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Water97FluidProperties.h
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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#pragma once
11
12#include "SinglePhaseFluidProperties.h"
13#include "NewtonInversion.h"
14#include <array>
15
16#pragma GCC diagnostic push
17#pragma GCC diagnostic ignored "-Woverloaded-virtual"
18
38class Water97FluidProperties : public SinglePhaseFluidProperties
39{
40public:
41 static InputParameters validParams();
42
43 Water97FluidProperties(const InputParameters & parameters);
44 virtual ~Water97FluidProperties();
45
46 virtual std::string fluidName() const override;
47
48 virtual Real molarMass() const override;
49
50 virtual Real criticalPressure() const override;
51
52 virtual Real criticalTemperature() const override;
53
54 virtual Real criticalDensity() const override;
55
56 virtual Real triplePointPressure() const override;
57
58 virtual Real triplePointTemperature() const override;
59
60 virtual Real rho_from_p_T(Real pressure, Real temperature) const override;
61 virtual ADReal rho_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
62
63 virtual Real v_from_p_T(Real pressure, Real temperature) const override;
64 virtual ADReal v_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
65 template <typename T>
66 T v_from_p_T_template(const T & pressure, const T & temperature) const;
67 virtual void
68 v_from_p_T(Real pressure, Real temperature, Real & v, Real & dv_dp, Real & dv_dT) const override;
69 virtual void v_from_p_T(const ADReal & pressure,
70 const ADReal & temperature,
71 ADReal & v,
72 ADReal & dv_dp,
73 ADReal & dv_dT) const override;
74 template <typename T>
75 void
76 v_from_p_T_template(const T & pressure, const T & temperature, T & v, T & dv_dp, T & dv_dt) const;
77
78 template <typename T>
79 T rho_from_p_T_template(const T & pressure, const T & temperature) const;
80 template <typename T>
81 void rho_from_p_T_template(
82 const T & pressure, const T & temperature, T & rho, T & drho_dp, T & drho_dt) const;
83
84 virtual void rho_from_p_T(
85 Real pressure, Real temperature, Real & rho, Real & drho_dp, Real & drho_dT) const override;
86 virtual void rho_from_p_T(const ADReal & pressure,
87 const ADReal & temperature,
88 ADReal & rho,
89 ADReal & drho_dp,
90 ADReal & drho_dT) const override;
91
92 Real p_from_v_e(Real v, Real e) const override;
93 ADReal p_from_v_e(const ADReal & v, const ADReal & e) const override;
94 template <typename T>
95 T p_from_v_e_template(const T & v, const T & e) const;
96
97 virtual Real e_from_p_rho(Real p, Real rho) const override;
98 virtual ADReal e_from_p_rho(const ADReal & p, const ADReal & rho) const override;
99 template <typename T>
100 T e_from_p_rho_template(const T & p, const T & rho) const;
101 void e_from_p_rho(Real p, Real rho, Real & e, Real & de_dp, Real & de_drho) const override;
102 void e_from_p_rho(const ADReal & p,
103 const ADReal & rho,
104 ADReal & e,
105 ADReal & de_dp,
106 ADReal & de_drho) const override;
107 template <typename T>
108 void e_from_p_rho_template(const T & p, const T & rho, T & e, T & de_dp, T & de_drho) const;
109
110 virtual Real e_from_p_T(Real pressure, Real temperature) const override;
111 virtual ADReal e_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
112 template <typename T>
113 T e_from_p_T_template(const T & pressure, const T & temperature) const;
114
115 virtual void
116 e_from_p_T(Real pressure, Real temperature, Real & e, Real & de_dp, Real & de_dT) const override;
117 virtual void e_from_p_T(const ADReal & pressure,
118 const ADReal & temperature,
119 ADReal & e,
120 ADReal & de_dp,
121 ADReal & de_dT) const override;
122 template <typename T>
123 void
124 e_from_p_T_template(const T & pressure, const T & temperature, T & e, T & de_dp, T & de_dT) const;
125
126 ADReal e_from_v_h(const ADReal & v, const ADReal & h) const override;
127
128 Real T_from_v_e(Real v, Real e) const override;
129 ADReal T_from_v_e(const ADReal & v, const ADReal & e) const override;
130
131 virtual Real c_from_p_T(Real pressure, Real temperature) const override;
132 virtual ADReal c_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
133 template <typename T>
134 T c_from_p_T_template(const T & pressure, const T & temperature) const;
135 virtual ADReal c_from_v_e(const ADReal & v, const ADReal & e) const override;
136
137 virtual Real cp_from_p_T(Real pressure, Real temperature) const override;
138 virtual ADReal cp_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
139 template <typename T>
140 T cp_from_p_T_template(const T & pressure, const T & temperature) const;
141
142 using SinglePhaseFluidProperties::cp_from_p_T;
143
144 virtual ADReal cp_from_v_e(const ADReal & v, const ADReal & e) const override;
145
146 virtual Real cv_from_p_T(Real pressure, Real temperature) const override;
147 virtual ADReal cv_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
148 template <typename T>
149 T cv_from_p_T_template(const T & pressure, const T & temperature) const;
150
151 virtual ADReal cv_from_v_e(const ADReal & v, const ADReal & e) const override;
152
153 virtual Real mu_from_p_T(Real pressure, Real temperature) const override;
154 virtual ADReal mu_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
155 template <typename T>
156 T mu_from_p_T_template(const T & pressure, const T & temperature) const;
157
158 virtual void mu_from_p_T(
159 Real pressure, Real temperature, Real & mu, Real & dmu_dp, Real & dmu_dT) const override;
160
161 virtual Real mu_from_rho_T(Real density, Real temperature) const override;
162 template <typename T>
163 T mu_from_rho_T_template(const T & density, const T & temperature) const;
164
165 void mu_from_rho_T(
166 Real rho, Real temperature, Real drho_dT, Real & mu, Real & dmu_drho, Real & dmu_dT) const;
167
168 ADReal mu_from_v_e(const ADReal & v, const ADReal & e) const override;
169
170 virtual void
171 rho_mu_from_p_T(Real pressure, Real temperature, Real & rho, Real & mu) const override;
172
173 virtual void rho_mu_from_p_T(Real pressure,
174 Real temperature,
175 Real & rho,
176 Real & drho_dp,
177 Real & drho_dT,
178 Real & mu,
179 Real & dmu_dp,
180 Real & dmu_dT) const override;
181
182 virtual Real k_from_p_T(Real pressure, Real temperature) const override;
183 virtual ADReal k_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
184 template <typename T>
185 T k_from_p_T_template(const T & pressure, const T & temperature) const;
186
187 virtual void
188 k_from_p_T(Real pressure, Real temperature, Real & k, Real & dk_dp, Real & dk_dT) const override;
189
190 virtual Real k_from_rho_T(Real density, Real temperature) const override;
191 template <typename T>
192 T k_from_rho_T_template(const T & density, const T & temperature) const;
193
194 Real k_from_v_e(Real v, Real e) const override;
195 ADReal k_from_v_e(const ADReal & v, const ADReal & e) const override;
196 template <typename T>
197 T k_from_v_e_template(const T & v, const T & e) const;
198
199 propfuncWithDefinitionOverride(s, p, T);
200
201 virtual Real h_from_p_T(Real pressure, Real temperature) const override;
202 virtual ADReal h_from_p_T(const ADReal & pressure, const ADReal & temperature) const override;
203 template <typename T>
204 T h_from_p_T_template(const T & pressure, const T & temperature) const;
205
206 virtual void
207 h_from_p_T(Real pressure, Real temperature, Real & h, Real & dh_dp, Real & dh_dT) const override;
208 virtual void h_from_p_T(const ADReal & pressure,
209 const ADReal & temperature,
210 ADReal & h,
211 ADReal & dh_dp,
212 ADReal & dh_dT) const override;
213 template <typename T>
214 void
215 h_from_p_T_template(const T & pressure, const T & temperature, T & h, T & dh_dp, T & dh_dT) const;
216
217 virtual Real s_from_h_p(Real enthalpy, Real pressure) const override;
218 virtual ADReal s_from_h_p(const ADReal & enthalpy, const ADReal & pressure) const override;
219 void virtual s_from_h_p(
220 Real enthalpy, Real pressure, Real & s, Real & ds_dh, Real & ds_dp) const override;
221
222 virtual Real vaporPressure(Real temperature) const override;
223
224 virtual void vaporPressure(Real temperature, Real & psat, Real & dpsat_dT) const override;
225
226 template <typename T>
227 void vaporPressureTemplate(const T & temperature, T & psat, T & dpsat_dT) const;
228
241 Real vaporTemperature(Real pressure) const override;
242 virtual void vaporTemperature(Real pressure, Real & Tsat, Real & dTsat_dp) const override;
243
254 Real b23p(Real temperature) const;
255
266 Real b23T(Real pressure) const;
267
276 unsigned int inRegion(Real pressure, Real temperature) const;
277
286 unsigned int inRegionPH(Real pressure, Real enthalpy) const;
287
299 unsigned int subregion3(Real pressure, Real temperature) const;
300
310 template <typename T>
311 T subregionVolume(const T & pi,
312 const T & theta,
313 Real a,
314 Real b,
315 Real c,
316 Real d,
317 Real e,
318 unsigned int sid) const;
319
333 template <typename T>
334 T densityRegion3(const T & pressure, const T & temperature) const;
335
345 virtual Real T_from_p_h(Real pressure, Real enthalpy) const override;
346 virtual void T_from_p_h(Real p, Real h, Real & T, Real & dT_dp, Real & dT_dh) const override;
347 virtual ADReal T_from_p_h(const ADReal & pressure, const ADReal & enthalpy) const override;
348
358 Real b2bc(Real pressure) const;
359
370 Real b3ab(Real pressure) const;
371
382 Real henryConstant(Real temperature, const std::vector<Real> & coeffs) const;
383 void
384 henryConstant(Real temperature, const std::vector<Real> & coeffs, Real & Kh, Real & dKh_dT) const;
385 ADReal henryConstant(const ADReal & temperature, const std::vector<Real> & coeffs) const;
386
391 template <typename T>
392 std::pair<T, T> p_T_from_v_e(const T & v, const T & e) const;
393
398 template <typename T>
399 std::pair<T, T> rho_T_from_v_e(const T & v, const T & e) const;
400
405 template <typename T>
406 std::pair<T, T> p_T_from_v_h(const T & v, const T & h) const;
407 using SinglePhaseFluidProperties::p_T_from_v_h;
408
409protected:
421 template <typename T>
422 T gamma1(const T & pi, const T & tau) const;
423
431 template <typename T>
432 T dgamma1_dpi(const T & pi, const T & tau) const;
433
441 template <typename T>
442 T d2gamma1_dpi2(const T & pi, const T & tau) const;
443
451 template <typename T>
452 T dgamma1_dtau(const T & pi, const T & tau) const;
453
461 template <typename T>
462 T d2gamma1_dtau2(const T & pi, const T & tau) const;
463
471 template <typename T>
472 T d2gamma1_dpitau(const T & pi, const T & tau) const;
473
485 template <typename T>
486 T gamma2(const T & pi, const T & tau) const;
487
495 template <typename T>
496 T dgamma2_dpi(const T & pi, const T & tau) const;
497
505 template <typename T>
506 T d2gamma2_dpi2(const T & pi, const T & tau) const;
507
515 template <typename T>
516 T dgamma2_dtau(const T & pi, const T & tau) const;
517
525 template <typename T>
526 T d2gamma2_dtau2(const T & pi, const T & tau) const;
527
535 template <typename T>
536 T d2gamma2_dpitau(const T & pi, const T & tau) const;
537
549 template <typename T>
550 T phi3(const T & delta, const T & tau) const;
551
559 template <typename T>
560 T dphi3_ddelta(const T & delta, const T & tau) const;
561
569 template <typename T>
570 T d2phi3_ddelta2(const T & delta, const T & tau) const;
571
579 template <typename T>
580 T dphi3_dtau(const T & delta, const T & tau) const;
581
589 template <typename T>
590 T d2phi3_dtau2(const T & delta, const T & tau) const;
591
599 template <typename T>
600 T d2phi3_ddeltatau(const T & delta, const T & tau) const;
601
613 template <typename T>
614 T gamma5(const T & pi, const T & tau) const;
615
623 template <typename T>
624 T dgamma5_dpi(const T & pi, const T & tau) const;
625
633 template <typename T>
634 T d2gamma5_dpi2(const T & pi, const T & tau) const;
635
643 template <typename T>
644 T dgamma5_dtau(const T & pi, const T & tau) const;
645
653 template <typename T>
654 T d2gamma5_dtau2(const T & pi, const T & tau) const;
655
663 template <typename T>
664 T d2gamma5_dpitau(const T & pi, const T & tau) const;
665
682
694 template <typename T>
695 T tempXY(const T & pressure, subregionEnum xy) const;
696
707 unsigned int subregion2ph(Real pressure, Real enthalpy) const;
708
720 unsigned int subregion3ph(Real pressure, Real enthalpy) const;
721
731 ADReal T_from_p_h_ad(const ADReal & pressure, const ADReal & enthalpy) const;
732
743 ADReal temperature_from_ph1(const ADReal & pressure, const ADReal & enthalpy) const;
744
755 ADReal temperature_from_ph2a(const ADReal & pressure, const ADReal & enthalpy) const;
756
767 ADReal temperature_from_ph2b(const ADReal & pressure, const ADReal & enthalpy) const;
768
779 ADReal temperature_from_ph2c(const ADReal & pressure, const ADReal & enthalpy) const;
780
792 ADReal temperature_from_ph3a(const ADReal & pressure, const ADReal & enthalpy) const;
793
805 ADReal temperature_from_ph3b(const ADReal & pressure, const ADReal & enthalpy) const;
806
819 ADReal vaporTemperature_ad(const ADReal & pressure) const;
820
822 const Real _Mh2o;
824 const Real _Rw;
826 const Real _p_critical;
828 const Real _T_critical;
830 const Real _rho_critical;
832 const Real _p_triple;
834 const Real _T_triple;
835
845 const std::array<Real, 34> _n1{
846 {0.14632971213167e0, -0.84548187169114e0, -0.37563603672040e1, 0.33855169168385e1,
847 -0.95791963387872e0, 0.15772038513228e0, -0.16616417199501e-1, 0.81214629983568e-3,
848 0.28319080123804e-3, -0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1,
849 -0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3, -0.30001780793026e-3,
850 0.47661393906987e-4, -0.44141845330846e-5, -0.72694996297594e-15, -0.31679644845054e-4,
851 -0.28270797985312e-5, -0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6,
852 -0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8, -0.17424871230634e-9,
