@neutrium/thermo.eos.iapws97/dist/HS.js

A javascript implementation of the IAWPS formulations for the thermodynamic properties of water and steam.

"use strict";
var NS = require('./base');
var PT = require('./PT');
var PH = require('./PH');
var R = NS.constants['R'];
//
//	Comments : Determines which IAPWS-IF97 region a entalphy and entropy combination lie in.
//
//	@param h is the enthalphy in kJ/kg
//	@param s is the entropy in kJ . K^-1 . kg^1
//
function solve(h, s) {
    var region = findRegion_HS(h, s), result = null;
    switch (region) {
        case 1:
            result = r1(h, s);
            break;
        case 2:
            result = r2(h, s);
            break;
        case 3:
            result = r3(h, s);
            break;
        case 4:
            result = r4(h, s);
            break;
        default: throw new Error('Insufficent inputs provided');
    }
    return result;
}
exports.solve = solve;
function findRegion_HS(h, s) {
    // Interpolate across the saturation curve to test if below P = 0.000611 MPa line
    // Refer to Figure 3 in IAPWS HS document for graphical depiction
    // dG = dH - T*dS where dG = 0 for equillibrium reactions like phase change
    var B23_S = 5.260578707, B3_S = 4.41202148223476, B13_S = 3.778281340, B23_H = 2812.942061, hcheck = 273.15 * (s - NS.CONST('MIN_S')) + NS.CONST('MIN_H');
    if ((s <= 9.155759395 && h < hcheck) || s < NS.CONST('MIN_S') || h < NS.CONST('MIN_H')) {
        return -1;
    }
    // Region 1
    if (-0.0001545495919 <= s && s <= B13_S && b14_S_H(s) <= h && h <= b13_S_H(s)) {
        return 1;
    }
    // Region 2 or 3 interface
    if (5.048096828 <= s && s <= B23_S && 2563.592004 <= h && h <= B23_H) {
        // Do check using the PB23
        var T = b23_HS_T(h, s), P = r2C_HS_P(h, s), Pcheck = PT.b23_T_P(T);
        if (Pcheck > P) {
            return 2;
        }
        else {
            return 3;
        }
    }
    // Region 2
    if ((h >= B23_H || s > B23_S) && ((s >= 5.85 && h >= b2ab_S_Hsat(s)) || (s < 5.85 && h >= b2c3b_S_H(s)))) {
        return 2;
    }
    // Region 3
    if ((s >= B3_S && h >= b2c3b_S_H(s)) || (B13_S < s && s < B3_S && h >= b3A_S_H(s)) || (s <= B13_S && h > b13_S_H(s))) {
        return 3;
    }
    return 4;
}
//
// Region Identification Equations
//
// h'_1 Equation 3 in HS Region 3 & 4 Supplementary release
// Exported for testing
function b14_S_H(s) {
    var R4_HS_I = [0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 7, 8, 12, 12, 14, 14, 16, 20, 20, 22, 24, 28, 32, 32], R4_HS_J = [14, 36, 3, 16, 0, 5, 4, 36, 4, 16, 24, 18, 24, 1, 4, 2, 4, 1, 22, 10, 12, 28, 8, 3, 0, 6, 8], R4_HS_N = [3.32171191705237E-1, 6.112177063234960E-4, -8.82092478906822, -4.5562819254325E-1, -2.63483840850452E-5, -2.23949661148062E1, -4.28398660164013, -6.16679338856916E-1, -1.468230311044E1, 2.84523138727299E2, -1.13398503195444E2, 1.15671380760859E3, 3.95551267359325E2, -1.54891257229285, 1.94486637751291E1, -3.57915139457043, -3.35369414148819, -6.6442679633246E-1, 3.23321885383934E4, 3.31766744667084E3, -2.23501257931087E4, 5.73953875852936E6, 1.73226193407919E2, -3.63968822121321E-2, 8.34596332878346E-7, 5.03611916682674, 6.55444787064505E1], sig = s / 3.8, h = 0;
