foam-extend4.1-coherent-io/src/thermophysicalModels/thermophysicalFunctions/freesteam-2.1/backwards.c

/*
freesteam - IAPWS-IF97 steam tables library
Copyright (C) 2004-2009  John Pye

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2
of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
*//** @file
	Backwards equations for IAPWS-IF97. Facilitate calculation of
	properties in terms of (p,h) without requiring any iteration.

	TODO add boundary curves?
	TODO add more equations for (p,s) calculation?

	Numerical data for T(p,h) and v(p,h) correlations was extracted from
	the Matlab version 2.6 of Xsteam by by Magnus Holmgren.
*/

#define FREESTEAM_BUILDING_LIB
#include "backwards.h"

#include "backwards_impl.h"
#include <math.h>

/*------------------------------------------------------------------------------
  REGION 1 BACKWARDS EQUATION T(P,H)
*/

typedef struct{
	int I, J;
	double n;
} BackwardsData;

/**
	Source: IAPWS-IF97-REV section 5.2.1
*/
BackwardsData REGION1_TPH_DATA[] = {
	{0, 0, -238.72489924521}
	,{0, 1, 404.21188637945}
	,{0, 2, 113.49746881718}
	,{0, 6, -5.8457616048039}
	,{0, 22, -1.528548241314E-04}
	,{0, 32, -1.0866707695377E-06}
	,{1, 0, -13.391744872602}
	,{1, 1, 43.211039183559}
	,{1, 2, -54.010067170506}
	,{1, 3, 30.535892203916}
	,{1, 4, -6.5964749423638}
	,{1,10, 9.3965400878363E-03}
	,{1,32, 1.157364750534E-07}
	,{2,10,-2.5858641282073E-05}
	,{2,32,-4.0644363084799E-09}
	,{3,10,6.6456186191635E-08}
	,{3,32,8.0670734103027E-11}
	,{4,32,-9.3477771213947E-13}
	,{5,32,5.8265442020601E-15}
	,{6,32,-1.5020185953503E-17}
};

const unsigned REGION1_TPH_MAX = sizeof(REGION1_TPH_DATA)/sizeof(BackwardsData);

const double REGION1_TPH_HSTAR = 2500e3; /* J/kg */
const double REGION1_TPH_PSTAR = 1e6; /* Pa */

/**
	Backward equation for temperature in terms of pressure and enthalpy
	in IAPWS-IF97 Region 1. Source: IAPWS-IF97-Rev section 5.2.1.

	@param p pressure in Pa
	@param h enthalpy in J/kg
	@return temperature in K
*/
double freesteam_region1_T_ph(double p, double h){
	double pi = p / REGION1_TPH_PSTAR;
	double e1 = 1. + (h / REGION1_TPH_HSTAR);
	unsigned i;
	BackwardsData *d;
	double sum = 0;
	for(i=0, d = REGION1_TPH_DATA; i<REGION1_TPH_MAX; ++i, ++d){
		/* TODO some optimisations are possible here with pow(pi,...) */
		sum += d->n * ipow(pi,d->I) * ipow(e1, d->J);
	}
	return sum /* * REGION1_TPH_TSTAR = 1. */;
}


/*------------------------------------------------------------------------------
  REGION 2 BACKWARDS EQUATION T(P,H)
*/

/* sub-region 2a */
BackwardsData REGION2A_TPH_DATA[] = {
	{0,	0,	1089.8952318288}
	,{0,	1,	849.51654495535}
	,{0,	2,	-107.81748091826}
	,{0,	3,	33.153654801263}
	,{0,	7,	-7.4232016790248}
	,{0,	20,	11.765048724356}
	,{1,	0,	1.844574935579}
	,{1,	1,	-4.1792700549624}
	,{1,	2,	6.2478196935812}
	,{1,	3,	-17.344563108114}
	,{1,	7,	-200.58176862096}
	,{1,	9,	271.96065473796}
	,{1,	11,	-455.11318285818}
	,{1,	18,	3091.9688604755}
	,{1,	44,	252266.40357872}
	,{2,	0,	-6.1707422868339E-03}
	,{2,	2,	-0.31078046629583}
	,{2,	7,	11.670873077107}
	,{2,	36,	128127984.04046}
	,{2,	38,	-985549096.23276}
	,{2,	40,	2822454697.3002}
	,{2,	42,	-3594897141.0703}
	,{2,	44,	1722734991.3197}
	,{3,	24,	-13551.334240775}
	,{3,	44,	12848734.66465}
	,{4,	12,	1.3865724283226}
	,{4,	32,	235988.32556514}
	,{4,	44,	-13105236.545054}
	,{5,	32,	7399.9835474766}
	,{5,	36,	-551966.9703006}
	,{5,	42,	3715408.5996233}
	,{6,	34,	19127.72923966}
	,{6,	44,	-415351.64835634}
	,{7,	28,	-62.459855192507}

