Component 614: Ideal Gas Nozzle by HVACSIM+
General Description
Component 614 models a convergent nozzle for any ideal gas and assumes
the nozzle to be isentropic, adiabatic, and without condensation. The model
calculates a mass flow rate and exit temperature given the upstream stagnation
pressure and temperature and the downstream pressure. The model uses absolute
pressures internally, but allows the input and output pressure to be gage
pressures. The second parameter is the absolute pressure corresponding to zero
gage pressure. The third and fourth parameters specify properties of the ideal
gas.
Nomenclature
A - nozzle exit cross sectional area
P - pressure
T - temperature
w - mass flow rate
y - specific heat ratio, Cp/Cv
Subscripts
c - critical
e - exit
o - stagnation
Mathematical Description
The two input pressures are first converted from gage to absolute
pressures by addition of the second parameter, which represents the absolute
pressure corresponding to zero gage pressure. The critical pressure ratio is
then defined as:
Pc = C1^(-C2)
where
C1 = 2/(1 + y)
C2 = y/(1 - y)
The method used to determine the flow rate depends on the critical pressure
ratio and on another pressure ratio, Ra:
Ra = Pe/Po
The maximum flow rate is obtained when the pressure ratio, Ra, is less than or
equal to the critical pressure ratio:
w = 1000*A*Po*[(y*C1^(C2*C3)) / (R*To)]^0.5
where
C3 = (1 + y)/y
Otherwise, the flow rate is defined by
w = 1000*A*Po*[(2*C2*{Ra^(C1*C3) - Ra^C3}) / (R*To)]^0.5
Lastly, the exit temperature is defined by the following equation:
Te = To*Ra^(-1/C2)
Component 614 Configuration
Inputs Description
1 Po - upstream stagnation pressure (kPa, gage)
2 Pe - downstream pressure (kPa, gage)
3 To - stagnation temperature (C)
Outputs Description
1 w - mass flow rate (kg/s)
2 Te - exit temperature (C)
Parameters Description
1 A - nozzle exit cross sectional area (m^2)
2 Pr - absolute pressure corresponding to zero
gage pressure (kPa)
3 y - ratio of specific heats ( - )
4 R - gas constant per unit mass (J/kg-K)
Reference:
1. HVACSIM+ Building Systems and Equipment Simulation Program Reference
Manual (NBSIR 84-2996)
Daniel R. Clark
United States Department of Commerce
National Institute of Standards and Technology
Gaithersburg, Maryland 20899-0001