Adding helium fluid properties

docs/CMakeLists.txt

@@ -34,6 +34,18 @@ if(DOXYGEN_FOUND)
         air_err_u.png
         air_err_w.png
     )
+    file(GLOB_RECURSE RST_FILES ${PROJECT_SOURCE_DIR}/docs/*.rst)
+    set(HE_ERR_IMGS
+        he_err_c_p.png
+        he_err_c_v.png
+        he_err_h.png
+        he_err_k.png
+        he_err_mu.png
+        he_err_rho.png
+        he_err_s.png
+        he_err_u.png
+        he_err_w.png
+    )
 
     add_custom_command(
         OUTPUT
@@ -46,6 +58,7 @@ if(DOXYGEN_FOUND)
             ${RST_FILES}
             ${N2_ERR_IMGS}
             ${AIR_ERR_IMGS}
+            ${HE_ERR_IMGS}
     )
 
     add_custom_command(
@@ -84,6 +97,19 @@ if(DOXYGEN_FOUND)
             ${PROJECT_SOURCE_DIR}/docs/pyplots/air.yml
     )
 
+    add_custom_command(
+        OUTPUT
+            ${HE_ERR_IMGS}
+        COMMAND
+            ${CMAKE_COMMAND} -E env "PYTHONPATH=${PROJECT_BINARY_DIR}/python/src:$ENV{PYTHONPATH}"
+            python3 plot_err.py he.yml
+        WORKING_DIRECTORY
+            ${PROJECT_SOURCE_DIR}/docs/pyplots
+        DEPENDS
+            ${PROJECT_SOURCE_DIR}/docs/pyplots/plot_err.py
+            ${PROJECT_SOURCE_DIR}/docs/pyplots/he.yml
+    )
+
     add_custom_command(
         TARGET doc
         POST_BUILD

docs/classes/helium.rst

@@ -0,0 +1,5 @@
+Helium
+======
+
+.. doxygenclass:: fprops::Helium
+   :members:

docs/classes/helmholtz.rst

@@ -16,6 +16,9 @@ Models
 .. doxygenclass:: fprops::Helmholtz::IdealGasPower
    :members:
 
+.. doxygenclass:: fprops::Helmholtz::IdealEnthalpyEntropyOffset
+   :members:
+
 .. doxygenclass:: fprops::Helmholtz::IdealPlanckEinsteinGeneralized
    :members:
 

docs/fluids/helium.rst

@@ -0,0 +1,32 @@
+Helium
+======
+
+Range of validity:
+
+- Temperature: `0.8 - 1500 K`
+- Pressure: to `2000 MPa`
+
+Computation of thermodynamic properties is based on :cite:t:`oritzvega2019`.
+Viscosity is based on :cite:t:`arp1989thermophysical`,
+thermal conductivity is based on :cite:t:`HANDS1981697`.
+
+Verification against CoolProp package
+-------------------------------------
+
+.. image:: ../pyplots/he_err_rho.png
+
+.. image:: ../pyplots/he_err_u.png
+
+.. image:: ../pyplots/he_err_h.png
+
+.. image:: ../pyplots/he_err_s.png
+
+.. image:: ../pyplots/he_err_w.png
+
+.. image:: ../pyplots/he_err_c_p.png
+
+.. image:: ../pyplots/he_err_c_v.png
+
+.. image:: ../pyplots/he_err_mu.png
+
+.. image:: ../pyplots/he_err_k.png

docs/pyplots/he.yml

@@ -0,0 +1,18 @@
+fprops:
+  name: he
+  coolprop: Helium
+  fprops: Helium
+  p: [
+    0.1, 0.2,
+    0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4,
+    5, 6, 8,
+    10, 15, 20, 25,
+    50, 75, 100,
+    200, 400, 600, 800, 1000
+  ]
+  T: [
+    60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150,
+    160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350,
+    400, 450, 500, 550,
+    600, 700, 800, 900, 1000
+  ]

docs/references.bib

@@ -30,3 +30,30 @@ @article{lemmon2004viscosity
   year={2004},
   publisher={Springer}
 }
+
+@unpublished{oritzvega2019,
+  author={D. O. Ortiz-Vega and K. R. Hall and J. C. Holste and V. D. Arp and A. H. Harvey and E. W. Lemmon},
+  title={Equation of state for Helium-4},
+  note={Coefficients from REPROP 10},
+  year={2019}
+}
+
+@article{HANDS1981697,
+    title = {A correlation of thermal conductivity data for helium},
+    journal = {Cryogenics},
+    volume = {21},
+    number = {12},
+    pages = {697-703},
+    year = {1981},
+    issn = {0011-2275},
+    doi = {https://doi.org/10.1016/0011-2275(81)90211-3},
+    author = {B.A. Hands and V.D. Arp},
+    abstract = {A correlation for the thermal conductivity of helium has been developed which covers the temperature range from temperatures just above the lambda line to 830 K, and densities up to about 160 kg m−3. The data used incorporate some recent experimental results which cover the temperature range from 4 K to 20 K including the critical region. The correlation gives an equation which generally fits the experimental data within ± 5%. However, at low temperature, the experimental data deviate up to about 10% from predictions based upon viscosity measurements or molecular dynamics calculations.}
+}
+
+@techreport{arp1989thermophysical,
+  title={Thermophysical Properties of Helium-4 from 0.8 to 1500 K with Pressures to 2000 MPa},
+  author={Arp, Vincent D and McCarty, Robert D},
+  year={1989},
+  institution={}
+}

