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3b38f73fe09699bf66f9ee65a129b0dd1bb885fc
SystemSimulationApp/native/components/kernels.c
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/* Helium Peng-Robinson and compressible-orifice kernels.
* Ported from the project's Python physical equations; validated independently
* against Python at ordinary, reverse-flow and contact trial states.
*/
#include "kernels.h"
#include <math.h>
#include <stddef.h>
#define RU 8.31446261815324
#define MOLAR_MASS 0.004002602
#define TC 5.1953
#define PC 227460.0
#define OMEGA (-0.382)
static const double PI=3.1415926535897932384626433832795;
static const double pr_a=.457235583*RU*RU*TC*TC/PC;
static const double pr_b=.07779607*RU*TC/PC;
static const double kappa=.37464+1.54226*OMEGA-.26992*OMEGA*OMEGA;
static const double rg=RU/MOLAR_MASS;
static double cube_root(double x) { return x==0 ? 0 : copysign(pow(fabs(x),1.0/3.0),x); }
static void attraction(double T, double *a, double *da, double *dda) {
double tr=T/TC, sr=sqrt(tr), base=1+kappa*(1-sr);
*a=pr_a*base*base;
*da=pr_a*(-base*kappa/(TC*sr));
*dda=pr_a*kappa/(2*TC*TC)*(kappa/tr+base/(tr*sr));
}
static double z_factor(double p,double T) {
double a,da,dda; attraction(T,&a,&da,&dda);
double A=a*p/(RU*RU*T*T), B=pr_b*p/(RU*T);
double ca=-(1-B),cb=A-3*B*B-2*B,cc=-(A*B-B*B-B*B*B);
double pp=cb-ca*ca/3,qq=2*ca*ca*ca/27-ca*cb/3+cc;
double disc=pow(qq/2,2)+pow(pp/3,3),off=-ca/3,roots[3]; int n;
if(disc>1e-14) { roots[0]=cube_root(-qq/2+sqrt(disc))+cube_root(-qq/2-sqrt(disc))+off;n=1; }
else if(fabs(disc)<=1e-14) { double u=cube_root(-qq/2);roots[0]=2*u+off;roots[1]=-u+off;n=2; }
else { if(pp>=0) return NAN; double radius=2*sqrt(-pp/3);
double arg=(3*qq/(2*pp))*sqrt(-3/pp),theta=acos(fmax(-1,fmin(1,arg)))/3;
for(int i=0;i<3;i++) { roots[i]=radius*cos(theta-2*PI*i/3)+off; }
n=3;
}
double z=-INFINITY;for(int i=0;i<n;i++) if(roots[i]>B && isfinite(roots[i])) z=fmax(z,roots[i]);
return isfinite(z)?z:NAN;
}
static double density(double p,double T) { return MOLAR_MASS/(z_factor(p,T)*RU*T/p); }
static double log_volume(double rho) {
double v=MOLAR_MASS/rho,sq=sqrt(2.0);
return log((v+(1+sq)*pr_b)/(v+(1-sq)*pr_b))/(2*sq*pr_b*MOLAR_MASS);
}
static double u_departure(double T,double rho) {
double a,da,dda;attraction(T,&a,&da,&dda);return (T*da-a)*log_volume(rho);
}
static double h_departure(double p,double T) {
double a,da,dda;attraction(T,&a,&da,&dda);
double z=z_factor(p,T),B=pr_b*p/(RU*T),sq=sqrt(2.0);
double dep=RU*T*(z-1)+(T*da-a)*log((z+(1+sq)*B)/(z+(1-sq)*B))/(2*sq*pr_b);
return dep/MOLAR_MASS;
}
static double u_ideal(double T) { return rg*(1.5*T-745.375); }
static double h_ideal(double T) { return rg*(2.5*T-745.375); }
static double temperature_u(double u) { return (u/rg+745.375)/1.5; }
static double temperature_h(double h) { return (h/rg+745.375)/2.5; }
static double pressure_rho(double T,double rho) {
double v=MOLAR_MASS/rho,a,da,dda;attraction(T,&a,&da,&dda);
if(v<=pr_b || T<=0) return NAN;
return RU*T/(v-pr_b)-a/(v*(v+pr_b)+pr_b*(v-pr_b));
}
static NativeGas gas_properties(double m,double U,double V) {
NativeGas g;g.rho=m/V;g.u=U/m;
double T=fmax(temperature_u(g.u),2.2);
for(int i=0;i<16;i++) { double next=fmax(temperature_u(g.u-u_departure(T,g.rho)),2.2);
