Line data Source code
1 : //* This file is part of the MOOSE framework
2 : //* https://mooseframework.inl.gov
3 : //*
4 : //* All rights reserved, see COPYRIGHT for full restrictions
5 : //* https://github.com/idaholab/moose/blob/master/COPYRIGHT
6 : //*
7 : //* Licensed under LGPL 2.1, please see LICENSE for details
8 : //* https://www.gnu.org/licenses/lgpl-2.1.html
9 :
10 : #include "NaKFluidProperties.h"
11 :
12 : registerMooseObject("FluidPropertiesApp", NaKFluidProperties);
13 :
14 : InputParameters
15 8 : NaKFluidProperties::validParams()
16 : {
17 8 : InputParameters params = SinglePhaseFluidProperties::validParams();
18 8 : params.addClassDescription("Fluid properties for NaK");
19 16 : params.addRequiredParam<Real>(
20 : "weight_fraction_K",
21 : "Weight fraction of potassium in NaK. Only eutectic is implemented (X_K = 0.778)");
22 8 : return params;
23 0 : }
24 :
25 4 : NaKFluidProperties::NaKFluidProperties(const InputParameters & parameters)
26 4 : : SinglePhaseFluidProperties(parameters), _MNaK((39.102 + 22.9898) / 1000)
27 : {
28 : // We did not implement other weight fractions
29 8 : const Real Xk = getParam<Real>("weight_fraction_K");
30 4 : if (Xk != 0.778)
31 0 : paramError("weight_fraction_K",
32 : "Only 0.778 weight percent potassium (eutectic) is implemented");
33 :
34 : // Compute mole fractions from mass fractions
35 : const Real AwK = 39.102;
36 : const Real AwNa = 22.9898;
37 4 : _Nk = Xk / AwK / (Xk / AwK + (1 - Xk) / AwNa);
38 4 : }
39 :
40 8 : NaKFluidProperties::~NaKFluidProperties() {}
41 :
42 : std::string
43 1 : NaKFluidProperties::fluidName() const
44 : {
45 1 : return "NaK";
46 : }
47 :
48 : Real
49 1 : NaKFluidProperties::molarMass() const
50 : {
51 1 : return _MNaK;
52 : }
53 :
54 : Real
55 3 : NaKFluidProperties::T_from_p_h(Real /* pressure */, Real enthalpy) const
56 : {
57 : // analytical inversion of h_from_p_T
58 3 : Real h2 = enthalpy * enthalpy;
59 : Real B1 =
60 3 : std::pow(183.357574154983 * std::sqrt(8405 * h2 - 8208700353 * enthalpy + 9265308922016000) +
61 3 : 16810 * enthalpy - 8208700353,
62 : 1. / 3);
63 3 : return _T_c2k + 0.174216027874564 * (3.65930571002297 * B1 - 2.28699205892461e7 / B1 + 3087);
64 : }
65 :
66 : Real
67 6 : NaKFluidProperties::T_from_p_rho(Real pressure, Real density) const
68 : {
69 : // NOTE we could also invert analytically the third degree polynomial, see Cardan's method
70 : auto lambda = [&](Real p, Real current_T, Real & new_rho, Real & drho_dp, Real & drho_dT)
71 24 : { rho_from_p_T(p, current_T, new_rho, drho_dp, drho_dT); };
72 6 : Real T = FluidPropertiesUtils::NewtonSolve(pressure,
73 : density,
74 6 : _T_initial_guess,
75 6 : _tolerance,
76 : lambda,
77 6 : name() + "::T_from_p_rho",
78 6 : _max_newton_its)
79 6 : .first;
80 : // check for nans
81 6 : if (std::isnan(T))
82 0 : mooseError("Conversion from pressure (p = ",
83 : pressure,
84 : ") and density (rho = ",
85 : density,
86 : ") to temperature failed to converge.");
87 6 : return T;
88 : }
89 :
90 : Real
91 75 : NaKFluidProperties::rho_from_p_T(Real /*pressure*/, Real temperature) const
92 : {
93 75 : const Real Tc = temperature - _T_c2k;
94 : // Range from liquid Na and K density correlation ranges
95 75 : if (Tc < 210 || Tc > 1110)
