how to plot the motor chamber pressure and the vacuum thrust as a function of both time and web assuming quasi-steady state (equilibrium)

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Christina Reid
Christina Reid 2021년 1월 24일
답변: Gaurav Garg 2021년 2월 23일
I have computed the equilibrium pressure assuming a quasi steady state condition: using the following eq attached to this question and below is my code. How do I plot Pc_eq as a function of time?
clear all
%% Step 1
% ========================================================================= %
% Basing on the motor and propellant data indicated in Table 1 and on the
% burning surface evolution shown in Figs. 5 and 6 and assuming a constant
% chambre temperature profile compute the following curves without taking
% into account the non-ideal parameters.
%% Step 1.1
%Find: The motor chamber pressure and the vaccume thrust as a
% function of both time and web assuming quasi-steady state (equilibrium)
% User inputs - First stage P80 SRM
% ========================================================================= %
mp = 88000; % Propellant Mass [kg]
ms = 7330; % Structural mass [kg]
l = 10.6; % length [m]
d = 3.0; % Diameter [m]
f = 3015; % Max thrust(vaccum) [kN]
bt = 110; % Buring time [sec]
isp = 280; % Specifi Impulse (vaccuum) [sec]
% User inputs - Propellant Ballistic Properties
% ========================================================================= %
a = 1.847e-05; % Temperature coefficient @ 300 K [m/s * Pae-0.4]
n = 0.4; % Combustion index
tau = 0.0015; % Temperature sensitivity [k^-1]
rho = 1790; % Density [kg/m^3]
% User inputs - Propellant thermochemocal properties
% ========================================================================= %
T_F = 3550; % Flame temperature [K]
M = 29; % Molecular mass [kg/kmole]
gamma = 1.13; % Specific heat ratio
% User inputs - Motor geometrical properties
% ========================================================================= %
d_throat = 0.496; % Throat diameter [m]
e = 16; % expansion ratio
v_c = 8.6; % Initial chamber volume [m^3]
v_frac = 0.85; % volumetric loading fraction (V_c/(V_c+V_p)
% constants
% ========================================================================= %
r = 8314.5 % gas constant [J/kmol)
% Calculations
% Find: The motor chamber pressure and the vaccum thrust as a
% ========================================================================= %
a_t = pi* (d_throat/2)^2; % Thrat area [m^2]
m_dot = mp/bt; % mass flow rate [kg/s]
s_b = 48; % burning surface area - pulled from the Sb vs Y plot [m^2]
cap_gamma = sqrt (gamma * (2/(gamma + 1))^((gamma+1)/(gamma-1))); % capital gamma
c_star = (1/cap_gamma)*sqrt((r*T_F)/M);
K = s_b/a_t; % Klemmung
Pc_eq = (a *rho*c_star*K)^(1/(1-n));
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Christina Reid
Christina Reid 2021년 1월 24일
Hi again Mishca,
I actually added an attachment which explains PC_eq dependecy. The variable,y, being the web thickness = 1.09.

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Gaurav Garg
Gaurav Garg 2021년 2월 23일
Hi Christina,
The variable Pc_eq is a scalar value, in your case. You need to have a vector in order to plot it.
Moreover, your equation doesn't seem to have any time dependency.
So, I would suggest you to rewrite the code and give the variables you want to plot, some dependency over time and then use plot funciton.

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