};

const unsigned REGION2A_TPH_MAX = sizeof(REGION2A_TPH_DATA)/sizeof(BackwardsData);

/* sub-region 2b */

BackwardsData REGION2B_TPH_DATA[] = {
	{0,	0,	1489.5041079516}
	,{0,	1,	743.07798314034}
	,{0,	2,	-97.708318797837}
	,{0,	12,	2.4742464705674}
	,{0,	18,	-0.63281320016026}
	,{0,	24,	1.1385952129658}
	,{0,	28,	-0.47811863648625}
	,{0,	40,	8.5208123431544E-03}
	,{1,	0,	0.93747147377932}
	,{1,	2,	3.3593118604916}
	,{1,	6,	3.3809355601454}
	,{1,	12,	0.16844539671904}
	,{1,	18,	0.73875745236695}
	,{1,	24,	-0.47128737436186}
	,{1,	28,	0.15020273139707}
	,{1,	40,	-0.002176411421975}
	,{2,	2,	-0.021810755324761}
	,{2,	8,	-0.10829784403677}
	,{2,	18,	-0.046333324635812}
	,{2,	40,	7.1280351959551E-05}
	,{3,	1,	1.1032831789999E-04}
	,{3,	2,	1.8955248387902E-04}
	,{3,	12,	3.0891541160537E-03}
	,{3,	24,	1.3555504554949E-03}
	,{4,	2,	2.8640237477456E-07}
	,{4,	12,	-1.0779857357512E-05}
	,{4,	18,	-7.6462712454814E-05}
	,{4,	24,	1.4052392818316E-05}
	,{4,	28,	-3.1083814331434E-05}
	,{4,	40,	-1.0302738212103E-06}
	,{5,	18,	2.821728163504E-07}
	,{5,	24,	1.2704902271945E-06}
	,{5,	40,	7.3803353468292E-08}
	,{6,	28,	-1.1030139238909E-08}
	,{7,	2,	-8.1456365207833E-14}
	,{7,	28,	-2.5180545682962E-11}
	,{9,	1,	-1.7565233969407E-18}
	,{9,	40,	8.6934156344163E-15}

};

const unsigned REGION2B_TPH_MAX = sizeof(REGION2B_TPH_DATA)/sizeof(BackwardsData);

/* sub-region 2c */
BackwardsData REGION2C_TPH_DATA[] ={
	{-7,	0,	-3236839855524.2}
	,{-7,	4,	7326335090218.1}
	,{-6,	0,	358250899454.47}
	,{-6,	2,	-583401318515.9}
	,{-5,	0,	-10783068217.47}
	,{-5,	2,	20825544563.171}
	,{-2,	0,	610747.83564516}
	,{-2,	1,	859777.2253558}
	,{-1,	0,	-25745.72360417}
	,{-1,	2,	31081.088422714}
	,{0,	0,	1208.2315865936}
	,{0,	1,	482.19755109255}
	,{1,	4,	3.7966001272486}
	,{1,	8,	-10.842984880077}
	,{2,	4,	-0.04536417267666}
	,{6,	0,	1.4559115658698E-13}
	,{6,	1,	1.126159740723E-12}
	,{6,	4,	-1.7804982240686E-11}
	,{6,	10,	1.2324579690832E-07}
	,{6,	12,	-1.1606921130984E-06}
	,{6,	16,	2.7846367088554E-05}
	,{6,	20,	-5.9270038474176E-04}
	,{6,	22,	1.2918582991878E-03}

};

const unsigned REGION2C_TPH_MAX = sizeof(REGION2C_TPH_DATA)/sizeof(BackwardsData);

const double REGION2AB_P = 4.e6; /* Pa */

const double REGION2_HSTAR = 2000e3;
const double REGION2_PSTAR = 1.e6;

/* REGION2_B2BC_PH defined in backwards_impl.h */

/**
	Backward equation for temperature in terms of pressure and enthalpy
	in IAPWS-IF97 Region 2 (composed of sub-regions 2a, 2b, 2c).
	Source: IAPWS-IF97-Rev section 5.2.1.