    for (var i = 0; i < 27; i++) {
        var N = R4_HS_N[i], I = R4_HS_I[i], J = R4_HS_J[i];
        h += N * Math.pow(sig - 1.09, I) * Math.pow(sig + 0.0000366, J);
    }
    return 1700 * h;
}
exports.b14_S_H = b14_S_H;
// Exported for testing
function b13_S_H(s) {
    var B13_HS_I = [0, 1, 1, 3, 5, 6], B13_HS_J = [0, -2, 2, -12, -4, -3], B13_HS_N = [0.913965547600543, -0.0000430944856041991, 60.3235694765419, 1.17518273082168E-18, 0.220000904781292, -69.0815545851641], sig = s / 3.8, h = 0;
    for (var i = 0; i < 6; i++) {
        var N = B13_HS_N[i], I = B13_HS_I[i], J = B13_HS_J[i];
        h += N * Math.pow(sig - 0.884, I) * Math.pow(sig - 0.864, J);
    }
    return 1700 * h;
}
exports.b13_S_H = b13_S_H;
// Calculates the temperature on the region 2-3 boundary S-curve
// T_B23(h,s) Equation 8 in HS Region 3 & 4 in suplementry
// Exported for testing
function b23_HS_T(h, s) {
    var B23_HS_I = [-12, -10, -8, -4, -3, -2, -2, -2, -2, 0, 1, 1, 1, 3, 3, 5, 6, 6, 8, 8, 8, 12, 12, 14, 14], B23_HS_J = [10, 8, 3, 4, 3, -6, 2, 3, 4, 0, -3, -2, 10, -2, -1, -5, -6, -3, -8, -2, -1, -12, -1, -12, 1], B23_HS_N = [6.2909626082981E-4, -8.23453502583165E-4, 5.15446951519474E-8, -1.17565945784945, 3.48519684726192, -5.07837382408313E-12, -2.84637670005479, -2.36092263939673, 6.01492324973779, 1.48039650824546, 3.60075182221907E-4, -1.26700045009952E-2, -1.22184332521413E6, 1.49276502463272E-1, 6.98733471798484E-1, -2.52207040114321E-2, 1.47151930985213E-2, -1.08618917681849, -9.36875039816322E-4, 8.19877897570217E1, -1.82041861521835E2, 2.61907376402688E-6, -2.91626417025961E4, 1.40660774926165E-5, 7.83237062349385E6], m = h / 3000, sig = s / 5.3, T = 0;
    for (var i = 0; i < 25; i++) {
        var N = B23_HS_N[i], I = B23_HS_I[i], J = B23_HS_J[i];
        T += N * Math.pow(m - 0.727, I) * Math.pow(sig - 0.864, J);
    }
    return 900 * T;
}
exports.b23_HS_T = b23_HS_T;
// The boundary equation for HS regions 2A and 2b (Equation 2 in supplementary release for HS)
// Exported for testing
function b2ab_S_H(s) {
    return (-3498.98083432139 + 2575.60716905876 * s + -421.073558227969 * s * s + 27.6349063799944 * s * s * s);
}
exports.b2ab_S_H = b2ab_S_H;
// Equation 5 in the region 3 & 4 HS suplementary release
// Exported for testing
function b2ab_S_Hsat(s) {
    var B2ab_I = [1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28, 32, 32, 32, 32, 32, 36, 36, 36, 36, 36], B2ab_J = [8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24, 2, 7, 12, 14, 24, 10, 12, 20, 22, 28], B2ab_N = [-0.524581170928788E3, -0.926947218142218E7, -0.237385107491666E3, 0.210770155812776E11, -0.239494562010986E2, 0.221802480294197E3, -0.510472533393438E7, 0.124981396109147E7, 0.200008436996201E10, -0.815158509791035E3, -0.157612685637523E3, -0.114200422332791E11, 