n-Hexane viscosity

Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
2026-04-01 03:00:13 -04:00 · 2014-05-22 14:53:26 +02:00
parent f35336b9e5
commit f084b843a3
8 changed files with 85 additions and 12 deletions
--- a/dev/fluids/n-Hexane.json
+++ b/dev/fluids/n-Hexane.json
@@ -265,5 +265,58 @@
      "rhoVtriple_units": "mol/m^3"
    }
  ], 
-  "NAME": "n-Hexane"
+  "NAME": "n-Hexane", 
+  "TRANSPORT": {
+    "viscosity": {
+      "BibTeX": "Michailidou-JCED-2013", 
+      "dilute": {
+        "C": 2.1357e-08, 
+        "a": [
+          0.1876, 
+          -0.4843, 
+          0.04477
+        ], 
+        "molar_mass": 0.08617536, 
+        "molar_mass_units": "kg/mol", 
+        "t": [
+          0, 
+          1, 
+          2
+        ], 
+        "type": "collision_integral"
+      }, 
+      "epsilon_over_k": 378.4, 
+      "epsilon_over_k_units": "K", 
+      "higher_order": {
+        "hardcoded": "n-Hexane"
+      }, 
+      "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": 6.334e-10, 
+      "sigma_eta_units": "m"
+    }
+  }
 }
--- a/doc/transport_table/table.tex
+++ b/doc/transport_table/table.tex
@@ -22,8 +22,8 @@ H2S & Quinones-Cisneros 2012 & $\eta^0 = 8.7721\dfrac{\sqrt{T}}{S^*(T^*)}$ \newl
 R23 & Shan 2000 & $\eta^0 = \frac{5}{16}\sqrt{\frac{MkT}{1000\pi N}}\frac{10^{24}}{\sigma^2\Omega^*(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$  & \\\hline
 Helium & Arp 1998 & NASTY & NASTY \\\hline
 Ethane & Friend 1991 & $\eta^0 = \dfrac{12.0085\sqrt{t}}{\Omega^{(2,2)*}(t)}$ \newline $\Omega^{(2,2)*}(t) = \left[\sum_i C_it^{(i-1)/3-1} \right]^{-1}$& $\Delta\eta = 15.977\left[\displaystyle\sum_i g_i\delta^{r_i}\tau^{s_i}\right]\left[1+\displaystyle\sum_{i=10}^{11}g_i\delta^{r_i}\tau^{s_i}\right]^{-1}$\\\hline
-n-Hexane & (data) Michailidou 2013 &$\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S(T^*)}$\newline$S(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$& $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = (\rho_r^{2/3}T_r^{1/2})\left\lbrace\dfrac{c_0}{T_r}+\dfrac{c_1}{c_2+T_r+c_3\rho_r^2}+\dfrac{c_4(1+\rho_r)}{c_5 + c_6T_r+c_7\rho_r+\rho_r^2+c_8\rho_rT_r} \right\rbrace$ \\\hline
-Hydrogen & Muzny 2013 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S^*(T^*)}$\newline$S^*(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{RF}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = c_1\rho_r^2\exp\left[c_2T_r+c_3/T_r+\frac{c_4\rho_r^2}{c_5+T_r}+c_6\rho_r^6\right]$\\\hline
+
+
 \hline\hline \multicolumn{4}{c}{DONE below this line}\\ \hline\hline
 Propane & (data) Vogel 1998 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+g_2\tau^{1/2})$\\\hline
 n-Butane & Vogel 1999 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta_h = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_1(1+\displaystyle\sum_{l=2}g_l\tau^{(l-1)/2})$ \\\hline
@@ -34,11 +34,13 @@ R125 & (data) Huber 2006 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{\pi N}}\dfra
 Carbon Dioxide & (data) Fenghour 1998 & $\eta^0 = \dfrac{1.00697\sqrt{T}}{\sigma^2\mathfrak{S}(T^*)}$ \newline $\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ &  $\Delta\eta = d_{11}\rho + d_{21}\rho^2+\frac{d_{64}\rho^6}{(T^*)^3}+d_{81}\rho^8+\frac{d_{82}\rho^8}{T^*}$ \newline $\Delta\eta = d_{11}\rho_c\delta + d_{21}\rho_c^2\delta^2+\frac{d_{64}\rho_c^6(\varepsilon/k)^3\delta^6\tau^3}{(T_c)^3}+\rho_c^8d_{81}\delta^8+\frac{\rho_c^8d_{82}\delta^8(\varepsilon/k)\tau}{T_c}$\\\hline
