1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
|
// SPDX-License-Identifier: GPL-2.0
/* gas-model.c */
/* gas compressibility model */
#include <stdio.h>
#include <stdlib.h>
#include "dive.h"
/* "Virial minus one" - the virial cubic form without the initial 1.0 */
static double virial_m1(const double coeff[], double x)
{
return x*coeff[0] + x*x*coeff[1] + x*x*x*coeff[2];
}
/*
* Z = pV/nRT
*
* Cubic virial least-square coefficients for O2/N2/He based on data from
*
* PERRY’S CHEMICAL ENGINEERS’ HANDBOOK SEVENTH EDITION
*
* with the lookup and curve fitting by Lubomir.
*
* The "virial" form of the compression factor polynomial is
*
* Z = 1.0 + C[0]*P + C[1]*P^2 + C[2]*P^3 ...
*
* and these tables do not contain the initial 1.0 term.
*
* NOTE! Helium coefficients are a linear mix operation between the
* 323K and one for 273K isotherms, to make everything be at 300K.
*/
double gas_compressibility_factor(struct gasmix gas, double bar)
{
static const double o2_coefficients[3] = {
-7.18092073703e-04,
+2.81852572808e-06,
-1.50290620492e-09
};
static const double n2_coefficients[3] = {
-2.19260353292e-04,
+2.92844845532e-06,
-2.07613482075e-09
};
static const double he_coefficients[3] = {
+4.87320026468e-04,
-8.83632921053e-08,
+5.33304543646e-11
};
int o2, he;
double Z;
/*
* The curve fitting range is only [0,500] bar.
* Anything else is way out of range for cylinder
* pressures.
*/
if (bar < 0) bar = 0;
if (bar > 500) bar = 500;
o2 = get_o2(gas);
he = get_he(gas);
Z = virial_m1(o2_coefficients, bar) * o2 +
virial_m1(he_coefficients, bar) * he +
virial_m1(n2_coefficients, bar) * (1000 - o2 - he);
/*
* We add the 1.0 at the very end - the linear mixing of the
* three 1.0 terms is still 1.0 regardless of the gas mix.
*
* The * 0.001 is because we did the linear mixing using the
* raw permille gas values.
*/
return Z * 0.001 + 1.0;
}
/* Compute the new pressure when compressing (expanding) volome v1 at pressure p1 bar to volume v2
* taking into account the compressebility (to first order) */
double isothermal_pressure(struct gasmix gas, double p1, int volume1, int volume2)
{
double p_ideal = p1 * volume1 / volume2 / gas_compressibility_factor(gas, p1);
return p_ideal * gas_compressibility_factor(gas, p_ideal);
}
double gas_density(struct gasmix gas, int pressure)
{
int density = gas.he.permille * HE_DENSITY + gas.o2.permille * O2_DENSITY + (1000 - gas.he.permille - gas.o2.permille) * N2_DENSITY;
return density * (double) pressure / gas_compressibility_factor(gas, pressure / 1000.0) / SURFACE_PRESSURE / 1000000.0;
}
|
