function [ w_NO ] = BSNOX( T_NO,P_atm,lambda,P_NO,T_BDC,P_BDC,P_EXH) R_u=8315; %Universal Gas Constant psi=3.773; %Molar N/O ratio y=18/8; %Molar H/C ratio (Using Iso-Octane) epsilon=4/(4+y); %y is the molar H/C ratio %Calculate Equilibrium Constant At Given Temperature (Water Gas Shift) K_wgs=exp(2.743-1.761*10^3/T_NO-1.611*10^6/(T_NO^2)+.2803*10^9/(T_NO^3)); %Atom Balance Based On Excess Air Coefficient if 1/lambda<1 n_CO2=epsilon*(1/lambda); n_H2O=2*(1-epsilon)*(1/lambda); n_CO=0; n_H2=0; n_O2=1-(1/lambda); n_N2=psi; n_b= (1-epsilon)*(1/lambda)+1+psi; end if 1/lambda>=1 A=(K_wgs-1); B=-K_wgs*(2*((1/lambda)-1)+epsilon*(1/lambda))+2*(1-epsilon*(1/lambda)); C=2*K_wgs*epsilon*(1/lambda)*((1/lambda)-1); %Watch Quadratic Equation, Moles Must Be Positive! c=(-B-sqrt(B^2-4*A*C))/(2*A); n_CO2=epsilon*(1/lambda)-c; n_H2O=2*(1-epsilon*(1/lambda))+c; n_CO=c; n_H2=2*((1/lambda)-1)-c; n_O2=0; n_N2=psi; n_b = (2-epsilon)*(1/lambda)+psi; end %__________________________________________________________________________ %Calculate Molar Fractions Of Each Constituent Element x_CO2=n_CO2/n_b; x_H2O=n_H2O/n_b; x_CO=n_CO/n_b; x_H2=n_H2/n_b; x_O2=n_O2/n_b; x_N2_e=n_N2/n_b; if 1/lambda>1 n_prod=1.5; z=(T_NO-2.3*10^3)/(7.6*10^2); K_p_CO2 = -.55*z^3+1.5*z^2-3*z+9.1; Z=(T_NO-2.3*10^3)/(7.6*10^2); K_p_CO = -.15*Z^3+.41*Z^2-.92*Z+7.1; K_P=10^(K_p_CO2-K_p_CO); P_p = (((P_EXH/101325)/n_prod)*(T_NO/T_BDC))^(-1); ALPHA= (2*P_p)/(3*K_P^2) + (((P_p/K_P^2 - (4*P_p^2)/(3*K_P^4) + ... (8*P_p^3)/(27*K_P^6))^2 +((4*P_p)/(3*K_P^2) -... (4*P_p^2)/(9*K_P^4))^3)^(1/2) + P_p/K_P^2 - (4*P_p^2)/(3*K_P^4) +... (8*P_p^3)/(27*K_P^6))^(1/3) - ((4*P_p)/(3*K_P^2) - ... (4*P_p^2)/(9*K_P^4))/(((P_p/K_P^2 -(4*P_p^2)/(3*K_P^4) + ... (8*P_p^3)/(27*K_P^6))^2 + ((4*P_p)/(3*K_P^2) - ... (4*P_p^2)/(9*K_P^4))^3)^(1/2) + P_p/K_P^2 - (4*P_p^2)/(3*K_P^4) + ... (8*P_p^3)/(27*K_P^6))^(1/3); x_O2=(ALPHA/(2*n_prod))*(x_CO2*((1-ALPHA)/n_prod)); %x_CO=x_CO+(ALPHA/n_prod); end %Calculate Equilibrium Concentrations X_O2_e=x_O2*P_BDC/(R_u*T_NO); %__________________________________________________________________________ %Equilibrium Constant For O2 to Oxygen Reaction Kp_7=3.6*10^3*exp(-31090/T_NO)*318.3; %318.3 converts atm^(1/2) to pa^(1/2) x_O_e= (Kp_7*X_O2_e^(1/2))/((R_u*T_NO)^(1/2))/(P_BDC/(R_u*T_NO)); %kmol/m^3 %The Forward Reaction Rate Constant (m^3/kmol-s) k_1f=1.82*10^11*exp(-38370/T_NO); %Calculate Change in NO Concentration as Function of Time dNOdt=2*k_1f*x_O_e*x_N2_e*P_BDC/(R_u*T_NO); %Calculate residence time t_NO=(8*10^(-16)*T_NO*exp(58300/T_NO))/(P_NO/101325)^(1/2); %Calculate NO PPM PPM_NO = dNOdt*t_NO*10^6; %__________________________________________________________________________ %Converting to mass fractions of constituents: m_CO2=x_CO2*(44.01); m_H2O=x_H2O*(18.015); m_CO=x_CO*(28.01); m_H2=x_H2*(2.01); m_O2=x_O2*32; m_N2_e=x_N2_e*28; %Adding mass fractions of all constituents: m_all=m_CO2+m_H2O+m_CO+m_H2+m_O2+m_N2_e; %Calculating mass fraction of NO: w_NO=dNOdt*t_NO*30.01/m_all; end