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thermochem.cpp
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/*
* thermochem.c
*
* Created on: 2014.01.14
*
*/
#include<string.h>
#include<math.h>
#include"comm.hpp"
#include"chemdata.hpp"
/*---------------------------------------------------
* Calculate the thermal properties
* ------------------------------------------------*/
void gettherm(int nc, double **q, double **qs, double *p,
double *t, double *gam1, double *rgas1, double *cv1)
{
int ic, ns, nr, nd, ntol, icount;
double hs, tol, told, tnew, energy, dum, tdiff,
tem_min, tem_max, temp, temp2, temp3, temp4,
cp, cps, u, v, etot, tem, rgas0;
double rwm[maxspec];
double c2 = 0.5, c3 = 1./3., c4 = 0.25, c5 = 0.2;
void endjob();
/*-- Set a range for the temperature. Terminate the program
* if un-physical conditions are encountered --*/
tem_min = 20.0;
tem_max = 20000.0;
FILE *outId;
if(config1.gasModel == 0)
{
/*-- for calorically perfect gas--*/
rgas0 = (ru/config2.molWeight);
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
temp = 0.5*(q[ic][1]*q[ic][1] + q[ic][2]*q[ic][2]);
rgas1[ic] = rgas0/rgasRef;
gam1[ic] = config2.gam0;
cv1[ic] = rgas0/(config2.gam0 - 1.)/cvRef;
p[ic] = (gam1[ic] - 1)*(q[ic][3] - temp)*q[ic][0]/Upsilon;
t[ic] = p[ic]/q[ic][0]/rgas1[ic];
tem = t[ic]*temRef;
if( !(tem_min<tem && tem<tem_max))
{
outId = fopen("outInfo.dat", "a");
fprintf(outId, "T = %f (K) at at i=%d, j=%d\n", tem, ic/config1.nj, ic%config1.nj);
fclose(outId);
printf("T = %f (K) at at i=%d, j=%d\n", tem, ic/config1.nj, ic%config1.nj);
printf("The temperature may be unphysical for ideal gas model \n");
exit(41);
}
}
}
else
{
/*-- for none calorically perfect gas--*/
ntol = 20;
tol = 1.0e-10;
for(ns = 0; ns<config1.nspec; ns++)
rwm[ns] = 1.0/specData[ns].wm;
/*-- calculate mixture heat capacity, ratio of
*-- specific heats and total energy per mass */
switch(config1.thermo_base)
{
case 0 : // NASA_glenn database
{
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
/*--recover dimension--*/
tem = t[ic]*temRef;
u = q[ic][1]*uRef;
v = q[ic][2]*uRef;
etot = q[ic][3]*uRef*uRef;
temp = 0.;
for(ns=0; ns<config1.nspec; ns++)
{
temp = temp + qs[ic][ns]*rwm[ns];
}
rgas1[ic] = ru*temp;
icount = 0;
dum = (etot - 0.5*(u*u + v*v));
told = tem;
/*----------------------Start Newton's iteration Method----------------------*/
do {
nr = 0;
cp = 0. ;
temp = 0.;
energy = 0. ;
for(ns = 0; ns<config1.nspec; ns++)
{
cps = 0.;
if( told > specData[ns].tempmax ) //exceeds maximum
{
nr = specData[ns].ntemrng;
temp = specData[ns].tempmax;
}
else if(told < specData[ns].tempmin) //exceeds minimum
{
nr = 0;
temp = specData[ns].tempmin;
}
else
{
for(nd = 0; nd<=specData[ns].ntemrng; nd++)
if((told >= specData[ns].temrng[nd][0]) && (told <= specData[ns].temrng[nd][1]) )
{
nr = nd;
temp = told;
break;
}
}
temp2 = temp*temp;
temp3 = temp*temp2;
temp4 = temp*temp3;
cps = ru*(specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]/temp
+ specData[ns].acoef[nr][2]
+ specData[ns].acoef[nr][3]*temp
+ specData[ns].acoef[nr][4]*temp2
+ specData[ns].acoef[nr][5]*temp3
+ specData[ns].acoef[nr][6]*temp4)*rwm[ns];
hs = ru*(-specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]*log(temp)/temp
+ specData[ns].acoef[nr][2]
+ c2*specData[ns].acoef[nr][3]*temp
+ c3*specData[ns].acoef[nr][4]*temp2
+ c4*specData[ns].acoef[nr][5]*temp3
+ c5*specData[ns].acoef[nr][6]*temp4
+ specData[ns].acoef[nr][7]/temp)*rwm[ns]*temp;
hs = hs + cps*(told - temp);
energy = energy + qs[ic][ns]*(hs - ru*rwm[ns]*told);
