Question

develop a mathematical model and rate of return code for helical compression first priority used individual which is operated at minus 273 degree centigrade with the help of liquid helium and liquid nitrogen.

write a fortran code for the same

Answer 1

"Properties at the inlet"

To=T1 "since velocity is zero"

Po=P1

"Throat properties"

T_throat=2*To/(k+1)

P_throat=Po*(2/(k+1))^(k/(k-1))

rho_throat=P_throat/(R*T_throat)

"The velocity at the throat is the velocity of sound,"

V_throat=SQRT(k*R*T_throat*1000)

m=rho_throat*A*V_throat

W1_mass=rho_throat*A*V1_throat; V1_throat=SQRT(k*R*T1_throat*1000); T1_throat=2*(To-273)/(k+1) "Using

C for temp"

W2_mass=rho2_throat*A*V_throat; rho2_throat=P1/(R*T1) "Using density at inlet"

k=1.4

Cp=1.005 [kJ/kg-K]

R=0.287 [kJ/kg-K]

"Properties at the inlet"

To=T1 "since velocity is zero"

Po=P1

"Throat properties"

T_throat=2*To/(k+1)

P_throat=Po*(2/(k+1))^(k/(k-1))

"The velocity at the throat is the velocity of sound,"

V_throat=SQRT(k*R*T_throat*1000)

W1_Vthroat=SQRT(k*R*T1*1000) "Using T1 for temperature"

W2_Vthroat=SQRT(k*R*T2_throat*1000); T2_throat=100

w1=HUMRAT(AirH2O,T=T1,P=P,R=RH1)

w2=HUMRAT(AirH2O,T=T2,P=P,R=RH2)

m_water=m_air*(w2-w1)

W1_mv=0 "sine RH = constant"

W2_mv=w2-w1 "Ignoring mass flow rate of air"

W3_mv=RH1*m_air

h1=enthalpy(AirH2O,T=Tdb,P=P1,B=Twb)

v1=volume(AirH2O,T=Tdb,P=P1,B=Twb)

Tdp1=dewpoint(AirH2O,T=Tdb,P=P1,B=Twb)

w1=humrat(AirH2O,T=Tdb,P=P1,B=Twb)

Rh1=relhum(AirH2O,T=Tdb,P=P1,B=Twb)

h2=enthalpy(AirH2O,T=Tdb,P=P2,B=Twb)

v2=volume(AirH2O,T=Tdb,P=P2,B=Twb)

Tdp2=dewpoint(AirH2O,T=Tdb,P=P2,B=Twb)

w2=humrat(AirH2O,T=Tdb,P=P2,B=Twb)

Rh2=relhum(AirH2O,T=Tdb,P=P2,B=Twb)

W1_Wout= - m*Cp_mix*(T22-T1); T22 = (T1-273)*(P2/P1)^((k_mix-1)/k_mix)+273 "Using C for T1 instead of K"

W2_Wout= - m*Cp_mix*(T222-T1); T222 = T1*(P2/P1)^((k_air-1)/k_air)-273; k_air=1.4 "Using k value for air"

W3_Wout= - m*Cp_mix*(T2222-T1); T2222 = T1*P2/P1 "Assuming T to be proportional to P"

W4_Wout= - m*0.5*(Cp_Ar+Cp_He)*(T2-T1) "Using arithmetic average for Cp"

h1=ENTHALPY(R134a,T=T1,P=P1)

Tlow=TEMPERATURE(R134a,h=h1,P=P1+100)

Thigh=TEMPERATURE(R134a,h=h1,P=P1-100)

JT=(Tlow-Thigh)/200