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jkpieterse/Excel-lambda-water97.txt

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Excel Lambda functions to calculate thermodynamic properties of water
Raw
Excel-lambda-water97.txt
cpreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
-0.001 * rgas_water * tau ^ 2 * gammatautaureg1(tau, pi)
)
);
cpreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
-0.001 * rgas_water * tau ^ 2 *
(gamma0tautaureg2(tau, pi) + gammartautaureg2(tau, pi))
)
);
cpreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
0.001 * rgas_water *
(-(tau ^ 2) * fitautaureg3(tau, delta) +
(delta * fideltareg3(tau, delta) -
delta * tau * fideltataureg3(tau, delta)) ^ 2 /
(2 * delta * fideltareg3(tau, delta) +
delta ^ 2 * fideltadeltareg3(tau, delta)))
)
);
cpSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
cpreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
cpreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
cpSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
cpreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
cpreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
cpSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
cpreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
cpreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
cpSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
cpreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
cpreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
cpW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
cpreg1(temp, press),
cpreg2(temp, press),
cpreg3(temp, densreg3(temp, press))
)
)
)
);
cvreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
0.001 * rgas_water *
(-(tau ^ 2) * gammatautaureg1(tau, pi) +
(gammapireg1(tau, pi) - tau * gammapitaureg1(tau, pi)) ^ 2 /
gammapipireg1(tau, pi))
)
);
cvreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
0.001 * rgas_water *
(-(tau ^ 2) *
(gamma0tautaureg2(tau, pi) + gammartautaureg2(tau, pi)) -
(1 + pi * gammarpireg2(tau, pi) -
tau * pi * gammarpitaureg2(tau, pi)) ^ 2 /
(1 - pi ^ 2 * gammarpipireg2(tau, pi)))
)
);
cvreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
0.001 * rgas_water * (-(tau ^ 2) * fitautaureg3(tau, delta))
)
);
cvSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
cvreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
cvreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
cvSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
cvreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
cvreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
cvSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
cvreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
cvreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
cvSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
cvreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
cvreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
cvW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
cvreg1(temp, press),
cvreg2(temp, press),
cvreg3(temp, densreg3(temp, press))
)
)
)
);
dc_water = 322;
densreg3 = LAMBDA(temp, press,
LET(
tau, tc_water / temp,
SolveDens3(
IF(AND(temp < tc_water, press < PSatW(temp)), 100, 600),
temp,
press
)
)
);
densSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