cp = cp + qs[ic][ns]*cps;
}
cv1[ic] = cp - rgas1[ic];
tnew = told + (dum-energy)/(cv1[ic] + 1.e-20);
tdiff = tnew - told;
told = tnew; //
icount = icount + 1;
//--Check for convergence or maximum trip count
}while ((fabs(tdiff) > tol) && (icount <= ntol));
/*----------------------End Newton's iteration Method----------------------*/
t[ic] = tnew;
if(icount == ntol)
{
printf("----------\n");
printf("myid%d Reached maximum iteration Nr. in determining temperature.\n",MyID);
printf("T_new=%le, T_old=%le T_diff=%le at i=%d, j=%d. icount=%d\n", tnew, told, tdiff, ic/config1.nj, ic%config1.nj, icount);
printf("----------\n");
}
if(!(tem_min<t[ic] && t[ic]<tem_max))
{
outId = fopen("outInfo.dat", "a");
fprintf(outId, "----------\n");
fprintf(outId, "myid%d Newton method T out of range. \n",MyID);
fprintf(outId, "Tem = %e at i=%d, j=%d, ic=%d\n", U.tem[ic], ic/config1.nj, ic%config1.nj,ic);
fprintf(outId, "U.tem = %e \n", U.tem[ic]);
fprintf(outId, "Maybe reduce time-step size...\n");
fprintf(outId, "----------\n");
fclose(outId);
/* At this stage, one can set temperature to the last time step value,
* i.e. t[ic] = tem; But it is recommended to kill the program and
* examine the running conditions*/
exit(42);
}
/*--non-dimension--*/
gam1[ic] = cp/cv1[ic];
t[ic] = t[ic]/temRef;
cv1[ic] = cv1[ic]/cvRef;
rgas1[ic] = rgas1[ic]/rgasRef;
p[ic] = q[ic][0]*rgas1[ic]*t[ic];
}
break;
}
default:
{
printf("the default thermo_base is NASA_glenn data\n");
endjob();
break;
}
}// end switch
}
}
/*---------------------------------------------------
* Calculate the mixture gas constant
* ------------------------------------------------*/
double getrgas(double qs[])
{
int ns;
double rgas1;
rgas1 = 0.0;
if(config1.gasModel==0)
{
rgas1 = (ru/config2.molWeight)/rgasRef;
}
else if(config1.gasModel==1)
{
for(ns = 0; ns<config1.nspec; ns++)
rgas1 = rgas1 + qs[ns]/specData[ns].wm;
rgas1 = ru*rgas1/rgasRef;
}
return(rgas1);
}
/*---------------------------------------------------
* Calculate the internal energy of species 'ns'
* ------------------------------------------------*/
double getes(int ns, double t)
{
int nr, nd;
double hs, es, temp, temp2, temp3, temp4, cps, rwm;
double c2 = 0.5, c3 = 1./3., c4 = 0.25, c5 = 0.2;
void endjob();
t = t*temRef;
if(config1.gasModel==1)
{
nr = 0;
temp = 0.;
rwm = 1.0/specData[ns].wm;
if( t > specData[ns].tempmax)
{
nr = specData[ns].ntemrng;
temp = specData[ns].tempmax;
}
else if(t < specData[ns].tempmin)
{
nr = 0;
temp = specData[ns].tempmin;
}
else
{
for(nd = 0; nd<=specData[ns].ntemrng; nd++)
if((t >= specData[ns].temrng[nd][0]) && (t <= specData[ns].temrng[nd][1]) )
{
nr = nd;
temp = t;
break;
}
}
temp2 = temp*temp;
temp3 = temp*temp2;
temp4 = temp*temp3;
cps = ru*(specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]/temp
+ specData[ns].acoef[nr][2]
+ specData[ns].acoef[nr][3]*temp
+ specData[ns].acoef[nr][4]*temp2
+ specData[ns].acoef[nr][5]*temp3
+ specData[ns].acoef[nr][6]*temp4)*rwm;
hs = ru*(-specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]*log(temp)/temp
+ specData[ns].acoef[nr][2]
+ c2*specData[ns].acoef[nr][3]*temp
+ c3*specData[ns].acoef[nr][4]*temp2
+ c4*specData[ns].acoef[nr][5]*temp3
+ c5*specData[ns].acoef[nr][6]*temp4
+ specData[ns].acoef[nr][7]/temp)*rwm*temp;
hs = hs + cps*(t-temp);
es = hs - ru*rwm*t;
es = es/(uRef*uRef); //non-dimension
}
else
{
printf("[getes] unsupported gasModel\n");
exit(43);
}
return(es);
}
/*--------------------------------------------------------------
* Calculate transport properties(viscosity, conductivity, ...