853 -0.68762131295531e-18, 0.14478307828521e-19, 0.26335781662795e-22, -0.11947622640071e-22,
854 0.18228094581404e-23, -0.93537087292458e-25}};
855
856 const std::array<int, 34> _I1{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2,
857 2, 2, 3, 3, 3, 4, 4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32}};
858
859 const std::array<int, 34> _J1{{-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0,
860 1, 3, -3, 0, 1, 3, 17, -4, 0, 6, -5, -2,
861 10, -8, -11, -6, -29, -31, -38, -39, -40, -41}};
862
863 const std::array<Real, 20> _nph1{
864 {-0.23872489924521e3, 0.40421188637945e3, 0.11349746881718e3, -0.58457616048039e1,
865 -0.15285482413140e-3, -0.10866707695377e-5, -0.13391744872602e2, 0.43211039183559e2,
866 -0.54010067170506e2, 0.30535892203916e2, -0.65964749423638e1, 0.93965400878363e-2,
867 0.11573647505340e-6, -0.25858641282073e-4, -0.40644363084799e-8, 0.66456186191635e-7,
868 0.80670734103027e-10, -0.93477771213947e-12, 0.58265442020601e-14, -0.15020185953503e-16}};
869
870 const std::array<int, 20> _Iph1{{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6}};
871
872 const std::array<int, 20> _Jph1{
873 {0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32}};
874
876 const std::array<Real, 9> _n02{{-0.96927686500217e1,
877 0.10086655968018e2,
878 -0.56087911283020e-2,
879 0.71452738081455e-1,
880 -0.40710498223928e0,
881 0.14240819171444e1,
882 -0.43839511319450e1,
883 -0.28408632460772e0,
884 0.21268463753307e-1}};
885
886 const std::array<Real, 43> _n2{
887 {-0.17731742473213e-2, -0.17834862292358e-1, -0.45996013696365e-1, -0.57581259083432e-1,
888 -0.50325278727930e-1, -0.33032641670203e-4, -0.18948987516315e-3, -0.39392777243355e-2,
889 -0.43797295650573e-1, -0.26674547914087e-4, 0.20481737692309e-7, 0.43870667284435e-6,
890 -0.32277677238570e-4, -0.15033924542148e-2, -0.40668253562649e-1, -0.78847309559367e-9,
891 0.12790717852285e-7, 0.48225372718507e-6, 0.22922076337661e-5, -0.16714766451061e-10,
892 -0.21171472321355e-2, -0.23895741934104e2, -0.59059564324270e-17, -0.12621808899101e-5,
893 -0.38946842435739e-1, 0.11256211360459e-10, -0.82311340897998e1, 0.19809712802088e-7,
894 0.10406965210174e-18, -0.10234747095929e-12, -0.10018179379511e-8, -0.80882908646985e-10,
895 0.10693031879409e0, -0.33662250574171e0, 0.89185845355421e-24, 0.30629316876232e-12,
896 -0.42002467698208e-5, -0.59056029685639e-25, 0.37826947613457e-5, -0.12768608934681e-14,
897 0.73087610595061e-28, 0.55414715350778e-16, -0.94369707241210e-6}};
898
899 const std::array<int, 9> _J02{{0, 1, -5, -4, -3, -2, -1, 2, 3}};
900
901 const std::array<int, 43> _I2{{1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,
902 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10,
903 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24, 24, 24}};
904
905 const std::array<int, 43> _J2{{0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35,
906 1, 2, 3, 7, 3, 16, 35, 0, 11, 25, 8, 36, 13, 4, 10,
907 14, 29, 50, 57, 20, 35, 48, 21, 53, 39, 26, 40, 58}};
908
909 const std::array<Real, 36> _nph2a{
910 {0.10898952318288e4, 0.84951654495535e3, -0.10781748091826e3, 0.33153654801263e2,
911 -0.74232016790248e1, 0.11765048724356e2, 0.18445749355790e1, -0.41792700549624e1,
912 0.62478196935812e1, -0.17344563108114e2, -0.20058176862096e3, 0.27196065473796e3,
913 -0.45511318285818e3, 0.30919688604755e4, 0.25226640357872e6, -0.61707422868339e-2,
914 -0.31078046629583, 0.11670873077107e2, 0.12812798404046e9, -0.98554909623276e9,
915 0.28224546973002e10, -0.35948971410703e10, 0.17227349913197e10, -0.13551334240775e5,
916 0.12848734664650e8, 0.13865724283226e1, 0.23598832556514e6, -0.13105236545054e8,
917 0.73999835474766e4, -0.55196697030060e6, 0.37154085996233e7, 0.19127729239660e5,
918 -0.41535164835634e6, -0.62459855192507e2}};
919
920 const std::array<int, 36> _Iph2a{{0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
921 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7}};
922
923 const std::array<int, 36> _Jph2a{{0, 1, 2, 3, 7, 20, 0, 1, 2, 3, 7, 9,
924 11, 18, 44, 0, 2, 7, 36, 38, 40, 42, 44, 24,
925 44, 12, 32, 44, 32, 36, 42, 34, 44, 28}};
926
927 const std::array<Real, 38> _nph2b{
928 {0.14895041079516e4, 0.74307798314034e3, -0.97708318797837e2, 0.24742464705674e1,
929 -0.63281320016026, 0.11385952129658e1, -0.47811863648625, 0.85208123431544e-2,
930 0.93747147377932, 0.33593118604916e1, 0.33809355601454e1, 0.16844539671904,
931 0.73875745236695, -0.47128737436186, 0.15020273139707, -0.21764114219750e-2,
932 -0.21810755324761e-1, -0.10829784403677, -0.46333324635812e-1, 0.71280351959551e-4,
933 0.11032831789999e-3, 0.18955248387902e-3, 0.30891541160537e-2, 0.13555504554949e-2,
934 0.28640237477456e-6, -0.10779857357512e-4, -0.76462712454814e-4, 0.14052392818316e-4,
935 -0.31083814331434e-4, -0.10302738212103e-5, 0.28217281635040e-6, 0.12704902271945e-5,
936 0.73803353468292e-7, -0.11030139238909e-7, -0.81456365207833e-13, -0.25180545682962e-10,
937 -0.17565233969407e-17, 0.86934156344163e-14}};
938
939 const std::array<int, 38> _Iph2b{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2,
940 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 7, 7, 9, 9}};
941
942 const std::array<int, 38> _Jph2b{{0, 1, 2, 12, 18, 24, 28, 40, 0, 2, 6, 12, 18,
943 24, 28, 40, 2, 8, 18, 40, 1, 2, 12, 24, 2, 12,
944 18, 24, 28, 40, 18, 24, 40, 28, 2, 28, 1, 40}};
945
946 const std::array<Real, 23> _nph2c{
947 {-0.32368398555242e13, 0.73263350902181e13, 0.35825089945447e12, -0.58340131851590e12,
948 -0.10783068217470e11, 0.20825544563171e11, 0.61074783564516e6, 0.85977722535580e6,
949 -0.25745723604170e5, 0.31081088422714e5, 0.12082315865936e4, 0.48219755109255e3,
950 0.37966001272486e1, -0.10842984880077e2, -0.45364172676660e-1, 0.14559115658698e-12,
951 0.11261597407230e-11, -0.17804982240686e-10, 0.12324579690832e-6, -0.11606921130984e-5,
952 0.27846367088554e-4, -0.59270038474176e-3, 0.12918582991878e-2}};
953
954 const std::array<int, 23> _Iph2c{
955 {-7, -7, -6, -6, -5, -5, -2, -2, -1, -1, 0, 0, 1, 1, 2, 6, 6, 6, 6, 6, 6, 6, 6}};
956
957 const std::array<int, 23> _Jph2c{
958 {0, 4, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 4, 8, 4, 0, 1, 4, 10, 12, 16, 20, 22}};
959
961 const std::array<Real, 5> _n23{{0.34805185628969e3,
962 -0.11671859879975e1,
963 0.10192970039326e-2,
964 0.57254459862746e3,
965 0.13918839778870e2}};
966
968 const std::array<Real, 40> _n3{
969 {0.10658070028513e1, -0.15732845290239e2, 0.20944396974307e2, -0.76867707878716e1,
970 0.26185947787954e1, -0.28080781148620e1, 0.12053369696517e1, -0.84566812812502e-2,
971 -0.12654315477714e1, -0.11524407806681e1, 0.88521043984318e0, -0.64207765181607e0,
972 0.38493460186671e0, -0.85214708824206e0, 0.48972281541877e1, -0.30502617256965e1,
973 0.39420536879154e-1, 0.12558408424308e0, -0.27999329698710e0, 0.13899799569460e1,
974 -0.20189915023570e1, -0.82147637173963e-2, -0.47596035734923e0, 0.43984074473500e-1,
975 -0.44476435428739e0, 0.90572070719733e0, 0.70522450087967e0, 0.10770512626332e0,
976 -0.32913623258954e0, -0.50871062041158e0, -0.22175400873096e-1, 0.94260751665092e-1,
977 0.16436278447961e0, -0.13503372241348e-1, -0.14834345352472e-1, 0.57922953628084e-3,
978 0.32308904703711e-2, 0.80964802996215e-4, -0.16557679795037e-3, -0.44923899061815e-4}};
979
980 const std::array<int, 40> _I3{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3,
981 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11}};
982
983 const std::array<int, 40> _J3{{0, 0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2,
984 6, 7, 22, 26, 0, 2, 4, 16, 26, 0, 2, 4, 26, 1,
985 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26}};
986
987 const std::array<std::array<Real, 8>, 26> _par3{
988 {{{0.0024, 100.0, 760.0, 0.085, 0.817, 1.0, 1.0, 1.0}},
989 {{0.0041, 100.0, 860.0, 0.280, 0.779, 1.0, 1.0, 1.0}},
990 {{0.0022, 40.0, 690.0, 0.259, 0.903, 1.0, 1.0, 1.0}},
991 {{0.0029, 40.0, 690.0, 0.559, 0.939, 1.0, 1.0, 4.0}},
992 {{0.0032, 40.0, 710.0, 0.587, 0.918, 1.0, 1.0, 1.0}},
993 {{0.0064, 40.0, 730.0, 0.587, 0.891, 0.5, 1.0, 4.0}},
994 {{0.0027, 25.0, 660.0, 0.872, 0.971, 1.0, 1.0, 4.0}},
995 {{0.0032, 25.0, 660.0, 0.898, 0.983, 1.0, 1.0, 4.0}},
996 {{0.0041, 25.0, 660.0, 0.910, 0.984, 0.5, 1.0, 4.0}},
997 {{0.0054, 25.0, 670.0, 0.875, 0.964, 0.5, 1.0, 4.0}},
998 {{0.0077, 25.0, 680.0, 0.802, 0.935, 1.0, 1.0, 1.0}},
999 {{0.0026, 24.0, 650.0, 0.908, 0.989, 1.0, 1.0, 4.0}},
1000 {{0.0028, 23.0, 650.0, 1.000, 0.997, 1.0, 0.25, 1.0}},
1001 {{0.0031, 23.0, 650.0, 0.976, 0.997, 0.0, 0.0, 0.0}},
1002 {{0.0034, 23.0, 650.0, 0.974, 0.996, 0.5, 1.0, 1.0}},
1003 {{0.0041, 23.0, 650.0, 0.972, 0.997, 0.5, 1.0, 1.0}},
1004 {{0.0022, 23.0, 650.0, 0.848, 0.983, 1.0, 1.0, 4.0}},
1005 {{0.0054, 23.0, 650.0, 0.874, 0.982, 1.0, 1.0, 1.0}},
1006 {{0.0022, 21.0, 640.0, 0.886, 0.990, 1.0, 1.0, 4.0}},
1007 {{0.0088, 20.0, 650.0, 0.803, 1.020, 1.0, 1.0, 1.0}},
1008 {{0.0026, 23.0, 650.0, 0.902, 0.988, 1.0, 1.0, 1.0}},
1009 {{0.0031, 23.0, 650.0, 0.960, 0.995, 1.0, 1.0, 1.0}},
1010 {{0.0039, 23.0, 650.0, 0.959, 0.995, 1.0, 1.0, 4.0}},
1011 {{0.0049, 23.0, 650.0, 0.910, 0.988, 1.0, 1.0, 1.0}},
1012 {{0.0031, 22.0, 650.0, 0.996, 0.994, 1.0, 1.0, 4.0}},
1013 {{0.0038, 22.0, 650.0, 0.993, 0.994, 1.0, 1.0, 4.0}}}};
1014
1015 const std::array<unsigned int, 26> _par3N{{30, 32, 35, 38, 29, 42, 38, 29, 42, 29, 34, 43, 40,
1016 39, 24, 27, 24, 27, 29, 33, 38, 39, 35, 36, 20, 23}};
1017
1019 const std::vector<std::vector<Real>> _n3s{
1020 {0.110879558823853e-2, 0.572616740810616e3, -0.767051948380852e5, -0.253321069529674e-1,
1021 0.628008049345689e4, 0.234105654131876e6, 0.216867826045856, -0.156237904341963e3,
1022 -0.269893956176613e5, -0.180407100085505e-3, 0.116732227668261e-2, 0.266987040856040e2,
1023 0.282776617243286e5, -0.242431520029523e4, 0.435217323022733e-3, -0.122494831387441e-1,
1024 0.179357604019989e1, 0.442729521058314e2, -0.593223489018342e-2, 0.453186261685774,
1025 0.135825703129140e1, 0.408748415856745e-1, 0.474686397863312, 0.118646814997915e1,
1026 0.546987265727549, 0.195266770452643, -0.502268790869663e-1, -0.369645308193377,
1027 0.633828037528420e-2, 0.797441793901017e-1},
1028 {-0.827670470003621e-1, 0.416887126010565e2, 0.483651982197059e-1, -0.291032084950276e5,
1029 -0.111422582236948e3, -0.202300083904014e-1, 0.294002509338515e3, 0.140244997609658e3,
1030 -0.344384158811459e3, 0.361182452612149e3, -0.140699677420738e4, -0.202023902676481e-2,
1031 0.171346792457471e3, -0.425597804058632e1, 0.691346085000334e-5, 0.151140509678925e-2,
1032 -0.416375290166236e-1, -0.413754957011042e2, -0.506673295721637e2, -0.572212965569023e-3,
1033 0.608817368401785e1, 0.239600660256161e2, 0.122261479925384e-1, 0.216356057692938e1,
1034 0.398198903368642, -0.116892827834085, -0.102845919373532, -0.492676637589284,
1035 0.655540456406790e-1, -0.240462535078530, -0.269798180310075e-1, 0.128369435967012},
1036 {0.311967788763030e1, 0.276713458847564e5, 0.322583103403269e8, -0.342416065095363e3,
1037 -0.899732529907377e6, -0.793892049821251e8, 0.953193003217388e2, 0.229784742345072e4,
1038 0.175336675322499e6, 0.791214365222792e7, 0.319933345844209e-4, -0.659508863555767e2,
1039 -0.833426563212851e6, 0.645734680583292e-1, -0.382031020570813e7, 0.406398848470079e-4,
1040 0.310327498492008e2, -0.892996718483724e-3, 0.234604891591616e3, 0.377515668966951e4,
1041 0.158646812591361e-1, 0.707906336241843, 0.126016225146570e2, 0.736143655772152,
1042 0.676544268999101, -0.178100588189137e2, -0.156531975531713, 0.117707430048158e2,
1043 0.840143653860447e-1, -0.186442467471949, -0.440170203949645e2, 0.123290423502494e7,
1044 -0.240650039730845e-1, -0.107077716660869e7, 0.438319858566475e-1},
1045 {-0.452484847171645e-9, 0.315210389538801e-4, -0.214991352047545e-2, 0.508058874808345e3,
1046 -0.127123036845932e8, 0.115371133120497e13, -0.197805728776273e-15, 0.241554806033972e-10,
1047 -0.156481703640525e-5, 0.277211346836625e-2, -0.203578994462286e2, 0.144369489909053e7,
1048 -0.411254217946539e11, 0.623449786243773e-5, -0.221774281146038e2, -0.689315087933158e5,
1049 -0.195419525060713e8, 0.316373510564015e4, 0.224040754426988e7, -0.436701347922356e-5,
1050 -0.404213852833996e-3, -0.348153203414663e3, -0.385294213555289e6, 0.135203700099403e-6,
1051 0.134648383271089e-3, 0.125031835351736e6, 0.968123678455841e-1, 0.225660517512438e3,
1052 -0.190102435341872e-3, -0.299628410819229e-1, 0.500833915372121e-2, 0.387842482998411,
1053 -0.138535367777182e4, 0.870745245971773, 0.171946252068742e1, -0.326650121426383e-1,
1054 0.498044171727877e4, 0.551478022765087e-2},
1055 {0.715815808404721e9, -0.114328360753449e12, 0.376531002015720e-11, -0.903983668691157e-4,
1056 0.665695908836252e6, 0.535364174960127e10, 0.794977402335603e11, 0.922230563421437e2,
1057 -0.142586073991215e6, -0.111796381424162e7, 0.896121629640760e4, -0.669989239070491e4,
1058 0.451242538486834e-2, -0.339731325977713e2, -0.120523111552278e1, 0.475992667717124e5,
1059 -0.266627750390341e6, -0.153314954386524e-3, 0.305638404828265, 0.123654999499486e3,
1060 -0.104390794213011e4, -0.157496516174308e-1, 0.685331118940253, 0.178373462873903e1,
1061 -0.544674124878910, 0.204529931318843e4, -0.228342359328752e5, 0.413197481515899,
1062 -0.341931835910405e2},
1063 {-0.251756547792325e-7, 0.601307193668763e-5, -0.100615977450049e-2,
1064 0.999969140252192, 0.214107759236486e1, -0.165175571959086e2,
1065 -0.141987303638727e-2, 0.269251915156554e1, 0.349741815858722e2,
1066 -0.300208695771783e2, -0.131546288252539e1, -0.839091277286169e1,
1067 0.181545608337015e-9, -0.591099206478909e-3, 0.152115067087106e1,
1068 0.252956470663225e-4, 0.100726265203786e-14, -0.14977453386065e1,
1069 -0.793940970562969e-9, -0.150290891264717e-3, 0.151205531275133e1,
1070 0.470942606221652e-5, 0.195049710391712e-12, -0.911627886266077e-8,
1071 0.604374640201265e-3, -0.225132933900136e-15, 0.610916973582981e-11,
