## Richard Nakka's Experimental Rocketry Web Site

### Technical Notepad #6 -- A24 Ideal Performance Calculations

Note 6

A24 (ANCP) @ 1000 psia chamber pressure

From PROPEP results, for 100 grams mixture: The effective Molecular Weight is given by dividing the number GAS moles into the system mass. Since the system mass is 100 grams: g/mole

Note that this is the proper molecular weight to use in the thermodynamic equations.

The mass fraction of condensed phase is given by the mass of the condensed phase (Al2O3) divided by the system mass

The MW of Al2O3 = 101.96 g/mole, thus A24 propellant @ 1000 psia chamber pressure

Mole fractions and mass fractions for each combustion product are calculated in the table below:  The values for Cp and Cs are obtained from NIST Chemistry WebBook. Units of Cp and Cs are J/mol-K.

The Cp for the gas only products and mixture (gas+condensed) is given by  where ni is the number of moles of gas component i , ns the number of moles of condensed component, n the total number of gas moles. The ratio of specific heats for the mixture, for the gas-only, and for two-phase flow is given by where = 8.314 J/mol-K (universal gas constant).  where y = X /(1-X).
Note that k for two-phase (gas+condensed) flow is a modified form of the gas-only k'. This is the correct form of k to use in the thermodynamic equations involving products with a significant fraction of condensed-phase particles. The value of k given in the PROPEP output (Cp/Cv) is for the mixture.

Note 3

Characteristic exhaust velocity is given by with
To = 2693 K
M = 29.43 kg/kmol
k = 1.159          Note: k for the mixture is the proper value to use, as c* represents a static condition = 8314 J/kmol-K
this gives c* = 1362 m/s (4469 ft/s).

Note 4

The propellant specific impulse is given by the effective exhaust velocity divided by g. with
To = 2693 K
M = 29.43 kg/kmol
k = 1.066          Note: k for 2-phase flow is the proper value to use, as Isp represents a dynamic condition

Thus, ideal Isp = 242 sec.
for standard conditions of Po = 68 atm. (1000 psia) and Pe = 1 atm., and g = 9.806 m/s
(maximum theoretical, assumes frozen equilibrium, and no particle velocity lag or thermal lag).