Week 2 Air standard Cycle

AIM : To plot PV diagram for otto cylce and find thermal efficiency.

THEORY :

Otto cycle idealizes operation of SI engine consists of following process

• Adiabatic Compression : Pressure increases from p1 to p2 and volume decreases from v1 to v2
• Constant volume heat addition : Pressure increases from p2 to p3
• Adiabatic Expansion : Pressure decreases from p2 to p3 and volume increases from v2 to v3.
• Constant volume heat rejection : Pressure drops down from p3 to p4.

CODING :

Following function was created which was later called in our main coding to find compression volume , expansion volume and based on which compression pressure , expansion pressure were found.

function [v] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)    a = stroke/2;  %crank pin radius   R = con_rod/a; %ratio between connecing rod length and crank pin radius     v_s = (pi/4)*bore^2*stroke;   %stroke volume  v_c = v_s/(cr-1);  %clearance volume    theta = linspace(start_crank,end_crank,180);  term1 = 0.5*(cr-1);   term2 = R+1-cosd(theta);  term3 = (R^2-sind(theta).^2).^0.5;    v = v_c.*(1+term1*(term2-term3));    endfunction

Main Coding

%program to draw air standard cycleclear allclose allclc%inputsgamma = 1.4;t3 = 2900; % temperature in kelvin%state variablesp1 = 101325;t1 = 500; % initial temperature ,temperature in kelvin%engine parametersstroke = 0.1; %stroke lengthbore = 0.1; %bore diametercon_rod = 0.2; %connecting rod lengthcr = 8; %compression ratio of SI engine%swept volume and clearance volumeswept_volume = (pi/4)*bore^2*stroke;clearance_volume = swept_volume/(cr-1);v1 = swept_volume + clearance_volume;v2 = clearance_volume;%state variables at point 2%p1*v1^gamma = p2*v2^gamma%p2 = p1*(v1/v2)^gamma , p1*cr^gammap2 = p1*cr^gamma;%p1v1/t1 = p2v2/t2;t2 = p2*v2*t1/(p1*v1);v_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0) % calling function constant_c = p1*v1^gamma; % since compression is adiabatic process %p_compreesion*v_compression.^gamma = constant_c;p_compression = constant_c./(v_compression.^gamma);%state variables at point 3v3 = v2;p3 = p2*t3/t2;v_expansion = engine_kinematics(bore,stroke,con_rod,cr,0,180) % calling function constant_c1 = p3*v3^gamma; % adiabatic process%p_expansion*v_expansion.^gamma = constant_c1;p_expansion = constant_c1./(v_expansion.^gamma);%state variables at point 4v4 = v1;p4 = p3*(v3/v4)^gamma;%thermal efficiencythermal_efficiency = (1-(1/(cr)^(gamma-1)))*100figure(1)hold onplot([v1 v2 v3 v4],[p1 p2 p3 p4],'*','color','r') % plots state points represented by *plot(v_compression,p_compression,'color','b') % plots adiabatic compression process plot([v2 v3],[p2 p3],'color','r') % plots constant volume heat addition processplot(v_expansion,p_expansion,'color','y') % plots adiabatic expansion process plot([v4 v1],[p4 p1],'color','g')  % plots constant volume heat rejection processlegend('parameter points at different process condition','compression process','heat addition at constant volume process','expansion process','heat rejection at constant volume process') title('pressure variation vs volume change in otto cycle') % provides title to plotxlabel('volume') ylabel('pressure')

PRESSURE VS VOLUME VARIATION PLOT FOR OTTO CYCLE

RESULT :

Thermal efficiency of cycle is found to be 56.472% .This efficiency can be increased by increasing compression ratio .But compression ratio can not be increased beyond one limit because of mechanical limitation and knocking creation.

ERRORS/DIFFICULTIES FACED WHILE CODING

1. Common mistake found was missing of elemental operator

2. Was unable to call function : Found that function and main coding was in different folders.