Trouble using ODE45 for coupled non-linear differential equation
Hi,
I am attempting to model the back filling of a large vacuum vessel with Nitrogen. The flow of the Nitrogen is controlled by the valve with a certain valve flow coefficient. P2 is constant and approximately one atmosphere. I have derivived the following equations to model this.
So I wrote the following code with ODE45 to monitor the pressure over time.
% IC Vector
IC_BF = [P01, Q0, dP0, dQ0];
t = [0 10];
options = odeset(‘RelTol’,1e-12 );
[t_ode45,Result] = ode45(@BF_dyn, t, IC_BF, options)
function result = BF_dyn(t, x)
% Constants
delta_P0 = 6894.76; % Pa
P01 = 1.33322e-5; % pa
dP01 =0; % Pa
R = 8.314; % J / mol·K
C_v = 0.28*(6.309e-5/1); % (gallons/min) ( 6.309e-5 (m^3/s)/ 1 (gallons/min)) = m^3/s
Tamb = 293; % K
G = 0.967;
dewar_vol = 4.4; % m^3
rho_N2 = 1.25; %kg/m^3
M_N2 = 28.02*(1/1000); % g/mol * (1 kg/1000g) = kg/mol
P02 = 6894.76; % Pa
b = (sqrt(G)/(C_v))^2;
a = rho_N2*R*Tamb/(M_N2*dewar_vol);
result = [
-2*x(2)*x(4)*b;
(1/a)*x(4);
x(3);
x(4);
];
end
However, when I plot the results I get the following, which goes significantly higher than P2 before attempting to go negative when in reality it should asymptote out to P2.
Am I implement this system into ODE45 wrong? Is there any way to incorporate the realtionship between P1 and P2 into ODE45 by adding additional arguement to my results vector?
Thank you for any assistance you can offer!Hi,
I am attempting to model the back filling of a large vacuum vessel with Nitrogen. The flow of the Nitrogen is controlled by the valve with a certain valve flow coefficient. P2 is constant and approximately one atmosphere. I have derivived the following equations to model this.
So I wrote the following code with ODE45 to monitor the pressure over time.
% IC Vector
IC_BF = [P01, Q0, dP0, dQ0];
t = [0 10];
options = odeset(‘RelTol’,1e-12 );
[t_ode45,Result] = ode45(@BF_dyn, t, IC_BF, options)
function result = BF_dyn(t, x)
% Constants
delta_P0 = 6894.76; % Pa
P01 = 1.33322e-5; % pa
dP01 =0; % Pa
R = 8.314; % J / mol·K
C_v = 0.28*(6.309e-5/1); % (gallons/min) ( 6.309e-5 (m^3/s)/ 1 (gallons/min)) = m^3/s
Tamb = 293; % K
G = 0.967;
dewar_vol = 4.4; % m^3
rho_N2 = 1.25; %kg/m^3
M_N2 = 28.02*(1/1000); % g/mol * (1 kg/1000g) = kg/mol
P02 = 6894.76; % Pa
b = (sqrt(G)/(C_v))^2;
a = rho_N2*R*Tamb/(M_N2*dewar_vol);
result = [
-2*x(2)*x(4)*b;
(1/a)*x(4);
x(3);
x(4);
];
end
However, when I plot the results I get the following, which goes significantly higher than P2 before attempting to go negative when in reality it should asymptote out to P2.
Am I implement this system into ODE45 wrong? Is there any way to incorporate the realtionship between P1 and P2 into ODE45 by adding additional arguement to my results vector?
Thank you for any assistance you can offer! Hi,
I am attempting to model the back filling of a large vacuum vessel with Nitrogen. The flow of the Nitrogen is controlled by the valve with a certain valve flow coefficient. P2 is constant and approximately one atmosphere. I have derivived the following equations to model this.
So I wrote the following code with ODE45 to monitor the pressure over time.
% IC Vector
IC_BF = [P01, Q0, dP0, dQ0];
t = [0 10];
options = odeset(‘RelTol’,1e-12 );
[t_ode45,Result] = ode45(@BF_dyn, t, IC_BF, options)
function result = BF_dyn(t, x)
% Constants
delta_P0 = 6894.76; % Pa
P01 = 1.33322e-5; % pa
dP01 =0; % Pa
R = 8.314; % J / mol·K
C_v = 0.28*(6.309e-5/1); % (gallons/min) ( 6.309e-5 (m^3/s)/ 1 (gallons/min)) = m^3/s
Tamb = 293; % K
G = 0.967;
dewar_vol = 4.4; % m^3
rho_N2 = 1.25; %kg/m^3
M_N2 = 28.02*(1/1000); % g/mol * (1 kg/1000g) = kg/mol
P02 = 6894.76; % Pa
b = (sqrt(G)/(C_v))^2;
a = rho_N2*R*Tamb/(M_N2*dewar_vol);
result = [
-2*x(2)*x(4)*b;
(1/a)*x(4);
x(3);
x(4);
];
end
However, when I plot the results I get the following, which goes significantly higher than P2 before attempting to go negative when in reality it should asymptote out to P2.
Am I implement this system into ODE45 wrong? Is there any way to incorporate the realtionship between P1 and P2 into ODE45 by adding additional arguement to my results vector?
Thank you for any assistance you can offer! ode45 MATLAB Answers — New Questions