 Nitrogen, argon, oxygen air & (data) Lemmon and Jacobsen 2004 & $\eta^0 = \dfrac{0.0266958\sqrt{MT}}{\sigma^2\Omega(T^*)}$\newline$\Omega(T^*)=\exp\left(\sum_{i=0}^{4}b_i[\ln T^*]^i\right)$ & $\eta^r = \sum_{i=1}^NN_i\tau^{\tau_i}\delta^{d_i}\exp(-\gamma_i\delta^{l_i})$\\\hline
 R134a & Huber 2003 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = c_1\delta+\left(\frac{c_2}{\tau^6}+\frac{c_3}{\tau^2}+\frac{c_4}{\sqrt{\tau}}+c_5\tau^2\right)\delta^2+c_6\delta^3+c_7\left(\frac{1}{\delta_0-\delta}-\frac{1}{\delta_0}\right)$ \newline $\delta_0(\tau)=\frac{c_{10}}{1+c_8\tau+c_9\tau^2}$\\\hline
-Dimethyl Ether & Meng 2012 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \Delta\eta$\newline$\Delta\eta = \sum_{i=0}^{1}n_i\tau^{t_i}\delta^{d_i} + \sum_{i=2}^{6}n_i\tau^{t_i}\delta^{d_i}\exp(-\delta^{p_i})$\\\hline
+Dimethyl Ether & (exp. data) Meng 2012 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\mathfrak{S}(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = \Delta\eta$\newline$\Delta\eta = \sum_{i=0}^{1}n_i\tau^{t_i}\delta^{d_i} + \sum_{i=2}^{6}n_i\tau^{t_i}\delta^{d_i}\exp(-\delta^{p_i})$\\\hline
 R123 & (data) Tanaka 1996 & $\eta^0 = \displaystyle\sum_{i}a_iT_i$ & $\eta^r = \eta^1\rho+\Delta\eta$ \newline $\eta^1 = b_0+b_1T$\newline$\Delta\eta = \frac{a_0}{\rho-\rho_0}+\frac{a_0}{\rho_0}+a_1\rho+a_2\rho^2+a_3\rho^3$\newline$\Delta\eta = \frac{a_0/\rho_c}{\delta-\delta_0}+\frac{a_0/\rho_c}{\delta_0}+a_1\rho_c\delta+a_2\rho_c^2\delta^2+a_3\rho_c^3\delta^3$\\\hline
 R152A & (data) Krauss 1996 & $\eta^0 = \dfrac{5}{16}\sqrt{\dfrac{MkT}{1000\pi N}}\dfrac{10^{24}}{\sigma^2\Omega^*(T^*)}=\dfrac{0.2169614\sqrt{T}}{\sigma^2\Omega(T^*)}$\newline $\Omega(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\dfrac{\Delta\eta}{H_c} = \displaystyle\sum_{i=1}^{4}E_i\left(\frac{\rho}{\rho_c}\right)^i + \frac{E_5}{\rho/\rho_c-E_6}+\frac{E_5}{E_6}$\\\hline
 Ethanol & Kiselev 2005 & $\eta^0 = \sum_i a_i T^{n_i}$ & $\eta^r = B_{RF}\rho\eta^0(T)+\Delta \eta$ \newline $\Delta\eta = \displaystyle\sum_{i=2}^n\displaystyle\sum_{j=0}^me_{ij}\frac{\delta^i}{\tau_j}+f_1\left(\frac{\delta}{\delta_0(\tau)-\delta}-\frac{\delta}{\delta_0(\tau)}\right)$ \newline $\delta_0(\tau)=g_2+g_3\sqrt{\tau}$\\\hline
 Water & (data) Huber 2009 & & \\\hline
+Hydrogen & (from v5) Muzny 2013 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S^*(T^*)}$\newline$S^*(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{RF}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = c_1\rho_r^2\exp\left[c_2T_r+c_3/T_r+\frac{c_4\rho_r^2}{c_5+T_r}+c_6\rho_r^6\right]$\\\hline
+n-Hexane & (data) Michailidou 2013 &$\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S(T^*)}$\newline$S(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$& $\eta^r = \eta^0(T)\rho B_{RF} + \Delta\eta$\newline$\Delta\eta = (\rho_r^{2/3}T_r^{1/2})\left\lbrace\dfrac{c_0}{T_r}+\dfrac{c_1}{c_2+T_r+c_3\rho_r^2}+\dfrac{c_4(1+\rho_r)}{c_5 + c_6T_r+c_7\rho_r+\rho_r^2+c_8\rho_rT_r} \right\rbrace$ \\\hline
 \hline\hline
 \end{tabular}