* -------------------------------------------------------------*/
void gettrans(int nc, double **qs, double *t, double *gam1,
double *cv1, double *mu, double *cond, double **diff)
{
int i, ic, ns, na, nb, nr;
double cp, rho, ratio1, ratio2, tem, dum1, dum2, dum3, As, Bs, Cs,
mixwm, tmin, tmax, upper, lower, omegamkc, redtem, sumxs, patm,
avewmab, avesigab, avekepab, omegadab, tiny;
double wm[maxspec], rwm[maxspec], mus[maxspec], phi[maxspec], xs[maxspec], ys[maxspec],
diffab[maxspec][maxspec];
struct strct_coll
{
double tstar[82], omegamk[82], omegad[82];
}coll;
void endjob();
void coll_integral(int len, double *f1, double *f2, double *f3);
tiny = 1.e-20;
if(config1.gasModel == 0)
{
/*---------- 1. ideal gas flow----------*/
if(config1.visModel == 0)
return;
else if(config1.visModel == 1)
{
/*---------- 1.1 constant "mu" and "cond"----------*/
cp = config2.gam0*cvRef;
ratio1 = config2.temRef/config2.suthC1;
ratio2 = (config2.suthC1 + config2.suthC2)/(config2.temRef+ config2.suthC2);
dum1 = config2.muRef*ratio2*pow(ratio1,1.5);
dum2 = dum1*cp/config2.Pr0;
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
mu[ic] = dum1/muRef;
cond[ic] = dum2/condRef;
}
}
else if(config1.visModel == 2)
{
/*---------- 1.2 Sutherland's law ----------*/
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
tem = t[ic]*temRef;
cp = gam1[ic]*(cv1[ic]*cvRef);
ratio1 = tem/config2.suthC1;
ratio2 = (config2.suthC1 + config2.suthC2)/(tem + config2.suthC2);
mu[ic] = config2.muRef*ratio2*pow(ratio1,1.5);
cond[ic] = mu[ic]*cp/config2.Pr0;
}
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
mu[ic] = mu[ic]/muRef;
cond[ic] = cond[ic]/condRef;
}
}
else
{
printf("unsupported viscosity model... \n");
exit(44);
}
}
else
{
/*---------- 2. real gas flow----------*/
if(config1.visModel == 0)
return;
for(ns = 0; ns<config1.nspec; ns++)
{
wm[ns] = specData[ns].wm;
rwm[ns] = 1./specData[ns].wm;
}
if(config1.transModel == 1)
{
/*---------- 2.1. Blonner's Curve fit data (for air)----------*/
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
tem = t[ic]*temRef;
rho = U.q[ic][0]*rhoRef;
cp = gam1[ic]*(cv1[ic]*cvRef);
mixwm = 0.;
for(ns = 0; ns<config1.nspec; ns++)
{
ys[ns] = qs[ic][ns];
mixwm = mixwm + ys[ns]/wm[ns];
}
mixwm = 1./mixwm;
for(ns = 0; ns<config1.nspec; ns++)
{
As = specData[ns].vis[0];
Bs = specData[ns].vis[1];
Cs = specData[ns].vis[2];
mus[ns] = 0.1*exp((As*log(tem) + Bs)*log(tem) + Cs);
xs[ns] = ys[ns]*mixwm*rwm[ns];
}
// using Wilke's semi-empirical mixing rule
for(ns = 0; ns<config1.nspec; ns++)
{
phi[ns] = 0.;
for(nr = 0; nr<config1.nspec; nr++)
{
dum1 = sqrt(8.*(1. + wm[ns]*rwm[nr]));
dum2 = sqrt(mus[ns]/mus[nr])*pow((wm[nr]*rwm[ns]),0.25);
dum3 = pow((1. + dum2), 2);
phi[ns] = phi[ns] + xs[nr]*dum3/dum1;
}
phi[ns] = 1./(phi[ns] + tiny);
}
// Mixture laminar viscosity
mu[ic] = 0.;
for(ns = 0; ns<config1.nspec; ns++)
{
mu[ic] = mu[ic] + xs[ns]*mus[ns]*phi[ns];
}
cond[ic] = mu[ic]*cp/config2.Pr0;
//assume all the species have the same diffusion coefficient
diff[ic][0] = mu[ic]/(rho*config2.Sc0 + tiny);
