Week 2 Air standard Cycle
*********** Comments by Grader ************
1. The formula for thermal efficiency is wrong. The correct formula is, '1 - (1/cr^(gamma - 1))'.
Marks have been deducted for the above reason.
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At first I defined the values of inputs (gamma,t3). Then the state variables (p1,t1) and Engine Geometric Parameter (bore,stroke,connecting rod,Compression Ratio).
After the I defined the formulas to calculate swept volume,clearance volume ,volume 1 volume 2.
Then for calculating the values for the second point in the otto cycle i defined the formulas for p2,t2,V_Compression and P_Compression. As the engine is in Compression cycle i gave the value stroke from 180 to 0.
Next for state variable 3, I defined the value of v3 and p3.Then I defined the formula to calculate the value for V_Expansion and P_Expansion.
Finally I defined the value of v4 and formula for p4.
Then I plotted the four points with red color. After that I used plot command to connect the first and second point using two arrays P_compression and V_Compression. Next I connected the 2nd and the third point with a vertical line as there is no change in the volume. Then i connected the 3rd and 4th point using the function to indicate volume is expanding. Then I connected the 4th and 1st point with a vertical line indicating that there is no change in the volume.Then I labelled the x and y axis with volume and pressure.
Then to calculate the thermal efficiency of the engine I used the formula
Where r is the compression ratio and γ is the specific heat ratio of the gas in the combustion chamber. As the value of γ for combustion products of the fuel/air mixture is often taken as approximately 1.3.I defined it as 1.3 and calculated thermal efficiency as 52.55%.
In the main Program I called a function named as engine_kinematics.
In the program of the function, I first defined the values of bore,stroke,compression ratio and the connecting rod.Then I defined the formulas to claculate crank pin radius and R. After that I defined the formulas to calculate swept volume and clearance volume. Then to defined the theta value I used a linspace command and defined from 0 to 720 with 720 no of divisions.
Finally to calculate the volume of compression I defined the final formula. I spilt the final formula into three terms and finally calculated the value of compression volume.
The error that I faced during this particular task is shown in the below image.
I searched online for the problem. I found out that while a function runs it has return some output but due to use of clear all command in the start of the command it did'nt return any value. So I deleated the first three lines and rectified the program.
clear allclose allclc%Otto Cycle%Input gamma = 1.4;t3 = 2300;%State Variablesp1 = 101325;t1 = 500;%Engine Geometric Parametersbore = 0.1;stroke = 0.1;con_rod = 0.15;cr = 12;%Calculating Swept and Clerance Volumev_swept = (pi/4)*bore^2*stroke;v_clearance = v_swept/(cr-1);v1 = v_swept + v_clearance;v2 = v_clearance;%State Variables for at state point 2p2 = p1*cr^gamma;t2 = p2*v2*t1/(p1*v1);constant_c = p1*v1^gamma;V_Compression = engine_kinematics (bore,stroke,con_rod,cr,180,0);P_Compression = constant_c./V_Compression.^gamma;%State Variables for at state point 3v3 = v2;p3 = (p2*t3)/t2;constant_c = p3*v3^gamma;V_Expansion = engine_kinematics (bore,stroke,con_rod,cr,0,180);P_Expansion = constant_c./V_Expansion.^gamma;%State Variables for at state point 4v4 = v1;p4 = p3*(v3/v4)^gamma;figure(1)hold onplot(v1,p1,'*','color','r');plot(V_Compression,P_Compression,'color','b');plot(v2,p2,'*','color','r');plot(v3,p3,'*','color','r');plot(V_Expansion,P_Expansion,'color','b');plot(v4,p4,'*','color','r');plot([v2 v3 ],[p2 p3],'color','b');plot([v4 v1 ],[p4 p1],'color','b');xlabel('Volume')ylabel('Pressure')specific_heat_ratio = 1.3;term1 = specific_heat_ratio-1;term2 = 1/cr^term1;Thermal_Efficiency = 1 - term2;% Defining a funcition for calcuating Volume of Compressionfunction [V_Compression] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)bore = 0.1;stroke = 0.1;con_rod = 0.15;cr = 12;a = stroke/2;R = con_rod/a;v_s = (pi/4)*bore^2*stroke;v_c = v_s/(cr-1);theta = linspace(0,720,720);term1 = 0.5*(cr-1);term2 = R+1- cosd(theta);term3 = (R^2 - sind(theta).^2).^0.5;V_Compression = (1+term1*(term2-term3)).*v_c;end