ODE system for a generic zero-dimensional reactor

Function REACTOR_ODE evaluates the system of ordinary differential equations for a zero-dimensional reactor with arbitrary heat transfer and volume change. Used in ignite.m.

Solution vector components:

y(1):

Total internal energy U

y(2):

Volume V

y(3):

Mass of species 1

….:

y(2+nsp):

Mass of last species

function dydt = reactor_ode(t, y, gas, vdot, area, heatflux)
    [m, n] = size(y);
    dydt = zeros(m, n);

    for j = 1:n
        this_y = y(:, j);
        int_energy = this_y(1);
        vol = this_y(2);
        masses = this_y(3:end);

        % evaluate the total mass, and the specific internal energy and volume.
        total_mass = sum(masses);
        u_mass = int_energy / total_mass;
        v_mass = vol / total_mass;

        % set the state of the gas by specifying (u,v,{Y_k})
        gas.Y = masses;
        gas.UV = {u_mass v_mass};
        p = gas.P;

        % volume equation
        vdt = feval(vdot, t, vol, gas);

        % energy equation
        a = feval(area, t, vol);
        q = feval(heatflux, t, gas);
        udt = -p * vdt + a * q;

        % species equations
        ydt = total_mass * gas.massProdRate;

        % set up column vector for dydt
        dydt(:, j) = [udt
                     vdt
                     ydt'];
    end

end