# Plug_Flow_Reactor.m (Source)

```% General_Plug_Flow_Reactor (PFR) - to solve PFR equations for reactors
%
%    This code snippet is to model a constant area and varying area
%    (converging and diverging) nozzle as Plug Flow Reactor with given
%    dimensions and an incoming gas. The pressure is not assumed to be
%    constant here, as opposed to the Python Version of the
%    Plug Flow Reactor model.
%
%    The reactor assumes that the flow follows the Ideal Gas Law.
%
%    The governing equations used in this code can be referenced at:
%    *S.R Turns, An Introduction to Combustion - Concepts and Applications,
%    McGraw Hill Education, India, 2012, 206-210.*
%
%    The current example is written for methane combustion, but can be readily
%    adapted for other chemistries.
%
%    Developed by Ashwin Kumar/Dr.Joseph Meadows (mgak@vt.edu/jwm84@vt.edu) on 3-June-2020
%    Research Assistant/Assistant Professor
%    Advanced Propulsion and Power Laboratory
%    Virginia Tech

%% Clear all variables, close all figures, clear the command line:
clear all
close all
clc

% Temperature of gas, in K
T0 = 1473;
% Pressure of gas, in Pa
P0 = 4.47*101325;

% Equivalence Ratio
Phi = 0.2899;

% Import the gas phase, read out key species indices:
gas_calc = Solution('gri30.yaml');
ich4 = speciesIndex(gas_calc,'CH4');
io2  = speciesIndex(gas_calc,'O2');
in2  = speciesIndex(gas_calc,'N2');
nsp = nSpecies(gas_calc);
x = zeros(nsp,1);

% Change the below values for different Phi values of methane Combustion
x(ich4,1) = Phi;
x(io2,1) = 2.0;
x(in2,1) = 7.52;

% Set the initial state and then equilibrate for a given enthalpy and pressure:
set(gas_calc,'T',T0,'P',P0,'MoleFractions',x);
gas_calc = equilibrate(gas_calc,'HP');

%% Calculation of properties along the reactor length
% The Dimensions and conditions of the reactor are given below

% Inlet Area, in m^2
A_in = 0.018;
% Exit Area, in m^2
A_out = 0.003;
% Length of the reactor, in m
L = 1.284*0.0254;
% The whole reactor is divided into n small reactors
n = 100;
% Mass flow rate into the reactor, in kg/s
mdot_calc = 1.125;

% Flag to indicate whether the area is converging, diverging, or constant:
% k = -1 makes the solver solve for converging area.
% k = +1 makes the solver solve for diverging area.
% k = 0 makes the solver solve for constant cross sectional area
if A_in>A_out
k = -1;
elseif A_out>A_in
k = 1;
else
k = 0;
end

dAdx = abs(A_in-A_out)/L;
% The whole length of the reactor is divided into n small lengths
dx = L/n;

x_calc = 0:dx:L;
nsp = nSpecies(gas_calc);

% Initialize arrays for T, Y, and rho at each location:
T_calc = zeros(length(x_calc),1);
Y_calc = zeros(length(x_calc),nsp);
rho_calc = zeros(length(x_calc),1);

T_calc(1) = temperature(gas_calc);
Y_calc(1,:) = massFractions(gas_calc);
rho_calc(1) = density(gas_calc);

for i = 2:length(x_calc)

%Solver location indicator
fprintf('Solving reactor %d of %d\n', i, length(x_calc))

%--------------------------------------------------------------------------
%------The values of variables at previous location are given as initial---
%------values to the current iteration and the limits of the current-------
%--------------reactor and the gas entering it are being set---------------
%--------------------------------------------------------------------------
inlet_soln(1) = rho_calc(i-1);
inlet_soln(2) = T_calc(i-1);
inlet_soln(3:nsp+2) = Y_calc(i-1,:);
limits = [x_calc(i-1),x_calc(i)];
set(gas_calc,'T',T_calc(i-1),'Density',rho_calc(i-1),'MoleFractions',Y_calc(i-1,:));
options = odeset('RelTol',1.e-10,'AbsTol',1e-10,'InitialStep',1e-8,'NonNegative',1);
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
% These values are passed onto the ode15s solver
[~,y] = ode15s(@PFR_solver,limits,inlet_soln,options,gas_calc,mdot_calc,A_in,dAdx,k);

T_calc(i) = y(end,2);
rho_calc(i) = y(end,1);
Y_calc(i,:) = y(end,3:nsp+2);
end

A_calc = A_in+k.*x_calc*dAdx;
vx_calc = zeros(length(x_calc),1);
R_calc = zeros(length(x_calc),1);
M_calc = zeros(length(x_calc),1);
P_calc = zeros(length(x_calc),1);
for i=1:length(x_calc)
% The gas is set to the solved property values at each location
set(gas_calc,'Temperature',T_calc(i),'Density',rho_calc(i),'MassFractions',Y_calc(i,:));
% Velocity is calculated from Mass flow rate, Area and Density
vx_calc(i) = mdot_calc./(A_calc(i)*rho_calc(i));
% Specific Gas Constant
R_calc(i) = gasconstant()/meanMolecularWeight(gas_calc);
% Mach No. is calculated from local velocity and local speed of sound
M_calc(i) = vx_calc(i)/soundspeed(gas_calc);
% Pressure is calculated from density, temeprature and gas constant
P_calc(i) = rho_calc(i)*R_calc(i)*T_calc(i);
end

%% Plotting
plot(x_calc,M_calc)
xlabel('X-Position (m)')
ylabel('Mach No')
title('Mach No. Variation')
figure(2)
plot(x_calc,A_calc)
xlabel('X-Position (m)')
ylabel('Area (m^2)')
title('Reactor Profile')
figure(3)
plot(x_calc,T_calc)
xlabel('X-Position (m)')
ylabel('Temperature')
title('Temperature Variation')
figure(4)
plot(x_calc,rho_calc)
xlabel('X-Position (m)')
ylabel('Density (kg/m^3)')
title('Density Variation')
figure(5)
plot(x_calc,P_calc)
xlabel('X-Position (m)')
ylabel('Pressure (Pa)')
title('Pressure Variation')
```