include/Helium.h

@@ -0,0 +1,42 @@
+#pragma once
+
+#include "Helmholtz.h"
+#include "TransportModels.h"
+
+namespace fprops {
+
+/// Helium (He) fluid properties
+///
+/// References:
+/// 1. D. O. Ortiz-Vega, K. R. Hall, J. C. Holste, V. D. Arp, A. H. Harvey, and E. W. Lemmon.
+///    Equation of state for Helium-4. Unpublished.
+/// 2. B.A. Hands and V.D. Arp. A Correlation of Thermal Conductivity Data for Helium. Cryogenics,
+///    21(12):697–703, 1981. doi:10.1016/0011-2275(81)90211-3.
+/// 3. V.D. Arp, R.D. McCarty, and D.G Friend. Thermophysical Properties of Helium-4 from 0.8 to
+///    1500 K with Pressures to 2000 MPa - NIST Technical Note 1334 (revised). Technical Report,
+///    NIST, 1998.
+class Helium : public Helmholtz {
+public:
+    Helium();
+
+protected:
+    [[nodiscard]] double alpha(double delta, double tau) const override;
+    [[nodiscard]] double dalpha_ddelta(double delta, double tau) const override;
+    [[nodiscard]] double dalpha_dtau(double delta, double tau) const override;
+    [[nodiscard]] double d2alpha_ddelta2(double delta, double tau) const override;
+    [[nodiscard]] double d2alpha_dtau2(double delta, double tau) const override;
+    [[nodiscard]] double d2alpha_ddeltatau(double delta, double tau) const override;
+
+    [[nodiscard]] double mu_from_rho_T(double rho, double T) const override;
+    [[nodiscard]] double k_from_rho_T(double rho, double T) const override;
+
+private:
+    IdealGasLead<double> lead;
+    IdealGasLogTau<double> log_tau;
+    IdealEnthalpyEntropyOffset<double> offset;
+    ResidualPower<double> power_r;
+    ResidualPowerExp<double, unsigned int> power_exp_r;
+    ResidualGaussian<double> gauss;
+};
+
+} // namespace fprops

include/Helmholtz.h

@@ -218,6 +218,33 @@ class Helmholtz : public SinglePhaseFluidProperties {
         std::vector<T> t;
     };
 
+    /// Offset for enthalpy and entropy
+    ///
+    /// @tparam T The basic data type
+    ///
+    /// \f$\alpha = a_1 + a_2 \tau\f$
+    template <typename T>
+    class IdealEnthalpyEntropyOffset {
+    public:
+        IdealEnthalpyEntropyOffset(double a1, double a2) : a1(a1), a2(a2) {}
+
+        T
+        alpha(T delta, T tau) const
+        {
+            return this->a1 + this->a2 * tau;
+        }
+
+        T
+        dtau(T delta, T tau) const
+        {
+            return this->a2;
+        }
+
+    private:
+        double a1;
+        double a2;
+    };
+
     /// Generalized Planck-Einstein model
     ///
     /// @tparam T The basic data type

python/src/fprops.cpp

@@ -4,6 +4,7 @@
 #include "Air.h"
 #include "IdealGas.h"
 #include "Nitrogen.h"
+#include "Helium.h"
 
 using namespace fprops;
 
@@ -44,4 +45,9 @@ PYBIND11_MODULE(pyfprops, m)
         .def(py::init())
         .def("p_T", &Nitrogen::p_T)
         .def("v_u", &Nitrogen::v_u);
+
+    py::class_<Helium>(m, "Helium")
+        .def(py::init())
+        .def("p_T", &Nitrogen::p_T)
+        .def("v_u", &Nitrogen::v_u);
 }

python/src/pyfprops/__init__.py

@@ -2,6 +2,7 @@
 
 __all__ = [
     Air,
+    Helium,
     IdealGas,
     Nitrogen
 ]

python/tests/test_helium.py

@@ -0,0 +1,10 @@
+import pyfprops as fp
+import pytest
+import math
+
+def test_he_valid():
+    n2 = fp.Helium()
+    state = n2.p_T(1e6, 280)
+    assert state.p == 1e6
+    assert state.T == 280
+    assert math.isclose(state.rho, 1.7109055009783694, abs_tol=1e-14)

src/CMakeLists.txt

@@ -3,6 +3,7 @@ add_library(
     SHARED
         Air.cpp
         FluidProperties.cpp
+        Helium.cpp
         Helmholtz.cpp
         IdealGas.cpp
         Nitrogen.cpp