Otto Cycle Simulation

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GOOD JOB !!!!

But please attach the code using insert code option.

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Code is correct but you have not followed the format as mentioned above.

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Graded by : Mehul Shah

%Creating a function :-%which can provide us how combustion chamber volume changes with change in crank anglefunction [volume] = chamber_volume_calci(bore,stroke,connecting_rod,CR,intial_angle,final_angle)%defining values that theta can havetheta = linspace(intial_angle,final_angle,100); % expression for crank pin radius,R,,swept_volume,clearance_volumecrankpin_radius = stroke/2R = connecting_rod/crankpin_radiusswept_volume = (pi/4)*bore^2*strokeclearance_volume = swept_volume/(CR - 1)%expression that determine  volume trace from  crank angle,parameters%since expression is long so breaking it into partspart_1 = 0.5*(CR-1);part_2 = R + 1 - cosd(theta);part_3 = (R^2 - sind(theta).^2).^0.5;volume = (1 + part_1*(part_2 - part_3)).*clearance_volume;endfunction%Creating PV plot for OTTO CYLCE%Defining Inputs%State variable at 1st state, (process 1->2 is Isentropic Compression)%given P1 = 101325;T1 = 300;gamma = 1.4;% Volume at 1st state is defined by the engine geometric parameters i.e bore,stroke,connecting rod,CR%givenbore = 0.1stroke = 0.1connecting_rod = 0.15CR = 12%With the of help of engine geometric parameters we will calculate swept volume and clearance volumeswept_volume = (pi/4)*bore^2*strokeclearance_volume = swept_volume/(CR - 1)%therfore volume at state 1V1 = swept_volume + clearance_volume%State variable at 2nd state,  (process 2->3 Constant volume heat addition)V2 = clearance_volume%calculating P2%P1*V1^gamma = P2*V2^gammaP2 = P1*(CR^gamma)% CR = compression ratio which is equal to V1/V2% to define temperature at 2 we will use ideal gas equation%(P1*V1)/T1 = (P2*V2)/T2T2 = (P2*V2*T1)/(P1*V1)%including all sets of values of volume that system have during the process 1->2%so as to have curve connection in our plot,according to points that (pressure,volume) have during processconstant_C = P1*V1^gammaV_compressionprocess = chamber_volume_calci(bore,stroke,connecting_rod,CR,180,0);P_compressionprocess = constant_C./(V_compressionprocess.^gamma);%State variable at 3rd state, (process 3->4 Isentropic expansion)%temperature at state 3 in our case will be given to usT3 = 3000V3 = V2%similarly by ideal gas equationP3 = (P2*T3)/T2%including all sets of values of (pressure,volume) that system have during expansion to reach state 4constant_C = P3*V3^gammaV_expansionprocess = chamber_volume_calci(bore,stroke,connecting_rod,CR,0,180);P_expansionprocess = constant_C./(V_expansionprocess.^gamma);%State variable at 4th state (process 4->1 Constant volume heat rejection)%since process from 4->1 is constant volume heat rejection,thereforeV4 = V1%Calculating P4P4 = P3*(V3/V4)^gamma %Calculating T4 T4 = P4*V4*T3/(P3*V3) %Plottingfigure(1)hold onplot(V1,P1,'o','color','m')plot(V_compressionprocess,P_compressionprocess,'color','b')plot(V2,P2,'o','color','m')plot([V2 V3],[P2 P3],'color','b')plot(V3,P3,'o','color','m')plot(V_expansionprocess,P_expansionprocess,'color','b')plot(V4,P4,'o','color','m')plot([V4 V1],[P4 P1],'color','b')xlabel('Volume','color','r')ylabel('Pressure','color','r')grid on%Calculating Thermal Efficiency%formula (1)eta_otto = 1 -((T4 -T1)/(T3-T2))%formula (2)%eta_otto_1 = 1 - (1/(CR^(gamma-1)))%now we will plot graph between Thermal efficiency and CR CR =[1:1:12] eta_otto_efficiency = 1 - (1./(CR.^(gamma-1)))eta_otto_efficiency_percentage = eta_otto_efficiency.*100figure(2)plot(CR,eta_otto_efficiency_percentage)xlabel('Compression Ratio','color','r')ylabel('Thermal Efficiency-OTTO CYLCE','color','r')grid on 

Output;-

P-V plot for Ideal Otto Cycle

#Output Plot between thermal efficiency percentage vs CR(compression ratio)

there are total four processes in an Ideal otto cycle:

1) Isentropic compression (state 1 --> state 2)

during this process , chamber volume does not change in a linear way , this change is accordingly with crank angle so , therefore we get a curve connection in between state 1 and state 2

How volume changes depends on engine geometric parameter and on different values of crank angle when it rotate. To include this in PV plot we have to define a function which provide as an array of values of volume of chamber for different values of crank anlges. (180,0)

2) Constant volume heat addition (state 2 --> state 3)

3)Isentropic Expansion (state 3 --> state 4)

similarly here also we have to again call the defined function to get different sets of values of volume for different angles (0,180)

4)Constant volume heat rejection (state 4 --> state 1 )