}
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
mu[ic] = mu[ic]/muRef;
cond[ic] = cond[ic]/condRef;
for(ns = 0; ns<config1.nspec; ns++)
{
diff[ic][ns] = diff[ic][0]/diffRef;
}
}
}
else if(config1.transModel == 2)
{
/* transport properties given by the kinetic theory
* ref: J.D. Anderson, 2th ed.,AIAA Inc. 2006
* page: 691-705 */
coll_integral(82, coll.tstar, coll.omegamk, coll.omegad);
/*--- 1. viscosity coefficient ---*/
tmin = coll.tstar[0];
tmax = coll.tstar[81];
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
tem = t[ic]*temRef;
rho = U.q[ic][0]*rhoRef;
patm = U.pre[ic]*preRef/1.0132e5;
cp = gam1[ic]*(cv1[ic]*cvRef);
mixwm = 0.;
for(ns = 0; ns<config1.nspec; ns++)
{
ys[ns] = qs[ic][ns];
mixwm = mixwm + ys[ns]/wm[ns];
}
mixwm = 1./mixwm;
for(ns = 0; ns<config1.nspec; ns++)
{
redtem = tem*specData[ns].vis[1];
// handle exceeds Min and Max limit
if(redtem < tmin) redtem = coll.tstar[0];
if(redtem > tmax) redtem = coll.tstar[81];
// linear interpolation
for(i=1; i<=81; i++)
{
if(redtem <= coll.tstar[i])
{
lower = coll.tstar[i] - coll.tstar[i-1];
upper = coll.omegamk[i] - coll.omegamk[i-1];
omegamkc = upper/lower*(redtem - coll.tstar[i-1]) + coll.omegamk[i-1];
break;
}
}
mus[ns] = 2.6693e-06*sqrt((wm[ns]*1000)*tem);
mus[ns] = mus[ns]/(specData[ns].vis[0]*specData[ns].vis[0]*omegamkc);
xs[ns] = ys[ns]*mixwm*rwm[ns];
}
// using Wilke's semi-empirical mixing rule
for(ns = 0; ns<config1.nspec; ns++)
{
phi[ns] = 0.;
for(nr = 0; nr<config1.nspec; nr++)
{
dum1 = sqrt(8.*(1. + wm[ns]*rwm[nr]));
dum2 = sqrt(mus[ns]/mus[nr])*pow((wm[nr]*rwm[ns]),0.25);
dum3 = pow((1. + dum2), 2);
phi[ns] = phi[ns] + xs[nr]*dum3/dum1;
}
phi[ns] = 1./(phi[ns] + tiny);
}
// Mixture laminar viscosity
mu[ic] = 0.;
for(ns = 0; ns<config1.nspec; ns++)
{
mu[ic] = mu[ic] + xs[ns]*mus[ns]*phi[ns];
}
//diff[ic][0] = mu[ic]/(rho*config2.Sc0 + tiny);
/*--- 2. diffusive coefficient ---*/
dum1 = 1.8583e-7*pow(tem,1.5)/patm;
for(nb=0; nb<config1.nspec; nb++)
for(na=0; na<config1.nspec; na++)
{
avewmab = (rwm[na] + rwm[nb])/1000.; // convert the unit.
avesigab = 0.5*(specData[na].vis[0] + specData[nb].vis[0]);
avekepab = sqrt(specData[na].vis[1] * specData[nb].vis[1]);
redtem = tem*avekepab;
if(redtem < tmin) redtem = coll.tstar[0];
if(redtem > tmax) redtem = coll.tstar[81];
for(i=1; i<=81; i++)
{
if(redtem <= coll.tstar[i])
{
lower = coll.tstar[i] - coll.tstar[i-1];
upper = coll.omegad[i] - coll.omegad[i-1];
omegadab = upper/lower*(redtem - coll.omegad[i-1]) + coll.omegad[i-1];
break;
}
}
diffab[na][nb] = dum1*sqrt(avewmab)/(avesigab*avesigab*omegadab);
}
// mixture diffusion coefficient
for(ns=0; ns<config1.nspec; ns++)
{
sumxs = 0.;
for(na=0; na<ns; na++)
sumxs = sumxs + xs[na]/(diffab[na][ns] + tiny);
for(na=ns+1; na<config1.nspec; na++)
sumxs = sumxs + xs[na]/(diffab[na][ns] + tiny);
diff[ic][ns] = (1.0 - xs[ns])/(sumxs + tiny);
}
/*--- 3. conductive coefficient ---*/
cond[ic] = mu[ic]*cp/config2.Pr0;
}
for (ic = MyID * nc; ic < (MyID + 1) * nc; ic++)
{
mu[ic] = mu[ic]/muRef;
cond[ic] = cond[ic]/condRef;