1072 -0.303063908043404e-6, -0.137796070798409e-4, -0.919296736666106e-3,
1073 0.639288223132545e-9, 0.753259479898699e-6, -0.400321478682929e-12,
1074 0.756140294351614e-8, -0.912082054034891e-11, -0.237612381140539e-7,
1075 0.269586010591874e-4, -0.732828135157839e-10, 0.241995578306660e-9,
1076 -0.405735532730322e-3, 0.189424143498011e-9, -0.486632965074563e-9},
1077 {0.412209020652996e-4, -0.114987238280587e7, 0.948180885032080e10, -0.195788865718971e18,
1078 0.4962507048713e25, -0.105549884548496e29, -0.758642165988278e12, -0.922172769596101e23,
1079 0.725379072059348e30, -0.617718249205859e2, 0.107555033344858e5, -0.379545802336487e8,
1080 0.228646846221831e12, -0.499741093010619e7, -0.280214310054101e31, 0.104915406769586e7,
1081 0.613754229168619e28, 0.802056715528378e32, -0.298617819828065e8, -0.910782540134681e2,
1082 0.135033227281565e6, -0.712949383408211e19, -0.104578785289542e37, 0.304331584444093e2,
1083 0.593250797959445e10, -0.364174062110798e28, 0.921791403532461, -0.337693609657471,
1084 -0.724644143758508e2, -0.110480239272601, 0.536516031875059e1, -0.291441872156205e4,
1085 0.616338176535305e40, -0.120889175861180e39, 0.818396024524612e23, 0.940781944835829e9,
1086 -0.367279669545448e5, -0.837513931798655e16},
1087 {0.561379678887577e-1, 0.774135421587083e10, 0.111482975877938e-8, -0.143987128208183e-2,
1088 0.193696558764920e4, -0.605971823585005e9, 0.171951568124337e14, -0.185461154985145e17,
1089 0.38785116807801e-16, -0.395464327846105e-13, -0.170875935679023e3, -0.21201062070122e4,
1090 0.177683337348191e8, 0.110177443629575e2, -0.234396091693313e6, -0.656174421999594e7,
1091 0.156362212977396e-4, -0.212946257021400e1, 0.135249306374858e2, 0.177189164145813,
1092 0.139499167345464e4, -0.703670932036388e-2, -0.152011044389648, 0.981916922991113e-4,
1093 0.147199658618076e-2, 0.202618487025578e2, 0.899345518944240, -0.211346402240858,
1094 0.249971752957491e2},
1095 {0.106905684359136e1, -0.148620857922333e1, 0.259862256980408e15,
1096 -0.446352055678749e-11, -0.566620757170032e-6, -0.235302885736849e-2,
1097 -0.269226321968839, 0.922024992944392e1, 0.357633505503772e-11,
1098 -0.173942565562222e2, 0.700681785556229e-5, -0.267050351075768e-3,
1099 -0.231779669675624e1, -0.753533046979752e-12, 0.481337131452891e1,
1100 -0.223286270422356e22, -0.118746004987383e-4, 0.646412934136496e-2,
1101 -0.410588536330937e-9, 0.422739537057241e20, 0.313698180473812e-12,
1102 0.16439533434504e-23, -0.339823323754373e-5, -0.135268639905021e-1,
1103 -0.723252514211625e-14, 0.184386437538366e-8, -0.463959533752385e-1,
1104 -0.99226310037675e14, 0.688169154439335e-16, -0.222620998452197e-10,
1105 -0.540843018624083e-7, 0.345570606200257e-2, 0.422275800304086e11,
1106 -0.126974478770487e-14, 0.927237985153679e-9, 0.612670812016489e-13,
1107 -0.722693924063497e-11, -0.383669502636822e-3, 0.374684572410204e-3,
1108 -0.931976897511086e5, -0.247690616026922e-1, 0.658110546759474e2},
1109 {-0.111371317395540e-3, 0.100342892423685e1, 0.530615581928979e1,
1110 0.179058760078792e-5, -0.728541958464774e-3, -0.187576133371704e2,
1111 0.199060874071849e-2, 0.243574755377290e2, -0.177040785499444e-3,
1112 -0.25968038522713e-2, -0.198704578406823e3, 0.738627790224287e-4,
1113 -0.236264692844138e-2, -0.161023121314333e1, 0.622322971786473e4,
1114 -0.960754116701669e-8, -0.510572269720488e-10, 0.767373781404211e-2,
1115 0.663855469485254e-14, -0.717590735526745e-9, 0.146564542926508e-4,
1116 0.309029474277013e-11, -0.464216300971708e-15, -0.390499637961161e-13,
1117 -0.236716126781431e-9, 0.454652854268717e-11, -0.422271787482497e-2,
1118 0.283911742354706e-10, 0.270929002720228e1},
1119 {-0.401215699576099e9, 0.484501478318406e11, 0.394721471363678e-14,
1120 0.372629967374147e5, -0.369794374168666e-29, -0.380436407012452e-14,
1121 0.475361629970233e-6, -0.879148916140706e-3, 0.844317863844331,
1122 0.122433162656600e2, -0.104529634830279e3, 0.589702771277429e3,
1123 -0.291026851164444e14, 0.170343072841850e-5, -0.277617606975748e-3,
1124 -0.344709605486686e1, 0.221333862447095e2, -0.194646110037079e3,
1125 0.808354639772825e-15, -0.18084520914547e-10, -0.696664158132412e-5,
1126 -0.181057560300994e-2, 0.255830298579027e1, 0.328913873658481e4,
1127 -0.173270241249904e-18, -0.661876792558034e-6, -0.39568892342125e-2,
1128 0.604203299819132e-17, -0.400879935920517e-13, 0.160751107464958e-8,
1129 0.383719409025556e-4, -0.649565446702457e-14, -0.149095328506e-11,
1130 0.541449377329581e-8},
1131 {0.260702058647537e10, -0.188277213604704e15, 0.554923870289667e19, -0.758966946387758e23,
1132 0.413865186848908e27, -0.81503800073806e12, -0.381458260489955e33, -0.123239564600519e-1,
1133 0.226095631437174e8, -0.49501780950672e12, 0.529482996422863e16, -0.444359478746295e23,
1134 0.521635864527315e35, -0.487095672740742e55, -0.714430209937547e6, 0.127868634615495,
1135 -0.100752127917598e2, 0.777451437960990e7, -0.108105480796471e25, -0.357578581169659e-5,
1136 -0.212857169423484e1, 0.270706111085238e30, -0.695953622348829e33, 0.110609027472280,
1137 0.721559163361354e2, -0.306367307532219e15, 0.265839618885530e-4, 0.253392392889754e-1,
1138 -0.214443041836579e3, 0.937846601489667, 0.223184043101700e1, 0.338401222509191e2,
1139 0.494237237179718e21, -0.198068404154428, -0.141415349881140e31, -0.993862421613651e2,
1140 0.125070534142731e3, -0.996473529004439e3, 0.473137909872765e5, 0.116662121219322e33,
1141 -0.315874976271533e16, -0.445703369196945e33, 0.642794932373694e33},
1142 {0.811384363481847, -0.568199310990094e4, -0.178657198172556e11, 0.795537657613427e32,
1143 -0.814568209346872e5, -0.659774567602874e8, -0.152861148659302e11, -0.560165667510446e12,
1144 0.458384828593949e6, -0.385754000383848e14, 0.453735800004273e8, 0.939454935735563e12,
1145 0.266572856432938e28, -0.547578313899097e10, 0.200725701112386e15, 0.185007245563239e13,
1146 0.185135446828337e9, -0.170451090076385e12, 0.157890366037614e15, -0.202530509748774e16,
1147 0.36819392618357e60, 0.170215539458936e18, 0.639234909918741e42, -0.821698160721956e15,
1148 -0.795260241872306e24, 0.23341586947851e18, -0.600079934586803e23, 0.594584382273384e25,
1149 0.189461279349492e40, -0.810093428842645e46, 0.188813911076809e22, 0.111052244098768e36,
1150 0.291133958602503e46, -0.329421923951460e22, -0.137570282536696e26, 0.181508996303902e28,
1151 -0.346865122768353e30, -0.21196114877426e38, -0.128617899887675e49, 0.479817895699239e65},
1152 {0.280967799943151e-38, 0.614869006573609e-30, 0.582238667048942e-27,
1153 0.390628369238462e-22, 0.821445758255119e-20, 0.402137961842776e-14,
1154 0.651718171878301e-12, -0.211773355803058e-7, 0.264953354380072e-2,
1155 -0.135031446451331e-31, -0.607246643970893e-23, -0.402352115234494e-18,
1156 -0.744938506925544e-16, 0.189917206526237e-12, 0.364975183508473e-5,
1157 0.177274872361946e-25, -0.334952758812999e-18, -0.421537726098389e-8,
1158 -0.391048167929649e-1, 0.541276911564176e-13, 0.705412100773699e-11,
1159 0.258585887897486e-8, -0.493111362030162e-10, -0.158649699894543e-5,
1160 -0.525037427886100, 0.220019901729615e-2, -0.643064132636925e-2,
1161 0.629154149015048e2, 0.135147318617061e3, 0.240560808321713e-6,
1162 -0.890763306701305e-3, -0.440209599407714e4, -0.302807107747776e3,
1163 0.159158748314599e4, 0.232534272709876e6, -0.792681207132600e6,
1164 -0.869871364662769e11, 0.354542769185671e12, 0.400849240129329e15},
1165 {0.128746023979718e-34, -0.735234770382342e-11, 0.28907869214915e-2,
1166 0.244482731907223, 0.141733492030985e-23, -0.354533853059476e-28,
1167 -0.594539202901431e-17, -.585188401782779e-8, .201377325411803e-5,
1168 0.138647388209306e1, -0.173959365084772e-4, 0.137680878349369e-2,
1169 0.814897605805513e-14, 0.425596631351839e-25, -0.387449113787755e-17,
1170 0.13981474793024e-12, -0.171849638951521e-2, 0.641890529513296e-21,
1171 0.118960578072018e-10, -0.155282762571611e-17, 0.233907907347507e-7,
1172 -0.174093247766213e-12, 0.377682649089149e-8, -0.516720236575302e-10},
1173 {-0.982825342010366e-4, 0.105145700850612e1, 0.116033094095084e3, 0.324664750281543e4,
1174 -0.123592348610137e4, -0.561403450013495e-1, 0.856677401640869e-7, 0.236313425393924e3,
1175 0.972503292350109e-2, -0.103001994531927e1, -0.149653706199162e-8, -0.215743778861592e-4,
1176 -0.834452198291445e1, 0.586602660564988, 0.343480022104968e-25, 0.816256095947021e-5,
1177 0.294985697916798e-2, 0.711730466276584e-16, 0.400954763806941e-9, 0.107766027032853e2,
1178 -0.409449599138182e-6, -0.729121307758902e-5, 0.677107970938909e-8, 0.602745973022975e-7,
1179 -0.382323011855257e-10, 0.179946628317437e-2, -0.345042834640005e-3},
1180 {-0.820433843259950e5, 0.473271518461586e11, -0.805950021005413e-1, 0.328600025435980e2,
1181 -0.35661702998249e4, -0.172985781433335e10, 0.351769232729192e8, -0.775489259985144e6,
1182 0.710346691966018e-4, 0.993499883820274e5, -0.642094171904570, -0.612842816820083e4,
1183 0.232808472983776e3, -0.142808220416837e-4, -0.643596060678456e-2, -0.428577227475614e1,
1184 0.225689939161918e4, 0.100355651721510e-2, 0.333491455143516, 0.109697576888873e1,
1185 0.961917379376452, -0.838165632204598e-1, 0.247795908411492e1, -0.319114969006533e4},
1186 {0.144165955660863e-2, -0.701438599628258e13, -0.830946716459219e-16, 0.261975135368109,
1187 0.393097214706245e3, -0.104334030654021e5, 0.490112654154211e9, -0.147104222772069e-3,
1188 0.103602748043408e1, 0.305308890065089e1, -0.399745276971264e7, 0.569233719593750e-11,
1189 -0.464923504407778e-1, -0.535400396512906e-17, 0.399988795693162e-12, -0.536479560201811e-6,
1190 0.159536722411202e-1, 0.270303248860217e-14, 0.244247453858506e-7, -0.983430636716454e-5,
1191 0.663513144224454e-1, -0.993456957845006e1, 0.546491323528491e3, -0.143365406393758e5,
1192 0.150764974125511e6, -0.337209709340105e-9, 0.377501980025469e-8},
1193 {-0.532466612140254e23, 0.100415480000824e32, -0.191540001821367e30, 0.105618377808847e17,
1194 0.202281884477061e59, 0.884585472596134e8, 0.166540181638363e23, -0.313563197669111e6,
1195 -0.185662327545324e54, -0.624942093918942e-1, -0.50416072413259e10, 0.187514491833092e5,
1196 0.121399979993217e-2, 0.188317043049455e1, -0.167073503962060e4, 0.965961650599775,
1197 0.294885696802488e1, -0.653915627346115e5, 0.604012200163444e50, -0.198339358557937,
1198 -0.175984090163501e58, 0.356314881403987e1, -0.575991255144384e3, 0.456213415338071e5,
1199 -0.109174044987829e8, 0.437796099975134e34, -0.616552611135792e46, 0.193568768917797e10,
1200 0.950898170425042e54},
1201 {0.155287249586268e1, 0.664235115009031e1, -0.289366236727210e4, -0.385923202309848e13,
1202 -0.291002915783761e1, -0.829088246858083e12, 0.176814899675218e1, -0.534686695713469e9,
1203 0.160464608687834e18, 0.196435366560186e6, 0.156637427541729e13, -0.178154560260006e1,
1204 -0.229746237623692e16, 0.385659001648006e8, 0.110554446790543e10, -0.677073830687349e14,
1205 -0.327910592086523e31, -0.341552040860644e51, -0.527251339709047e21, 0.245375640937055e24,
1206 -0.168776617209269e27, 0.358958955867578e29, -0.656475280339411e36, 0.355286045512301e39,
1207 0.569021454413270e58, -0.700584546433113e48, -0.705772623326374e65, 0.166861176200148e53,
1208 -0.300475129680486e61, -0.668481295196808e51, 0.428432338620678e69, -0.444227367758304e72,
1209 -0.281396013562745e77},
1210 {0.122088349258355e18, 0.104216468608488e10, -.882666931564652e16, 0.259929510849499e20,
1211 0.222612779142211e15, -0.878473585050085e18, -0.314432577551552e22, -0.216934916996285e13,
1212 0.159079648196849e21, -0.339567617303423e3, 0.884387651337836e13, -0.843405926846418e21,
1213 0.114178193518022e2, -0.122708229235641e-3, -0.106201671767107e3, 0.903443213959313e25,
1214 -0.693996270370852e28, 0.648916718965575e-8, 0.718957567127851e4, 0.105581745346187e-2,
1215 -0.651903203602581e15, -0.160116813274676e25, -0.510254294237837e-8, -0.152355388953402,
1216 0.677143292290144e12, 0.276378438378930e15, 0.116862983141686e-1, -0.301426947980171e14,
1217 0.169719813884840e-7, 0.104674840020929e27, -0.10801690456014e5, -0.990623601934295e-12,
1218 0.536116483602738e7, 0.226145963747881e22, -0.488731565776210e-9, 0.151001548880670e-4,
1219 -0.227700464643920e5, -0.781754507698846e28},
1220 {-0.415652812061591e-54, 0.177441742924043e-60, -0.357078668203377e-54,
1221 0.359252213604114e-25, -0.259123736380269e2, 0.594619766193460e5,
1222 -0.624184007103158e11, 0.313080299915944e17, 0.105006446192036e-8,
1223 -0.192824336984852e-5, 0.654144373749937e6, 0.513117462865044e13,
1224 -0.697595750347391e19, -0.103977184454767e29, 0.119563135540666e-47,
1225 -0.436677034051655e-41, 0.926990036530639e-29, 0.587793105620748e21,
1226 0.280375725094731e-17, -0.192359972440634e23, 0.742705723302738e27,
1227 -0.517429682450605e2, 0.820612048645469e7, -0.188214882341448e-8,
1228 0.184587261114837e-1, -0.135830407782663e-5, -0.723681885626348e17,
1229 -0.223449194054124e27, -0.111526741826431e-34, 0.276032601145151e-28,
1230 0.134856491567853e15, 0.652440293345860e-9, 0.510655119774360e17,
1231 -0.468138358908732e32, -0.760667491183279e16, -0.417247986986821e-18,
1232 0.312545677756104e14, -0.100375333864186e15, 0.247761392329058e27},
1233 {-0.586219133817016e-7, -0.894460355005526e11, 0.531168037519774e-30,
1234 0.109892402329239, -0.575368389425212e-1, 0.228276853990249e5,
1235 -0.158548609655002e19, 0.329865748576503e-27, -0.634987981190669e-24,
1236 0.615762068640611e-8, -0.961109240985747e8, -0.406274286652625e-44,
1237 -0.471103725498077e-12, 0.725937724828145, 0.187768525763682e-38,
1238 -0.103308436323771e4, -0.662552816342168e-1, 0.579514041765710e3,
1239 0.237416732616644e-26, 0.271700235739893e-14, -0.9078862134836e2,
1240 -0.171242509570207e-36, 0.156792067854621e3, 0.923261357901470,
1241 -0.597865988422577e1, 0.321988767636389e7, -0.399441390042203e-29,
1242 0.493429086046981e-7, 0.812036983370565e-19, -0.207610284654137e-11,
1243 -0.340821291419719e-6, 0.542000573372233e-17, -0.856711586510214e-12,
