## Richard Nakka's Experimental Rocketry Web Site

### Technical Notepad #1 -- KNSU Ideal Performance Calculations

Note 1

Potassium Nitrate -Sucrose 65/35 O/F ratio @ 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 (K2CO3) divided by the system mass

The MW of K2CO3 = 138.21 g/mole, thus

KN-Sucrose 65/35 O/F ratio @ 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 taken from the JANAF Thermochemical Tables and NIST Chemistry WebBook.

Note that the highlighted range (yellow) is applicable for interpolation of the values at 1720 K, the chamber combustion temperature under consideration.

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 = 1720 K
M = 41.98 kg/kmol
k = 1.133          Note: k for the mixture is the proper value to use, as c* represents a static condition
= 8314 J/kmol-K
this gives c* = 919 m/s (3014 ft/s).

Note 4

The propellant specific impulse is given by the effective exhaust velocity divided by g.

with
To = 1720 K
M = 41.98 kg/kmol
k = 1.0437          Note: k for 2-phase flow is the proper value to use, as Isp represents a dynamic condition

Thus, Isp = 166 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).