Initial commit from Polytechnique Montreal

1 files changed, 841 insertions, 0 deletions

diff --git a/Utilib/src/backwards.c b/Utilib/src/backwards.c
new file mode 100644
index 0000000..0e3e352
--- /dev/null
+++ b/Utilib/src/backwards.c
@@ -0,0 +1,841 @@
+/*
+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., 59 Temple Place - Suite 330, Boston, MA  02111-1307, 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){
+	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){
+		pi1 = pi; eta1 = eta - 2.1;
+		d = REGION2A_TPH_DATA;
+		n = REGION2A_TPH_MAX;
+	}else{
+		if(REGION2_B2BC_PH(p,h) < 0.){
+			pi1 = pi - 2.; eta1 = eta - 2.6;
+			d = REGION2B_TPH_DATA;
+			n = REGION2B_TPH_MAX;
+		}else{
+			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){
+	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){
+	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){
+	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){
+	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){
+	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){
+	double p1, s1;
+	double vstar;
+	BackwardsData *d;
+	unsigned i, n;
+	double sum = 0;
+	if(s < REGION3AB_SC){
+		/* sub-region 3a */
+		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 */
+		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;
+}