1244 0.266170454405981e-13, 0.858133791857099e-5},
1245 {0.377373741298151e19, -0.507100883722913e13, -0.10336322559886e16, 0.184790814320773e-5,
1246 -0.924729378390945e-3, -0.425999562292738e24, -0.462307771873973e-12, 0.107319065855767e22,
1247 0.648662492280682e11, 0.244200600688281e1, -0.851535733484258e10, 0.169894481433592e22,
1248 0.215780222509020e-26, -0.320850551367334, -0.382642448458610e17, -0.275386077674421e-28,
1249 -0.563199253391666e6, -0.326068646279314e21, 0.397949001553184e14, 0.100824008584757e-6,
1250 0.162234569738433e5, -0.432355225319745e11, -0.59287424559861e12, 0.133061647281106e1,
1251 0.157338197797544e7, 0.258189614270853e14, 0.262413209706358e25, -0.920011937431142e-1,
1252 0.220213765905426e-2, -0.110433759109547e2, 0.847004870612087e7, -0.592910695762536e9,
1253 -0.183027173269660e-4, 0.181339603516302, -0.119228759669889e4, 0.430867658061468e7},
1254 {-0.525597995024633e-9, 0.583441305228407e4, -0.134778968457925e17, 0.118973500934212e26,
1255 -0.159096490904708e27, -0.315839902302021e-6, 0.496212197158239e3, 0.327777227273171e19,
1256 -0.527114657850696e22, 0.210017506281863e-16, 0.705106224399834e21, -0.266713136106469e31,
1257 -0.145370512554562e-7, 0.149333917053130e28, -0.149795620287641e8, -0.3818819062711e16,
1258 0.724660165585797e-4, -0.937808169550193e14, 0.514411468376383e10, -0.828198594040141e5},
1259 {0.24400789229065e-10, -0.463057430331242e7, 0.728803274777712e10, 0.327776302858856e16,
1260 -0.110598170118409e10, -0.323899915729957e13, 0.923814007023245e16, 0.842250080413712e-12,
1261 0.663221436245506e12, -0.167170186672139e15, 0.253749358701391e4, -0.819731559610523e-20,
1262 0.328380587890663e12, -0.625004791171543e8, 0.803197957462023e21, -0.204397011338353e-10,
1263 -0.378391047055938e4, 0.97287654593862e-2, 0.154355721681459e2, -0.373962862928643e4,
1264 -0.682859011374572e11, -0.248488015614543e-3, 0.394536049497068e7}};
1265
1266 const std::vector<std::vector<int>> _I3s{
1267 {-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -3,
1268 -3, -3, -3, -2, -2, -2, -1, -1, -1, 0, 0, 1, 1, 2, 2},
1269 {-12, -12, -10, -10, -8, -6, -6, -6, -5, -5, -5, -4, -4, -4, -3, -3,
1270 -3, -3, -3, -2, -2, -2, -1, -1, 0, 0, 1, 1, 2, 3, 4, 4},
1271 {-12, -12, -12, -10, -10, -10, -8, -8, -8, -6, -5, -5, -5, -4, -4, -3, -3, -2,
1272 -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 8},
1273 {-12, -12, -12, -12, -12, -12, -10, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6,
1274 -5, -5, -5, -5, -4, -4, -4, -3, -3, -2, -2, -1, -1, -1, 0, 0, 1, 1, 3},
1275 {-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -6, -5, -4, -4, -3,
1276 -3, -3, -2, -2, -2, -2, -1, 0, 0, 1, 1, 1, 2, 2},
1277 {0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 5, 5, 6, 7, 7,
1278 10, 12, 12, 12, 14, 14, 14, 14, 14, 16, 16, 18, 18, 20, 20, 20, 22, 24, 24, 28, 32},
1279 {-12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8, -6, -6, -5, -5, -4, -3,
1280 -2, -2, -2, -2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 3, 5, 6, 8, 10, 10},
1281 {-12, -12, -10, -10, -10, -10, -10, -10, -8, -8, -8, -8, -8, -6, -6,
1282 -6, -5, -5, -5, -4, -4, -3, -3, -2, -1, -1, 0, 1, 1},
1283 {0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 7, 7, 8, 8, 10,
1284 12, 12, 12, 14, 14, 14, 14, 18, 18, 18, 18, 18, 20, 20, 22, 24, 24, 32, 32, 36, 36},
1285 {0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 5, 5, 6,
1286 10, 12, 12, 14, 14, 14, 16, 18, 20, 20, 24, 24, 28, 28},
1287 {-2, -2, -1, -1, 0, -0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1,
1288 1, 2, 2, 2, 2, 2, 2, 5, 5, 5, 6, 6, 6, 6, 8, 10, 12},
1289 {-12, -12, -12, -12, -12, -10, -10, -8, -8, -8, -8, -8, -8, -8, -6,
1290 -5, -5, -4, -4, -3, -3, -3, -3, -2, -2, -2, -1, -1, -1, 0,
1291 0, 0, 0, 1, 1, 2, 4, 5, 5, 6, 10, 10, 14},
1292 {0, 3, 8, 20, 1, 3, 4, 5, 1, 6, 2, 4, 14, 2, 5, 3, 0, 1, 1, 1,
1293 28, 2, 16, 0, 5, 0, 3, 4, 12, 16, 1, 8, 14, 0, 2, 3, 4, 8, 14, 24},
1294 {0, 3, 4, 6, 7, 10, 12, 14, 18, 0, 3, 5, 6, 8, 12, 0, 3, 7, 12, 2,
1295 3, 4, 2, 4, 7, 4, 3, 5, 6, 0, 0, 3, 1, 0, 1, 0, 1, 0, 1},
1296 {0, 0, 0, 2, 3, 4, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 10, 10, 14, 14, 20, 20, 24},
1297 {0, 0, 0, 0, 1, 2, 3, 3, 4, 6, 7, 7, 8, 10,
1298 12, 12, 12, 14, 14, 14, 16, 18, 20, 22, 24, 24, 36},
1299 {-12, -12, -10, -10, -10, -10, -8, -6, -5, -5, -4, -4,
1300 -3, -2, -2, -2, -2, -1, -1, -1, 0, 1, 1, 1},
1301 {-8, -8, -3, -3, -3, -3, -3, 0, 0, 0, 0, 3, 3, 8,
1302 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 12, 14},
1303 {-12, -12, -10, -8, -6, -5, -5, -4, -4, -3, -3, -2, -1, -1, -1,
1304 0, 0, 0, 0, 1, 1, 3, 3, 3, 4, 4, 4, 5, 14},
1305 {0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 7, 7, 7, 7,
1306 7, 10, 10, 10, 10, 10, 18, 20, 22, 22, 24, 28, 32, 32, 32, 36},
1307 {-12, -10, -10, -10, -8, -8, -8, -6, -6, -5, -5, -5, -3, -1, -1, -1, -1, 0, 0,
1308 1, 2, 2, 3, 5, 5, 5, 6, 6, 8, 8, 10, 12, 12, 12, 14, 14, 14, 14},
1309 {-10, -8, -6, -6, -6, -6, -6, -6, -5, -5, -5, -5, -5, -5, -4, -4, -4, -4, -3, -3,
1310 -3, -2, -2, -1, -1, 0, 0, 0, 1, 1, 3, 4, 4, 4, 5, 8, 10, 12, 14},
1311 {-12, -12, -10, -10, -8, -8, -8, -6, -6, -6, -6, -5, -4, -4, -3, -3, -2, -2,
1312 -1, -1, -1, 0, 0, 1, 2, 2, 3, 3, 5, 5, 5, 8, 8, 10, 10},
1313 {-8, -6, -5, -4, -4, -4, -3, -3, -1, 0, 0, 0, 1, 1, 2, 3, 3, 3,
1314 4, 5, 5, 5, 6, 8, 8, 8, 8, 10, 12, 12, 12, 12, 14, 14, 14, 14},
1315 {0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 8, 8, 10, 12},
1316 {-8, -6, -5, -5, -4, -4, -4, -3, -3, -3, -2, -1, 0, 1, 2, 3, 3, 6, 6, 6, 6, 8, 8}};
1317
1318 const std::vector<std::vector<int>> _J3s{
1319 {5, 10, 12, 5, 10, 12, 5, 8, 10, 1, 1, 5, 10, 8, 0,
1320 1, 3, 6, 0, 2, 3, 0, 1, 2, 0, 1, 0, 2, 0, 2},
1321 {10, 12, 8, 14, 8, 5, 6, 8, 5, 8, 10, 2, 4, 5, 0, 1,
1322 2, 3, 5, 0, 2, 5, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1},
1323 {6, 8, 10, 6, 8, 10, 5, 6, 7, 8, 1, 4, 7, 2, 8, 0, 3, 0,
1324 4, 5, 0, 1, 2, 0, 1, 2, 0, 2, 0, 1, 3, 7, 0, 7, 1},
1325 {4, 6, 7, 10, 12, 16, 0, 2, 4, 6, 8, 10, 14, 3, 7, 8, 10, 6, 8,
1326 1, 2, 5, 7, 0, 1, 7, 2, 4, 0, 1, 0, 1, 5, 0, 2, 0, 6, 0},
1327 {14, 16, 3, 6, 10, 14, 16, 7, 8, 10, 6, 6, 2, 4, 2, 6, 7, 0, 1, 3, 4, 0, 0, 1, 0, 4, 6, 0, 2},
1328 {-3, -2, -1, 0, 1, 2, -1, 1, 2, 3, 0, 1, -5, -2,
1329 0, -3, -8, 1, -6, -4, 1, -6, -10, -8, -4, -12, -10, -8,
1330 -6, -4, -10, -8, -12, -10, -12, -10, -6, -12, -12, -4, -12, -12},
1331 {7, 12, 14, 18, 22, 24, 14, 20, 24, 7, 8, 10, 12, 8, 22, 7, 20, 22, 7,
1332 3, 5, 14, 24, 2, 8, 18, 0, 1, 2, 0, 1, 3, 24, 22, 12, 3, 0, 6},
1333 {8, 12, 4, 6, 8, 10, 14, 16, 0, 1, 6, 7, 8, 4, 6, 8, 2, 3, 4, 2, 4, 1, 2, 0, 0, 2, 0, 0, 2},
1334 {0, 1, 10, -4, -2, -1, 0, 0, -5, 0, -3, -2, -1, -6, -1, 12, -4, -3, -6, 10, -8,
1335 -12, -6, -4, -10, -8, -4, 5, -12, -10, -8, -6, 2, -12, -10, -12, -12, -8, -10, -5, -10, -8},
1336 {-1, 0, 1, -2, -1, 1, -1, 1, -2, -2, 2, -3, -2, 0, 3,
1337 -6, -8, -3, -10, -8, -5, -10, -12, -12, -10, -12, -6, -12, -5},
1338 {10, 12, -5, 6, -12, -6, -2, -1, 0, 1, 2, 3, 14, -3, -2, 0, 1,
1339 2, -8, -6, -3, -2, 0, 4, -12, -6, -3, -12, -10, -8, -5, -12, -12, -10},
1340 {14, 16, 18, 20, 22, 14, 24, 6, 10, 12, 14, 18, 24, 36, 8, 4, 5, 7, 16, 1, 3, 18,
1341 20, 2, 3, 10, 0, 1, 3, 0, 1, 2, 12, 0, 16, 1, 0, 0, 1, 14, 4, 12, 10},
1342 {0, 0, 0, 2, 5, 5, 5, 5, 6, 6, 7, 8, 8, 10, 10, 12, 14, 14, 18, 20,
1343 20, 22, 22, 24, 24, 28, 28, 28, 28, 28, 32, 32, 32, 36, 36, 36, 36, 36, 36, 36},
1344 {-12, -12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -10,
1345 -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5, -4,
1346 -3, -3, -3, -2, -1, -1, 0, 1, 1, 2, 4, 5, 6},
1347 {-12, -4, -1, -1, -10, -12, -8, -5, -4, -1, -4, -3,
1348 -8, -12, -10, -8, -4, -12, -8, -12, -8, -12, -10, -12},
1349 {-1, 0, 1, 2, 1, -1, -3, 0, -2, -2, -5, -4, -2, -3,
1350 -12, -6, -5, -10, -8, -3, -8, -8, -10, -10, -12, -8, -12},
1351 {10, 12, 6, 7, 8, 10, 8, 6, 2, 5, 3, 4, 3, 0, 1, 2, 4, 0, 1, 2, 0, 0, 1, 3},
1352 {6, 14, -3, 3, 4, 5, 8, -1, 0, 1, 5, -6, -2, -12,
1353 -10, -8, -5, -12, -10, -8, -6, -5, -4, -3, -2, -12, -12},
1354 {20, 24, 22, 14, 36, 8, 16, 6, 32, 3, 8, 4, 1, 2, 3,
1355 0, 1, 4, 28, 0, 32, 0, 1, 2, 3, 18, 24, 4, 24},
1356 {0, 1, 4, 12, 0, 10, 0, 6, 14, 3, 8, 0, 10, 3, 4, 7, 20,
1357 36, 10, 12, 14, 16, 22, 18, 32, 22, 36, 24, 28, 22, 32, 36, 36},
1358 {14, 10, 12, 14, 10, 12, 14, 8, 12, 4, 8, 12, 2, -1, 1, 12, 14, -3, 1,
1359 -2, 5, 10, -5, -4, 2, 3, -5, 2, -8, 8, -4, -12, -4, 4, -12, -10, -6, 6},
1360 {-8, -12, -12, -3, 5, 6, 8, 10, 1, 2, 6, 8, 10, 14, -12, -10, -6, 10, -3, 10,
1361 12, 2, 4, -2, 0, -2, 6, 10, -12, -10, 3, -6, 3, 10, 2, -12, -2, -3, 1},
1362 {8, 14, -1, 8, 6, 8, 14, -4, -3, 2, 8, -10, -1, 3, -10, 3, 1, 2,
1363 -8, -4, 1, -12, 1, -1, -1, 2, -12, -5, -10, -8, -6, -12, -10, -12, -8},
1364 {14, 10, 10, 1, 2, 14, -2, 12, 5, 0, 4, 10, -10, -1, 6, -12, 0, 8,
1365 3, -6, -2, 1, 1, -6, -3, 1, 8, -8, -10, -8, -5, -4, -12, -10, -8, -6},
1366 {-3, 1, 5, 8, 8, -4, -1, 4, 5, -8, 4, 8, -6, 6, -2, 1, -8, -2, -5, -8},
1367 {3, 6, 6, 8, 5, 6, 8, -2, 5, 6, 2, -6, 3, 1, 6, -6, -2, -6, -5, -4, -1, -8, -4}};
1368
1369 const std::array<Real, 31> _nph3a{
1370 {-0.133645667811215e-6, 0.455912656802978e-5, -0.146294640700979e-4, 0.639341312970080e-2,
1371 0.372783927268847e3, -0.718654377460447e4, 0.573494752103400e6, -0.267569329111439e7,
1372 -0.334066283302614e-4, -0.245479214069597e-1, 0.478087847764996e2, 0.764664131818904e-5,
1373 0.128350627676972e-2, 0.171219081377331e-1, -0.851007304583213e1, -0.136513461629781e-1,
1374 -0.384460997596657e-5, 0.337423807911655e-2, -0.551624873066791, 0.729202277107470,
1375 -0.992522757376041e-2, -.119308831407288, .793929190615421, .454270731799386,
1376 .20999859125991, -0.642109823904738e-2, -0.235155868604540e-1, 0.252233108341612e-2,
1377 -0.764885133368119e-2, 0.136176427574291e-1, -0.133027883575669e-1}};
1378
1379 const std::array<int, 31> _Iph3a{{-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10,
1380 -8, -8, -8, -8, -5, -3, -2, -2, -2, -1, -1,
1381 0, 0, 1, 3, 3, 4, 4, 10, 12}};
1382
1383 const std::array<int, 31> _Jph3a{{0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2,
1384 0, 1, 3, 4, 0, 2, 0, 1, 1, 0, 1, 0, 3, 4, 5}};
1385
1386 const std::array<Real, 33> _nph3b{
1387 {0.323254573644920e-4, -0.127575556587181e-3, -0.475851877356068e-3, 0.156183014181602e-2,
1388 0.105724860113781, -0.858514221132534e2, 0.724140095480911e3, 0.296475810273257e-2,
1389 -0.592721983365988e-2, -0.126305422818666e-1, -0.115716196364853, 0.849000969739595e2,
1390 -0.108602260086615e-1, 0.154304475328851e-1, 0.750455441524466e-1, 0.252520973612982e-1,
1391 -0.602507901232996e-1, -0.307622221350501e1, -0.574011959864879e-1, 0.503471360939849e1,
1392 -0.925081888584834, 0.391733882917546e1, -0.773146007130190e2, 0.949308762098587e4,
1393 -0.141043719679409e7, 0.849166230819026e7, 0.861095729446704, 0.323346442811720,
1394 0.873281936020439, -0.436653048526683, 0.286596714529479, -0.131778331276228,
1395 0.676682064330275e-2}};
1396
1397 const std::array<int, 33> _Iph3b{{-12, -12, -10, -10, -10, -10, -10, -8, -8, -8, -8,
1398 -8, -6, -6, -6, -4, -4, -3, -2, -2, -1, -1,
1399 -1, -1, -1, -1, 0, 0, 1, 3, 5, 6, 8}};
1400
1401 const std::array<int, 33> _Jph3b{{0, 1, 0, 1, 5, 10, 12, 0, 1, 2, 4, 10, 0, 1, 2, 0, 1,
1402 5, 0, 4, 2, 4, 6, 10, 14, 16, 0, 2, 1, 1, 1, 1, 1}};
1403
1405 const std::array<Real, 10> _n4{{0.11670521452767e4,
1406 -0.72421316703206e6,
1407 -0.17073846940092e2,
1408 0.12020824702470e5,
1409 -0.32325550322333e7,
1410 0.14915108613530e2,
1411 -0.48232657361591e4,
1412 0.40511340542057e6,
1413 -0.238555575678490,
1414 0.65017534844798e3}};
1415
1417 const std::array<int, 6> _J05{{0, 1, -3, -2, -1, 2}};
1418 const std::array<Real, 6> _n05{{-0.13179983674201e2,
1419 0.68540841634434e1,
1420 -0.24805148933466e-1,
1421 0.36901534980333,
1422 -0.31161318213925e1,
1423 -0.32961626538917}};
1424
1425 const std::array<int, 6> _I5{{1, 1, 1, 2, 2, 3}};
1426 const std::array<int, 6> _J5{{1, 2, 3, 3, 9, 7}};
1427 const std::array<Real, 6> _n5{{0.15736404855259e-2,
1428 0.90153761673944e-3,
1429 -0.50270077677648e-2,
1430 0.22440037409485e-5,
1431 -0.41163275453471e-5,
1432 0.37919454822955e-7}};
1433
1435 const std::vector<std::vector<int>> _tempXY_I{{0, 1, 2, -1, -2},
1436 {0, 1, 2, 3},
1437 {0, 1, 2, 3, 4},
1438 {0, 1, 2, 3, 4},
1439 {0, 1, 2, 3, 4},
1440 {0, 1, 2, 3},
1441 {0, 1, 2, -1, -2},
1442 {0, 1, 2, 3},
1443 {0, 1, 2, 3},
1444 {0, 1, 2, 3, 4},
1445 {0, 1, 2, -1, -2}};
1446
1447 const std::vector<std::vector<Real>> _tempXY_n{
1448 {0.154793642129415e4,
1449 -0.187661219490113e3,
1450 0.213144632222113e2,
1451 -0.191887498864292e4,
1452 0.918419702359447e3},
1453 {0.585276966696349e3, 0.278233532206915e1, -0.127283549295878e-1, 0.159090746562729e-3},
1454 {-0.249284240900418e5,
1455 0.428143584791546e4,
1456 -0.269029173140130e3,
1457 0.751608051114157e1,
1458 -0.787105249910383e-1},
1459 {0.584814781649163e3,
1460 -0.616179320924617,
1461 0.260763050899562,
1462 -0.587071076864459e-2,
1463 0.515308185433082e-4},
1464 {0.617229772068439e3,
1465 -0.770600270141675e1,
1466 0.697072596851896,
1467 -0.157391839848015e-1,
1468 0.137897492684194e-3},
1469 {0.535339483742384e3, 0.761978122720128e1, -0.158365725441648, 0.192871054508108e-2},
1470 {0.969461372400213e3,
1471 -0.332500170441278e3,
1472 0.642859598466067e2,
1473 0.773845935768222e3,
1474 -0.152313732937084e4},
1475 {0.565603648239126e3, 0.529062258221222e1, -0.102020639611016, 0.122240301070145e-2},
1476 {0.584561202520006e3, -0.102961025163669e1, 0.243293362700452, -0.294905044740799e-2},
1477 {0.528199646263062e3, 0.890579602135307e1, -0.222814134903755, 0.286791682263697e-2},
1478 {0.728052609145380e1,
1479 0.973505869861952e2,
1480 0.147370491183191e2,
1481 0.329196213998375e3,
1482 0.873371668682417e3}};
1483
1486 const std::array<Real, 4> _mu_H0{{1.67752, 2.20462, 0.6366564, -0.241605}};
