Air standard cycle
https://drive.google.com/file/d/1NyacFHnRz8ESzNLY_JX7dpBl_jJ9fD-0/view?usp=sharing
Objective
1.To solve an otto cycle and make plots for it.
2.To find the thermal efficiency of the engine.
Introduction
Otto cycle The Otto Cycle is named after Nikolaus Otto (1832–1891, German) who is credited as the first creator of a petroleum
fuel based internal combustion engine operating under a four stroke cycle. Otto’s engine work during the eve of the industrial
revolution was a critical development leading to the dawn of the automotive
industry in the late 19th century.
Theory
The Otto cycle is the ideal cycle for spark-ignition reciprocating engines. The name come from Nikolaus A.
Otto who built a successful four-stroke engine in 1876 in Germany using the cycle proposed by Frenchman
Beau de Rochas in 1862.
A four-stroke engine is an internal combustion (IC) engine in which the piston completes four separate
strokes. A stroke refers to the full travel of the piston along the cylinder in one of the two reciprocal
directions. The four separate strokes are termed and described as follows:
1. Intake stroke: In this stroke, the intake valve must be in the open position while the piston pulls an
air-fuel mixture into the cylinder by producing below-atmospheric pressure inside the chamber
through its downward motion.
2. Compression stroke: In this stroke the piston compresses the air-fuel mixture in preparation for
ignition during the next stroke. Both the intake and exhaust valves are closed during this stage.
3. Power (Expansion stroke): While the piston is at the end of the compression stroke, the compressed
air-fuel mixture is ignited by a spark plug. The hot combustion gases expand and forcefully return the
piston to the bottom position.
4. Exhaust stroke: During the exhaust stroke, the piston expels the spent air-fuel mixture while the
exhaust valve is open through its upward motion.
Contents
1.pressure is denoted by p1,p2,p3,p4.
2.temperature is denoted by t1,t2,t3,t4.
3.swept_volume-the volume through which a piston or plunger moves as it makes a stroke.
4.clearance volume-The clearance volume is the volume remaining above the piston of an engine when it reaches top dead center.
The maximum compression pressure in the piston is controlled by the clearance volume
Engine geometric parameters
1. bore - An engine's bore is the diameter of each cylinder
2.stroke-stroke is the distance within the cylinder the piston travels.
3.connecting rod- A connecting rod is the part of a piston engine which connects the piston to the crankshaft.
4.compression ratio-The compression ratio is calculated as the ratio between the maximum (total)
volume of the cylinder (when the piston is at BDC) and the minimum (clearance) volume (when the piston is as TDC).
program solution
%program to solve an otto cycle
%p1,p2,p3,p4 are pressures
%t1,t2,t3,t4 are temperatures
%Inputs
t1=500;
gamma=1.4;
%state variables at point 1
p1=101325;
t3=2300;
%engine geometric parameters
bore=0.1;
stroke=0.1;
con_rod=0.15; %connecting rod
cr=12; %compression ratio
%formula to calculate swept volume
%swept volume = v_swept
v_swept=(pi/4)*bore^2*stroke;
%formula to calculate clearance volume
%clearance volume = v_clearance
v_clearance=v_swept/(cr-1);
v1=v_swept+v_clearance; %formula to calculate v1
v2=v_clearance; %formula to calculate v2
%state variables at state point 2
%below are equations due to isentropic compression
%P2v2^gamma=P1v1^gamma
%P2=P1*(v1/v2)^gamma=P1*cr^gamma
%using P2 and P1 relation we get,
p2=p1*cr^gamma; %formula to calculate P2
%p1v1/t1=p2v2/t2 | t2= p2*v2*t1/(p1*v1)
t2=p2*v2*t1/(p1*v1); %formula to calculate T2
%when i am using these three lines for compression ,graph is not showing curve
%but a straight line so i have deleted these lines from my code and made them comment
%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 at state point 3
v3=v2;
p3=p2*t3/t2;
%when i am using these three lines for expansion ,graph is not showing curve
%but a straight line so i have deleted these lines from my code and made them comment
%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 at state point 4
v4=v1;
p4=p3*(v3/v4)^gamma;
t4=(p4*v4*t3)/(p3*v3);
%thermal efficiency
efficiency=1-1/cr^(gamma-1); %formula to calculate thermal effiency
figure(1)
hold on %Use hold on to add a second line plot without deleting the existing line plot.
plot(v1,p1,'*','color','r') %plotting the red color * on the specific point
plot(v_compression, p_compression) %for making a curve of isentropic compression
plot(v2,p2,'*','color','r') %plotting the red color * on the specific point
plot([v2 v3],[p2 p3],'color','r'); %for joining the points
plot(v3,p3,'*','color','r') %plotting the red color * on the specific point
plot(v_expansion, p_expansion)%for making a curve of isentropic expansion
plot(v4,p4,'*','color','r') %plotting the red color * on the specific point
plot([v1 v4],[p1 p4],'color','r') %for joining the points
xlabel('volume' )
ylabel('pressure')
figure(2)
plot([v1 v2 v3 v4 v1], [p1 p2 p3 p4 p1],'color','b') %to connect all points
%function file i am not able to insert it otherwise
function [V] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)
a=stroke/2;
R=con_rod/a;
v_s=(pi/4)*bore^2*stroke;
v_c= v_s/(cr-1);
theta=linspace(start_crank,end_crank,100);
term1=0.5*(cr-1);
term2=R+1-cosd(theta);
term3=(R^2-sind(theta).^2).^0.5;
V=(1+term1*(term2-term3)).* v_c;
plot(theta,V,'linewidth',3)
end
conclusion
1.by doing this project we have found how the the pressure,volume changes in otto cycle.
2.we have also found the thermal effiency.https://drive.google.com/file/d/1NyacFHnRz8ESzNLY_JX7dpBl_jJ9fD-0/view?usp=sharing