	@param p pressure in Pa
	@param h enthalpy in J/kg
	@return temperature in K
*/
double freesteam_region2_T_ph(double p, double h){

	IAPWS97_APPROXIMATE;

	double eta = h / REGION2_HSTAR;
	double pi = p / REGION2_PSTAR;
	double pi1, eta1;
	BackwardsData *d;
	unsigned i, n;
	double sum = 0;
	if(p < REGION2AB_P){
		//fprintf(stderr,"region 2a\n");
		pi1 = pi; eta1 = eta - 2.1;
		d = REGION2A_TPH_DATA;
		n = REGION2A_TPH_MAX;
	}else{
		if(REGION2_B2BC_PH(p,h) < 0.){
			//fprintf(stderr,"region 2b\n");
			pi1 = pi - 2.; eta1 = eta - 2.6;
			d = REGION2B_TPH_DATA;
			n = REGION2B_TPH_MAX;
		}else{
			//fprintf(stderr,"region 2c\n");
			pi1 = pi + 25.; eta1 = eta - 1.8;
			d = REGION2C_TPH_DATA;
			n = REGION2C_TPH_MAX;
		}
	}

	for(i = 0; i<n; ++i, ++d){
		sum += d->n * ipow(pi1, d->I) * ipow(eta1, d->J);
	}

	return sum /* * REGION2_TSTAR = 1 K */;
}


/*------------------------------------------------------------------------------
  REGION 3 BACKWARDS EQUATION T(P,H)
*/

/* sub-region 3a */
BackwardsData REGION3A_TPH_DATA[] = {
	{-12,	0,	-1.33645667811215E-07}
	,{-12,	1,	4.55912656802978E-06}
	,{-12,	2,	-1.46294640700979E-05}
	,{-12,	6,	6.3934131297008E-03}
	,{-12,	14,	372.783927268847}
	,{-12,	16,	-7186.54377460447}
	,{-12,	20,	573494.7521034}
	,{-12,	22,	-2675693.29111439}
	,{-10,	1,	-3.34066283302614E-05}
	,{-10,	5,	-2.45479214069597E-02}
	,{-10,	12,	47.8087847764996}
	,{-8,	0,	7.64664131818904E-06}
	,{-8,	2,	1.28350627676972E-03}
	,{-8,	4,	1.71219081377331E-02}
	,{-8,	10,	-8.51007304583213}
	,{-5,	2,	-1.36513461629781E-02}
	,{-3,	0,	-3.84460997596657E-06}
	,{-2,	1,	3.37423807911655E-03}
	,{-2,	3,	-0.551624873066791}
	,{-2,	4,	0.72920227710747}
	,{-1,	0,	-9.92522757376041E-03}
	,{-1,	2,	-0.119308831407288}
	,{0,	0,	0.793929190615421}
	,{0,	1,	0.454270731799386}
	,{1,	1,	0.20999859125991}
	,{3,	0,	-6.42109823904738E-03}
	,{3,	1,	-0.023515586860454}
	,{4,	0,	2.52233108341612E-03}
	,{4,	3,	-7.64885133368119E-03}
	,{10,	4,	1.36176427574291E-02}
	,{12,	5,	-1.33027883575669E-02}
};

const unsigned REGION3A_TPH_MAX = sizeof(REGION3A_TPH_DATA)/sizeof(BackwardsData);

BackwardsData REGION3B_TPH_DATA[] = {
	{-12,	0,	3.2325457364492E-05}
	,{-12,	1,	-1.27575556587181E-04}
	,{-10,	0,	-4.75851877356068E-04}
	,{-10,	1,	1.56183014181602E-03}
	,{-10,	5,	0.105724860113781}
	,{-10,	10,	-85.8514221132534}
	,{-10,	12,	724.140095480911}
	,{-8,	0,	2.96475810273257E-03}
	,{-8,	1,	-5.92721983365988E-03}
	,{-8,	2,	-1.26305422818666E-02}
	,{-8,	4,	-0.115716196364853}
	,{-8,	10,	84.9000969739595}
	,{-6,	0,	-1.08602260086615E-02}
	,{-6,	1,	1.54304475328851E-02}
	,{-6,	2,	7.50455441524466E-02}
	,{-4,	0,	2.52520973612982E-02}
	,{-4,	1,	-6.02507901232996E-02}
	,{-3,	5,	-3.07622221350501}
	,{-2,	0,	-5.74011959864879E-02}
	,{-2,	4,	5.03471360939849}
	,{-1,	2,	-0.925081888584834}
	,{-1,	4,	3.91733882917546}
	,{-1,	6,	-77.314600713019}
	,{-1,	10,	9493.08762098587}
	,{-1,	14,	-1410437.19679409}
	,{-1,	16,	8491662.30819026}
	,{0,	0,	0.861095729446704}
	,{0,	2,	0.32334644281172}
	,{1,	1,	0.873281936020439}
	,{3,	1,	-0.436653048526683}
	,{5,	1,	0.286596714529479}
	,{6,	1,	-0.131778331276228}
	,{8,	1,	6.76682064330275E-03}
};

const unsigned REGION3B_TPH_MAX = sizeof(REGION3B_TPH_DATA)/sizeof(BackwardsData);