96 31 : flagInvalidSolution(
97 : "NaK density evaluated outside of Na density temperature range [210, 1110] C");
98 75 : if (Tc < 63.2 || Tc > 1250)
99 0 : flagInvalidSolution(
100 : "NaK density evaluated outside of K density temperature range [63, 1250] C");
101 :
102 : // Eq. 1.8 page 18 of NaK handbook
103 75 : const Real v_k = 1. / (0.8415 - 2.172e-4 * Tc - 2.7e-8 * Tc * Tc + 4.77e-12 * Tc * Tc * Tc);
104 : // Eq. 1.5 page 15 of NaK handbook
105 75 : const Real v_Na = 1. / (0.9453 - 2.2473e-4 * Tc);
106 : // Eq. 1.9 page 15 of NaK handbook
107 75 : return 1000 / (_Nk * v_k + (1 - _Nk) * v_Na);
108 : }
109 :
110 : void
111 32 : NaKFluidProperties::rho_from_p_T(
112 : Real pressure, Real temperature, Real & rho, Real & drho_dp, Real & drho_dT) const
113 : {
114 32 : rho = this->rho_from_p_T(pressure, temperature);
115 32 : drho_dp = 0;
116 :
117 32 : const Real Tc = temperature - _T_c2k;
118 : // Eq. 1.8 page 18 of NaK handbook
119 32 : const Real v_k = 1. / (0.8415 - 2.172e-4 * Tc - 2.7e-8 * Tc * Tc + 4.77e-12 * Tc * Tc * Tc);
120 : // Eq. 1.5 page 15 of NaK handbook
121 32 : const Real v_Na = 1. / (0.9453 - 2.2473e-4 * Tc);
122 32 : drho_dT =
123 32 : 1000 *
124 32 : -(_Nk * -(-2.172e-4 - 2 * 2.7e-8 * Tc + 3 * 4.77e-12 * Tc * Tc) * MathUtils::pow(v_k, 2) +
125 32 : (1 - _Nk) * 2.2473e-4 * MathUtils::pow(v_Na, 2)) /
126 32 : MathUtils::pow(_Nk * v_k + (1 - _Nk) * v_Na, 2);
127 32 : }
128 :
129 : Real
130 11 : NaKFluidProperties::e_from_p_T(Real pressure, Real temperature) const
131 : {
132 11 : return h_from_p_T(pressure, temperature) - pressure / rho_from_p_T(pressure, temperature);
133 : }
134 :
135 : Real
136 3 : NaKFluidProperties::e_from_p_rho(Real pressure, Real density) const
137 : {
138 3 : Real temperature = T_from_p_rho(pressure, density);
139 3 : return e_from_p_T(pressure, temperature);
140 : }
141 :
142 : void
143 4 : NaKFluidProperties::e_from_p_T(
144 : Real pressure, Real temperature, Real & e, Real & de_dp, Real & de_dT) const
145 : {
146 : Real h, dh_dp, dh_dT;
147 4 : h_from_p_T(pressure, temperature, h, dh_dp, dh_dT);
148 : Real rho, drho_dp, drho_dT;
149 4 : rho_from_p_T(pressure, temperature, rho, drho_dp, drho_dT);
150 :
151 4 : e = h - pressure / rho;
152 4 : de_dp = dh_dp + pressure * drho_dp / rho / rho - 1.0 / rho;
153 4 : de_dT = dh_dT + pressure * drho_dT / rho / rho;
154 4 : }
155 :
156 : Real
157 14 : NaKFluidProperties::cp_from_p_T(Real /*pressure*/, Real temperature) const
158 : {
159 14 : const Real Tc = temperature - _T_c2k;
160 : // Eq. 1.59 page 53 of the NaK handbook
161 : // converted from cal/g/C
162 14 : return (0.232 - 8.82e-5 * Tc + 8.2e-8 * Tc * Tc) * 4200;
163 : }
164 :
165 : void
166 1 : NaKFluidProperties::cp_from_p_T(
167 : Real /*pressure*/, Real temperature, Real & cp, Real & dcp_dp, Real & dcp_dT) const
168 : {
169 1 : const Real Tc = temperature - _T_c2k;
170 : // Eq. 1.59 page 53 of the NaK handbook
171 : // converted from cal/g/C
172 1 : cp = cp_from_p_T(-1, temperature);
173 1 : dcp_dp = 0;
174 1 : dcp_dT = (-8.82e-5 + 2 * 8.2e-8 * Tc) * 4200;
175 1 : }
176 :
177 : Real
178 3 : NaKFluidProperties::cv_from_p_T(Real pressure, Real temperature) const
179 : {
180 : Real e, de_dp, de_dT;
181 3 : e_from_p_T(pressure, temperature, e, de_dp, de_dT);
