double viscosity_hydrogen_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
    static long double viscosity_hexane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
+    static long double viscosity_heptane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
    static long double viscosity_higher_order_friction_theory(HelmholtzEOSMixtureBackend &HEOS);

    /**
@@ -110,7 +111,7 @@ public:
    \Delta\lambda(\rho,T) = \displaystyle\sum_iA_i\tau^{t,i}\delta^{d_i}
    \f]

-    As used by Assael, Perkins, Huber, etc., the residual term is given by 
+    As used by Assael, Perkins, Huber, etc., the residual term is given by
    \f[
    \Delta\lambda(\rho,T) = \displaystyle\sum_i(B_{1,i}+B_{2,i}(T/T_c))(\rho/\rho_c)^i
    \f]
@@ -135,9 +136,9 @@ public:
    \f[
        \zeta = \zeta_0\left(\frac{p_c\rho}{\Gamma\rho_c^2}\right)^{\nu/\gamma}\left[\left.\frac{\partial \rho(T,\rho)}{\partial p} \right|_{T}- \frac{T_R}{T}\left.\frac{\partial \rho(T_R,\rho)}{\partial p} \right|_{T}  \right]^{\nu/\gamma},
    \f]
-    where \f$\lambda^{(c)}\f$ is in W\f$\cdot\f$m\f$^{-1}\f$\f$\cdot\f$K\f$^{-1}\f$, \f$\zeta\f$ is in m, 
-    \f$c_p\f$ and \f$c_v\f$ are in J\f$\cdot\f$kg\f$^{-1}\cdot\f$K\f$^{-1}\f$, \f$p\f$ and \f$p_c\f$ are in Pa, 
-    \f$\rho\f$ and \f$\rho_c\f$ are in mol\f$\cdot\f$m\f$^{-3}\f$, \f$\eta\f$ is the viscosity in Pa\f$\cdot\f$s, 
+    where \f$\lambda^{(c)}\f$ is in W\f$\cdot\f$m\f$^{-1}\f$\f$\cdot\f$K\f$^{-1}\f$, \f$\zeta\f$ is in m,
+    \f$c_p\f$ and \f$c_v\f$ are in J\f$\cdot\f$kg\f$^{-1}\cdot\f$K\f$^{-1}\f$, \f$p\f$ and \f$p_c\f$ are in Pa,
+    \f$\rho\f$ and \f$\rho_c\f$ are in mol\f$\cdot\f$m\f$^{-3}\f$, \f$\eta\f$ is the viscosity in Pa\f$\cdot\f$s,
    and the remaining parameters are defined in the following tables.

    It should be noted that some authors use slightly different values for the "universal" constants
@@ -145,9 +146,9 @@ public:
    Coefficients for use in the simplified Olchowy-Sengers critical term
    Parameter             | Variable     | Value
    ---------             | --------     | ------
-    Boltzmann constant    | \f$k\f$      | \f$1.3806488\times 10^{-23}\f$ J\f$\cdot\f$K\f$^{-1}\f$ 
-    Universal amplitude   | \f$R_D\f$    | 1.03 
-    Critical exponent     | \f$\nu\f$    | 0.63 
+    Boltzmann constant    | \f$k\f$      | \f$1.3806488\times 10^{-23}\f$ J\f$\cdot\f$K\f$^{-1}\f$
+    Universal amplitude   | \f$R_D\f$    | 1.03
+    Critical exponent     | \f$\nu\f$    | 0.63
    Critical exponent     | \f$\gamma\f$ | 1.239
    Reference temperature | \f$T_R\f$    | 1.5\f$T_c\f$

@@ -182,7 +183,7 @@ public:

    Bell, I. H.; Wronski, J.; Quoilin, S. & Lemort, V. (2014), Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp, Industrial & Engineering Chemistry Research, 53, (6), 2498-2508

-    which is originally based on the methods presented in 
+    which is originally based on the methods presented in

    Huber, M. L., Laesecke, A. and Perkins, R. A., (2003), Model for the Viscosity and Thermal Conductivity of Refrigerants, Including a New Correlation for the Viscosity of R134a, Industrial & Engineering Chemistry Research, v. 42, pp. 3163-3178

@@ -200,4 +201,4 @@ public:
 }; /* class TransportRoutines */

 }; /* namespace CoolProp */
-#endif
+#endif
--- a/src/Tests/CoolProp-Tests.cpp
+++ b/src/Tests/CoolProp-Tests.cpp
@@ -108,6 +108,14 @@ vel("Hexane", "T", 250, "Dmass", 700, "V", 528.2e-6, 1e-3),
 vel("Hexane", "T", 400, "Dmass", 600, "V", 177.62e-6, 1e-3),
 vel("Hexane", "T", 550, "Dmass", 500, "V", 95.002e-6, 1e-3),

+// From Assael, JPCRD, 2014
+vel("Heptane", "T", 250, "Dmass", 1e-14, "V", 4.9717e-6, 1e-3),
+vel("Heptane", "T", 400, "Dmass", 1e-14, "V", 7.8361e-6, 1e-3),
+vel("Heptane", "T", 550, "Dmass", 1e-14, "V", 10.7394e-6, 1e-3),
+vel("Heptane", "T", 250, "Dmass", 720, "V", 725.69e-6, 1e-3),
+vel("Heptane", "T", 400, "Dmass", 600, "V", 175.94e-6, 1e-3),
+vel("Heptane", "T", 550, "Dmass", 500, "V", 95.105e-6, 1e-3),
+
 // From Fenghour, JPCRD, 1998
 vel("CO2", "T", 220, "Dmass", 2.440, "V", 11.06e-6, 1e-3),
 vel("CO2", "T", 300, "Dmass", 1.773, "V", 15.02e-6, 1e-3),
@@ -263,10 +271,10 @@ vel("Hexane", "T", 400, "Dmass", 650, "L", 129.28e-3, 2e-4),
 vel("Hexane", "T", 510, "Dmass", 2, "L", 36.772e-3, 1e-4),

 // From Assael, JPCRD, 2013
-//vel("Heptane", "T", 250, "Dmass", 720, "L", 137.09e-3, 1e-4),
-//vel("Heptane", "T", 400, "Dmass", 2, "L", 21.794e-3, 1e-4),
-//vel("Heptane", "T", 400, "Dmass", 650, "L", 120.75e-3, 1e-4),
-//vel("Heptane", "T", 535, "Dmass", 100, "L", 51.655e-3, 1e-4),
+vel("Heptane", "T", 250, "Dmass", 720, "L", 137.09e-3, 1e-4),
+vel("Heptane", "T", 400, "Dmass", 2, "L", 21.794e-3, 1e-4),
+vel("Heptane", "T", 400, "Dmass", 650, "L", 120.75e-3, 1e-4),
+vel("Heptane", "T", 535, "Dmass", 100, "L", 51.655e-3, 1e-4),

 // From Assael, JPCRD, 2013
 vel("Ethanol", "T", 300, "Dmass", 850, "L", 209.68e-3, 1e-4),