0.662364680776872E16, -0.227622818296144E19, -0.171048081348406E32, 6.60788766938091E15, 1.66320055886021E22, -2.18003784381501E29, -7.87276140295618E29, 1.51062329700346E31, 7.95732170300541E6, 1.31957647355347E15, -3.2509706829914E23, -4.18600611419248E25, 2.97478906557467E34, -9.53588761745473E19, 1.66957699620939E24, -1.75407764869978E32, 3.47581490626396E34, -7.10971318427851E38], sig1 = s / 5.21, sig2 = s / 9.2, Hsat = 0;
    for (var i = 0; i < 30; i++) {
        var I = B2ab_I[i], J = B2ab_J[i], N = B2ab_N[i];
        Hsat += N * Math.pow(1 / sig1 - 0.513, I) * Math.pow(sig2 - 0.524, J);
    }
    return 2800 * Math.exp(Hsat);
}
exports.b2ab_S_Hsat = b2ab_S_Hsat;
// h"_2c3b(s) Equation 6 in HS region 3 and 4 suplementary release
// Exported for testing
function b2c3b_S_H(s) {
    // Table 17 in in IAPWS-97 HS region 3 and 4
    var B2c3b_HS_I = [0, 0, 0, 1, 1, 5, 6, 7, 8, 8, 12, 16, 22, 22, 24, 36], B2c3b_HS_J = [0, 3, 4, 0, 12, 36, 12, 16, 2, 20, 32, 36, 2, 32, 7, 20], B2c3b_HS_N = [1.04351280732769, -2.27807912708513, 1.80535256723202, 0.420440834792042, -1.0572124483466E5, 4.36911607493884E24, -3.28032702839753E11, -6.7868676080427E15, 7.43957464645363E3, -3.56896445355761E19, 1.67590585186801E31, -3.55028625419105E37, 3.96611982166538E11, -4.14716268484468E40, 3.59080103867382E18, -1.16994334851995E40], h = 0, sigma = s / 5.9;
    for (var i = 0; i < 16; i++) {
        var I = B2c3b_HS_I[i], J = B2c3b_HS_J[i], N = B2c3b_HS_N[i];
        h += N * Math.pow(sigma - 1.02, I) * Math.pow(sigma - 0.726, J);
    }
    return 2800 * Math.pow(h, 4);
}
exports.b2c3b_S_H = b2c3b_S_H;
// h'_3a Equation 4 in HS Region 3 and 4
// Used as a boundary check between 3a and 3b when P < Pc
// Function to work out the backwards (h,s) boundry for region 3A
// Exported for testing
function b3A_S_H(s) {
    // Table 10 in IAPWS-97 HS region 3 and 4
    var B3A_HS_I = [0, 0, 0, 0, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 10, 10, 10, 32, 32], B3A_HS_J = [1, 4, 10, 16, 1, 36, 3, 16, 20, 36, 4, 2, 28, 32, 14, 32, 36, 0, 6], B3A_HS_N = [0.822673364673336, 0.181977213534479, -0.0112000260313624, -0.000746778287048033, -0.179046263257381, 0.0424220110836657, -0.341355823438768, -2.09881740853565, -8.22477343323596, -4.99684082076008, 0.191413958471069, 0.0581062241093136, -1655.05498701029, 1588.70443421201, -85.0623535172818, -31771.4386511207, -94589.0406632871, -1.3927384708869E-6, 0.63105253224098], sig = s / 3.8, hdash = 0;
    for (var i = 0; i < 19; i++) {
        var N = B3A_HS_N[i], I = B3A_HS_I[i], J = B3A_HS_J[i];
        hdash += N * Math.pow(sig - 1.09, I) * Math.pow(sig + 0.0000366, J);
    }
    return 1700 * hdash;
}
exports.b3A_S_H = b3A_S_H;
//
//	Backwards equation for region 1 (h and s given)
//	Calculates P and uses it in the forwards equations
//
function r1(h, s) {
    var P = r1_HS_P(h, s), T = PH.r1_PH_T(P, h);
    if (P >= NS.CONST('MIN_P') && P <= NS.CONST('MAX_P')) {
        return PT.r1(P, T);