for(ns = 0; ns<config1.nspec; ns++)
{
diff[ic][ns] = diff[ic][ns]/diffRef;
}
}
}
else
{
printf("unsupported viscosity model... \n");
exit(45);
}
}
}
/*---------------------------------------------------
* collision integral, Hirschfelder, 1954
* ------------------------------------------------*/
void coll_integral(int ik, double *ftstar, double *fomegamk, double *fomegad)
{
int i;
double tstar[] = {0.30, 0.35, 0.40, 0.45, 0.50, 0.55, 0.60,
0.65, 0.70 , 0.75, 0.80, 0.85, 0.90, 0.95,
1.00, 1.05, 1.10, 1.15, 1.20, 1.25, 1.30,
1.35, 1.40, 1.45, 1.50, 1.55, 1.60, 1.65,
1.70, 1.75, 1.80, 1.85, 1.90, 1.95, 2.00,
2.10, 2.20, 2.30, 2.40, 2.50, 2.60, 2.70,
2.80, 2.90, 3.00, 3.10, 3.20, 3.30, 3.40,
3.50, 3.60, 3.70, 3.80, 3.90, 4.00, 4.10,
4.20, 4.30, 4.40, 4.50, 4.60, 4.70, 4.80,
4.90, 5.00, 6.00, 7.00, 8.00, 9.00, 10.00,
20.00, 30.00, 40.00, 50.00, 60.00, 70.00, 80.00,
90.00, 100.00, 200.00, 300.00, 400.00};
double omegamk[] = {2.7850,2.6280,2.4920,2.3680,2.2570,2.1560, 2.0650,
1.9820,1.9080,1.8410,1.7800,1.7250,1.6750, 1.6290,
1.5870,1.5490,1.5140,1.4820,1.4520,1.4240, 1.3990,
1.3750,1.3530,1.3330,1.3140,1.2960,1.2790, 1.2640,
1.2480,1.2340,1.2210,1.2090,1.1970,1.1860, 1.1750,
1.1560,1.1380,1.1220,1.1070,1.0930,1.0810, 1.0690,
1.0580,1.0480,1.0390,1.0300,1.0220,1.0140, 1.0070,
0.9999,0.9932,0.9870,0.9811,0.9755,0.9700, 0.9649,
0.9600,0.9553,0.9507,0.9464,0.9422,0.9382, 0.9343,
0.9305,0.9269,0.8963,0.8727,0.8538,0.8379, 0.8242,
0.7432,0.7005,0.6718,0.6504,0.6335,0.6194, 0.6076,
0.5973,0.5882,0.5320,0.5016,0.4811};
double omegad[] = {2.6620,2.4760,2.3180,2.1840,2.0660,1.9660,1.8770,
1.7980,1.7290,1.6670,1.6120,1.5620,1.5170,1.4760,
1.4390,1.4060,1.3750,1.3460,1.3200,1.2960,1.2730,
1.2530,1.2330,1.2150,1.1980,1.1820,1.1670,1.1530,
1.1400,1.1280,1.1160,1.1050,1.0940,1.0840,1.0750,
1.0570,1.0410,1.0260,1.0120,0.9996,0.9878,0.9770,
0.9672,0.9576,0.9490,0.9406,0.9328,0.9256,0.9186,
0.9120,0.9058,0.8998,0.8942,0.8888,0.8836,0.8788,
0.8740,0.8694,0.8652,0.8610,0.8568,0.8530,0.8492,
0.8456,0.8422,0.8124,0.7896,0.7712,0.7556,0.7424,
0.6640,0.6232,0.5960,0.5756,0.5596,0.5464,0.5352,
0.5256,0.5130,0.4644,0.4360,0.4170};
for(i=0; i<ik; i++)
{
ftstar[i] = tstar[i];
fomegamk[i] = omegamk[i];
fomegad[i] = omegad[i];
}
}
/*---------------------------------------------------
* Calculate the chemical source terms and the
* related jacobian matrix
* ------------------------------------------------*/
void chemsource(int nc, double **q, double **qs, double *tem, double **rhs)
{
int ic, i, j, ii, jj, ns, nr, m, ic1;
double rdum, multf, multb, third, temp, sumrs, tiny, dkeqdt, tem1, rtem,
Trigger_T, kfterm, kbterm, termU, termV, termE, zt, z2, alfa, yas,
kf, kb, keq, gibbs[2];
double rhos[maxspec], term[maxspec], rwm[maxspec], dkfdq[maxeqn], dkbdq[maxeqn];
double dimen_factor[9] = {1.e6, 1.e6, 1.e6, 1.e6, 1.e6, 1.e6, 1.e6, 1., 1.};
void gibbsenergy(int nr, int nc, double t, double f[]);
void tem_derivative(double **dtdq);
m = config1.nspec;
tiny = 1.e-20;
// the lowest temperature to trigger the reaction.