1 / volreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
densreg3(temp, press + 0.00001),
-1
)
)
)
);
densSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
1 / volreg1(temp, press),
IF(AND(temp > 623.15, temp <= tc_water), densreg3(temp, press), -1)
)
)
);
densSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
1 / volreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
densreg3(temp, press - 0.00001),
-1
)
)
)
);
densSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
1 / volreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
densreg3(temp, press - 0.00001),
-1
)
)
)
);
densW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
1 / volreg1(temp, press),
1 / volreg2(temp, press),
densreg3(temp, press)
)
)
)
);
energyreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
0.001 * rgas_water * temp *
(tau * gammataureg1(tau, pi) - pi * gammapireg1(tau, pi))
)
);
energyreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
0.001 * rgas_water * temp *
(tau * (gamma0taureg2(tau, pi) + gammartaureg2(tau, pi)) -
pi * (gamma0pireg2(tau, pi) + gammarpireg2(tau, pi)))
)
);
energyreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
0.001 * rgas_water * temp * tau * fitaureg3(tau, delta)
)
);
energySatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
energyreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
energyreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
energySatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
energyreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
energyreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
energySatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
energyreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
energyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
energySatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
enthalpyreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
enthalpyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
energyW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
energyreg1(temp, press),
energyreg2(temp, press),
energyreg3(temp, densreg3(temp, press))
)
)
)
);
enthalpyreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
0.001 * rgas_water * temp * tau * gammataureg1(tau, pi)
)
);
enthalpyreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
0.001 * rgas_water * temp * tau *
(gamma0taureg2(tau, pi) + gammartaureg2(tau, pi))
)
);
enthalpyreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
0.001 * rgas_water * temp *
(tau * fitaureg3(tau, delta) + delta * fideltareg3(tau, delta))
)
);
enthalpySatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
enthalpyreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
enthalpyreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
enthalpySatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
enthalpyreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
enthalpyreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
enthalpySatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
enthalpyreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
enthalpyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
enthalpySatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
enthalpyreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
enthalpyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
enthalpyW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
enthalpyreg1(temp, press),
enthalpyreg2(temp, press),
enthalpyreg3(temp, densreg3(temp, press))
)
)
)
);
entropyreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
0.001 * rgas_water * (tau * gammataureg1(tau, pi) - gammareg1(tau, pi))
)
);
entropyreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
0.001 * rgas_water *
(tau * (gamma0taureg2(tau, pi) + gammartaureg2(tau, pi)) -
(gamma0reg2(tau, pi) + gammarreg2(tau, pi)))
)
);
entropyreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
0.001 * rgas_water * (tau * fitaureg3(tau, delta) - fireg3(tau, delta))
)
);
entropySatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
entropyreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
entropyreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
entropySatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
entropyreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
entropyreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
entropySatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
entropyreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
entropyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
entropySatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
entropyreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
entropyreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
entropyW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
entropyreg1(temp, press),
entropyreg2(temp, press),
entropyreg3(temp, densreg3(temp, press))
)
)
)
);
fideltadeltareg3 = LAMBDA(tau, delta,
-nreg3(1) / delta / delta +
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(
nreg3(i) * ireg3(i) * (ireg3(i) - 1) * delta ^ (ireg3(i) - 2) *
tau ^ jreg3(i)
)
)
);
fideltareg3 = LAMBDA(tau, delta,
nreg3(1) / delta +
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(nreg3(i) * ireg3(i) * delta ^ (ireg3(i) - 1) * tau ^ jreg3(i))
)
);
fideltataureg3 = LAMBDA(tau, delta,
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(
nreg3(i) * ireg3(i) * delta ^ (ireg3(i) - 1) * jreg3(i) *
tau ^ (jreg3(i) - 1)
)
)
);
fireg3 = LAMBDA(tau, delta,
nreg3(1) * LOG(delta) / LOG(EXP(1)) +
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(nreg3(i) * delta ^ ireg3(i) * tau ^ jreg3(i))
)
);
fitaureg3 = LAMBDA(tau, delta,
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(nreg3(i) * delta ^ ireg3(i) * jreg3(i) * tau ^ (jreg3(i) - 1))
)
);
fitautaureg3 = LAMBDA(tau, delta,
LET(
i, SEQUENCE(39, 1, 2, 1),
SUM(
nreg3(i) * delta ^ ireg3(i) * jreg3(i) * (jreg3(i) - 1) *
tau ^ (jreg3(i) - 2)
)
)
);
gamma0pipireg2 = LAMBDA(tau, pi, -1 / pi / pi);
gamma0pireg2 = LAMBDA(tau, pi, 1 / pi);
gamma0pitaureg2 = LAMBDA(tau, pi, 0);
gamma0reg2 = LAMBDA(tau, pi,
LOG(pi) / LOG(EXP(1)) +
LET(i, SEQUENCE(9, 1, 1, 1), SUM(n0reg2(i) * tau ^ j0reg2(i)))
);
gamma0taureg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(9, 1, 1, 1),
SUM(n0reg2(i) * j0reg2(i) * tau ^ (j0reg2(i) - 1))
)
);
gamma0tautaureg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(9, 1, 1, 1),
SUM(n0reg2(i) * j0reg2(i) * (j0reg2(i) - 1) * tau ^ (j0reg2(i) - 2))
)
);
gammapipireg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(