int done=fabs(next-T)<=1e-10*fmax(T,1);T=next;if(done) break; }
g.T=T;g.p=pressure_rho(T,g.rho);g.h=h_ideal(T)+h_departure(g.p,T);return g;
}
static double temperature_ph(double p,double h) {
double T=fmax(temperature_h(h),2.2);
for(int i=0;i<16;i++) { double next=fmax(temperature_h(h-h_departure(p,T)),2.2);
int done=fabs(next-T)<=1e-10*fmax(T,1);T=next;if(done) break; }return T;
}
static void local_isentropic(double p,double T,double *factor,double *exponent) {
double rho=density(p,T),v=MOLAR_MASS/rho,a,da,dda;attraction(T,&a,&da,&dda);
double d=v*(v+pr_b)+pr_b*(v-pr_b);
double dpT=RU/(v-pr_b)-da/d;
double dpR=(-RU*T/pow(v-pr_b,2)+a*2*(v+pr_b)/(d*d))*(-MOLAR_MASS/(rho*rho));
double cv=1.5*rg+T*dda*log_volume(rho);
double cp=cv+T*dpT*dpT/(rho*rho*dpR),gamma=cp/cv;
*factor=p/(rho*dpR*gamma);*exponent=p*(gamma-1)/(gamma*T*dpT);
}
static double isentropic(double p,double T,double pd) {
double f,e,fd,ed;local_isentropic(p,T,&f,&e);if(pd>=p) return f;
double Td=fmax(T*pow(fmax(pd/p,1e-12),e),2.2);
local_isentropic(fmax(pd,1),Td,&fd,&ed);return .5*(f+fd);
}
static double subsonic_cm(double r,double gamma,double rho,double T,double p) {
return sqrt(fmax(2/(1-gamma)*rho*T/p*(pow(r,2*gamma)-pow(r,1+gamma)),0));
}
static void valve(double p,double pd,double T,double *cm,double *vel) {
p=fmax(p,1);pd=fmax(fmin(pd,p),0);T=fmax(T,1);
double g=fmax(1e-9,fmin(1-1e-9,isentropic(p,T,pd))),rho=fmax(density(p,T),1e-12);
double r=fmax(pd/p,0),critical=pow(2*g/(g+1),1/(1-g)),eff;
if(r<=critical) { eff=critical;*cm=sqrt(2/(1+g)*rho*T/p)*pow(2*g/(g+1),g/(1-g));*vel=sqrt(2/(1+g)*p/rho); }
else { eff=r;*cm=subsonic_cm(r,g,rho,T,p);*vel=sqrt(fmax(2/(1-g)*p/rho*(1-pow(r,1-g)),0)); }
double ref=subsonic_cm(.9999,g,rho,T,p);
if(*cm>0 && ref>0) { double smooth=tanh(fmax(12*fabs(*cm/ref)*log(eff)/log(.9999),0));*cm*=smooth;*vel*=smooth; }
}
int native_gas_init(double p, double T, double volume, double *mU) {
if (!(p > 0 && T >= 2.2 && volume > 0)) return 0;
double rho = density(p, T);
mU[0] = rho * volume;
mU[1] = mU[0] * (u_ideal(T) + u_departure(T, rho));
return isfinite(mU[0]) && isfinite(mU[1]) && mU[0] > 0;
}
int native_gas(double m, double U, double volume, NativeGas *gas) {
if (!(m > 0 && volume > 0) || !isfinite(U)) return 0;
*gas = gas_properties(m, U, volume);
return gas->p > 0 && isfinite(gas->p) && isfinite(gas->h);
}
int native_orifice(double p1, double p2, double h1, double h2,
double cq_area, double opening, double *flow,
double *cm, double *velocity) {
int forward = p1 >= p2;
double p = forward ? p1 : p2, pd = forward ? p2 : p1;
double T = temperature_ph(fmax(p, 1), forward ? h1 : h2);
valve(p, pd, T, cm, velocity);
double sign = forward ? 1 : -1;
*velocity *= sign;
*flow = opening == 0 || fabs(p1-p2) <= 1e-8 ? 0 :
sign * cq_area * opening * fmax(p, 1) * *cm / sqrt(fmax(T, 1));
if (opening == 0) *velocity = 0;
return isfinite(*flow) && isfinite(*cm) && isfinite(*velocity);
}
double native_contact(double penetration, double velocity, double stiffness,
double damping, double pdis, int signed_force) {
if (penetration <= 0) return 0;
double fraction = pdis > 0 ? -expm1(-penetration / pdis) : 1;
double force = stiffness * penetration + fraction * damping * velocity;
return signed_force == 1 ? force : fmax(force, 0);