/* REGION3_B3AB_PH(P,H) boundary test declared in backwards_impl.h */

const double REGION3A_TPH_HSTAR = 2300e3;
const double REGION3A_TPH_PSTAR = 100.e6;
const double REGION3A_TPH_TSTAR = 760;

const double REGION3B_TPH_HSTAR = 2800e3;
const double REGION3B_TPH_PSTAR = 100.e6;
const double REGION3B_TPH_TSTAR = 860;

/**
	Backward equation for temperature in terms of pressure and enthalpy
	in IAPWS-IF97 Region 3 (composed of sub-regions 3a, 3b).

	Source: IAPWS 'Revised Supplementary Release on Backward Equations for the Functions
	T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial
	Formulation 1997 for the Thermodynamic Properties of Water and Steam', 2004.

	@param p pressure in Pa
	@param h enthalpy in J/kg
	@return temperature in K
*/
double freesteam_region3_T_ph(double p, double h){

	IAPWS97_APPROXIMATE;

	double pi1, eta1;
	double Tstar;
	BackwardsData *d;
	unsigned i, n;
	double sum = 0;
	if(REGION3_B3AB_PH(p,h) <= 0.){
		/* sub-region 3a */
		pi1 = p/REGION3A_TPH_PSTAR + 0.240; eta1 = h/REGION3A_TPH_HSTAR - 0.615;
		d = REGION3A_TPH_DATA;
		n = REGION3A_TPH_MAX;
		Tstar = REGION3A_TPH_TSTAR;
	}else{
		/* sub-region 3b */
		pi1 = p/REGION3B_TPH_PSTAR + 0.298; eta1 = h/REGION3B_TPH_HSTAR - 0.720;
		d = REGION3B_TPH_DATA;
		n = REGION3B_TPH_MAX;
		Tstar = REGION3B_TPH_TSTAR;
	}

	for(i = 0; i<n; ++i, ++d){
		sum += d->n * ipow(pi1, d->I) * ipow(eta1, d->J);
	}

	return sum * Tstar;
}


/*------------------------------------------------------------------------------
  REGION 3 V(P,H)
*/

BackwardsData REGION3A_VPH_DATA[] = {
	{-12,	6,	5.29944062966028E-03}
	,{-12,	8,	-0.170099690234461}
	,{-12,	12,	11.1323814312927}
	,{-12,	18,	-2178.98123145125}
	,{-10,	4,	-5.06061827980875E-04}
	,{-10,	7,	0.556495239685324}
	,{-10,	10,	-9.43672726094016}
	,{-8,	5,	-0.297856807561527}
	,{-8,	12,	93.9353943717186}
	,{-6,	3,	1.92944939465981E-02}
	,{-6,	4,	0.421740664704763}
	,{-6,	22,	-3689141.2628233}
	,{-4,	2,	-7.37566847600639E-03}
	,{-4,	3,	-0.354753242424366}
	,{-3,	7,	-1.99768169338727}
	,{-2,	3,	1.15456297059049}
	,{-2,	16,	5683.6687581596}
	,{-1,	0,	8.08169540124668E-03}
	,{-1,	1,	0.172416341519307}
	,{-1,	2,	1.04270175292927}
	,{-1,	3,	-0.297691372792847}
	,{0,	0,	0.560394465163593}
	,{0,	1,	0.275234661176914}
	,{1,	0,	-0.148347894866012}
	,{1,	1,	-6.51142513478515E-02}
	,{1,	2,	-2.92468715386302}
	,{2,	0,	6.64876096952665E-02}
	,{2,	2,	3.52335014263844}
	,{3,	0,	-1.46340792313332E-02}
	,{4,	2,	-2.24503486668184}
	,{5,	2,	1.10533464706142}
	,{8,	2,	-4.08757344495612E-02}
};

const unsigned REGION3A_VPH_MAX = sizeof(REGION3A_VPH_DATA)/sizeof(BackwardsData);