nreg1(i) * ireg1(i) * (ireg1(i) - 1) * (7.1 - pi) ^ (ireg1(i) - 2) *
(tau - 1.222) ^ jreg1(i)
)
)
);
gammapireg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(
-nreg1(i) * ireg1(i) * (7.1 - pi) ^ (ireg1(i) - 1) *
(tau - 1.222) ^ jreg1(i)
)
)
);
gammapitaureg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(
-nreg1(i) * ireg1(i) * (7.1 - pi) ^ (ireg1(i) - 1) * jreg1(i) *
(tau - 1.222) ^ (jreg1(i) - 1)
)
)
);
gammareg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(nreg1(i) * (7.1 - pi) ^ ireg1(i) * (tau - 1.222) ^ jreg1(i))
)
);
gammarpipireg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(
nreg2(i) * ireg2(i) * (ireg2(i) - 1) * pi ^ (ireg2(i) - 2) *
(tau - 0.5) ^ jreg2(i)
)
)
);
gammarpireg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(nreg2(i) * ireg2(i) * pi ^ (ireg2(i) - 1) * (tau - 0.5) ^ jreg2(i))
)
);
gammarpitaureg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(
nreg2(i) * ireg2(i) * pi ^ (ireg2(i) - 1) * jreg2(i) *
(tau - 0.5) ^ (jreg2(i) - 1)
)
)
);
gammarreg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(nreg2(i) * pi ^ ireg2(i) * (tau - 0.5) ^ jreg2(i))
)
);
gammartaureg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(nreg2(i) * pi ^ ireg2(i) * jreg2(i) * (tau - 0.5) ^ (jreg2(i) - 1))
)
);
gammartautaureg2 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(43, 1, 1, 1),
SUM(
nreg2(i) * pi ^ ireg2(i) * jreg2(i) * (jreg2(i) - 1) *
(tau - 0.5) ^ (jreg2(i) - 2)
)
)
);
gammataureg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(
nreg1(i) * (7.1 - pi) ^ ireg1(i) * jreg1(i) *
(tau - 1.222) ^ (jreg1(i) - 1)
)
)
);
gammatautaureg1 = LAMBDA(tau, pi,
LET(
i, SEQUENCE(34, 1, 1, 1),
SUM(
nreg1(i) * (7.1 - pi) ^ ireg1(i) * jreg1(i) * (jreg1(i) - 1) *
(tau - 1.222) ^ (jreg1(i) - 2)
)
)
);
getreg = LAMBDA(temp, press,
IF(
AND(temp >= 273.15, temp <= 623.15, press >= PSatW(temp), press < 1000),
1,
IF(
OR(
AND(
temp >= 273.15,
temp <= 623.15,
press > 0,
press <= PSatW(temp)
),
AND(
temp >= 623.15,
temp <= 863.15,
press > 0,
press <= pBound(temp)
),
AND(temp >= 863.15, temp <= 1073.15, press > 0, press <= 1000)
),
2,
IF(
AND(
temp >= 623.15,
temp <= tBound(press),
press >= pBound(temp),
press <= 1000
),
3,
-1
)
)
)
);
ireg1 = LAMBDA(x,
INDEX(
{
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
3,
3,
3,
4,
4,
4,
5,
8,
8,
21,
23,
29,
30,
31,
32
},
x
)
);
ireg2 = LAMBDA(x,
INDEX(
{
1,
1,
1,
1,
1,
2,
2,
2,
2,
2,
3,
3,
3,
3,
3,
4,
4,
4,
5,
6,
6,
6,
7,
7,
7,
8,
8,
9,
10,
10,
10,
16,
16,
18,
20,
20,
20,
21,
22,
23,
24,
24,
24
},
x
)
);
ireg3 = LAMBDA(x,
INDEX(
{
0,
0,
0,
0,
0,
0,
0,
0,
1,
1,
1,
1,
2,
2,
2,
2,
2,
2,
3,
3,
3,
3,
3,
4,
4,
4,
4,
5,
5,
5,
6,
6,
6,
7,
8,
9,
9,
10,
10,
11
},
x
)
);
ivisc = LAMBDA(x,
INDEX({0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6}, x)
);
j0reg2 = LAMBDA(x, INDEX({0, 1, -5, -4, -3, -2, -1, 2, 3}, x));
jreg1 = LAMBDA(x,
INDEX(
{
-2,
-1,
0,
1,
2,
3,
4,
5,
-9,
-7,
-1,
0,
1,
3,
-3,
0,
1,
3,
17,
-4,
0,
6,
-5,
-2,
10,
-8,
-11,
-6,
-29,
-31,
-38,
-39,
-40,
-41
},
x
)
);
jreg2 = LAMBDA(x,
INDEX(
{
0,
1,
2,
3,
6,
1,
2,
4,
7,
36,
0,
1,
3,
6,
35,
1,
2,
3,
7,
3,
16,
35,
0,
11,
25,
8,
36,
13,
4,
10,
14,
29,
50,
57,
20,
35,
48,
21,
53,
39,
26,
40,
58
},
x
)
);
jreg3 = LAMBDA(x,
INDEX(
{
0,
0,
1,
2,
7,
10,
12,
23,
2,
6,
15,
17,
0,
2,
6,
7,
22,
26,
0,
2,
4,
16,
26,
0,
2,
4,
26,
1,
3,
26,
0,
2,
26,
