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3260dd9c15
This goes back to just doing air compressibility, but using the least-squares quintic polynomial equation that Lubomir generated based on the Wikipedia table for air at 300K in the 1-500 bar range. We might be able to do similar things for mixed gases.. Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org> Signed-off-by: Dirk Hohndel <dirk@hohndel.org>
111 lines
2.9 KiB
C
111 lines
2.9 KiB
C
/* gas-model.c */
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/* gas compressibility model */
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#include <stdio.h>
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#include <stdlib.h>
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#include "dive.h"
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/*
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* This gives an interative solution of hte Redlich-Kwong equation for the compressibility factor
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* according to https://en.wikipedia.org/wiki/Redlich–Kwong_equation_of_state
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* in terms of the reduced temperature T/T_crit and pressure p/p_crit.
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*
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* Iterate this three times for good results in our pressur range.
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*
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*/
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static double redlich_kwong_equation(double t_red, double p_red, double z_init)
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{
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return (1.0/(1.0 - 0.08664*p_red/(t_red * z_init)) -
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0.42748/(sqrt(t_red * t_red * t_red) * ((t_red*z_init/p_red + 0.08664))));
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}
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/*
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* At high pressures air becomes less compressible, and
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* does not follow the ideal gas law any more.
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*/
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#define STANDARD_TEMPERATURE 293.0
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static double redlich_kwong_compressibility_factor(struct gasmix *gas, double bar)
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{
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/* Critical points according to https://en.wikipedia.org/wiki/Critical_point_(thermodynamics) */
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double tcn2 = 126.2;
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double tco2 = 154.6;
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double tche = 5.19;
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double pcn2 = 33.9;
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double pco2 = 50.5;
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double pche = 2.27;
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double tc, pc;
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tc = (tco2 * get_o2(gas) + tche * get_he(gas) + tcn2 * (1000 - get_o2(gas) - get_he(gas))) / 1000.0;
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pc = (pco2 * get_o2(gas) + pche * get_he(gas) + pcn2 * (1000 - get_o2(gas) - get_he(gas))) / 1000.0;
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return (redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,
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redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,
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redlich_kwong_equation(STANDARD_TEMPERATURE/tc, bar/pc,1.0))));
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}
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/*
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* This is a quintic formula by Lubomir I. Ivanov that has
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* been optimized for the least-square error to the air
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* compressibility factor table (at 300K) taken from Wikipedia:
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*
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* bar z_factor
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* --- ------
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* 1: 0.9999
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* 5: 0.9987
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* 10: 0.9974
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* 20: 0.9950
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* 40: 0.9917
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* 60: 0.9901
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* 80: 0.9903
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* 100: 0.9930
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* 150: 1.0074
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* 200: 1.0326
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* 250: 1.0669
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* 300: 1.1089
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* 400: 1.2073
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* 500: 1.3163
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*/
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static double air_compressibility_factor(double bar)
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{
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double x0 = 1.0,
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x1 = bar,
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x2 = x1*x1,
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x3 = x2*x1,
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x4 = x2*x2,
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x5 = x2*x3;
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return + x0 * 1.0002556612420115
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- x1 * 0.0003115084635183305
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+ x2 * 0.00000227808965401253
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+ x3 * 1.91596422989e-9
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- x4 * 8.78421542e-12
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+ x5 * 6.77746e-15;
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}
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/*
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* We end up using specialized functions for known gases, because
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* we have special tables for them.
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*
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* For now, let's do just air.
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*
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* We have other tables for other gases, see for example:
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*
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* http://ww.baue.org/library/zfactor_table.php
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*
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* and then we have the Redlich-Kwong function, but that seems
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* to be almost too generic, and not specific enough to the very
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* particular pressure and temperature ranges we care about..
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*/
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double gas_compressibility_factor(struct gasmix *gas, double bar)
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{
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#if 1
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return air_compressibility_factor(bar);
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#else
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/* Fall back on generic function */
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return redlich_kwong_compressibility_factor(gas, bar);
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#endif
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}
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