1487 const std::array<std::array<Real, 7>, 6> _mu_Hij{
1488 {{{5.20094e-1, 2.22531e-1, -2.81378e-1, 1.61913e-1, -3.25372e-2, 0.0, 0.0}},
1489 {{8.50895e-2, 9.99115e-1, -9.06851e-1, 2.57399e-1, 0.0, 0.0, 0.0}},
1490 {{-1.08374, 1.88797, -7.72479e-1, 0.0, 0.0, 0.0, 0.0}},
1491 {{-2.89555e-1, 1.26613, -4.89837e-1, 0.0, 6.98452e-2, 0.0, -4.35673e-3}},
1492 {{0.0, 0.0, -2.57040e-1, 0.0, 0.0, 8.72102e-3, 0.0}},
1493 {{0.0, 1.20573e-1, 0.0, 0.0, 0.0, 0.0, -5.93264e-4}}}};
1494
1496 std::array<Real, 4> _k_a{{0.0102811, 0.0299621, 0.0156146, -0.00422464}};
1497
1499 const std::array<Real, 5> _T_star{{1386.0, 540.0, _T_critical, 1.0, 1000.0}};
1501 const std::array<Real, 5> _p_star{{16.53e6, 1.0e6, 1.0e6, 1.0e6, 1.0e6}};
1502
1503private:
1508 template <typename T>
1509 std::pair<T, T> T_drhodT_from_p_rho(const T & p, const T & rho) const;
1510};
1511
1512#pragma GCC diagnostic pop
1513
1514template <typename T>
1515T
1516Water97FluidProperties::dgamma1_dpi(const T & pi, const T & tau) const
1517{
1518 T sum = 0.0;
1519 for (std::size_t i = 0; i < _n1.size(); ++i)
1520 sum += -_n1[i] * _I1[i] * MathUtils::pow(7.1 - pi, _I1[i] - 1) *
1521 MathUtils::pow(tau - 1.222, _J1[i]);
1522
1523 return sum;
1524}
1525
1526template <typename T>
1527T
1528Water97FluidProperties::dgamma2_dpi(const T & pi, const T & tau) const
1529{
1530 // Ideal gas part of the Gibbs free energy
1531 T dg0 = 1.0 / pi;
1532
1533 // Residual part of the Gibbs free energy
1534 T dgr = 0.0;
1535 for (std::size_t i = 0; i < _n2.size(); ++i)
1536 dgr += _n2[i] * _I2[i] * MathUtils::pow(pi, _I2[i] - 1) * MathUtils::pow(tau - 0.5, _J2[i]);
1537
1538 return dg0 + dgr;
1539}
1540
1541template <typename T>
1542T
1543Water97FluidProperties::densityRegion3(const T & pressure, const T & temperature) const
1544{
1545 using std::exp;
1546
1547 // Region 3 is subdivided into 26 subregions, each with a given backwards equation
1548 // to directly calculate density from pressure and temperature without the need for
1549 // expensive iterations. Find the subregion id that the point is in:
1550 unsigned int sid =
1551 subregion3(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
1552
1553 T vstar, pi, theta;
1554 Real a, b, c, d, e;
1555 unsigned int N;
1556
1557 vstar = _par3[sid][0];
1558 pi = pressure / _par3[sid][1] / 1.0e6;
1559 theta = temperature / _par3[sid][2];
1560 a = _par3[sid][3];
1561 b = _par3[sid][4];
1562 c = _par3[sid][5];
1563 d = _par3[sid][6];
1564 e = _par3[sid][7];
1565 N = _par3N[sid];
1566
1567 T sum = 0.0;
1568 T volume = 0.0;
1569
1570 // Note that subregion 13 is the only different formulation
1571 if (sid == 13)
1572 {
1573 for (std::size_t i = 0; i < N; ++i)
1574 sum += _n3s[sid][i] * MathUtils::pow(pi - a, _I3s[sid][i]) *
1575 MathUtils::pow(theta - b, _J3s[sid][i]);
1576
1577 volume = vstar * exp(sum);
1578 }
1579 else
1580 volume = vstar * subregionVolume(pi, theta, a, b, c, d, e, sid);
1581
1582 // Density is the inverse of volume
1583 return 1.0 / volume;
1584}
1585
1586template <typename T>
1587T
1588Water97FluidProperties::gamma1(const T & pi, const T & tau) const
1589{
1590 T sum = 0.0;
1591 for (std::size_t i = 0; i < _n1.size(); ++i)
1592 sum += _n1[i] * MathUtils::pow(7.1 - pi, _I1[i]) * MathUtils::pow(tau - 1.222, _J1[i]);
1593
1594 return sum;
1595}
1596
1597template <typename T>
1598T
1599Water97FluidProperties::d2gamma1_dpi2(const T & pi, const T & tau) const
1600{
1601 T sum = 0.0;
1602 for (std::size_t i = 0; i < _n1.size(); ++i)
1603 sum += _n1[i] * _I1[i] * (_I1[i] - 1) * MathUtils::pow(7.1 - pi, _I1[i] - 2) *
1604 MathUtils::pow(tau - 1.222, _J1[i]);
1605
1606 return sum;
1607}
1608
1609template <typename T>
1610T
1611Water97FluidProperties::dgamma1_dtau(const T & pi, const T & tau) const
1612{
1613 T g = 0.0;
1614 for (std::size_t i = 0; i < _n1.size(); ++i)
1615 g += _n1[i] * _J1[i] * MathUtils::pow(7.1 - pi, _I1[i]) *
1616 MathUtils::pow(tau - 1.222, _J1[i] - 1);
1617
1618 return g;
1619}
1620
1621template <typename T>
1622T
1623Water97FluidProperties::d2gamma1_dtau2(const T & pi, const T & tau) const
1624{
1625 T dg = 0.0;
1626 for (std::size_t i = 0; i < _n1.size(); ++i)
1627 dg += _n1[i] * _J1[i] * (_J1[i] - 1) * MathUtils::pow(7.1 - pi, _I1[i]) *
1628 MathUtils::pow(tau - 1.222, _J1[i] - 2);
1629
1630 return dg;
1631}
1632
1633template <typename T>
1634T
1635Water97FluidProperties::d2gamma1_dpitau(const T & pi, const T & tau) const
1636{
1637 T dg = 0.0;
1638 for (std::size_t i = 0; i < _n1.size(); ++i)
1639 dg += -_n1[i] * _I1[i] * _J1[i] * MathUtils::pow(7.1 - pi, _I1[i] - 1) *
1640 MathUtils::pow(tau - 1.222, _J1[i] - 1);
1641
1642 return dg;
1643}
1644
1645template <typename T>
1646T
1647Water97FluidProperties::gamma2(const T & pi, const T & tau) const
1648{
1649 using std::log;
1650
1651 // Ideal gas part of the Gibbs free energy
1652 T sum0 = 0.0;
1653 for (std::size_t i = 0; i < _n02.size(); ++i)
1654 sum0 += _n02[i] * MathUtils::pow(tau, _J02[i]);
1655
1656 T g0 = log(pi) + sum0;
1657
1658 // Residual part of the Gibbs free energy
1659 T gr = 0.0;
1660 for (std::size_t i = 0; i < _n2.size(); ++i)
1661 gr += _n2[i] * MathUtils::pow(pi, _I2[i]) * MathUtils::pow(tau - 0.5, _J2[i]);
1662
1663 return g0 + gr;
1664}
1665
1666template <typename T>
1667T
1668Water97FluidProperties::d2gamma2_dpi2(const T & pi, const T & tau) const
1669{
1670 // Ideal gas part of the Gibbs free energy
1671 T dg0 = -1.0 / pi / pi;
1672
1673 // Residual part of the Gibbs free energy
1674 T dgr = 0.0;
1675 for (std::size_t i = 0; i < _n2.size(); ++i)
1676 dgr += _n2[i] * _I2[i] * (_I2[i] - 1) * MathUtils::pow(pi, _I2[i] - 2) *
1677 MathUtils::pow(tau - 0.5, _J2[i]);
1678
1679 return dg0 + dgr;
1680}
1681
1682template <typename T>
1683T
1684Water97FluidProperties::dgamma2_dtau(const T & pi, const T & tau) const
1685{
1686 // Ideal gas part of the Gibbs free energy
1687 T dg0 = 0.0;
1688 for (std::size_t i = 0; i < _n02.size(); ++i)
1689 dg0 += _n02[i] * _J02[i] * MathUtils::pow(tau, _J02[i] - 1);
1690
1691 // Residual part of the Gibbs free energy
1692 T dgr = 0.0;
1693 for (std::size_t i = 0; i < _n2.size(); ++i)
1694 dgr += _n2[i] * _J2[i] * MathUtils::pow(pi, _I2[i]) * MathUtils::pow(tau - 0.5, _J2[i] - 1);
1695
1696 return dg0 + dgr;
1697}
1698
1699template <typename T>
1700T
1701Water97FluidProperties::d2gamma2_dtau2(const T & pi, const T & tau) const
1702{
1703 // Ideal gas part of the Gibbs free energy
1704 T dg0 = 0.0;
1705 for (std::size_t i = 0; i < _n02.size(); ++i)
1706 dg0 += _n02[i] * _J02[i] * (_J02[i] - 1) * MathUtils::pow(tau, _J02[i] - 2);
1707
1708 // Residual part of the Gibbs free energy
1709 T dgr = 0.0;
1710 for (std::size_t i = 0; i < _n2.size(); ++i)
1711 dgr += _n2[i] * _J2[i] * (_J2[i] - 1) * MathUtils::pow(pi, _I2[i]) *
1712 MathUtils::pow(tau - 0.5, _J2[i] - 2);
1713
1714 return dg0 + dgr;
1715}
1716
1717template <typename T>
1718T
1719Water97FluidProperties::d2gamma2_dpitau(const T & pi, const T & tau) const
1720{
1721 // Ideal gas part of the Gibbs free energy
1722 T dg0 = 0.0;
1723
1724 // Residual part of the Gibbs free energy
1725 T dgr = 0.0;
1726 for (std::size_t i = 0; i < _n2.size(); ++i)
1727 dgr += _n2[i] * _I2[i] * _J2[i] * MathUtils::pow(pi, _I2[i] - 1) *
1728 MathUtils::pow(tau - 0.5, _J2[i] - 1);
1729
1730 return dg0 + dgr;
1731}
1732
1733template <typename T>
1734T
1735Water97FluidProperties::phi3(const T & delta, const T & tau) const
1736{
1737 using std::log;
1738
1739 T sum = 0.0;
1740 for (std::size_t i = 1; i < _n3.size(); ++i)
1741 sum += _n3[i] * MathUtils::pow(delta, _I3[i]) * MathUtils::pow(tau, _J3[i]);
1742
1743 return _n3[0] * log(delta) + sum;
1744}
1745
1746template <typename T>
1747T
1748Water97FluidProperties::dphi3_ddelta(const T & delta, const T & tau) const
1749{
1750 T sum = 0.0;
1751 for (std::size_t i = 1; i < _n3.size(); ++i)
1752 sum += _n3[i] * _I3[i] * MathUtils::pow(delta, _I3[i] - 1) * MathUtils::pow(tau, _J3[i]);
1753
1754 return _n3[0] / delta + sum;
1755}
1756
1757template <typename T>
1758T
1759Water97FluidProperties::d2phi3_ddelta2(const T & delta, const T & tau) const
1760{
1761 T sum = 0.0;
1762 for (std::size_t i = 1; i < _n3.size(); ++i)
1763 sum += _n3[i] * _I3[i] * (_I3[i] - 1) * MathUtils::pow(delta, _I3[i] - 2) *
1764 MathUtils::pow(tau, _J3[i]);
1765
1766 return -_n3[0] / delta / delta + sum;
1767}
1768
1769template <typename T>
1770T
1771Water97FluidProperties::dphi3_dtau(const T & delta, const T & tau) const
1772{
1773 T sum = 0.0;
1774 for (std::size_t i = 1; i < _n3.size(); ++i)
1775 sum += _n3[i] * _J3[i] * MathUtils::pow(delta, _I3[i]) * MathUtils::pow(tau, _J3[i] - 1);
1776
1777 return sum;
1778}
1779
1780template <typename T>
1781T
1782Water97FluidProperties::d2phi3_dtau2(const T & delta, const T & tau) const
1783{
1784 T sum = 0.0;
1785 for (std::size_t i = 1; i < _n3.size(); ++i)
1786 sum += _n3[i] * _J3[i] * (_J3[i] - 1) * MathUtils::pow(delta, _I3[i]) *
1787 MathUtils::pow(tau, _J3[i] - 2);
1788
1789 return sum;
1790}
1791
1792template <typename T>
1793T
1794Water97FluidProperties::d2phi3_ddeltatau(const T & delta, const T & tau) const
1795{
1796 T sum = 0.0;
1797 for (std::size_t i = 1; i < _n3.size(); ++i)
1798 sum += _n3[i] * _I3[i] * _J3[i] * MathUtils::pow(delta, _I3[i] - 1) *
1799 MathUtils::pow(tau, _J3[i] - 1);
1800
1801 return sum;
1802}
1803
1804template <typename T>
1805T
1806Water97FluidProperties::gamma5(const T & pi, const T & tau) const
1807{
1808 using std::log;
1809
1810 // Ideal gas part of the Gibbs free energy
1811 T sum0 = 0.0;
1812 for (std::size_t i = 0; i < _n05.size(); ++i)
1813 sum0 += _n05[i] * MathUtils::pow(tau, _J05[i]);
1814
1815 T g0 = log(pi) + sum0;
1816
1817 // Residual part of the Gibbs free energy
1818 T gr = 0.0;
1819 for (std::size_t i = 0; i < _n5.size(); ++i)
1820 gr += _n5[i] * MathUtils::pow(pi, _I5[i]) * MathUtils::pow(tau, _J5[i]);
1821
1822 return g0 + gr;
1823}
1824
1825template <typename T>
1826T
1827Water97FluidProperties::dgamma5_dpi(const T & pi, const T & tau) const
1828{
1829 // Ideal gas part of the Gibbs free energy
1830 T dg0 = 1.0 / pi;
1831
1832 // Residual part of the Gibbs free energy
1833 T dgr = 0.0;
1834 for (std::size_t i = 0; i < _n5.size(); ++i)
1835 dgr += _n5[i] * _I5[i] * MathUtils::pow(pi, _I5[i] - 1) * MathUtils::pow(tau, _J5[i]);
1836
1837 return dg0 + dgr;
1838}
1839
1840template <typename T>
1841T
1842Water97FluidProperties::d2gamma5_dpi2(const T & pi, const T & tau) const
1843{
1844 // Ideal gas part of the Gibbs free energy
1845 T dg0 = -1.0 / pi / pi;
1846
1847 // Residual part of the Gibbs free energy
1848 T dgr = 0.0;
1849 for (std::size_t i = 0; i < _n5.size(); ++i)
1850 dgr += _n5[i] * _I5[i] * (_I5[i] - 1) * MathUtils::pow(pi, _I5[i] - 2) *
1851 MathUtils::pow(tau, _J5[i]);
1852
1853 return dg0 + dgr;
1854}
1855
1856template <typename T>
1857T
1858Water97FluidProperties::dgamma5_dtau(const T & pi, const T & tau) const
1859{
1860 // Ideal gas part of the Gibbs free energy
1861 T dg0 = 0.0;
1862 for (std::size_t i = 0; i < _n05.size(); ++i)
1863 dg0 += _n05[i] * _J05[i] * MathUtils::pow(tau, _J05[i] - 1);
1864
1865 // Residual part of the Gibbs free energy
1866 T dgr = 0.0;
1867 for (std::size_t i = 0; i < _n5.size(); ++i)
1868 dgr += _n5[i] * _J5[i] * MathUtils::pow(pi, _I5[i]) * MathUtils::pow(tau, _J5[i] - 1);
1869
1870 return dg0 + dgr;
1871}
1872
1873template <typename T>
1874T
1875Water97FluidProperties::d2gamma5_dtau2(const T & pi, const T & tau) const
1876{
1877 // Ideal gas part of the Gibbs free energy
1878 T dg0 = 0.0;
1879 for (std::size_t i = 0; i < _n05.size(); ++i)
1880 dg0 += _n05[i] * _J05[i] * (_J05[i] - 1) * MathUtils::pow(tau, _J05[i] - 2);
1881
1882 // Residual part of the Gibbs free energy
1883 T dgr = 0.0;
1884 for (std::size_t i = 0; i < _n5.size(); ++i)
1885 dgr += _n5[i] * _J5[i] * (_J5[i] - 1) * MathUtils::pow(pi, _I5[i]) *
1886 MathUtils::pow(tau, _J5[i] - 2);
1887
1888 return dg0 + dgr;
1889}
1890
1891template <typename T>
1892T
1893Water97FluidProperties::d2gamma5_dpitau(const T & pi, const T & tau) const
1894{
1895 // Ideal gas part of the Gibbs free energy
1896 T dg0 = 0.0;
1897
1898 // Residual part of the Gibbs free energy
1899 T dgr = 0.0;
1900 for (std::size_t i = 0; i < _n5.size(); ++i)
1901 dgr +=
1902 _n5[i] * _I5[i] * _J5[i] * MathUtils::pow(pi, _I5[i] - 1) * MathUtils::pow(tau, _J5[i] - 1);
1903
1904 return dg0 + dgr;
1905}
1906
1907template <typename T>
1908T
1909Water97FluidProperties::tempXY(const T & pressure, const subregionEnum xy) const
1910{
1911 T pi = pressure / 1.0e6;
1912
1913 // Choose the constants based on the string xy
1914 unsigned int row;
1915
1916 switch (xy)
1917 {
1918 case AB:
1919 row = 0;
1920 break;
1921 case CD:
1922 row = 1;
1923 break;
1924 case GH:
1925 row = 2;
1926 break;
1927 case IJ:
1928 row = 3;
1929 break;
1930 case JK:
1931 row = 4;
1932 break;
1933 case MN:
1934 row = 5;
1935 break;
1936 case OP:
1937 row = 6;
1938 break;
1939 case QU:
1940 row = 7;
1941 break;
1942 case RX:
1943 row = 8;
1944 break;
1945 case UV:
1946 row = 9;
1947 break;
1948 case WX:
1949 row = 10;
1950 break;
1951 default:
1952 row = 0;
1953 }
1954
1955 T sum = 0.0;
1956
1957 using std::log;
1958
1959 if (xy == AB || xy == OP || xy == WX)
1960 for (std::size_t i = 0; i < _tempXY_n[row].size(); ++i)
1961 sum += _tempXY_n[row][i] * MathUtils::pow(log(pi), _tempXY_I[row][i]);
1962 else if (xy == EF)
1963 sum += 3.727888004 * (pi - _p_critical / 1.0e6) + _T_critical;
1964 else
1965 for (std::size_t i = 0; i < _tempXY_n[row].size(); ++i)
1966 sum += _tempXY_n[row][i] * MathUtils::pow(pi, _tempXY_I[row][i]);
1967
1968 return sum;
1969}
1970
1971template <typename T>
1972void
1973Water97FluidProperties::vaporPressureTemplate(const T & temperature, T & psat, T & dpsat_dT) const
1974{
1975 using std::sqrt, std::pow;
1976
1977 // Check whether the input temperature is within the region of validity of this equation.