    }
    else {
        throwOutOfRange();
    }
}
function r1_HS_P(h, s) {
    var R1_HS_I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5], R1_HS_J = [0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0], R1_HS_N = [-0.691997014660582, -18.361254878756, -9.28332409297335, 65.9639569909906, -16.2060388912024, 450.620017338667, 854.68067822417, 6075.23214001161, 32.6487682621856, -26.9408844582931, -319.9478483343, -928.35430704332, 30.3634537455249, -65.0540422444146, -4309.9131651613, -747.512324096068, 730.000345529245, 1142.84032569021, -436.407041874559], m = h / 3400, sig = s / 7.6, P = 0;
    for (var i = 0; i < 19; i++) {
        var N = R1_HS_N[i], I = R1_HS_I[i], J = R1_HS_J[i];
        P += N * Math.pow(m + 0.05, I) * Math.pow(sig + 0.05, J);
    }
    return 100 * P;
}
//
//	Backwards equation for region 2 (h and s given)
//	Calculates P and uses it in the forwards equations
//
function r2(h, s) {
    var P = r2_HS_P(h, s);
    if (P >= NS.CONST('MIN_P') && P <= NS.CONST('MAX_P')) {
        return PH.r2(P, h);
    }
    else {
        throwOutOfRange();
    }
}
function r2_HS_P(h, s) {
    var P;
    if (h <= b2ab_S_H(s)) {
        P = r2A_HS_P(h, s);
    }
    else {
        if (s >= 5.85) {
            P = r2B_HS_P(h, s);
        }
        else {
            P = r2C_HS_P(h, s);
        }
    }
    return P;
}
function r2A_HS_P(h, s) {
    var R2A_HS_I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 6, 7], R2A_HS_J = [1, 3, 6, 16, 20, 22, 0, 1, 2, 3, 5, 6, 10, 16, 20, 22, 3, 16, 20, 0, 2, 3, 6, 16, 16, 3, 16, 3, 1], R2A_HS_N = [-0.0182575361923032, -0.125229548799536, 0.592290437320145, 6.04769706185122, 238.624965444474, -298.639090222922, 0.051225081304075, -0.437266515606486, 0.413336902999504, -5.16468254574773, -5.57014838445711, 12.8555037824478, 11.414410895329, -119.504225652714, -2847.7798596156, 4317.57846408006, 1.1289404080265, 1974.09186206319, 1516.12444706087, 0.0141324451421235, 0.585501282219601, -2.97258075863012, 5.94567314847319, -6236.56565798905, 9659.86235133332, 6.81500934948134, -6332.07286824489, -5.5891922446576, 0.0400645798472063], m = h / 4200, sig = s / 12, P = 0;
    for (var i = 0; i < 29; i++) {
        var N = R2A_HS_N[i], I = R2A_HS_I[i], J = R2A_HS_J[i];
        P += N * Math.pow(m - 0.5, I) * Math.pow(sig - 1.2, J);
    }
    return 4 * Math.pow(P, 4); // Corresponding pressure for h, s
}
function r2B_HS_P(h, s) {
    var R2B_HS_I = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 12, 14], R2B_HS_J = [0, 1, 2, 4, 8, 0, 1, 2, 3, 5, 12, 1, 6, 18, 0, 1, 7, 12, 1, 16, 1, 12, 1, 8, 18, 1, 16, 1, 3, 14, 18, 10, 16], R2B_HS_N = [0.0801496989929495, -0.543862807146111, 0.337455597421283, 8.9055545115745, 313.840736431485, 0.797367065977789, -1.2161697355624, 8.72803386937477, -16.9769781757602, -186.552827328416, 95115.9274344237, -18.9168510120494, -4334.0703719484, 543212633.012715, 0.144793408386013, 128.024559637516, -67230.9534071268, 33697238.0095287, -586.63419676272, -22140322476.9889, 1716.06668708389, -570817595.806302, -3121.09693178482, -2078413.8463301, 3056059461577.86, 3221.57004314333, 326810259797.295, -1441.04158934487, 410.694867802691, 109077066873.024, -24796465425889.3, 1888019068.65134, -123651009018773], m = h / 4100, sig = s / 7.9, P = 0;