2,
26,
2,
26,
0,
1,
26
},
x
)
);
jvisc = LAMBDA(x,
INDEX({0, 1, 4, 5, 0, 1, 2, 3, 0, 1, 2, 0, 1, 2, 3, 0, 3, 1, 3}, x)
);
lamb2Reg1 = LAMBDA(temp, press, tau, delta,
LET(
taus, 1386 / temp,
pis, press / 165.3,
dpidtau, (647.226 * 165.3 *
(gammapitaureg1(taus, pis) * 1386 -
gammapireg1(taus, pis) * temp)) /
(221.15 * temp ^ 2 * gammapipireg1(taus, pis)),
ddeltadpi, -(22115000 * gammapipireg1(taus, pis)) /
(317.763 * rgas_water * temp * gammapireg1(taus, pis) ^ 2),
0.0013848 / psivisc(tau, delta) * (tau * delta) ^ (-2) * dpidtau ^ 2 *
(delta * ddeltadpi) ^ 0.4678 * delta ^ 0.5 *
EXP(-18.66 * (1 / tau - 1) ^ 2 - (delta - 1) ^ 4)
)
);
lamb2Reg2 = LAMBDA(temp, press, tau, delta,
LET(
taus, 540 / temp,
pis, press / 10,
dpidtau, (647.226 * 10 *
((gamma0pitaureg2(taus, pis) + gammarpitaureg2(taus, pis)) * 540 -
(gamma0pireg2(taus, pis) + gammarpireg2(taus, pis)) * temp)) /
(221.15 * temp ^ 2 *
(gamma0pipireg2(taus, pis) + gammarpipireg2(taus, pis))),
ddeltadpi, -(22115000 *
(gamma0pipireg2(taus, pis) + gammarpipireg2(taus, pis))) /
(317.763 * rgas_water * temp *
(gamma0pireg2(taus, pis) + gammarpireg2(taus, pis)) ^ 2),
0.0013848 / psivisc(tau, delta) * (tau * delta) ^ (-2) * dpidtau ^ 2 *
(delta * ddeltadpi) ^ 0.4678 * delta ^ 0.5 *
EXP(-18.66 * (1 / tau - 1) ^ 2 - (delta - 1) ^ 4)
)
);
lamb2Reg3 = LAMBDA(temp, press, tau, delta,
LET(
taus, 647.096 / temp,
deltas, delta * 317.763 / 322,
dpidtau, (647.226 * rgas_water * (delta * 317.763) ^ 2 *
(fideltareg3(taus, deltas) -
(647.096 / temp) * fideltataureg3(taus, deltas))) /
(22115000 * 322),
ddeltadpi, (22115000 * 322) /
(317.763 * delta * 317.763 * rgas_water * temp *
(2 * fideltareg3(taus, deltas) +
(delta * 317.763 / 322) * fideltadeltareg3(taus, deltas))),
0.0013848 / psivisc(tau, delta) * (tau * delta) ^ (-2) * dpidtau ^ 2 *
(delta * ddeltadpi) ^ 0.4678 * delta ^ 0.5 *
EXP(-18.66 * (1 / tau - 1) ^ 2 - (delta - 1) ^ 4)
)
);
lambthcon = LAMBDA(temp, press, tau, delta,
LET(
lamb0, 1 / tau ^ 0.5 /
LET(i, SEQUENCE(4, 1, 0, 1), SUM(n0thcon(i) * tau ^ i)),
lamb1, EXP(
LET(
i, SEQUENCE(5, 1, 0, 1),
j, SEQUENCE(1, 6, 0, 1),
SUM(nthcon(i, j) * (tau - 1) ^ i * (delta - 1) ^ j)
) * delta
),
lamb2, CHOOSE(
getreg(temp, press),
lamb2Reg1(temp, press, tau, delta),
lamb2Reg2(temp, press, tau, delta),
lamb2Reg3(temp, press, tau, delta)
),
lamb0 * lamb1 + lamb2
)
);
n0reg2 = LAMBDA(x,
INDEX(
{
-9.6927686500217,
10.086655968018,
-0.005608791128302,
0.071452738081455,
-0.40710498223928,
1.4240819171444,
-4.383951131945,
-0.28408632460772,
0.021268463753307
},
x
)
);
n0thcon = LAMBDA(x, INDEX({1, 6.978267, 2.599096, -0.998254}, x + 1));
n0visc = LAMBDA(x, INDEX({1, 0.978197, 0.579829, -0.202354}, x + 1));
nbound = LAMBDA(x,
INDEX(
{
348.05185628969,
-1.1671859879975,
0.0010192970039326,
572.54459862746,
13.91883977887
},
x
)
);
nreg1 = LAMBDA(x,
INDEX(
{
0.14632971213167,
-0.84548187169114,
-3.756360367204,
3.3855169168385,
-0.95791963387872,
0.15772038513228,
-0.016616417199501,
0.00081214629983568,
0.00028319080123804,
-0.00060706301565874,
-0.018990068218419,
-0.032529748770505,
-0.021841717175414,
-0.00005283835796993,
-0.00047184321073267,
-0.00030001780793026,
0.000047661393906987,
-0.0000044141845330846,
-7.2694996297594E-16,
-0.000031679644845054,
-0.0000028270797985312,
-8.5205128120103E-10,
