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August 30, 2006, 18:38 |
REAL GAS UDF
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#1 |
Guest
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I'm modeling a blowdown from a high pressure vessel (7 MPa) to ambient conditions, that go through a nozzle at choked conditions. Does anyone know of a way to model the density accurately, accounting for compressibility? Do you have a UDF? Thanks in advance.
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September 1, 2006, 05:19 |
Re: REAL GAS UDF
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#2 |
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There's a Redlich-Kwong Equation of State based UDF available from Fluent UDF archive, which can be used to model real gases. This may help you...
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September 4, 2006, 10:07 |
SRK ?
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#3 |
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Please wich version of fluent contain the SRK equation of state I am searching it to model h2/o2 combustion ???
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September 5, 2006, 01:47 |
Re: SRK ?
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#4 |
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The UDF is available from the UDF archive at fluentusers.com, and it is a Redlich-Kwong Real Gas UDF, the Soave modified version. However, for H2/O2 combustion I doubt that you will need a real gas model. Have you tried to calculate some compressability factors in order to determine the deviation from an ideal gas at you relevant conditions?
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September 6, 2006, 09:32 |
Re: SRK ?
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#5 |
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Dear Skov,
these are my operating conditions GH2 P=70 bars , T = 287 K GO2 P=70 bars , T = 100 K A+ |
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September 6, 2006, 09:47 |
Re: SRK ?
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#6 |
Guest
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What are the respective mole/mass fractions or flow rates -the ratio between H2 and O2.
By the way a real gas model should be available with the coupled solver, thus you do not need to go into UDF modeling of the real gas state... |
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September 11, 2006, 09:23 |
Re: REAL GAS UDF
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#7 |
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hello brian, here is the redlich kwong model if you havent found it..
/* The variables below need to be set for a particular gas */ /* CO2 */ /* REAL GAS EQUATION OF STATE MODEL - BASIC VARIABLES */ /* ALL VARIABLES ARE IN SI UNITS! */ #define RGASU UNIVERSAL_GAS_CONSTANT #define PI 3.141592654 #define MWT 44.01 #define PCRIT 7.3834e6 #define TCRIT 304.21 #define ZCRIT 0.2769 #define VCRIT 2.15517e-3 #define NRK 0.77 /* IDEAL GAS SPECIFIC HEAT CURVE FIT */ #define CC1 453.577 #define CC2 1.65014 #define CC3 -1.24814e-3 #define CC4 3.78201e-7 #define CC5 0.00 /* REFERENCE STATE */ #define P_REF 101325 #define T_REF 288.15 Redlich-Kwong Real Gas UDRGM Code Listing /************************************************** ************/ /* */ /* User-Defined Function: Redlich-Kwong Equation of State */ /* for Real Gas Modeling */ /* */ /* Author: Frank Kelecy */ /* Date: May 2003 */ /* Version: 1.02 */ /* */ /* This implementation is completely general. */ /* Parameters set for CO2. */ /* */ /************************************************** ************/ #include "udf.h" #include "stdio.h" #include "ctype.h" #include "stdarg.h" /* The variables below need to be set for a particular gas */ /* CO2 */ /* REAL GAS EQUATION OF STATE MODEL - BASIC VARIABLES */ /* ALL VARIABLES ARE IN SI UNITS! */ #define RGASU UNIVERSAL_GAS_CONSTANT #define PI 3.141592654 #define MWT 44.01 #define PCRIT 7.3834e6 #define TCRIT 304.21 #define ZCRIT 0.2769 #define VCRIT 2.15517e-3 #define NRK 0.77 /* IDEAL GAS SPECIFIC HEAT CURVE FIT */ #define CC1 453.577 #define CC2 1.65014 #define CC3 -1.24814e-3 #define CC4 3.78201e-7 #define CC5 0.00 /* REFERENCE STATE */ #define P_REF 101325 #define T_REF 288.15 /* OPTIONAL REFERENCE (OFFSET) VALUES FOR ENTHALPY AND ENTROPY */ #define H_REF 0.0 #define S_REF 0.0 static int (*usersMessage)(char *,...); static void (*usersError)(char *,...); /* Static variables associated with Redlich-Kwong Model */ static double rgas, a0, b0, c0, bb, cp_int_ref; DEFINE_ON_DEMAND(I_do_nothing) { /* this is a dummy function to allow us */ /* to use the compiled UDFs utility */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_error */ /*------------------------------------------------------------*/ void RKEOS_error(int err, char *f, char *msg) { if (err) usersError("RKEOS_error (%d) from function: %s\n%s\n",err,f,msg); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_Setup */ /*------------------------------------------------------------*/ void RKEOS_Setup(Domain *domain, char *filename, void (*messagefunc)(char *format, ...), void (*errorfunc)(char *format, ...)) { rgas = RGASU/MWT; a0 = 0.42747*rgas*rgas*TCRIT*TCRIT/PCRIT; b0 = 0.08664*rgas*TCRIT/PCRIT; c0 = rgas*TCRIT/(PCRIT+a0/(VCRIT*(VCRIT+b0)))+b0-VCRIT; bb = b0-c0; cp_int_ref = CC1*log(T_REF)+T_REF*(CC2+ T_REF*(0.5*CC3+T_REF*(0.333333*CC4+0.25*CC5*T_REF) )); usersMessage = messagefunc; usersError = errorfunc; usersMessage("\nLoading Redlich-Kwong Library: %s\n", filename); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_pressure */ /* Returns density given T and density */ /*------------------------------------------------------------*/ double RKEOS_pressure(double temp, double density) { double v = 1./density; double afun = a0*pow(TCRIT/temp,NRK); return rgas*temp/(v-bb)-afun/(v*(v+b0)); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_spvol */ /* Returns specific volume given T and P */ /*------------------------------------------------------------*/ double RKEOS_spvol(double temp, double press) { double a1,a2,a3; double vv,vv1,vv2,vv3; double qq,qq3,sqq,rr,tt,dd; double afun = a0*pow(TCRIT/temp,NRK); a1 = c0-rgas*temp/press; a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a3 = -afun*bb/press; /* Solve cubic equation for specific volume */ qq = (a1*a1-3.*a2)/9.; rr = (2*a1*a1*a1-9.*a1*a2+27.*a3)/54.; qq3 = qq*qq*qq; dd = qq3-rr*rr; /* If dd < 0, then we have one real root */ /* If dd >= 0, then we have three roots -> choose largest root */ if (dd < 0.) { tt = sqrt(-dd)+pow(fabs(rr),0.333333); vv = (tt+qq/tt)-a1/3.; } else { tt = acos(rr/sqrt(qq3)); sqq = sqrt(qq); vv1 = -2.*sqq*cos(tt/3.)-a1/3.; vv2 = -2.*sqq*cos((tt+2.*PI)/3.)-a1/3.; vv3 = -2.*sqq*cos((tt+4.*PI)/3.)-a1/3.; vv = (vv1 > vv2) ? vv1 : vv2; vv = (vv > vv3) ? vv : vv3; } return vv; } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_density */ /* Returns density given T and P */ /*------------------------------------------------------------*/ double RKEOS_density(double temp, double press, double yi[]) { return 1./RKEOS_spvol(temp, press); /* (Kg/m3) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_dvdp */ /* Returns dv/dp given T and rho */ /*------------------------------------------------------------*/ double RKEOS_dvdp(double temp, double density) { double a1,a2,a1p,a2p,a3p,v,press; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; a1 = c0-rgas*temp/press; a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a1p = rgas*temp/(press*press); a2p = a1p*b0-afun/(press*press); a3p = afun*bb/(press*press); return -(a3p+v*(a2p+v*a1p))/(a2+v*(2.*a1+3.*v)); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_dvdt */ /* Returns dv/dT given T and rho */ /*------------------------------------------------------------*/ double RKEOS_dvdt(double temp, double density) { double a1,a2,dadt,a1t,a2t,a3t,v,press; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; dadt = -NRK*afun/temp; a1 = c0-rgas*temp/press; a2 = -(bb*b0+rgas*temp*b0/press-afun/press); a1t = -rgas/press; a2t = a1t*b0+dadt/press; a3t = -dadt*bb/press; return -(a3t+v*(a2t+v*a1t))/(a2+v*(2.*a1+3.*v)); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_Cp_ideal_gas */ /* Returns ideal gas specific heat given T */ /*------------------------------------------------------------*/ double RKEOS_Cp_ideal_gas(double temp) { return (CC1+temp*(CC2+temp*(CC3+temp*(CC4+temp*CC5)))); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_H_ideal_gas */ /* Returns ideal gas specific enthalpy given T */ /*------------------------------------------------------------*/ double RKEOS_H_ideal_gas(double temp) { return temp*(CC1+temp*(0.5*CC2+temp*(0.333333*CC3+ temp*(0.25*CC4+temp*0.2*CC5)))); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_specific_heat */ /* Returns specific heat given T and rho */ /*------------------------------------------------------------*/ double RKEOS_specific_heat(double temp, double density, double yi[]) { double delta_Cp,press,v,dvdt,dadt; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; dvdt = RKEOS_dvdt(temp, density); dadt = -NRK*afun/temp; delta_Cp = press*dvdt-rgas-dadt*(1.