--- a/include/CoolPropFluid.h
+++ b/include/CoolPropFluid.h
@@ -82,6 +82,7 @@ struct ViscosityHigherOrderVariables
 {
    enum ViscosityDiluteEnum {VISCOSITY_HIGHER_ORDER_BATSCHINKI_HILDEBRAND, 
                              VISCOSITY_HIGHER_ORDER_HYDROGEN,
+                              VISCOSITY_HIGHER_ORDER_HEXANE,
                              VISCOSITY_HIGHER_ORDER_FRICTION_THEORY,
                              VISCOSITY_HIGHER_ORDER_NOT_SET
                              };
--- a/src/Backends/Helmholtz/Fluids/FluidLibrary.h
+++ b/src/Backends/Helmholtz/Fluids/FluidLibrary.h
@@ -319,6 +319,10 @@ protected:
                fluid.transport.viscosity_higher_order.type = CoolProp::ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HYDROGEN;
                return;
            }
+            else if (!target.compare("n-Hexane")){
+                fluid.transport.viscosity_higher_order.type = CoolProp::ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HEXANE;
+                return;
+            }
            else{
                throw ValueError(format("hardcoded higher order viscosity term [%s] is not understood for fluid %s",target.c_str(), fluid.name.c_str()));
            }
--- a/src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
+++ b/src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
@@ -169,6 +169,8 @@ long double HelmholtzEOSMixtureBackend::calc_viscosity(void)
            delta_eta_h = TransportRoutines::modified_Batschinski_Hildebrand_viscosity_term(*this); break;
        case ViscosityHigherOrderVariables::VISCOSITY_HIGHER_ORDER_HYDROGEN:
            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;
        default:
            throw ValueError(format("higher order viscosity type [%d] is invalid for fluid %s", components[0]->transport.viscosity_dilute.type, name().c_str()));
        }
--- a/src/Backends/Helmholtz/TransportRoutines.cpp
+++ b/src/Backends/Helmholtz/TransportRoutines.cpp
@@ -258,5 +258,14 @@ long double TransportRoutines::viscosity_hydrogen_higher_order_hardcoded(Helmhol
    return c[1]*pow(rhor,2)*exp(c[2]*Tr+c[3]/Tr+c[4]*pow(rhor,2)/(c[5]+Tr)+c[6]*pow(rhor,6));
 }

+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
+    double c[] = {2.53402335/1e6, -9.724061002/1e6, 0.469437316, 158.5571631, 72.42916856/1e6, 10.60751253, 8.628373915, -6.61346441, -2.212724566};
+	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));
+}
+

 }; /* namespace CoolProp */
--- a/src/Backends/Helmholtz/TransportRoutines.h
+++ b/src/Backends/Helmholtz/TransportRoutines.h
@@ -83,6 +83,8 @@ public:
    static long double viscosity_water_hardcoded(HelmholtzEOSMixtureBackend &HEOS);

    static long double viscosity_hydrogen_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
+
+    static long double viscosity_hexane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
    
 }; /* class TransportRoutines */

--- a/src/Tests/CoolProp-Tests.cpp
+++ b/src/Tests/CoolProp-Tests.cpp
@@ -98,14 +98,14 @@ vel("Air", "T", 200, "Dmolar", 10000, "V", 21.1392e-6, 1e-3),
 vel("Air", "T", 300, "Dmolar", 5000, "V", 21.3241e-6, 1e-3),
 vel("Air", "T", 132.64, "Dmolar", 10400, "V", 17.7623e-6, 1e-3),

-//// From Michailidou, JPCRD, 2013
-//vel("Hexane", "T", 250, "Dmass", 1e-14, "V", 5.2584e-6, 1e-3),
-//vel("Hexane", "T", 400, "Dmass", 1e-14, "V", 8.4149e-6, 1e-3),
-//vel("Hexane", "T", 550, "Dmass", 1e-14, "V", 11.442e-6, 1e-3),
-//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 Michailidou, JPCRD, 2013
+vel("Hexane", "T", 250, "Dmass", 1e-14, "V", 5.2584e-6, 1e-3),
+vel("Hexane", "T", 400, "Dmass", 1e-14, "V", 8.4149e-6, 1e-3),
+vel("Hexane", "T", 550, "Dmass", 1e-14, "V", 11.442e-6, 1e-3),
+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 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),