Trigger_T = 1800.;
alfa = LRef/(rhoRef*uRef);
for(ic = 0; ic<nc; ic++)
for(ns = 0; ns<m; ns++)
{
sour[ic][ns] = 0.;
for(j = 0; j<neqn; j++)
dsdq[ic][ns][j] = 0.;
}
/*--- 1. Calculated temperature derivatives ---*/
tem_derivative(dtdq);
for(ns = 0; ns<m; ns++)
rwm[ns] = 1.0/(specData[ns].wm);
switch(config1.gasModel)
{
case 1:
{
for(ic = 0; ic<nc; ic++)
{
int ic1 = ic + MyID * nc;
tem1 = tem[ic1]*temRef;
for(ns = 0; ns<m; ns++)
rhos[ns] = (q[ic1][0]*rhoRef)*qs[ic1][ns];
rtem = 1./tem1;
if(tem1 < Trigger_T)
continue;
for(nr = 0; nr<config1.nreac; nr++)
{
/*--- 2. Determine the forward reaction rate ---*/
kf = reacData[nr].af*pow(tem1,reacData[nr].nf)*
exp(-reacData[nr].thetaf*rtem);
/*--- 3. Determine the backward reaction rate ---*/
if(reacData[nr].backrate == 1)
{
kb = reacData[nr].ab*pow(tem1,reacData[nr].nb)*
exp(-reacData[nr].thetab*rtem);
}
else if(reacData[nr].backrate == 2)
{
//use park curve fit
zt = 10000*rtem;
z2 = zt*zt;
keq = exp(reacData[nr].Br[0] + reacData[nr].Br[1]*log(zt)
+ reacData[nr].Br[2]*zt + reacData[nr].Br[3]*z2
+ reacData[nr].Br[4]*zt*z2)*dimen_factor[nr];
kb = kf/(keq + tiny);
}
else
{
//use Gibbs energy
gibbsenergy(nr, ic, tem1, gibbs);
sumrs = 0.;
for(ns = 0; ns<m; ns++)
sumrs = sumrs + reacData[nr].npsr[ns] - reacData[nr].nrsr[ns];
rdum = 101300.0/ru;
keq = pow((rdum*rtem),sumrs)*exp(-gibbs[0]);
kb = kf/(keq + tiny);
}
if(reacData[nr].thirdbody)
{
/*---4.1 Determine chemical source term for
* reactions with third body efficiencies ---*/
multf = 1.;
multb = 1.;
third = 0.;
for(ns = 0; ns<m; ns++)
{
rdum = rhos[ns]*rwm[ns];
third = third + reacData[nr].thrdeff[ns]*rdum;
rdum = MAX(rdum,tiny);
multf = multf*pow(rdum,reacData[nr].nrsr[ns]);
multb = multb*pow(rdum,reacData[nr].npsr[ns]);
}
for(ns = 0; ns<m; ns++)
sour[ic][ns] = sour[ic][ns]
+ specData[nr].wm*(reacData[nr].npsr[ns]-reacData[nr].nrsr[ns])
* third*(kf*multf-kb*multb)*alfa;
}
else
{
/*--- 4.2 Determine chemical source term for
* reactions without third body efficiencies ---*/
multf = 1.;
multb = 1.;
for(ns = 0; ns<m; ns++)
{
rdum = rhos[ns]*rwm[ns];
rdum = MAX(rdum,tiny);
multf = multf*pow(rdum,reacData[nr].nrsr[ns]);
multb = multb*pow(rdum,reacData[nr].npsr[ns]);
}
for(ns = 0; ns<m; ns++)
{
sour[ic][ns] = sour[ic][ns]
+ specData[ns].wm*(reacData[nr].npsr[ns]-reacData[nr].nrsr[ns])
*(kf*multf - kb*multb)*alfa;
}
}
/*--- 5. Calculate the chemical source Jacobian ds/dq ---*/
//5.1 Determine d(k_f)/dU
rdum = kf*rtem*(reacData[nr].nf + reacData[nr].thetaf*rtem);
for(ns=0; ns<m; ns++)
dkfdq[ns] = rdum*dtdq[ic][ns];
dkfdq[m] = rdum*dtdq[ic][m];
dkfdq[m+1] = rdum*dtdq[ic][m+1];
dkfdq[m+2] = rdum*dtdq[ic][m+2];
//5.2 Determine d(k_b)/dU
if(reacData[nr].backrate == 1)
rdum = kb*rtem*(reacData[nr].nb + reacData[nr].thetab*rtem);
else if(reacData[nr].backrate == 2)
{
dkeqdt = keq*(reacData[nr].Br[1]/zt + reacData[nr].Br[2]
+ 2.*reacData[nr].Br[3]*zt + 3.*reacData[nr].Br[4]*z2);
rdum = kb*rtem*(reacData[nr].nf + reacData[nr].thetaf*rtem - dkeqdt/(keq + tiny));
}
else
{
