quasar:nozzle_design

I successfully (at least I believe it works) made simple MatLab script which calculates key conical nozzle parameters with input of:

- Combustion chamber temperature and pressure
- Gas properties (Molecular mass and cp/cv coefficient)
- Ambient pressure
- Half angle of nozzle
- Combustion products flow rate.

All these values are calculated under following assumptions:

- Working gas is homogeneous
- All combustion products are gaseous
- Working gas is a perfect gas
- Flow is adiabatic
- Friction and boundary layer effects are neglected
- There are no shock waves or discontinuities in the nozzle flow
- Flow is steady.
- All gases at the exhaust have axially directed velocity
- Gas pressure, velocity, temperature and density are uniform across any section normal to the nozzle axis.
- Flow is frozen i.e. there is no change in gas composition during nozzle expansion

(All theory is taken from a lovely book “Rocket Propulsion Elements” by G.P. Sutton and O. Biblarz)

Here is a code:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Nozzle and gas properties definitions (You need to fill this section, User!)%% T1 = 2000; % Combustion chamber temperature [K] p1 = 2 * 10^6; % Combustion chamber pressure [Pa] k = 1.3; % cp/cv of the gas miu = 16; % Molar mass of gas [kg/kmol] p2 = 10^5; % Ambient pressure [Pa] mdot = 0.1028; % Mass flow rate [kg/s] alpha = 15 * pi/180; % half angle of the conical nozzle %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Key preformance parameters equations (Just lots of equations) %% R = 8314.3 / miu; disp ('Supersonic throat condition') condition = p1/p2 - ((k+1)/2)^(k/(k-1)) disp ('All calculations are valid only if above number is positive') disp ('Throat area') At = mdot * (p1 * k * sqrt( (2/(k+1)) ^ ((k+1)/(k-1)) / (k * R * T1)))^(-1) disp (' Throat temperature [K]') Tt = 2* T1 /(k+1) disp('Ratio of exit to throat area') epsilon = (((k+1)/2)^(1/(k-1)) * (p2/p1)^(1/k) * sqrt( (k+1)/(k-1) * (1-(p2/p1)^((k-1)/k))) )^(-1) disp ('Exit area [m^2]') A2= epsilon * At % Exit area [m^2] disp ('Nozzle lenght [m]') L = cot(alpha) * sqrt(At/pi) * (sqrt(epsilon)-1) % Nozzle lenght [m] disp ('Exit velocity [m/s]') v2 = sqrt ( 2*k /(k-1) * R * T1 * (1 - (p2/p1)^((k-1)/k) ) ) disp ('Total Theoretical Thrust [N]') F = mdot * v2 disp ('Theoretical Specific Impulse') Is = v2/9.81 %% End of the script %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

quasar/nozzle_design.txt · Last modified: 2012/10/25 21:50 (external edit)