BackwardsData REGION3B_VPH_DATA[] = {
	{-12,	0,	-2.25196934336318E-09}
	,{-12,	1,	1.40674363313486E-08}
	,{-8,	0,	2.3378408528056E-06}
	,{-8,	1,	-3.31833715229001E-05}
	,{-8,	3,	1.07956778514318E-03}
	,{-8,	6,	-0.271382067378863}
	,{-8,	7,	1.07202262490333}
	,{-8,	8,	-0.853821329075382}
	,{-6,	0,	-2.15214194340526E-05}
	,{-6,	1,	7.6965608822273E-04}
	,{-6,	2,	-4.31136580433864E-03}
	,{-6,	5,	0.453342167309331}
	,{-6,	6,	-0.507749535873652}
	,{-6,	10,	-100.475154528389}
	,{-4,	3,	-0.219201924648793}
	,{-4,	6,	-3.21087965668917}
	,{-4,	10,	607.567815637771}
	,{-3,	0,	5.57686450685932E-04}
	,{-3,	2,	0.18749904002955}
	,{-2,	1,	9.05368030448107E-03}
	,{-2,	2,	0.285417173048685}
	,{-1,	0,	3.29924030996098E-02}
	,{-1,	1,	0.239897419685483}
	,{-1,	4,	4.82754995951394}
	,{-1,	5,	-11.8035753702231}
	,{0,	0,	0.169490044091791}
	,{1,	0,	-1.79967222507787E-02}
	,{1,	1,	3.71810116332674E-02}
	,{2,	2,	-5.36288335065096E-02}
	,{2,	6,	1.6069710109252}
};

const unsigned REGION3B_VPH_MAX = sizeof(REGION3B_VPH_DATA)/sizeof(BackwardsData);

const double REGION3A_VPH_HSTAR = 2100e3; /* J/kg */
const double REGION3A_VPH_PSTAR = 100.e6; /* Pa */
const double REGION3A_VPH_VSTAR = 0.0028; /* m³/kg */

const double REGION3B_VPH_HSTAR = 2800e3;
const double REGION3B_VPH_PSTAR = 100.e6;
const double REGION3B_VPH_VSTAR = 0.0088;

/**
	Backward equation for specific volume in terms of pressure and enthalpy
	in IAPWS-IF97 Region 3 (composed of sub-regions 3a, 3b).

	Source: IAPWS 'Revised Supplementary Release on Backward Equations for the Functions
	T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial
	Formulation 1997 for the Thermodynamic Properties of Water and Steam', 2004.

	@param p pressure in Pa
	@param h enthalpy in J/kg
	@return temperature in K
*/
double freesteam_region3_v_ph(double p, double h){

	IAPWS97_APPROXIMATE;

	double pi1, eta1;
	BackwardsData *d;
	unsigned i, n;
	double sum = 0;
	double vstar;
	if(REGION3_B3AB_PH(p,h) <= 0.){
		/* sub-region 3a */
		pi1 = p/REGION3A_VPH_PSTAR + 0.128; eta1 = h/REGION3A_VPH_HSTAR - 0.727;
		d = REGION3A_VPH_DATA;
		n = REGION3A_VPH_MAX;
		vstar = REGION3A_VPH_VSTAR;
	}else{
		/* sub-region 3b */
		pi1 = p/REGION3B_VPH_PSTAR + 0.0661; eta1 = h/REGION3B_VPH_HSTAR - 0.720;
		d = REGION3B_VPH_DATA;
		n = REGION3B_VPH_MAX;
		vstar = REGION3B_VPH_VSTAR;
	}

	for(i = 0; i<n; ++i, ++d){
		sum += d->n * ipow(pi1, d->I) * ipow(eta1, d->J);
	}

	return sum * vstar;
}

/*------------------------------------------------------------------------------
  REGION 3 PSAT(H) BOUNDARY
*/

BackwardsData REGION3_PSATH_DATA[] = {
	{ 0,	0,	 0.600073641753024}
	,{1,	1,	-0.936203654849857e1}
	,{1,	3,	 0.246590798594147e2}
	,{1,	4,	-0.107014222858224e3}
	,{1,	36,	-0.915821315805768e14}
	,{5,	3,	-0.862332011700662e4}
	,{7,	0,	-0.235837344740032e2}
	,{8,	24,	 0.252304969384128e18}
	,{14,	16,	-0.389718771997719e19}
	,{20,	16,	-0.333775713645296e23}
	,{22,	3,	 0.356499469636328e11}
	,{24,	18,	-0.148547544720641e27}
	,{28,	8,	 0.330611514838798e19}
	,{36,	24,	 0.813641294467829e38}
};

const unsigned REGION3_PSATH_MAX = sizeof(REGION3_PSATH_DATA)/sizeof(BackwardsData);

const double REGION3_PSATH_HSTAR = 2600e3;
const double REGION3_PSATH_PSTAR = 22.e6;

double freesteam_region3_psat_h(double h){

	IAPWS97_APPROXIMATE;