-0.0000022425281908,
-6.5171222895601E-07,
-1.4341729937924E-13,
-4.0516996860117E-07,
-1.2734301741641E-09,
-1.7424871230634E-10,
-6.8762131295531E-19,
1.4478307828521E-20,
2.6335781662795E-23,
-1.1947622640071E-23,
1.8228094581404E-24,
-9.3537087292458E-26
},
x
)
);
nreg2 = LAMBDA(x,
INDEX(
{
-0.0017731742473213,
-0.017834862292358,
-0.045996013696365,
-0.057581259083432,
-0.05032527872793,
-0.000033032641670203,
-0.00018948987516315,
-0.0039392777243355,
-0.043797295650573,
-0.000026674547914087,
2.0481737692309E-08,
4.3870667284435E-07,
-0.00003227767723857,
-0.0015033924542148,
-0.040668253562649,
-7.8847309559367E-10,
1.2790717852285E-08,
4.8225372718507E-07,
0.0000022922076337661,
-1.6714766451061E-11,
-0.0021171472321355,
-23.895741934104,
-5.905956432427E-18,
-0.0000012621808899101,
-0.038946842435739,
1.1256211360459E-11,
-8.2311340897998,
1.9809712802088E-08,
1.0406965210174E-19,
-1.0234747095929E-13,
-1.0018179379511E-09,
-8.0882908646985E-11,
0.10693031879409,
-0.33662250574171,
8.9185845355421E-25,
3.0629316876232E-13,
-0.0000042002467698208,
-5.9056029685639E-26,
0.0000037826947613457,
-1.2768608934681E-15,
7.3087610595061E-29,
5.5414715350778E-17,
-0.0000009436970724121
},
x
)
);
nreg3 = LAMBDA(x,
INDEX(
{
1.0658070028513,
-15.732845290239,
20.944396974307,
-7.6867707878716,
2.6185947787954,
-2.808078114862,
1.2053369696517,
-0.0084566812812502,
-1.2654315477714,
-1.1524407806681,
0.88521043984318,
-0.64207765181607,
0.38493460186671,
-0.85214708824206,
4.8972281541877,
-3.0502617256965,
0.039420536879154,
0.12558408424308,
-0.2799932969871,
1.389979956946,
-2.018991502357,
-0.0082147637173963,
-0.47596035734923,
0.0439840744735,
-0.44476435428739,
0.90572070719733,
0.70522450087967,
0.10770512626332,
-0.32913623258954,
-0.50871062041158,
-0.022175400873096,
0.094260751665092,
0.16436278447961,
-0.013503372241348,
-0.014834345352472,
0.00057922953628084,
0.0032308904703711,
0.000080964802996215,
-0.00016557679795037,
-0.000044923899061815
},
x
)
);
nreg4 = LAMBDA(x,
INDEX(
{
1167.0521452767,
-724213.16703206,
-17.073846940092,
12020.82470247,
-3232555.0322333,
14.91510861353,
-4823.2657361591,
405113.40542057,
-0.23855557567849,
650.17534844798
},
x
)
);
nthcon = LAMBDA(x, y,
INDEX(
{
1.3293046, -0.40452437, 0.2440949, 0.018660751, -0.12961068, 0.044809953;
1.7018363, -2.2156845, 1.6511057, -0.76736002, 0.37283344, -0.1120316;
5.2246158, -10.124111, 4.9874687, -0.27297694, -0.43083393, 0.13333849;
8.7127675, -9.5000611, 4.3786606, -0.91783782, 0, 0;
-1.8525999, 0.9340469, 0, 0, 0, 0
},
x + 1,
y + 1
)
);
nvisc = LAMBDA(x,
INDEX(
{
0.5132047,
0.3205656,
-0.7782567,
0.1885447,
0.2151778,
0.7317883,
1.241044,
1.476783,
-0.2818107,
-1.070786,
-1.263184,
0.1778064,
0.460504,
0.2340379,
-0.4924179,
-0.0417661,
0.1600435,
-0.01578386,
-0.003629481
},
x
)
);
pBound = LAMBDA(temp,
IF(
OR(temp < 623.15, temp > 863.15),
-1,
(nbound(1) + nbound(2) * temp + nbound(3) * temp * temp) * 10
)
);
pc_water = 220.64;
pressreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
density * rgas_water * temp * delta * fideltareg3(tau, delta) / 100000
)
);
PSatW = LAMBDA(temperature,
LET(
t, temperature,
del, t + nreg4(9) / (t - nreg4(10)),
aco, del ^ 2 + nreg4(1) * del + nreg4(2),
bco, nreg4(3) * del ^ 2 + nreg4(4) * del + nreg4(5),