    for (var i = 0; i < 33; i++) {
        var N = R2B_HS_N[i], I = R2B_HS_I[i], J = R2B_HS_J[i];
        P += N * Math.pow(m - 0.6, I) * Math.pow(sig - 1.01, J);
    }
    return 100 * Math.pow(P, 4);
}
function r2C_HS_P(h, s) {
    var R2C_HS_I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 10, 12, 16], R2C_HS_J = [0, 1, 2, 3, 4, 8, 0, 2, 5, 8, 14, 2, 3, 7, 10, 18, 0, 5, 8, 16, 18, 18, 1, 4, 6, 14, 8, 18, 7, 7, 10], R2C_HS_N = [0.112225607199012, -3.39005953606712, -32.0503911730094, -197.5973051049, -407.693861553446, 13294.3775222331, 1.70846839774007, 37.3694198142245, 3581.44365815434, 423014.446424664, -751071025.760063, 52.3446127607898, -228.351290812417, -960652.417056937, -80705929.2526074, 1626980172256.69, 0.772465073604171, 46392.9973837746, -13731788.5134128, 1704703926305.12, -25110462818730.8, 31774883083552.0, 53.8685623675312, -55308.9094625169, -1028615.22421405, 2042494187562.34, 273918446.626977, -2639631463126850.0, -1078908541.08088, -29649262098.0124, -1117549073234240.0], m = h / 3500, sig = s / 5.9, P = 0;
    for (var i = 0; i < 31; i++) {
        var N = R2C_HS_N[i], I = R2C_HS_I[i], J = R2C_HS_J[i];
        P += N * Math.pow(m - 0.7, I) * Math.pow(sig - 1.1, J);
    }
    return 100 * Math.pow(P, 4);
}
//
// Region 3
//
function r3(h, s) {
    var P = r3_HS_P(h, s);
    if (P >= NS.CONST('MIN_P') && P <= NS.CONST('MAX_P')) {
        return PH.r2(P, h);
    }
    else {
        throwOutOfRange();
    }
}
function r3_HS_P(h, s) {
    if (s <= NS.CONST('R3_CRT_S')) {
        return r3A_HS_P(h, s);
    }
    else {
        return r3B_HS_P(h, s);
    }
}
function r3A_HS_P(h, s) {
    var R3A_HS_I = [0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 6, 7, 8, 10, 10, 14, 18, 20, 22, 22, 24, 28, 28, 32, 32], R3A_HS_J = [0, 1, 5, 0, 3, 4, 8, 14, 6, 16, 0, 2, 3, 0, 1, 4, 5, 28, 28, 24, 1, 32, 36, 22, 28, 36, 16, 28, 36, 16, 36, 10, 28,], R3A_HS_N = [7.70889828326934, -26.0835009128688, 267.416218930389, 17.2221089496844, -293.54233214597, 614.135601882478, -61056.2757725674, -65127225.1118219, 73591.9313521937, -11664650591.4191, 35.5267086434461, -596.144543825955, -475.842430145708, 69.6781965359503, 335.674250377312, 25052.6809130882, 146997.380630766, 53806931509153400000.0, 1.43619827291346E+21, 36498586616599400000.0, -2547.41561156775, 2.40120197096563E+27, -3.93847464679496E+29, 1.47073407024852E+24, -4.26391250432059E+31, 1.94509340621077E+38, 6.66212132114896E+23, 7.06777016552858E+33, 1.75563621975576E+41, 1.08408607429124E+28, 7.30872705175151E+43, 1.5914584739887E+24, 3.77121605943324E+40], m = h / 2300, sig = s / 4.4, P = 0;
    for (var i = 0; i < 33; i++) {
        var N = R3A_HS_N[i], I = R3A_HS_I[i], J = R3A_HS_J[i];