	BackwardsData *d, *e = REGION3_PSATH_DATA + REGION3_PSATH_MAX;
	double eta = h / REGION3_PSATH_HSTAR;
	double eta1 = eta - 1.02;
	double eta2 = eta - 0.608;
	double sum = 0;
	for(d = REGION3_PSATH_DATA; d<e; ++d){
		sum += d->n * ipow(eta1, d->I) * ipow(eta2, d->J);
	}
	return sum * REGION3_PSATH_PSTAR;
}

/*------------------------------------------------------------------------------
  REGION 3 PSAT(S) BOUNDARY
*/

BackwardsData REGION3_PSATS_DATA[] = {
	{  0,	0,	 0.639767553612785}
	, {1,	1,	-0.129727445396014e2}
	, {1,	32,	-0.224595125848403e16}
	, {4,	7,	 0.177466741801846e7}
	, {12,	4,	 0.717079349571538e10}
	, {12,	14,	-0.378829107169011e18}
	, {16,	36,	-0.955586736431328e35}
	, {24,	10,	 0.187269814676188e24}
	, {28,	0,	 0.119254746466473e12}
	, {32,	18,	 0.110649277244882e37}
};

const unsigned REGION3_PSATS_MAX = sizeof(REGION3_PSATS_DATA)/sizeof(BackwardsData);

const double REGION3_PSATS_SSTAR = 5.2e3;
const double REGION3_PSATS_PSTAR = 22.e6;

double freesteam_region3_psat_s(double s){

	IAPWS97_APPROXIMATE;

	BackwardsData *d, *e = REGION3_PSATS_DATA + REGION3_PSATS_MAX;
	double sig = s / REGION3_PSATS_SSTAR;
	double sig1 = sig - 1.03;
	double sig2 = sig - 0.699;
	double sum = 0;
	for(d = REGION3_PSATS_DATA; d<e; ++d){
		sum += d->n * ipow(sig1, d->I) * ipow(sig2, d->J);
	}
	return sum * REGION3_PSATS_PSTAR;
}


/*------------------------------------------------------------------------------
  REGION 3 BACKWARDS EQUATION T(P,S)
*/

/**
	Source: Revised_Release_Tv3ph_Tv3ps_Rev3.doc sect 3.4
*/
BackwardsData REGION3A_TPS_DATA[] = {
	{-12,	28,	1500420082.63875}
	,{-12,	32,	-159397258480.424}
	,{-10,	4,	5.02181140217975E-04}
	,{-10,	10,	-67.2057767855466}
	,{-10,	12,	1450.58545404456}
	,{-10,	14,	-8238.8953488889}
	,{-8,	5,	-0.154852214233853}
	,{-8,	7,	11.2305046746695}
	,{-8,	8,	-29.7000213482822}
	,{-8,	28,	43856513263.5495}
	,{-6,	2,	1.37837838635464E-03}
	,{-6,	6,	-2.97478527157462}
	,{-6,	32,	9717779473494.13}
	,{-5,	0,	-5.71527767052398E-05}
	,{-5,	14,	28830.794977842}
	,{-5,	32,	-74442828926270.3}
	,{-4,	6,	12.8017324848921}
	,{-4,	10,	-368.275545889071}
	,{-4,	36,	6.64768904779177E+15}
	,{-2,	1,	0.044935925195888}
	,{-2,	4,	-4.22897836099655}
	,{-1,	1,	-0.240614376434179}
	,{-1,	6,	-4.74341365254924}
	,{0,	0,	0.72409399912611}
	,{0,	1,	0.923874349695897}
	,{0,	4,	3.99043655281015}
	,{1,	0,	3.84066651868009E-02}
	,{2,	0,	-3.59344365571848E-03}
	,{2,	3,	-0.735196448821653}
	,{3,	2,	0.188367048396131}
	,{8,	0,	1.41064266818704E-04}
	,{8,	1,	-2.57418501496337E-03}
	,{10,	2,	1.23220024851555E-03}
};

const unsigned REGION3A_TPS_MAX = sizeof(REGION3A_TPS_DATA)/sizeof(BackwardsData);