1978 // Valid for 273.15 K <= t <= 647.096 K
1979 if (temperature < 273.15 || temperature > _T_critical)
1980 mooseException(name(),
1981 ": vaporPressure(): Temperature is outside range 273.15 K <= T <= 647.096 K");
1982
1983 T theta, dtheta_dT, theta2, a, b, c, da_dtheta, db_dtheta, dc_dtheta;
1984 theta = temperature + _n4[8] / (temperature - _n4[9]);
1985 dtheta_dT = 1.0 - _n4[8] / (temperature - _n4[9]) / (temperature - _n4[9]);
1986 theta2 = theta * theta;
1987
1988 a = theta2 + _n4[0] * theta + _n4[1];
1989 b = _n4[2] * theta2 + _n4[3] * theta + _n4[4];
1990 c = _n4[5] * theta2 + _n4[6] * theta + _n4[7];
1991
1992 da_dtheta = 2.0 * theta + _n4[0];
1993 db_dtheta = 2.0 * _n4[2] * theta + _n4[3];
1994 dc_dtheta = 2.0 * _n4[5] * theta + _n4[6];
1995
1996 T denominator = -b + sqrt(b * b - 4.0 * a * c);
1997
1998 psat = Utility::pow<4>(2.0 * c / denominator) * 1.0e6;
1999
2000 // The derivative wrt temperature is given by the chain rule
2001 T dpsat = 4.0 * Utility::pow<3>(2.0 * c / denominator);
2002 dpsat *= (2.0 * dc_dtheta / denominator -
2003 2.0 * c / denominator / denominator *
2004 (-db_dtheta + pow(b * b - 4.0 * a * c, -0.5) *
2005 (b * db_dtheta - 2.0 * da_dtheta * c - 2.0 * a * dc_dtheta)));
2006 dpsat_dT = dpsat * dtheta_dT * 1.0e6;
2007}
2008
2009inline void
2010Water97FluidProperties::vaporPressure(const Real temperature, Real & psat, Real & dpsat_dT) const
2011{
2012 vaporPressureTemplate(temperature, psat, dpsat_dT);
2013}
2014
2015template <typename T>
2016void
2017Water97FluidProperties::rho_from_p_T_template(
2018 const T & pressure, const T & temperature, T & rho, T & drho_dp, T & drho_dT) const
2019{
2020 auto functor = [this](const auto & pressure, const auto & temperature)
2021 { return this->rho_from_p_T_template(pressure, temperature); };
2022
2023 xyDerivatives(pressure, temperature, rho, drho_dp, drho_dT, functor);
2024}
2025
2026template <typename T>
2027T
2028Water97FluidProperties::v_from_p_T_template(const T & pressure, const T & temperature) const
2029{
2030 return 1 / rho_from_p_T_template(pressure, temperature);
2031}
2032
2033template <typename T>
2034void
2035Water97FluidProperties::v_from_p_T_template(
2036 const T & pressure, const T & temperature, T & v, T & dv_dp, T & dv_dT) const
2037{
2038 auto functor = [this](const auto & pressure, const auto & temperature)
2039 { return this->v_from_p_T_template(pressure, temperature); };
2040
2041 xyDerivatives(pressure, temperature, v, dv_dp, dv_dT, functor);
2042}
2043
2044template <typename T>
2045T
2046Water97FluidProperties::e_from_p_T_template(const T & pressure, const T & temperature) const
2047{
2048 T internal_energy, pi, tau;
2049
2050 // Determine which region the point is in
2051 unsigned int region =
2052 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2053 switch (region)
2054 {
2055 case 1:
2056 pi = pressure / _p_star[0];
2057 tau = _T_star[0] / temperature;
2058 internal_energy =
2059 _Rw * temperature * (tau * dgamma1_dtau(pi, tau) - pi * dgamma1_dpi(pi, tau));
2060 break;
2061
2062 case 2:
2063 pi = pressure / _p_star[1];
2064 tau = _T_star[1] / temperature;
2065 internal_energy =
2066 _Rw * temperature * (tau * dgamma2_dtau(pi, tau) - pi * dgamma2_dpi(pi, tau));
2067 break;
2068
2069 case 3:
2070 {
2071 // Calculate density first, then use that in Helmholtz free energy
2072 T density3 = densityRegion3(pressure, temperature);
2073 T delta = density3 / _rho_critical;
2074 tau = _T_star[2] / temperature;
2075 internal_energy = _Rw * temperature * tau * dphi3_dtau(delta, tau);
2076 break;
2077 }
2078
2079 case 5:
2080 pi = pressure / _p_star[4];
2081 tau = _T_star[4] / temperature;
2082 internal_energy =
2083 _Rw * temperature * (tau * dgamma5_dtau(pi, tau) - pi * dgamma5_dpi(pi, tau));
2084 break;
2085
2086 default:
2087 mooseError("inRegion() has given an incorrect region");
2088 }
2089 // Output in J/kg
2090 return internal_energy;
2091}
2092
2093template <typename T>
2094void
2095Water97FluidProperties::e_from_p_T_template(
2096 const T & pressure, const T & temperature, T & e, T & de_dp, T & de_dT) const
2097{
2098 T pi, tau, dinternal_energy_dp, dinternal_energy_dT;
2099
2100 // Determine which region the point is in
2101 unsigned int region =
2102 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2103 switch (region)
2104 {
2105 case 1:
2106 {
2107 pi = pressure / _p_star[0];
2108 tau = _T_star[0] / temperature;
2109 T dgdp = dgamma1_dpi(pi, tau);
2110 T d2gdpt = d2gamma1_dpitau(pi, tau);
2111 dinternal_energy_dp =
2112 _Rw * temperature * (tau * d2gdpt - dgdp - pi * d2gamma1_dpi2(pi, tau)) / _p_star[0];
2113 dinternal_energy_dT =
2114 _Rw * (pi * tau * d2gdpt - tau * tau * d2gamma1_dtau2(pi, tau) - pi * dgdp);
2115 break;
2116 }
2117
2118 case 2:
2119 {
2120 pi = pressure / _p_star[1];
2121 tau = _T_star[1] / temperature;
2122 T dgdp = dgamma2_dpi(pi, tau);
2123 T d2gdpt = d2gamma2_dpitau(pi, tau);
2124 dinternal_energy_dp =
2125 _Rw * temperature * (tau * d2gdpt - dgdp - pi * d2gamma2_dpi2(pi, tau)) / _p_star[1];
2126 dinternal_energy_dT =
2127 _Rw * (pi * tau * d2gdpt - tau * tau * d2gamma2_dtau2(pi, tau) - pi * dgdp);
2128 break;
2129 }
2130
2131 case 3:
2132 {
2133 // Calculate density first, then use that in Helmholtz free energy
2134 T density3 = densityRegion3(pressure, temperature);
2135 T delta = density3 / _rho_critical;
2136 tau = _T_star[2] / temperature;
2137 T dpdd = dphi3_ddelta(delta, tau);
2138 T d2pddt = d2phi3_ddeltatau(delta, tau);
2139 T d2pdd2 = d2phi3_ddelta2(delta, tau);
2140 dinternal_energy_dp =
2141 _T_star[2] * d2pddt / _rho_critical /
2142 (2.0 * temperature * delta * dpdd + temperature * delta * delta * d2pdd2);
2143 dinternal_energy_dT =
2144 -_Rw * (delta * tau * d2pddt * (dpdd - tau * d2pddt) / (2.0 * dpdd + delta * d2pdd2) +
2145 tau * tau * d2phi3_dtau2(delta, tau));
2146 break;
2147 }
2148
2149 case 5:
2150 {
2151 pi = pressure / _p_star[4];
2152 tau = _T_star[4] / temperature;
2153 T dgdp = dgamma5_dpi(pi, tau);
2154 T d2gdpt = d2gamma5_dpitau(pi, tau);
2155 dinternal_energy_dp =
2156 _Rw * temperature * (tau * d2gdpt - dgdp - pi * d2gamma5_dpi2(pi, tau)) / _p_star[4];
2157 dinternal_energy_dT =
2158 _Rw * (pi * tau * d2gdpt - tau * tau * d2gamma5_dtau2(pi, tau) - pi * dgdp);
2159 break;
2160 }
2161
2162 default:
2163 mooseError("inRegion has given an incorrect region");
2164 }
2165
2166 e = this->e_from_p_T(pressure, temperature);
2167 de_dp = dinternal_energy_dp;
2168 de_dT = dinternal_energy_dT;
2169}
2170
2171template <typename T>
2172T
2173Water97FluidProperties::subregionVolume(
2174 const T & pi, const T & theta, Real a, Real b, Real c, Real d, Real e, unsigned int sid) const
2175{
2176 using std::pow;
2177
2178 T sum = 0.0;
2179
2180 for (std::size_t i = 0; i < _n3s[sid].size(); ++i)
2181 sum += _n3s[sid][i] * MathUtils::pow(pow(pi - a, c), _I3s[sid][i]) *
2182 MathUtils::pow(pow(theta - b, d), _J3s[sid][i]);
2183
2184 return pow(sum, e);
2185}
2186
2187template <typename T>
2188std::pair<T, T>
2189Water97FluidProperties::T_drhodT_from_p_rho(const T & p, const T & rho) const
2190{
2191 // For NewtonSolve
2192 // y = rho
2193 // x = p
2194 // z = T
2195 auto lambda =
2196 [this](const T & p, const T & temperature, T & rho, T & drho_dp, T & drho_dtemperature)
2197 { rho_from_p_T_template(p, temperature, rho, drho_dp, drho_dtemperature); };
2198 return FluidPropertiesUtils::NewtonSolve(
2199 p, rho, _T_initial_guess, _tolerance, lambda, name() + "::T_drhodT_from_p_rho");
2200}
2201
2202template <typename T>
2203std::pair<T, T>
2204Water97FluidProperties::p_T_from_v_e(const T & v, const T & e) const
2205{
2206 const auto rho = 1 / v;
2207 const auto p = p_from_v_e(v, e);
2208 return {p, T_drhodT_from_p_rho(p, rho).first};
2209}
2210
2211template <typename T>
2212std::pair<T, T>
2213Water97FluidProperties::rho_T_from_v_e(const T & v, const T & e) const
2214{
2215 const auto rho = 1 / v;
2216 const auto p = p_from_v_e(v, e);
2217 return {rho, T_drhodT_from_p_rho(p, rho).first};
2218}
2219
2220template <typename T>
2221T
2222Water97FluidProperties::c_from_p_T_template(const T & pressure, const T & temperature) const
2223{
2224 T speed2, pi, tau, delta;
2225
2226 // Determine which region the point is in
2227 unsigned int region =
2228 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2229 switch (region)
2230 {
2231 case 1:
2232 pi = pressure / _p_star[0];
2233 tau = _T_star[0] / temperature;
2234 speed2 = _Rw * temperature * Utility::pow<2>(dgamma1_dpi(pi, tau)) /
2235 (Utility::pow<2>(dgamma1_dpi(pi, tau) - tau * d2gamma1_dpitau(pi, tau)) /
2236 (tau * tau * d2gamma1_dtau2(pi, tau)) -
2237 d2gamma1_dpi2(pi, tau));
2238 break;
2239
2240 case 2:
2241 pi = pressure / _p_star[1];
2242 tau = _T_star[1] / temperature;
2243 speed2 = _Rw * temperature * Utility::pow<2>(pi * dgamma2_dpi(pi, tau)) /
2244 ((-pi * pi * d2gamma2_dpi2(pi, tau)) +
2245 Utility::pow<2>(pi * dgamma2_dpi(pi, tau) - tau * pi * d2gamma2_dpitau(pi, tau)) /
2246 (tau * tau * d2gamma2_dtau2(pi, tau)));
2247 break;
2248
2249 case 3:
2250 {
2251 // Calculate density first, then use that in Helmholtz free energy
2252 T density3 = densityRegion3(pressure, temperature);
2253 delta = density3 / _rho_critical;
2254 tau = _T_star[2] / temperature;
2255 speed2 =
2256 _Rw * temperature *
2257 (2.0 * delta * dphi3_ddelta(delta, tau) + delta * delta * d2phi3_ddelta2(delta, tau) -
2258 Utility::pow<2>(delta * dphi3_ddelta(delta, tau) -
2259 delta * tau * d2phi3_ddeltatau(delta, tau)) /
2260 (tau * tau * d2phi3_dtau2(delta, tau)));
2261 break;
2262 }
2263
2264 case 5:
2265 pi = pressure / _p_star[4];
2266 tau = _T_star[4] / temperature;
2267 speed2 = _Rw * temperature * Utility::pow<2>(pi * dgamma5_dpi(pi, tau)) /
2268 ((-pi * pi * d2gamma5_dpi2(pi, tau)) +
2269 Utility::pow<2>(pi * dgamma5_dpi(pi, tau) - tau * pi * d2gamma5_dpitau(pi, tau)) /
2270 (tau * tau * d2gamma5_dtau2(pi, tau)));
2271 break;
2272
2273 default:
2274 mooseError("inRegion() has given an incorrect region");
2275 }
2276
2277 using std::sqrt;
2278 return sqrt(speed2);
2279}
2280
2281template <typename T>
2282T
2283Water97FluidProperties::cp_from_p_T_template(const T & pressure, const T & temperature) const
2284{
2285 T specific_heat, pi, tau, delta;
2286
2287 // Determine which region the point is in
2288 unsigned int region =
2289 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2290 switch (region)
2291 {
2292 case 1:
2293 pi = pressure / _p_star[0];
2294 tau = _T_star[0] / temperature;
2295 specific_heat = -_Rw * tau * tau * d2gamma1_dtau2(pi, tau);
2296 break;
2297
2298 case 2:
2299 pi = pressure / _p_star[1];
2300 tau = _T_star[1] / temperature;
2301 specific_heat = -_Rw * tau * tau * d2gamma2_dtau2(pi, tau);
2302 break;
2303
2304 case 3:
2305 {
2306 // Calculate density first, then use that in Helmholtz free energy
2307 T density3 = densityRegion3(pressure, temperature);
2308 delta = density3 / _rho_critical;
2309 tau = _T_star[2] / temperature;
2310 specific_heat =
2311 _Rw *
2312 (-tau * tau * d2phi3_dtau2(delta, tau) +
2313 (delta * dphi3_ddelta(delta, tau) - delta * tau * d2phi3_ddeltatau(delta, tau)) *
2314 (delta * dphi3_ddelta(delta, tau) - delta * tau * d2phi3_ddeltatau(delta, tau)) /
2315 (2.0 * delta * dphi3_ddelta(delta, tau) +
2316 delta * delta * d2phi3_ddelta2(delta, tau)));
2317 break;
2318 }
2319
2320 case 5:
2321 pi = pressure / _p_star[4];
2322 tau = _T_star[4] / temperature;
2323 specific_heat = -_Rw * tau * tau * d2gamma5_dtau2(pi, tau);
2324 break;
2325
2326 default:
2327 mooseError("inRegion() has given an incorrect region");
2328 }
2329 return specific_heat;
2330}
2331
2332template <typename T>
2333T
2334Water97FluidProperties::cv_from_p_T_template(const T & pressure, const T & temperature) const
2335{
2336 T specific_heat, pi, tau, delta;
2337
2338 // Determine which region the point is in
2339 unsigned int region =
2340 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2341 switch (region)
2342 {
2343 case 1:
2344 pi = pressure / _p_star[0];
2345 tau = _T_star[0] / temperature;
2346 specific_heat =
2347 _Rw * (-tau * tau * d2gamma1_dtau2(pi, tau) +
2348 Utility::pow<2>(dgamma1_dpi(pi, tau) - tau * d2gamma1_dpitau(pi, tau)) /
2349 d2gamma1_dpi2(pi, tau));
2350 break;
2351
2352 case 2:
2353 pi = pressure / _p_star[1];
2354 tau = _T_star[1] / temperature;
2355 specific_heat =
2356 _Rw * (-tau * tau * d2gamma2_dtau2(pi, tau) +
2357 Utility::pow<2>(dgamma2_dpi(pi, tau) - tau * d2gamma2_dpitau(pi, tau)) /
2358 d2gamma2_dpi2(pi, tau));
2359 break;
2360
2361 case 3:
2362 {
2363 // Calculate density first, then use that in Helmholtz free energy
2364 T density3 = densityRegion3(pressure, temperature);
2365 delta = density3 / _rho_critical;
2366 tau = _T_star[2] / temperature;
2367 specific_heat = _Rw * (-tau * tau * d2phi3_dtau2(delta, tau));
2368 break;
2369 }
2370
2371 case 5:
2372 pi = pressure / _p_star[4];
2373 tau = _T_star[4] / temperature;
2374 specific_heat =
2375 _Rw * (-tau * tau * d2gamma5_dtau2(pi, tau) +
2376 Utility::pow<2>(dgamma5_dpi(pi, tau) - tau * d2gamma5_dpitau(pi, tau)) /
2377 d2gamma5_dpi2(pi, tau));
2378 break;
2379
2380 default:
2381 mooseError("inRegion() has given an incorrect region");
2382 }
2383 return specific_heat;
2384}
2385
2386template <typename T>
2387T
2388Water97FluidProperties::k_from_rho_T_template(const T & density, const T & temperature) const
2389{
2390 using std::sqrt, std::exp, std::abs, std::pow;
2391 // Scale the density and temperature. Note that the scales are slightly
2392 // different to the critical values used in IAPWS-IF97
2393 T Tbar = temperature / 647.26;
2394 T rhobar = density / 317.7;
2395
2396 // Ideal gas component
2397 T sum0 = 0.0;
2398
2399 for (std::size_t i = 0; i < _k_a.size(); ++i)
2400 sum0 += _k_a[i] * MathUtils::pow(Tbar, i);
2401
2402 T lambda0 = sqrt(Tbar) * sum0;
2403
2404 // The contribution due to finite density
2405 T lambda1 =
2406 -0.39707 + 0.400302 * rhobar + 1.06 * exp(-0.171587 * Utility::pow<2>(rhobar + 2.392190));
2407
2408 // Critical enhancement
2409 T DeltaT = abs(Tbar - 1.0) + 0.00308976;
2410 T Q = 2.0 + 0.0822994 / pow(DeltaT, 0.6);
2411 T S = (Tbar >= 1.0 ? 1.0 / DeltaT : 10.0932 / pow(DeltaT, 0.6));
2412
2413 T lambda2 =
2414 (0.0701309 / Utility::pow<10>(Tbar) + 0.011852) * pow(rhobar, 1.8) *
2415 exp(0.642857 * (1.0 - pow(rhobar, 2.8))) +
2416 0.00169937 * S * pow(rhobar, Q) * exp((Q / (1.0 + Q)) * (1.0 - pow(rhobar, 1.0 + Q))) -
2417 1.02 * exp(-4.11717 * pow(Tbar, 1.5) - 6.17937 / Utility::pow<5>(rhobar));
2418
2419 return lambda0 + lambda1 + lambda2;
2420}
2421
2422template <typename T>
2423T
2424Water97FluidProperties::k_from_p_T_template(const T & pressure, const T & temperature) const
2425{
2426 T rho = this->rho_from_p_T(pressure, temperature);
2427 return this->k_from_rho_T_template(rho, temperature);
2428}
2429
