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/* ASCEND modelling environment |
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Copyright (C) 2008 Carnegie Mellon University |
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|
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This program is free software; you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation; either version 2, or (at your option) |
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any later version. |
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|
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This program is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU General Public License for more details. |
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|
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You should have received a copy of the GNU General Public License |
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along with this program; if not, write to the Free Software |
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Foundation, Inc., 59 Temple Place - Suite 330, |
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Boston, MA 02111-1307, USA. |
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*/ |
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|
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#include <math.h> |
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|
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#include "ideal.h" |
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|
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#ifdef TEST |
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#include <assert.h> |
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#include <stdlib.h> |
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#include <stdio.h> |
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#endif |
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|
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/*--------------------------------------------- |
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IDEAL COMPONENT RELATIONS |
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*/ |
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|
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/** |
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Zero-pressure specific heat function (ideal gas limit) |
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|
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This is returned in the units of data->cp0star. |
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*/ |
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double helm_cp0(double T, const IdealData *data){ |
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const IdealPowTerm *pt; |
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const IdealExpTerm *et; |
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|
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unsigned i; |
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double sum = 0; |
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double term; |
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|
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/* power terms */ |
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pt = &(data->pt[0]); |
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#if 0 |
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fprintf(stderr,"np = %d\n",data->np); |
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#endif |
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for(i = 0; i<data->np; ++i, ++pt){ |
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term = pt->a0 * pow(T, pt->t0); |
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#if 0 |
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fprintf(stderr,"i = %d: ",i); |
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fprintf(stderr,"power term, a = %f, t = %f, val = %f\n",pt->a0, pt->t0, term); |
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#endif |
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sum += term; |
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} |
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|
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/* 'exponential' terms */ |
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et = &(data->et[0]); |
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for(i=0; i<data->ne; ++i, ++et){ |
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#if 0 |
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fprintf(stderr,"exp term\n"); |
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#endif |
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double x = et->beta / T; |
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double e = exp(-x); |
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double d = (1-e)*(1-e); |
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term = et->b * x*x * e / d; |
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#if 0 |
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fprintf(stderr,"exp term, b = %f, beta = %f, val = %f\n",et->b, et->beta, term); |
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#endif |
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sum += term; |
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} |
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|
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#if 0 |
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fprintf(stderr,"Mult by cp0* = %f\n",data->cp0star); |
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#endif |
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return data->cp0star * sum; |
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} |
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|
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/* |
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Hypothesis: |
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in calculating the ideal component relations, we have some integration |
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constants that ultimately allow the arbitrary scales of h and s to |
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be specified. Hence we can ignore components of helm_ideal that |
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are either constant or linear in tau, and work them out later when we |
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stick in the values of data->c and data->m. |
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*/ |
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|
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/** |
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Ideal component of helmholtz function |
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*/ |
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double helm_ideal(double tau, double delta, const IdealData *data){ |
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|
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const IdealPowTerm *pt; |
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const IdealExpTerm *et; |
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|
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unsigned i; |
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double sum = log(delta) - log(tau) + data->c + data->m * tau; |
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double term; |
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double Tstar_on_tau = data->Tstar / tau; |
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|
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/* power terms */ |
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pt = &(data->pt[0]); |
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for(i = 0; i<data->np; ++i, ++pt){ |
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double a = pt->a0; |
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double t = pt->t0; |
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if(t == 0){ |
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term = a*log(tau); |
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}else{ |
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#ifdef TEST |
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assert(t!=-1); |
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#endif |
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term = -a / (t*(t+1)) * pow(Tstar_on_tau,t); |
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} |
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sum += pt->a0 * pow(tau, pt->t0); |
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} |
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|
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/* 'exponential' terms */ |
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et = &(data->et[0]); |
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for(i=0; i<data->ne; ++i, ++et){ |
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sum += et->b * log(1 - exp(-et->beta / Tstar_on_tau)); |
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} |
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|
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return sum; |
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} |
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|
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/** |
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Partial dervivative of ideal component of helmholtz residual function with |
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respect to tau. |
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*/ |
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double helm_ideal_tau(double tau, double delta, const IdealData *data){ |
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const IdealPowTerm *pt; |
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const IdealExpTerm *et; |
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|
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unsigned i; |
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double term; |
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double sum = -1./tau + data->m; |
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double Tstar_on_tau = data->Tstar / tau; |
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|
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pt = &(data->pt[0]); |
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for(i = 0; i<data->np; ++i, ++pt){ |
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double a = pt->a0; |
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double t = pt->t0; |
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if(t==0){ |
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term = a / tau; |
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}else{ |
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// term = -a / (t*(t+1)) * pow(Tstar_on_tau,t); |
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term = a*pow(Tstar_on_tau,t)*tau/(t+1); |
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} |
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#ifdef TEST |
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if(isinf(term)){ |
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fprintf(stderr,"Error with infinite-valued term with i = %d, a = %f, t = %f\n", i,a ,t); |
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abort(); |
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} |
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#endif |
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sum += term; |
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} |
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|
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/* 'exponential' terms */ |
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et = &(data->et[0]); |
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for(i=0; i<data->ne; ++i, ++et){ |
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term = et->b * et->beta / data->Tstar / (1 - exp(-et->beta/Tstar_on_tau)); |
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#ifdef TEST |
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assert(!isinf(term)); |
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#endif |
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sum += term; |
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} |
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|
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#ifdef TEST |
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assert(!isinf(sum)); |
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#endif |
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return sum; |
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} |
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