/**
	Source: Revised_Release_Tv3ph_Tv3ps_Rev3.doc sect 3.4
*/
BackwardsData REGION3B_TPS_DATA[] = {
	{-12,	1,	0.52711170160166}
	,{-12,	3,	-40.1317830052742}
	,{-12,	4,	153.020073134484}
	,{-12,	7,	-2247.99398218827}
	,{-8,	0,	-0.193993484669048}
	,{-8,	1,	-1.40467557893768}
	,{-8,	3,	42.6799878114024}
	,{-6,	0,	0.752810643416743}
	,{-6,	2,	22.6657238616417}
	,{-6,	4,	-622.873556909932}
	,{-5,	0,	-0.660823667935396}
	,{-5,	1,	0.841267087271658}
	,{-5,	2,	-25.3717501764397}
	,{-5,	4,	485.708963532948}
	,{-5,	6,	880.531517490555}
	,{-4,	12,	2650155.92794626}
	,{-3,	1,	-0.359287150025783}
	,{-3,	6,	-656.991567673753}
	,{-2,	2,	2.41768149185367}
	,{0,	0,	0.856873461222588}
	,{2,	1,	0.655143675313458}
	,{3,	1,	-0.213535213206406}
	,{4,	0,	5.62974957606348E-03}
	,{5,	24,	-316955725450471.}
	,{6,	0,	-6.99997000152457E-04}
	,{8,	3,	1.19845803210767E-02}
	,{12,	1,	1.93848122022095E-05}
	,{14,	2,	-2.15095749182309E-05}
};

const unsigned REGION3B_TPS_MAX = sizeof(REGION3B_TPS_DATA)/sizeof(BackwardsData);

const double REGION3A_TPS_TSTAR = 760.; /* K */
const double REGION3A_TPS_SSTAR = 4.4e3; /* J/kgK */
const double REGION3A_TPS_PSTAR = 100e6; /* Pa */

const double REGION3B_TPS_TSTAR = 860.; /* K */
const double REGION3B_TPS_SSTAR = 5.3e3; /* J/kgK */
const double REGION3B_TPS_PSTAR = 100e6; /* Pa */

const double REGION3AB_SC = 4.41202148223476e3; /* J/kgK */

/**
	Backward equation for temperature in terms of pressure and entropy
	in IAPWS-IF97 Region 3 (composed of sub-regions 3a, 3b).

	Source: IAPWS 'Revised Supplementary Release on Backward Equations for the Functions
	T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial
	Formulation 1997 for the Thermodynamic Properties of Water and Steam', 2004.

	@param p pressure in Pa
	@param s specific entropy in J/kgK
	@return temperature in K
*/
double freesteam_region3_T_ps(double p, double s){

	IAPWS97_APPROXIMATE;

	double p1, s1;
	double Tstar;
	BackwardsData *d;
	unsigned i, n;
	double sum = 0;
	if(s < REGION3AB_SC){
		/* sub-region 3a */
		p1 = p/REGION3A_TPS_PSTAR + 0.240; s1 = s/REGION3A_TPS_SSTAR - 0.703;
		d = REGION3A_TPS_DATA;
		n = REGION3A_TPS_MAX;
		Tstar = REGION3A_TPS_TSTAR;
	}else{
		/* sub-region 3b */
		p1 = p/REGION3B_TPS_PSTAR + 0.760; s1 = s/REGION3B_TPS_SSTAR - 0.818;
		d = REGION3B_TPS_DATA;
		n = REGION3B_TPS_MAX;
		Tstar = REGION3B_TPS_TSTAR;
	}

	for(i = 0; i<n; ++i, ++d){
		sum += d->n * ipow(p1, d->I) * ipow(s1, d->J);
	}

	return sum * Tstar;
}


/**
	Source: Revised_Release_Tv3ph_Tv3ps_Rev3.doc sect 3.4
*/
BackwardsData REGION3A_VPS_DATA[] = {
	{-12,	10,	0.795544074093975e2}
	, {-12,	12,	-0.238261242984590e4}
	, {-12,	14,	0.176813100617787e5}
	, {-10,	4,	-0.110524727080379e-2}
	, {-10,	8,	-0.153213833655326e2}
	, {-10,	10,	0.297544599376982e3}
	, {-10,	20,	-0.350315206871242e8}
	, {-8,	5,	0.277513761062119}
	, {-8,	6,	-0.523964271036888}
	, {-8,	14,	-0.148011182995403e6}
	, {-8,	16,	0.160014899374266e7}
	, {-6,	28,	0.170802322663427e13}
	, {-5,	1,	0.246866996006494e-3}
	, {-4,	5,	0.165326084797980e1}
	, {-3,	2,	-0.118008384666987}
	, {-3,	4,	0.253798642355900e1}
	, {-2,	3,	0.965127704669424}
	, {-2,	8,	-0.282172420532826e2}
	, {-1,	1,	0.203224612353823}
	, {-1,	2,	0.110648186063513e1}
	, {0,	0,	0.526127948451280}
	, {0,	1,	0.277000018736321}
	, {0,	3,	0.108153340501132e1}
	, {1,	0,	-0.744127885357893e-1}
	, {2,	0,	0.164094443541384e-1}
	, {4,	2,	-0.680468275301065e-1}
	, {5,	2,	0.257988576101640e-1}
	, {6,	0,	-0.145749861944416e-3}
};

const unsigned REGION3A_VPS_MAX = sizeof(REGION3A_VPS_DATA)/sizeof(BackwardsData);