}
void native_stop_motion(double x, double v, double lower, double upper,
double *acceleration, double *velocity) {
double vt = 1e-12 * fmax(fabs(v), 1);
if ((x <= lower + 1e-12*fmax(fabs(lower),1) && v <= vt && *acceleration <= 0) ||
(x >= upper - 1e-12*fmax(fabs(upper),1) && v >= -vt && *acceleration >= 0)) {
*acceleration = 0;
*velocity = 0;
}
}
double native_signal(double t, double start, int stages, int cyclic, const double *data) {
double elapsed = fmax(t-start,0), duration = 0, offset = 0;
for (int i=0;i<stages;i++) duration += data[16+i];
if (cyclic && duration > 0) elapsed = fmod(elapsed,duration);
for (int i=0;i<stages;i++) {
double d = data[16+i];
if (elapsed < offset+d || i == stages-1)
return d <= 0 ? data[8+i] : data[i] + (elapsed-offset)/d*(data[8+i]-data[i]);
offset += d;
}
return data[8+stages-1];
}
double native_signal_break(double t, double end, double start, int stages,
int cyclic, const double *data) {
double duration=0, offset=0, result=end;
for (int i=0;i<stages;i++) duration += data[16+i];
for (int i=0;i<stages;i++) {
double event=start+offset;
if (cyclic && duration > 0 && event <= t) {
double cycle=fmax(0,floor((t-event)/duration)+1);
event += cycle*duration;
if (event <= t) event += duration;
}
if (event > t) result=fmin(result,event);
offset += data[16+i];
}
return result;
}
static double ideal_temperature(const NativeMedium *m, double energy, double c) {
double delta = energy - c*m->Tref;
if (fabs(m->slope) <= 1e-15) return m->Tref + delta/c;
double root = sqrt(fmax(c*c + 2*m->slope*delta, 0));
double a = (-c+root)/m->slope, b = (-c-root)/m->slope;
return m->Tref + (fabs(a)<=fabs(b) ? a : b);
}
int native_medium_init(const NativeMedium *medium, double p, double T, double V,
int legacy_ideal_initial, double *mU) {
if (!(p>0 && T>0 && V>0)) return 0;
if (medium->real_helium && !legacy_ideal_initial) return native_gas_init(p,T,V,mU);
double mass=p*V/(medium->R*T),dt=T-medium->Tref;
double u=medium->real_helium?u_ideal(T):(medium->cp-medium->R)*T+.5*medium->slope*dt*dt;
mU[0]=mass;mU[1]=mass*u;
return isfinite(mU[0]) && isfinite(mU[1]);
}
double native_density(const NativeMedium *m, double p, double T) {
return m->real_helium ? density(p,T) : p/(m->R*T);
}
double native_temperature_ph(const NativeMedium *m, double p, double h) {
return m->real_helium ? temperature_ph(p,h) : ideal_temperature(m,h,m->cp);
}
double native_viscosity(const NativeMedium *m, double T, int diagnostic) {
if (diagnostic && m->real_helium)
return 1e-7*exp(.7501594*log(T)+35.76324/T-2212.129/(T*T)+.9212635);
return m->mu*pow(T/m->muT,1.5)*(m->muT+m->S)/(T+m->S);
}
int native_medium_gas(const NativeMedium *medium, double m, double U, double V, NativeGas *g) {
if (medium->real_helium) return native_gas(m,U,V,g);
if (!(m>0 && V>0)) return 0;
g->u=U/m; g->rho=m/V;
g->T=ideal_temperature(medium,g->u,medium->cp-medium->R);
g->p=g->rho*medium->R*g->T;
double dt=g->T-medium->Tref;
g->h=medium->cp*g->T+.5*medium->slope*dt*dt;
return g->T>0 && isfinite(g->p) && isfinite(g->h);
}
static void medium_valve(const NativeMedium *m, double p, double pd, double T, double *cm, double *vel) {
if (m->real_helium) { valve(p,pd,T,cm,vel); return; }
p=fmax(p,1); pd=fmax(fmin(pd,p),0); T=fmax(T,1);