cco, nreg4(6) * del ^ 2 + nreg4(7) * del + nreg4(8),
IF(
OR(t < 273.15, t > 647.096),
-1,
(2 * cco / (-bco + (bco ^ 2 - 4 * aco * cco) ^ 0.5)) ^ 4 * 10
)
)
);
psivisc = LAMBDA(tau, delta,
1 / (tau ^ 0.5 * LET(i, SEQUENCE(4, 1, 0, 1), SUM(n0visc(i) * tau ^ i))) *
EXP(
delta *
LET(
i, SEQUENCE(19, 1, 1, 1),
SUM(
nvisc(i) * (delta - 1) ^ ivisc(i) * (tau - 1) ^ jvisc(i)
)
)
)
);
rgas_water = 461.526;
SolveDens3 = LAMBDA(densin, temp, press,
LET(
tau, tc_water / temp,
delta, densin / dc_water,
fidel3, fideltareg3(tau, delta),
ddens, (press * 100000 -
rgas_water * temp * densin ^ 2 / dc_water * fidel3) /
(rgas_water * temp / dc_water *
(2 * densin * fidel3 +
densin ^ 2 / dc_water * fideltadeltareg3(tau, delta))),
IF(
ABS(ddens) > 0.000005,
SolveDens3(densin + ddens, temp, press),
densin + ddens
)
)
);
spsoundreg1 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press / 16.53,
(rgas_water * temp *
(gammapireg1(tau, pi) ^ 2 /
((gammapireg1(tau, pi) - tau * gammapitaureg1(tau, pi)) ^ 2 /
(tau ^ 2 * gammatautaureg1(tau, pi)) -
gammapipireg1(tau, pi)))) ^ 0.5
)
);
spsoundreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
(rgas_water * temp *
(1 + 2 * pi * gammarpireg2(tau, pi) +
pi ^ 2 * gammarpireg2(tau, pi) ^ 2) /
((1 - pi ^ 2 * gammarpipireg2(tau, pi)) +
(1 + pi * gammarpireg2(tau, pi) -
tau * pi * gammarpitaureg2(tau, pi)) ^ 2 /
(tau ^ 2 *
(gamma0tautaureg2(tau, pi) +
gammartautaureg2(tau, pi))))) ^ 0.5
)
);
spsoundreg3 = LAMBDA(temp, density,
LET(
tau, tc_water / temp,
delta, density / dc_water,
(rgas_water * temp *
(2 * delta * fideltareg3(tau, delta) +
delta ^ 2 * fideltadeltareg3(tau, delta) -
(delta * fideltareg3(tau, delta) -
delta * tau * fideltataureg3(tau, delta)) ^ 2 /
(tau ^ 2 * fitautaureg3(tau, delta)))) ^ 0.5
)
);
spsoundSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
spsoundreg1(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
spsoundreg3(temp, densreg3(temp, press + 0.00001)),
-1
)
)
)
);
spsoundSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
spsoundreg1(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
spsoundreg3(temp, densreg3(temp, press)),
-1
)
)
)
);
spsoundSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
spsoundreg2(temp, press),
IF(
AND(press > tSatW(623.15), press <= pc_water),
spsoundreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
spsoundSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
spsoundreg2(temp, press),
IF(
AND(temp > 623.15, temp <= tc_water),
spsoundreg3(temp, densreg3(temp, press - 0.00001)),
-1
)
)
)
);
spsoundW = LAMBDA(temp, press,
LET(
reg, getreg(temp, press),
IF(
reg = -1,
"NA",
CHOOSE(
reg,
spsoundreg1(temp, press),
spsoundreg2(temp, press),
spsoundreg3(temp, densreg3(temp, press))
)
)
)
);
tBound = LAMBDA(press,
IF(
OR(press < 165.292, press > 1000),
-1,
nbound(4) + ((0.1 * press - nbound(5)) / nbound(3)) ^ 0.5
)
);
tc_water = 647.096;
thconSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
0.4945 *
lambthcon(
temp,
press,
647.226 / temp,
1 / volreg1(temp, press) / 317.763
),
IF(
AND(press > tSatW(623.15), press <= pc_water),
0.4945 *
lambthcon(
tSatW(press),
press,
647.226 / temp,
densreg3(tSatW(press), press + 0.00001) / 317.763
),
-1
)
)
)
);
thconSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
0.4945 *
lambthcon(
temp,
press,
647.226 / temp,