/**
	Source: Revised_Release_Tv3ph_Tv3ps_Rev3.doc sect 3.4
*/
BackwardsData REGION3B_VPS_DATA[] = {
	{-12,	0,	0.591599780322238e-4}
	, {-12,	1,	-0.185465997137856e-2}
	, {-12,	2,	0.104190510480013e-1}
	, {-12,	3,	0.598647302038590e-2}
	, {-12,	5,	-0.771391189901699}
	, {-12,	6,	0.172549765557036e1}
	, {-10,	0,	-0.467076079846526e-3}
	, {-10,	1,	0.134533823384439e-1}
	, {-10,	2,	-0.808094336805495e-1}
	, {-10,	4,	0.508139374365767}
	, {-8,	0,	0.128584643361683e-2}
	, {-5,	1,	-0.163899353915435e1}
	, {-5,	2,	0.586938199318063e1}
	, {-5,	3,	-0.292466667918613e1}
	, {-4,	0,	-0.614076301499537e-2}
	, {-4,	1,	0.576199014049172e1}
	, {-4,	2,	-0.121613320606788e2}
	, {-4,	3,	0.167637540957944e1}
	, {-3,	1,	-0.744135838773463e1}
	, {-2,	0,	0.378168091437659e-1}
	, {-2,	1,	0.401432203027688e1}
	, {-2,	2,	0.160279837479185e2}
	, {-2,	3,	0.317848779347728e1}
	, {-2,	4,	-0.358362310304853e1}
	, {-2,	12,	-0.115995260446827e7}
	, {0,	0,	0.199256573577909}
	, {0,	1,	-0.122270624794624}
	, {0,	2,	-0.191449143716586e2}
	, {1,	0,	-0.150448002905284e-1}
	, {1,	2,	0.146407900162154e2}
	, {2,	2,	-0.327477787188230e1}
};

const unsigned REGION3B_VPS_MAX = sizeof(REGION3B_VPS_DATA)/sizeof(BackwardsData);

const double REGION3A_VPS_VSTAR = 0.0028; /* kg/m³ */
const double REGION3A_VPS_SSTAR = 4.4e3; /* J/kgK */
const double REGION3A_VPS_PSTAR = 100e6; /* Pa */

const double REGION3B_VPS_VSTAR = 0.0088; /* kg/m³ */
const double REGION3B_VPS_SSTAR = 5.3e3; /* J/kgK */
const double REGION3B_VPS_PSTAR = 100e6; /* Pa */

/**
	Backward equation for temperature in terms of pressure and entropy
	in IAPWS-IF97 Region 3 (composed of sub-regions 3a, 3b).

	Source: IAPWS 'Revised Supplementary Release on Backward Equations for the Functions
	T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS Industrial
	Formulation 1997 for the Thermodynamic Properties of Water and Steam', 2004.

	@param p pressure in Pa
	@param s specific entropy in J/kgK
	@return temperature in K
*/
double freesteam_region3_v_ps(double p, double s){

	IAPWS97_APPROXIMATE;

	double p1, s1;
	double vstar;
	BackwardsData *d;
	unsigned i, n;
	double sum = 0;
	if(s < REGION3AB_SC){
		/* sub-region 3a */
		//fprintf(stderr,"3A\n");
		p1 = p/REGION3A_VPS_PSTAR + 0.187; s1 = s/REGION3A_VPS_SSTAR - 0.755;
		d = REGION3A_VPS_DATA;
		n = REGION3A_VPS_MAX;
		vstar = REGION3A_VPS_VSTAR;
	}else{
		/* sub-region 3b */
		//fprintf(stderr,"3B\n");
		p1 = p/REGION3B_VPS_PSTAR + 0.298; s1 = s/REGION3B_VPS_SSTAR - 0.816;
		d = REGION3B_VPS_DATA;
		n = REGION3B_VPS_MAX;
		vstar = REGION3B_VPS_VSTAR;
	}

	for(i = 0; i<n; ++i, ++d){
		sum += d->n * ipow(p1, d->I) * ipow(s1, d->J);
	}

	return sum * vstar;
}