2430template <typename T>
2431T
2432Water97FluidProperties::k_from_v_e_template(const T & v, const T & e) const
2433{
2434 const auto [p, temperature] = p_T_from_v_e(v, e);
2435 return k_from_p_T_template(p, temperature);
2436}
2437
2438template <typename T>
2439T
2440Water97FluidProperties::p_from_v_e_template(const T & v, const T & e) const
2441{
2442 const auto rho = 1 / v;
2443 // For NewtonSolve
2444 // y = e
2445 // x = rho
2446 // z = p
2447 auto lambda = [this](const T & rho, const T & p, T & e, T & de_drho, T & de_dp)
2448 { e_from_p_rho(p, rho, e, de_dp, de_drho); };
2449 return FluidPropertiesUtils::NewtonSolve(
2450 rho, e, _p_initial_guess, _tolerance, lambda, name() + "::p_from_v_e")
2451 .first;
2452}
2453
2454template <typename T>
2455T
2456Water97FluidProperties::e_from_p_rho_template(const T & p, const T & rho) const
2457{
2458 const auto temperature = T_drhodT_from_p_rho(p, rho).first;
2459 return e_from_p_T_template(p, temperature);
2460}
2461
2462template <typename T>
2463void
2464Water97FluidProperties::e_from_p_rho_template(
2465 const T & p, const T & rho, T & e, T & de_dp, T & de_drho) const
2466{
2467 auto functor = [this](const auto & p, const auto & rho)
2468 { return this->e_from_p_rho_template(p, rho); };
2469
2470 xyDerivatives(p, rho, e, de_dp, de_drho, functor);
2471}
2472
2473template <typename T>
2474T
2475Water97FluidProperties::mu_from_rho_T_template(const T & density, const T & temperature) const
2476{
2477 using std::sqrt, std::exp;
2478
2479 const T mu_star = 1.e-6;
2480 const T rhobar = density / _rho_critical;
2481 const T Tbar = temperature / _T_critical;
2482
2483 // Viscosity in limit of zero density
2484 T sum0 = 0.0;
2485 for (std::size_t i = 0; i < _mu_H0.size(); ++i)
2486 sum0 += _mu_H0[i] / MathUtils::pow(Tbar, i);
2487
2488 const T mu0 = 100.0 * sqrt(Tbar) / sum0;
2489
2490 // Residual component due to finite density
2491 T sum1 = 0.0;
2492 for (unsigned int i = 0; i < 6; ++i)
2493 {
2494 const T fact = MathUtils::pow(1.0 / Tbar - 1.0, i);
2495 for (unsigned int j = 0; j < 7; ++j)
2496 sum1 += fact * _mu_Hij[i][j] * MathUtils::pow(rhobar - 1.0, j);
2497 }
2498
2499 const T mu1 = exp(rhobar * sum1);
2500
2501 // The water viscosity (in Pa.s) is then given by
2502 return mu_star * mu0 * mu1;
2503}
2504
2505template <typename T>
2506std::pair<T, T>
2507Water97FluidProperties::p_T_from_v_h(const T & v, const T & h) const
2508{
2509 T pressure, temperature;
2510 bool conversion_succeeded;
2511 p_T_from_v_h(
2512 v, h, _p_initial_guess, _T_initial_guess, pressure, temperature, conversion_succeeded);
2513 return {std::move(pressure), std::move(temperature)};
2514}
2515
2516template <typename T>
2517T
2518Water97FluidProperties::h_from_p_T_template(const T & pressure, const T & temperature) const
2519{
2520 T enthalpy, pi, tau, delta;
2521
2522 // Determine which region the point is in
2523 unsigned int region =
2524 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2525 switch (region)
2526 {
2527 case 1:
2528 pi = pressure / _p_star[0];
2529 tau = _T_star[0] / temperature;
2530 enthalpy = _Rw * _T_star[0] * dgamma1_dtau(pi, tau);
2531 break;
2532
2533 case 2:
2534 pi = pressure / _p_star[1];
2535 tau = _T_star[1] / temperature;
2536 enthalpy = _Rw * _T_star[1] * dgamma2_dtau(pi, tau);
2537 break;
2538
2539 case 3:
2540 {
2541 // Calculate density first, then use that in Helmholtz free energy
2542 T density3 = densityRegion3(pressure, temperature);
2543 delta = density3 / _rho_critical;
2544 tau = _T_star[2] / temperature;
2545 enthalpy =
2546 _Rw * temperature * (tau * dphi3_dtau(delta, tau) + delta * dphi3_ddelta(delta, tau));
2547 break;
2548 }
2549
2550 case 5:
2551 pi = pressure / _p_star[4];
2552 tau = _T_star[4] / temperature;
2553 enthalpy = _Rw * _T_star[4] * dgamma5_dtau(pi, tau);
2554 break;
2555
2556 default:
2557 mooseError("Water97FluidProperties::inRegion has given an incorrect region");
2558 }
2559 return enthalpy;
2560}
2561
2562template <typename T>
2563void
2564Water97FluidProperties::h_from_p_T_template(
2565 const T & pressure, const T & temperature, T & h, T & dh_dp, T & dh_dT) const
2566{
2567 auto functor = [this](const auto & pressure, const auto & temperature)
2568 { return this->h_from_p_T_template(pressure, temperature); };
2569
2570 xyDerivatives(pressure, temperature, h, dh_dp, dh_dT, functor);
2571}
2572
2573template <typename T>
2574T
2575Water97FluidProperties::rho_from_p_T_template(const T & pressure, const T & temperature) const
2576{
2577 T density, pi, tau;
2578
2579 // Determine which region the point is in
2580 unsigned int region =
2581 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2582
2583 switch (region)
2584 {
2585 case 1:
2586 pi = pressure / _p_star[0];
2587 tau = _T_star[0] / temperature;
2588 density = pressure / (pi * _Rw * temperature * dgamma1_dpi(pi, tau));
2589 break;
2590
2591 case 2:
2592 pi = pressure / _p_star[1];
2593 tau = _T_star[1] / temperature;
2594 density = pressure / (pi * _Rw * temperature * dgamma2_dpi(pi, tau));
2595 break;
2596
2597 case 3:
2598 density = densityRegion3(pressure, temperature);
2599 break;
2600
2601 case 5:
2602 pi = pressure / _p_star[4];
2603 tau = _T_star[4] / temperature;
2604 density = pressure / (pi * _Rw * temperature * dgamma5_dpi(pi, tau));
2605 break;
2606
2607 default:
2608 mooseError("inRegion() has given an incorrect region");
2609 }
2610 return density;
2611}
2612
2613template <typename T>
2614T
2615Water97FluidProperties::mu_from_p_T_template(const T & pressure, const T & temperature) const
2616{
2617 T rho = this->rho_from_p_T_template(pressure, temperature);
2618 return this->mu_from_rho_T_template(rho, temperature);
2619}
2620
2621template <typename T>
2622T
2623Water97FluidProperties::s_from_p_T_template(const T & pressure, const T & temperature) const
2624{
2625 T entropy, pi, tau, density3, delta;
2626
2627 // Determine which region the point is in
2628 unsigned int region =
2629 inRegion(MetaPhysicL::raw_value(pressure), MetaPhysicL::raw_value(temperature));
2630 switch (region)
2631 {
2632 case 1:
2633 pi = pressure / _p_star[0];
2634 tau = _T_star[0] / temperature;
2635 entropy = _Rw * (tau * dgamma1_dtau(pi, tau) - gamma1(pi, tau));
2636 break;
2637
2638 case 2:
2639 pi = pressure / _p_star[1];
2640 tau = _T_star[1] / temperature;
2641 entropy = _Rw * (tau * dgamma2_dtau(pi, tau) - gamma2(pi, tau));
2642 break;
2643
2644 case 3:
2645 // Calculate density first, then use that in Helmholtz free energy
2646 density3 = densityRegion3(pressure, temperature);
2647 delta = density3 / _rho_critical;
2648 tau = _T_star[2] / temperature;
2649 entropy = _Rw * (tau * dphi3_dtau(delta, tau) - phi3(delta, tau));
2650 break;
2651
2652 case 5:
2653 pi = pressure / _p_star[4];
2654 tau = _T_star[4] / temperature;
2655 entropy = _Rw * (tau * dgamma5_dtau(pi, tau) - gamma5(pi, tau));
2656 break;
2657
2658 default:
2659 mooseError("inRegion() has given an incorrect region");
2660 }
2661 return entropy;
2662}
2663
2664template <typename T>
2665void
2666Water97FluidProperties::s_from_p_T_template(
2667 const T & pressure, const T & temperature, T & s, T & ds_dp, T & ds_dT) const
2668{
2669 auto functor = [this](const auto & pressure, const auto & temperature)
2670 { return this->s_from_p_T_template(pressure, temperature); };
2671
2672 xyDerivatives(pressure, temperature, s, ds_dp, ds_dT, functor);
2673}
ADReal
DualNumber< Real, DNDerivativeType, true > ADReal
pow
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Definition ExpressionBuilder.h:690
mu
const double mu
Definition GasLiquidMassTransferTest.C:22
p
const Real p
Definition GasLiquidMassTransferTest.C:18
rho
const double rho
Definition GasLiquidMassTransferTest.C:27
T
const double T
Definition GasLiquidMassTransferTest.C:19
v
const double v
Definition GasLiquidMassTransferTest.C:23
ThreadedGeneralUserObject::parameters
const InputParameters & parameters() const
ThreadedGeneralUserObject::name
const std::string & name() const
ThreadedGeneralUserObject::mooseError
void mooseError(Args &&... args) const
SinglePhaseFluidProperties
Common class for single phase fluid properties.
Definition SinglePhaseFluidProperties.h:115
SinglePhaseFluidProperties::_T_initial_guess
const Real _T_initial_guess
Initial guess for temperature (or temperature used to compute the initial guess)
Definition SinglePhaseFluidProperties.h:445
SinglePhaseFluidProperties::_p_initial_guess
const Real _p_initial_guess
Initial guess for pressure (or pressure used to compute the initial guess)
Definition SinglePhaseFluidProperties.h:447
SinglePhaseFluidProperties::_tolerance
const Real _tolerance
Newton's method may be used to convert between variable sets.
Definition SinglePhaseFluidProperties.h:443
SinglePhaseFluidProperties::p_T_from_v_h
void p_T_from_v_h(const T &v, const T &h, Real p0, Real T0, T &pressure, T &temperature, bool &conversion_succeeded) const
Determines (p,T) from (v,h) using Newton Solve in 2D Useful for conversion between different sets of ...
Definition SinglePhaseFluidProperties.h:559
SinglePhaseFluidProperties::h
e e e e s T T T T T rho v v T e h
Definition SinglePhaseFluidProperties.h:212
SinglePhaseFluidProperties::xyDerivatives
static void xyDerivatives(const T x, const T &y, T &z, T &dz_dx, T &dz_dy, const Functor &z_from_x_y)
Computes the dependent variable z and its derivatives with respect to the independent variables x and...
Definition SinglePhaseFluidProperties.h:492
Water97FluidProperties
Water (H2O) fluid properties as a function of pressure (Pa) and temperature (K) from IAPWS-IF97: Revi...
Definition Water97FluidProperties.h:39
Water97FluidProperties::_k_a
std::array< Real, 4 > _k_a
Constants for thermal conductivity.
Definition Water97FluidProperties.h:1496
Water97FluidProperties::cp_from_p_T_template
T cp_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2283
Water97FluidProperties::_nph3b
const std::array< Real, 33 > _nph3b
Definition Water97FluidProperties.h:1386
Water97FluidProperties::_T_triple
const Real _T_triple
Triple point temperature (K)
Definition Water97FluidProperties.h:834
Water97FluidProperties::d2gamma2_dpitau
T d2gamma2_dpitau(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 2 wrt pi and tau.
Definition Water97FluidProperties.h:1719
Water97FluidProperties::h_from_p_T_template
T h_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2518
Water97FluidProperties::rho_T_from_v_e
std::pair< T, T > rho_T_from_v_e(const T &v, const T &e) const
Computes the density (first member of the pair) and temperature (second member of the pair) as functi...
Definition Water97FluidProperties.h:2213
Water97FluidProperties::_Iph1
const std::array< int, 20 > _Iph1
Definition Water97FluidProperties.h:870
Water97FluidProperties::_J5
const std::array< int, 6 > _J5
Definition Water97FluidProperties.h:1426
Water97FluidProperties::temperature_from_ph2c
ADReal temperature_from_ph2c(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 2c Eq.
Definition Water97FluidProperties.C:883
Water97FluidProperties::vaporTemperature_ad
ADReal vaporTemperature_ad(const ADReal &pressure) const
AD version of saturation temperature as a function of pressure (used internally)
Definition Water97FluidProperties.C:544
Water97FluidProperties::d2phi3_dtau2
T d2phi3_dtau2(const T &delta, const T &tau) const
Second derivative of Helmholtz free energy in Region 3 wrt tau.
Definition Water97FluidProperties.h:1782
Water97FluidProperties::e_from_v_h
ADReal e_from_v_h(const ADReal &v, const ADReal &h) const override
Definition Water97FluidProperties.C:206
Water97FluidProperties::mu_from_v_e
ADReal mu_from_v_e(const ADReal &v, const ADReal &e) const override
Definition Water97FluidProperties.C:362
Water97FluidProperties::d2gamma1_dpitau
T d2gamma1_dpitau(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 1 wrt pi and tau.
Definition Water97FluidProperties.h:1635
Water97FluidProperties::_tempXY_I
const std::vector< std::vector< int > > _tempXY_I
Constnats for the tempXY() method.
Definition Water97FluidProperties.h:1435
Water97FluidProperties::_n3
const std::array< Real, 40 > _n3
Constants for region 3.
Definition Water97FluidProperties.h:968
Water97FluidProperties::d2gamma5_dpitau
T d2gamma5_dpitau(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 5 wrt pi and tau.
Definition Water97FluidProperties.h:1893
Water97FluidProperties::e_from_p_T_template
T e_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2046
Water97FluidProperties::henryConstant
Real henryConstant(Real temperature, const std::vector< Real > &coeffs) const
IAPWS formulation of Henry's law constant for dissolution in water From Guidelines on the Henry's con...
Definition Water97FluidProperties.C:950
Water97FluidProperties::b23p
Real b23p(Real temperature) const
Auxillary equation for the boundary between regions 2 and 3.
Definition Water97FluidProperties.C:585
Water97FluidProperties::dgamma5_dtau
T dgamma5_dtau(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 5 wrt tau.
Definition Water97FluidProperties.h:1858
Water97FluidProperties::_Jph3a
const std::array< int, 31 > _Jph3a
Definition Water97FluidProperties.h:1383
Water97FluidProperties::dphi3_ddelta
T dphi3_ddelta(const T &delta, const T &tau) const
Derivative of Helmholtz free energy in Region 3 wrt delta.
Definition Water97FluidProperties.h:1748
Water97FluidProperties::d2phi3_ddelta2
T d2phi3_ddelta2(const T &delta, const T &tau) const
Second derivative of Helmholtz free energy in Region 3 wrt delta.
Definition Water97FluidProperties.h:1759
Water97FluidProperties::mu_from_rho_T_template
T mu_from_rho_T_template(const T &density, const T &temperature) const
Definition Water97FluidProperties.h:2475
Water97FluidProperties::k_from_v_e
Real k_from_v_e(Real v, Real e) const override
Definition Water97FluidProperties.C:419
Water97FluidProperties::subregionVolume
T subregionVolume(const T &pi, const T &theta, Real a, Real b, Real c, Real d, Real e, unsigned int sid) const
Specific volume in all subregions of region 3 EXCEPT subregion n (13).
Definition Water97FluidProperties.h:2173
Water97FluidProperties::_nph2b
const std::array< Real, 38 > _nph2b
Definition Water97FluidProperties.h:927
Water97FluidProperties::rho_from_p_T
virtual Real rho_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:81
Water97FluidProperties::_n2
const std::array< Real, 43 > _n2
Definition Water97FluidProperties.h:886
Water97FluidProperties::d2gamma1_dpi2
T d2gamma1_dpi2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 1 wrt pi.
Definition Water97FluidProperties.h:1599
Water97FluidProperties::gamma5
T gamma5(const T &pi, const T &tau) const
Gibbs free energy in Region 5.
Definition Water97FluidProperties.h:1806
Water97FluidProperties::temperature_from_ph2a
ADReal temperature_from_ph2a(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 2a Eq.