1 / volreg1(temp, press) / 317.763
),
IF(
AND(temp > 623.15, temp <= tc_water),
0.4945 *
lambthcon(
temp,
press,
647.226 / temp,
densreg3(temp, press) / 317.763
),
-1
)
)
)
);
thconSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(temp >= 273.15, temp <= 623.15),
0.4945 *
lambthcon(
temp,
press - 0.0001 * press,
647.226 / temp,
1 / volreg2(temp, press) / 317.763
),
IF(
AND(temp > 623.15, temp <= tc_water),
0.4945 *
lambthcon(
temp,
press - 0.00001,
647.226 / temp,
densreg3(temp, press - 0.00001) / 317.763
),
-1
)
)
)
);
thconSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
0.4945 *
lambthcon(
temp,
press - 0.0001 * press,
647.226 / temp,
1 / volreg2(temp, press) / 317.763
),
IF(
AND(temp > 623.15, temp <= tc_water),
0.4945 *
lambthcon(
temp,
press - 0.00001 * press,
647.226 / temp,
densreg3(temp, press - 0.00001) / 317.763
),
-1
)
)
)
);
thconW = LAMBDA(temp, press,
IF(
AND(temp >= 273.15, temp <= 1073.15, press > 0, press <= 1000),
0.4945 *
lambthcon(
temp,
press,
647.226 / temp,
densW(temp, press) / 317.763
),
-1
)
);
tSatW = LAMBDA(pressure,
LET(
bet, (0.1 * pressure) ^ 0.25,
eco, bet ^ 2 + nreg4(3) * bet + nreg4(6),
fco, nreg4(1) * bet ^ 2 + nreg4(4) * bet + nreg4(7),
gco, nreg4(2) * bet ^ 2 + nreg4(5) * bet + nreg4(8),
dco, 2 * gco / (-fco - (fco ^ 2 - 4 * eco * gco) ^ 0.5),
IF(
OR(pressure < 0.00611213, pressure > 220.64),
-1,
0.5 *
(nreg4(10) + dco -
((nreg4(10) + dco) ^ 2 - 4 * (nreg4(9) + nreg4(10) * dco)) ^
0.5)
)
)
);
viscSatLiqPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
0.000055071 *
psivisc(647.226 / temp, 1 / volreg1(temp, press) / 317.763),
IF(
AND(press > tSatW(623.15), press <= pc_water),
0.000055071 *
psivisc(
647.226 / temp,
densreg3(temp, press + 0.00001) / 317.763
),
-1
)
)
)
);
viscSatLiqTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
0.000055071 *
psivisc(647.226 / temp, 1 / volreg1(temp, press) / 317.763),
IF(
AND(temp > 623.15, temp <= tc_water),
0.000055071 *
psivisc(647.226 / temp, densreg3(temp, press) / 317.763),
-1
)
)
)
);
viscSatVapPW = LAMBDA(press,
LET(
temp, tSatW(press),
IF(
AND(press >= PSatW(273.15), press <= PSatW(623.15)),
0.000055071 *
psivisc(647.226 / temp, 1 / volreg2(temp, press) / 317.763),
IF(
AND(press > tSatW(623.15), press <= pc_water),
0.000055071 *
psivisc(
647.226 / temp,
densreg3(temp, press - 0.00001) / 317.763
),
-1
)
)
)
);
viscSatVapTW = LAMBDA(temp,
LET(
press, PSatW(temp),
IF(
AND(temp >= 273.15, temp <= 623.15),
0.000055071 *
psivisc(647.226 / temp, 1 / volreg2(temp, press) / 317.763),
IF(
AND(temp > 623.15, temp <= tc_water),
0.000055071 *
psivisc(
647.226 / temp,
densreg3(temp, press - 0.00001) / 317.763
),
-1
)
)
)
);
viscW = LAMBDA(temp, press,
IF(
AND(temp >= 273.15, temp <= 1073.15, press <= 1000),
0.000055071 * psivisc(647.226 / temp, densW(temp, press) / 317.763),
-1
)
);
volreg1 = LAMBDA(temp, press,
LET(
tau, 1386 / temp,
pi, 0.1 * press / 16.53,
rgas_water * temp * pi * gammapireg1(tau, pi) / (press * 100000)
)
);
volreg2 = LAMBDA(temp, press,
LET(
tau, 540 / temp,
pi, 0.1 * press,
rgas_water * temp * pi *
(gamma0pireg2(tau, pi) + gammarpireg2(tau, pi)) / (press * 100000)
)
);
@ncalm
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ncalm commented Apr 8, 2022

Wow. Incredible work.

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