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Common.hpp
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27 #ifndef OPM_IAPWS_COMMON_HPP
28 #define OPM_IAPWS_COMMON_HPP
29 
32 
33 #include <cmath>
34 
35 namespace Opm {
36 namespace IAPWS {
37 
53 template <class Scalar>
54 class Common
55 {
56 public:
58  static const Scalar molarMass;
59 
61  static const Scalar Rs;
62 
64  static const Scalar criticalTemperature;
65 
67  static const Scalar criticalPressure;
68 
70  static const Scalar criticalDensity;
71 
73  static const Scalar criticalMolarVolume;
74 
76  static const Scalar acentricFactor;
77 
79  static const Scalar tripleTemperature;
80 
82  static const Scalar triplePressure;
83 
98  template <class Evaluation>
99  static Evaluation viscosity(const Evaluation& temperature, const Evaluation& rho)
100  {
101  Evaluation rhoBar = rho/322.0;
102  Evaluation TBar = temperature/criticalTemperature;
103 
104  // muBar = muBar_1
105  const Scalar Hij[6][7] = {
106  { 5.20094e-1, 2.22531e-1,-2.81378e-1, 1.61913e-1,-3.25372e-2, 0, 0 },
107  { 8.50895e-2, 9.99115e-1,-9.06851e-1, 2.57399e-1, 0, 0, 0 },
108  { -1.08374, 1.88797 ,-7.72479e-1, 0, 0, 0, 0 },
109  { -2.89555e-1, 1.26613 ,-4.89837e-1, 0, 6.98452e-2, 0,-4.35673e-3 },
110  { 0, 0,-2.57040e-1, 0, 0, 8.72102e-3, 0 },
111  { 0, 1.20573e-1, 0, 0, 0, 0,-5.93264e-4 }
112  };
113 
114  Evaluation tmp, tmp2, tmp3 = 1;
115  Evaluation muBar = 0;
116  for (int i = 0; i <= 5; ++i) {
117  tmp = 0;
118  tmp2 = 1;
119  for (int j = 0; j <= 6; ++j) {
120  tmp += Hij[i][j]*tmp2;
121  tmp2 *= (rhoBar - 1);
122  };
123  muBar += tmp3 * tmp;
124  tmp3 *= 1.0/TBar - 1;
125  };
126  muBar *= rhoBar;
127  muBar = exp(muBar);
128 
129  // muBar *= muBar_0
130  muBar *= 100*sqrt(TBar);
131  const Scalar H[4] = {
132  1.67752, 2.20462, 0.6366564, -0.241605
133  };
134 
135  tmp = 0, tmp2 = 1;
136  for (int i = 0; i < 4; ++i) {
137  tmp += H[i]/tmp2;
138  tmp2 *= TBar;
139  };
140  muBar /= tmp;
141 
142  return 1e-6*muBar;
143  }
144 
158  template <class Evaluation>
159  static Evaluation thermalConductivityIAPWS(const Evaluation& T, const Evaluation& rho)
160  {
161  static const Scalar thcond_tstar = 647.26 ;
162  static const Scalar thcond_rhostar = 317.7 ;
163  /*static const Scalar thcond_kstar = 1.0 ;*/
164 
165  static const Scalar thcond_b0 = -0.397070 ;
166  static const Scalar thcond_b1 = 0.400302 ;
167  static const Scalar thcond_b2 = 1.060000 ;
168  static const Scalar thcond_B1 = -0.171587 ;
169  static const Scalar thcond_B2 = 2.392190 ;
170 
171  static const Scalar thcond_c1 = 0.642857 ;
172  static const Scalar thcond_c2 = -4.11717 ;
173  static const Scalar thcond_c3 = -6.17937 ;
174  static const Scalar thcond_c4 = 0.00308976 ;
175  static const Scalar thcond_c5 = 0.0822994 ;
176  static const Scalar thcond_c6 = 10.0932 ;
177 
178  static const Scalar thcond_d1 = 0.0701309 ;
179  static const Scalar thcond_d2 = 0.0118520 ;
180  static const Scalar thcond_d3 = 0.00169937 ;
181  static const Scalar thcond_d4 = -1.0200 ;
182  static const int thcond_a_count = 4;
183  static const Scalar thcond_a[thcond_a_count] = {
184  0.0102811
185  ,0.0299621
186  ,0.0156146
187  ,-0.00422464
188  };
189 
190  Evaluation Tbar = T / thcond_tstar;
191  Evaluation rhobar = rho / thcond_rhostar;
192 
193  /* fast implementation... minimised calls to 'pow' routine... */
194  Evaluation Troot = sqrt(Tbar);