double cp=m->cp+m->slope*(T-m->Tref);
double g=fmax(1e-9,fmin(1-1e-9,(cp-m->R)/cp)),rho=fmax(native_density(m,p,T),1e-12);
double r=pd/p,critical=pow(2*g/(g+1),1/(1-g)),eff;
if(r<=critical) { eff=critical;*cm=sqrt(2/(1+g)*rho*T/p)*pow(2*g/(g+1),g/(1-g));*vel=sqrt(2/(1+g)*p/rho); }
else { eff=r;*cm=subsonic_cm(r,g,rho,T,p);*vel=sqrt(fmax(2/(1-g)*p/rho*(1-pow(r,1-g)),0)); }
double ref=subsonic_cm(.9999,g,rho,T,p);
if(*cm>0 && ref>0) { double smooth=tanh(fmax(12*fabs(*cm/ref)*log(eff)/log(.9999),0));*cm*=smooth;*vel*=smooth; }
}
int native_medium_orifice(const NativeMedium *m, double p1, double p2, double h1, double h2,
double area, double opening, double *q, double *cm, double *v) {
double p=fmax(p1,p2),pd=fmin(p1,p2),sign=p1>=p2?1:-1;
double T=fmax(native_temperature_ph(m,fmax(p,1),p1>=p2?h1:h2),1);
medium_valve(m,p,pd,T,cm,v);
*q=fabs(p1-p2)<=1e-8?0:sign*area*opening*fmax(p,1)*(*cm)/sqrt(T);
*v*=fabs(opening)<=1e-12?0:sign;
return isfinite(*q) && isfinite(*cm) && isfinite(*v);
}
static double pipe_friction(double re, double rr) {
if(re<=0) return 64000000;
double lam=64/re;
if(re<=89.96829989) return lam;
double smooth=1/pow(-1.8*log10(6.9/re),2),turb=smooth;
if(rr>0) { double r=re*rr,weight=r*r/(r*r+180*180);turb+=weight*(1/pow(-2*log10(rr/3.7),2)-smooth); }
double trans=pow((re-89.96829989)/2741.96700831,8.37293695);
return lam+trans/(1+trans)*(turb-lam);
}
double native_pipe_flow(const NativeMedium *m, double p1, double p2, double T,
double d, double length, double rr, int kind) {
if(fabs(p1-p2)<=1e-8) return 0;
double p=fmax(fmax(p1,p2),1),pd=fmin(p1,p2),sign=p1>p2?1:-1;
T=fmax(T,1);
double area=PI*d*d/4,mu=native_viscosity(m,T,0),den=PI*d*mu;
if(kind==3) { /* PNL0003: Darcy loss between two stored states. */
double rho=fmax(native_density(m,p,T),1e-12),dp=fabs(p1-p2),lo=0,hi=1e-9;
while(pipe_friction(4*hi/den,rr)*(length/d)*hi*hi/(2*rho*area*area)<dp) {
hi*=10; if(hi>=1000) return sign*1000;
}
for(int i=0;i<48;i++) { double q=.5*(lo+hi);
if(pipe_friction(4*q/den,rr)*(length/d)*q*q/(2*rho*area*area)<dp) lo=q;else hi=q;
}
return sign*.5*(lo+hi);
}
double cm,vel;medium_valve(m,p,pd,T,&cm,&vel);
if(kind==0) {
double lam=pow(area*p*cm,2)/(16*PI*mu*length*T);
if(4*lam/den<=1000) return sign*lam;
}
double base=area*p*cm/sqrt(T),q=sqrt(d/(length*.02))*base;
for(int i=0;i<(kind==0?64:16);i++) {
double next=sqrt(d/(length*pipe_friction(4*fabs(q)/den,rr)))*base;
if(fabs(next-q)<=fmax(1e-12,fabs(q)*1e-9)) return sign*next;
q=.5*(q+next);
}
return sign*q;
}
void native_pipe_diagnostics(const NativeMedium *m, double q, double p, double T,
double d, double length, double rr, int diagnostic, double *r) {
double area=PI*d*d/4,re=4*fabs(q)/(PI*d*native_viscosity(m,T,0)),ff=pipe_friction(re,rr);
r[0]=4*fabs(q)/(PI*d*native_viscosity(m,T,diagnostic));
r[1]=fabs(q)*sqrt(T)/fmax(sqrt(d/(length*ff))*area*p,1e-18);
r[2]=q/(fmax(native_density(m,p,T),1e-12)*area);r[3]=ff;
}
double native_limit_force(double penetration, double velocity, double stiffness,
double damping, double depth, int signed_force) {
if(penetration<=0) return 0;
double force=stiffness*penetration+(depth>0?fmin(penetration/depth,1):1)*damping*velocity;
return signed_force==1?force:fmax(force,0);
}
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