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samples/matlab/General_Plug_Flow_Reactor.m

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+% 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 modelling.
+%    
+%    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.*
+%
+
+%% Setting the Gas
+clear all
+close all
+clc
+
+%Temperature of gas
+T0=1473;
+%Pressure of gas
+P0=4.47*101325;
+
+%Equivalence Ratio
+Phi=0.2899;
+
+gas_calc = IdealGasMix('gri30.cti');
+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(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
+A_in = 0.018;
+% Exit Area
+A_out = 0.003;
+% Length of the reactor
+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;
+% 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
+
+% The above values are passed on to the PFR function to solve for density, temperature and Mass fractions
+dAdx = abs(A_in-A_out)/L;
+[T_calc,rho_calc,x_calc,Y_calc] = PFR_setup(A_in,A_out,L,n,k,gas_calc,mdot_calc); 
+A_calc = A_in+k.*x_calc*dAdx;
+for i=1:length(x_calc)
+    gas_after_solving_calc = gas_calc;
+    % The gas is set to the solved property values at each location
+    set(gas_after_solving_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) = 8314/meanMolecularWeight(gas_after_solving_calc);
+    % Mach  No. is calculated from local velocity and local speed of sound
+    M_calc(i) = vx_calc(i)/soundspeed(gas_after_solving_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')

samples/matlab/PFR_setup.m

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+function [T,rho,x,Y] = PFR_setup(A_in,A_out,L,n,k,gas,mdot)
+
+dAdx = abs(A_in-A_out)/L;
+dx = L/n;% The whole length of the reactor is divided into n small lengths
+
+T(1) = temperature(gas);
+P(1) = pressure(gas);
+Y(1,:) = massFractions(gas);    
+rho(1) = density(gas);
+
+x = 0:dx:L;
+
+for i = 2:length(x)
+
+    %Solver location indicator
+    Solving_current_reactor = i
+    Total_reactors = length(x)
+    nsp = nSpecies(gas);
+%--------------------------------------------------------------------------
+%------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---------------
+%--------------------------------------------------------------------------
+    init(1) = rho(i-1);
+    init(2) = T(i-1);
+    init(3:nsp+2) = Y(i-1,:);
+    limits = [x(i-1),x(i)];
+    set(gas,'T',T(i-1),'Density',rho(i-1),'MoleFractions',Y(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,init,options,gas,mdot,A_in,dAdx,k);
+
+    T(i) =y(end,2);
+    rho(i)=y(end,1);
+    Y(i,:)=y(end,3:nsp+2);
+end
+
+
+
+end

samples/matlab/PFR_solver.m

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+function [F] = PFR_solver(x,initial,gas,mdot,A_in,dAdx,k)
+
+rho = initial(1);
+T = initial(2);
+Y = initial(3:length(initial));
+
+if k==1
+    A = A_in+k*dAdx*x;
+elseif k==-1
+    A = A_in+k*dAdx*x;
+    dAdx = -dAdx;
+else
+    A = A_in+k*dAdx*x;
+end
+
+MW_mix = meanMolecularWeight(gas);
+Ru = 8314;
+R = Ru/MW_mix;
+nsp = nSpecies(gas);
+vx = mdot/(rho*A);
+P = rho*R*T;
+
+% the gas is set to the corresponding properties during each iteration of the ode loop
+set(gas,'Temperature',T,'Density',rho,'MassFractions',Y);
+
+
+MW = molecularWeights(gas);
+h = enthalpies_RT(gas).*R.*T;
+w = netProdRates(gas);
+Cp = cp_mass(gas);
+%--------------------------------------------------------------------------
+%---F(1), F(2) and F(3:end) are the differential equations modelling the---
+%---density, temperature and mass fractions variations along a plug flow---
+%-------------------------reactor------------------------------------------
+%--------------------------------------------------------------------------
+F(1)=((1-R/Cp)*((rho*vx)^2)*(1/A)*(dAdx)...
+    + rho*R*sum(MW.*w.*(h-MW_mix*Cp*T./MW))/(vx*Cp) )...
+    / (P*(1+vx^2/(Cp*T)) - rho*vx^2);
+
+F(2) = (vx*vx/(rho*Cp))*F(1) + vx*vx*(1/A)*(dAdx)/Cp...
+    - (1/(vx*rho*Cp))*sum(h.*w.*MW);
+
+F(3:nsp+2) = w(1:nsp).*MW(1:nsp)./(rho*vx);
+
+F = F';
+
+end
+