195  Evaluation Tpow = Troot;
196  Evaluation lam = 0;
197 
198  for(int k = 0; k < thcond_a_count; ++k) {
199  lam += thcond_a[k] * Tpow;
200  Tpow *= Tbar;
201  }
202 
203  lam +=
204  thcond_b0 + thcond_b1
205  * rhobar + thcond_b2
206  * exp(thcond_B1 * ((rhobar + thcond_B2)*(rhobar + thcond_B2)));
207 
208  Evaluation DTbar = abs(Tbar - 1) + thcond_c4;
209  Evaluation DTbarpow = pow(DTbar, 3./5);
210  Evaluation Q = 2. + thcond_c5 / DTbarpow;
211 
212  Evaluation S;
213  if(Tbar >= 1)
214  S = 1. / DTbar;
215  else
216  S = thcond_c6 / DTbarpow;
217 
218  Evaluation rhobar18 = pow(rhobar, 1.8);
219  Evaluation rhobarQ = pow(rhobar, Q);
220 
221  lam +=
222  (thcond_d1 / pow(Tbar,10.0) + thcond_d2) * rhobar18 *
223  exp(thcond_c1 * (1 - rhobar * rhobar18))
224  + thcond_d3 * S * rhobarQ *
225  exp((Q/(1+Q))*(1 - rhobar*rhobarQ))
226  + thcond_d4 *
227  exp(thcond_c2 * pow(Troot,3.0) + thcond_c3 / pow(rhobar,5.0));
228  return /*thcond_kstar * */ lam;
229  }
230 };
231 
232 template <class Scalar>
233 const Scalar Common<Scalar>::molarMass = 18.01518e-3;
234 template <class Scalar>
235 const Scalar Common<Scalar>::Rs = Constants<Scalar>::R/molarMass;
236 template <class Scalar>
237 const Scalar Common<Scalar>::criticalTemperature = 647.096;
238 template <class Scalar>
239 const Scalar Common<Scalar>::criticalPressure = 22.064e6;
240 template <class Scalar>
241 const Scalar Common<Scalar>::criticalDensity = 322.0;
242 template <class Scalar>
243 const Scalar Common<Scalar>::criticalMolarVolume = molarMass/criticalDensity;
244 template <class Scalar>
245 const Scalar Common<Scalar>::acentricFactor = 0.344;
246 template <class Scalar>
247 const Scalar Common<Scalar>::tripleTemperature = 273.16;
248 template <class Scalar>
249 const Scalar Common<Scalar>::triplePressure = 611.657;
250 
251 } // namespace IAPWS
252 } // namespace Opm
253 
254 #endif
A central place for various physical constants occuring in some equations.
A traits class which provides basic mathematical functions for arbitrary scalar floating point values...
A central place for various physical constants occuring in some equations.
Definition: Constants.hpp:41
Implements relations which are common for all regions of the IAPWS '97 formulation.
Definition: Common.hpp:55
static const Scalar criticalPressure
Critical pressure of water .
Definition: Common.hpp:67
static Evaluation viscosity(const Evaluation &temperature, const Evaluation &rho)
The dynamic viscosity of pure water.
Definition: Common.hpp:99
static const Scalar criticalDensity
Density of water at the critical point .
Definition: Common.hpp:70
static const Scalar criticalMolarVolume
Critical molar volume of water .
Definition: Common.hpp:73
static const Scalar criticalTemperature
Critical temperature of water .
Definition: Common.hpp:64
static Evaluation thermalConductivityIAPWS(const Evaluation &T, const Evaluation &rho)
Thermal conductivity water (IAPWS) .
Definition: Common.hpp:159
static const Scalar tripleTemperature
Triple temperature of water .
Definition: Common.hpp:79
static const Scalar triplePressure
Triple pressure of water .
Definition: Common.hpp:82
static const Scalar molarMass
The molar mass of water .
Definition: Common.hpp:58
static const Scalar acentricFactor
The acentric factor of water .
Definition: Common.hpp:76
static const Scalar Rs
Specific gas constant of water .
Definition: Common.hpp:61