//use Gibbs energy
sumrs = 0.;
for(ns=0; ns<m; ns++)
sumrs = sumrs + (reacData[nr].npsr[ns] - reacData[nr].nrsr[ns]);
dkeqdt = -keq*(sumrs*rtem + gibbs[1]);
rdum = kb*rtem*(reacData[nr].nf + reacData[nr].thetaf*rtem - dkeqdt/(keq + tiny));
}
for(ns=0; ns<m; ns++)
dkbdq[ns] = rdum*dtdq[ic][ns];
dkbdq[m] = rdum*dtdq[ic][m];
dkbdq[m+1] = rdum*dtdq[ic][m+1];
dkbdq[m+2] = rdum*dtdq[ic][m+2];
//5.3 Calculate the concentration term
multf = 1.;
multb = 1.;
for(ns = 0; ns<m; ns++)
{
rdum = rhos[ns]*rwm[ns];
rdum = MAX(rdum,tiny);
multf = multf*pow(rdum,reacData[nr].nrsr[ns]);
multb = multb*pow(rdum,reacData[nr].npsr[ns]);
}
kfterm = kf*multf;
kbterm = kb*multb;
if(reacData[nr].thirdbody)
{
third = 0.;
for(j=0; j<m; j++)
{
rdum = rhos[j]*rwm[j];
third = third + reacData[nr].thrdeff[j]*rdum;
term[j] = reacData[nr].thrdeff[ns]*rwm[j]*(kfterm - kbterm);
}
}
else
{
third = 1.;
for(j=0; j<m; j++)
term[j] = 0.;
}
//5.4 Determine the first term of dS/dU
for(j=0; j<m; j++)
{
rdum = MAX(rhos[j],tiny);
term[j] = term[j] + third*(reacData[nr].nrsr[j]*kfterm
- reacData[nr].npsr[j]*kbterm)/rdum;
}
//5.5 Determine the second term of dS/dU
for(j=0; j<m; j++)
term[j] = term[j] + third*(dkfdq[j]*multf - dkbdq[j]*multb);
termU = third*(dkfdq[m]*multf - dkbdq[m]*multb);
termV = third*(dkfdq[m+1]*multf - dkbdq[m+1]*multb);
termE = third*(dkfdq[m+2]*multf - dkbdq[m+2]*multb);
/*5.6 Sum for all the reaction, and store the source Jacobian.
Mutiply non-dimensional factor for Jacobian term 'ds/dq' */
for(i=0; i<m; i++)
{
temp = specData[i].wm*(reacData[nr].npsr[i] - reacData[nr].nrsr[i]);
for(j=0; j<m; j++)
dsdq[ic][i][j] = dsdq[ic][i][j] + temp*term[j]*(alfa*rhoRef);
dsdq[ic][i][m] = dsdq[ic][i][m] + temp*termU*(alfa*rhoRef*uRef);
dsdq[ic][i][m+1] = dsdq[ic][i][m+1] + temp*termV*(alfa*rhoRef*uRef);
dsdq[ic][i][m+2] = dsdq[ic][i][m+2] + temp*termE*(alfa*rhoRef*uRef*uRef);
}
}// end nr -> nreac;
} // end ic -> nc;
break;
} // end case1
default:
{
printf("unsupported chemical model [void chemsource]\n");
break;
}
}
/*----- 6. Add source term to numerical right hand side-----*/
for(i=0; i<config1.ni; i++)
{
ii = i + config1.Ng;
for(j=0; j<config1.nj; j++) // without ghost cells
{
jj = j + config1.Ng;
ic = i*config1.nj + j;
ic1 = (ii + MyID * config1.ni) * J0 + jj;
yas = mesh.yaks[ic1];
for(ns=0; ns<m; ns++)
rhs[ic][ns] = rhs[ic][ns] + sour[ic][ns]*yas;
}
}
}
/*--------------------------------------------------------------
* Determine the Gibbs free energy for the equilibrium constant
* ------------------------------------------------------------*/
void gibbsenergy(int nr, int nc, double tem, double f[])
{
int nd, ns, ntr , outofrange;
double c2 = 0.5, c3 = 1./3., c4 = 0.25, c5 = 0.2;
double temp, temp2, temp3, temp4, cps, gibbs, dgibbs;
double hsbar, sbar, hsbar_im, dhsbardt, dsbardt, gibbsterm, dgibbsterm;
void endjob();
ntr = 0;
temp = 0.;
switch(config1.thermo_base)
{
case 0:
{
gibbs = 0.;
dgibbs = 0.;
//-- check temperature range validity
for(ns = 0; ns<config1.nspec; ns++)
{
outofrange = 0;