        P += N * Math.pow(m - 1.01, I) * Math.pow(sig - 0.75, J);
    }
    return 99 * P;
}
function r3B_HS_P(h, s) {
    // Table X data from IAPWS-97
    var R3B_HS_I = [-12, -12, -12, -12, -12, -10, -10, -10, -10, -8, -8, -6, -6, -6, -6, -5, -4, -4, -4, -3, -3, -3, -3, -2, -2, -1, 0, 2, 2, 5, 6, 8, 10, 14, 14], R3B_HS_J = [2, 10, 12, 14, 20, 2, 10, 14, 18, 2, 8, 2, 6, 7, 8, 10, 4, 5, 8, 1, 3, 5, 6, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 3, 7], R3B_HS_N = [1.25244360717979E-13, -0.0126599322553713, 5.06878030140626, 31.7847171154202, -391041.161399932, -9.75733406392044E-11, -18.6312419488279, 510.973543414101, 373847.005822362, 2.99804024666572E-8, 20.0544393820342, -4.98030487662829E-6, -10.230180636003, 55.2819126990325, -206.211367510878, -7940.12232324823, 7.82248472028153, -58.6544326902468, 3550.73647696481, -0.000115303107290162, -1.75092403171802, 257.98168774816, -727.048374179467, 0.000121644822609198, 0.0393137871762692, 0.00704181005909296, -82.910820069811, -0.26517881813125, 13.7531682453991, -52.2394090753046, 2405.56298941048, -22736.1631268929, 89074.6343932567, -23923456.5822486, 5687958081.29714], m = h / 2800, sig = s / 5.3, P = 0;
    for (var i = 0; i < 35; i++) {
        var N = R3B_HS_N[i], I = R3B_HS_I[i], J = R3B_HS_J[i];
        P += N * Math.pow(m - 0.681, I) * Math.pow(sig - 0.792, J);
    }
    return 16.6 / P;
}
//
// Region 4
//
function r4(h, s) {
    var T = r4_HS_Tsat(h, s), P = PT.r4_T_Psat(T);
    return PT.solve(P, T);
}
// Tsat(h,s) Equation 9 in the HS Region 3 & 4 Supplementary release
// Exported for texting
function r4_HS_Tsat(h, s) {
    var R4_I = [0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 8, 10, 10, 12, 14, 14, 16, 16, 18, 18, 18, 20, 28], R4_J = [0, 3, 12, 0, 1, 2, 5, 0, 5, 8, 0, 2, 3, 4, 0, 1, 1, 2, 4, 16, 6, 8, 22, 1, 20, 36, 24, 1, 28, 12, 32, 14, 22, 36, 24, 36], R4_N = [0.179882673606601, -0.267507455199603, 0.11627672261266E1, 0.147545428713616, -0.512871635973248, 0.421333567697984, 0.56374952218987, 0.429274443819153, -0.33570455214214E1, 0.108890916499278E2, -0.248483390456012, 0.30415322190639, -0.494819763939905, 0.107551674933261E1, 0.733888415457688E-1, 0.140170545411085E-1, -0.106110975998808, 0.168324361811875E-1, 0.125028363714877E1, 0.101316840309509E4, -0.151791558000712E1, 0.524277865990866E2, 0.230495545563912E5, 0.249459806365456E-1, 0.210796467412137E7, 0.366836848613065E9, -0.144814105365163E9, -0.17927637300359E-2, 0.489955602100459E10, 0.471262212070518E3, -0.829294390198652E11, -0.171545662263191E4, 0.355777682973575E7, 0.586062760258436E12, -0.129887635078195E8, 0.317247449371057057E11], mu = h / 2800, sig = s / 9.2, T = 0;
    for (var i = 0; i < 36; i++) {
        var I = R4_I[i], J = R4_J[i], N = R4_N[i];
        T += N * Math.pow(mu - 0.119, I) * Math.pow(sig - 1.07, J);
    }
    return 550 * T;
}
exports.r4_HS_Tsat = r4_HS_Tsat;
function throwOutOfRange() {
    throw new Error("Input values out of range");
}