182 3 : return de_dT;
183 : }
184 :
185 : Real
186 13 : NaKFluidProperties::mu_from_p_T(Real /*pressure*/, Real temperature) const
187 : {
188 : /* eq. 1.18-19 page 24 of NaK handbook */
189 : // No range given
190 : // Converted from centipoise
191 13 : const Real rho = rho_from_p_T(-1, temperature) / 1000;
192 13 : if (temperature < _T_c2k + 400)
193 6 : return 0.001 * 0.116 * std::pow(rho, 1 / 3.) * exp(688 * rho / temperature);
194 : else
195 7 : return 0.001 * 0.082 * std::pow(rho, 1 / 3.) * exp(979 * rho / temperature);
196 : }
197 :
198 : void
199 2 : NaKFluidProperties::mu_from_p_T(
200 : Real /*pressure*/, Real temperature, Real & mu, Real & dmu_dp, Real & dmu_dT) const
201 : {
202 : /* eq. 1.18-19 page 24 of NaK handbook */
203 : // No range given
204 : // Converted from centipoise
205 : Real rho, drho_dp, drho_dT;
206 2 : rho_from_p_T(-1, temperature, rho, drho_dp, drho_dT);
207 2 : rho /= 1000;
208 2 : drho_dT /= 1000;
209 2 : if (temperature < _T_c2k + 400)
210 : {
211 1 : mu = 0.001 * 0.116 * std::pow(rho, 1 / 3.) * exp(688 * rho / temperature);
212 1 : dmu_dp = 0;
213 1 : dmu_dT =
214 1 : 0.001 * 0.116 * exp(688 * rho / temperature) *
215 1 : (1 / 3. * drho_dT * std::pow(rho, -2 / 3.) +
216 1 : std::pow(rho, 1 / 3.) * 688 * (drho_dT * temperature - rho) / temperature / temperature);
217 : }
218 : else
219 : {
220 1 : mu = 0.001 * 0.082 * std::pow(rho, 1 / 3.) * exp(979 * rho / temperature);
221 1 : dmu_dp = 0;
222 1 : dmu_dT =
223 1 : 0.001 * 0.082 * exp(979 * rho / temperature) *
224 1 : (1 / 3. * drho_dT * std::pow(rho, -2 / 3.) +
225 1 : std::pow(rho, 1 / 3.) * 979 * (drho_dT * temperature - rho) / temperature / temperature);
226 : }
227 2 : }
228 :
229 : Real
230 9 : NaKFluidProperties::k_from_p_T(Real /*pressure*/, Real temperature) const
231 : {
232 9 : const Real Tc = temperature - _T_c2k;
233 : /* eq. 1.53 page 46 handbook */
234 : // Note: reported as very sensitive to the composition
235 : // Range: 150 - 680 C
236 : // Converted from (W/cm-C)
237 9 : if (Tc < 150 || Tc > 680)
238 8 : flagInvalidSolution(
239 : "NaK thermal diffusivity evaluated outside of temperature range [150, 680] C");
240 9 : return 100 * (0.214 + 2.07e-4 * Tc - 2.2e-7 * Tc * Tc);
241 : }
242 :
243 : void
244 1 : NaKFluidProperties::k_from_p_T(
245 : Real /*pressure*/, Real temperature, Real & k, Real & dk_dp, Real & dk_dT) const
246 : {
247 1 : const Real Tc = temperature - _T_c2k;
248 1 : k = k_from_p_T(0, temperature);
249 1 : dk_dp = 0.0;
250 1 : dk_dT = 100 * (2.07e-4 - 2 * 2.2e-7 * Tc);
251 1 : }
252 :
253 : Real
254 22 : NaKFluidProperties::h_from_p_T(Real /*pressure*/, Real temperature) const
255 : {
256 : // Integration of cv
257 22 : const Real Tc = temperature - _T_c2k;
258 22 : return (0.232 * Tc - 8.82e-5 / 2 * Tc * Tc + 8.2e-8 / 3 * Tc * Tc * Tc) * 4200;
259 : }
260 :
261 : void
262 5 : NaKFluidProperties::h_from_p_T(
263 : Real pressure, Real temperature, Real & h, Real & dh_dp, Real & dh_dT) const
264 : {
265 5 : const Real Tc = temperature - _T_c2k;
266 5 : h = (0.232 * Tc - 8.82e-5 / 2 * Tc * Tc + 8.2e-8 / 3 * Tc * Tc * Tc) * 4200;
267 5 : dh_dp = 0;
268 5 : dh_dT = cp_from_p_T(pressure, temperature);
269 5 : }
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