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/* 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 */
#define virial_m1(C, x1, x2, x3) (C[0]*x1+C[1]*x2+C[2]*x3)
/*
* 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 x1, x2, x3;
double Z;
o2 = get_o2(gas);
he = get_he(gas);
x1 = bar; x2 = x1*x1; x3 = x2*x1;
Z = virial_m1(o2_coefficients, x1, x2, x3) * o2 +
virial_m1(he_coefficients, x1, x2, x3) * he +
virial_m1(n2_coefficients, x1, x2, x3) * (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);
}
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