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periodic_cstr.m

function periodic_cstr
%
%  Periodic CSTR
%
%  This example illustrates a CSTR with steady inputs but periodic
%  interior state.  A stoichiometric hydrogen/oxygen mixture is
%  introduced and reacts to produce water.  But since water has a
%  large efficiency as a third body in the chain termination reaction
%
%         H + O2 + M = HO2 + M
%
%  as soon as a significant amount of water is produced the reaction
%  stops. After enough time has passed that the water is exhausted from
%  the reactor, the mixture explodes again and the process
%  repeats. This explanation can be verified by decreasing the rate for
%  reaction 7 in file 'h2o2.cti' and re-running the example.
%
%  Acknowledgments: The idea for this example and an estimate of the
%  conditions needed to see the oscillations came from Bob Kee,
%  Colorado School of Mines
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

help periodic_cstr

% create the gas mixture
gas = IdealGasMix('h2o2.cti');

% pressure = 60 Torr, T = 770 K
p = 60.0*133.3;
t = 770.0;

OneAtm = 1.01325e5;

set(gas,'T', 300.0, 'P', p, 'X', 'H2:2, O2:1');


% create an upstream reservoir that will supply the reactor.  The
% temperature, pressure, and composition of the upstream reservoir are
% set to those of the 'gas' object at the time the reservoir is
% created.
upstream = Reservoir(gas);


% Now set the gas to the initial temperature of the reactor, and create
% the reactor object.
set(gas, 'T', t, 'P', p);
cstr = IdealGasReactor(gas);

% Set its volume to 10 cm^3. In this problem, the reactor volume is
% fixed, so the initial volume is the volume at all later times.
setInitialVolume(cstr, 10.0*1.0e-6);


% We need to have heat loss to see the oscillations. Create a
% reservoir to represent the environment, and initialize its
% temperature to the reactor temperature.
env = Reservoir(gas);


% Create a heat-conducting wall between the reactor and the
% environment. Set its area, and its overall heat transfer
% coefficient. Larger U causes the reactor to be closer to isothermal.
% If U is too small, the gas ignites, and the temperature spikes and
% stays high.
w = Wall;
install(w, cstr, env);
setArea(w, 1.0);
setHeatTransferCoeff(w, 0.02);


% Connect the upstream reservoir to the reactor with a mass flow
% controller (constant mdot). Set the mass flow rate to 1.25 sccm.
sccm = 1.25;
vdot = sccm * 1.0e-6/60.0 * ((OneAtm / pressure(gas)) * ( temperature(gas) / 273.15));  % m^3/s
mdot = density(gas) * vdot;   % kg/s
mfc = MassFlowController;
install(mfc, upstream, cstr);
setMassFlowRate(mfc, mdot);


% now create a downstream reservoir to exhaust into.
downstream = Reservoir(gas);


% connect the reactor to the downstream reservoir with a valve, and
% set the coefficient sufficiently large to keep the reactor pressure
% close to the downstream pressure of 60 Torr.
v = Valve;
install(v, cstr, downstream);
setValveCoeff(v, 1.0e-9);

% create the network
network = ReactorNet({cstr});

% now integrate in time
tme = 0.0;
dt   = 0.1;

n = 0;
while tme < 300.0
    n = n + 1;
    tme = tme + dt;
    advance(network, tme);
    tm(n) = tme;
    y(1,n) = massFraction(cstr,'H2');
    y(2,n) = massFraction(cstr,'O2');    
    y(3,n) = massFraction(cstr,'H2O');    
end
clf
figure(1)
plot(tm,y)
legend('H2','O2','H2O')
title('Mass Fractions')