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Helium viscosity

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Signed-off-by: Ian Bell <ian.h.bell@gmail.com>
This commit is contained in:
Ian Bell
2014-05-22 22:56:19 +02:00
parent 7477a8db80
commit 809ec14df2
7 changed files with 64 additions and 3 deletions
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8
dev/fluids/Helium.json
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@@ -322,5 +322,11 @@
"rhoVtriple_units": "mol/m^3"
}
],
"NAME": "Helium"
"NAME": "Helium",
"TRANSPORT": {
"viscosity": {
"BibTeX": "ARP-NIST-1998",
"hardcoded": "Helium"
}
}
}

5
doc/transport_table/table.tex
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@@ -16,9 +16,9 @@ Fluid & Reference & $\eta^0$ & $\eta^r$ \\
Ammonia & (data) Fenghour 1995 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2\Game(T^*)}$\newline$\mathfrak{S}(T^*)=\exp\left(\sum_{i=0}^{4}a_i[\ln T^*]^i\right)$ & $\eta^r = B_{BV}\rho\eta^0(T) + \Delta\eta$\newline$\Delta\eta = \sum_i b_i(T)\rho^i$\\\hline
\hline\hline
H2S & Quinones-Cisneros 2012 & $\eta^0 = 8.7721\dfrac{\sqrt{T}}{S^*(T^*)}$ \newline $S^*(T^*) = \sum_i \frac{\alpha_i}{T^{*i}}$ & FRICTION THEORY\\\hline
H2S & Quinones-Cisneros 2012 & $\eta^0 = 0.87721\dfrac{\sqrt{T}}{S^*(T^*)}$ \newline $S^*(T^*) = \sum_i \frac{\alpha_i}{T^{*i}}$ & FRICTION THEORY\\\hline
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
\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
@@ -39,6 +39,7 @@ Hydrogen & (from v5) Muzny 2013 & $\eta^0 = \dfrac{0.021357\sqrt{MT}}{\sigma^2S^
n-Hexane & (data) Michailidou 2013 &$\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
SF6 & (data) Quinones-Cisneros 2012 & $\eta^0 = \sum_i d_i T_r^{n_i}$ & FRICTION THEORY\\\hline
R404A, R410A, R507, R407 & (data) Geller 2000 & $\eta^0 = \sum_i A_iT^i$&$\eta^r = \sum_j b_j\rho^j$ \\\hline
Helium & Arp 1998 & hardcoded & hardcoded \\\hline
\hline\hline
\end{tabular}

4
src/Backends/Helmholtz/Fluids/FluidLibrary.h
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@@ -436,6 +436,10 @@ protected:
fluid.transport.hardcoded = CoolProp::TransportPropertyData::VISCOSITY_HARDCODED_WATER;
return;
}
else if (!target.compare("Helium")){
fluid.transport.hardcoded = CoolProp::TransportPropertyData::VISCOSITY_HARDCODED_HELIUM;
return;
}
else{
throw ValueError();
}

2
src/Backends/Helmholtz/HelmholtzEOSMixtureBackend.cpp
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@@ -138,6 +138,8 @@ long double HelmholtzEOSMixtureBackend::calc_viscosity(void)
{
case CoolProp::TransportPropertyData::VISCOSITY_HARDCODED_WATER:
return TransportRoutines::viscosity_water_hardcoded(*this);
case CoolProp::TransportPropertyData::VISCOSITY_HARDCODED_HELIUM:
return TransportRoutines::viscosity_helium_hardcoded(*this);
default:
throw ValueError(format("hardcoded viscosity type [%d] is invalid for fluid %s", components[0]->transport.hardcoded, name().c_str()));
}

42
src/Backends/Helmholtz/TransportRoutines.cpp
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@@ -340,4 +340,46 @@ long double TransportRoutines::viscosity_higher_order_friction_theory(HelmholtzE
}
long double TransportRoutines::viscosity_helium_hardcoded(HelmholtzEOSMixtureBackend &HEOS)
{
double eta_0,eta_0_slash, eta_E_slash, B,C,D,ln_eta,x;
//
// Arp, V.D., McCarty, R.D., and Friend, D.G.,
// "Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa",
// NIST Technical Note 1334 (revised), 1998.
//
// Using Arp NIST report
// Report is not clear on viscosity, referring to REFPROP source code for clarity
// Correlation wants density in g/cm^3; kg/m^3 --> g/cm^3, divide by 1000
long double rho = HEOS.keyed_output(CoolProp::iDmass)/1000.0, T = HEOS.T();
if (T <= 300){
x = log(T);
}
else{
x = log(300.0);
}
// Evaluate the terms B,C,D
B = -47.5295259/x+87.6799309-42.0741589*x+8.33128289*x*x-0.589252385*x*x*x;
C = 547.309267/x-904.870586+431.404928*x-81.4504854*x*x+5.37008433*x*x*x;
D = -1684.39324/x+3331.08630-1632.19172*x+308.804413*x*x-20.2936367*x*x*x;
eta_0_slash = -0.135311743/x+1.00347841+1.20654649*x-0.149564551*x*x+0.012520841*x*x*x;
eta_E_slash = rho*B+rho*rho*C+rho*rho*rho*D;
if (T<=100)
{
ln_eta = eta_0_slash + eta_E_slash;
// Correlation yields viscosity in micro g/(cm-s); to get Pa-s, divide by 10 to get micro Pa-s, then another 1e6 to get Pa-s
return exp(ln_eta)/10.0/1e6;
}
else
{
ln_eta = eta_0_slash + eta_E_slash;
eta_0 = 196*pow(T,static_cast<long double>(0.71938))*exp(12.451/T-295.67/T/T-4.1249);
// Correlation yields viscosity in micro g/(cm-s); to get Pa-s, divide by 10 to get micro Pa-s, then another 1e6 to get Pa-s
return (exp(ln_eta)+eta_0-exp(eta_0_slash))/10.0/1e6;
}
}
}; /* namespace CoolProp */

2
src/Backends/Helmholtz/TransportRoutines.h
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@@ -84,6 +84,8 @@ public:
static long double viscosity_water_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
static long double viscosity_helium_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
static long double viscosity_hydrogen_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);
static long double viscosity_hexane_higher_order_hardcoded(HelmholtzEOSMixtureBackend &HEOS);

4
src/Tests/CoolProp-Tests.cpp
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@@ -173,6 +173,10 @@ vel("R507A", "T", 243.15, "Q", 0, "V", 284.59e-6, 3e-2),
vel("R507A", "T", 243.15, "Q", 1, "V", 9.83e-6, 1e-2),
vel("R507A", "T", 333.15, "Q", 0, "V", 74.37e-6, 1e-2),
vel("R507A", "T", 333.15, "Q", 1, "V", 19.35e-6, 1e-2),
vel("Helium", "T", 3.6, "P", 0.180e6, "V", 3.745e-6, 1e-2),
vel("Helium", "T", 50, "P", 0.180e6, "V", 6.376e-6, 1e-2),
vel("Helium", "T", 400, "P", 0.180e6, "V", 24.29e-6, 1e-2),
};
class ViscosityValidationFixture