+NRK)/b0*log((v+b0)/v) + afun*(1.+NRK)*dvdt/(v*(v+b0)); return RKEOS_Cp_ideal_gas(temp)+delta_Cp; /* (J/Kg-K) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy */ /* Returns specific enthalpy given T and rho */ /*------------------------------------------------------------*/ double RKEOS_enthalpy(double temp, double density, double yi[]) { double delta_h ,press, v; double afun = a0*pow(TCRIT/temp,NRK); press = RKEOS_pressure(temp, density); v = 1./density; delta_h = press*v-rgas*temp-afun*(1+NRK)/b0*log((v+b0)/v); return H_REF+RKEOS_H_ideal_gas(temp)+delta_h; /* (J/Kg) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_entropy */ /* Returns entropy given T and rho */ /*------------------------------------------------------------*/ double RKEOS_entropy(double temp, double density, double yi[]) { double delta_s,v,v0,dadt,cp_integral; double afun = a0*pow(TCRIT/temp,NRK); cp_integral = CC1*log(temp)+temp*(CC2+temp*(0.5*CC3+ temp*(0.333333*CC4+0.25*CC5*temp))) - cp_int_ref; v = 1./density; v0 = rgas*temp/P_REF; dadt = -NRK*afun/temp; delta_s = rgas*log((v-bb)/v0)+dadt/b0*log((v+b0)/v); return S_REF+cp_integral+delta_s; /* (J/Kg-K) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_mw */ /* Returns molecular weight */ /*------------------------------------------------------------*/ double RKEOS_mw(double yi[]) { return MWT; /* (Kg/Kmol) */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_speed_of_sound */ /* Returns s.o.s given T and rho */ /*------------------------------------------------------------*/ double RKEOS_speed_of_sound(double temp, double density, double yi[]) { double cp = RKEOS_specific_heat(temp, density, yi); double dvdt = RKEOS_dvdt(temp, density); double dvdp = RKEOS_dvdp(temp, density); double v = 1./density; double delta_c = -temp*dvdt*dvdt/dvdp; return sqrt(cp/((delta_c-cp)*dvdp))*v; /* m/s */ } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_rho_t */ /*------------------------------------------------------------*/ double RKEOS_rho_t(double temp, double density, double yi[]) { return -density*density*RKEOS_dvdt(temp, density); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_rho_p */ /*------------------------------------------------------------*/ double RKEOS_rho_p(double temp, double density, double yi[]) { return -density*density*RKEOS_dvdp(temp, density); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy_t */ /*------------------------------------------------------------*/ double RKEOS_enthalpy_t(double temp, double density, double yi[]) { return RKEOS_specific_heat(temp, density, yi); } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_enthalpy_p */ /*------------------------------------------------------------*/ double RKEOS_enthalpy_p(double temp, double density, double yi[]) { double v = 1./density; double dvdt = RKEOS_dvdt(temp, density); return v-temp*dvdt; } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_viscosity */ /*------------------------------------------------------------*/ double RKEOS_viscosity(double temp, double density, double yi[]) { double mu,tr,tc,pcatm; tr = temp/TCRIT; tc = TCRIT; pcatm = PCRIT/101325.; mu = 6.3e-7*sqrt(MWT)*pow(pcatm,0.6666)/pow(tc,0.16666)* (pow(tr,1.5)/(tr+0.8)); return mu; } /*------------------------------------------------------------*/ /* FUNCTION: RKEOS_thermal_conductivity */ /*------------------------------------------------------------*/ double RKEOS_thermal_conductivity(double temp, double density, double yi[]) { double cp, mu; cp = RKEOS_Cp_ideal_gas(temp); mu = RKEOS_viscosity(temp, density, yi); return (cp+1.25*rgas)*mu; } /* Export Real Gas Functions to Solver */ UDF_EXPORT RGAS_Functions RealGasFunctionList = { RKEOS_Setup, /* initialize */ RKEOS_density, /* density */ RKEOS_enthalpy, /* enthalpy */ RKEOS_entropy, /* entropy */ RKEOS_specific_heat, /* specific_heat */ RKEOS_mw, /* molecular_weight */ RKEOS_speed_of_sound, /* speed_of_sound */ RKEOS_viscosity, /* viscosity */ RKEOS_thermal_conductivity, /* thermal_conductivity */ RKEOS_rho_t, /* drho/dT |const p */ RKEOS_rho_p, /* drho/dp |const T */ RKEOS_enthalpy_t, /* dh/dT |const p */ RKEOS_enthalpy_p /* dh/dp |const T */ }; |
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