cps = 0.;
if(tem > specData[ns].tempmax)
{
outofrange = 1;
ntr = specData[ns].ntemrng;
temp = specData[ns].tempmax;
temp2 = temp*temp;
temp3 = temp*temp2;
temp4 = temp*temp3;
cps = (specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]/temp
+ specData[ns].acoef[nr][2]
+ specData[ns].acoef[nr][3]*temp
+ specData[ns].acoef[nr][4]*temp2
+ specData[ns].acoef[nr][5]*temp3
+ specData[ns].acoef[nr][6]*temp4);
}
else if(tem < specData[ns].tempmin)
{
outofrange = 1;
ntr = 0;
temp = specData[ns].tempmin;
temp2 = temp*temp;
temp3 = temp*temp2;
temp4 = temp*temp3;
cps = (specData[ns].acoef[nr][0]/temp2
+ specData[ns].acoef[nr][1]/temp
+ specData[ns].acoef[nr][2]
+ specData[ns].acoef[nr][3]*temp
+ specData[ns].acoef[nr][4]*temp2
+ specData[ns].acoef[nr][5]*temp3
+ specData[ns].acoef[nr][6]*temp4);
}
else
{
for(nd = 0; nd<=specData[ns].ntemrng; nd++)
if((tem >= specData[ns].temrng[nd][0]) && (tem <= specData[ns].temrng[nd][1]) )
{
ntr = nd;
temp = tem;
temp2 = temp*temp;
temp3 = temp*temp2;
temp4 = temp*temp3;
cps = 0.;
break;
}
}
hsbar = (-specData[ns].acoef[ntr][0]/temp2
+ specData[ns].acoef[ntr][1]*log(temp)/temp
+ specData[ns].acoef[ntr][2]
+ c2*specData[ns].acoef[ntr][3]*temp
+ c3*specData[ns].acoef[ntr][4]*temp2
+ c4*specData[ns].acoef[ntr][5]*temp3
+ c5*specData[ns].acoef[ntr][6]*temp4
+ specData[ns].acoef[ntr][7]/temp); // h/RT
hsbar_im = hsbar;
sbar = (-c2*specData[ns].acoef[ntr][0]/temp2
- specData[ns].acoef[ntr][1]/temp
+ specData[ns].acoef[ntr][2]*log(temp)
+ specData[ns].acoef[ntr][3]*temp
+ c2*specData[ns].acoef[ntr][4]*temp2
+ c3*specData[ns].acoef[ntr][5]*temp3
+ c4*specData[ns].acoef[ntr][6]*temp4
+ specData[ns].acoef[ntr][8]); // S/R
hsbar = (hsbar*temp + cps*(tem-temp))/tem;
sbar = sbar + cps*(log(tem/temp)); //
gibbsterm = hsbar - sbar;
gibbs = gibbs + (reacData[nr].npsr[ns]- reacData[nr].nrsr[ns])*gibbsterm;
/* Implicit terms for source Jacobian */
if(outofrange)
{
dgibbsterm = (- temp*hsbar_im + cps*(tem + temp))/(tem*tem);
}
else
{
dhsbardt = (2.*specData[ns].acoef[ntr][0]/temp3
+ specData[ns].acoef[ntr][1]*(1.-log(temp))/temp2
+ c2*specData[ns].acoef[ntr][3]
+ 2.*c3*specData[ns].acoef[ntr][4]*temp
+ 3.*c4*specData[ns].acoef[ntr][5]*temp2
+ 4.*c5*specData[ns].acoef[ntr][6]*temp3
- specData[ns].acoef[ntr][7]/temp2);
dsbardt = ( specData[ns].acoef[ntr][0]/temp3
+ specData[ns].acoef[ntr][1]/temp2
+ specData[ns].acoef[ntr][2]/temp
+ specData[ns].acoef[ntr][3]
+ specData[ns].acoef[ntr][4]*temp
+ specData[ns].acoef[ntr][5]*temp2
+ specData[ns].acoef[ntr][6]*temp3);
dgibbsterm = dhsbardt - dsbardt;
}
dgibbs = dgibbs + (reacData[nr].npsr[ns]- reacData[nr].nrsr[ns])*dgibbsterm;
}
break;
}
default:
{
printf("the default thermo_base is NASA_glenn data\n");
endjob();
break;
}
}// end switch
f[0] = gibbs;
f[1] = dgibbs;
}
/*---------------------------------------------------
* calculate source term derivatives with respect to
* species density & total density
* ------------------------------------------------*/
void tem_derivative(double **dtdq)
{