Definition Water97FluidProperties.C:842
Water97FluidProperties::mu_from_p_T
virtual Real mu_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:282
Water97FluidProperties::rho_from_p_T_template
T rho_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2575
Water97FluidProperties::_Iph2a
const std::array< int, 36 > _Iph2a
Definition Water97FluidProperties.h:920
Water97FluidProperties::phi3
T phi3(const T &delta, const T &tau) const
Helmholtz free energy in Region 3.
Definition Water97FluidProperties.h:1735
Water97FluidProperties::b23T
Real b23T(Real pressure) const
Auxillary equation for the boundary between regions 2 and 3.
Definition Water97FluidProperties.C:599
Water97FluidProperties::_Iph2b
const std::array< int, 38 > _Iph2b
Definition Water97FluidProperties.h:939
Water97FluidProperties::b3ab
Real b3ab(Real pressure) const
Boundary between subregions a and b in region 3.
Definition Water97FluidProperties.C:903
Water97FluidProperties::criticalDensity
virtual Real criticalDensity() const override
Critical density.
Definition Water97FluidProperties.C:63
Water97FluidProperties::v_from_p_T_template
T v_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2028
Water97FluidProperties::mu_from_rho_T
virtual Real mu_from_rho_T(Real density, Real temperature) const override
Definition Water97FluidProperties.C:305
Water97FluidProperties::dphi3_dtau
T dphi3_dtau(const T &delta, const T &tau) const
Derivative of Helmholtz free energy in Region 3 wrt tau.
Definition Water97FluidProperties.h:1771
Water97FluidProperties::d2gamma2_dtau2
T d2gamma2_dtau2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 2 wrt tau.
Definition Water97FluidProperties.h:1701
Water97FluidProperties::k_from_p_T
virtual Real k_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:395
Water97FluidProperties::T_from_v_e
Real T_from_v_e(Real v, Real e) const override
Definition Water97FluidProperties.C:213
Water97FluidProperties::cp_from_p_T
virtual Real cp_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:244
Water97FluidProperties::k_from_p_T_template
T k_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2424
Water97FluidProperties::vaporPressure
virtual Real vaporPressure(Real temperature) const override
Vapor pressure.
Definition Water97FluidProperties.C:521
Water97FluidProperties::inRegion
unsigned int inRegion(Real pressure, Real temperature) const
Determines the phase region that the given pressure and temperature values lie in.
Definition Water97FluidProperties.C:1223
Water97FluidProperties::triplePointTemperature
virtual Real triplePointTemperature() const override
Triple point temperature.
Definition Water97FluidProperties.C:75
Water97FluidProperties::cv_from_v_e
virtual ADReal cv_from_v_e(const ADReal &v, const ADReal &e) const override
Definition Water97FluidProperties.C:275
Water97FluidProperties::_J1
const std::array< int, 34 > _J1
Definition Water97FluidProperties.h:859
Water97FluidProperties::T_from_p_h
virtual Real T_from_p_h(Real pressure, Real enthalpy) const override
Backwards equation T(p, h) From Revised Release on the IAPWS Industrial Formulation 1997 for the Ther...
Definition Water97FluidProperties.C:718
Water97FluidProperties::dgamma2_dtau
T dgamma2_dtau(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 2 wrt tau.
Definition Water97FluidProperties.h:1684
Water97FluidProperties::_T_star
const std::array< Real, 5 > _T_star
Temperature scale for each region.
Definition Water97FluidProperties.h:1499
Water97FluidProperties::_Jph2a
const std::array< int, 36 > _Jph2a
Definition Water97FluidProperties.h:923
Water97FluidProperties::rho_mu_from_p_T
virtual void rho_mu_from_p_T(Real pressure, Real temperature, Real &rho, Real &mu) const override
Combined methods.
Definition Water97FluidProperties.C:369
Water97FluidProperties::d2gamma5_dtau2
T d2gamma5_dtau2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 5 wrt tau.
Definition Water97FluidProperties.h:1875
Water97FluidProperties::_mu_Hij
const std::array< std::array< Real, 7 >, 6 > _mu_Hij
Definition Water97FluidProperties.h:1487
Water97FluidProperties::_n1
const std::array< Real, 34 > _n1
Reference constants used in to calculate thermophysical properties of water.
Definition Water97FluidProperties.h:845
Water97FluidProperties::_n05
const std::array< Real, 6 > _n05
Definition Water97FluidProperties.h:1418
Water97FluidProperties::T_drhodT_from_p_rho
std::pair< T, T > T_drhodT_from_p_rho(const T &p, const T &rho) const
Computes the temperature (first member of the pair) and the derivative of density (second member of t...
Definition Water97FluidProperties.h:2189
Water97FluidProperties::p_T_from_v_h
std::pair< T, T > p_T_from_v_h(const T &v, const T &h) const
Computes the pressure (first member of the pair) and temperature (second member of the pair) as funct...
Definition Water97FluidProperties.h:2507
Water97FluidProperties::temperature_from_ph3a
ADReal temperature_from_ph3a(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 3a Eq.
Definition Water97FluidProperties.C:918
Water97FluidProperties::criticalTemperature
virtual Real criticalTemperature() const override
Critical temperature.
Definition Water97FluidProperties.C:57
Water97FluidProperties::d2gamma5_dpi2
T d2gamma5_dpi2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 5 wrt pi.
Definition Water97FluidProperties.h:1842
Water97FluidProperties::temperature_from_ph1
ADReal temperature_from_ph1(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 1 Eq.
Definition Water97FluidProperties.C:827
Water97FluidProperties::_n4
const std::array< Real, 10 > _n4
Constants for region 4 (the saturation curve up to the critical point)
Definition Water97FluidProperties.h:1405
Water97FluidProperties::temperature_from_ph3b
ADReal temperature_from_ph3b(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 3b Eq.
Definition Water97FluidProperties.C:934
Water97FluidProperties::temperature_from_ph2b
ADReal temperature_from_ph2b(const ADReal &pressure, const ADReal &enthalpy) const
Backwards equation T(p, h) in Region 2b Eq.
Definition Water97FluidProperties.C:861
Water97FluidProperties::_rho_critical
const Real _rho_critical
Critical density (kg/m^3)
Definition Water97FluidProperties.h:830
Water97FluidProperties::_n3s
const std::vector< std::vector< Real > > _n3s
Constants for all 26 subregions in region 3.
Definition Water97FluidProperties.h:1019
Water97FluidProperties::_Jph2c
const std::array< int, 23 > _Jph2c
Definition Water97FluidProperties.h:957
Water97FluidProperties::_J2
const std::array< int, 43 > _J2
Definition Water97FluidProperties.h:905
Water97FluidProperties::cp_from_v_e
virtual ADReal cp_from_v_e(const ADReal &v, const ADReal &e) const override
Definition Water97FluidProperties.C:256
Water97FluidProperties::tempXY
T tempXY(const T &pressure, subregionEnum xy) const
Boundaries between subregions in region 3.
Definition Water97FluidProperties.h:1909
Water97FluidProperties::_tempXY_n
const std::vector< std::vector< Real > > _tempXY_n
Definition Water97FluidProperties.h:1447
Water97FluidProperties::_Jph2b
const std::array< int, 38 > _Jph2b
Definition Water97FluidProperties.h:942
Water97FluidProperties::k_from_rho_T
virtual Real k_from_rho_T(Real density, Real temperature) const override
Definition Water97FluidProperties.C:413
Water97FluidProperties::p_T_from_v_e
std::pair< T, T > p_T_from_v_e(const T &v, const T &e) const
Computes the pressure (first member of the pair) and temperature (second member of the pair) as funct...
Definition Water97FluidProperties.h:2204
Water97FluidProperties::_n02
const std::array< Real, 9 > _n02
Constants for region 2.
Definition Water97FluidProperties.h:876
Water97FluidProperties::b2bc
Real b2bc(Real pressure) const
Boundary between subregions b and c in region 2.
Definition Water97FluidProperties.C:705
Water97FluidProperties::subregion2ph
unsigned int subregion2ph(Real pressure, Real enthalpy) const
Provides the correct subregion index for a (P,h) point in region 2.
Definition Water97FluidProperties.C:672
Water97FluidProperties::vaporPressureTemplate
void vaporPressureTemplate(const T &temperature, T &psat, T &dpsat_dT) const
Definition Water97FluidProperties.h:1973
Water97FluidProperties::v_from_p_T
virtual Real v_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:110
Water97FluidProperties::e_from_p_rho
virtual Real e_from_p_rho(Real p, Real rho) const override
Definition Water97FluidProperties.C:151
Water97FluidProperties::p_from_v_e
Real p_from_v_e(Real v, Real e) const override
Definition Water97FluidProperties.C:139
Water97FluidProperties::_I2
const std::array< int, 43 > _I2
Definition Water97FluidProperties.h:901
Water97FluidProperties::gamma1
T gamma1(const T &pi, const T &tau) const
Gibbs free energy in Region 1 - single phase liquid region.
Definition Water97FluidProperties.h:1588
Water97FluidProperties::_p_critical
const Real _p_critical
Critical pressure (Pa)
Definition Water97FluidProperties.h:826
Water97FluidProperties::dgamma1_dpi
T dgamma1_dpi(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 1 wrt pi.
Definition Water97FluidProperties.h:1516
Water97FluidProperties::_nph2c
const std::array< Real, 23 > _nph2c
Definition Water97FluidProperties.h:946
Water97FluidProperties::_I3s
const std::vector< std::vector< int > > _I3s
Definition Water97FluidProperties.h:1266
Water97FluidProperties::_par3
const std::array< std::array< Real, 8 >, 26 > _par3
Definition Water97FluidProperties.h:987
Water97FluidProperties::subregionEnum
subregionEnum
Enum of subregion ids for region 3.
Definition Water97FluidProperties.h:668
Water97FluidProperties::h_from_p_T
virtual Real h_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:492
Water97FluidProperties::vaporTemperature
Real vaporTemperature(Real pressure) const override
Saturation temperature as a function of pressure.
Definition Water97FluidProperties.C:565
Water97FluidProperties::_I5
const std::array< int, 6 > _I5
Definition Water97FluidProperties.h:1425
Water97FluidProperties::_Iph3b
const std::array< int, 33 > _Iph3b
Definition Water97FluidProperties.h:1397
Water97FluidProperties::criticalPressure
virtual Real criticalPressure() const override
Critical pressure.
Definition Water97FluidProperties.C:51
Water97FluidProperties::_p_triple
const Real _p_triple
Triple point pressure (Pa)
Definition Water97FluidProperties.h:832
Water97FluidProperties::_nph3a
const std::array< Real, 31 > _nph3a
Definition Water97FluidProperties.h:1369
Water97FluidProperties::fluidName
virtual std::string fluidName() const override
Fluid name.
Definition Water97FluidProperties.C:39
Water97FluidProperties::_par3N
const std::array< unsigned int, 26 > _par3N
Definition Water97FluidProperties.h:1015
Water97FluidProperties::d2gamma2_dpi2
T d2gamma2_dpi2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 2 wrt pi.
Definition Water97FluidProperties.h:1668
Water97FluidProperties::_Iph3a
const std::array< int, 31 > _Iph3a
Definition Water97FluidProperties.h:1379
Water97FluidProperties::_I3
const std::array< int, 40 > _I3
Definition Water97FluidProperties.h:980
Water97FluidProperties::_nph1
const std::array< Real, 20 > _nph1
Definition Water97FluidProperties.h:863
Water97FluidProperties::_J05
const std::array< int, 6 > _J05
Constants for region 5.
Definition Water97FluidProperties.h:1417
Water97FluidProperties::e_from_p_rho_template
T e_from_p_rho_template(const T &p, const T &rho) const
Definition Water97FluidProperties.h:2456
Water97FluidProperties::c_from_v_e
virtual ADReal c_from_v_e(const ADReal &v, const ADReal &e) const override
Definition Water97FluidProperties.C:225
Water97FluidProperties::densityRegion3
T densityRegion3(const T &pressure, const T &temperature) const
Density function for Region 3 - supercritical water and steam.
Definition Water97FluidProperties.h:1543
Water97FluidProperties::mu_from_p_T_template
T mu_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2615
Water97FluidProperties::validParams
static InputParameters validParams()
Definition Water97FluidProperties.C:17
Water97FluidProperties::_T_critical
const Real _T_critical
Critical temperature (K)
Definition Water97FluidProperties.h:828
Water97FluidProperties::_Jph1
const std::array< int, 20 > _Jph1
Definition Water97FluidProperties.h:872
Water97FluidProperties::e_from_p_T
virtual Real e_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:177
Water97FluidProperties::propfuncWithDefinitionOverride
propfuncWithDefinitionOverride(s, p, T)
Water97FluidProperties::molarMass
virtual Real molarMass() const override
Molar mass [kg/mol].
Definition Water97FluidProperties.C:45
Water97FluidProperties::T_from_p_h_ad
ADReal T_from_p_h_ad(const ADReal &pressure, const ADReal &enthalpy) const
AD version of backwards equation T(p, h) (used internally) From Revised Release on the IAPWS Industri...
Definition Water97FluidProperties.C:749
Water97FluidProperties::_mu_H0
const std::array< Real, 4 > _mu_H0
Constants from Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance.
Definition Water97FluidProperties.h:1486
Water97FluidProperties::c_from_p_T
virtual Real c_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:232
Water97FluidProperties::k_from_rho_T_template
T k_from_rho_T_template(const T &density, const T &temperature) const
Definition Water97FluidProperties.h:2388
Water97FluidProperties::d2gamma1_dtau2
T d2gamma1_dtau2(const T &pi, const T &tau) const
Second derivative of Gibbs free energy in Region 1 wrt tau.
Definition Water97FluidProperties.h:1623
Water97FluidProperties::cv_from_p_T_template
T cv_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2334
Water97FluidProperties::_nph2a
const std::array< Real, 36 > _nph2a
Definition Water97FluidProperties.h:909
Water97FluidProperties::subregion3ph
unsigned int subregion3ph(Real pressure, Real enthalpy) const
Provides the correct subregion index for a (P,h) point in region 3.
Definition Water97FluidProperties.C:692
Water97FluidProperties::k_from_v_e_template
T k_from_v_e_template(const T &v, const T &e) const
Definition Water97FluidProperties.h:2432
Water97FluidProperties::_J3s
const std::vector< std::vector< int > > _J3s
Definition Water97FluidProperties.h:1318
Water97FluidProperties::gamma2
T gamma2(const T &pi, const T &tau) const
Gibbs free energy in Region 2 - superheated steam.
Definition Water97FluidProperties.h:1647
Water97FluidProperties::_I1
const std::array< int, 34 > _I1
Definition Water97FluidProperties.h:856
Water97FluidProperties::inRegionPH
unsigned int inRegionPH(Real pressure, Real enthalpy) const
Determines the phase region that the given pressure and enthaply values lie in.
Definition Water97FluidProperties.C:611
Water97FluidProperties::triplePointPressure
virtual Real triplePointPressure() const override
Triple point pressure.
Definition Water97FluidProperties.C:69
Water97FluidProperties::_n5
const std::array< Real, 6 > _n5
Definition Water97FluidProperties.h:1427
Water97FluidProperties::dgamma1_dtau
T dgamma1_dtau(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 1 wrt tau.
Definition Water97FluidProperties.h:1611
Water97FluidProperties::_Mh2o
const Real _Mh2o
Water molar mass (kg/mol)
Definition Water97FluidProperties.h:822
Water97FluidProperties::d2phi3_ddeltatau
T d2phi3_ddeltatau(const T &delta, const T &tau) const
Second derivative of Helmholtz free energy in Region 3 wrt delta and tau.
Definition Water97FluidProperties.h:1794
Water97FluidProperties::dgamma2_dpi
T dgamma2_dpi(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 2 wrt pi.
Definition Water97FluidProperties.h:1528
Water97FluidProperties::subregion3
unsigned int subregion3(Real pressure, Real temperature) const
Provides the correct subregion index for a (P,T) point in region 3.
Definition Water97FluidProperties.C:1034
Water97FluidProperties::c_from_p_T_template
T c_from_p_T_template(const T &pressure, const T &temperature) const
Definition Water97FluidProperties.h:2222
Water97FluidProperties::_p_star
const std::array< Real, 5 > _p_star
Pressure scale for each region.
Definition Water97FluidProperties.h:1501
Water97FluidProperties::_n23
const std::array< Real, 5 > _n23
Constants for the boundary between regions 2 and 3.
Definition Water97FluidProperties.h:961
Water97FluidProperties::p_from_v_e_template
T p_from_v_e_template(const T &v, const T &e) const
Definition Water97FluidProperties.h:2440
Water97FluidProperties::_J02
const std::array< int, 9 > _J02
Definition Water97FluidProperties.h:899
Water97FluidProperties::_Iph2c
const std::array< int, 23 > _Iph2c
Definition Water97FluidProperties.h:954
Water97FluidProperties::_J3
const std::array< int, 40 > _J3
Definition Water97FluidProperties.h:983
Water97FluidProperties::_Jph3b
const std::array< int, 33 > _Jph3b
Definition Water97FluidProperties.h:1401
Water97FluidProperties::s_from_h_p
virtual Real s_from_h_p(Real enthalpy, Real pressure) const override
Definition Water97FluidProperties.C:450
Water97FluidProperties::_Rw
const Real _Rw
Specific gas constant for H2O (universal gas constant / molar mass of water - J/kg/K)
Definition Water97FluidProperties.h:824
Water97FluidProperties::cv_from_p_T
virtual Real cv_from_p_T(Real pressure, Real temperature) const override
Definition Water97FluidProperties.C:263
Water97FluidProperties::dgamma5_dpi
T dgamma5_dpi(const T &pi, const T &tau) const
Derivative of Gibbs free energy in Region 5 wrt pi.
Definition Water97FluidProperties.h:1827
FluidPropertiesUtils::NewtonSolve
std::pair< T, T > NewtonSolve(const T &x, const T &y, const Real z_initial_guess, const Real tolerance, const Functor &y_from_x_z, const std::string &caller_name, const unsigned int max_its=100, const bool verbose=false)
NewtonSolve does a 1D Newton Solve to solve the equation y = f(x, z) for variable z.
Definition NewtonInversion.h:44
MathUtils::pow
T pow(T x, int e)
MetaPhysicL::raw_value
auto raw_value(const Eigen::Map< T > &in)
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