AIR STANDARD CYCLE

Aim : write a program for air standard cycle to plot a pv diagram and calculate thermal efficiency

Introduction :

The Otto cycle is a set of processes used by spark ignition internal combustion engines (2-stroke or 4-stroke cycles). These engines a) ingest a mixture of fuel and air, b) compress it, c) cause it to react, thus effectively adding heat through converting chemical energy into thermal energy, d) expand the combustion products, and then e) eject the combustion products and replace them with a new charge of fuel and air.

1. Intake stroke, gasoline vapor and air drawn into engine (0-1).
2. Compression stroke, p, T increase (1-2).
3. Combustion (spark), short time, essentially constant volume (2-3). Model: heat absorbed from a series of reservoirs at temperatures T2 to T3 .
4. Power stroke: expansion (3-4).
5. Valve exhaust: valve opens, gas escapes.
6. (4-1) Model: rejection of heat to series of reservoirs at temperatures T4to T1 .
7. Exhaust stroke, piston pushes remaining combustion products out of chamber (1-0).

Objective:

1. create pv diagram
2. calculate thermal efficiency

Governing equation:

piston volume `v=1+1/2*(cr-1)*(R + 1- cos(theta)-(R^2 - sind(theta)^2)^(1/2)`

efficiency `eta=(1-1/(cr)^(gamma-1))*100`

Procedure : create the function for piston volume

function [v] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)
   
   a = stroke/2;
   R = con_rod/a;
   
   % swept volume and clearance volume 
   v_swept = (pi/4)*bore^2*stroke;
   v_clearance = v_swept/(cr-1);
   
   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 = (1+term1*(term2-term3)).*v_clearance;
   
end

create the code for plot and calculation

   clear all
   close all
   clc
   
   % Inputs
   gamma = 1.4
   t3 = 2000
   
   % state variables
   p1 = 101325
   t1 = 400
   
   % engine geometric parameters
   bore = 0.2;
   stroke = 0.2;
   con_rod = 0.15;
   cr = 10;
   
   % calculating the swept volume and clearance volume 
   v_swept = (pi/4)*bore^2*stroke;
   v_clearance = v_swept/(cr-1);
   
   v1 = v_swept+ v_clearance;
   v2 = v_clearance;
   
   % state variable at state point 2
   %p2v2^gamma = p1v1^gamma
   %p2 = p1(v1/v2)^gamma = p1*cr^gamma
   p2 = p1*cr^gamma;
   
   %p1v1/t1 = p2v2/t2 | t2 = p2*v2*t1/(p1*v1)
   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 variable at state point 3
   v3 = v2
   
   %p3v3/t3 = p2v2/t2 | p3 = p2*t3/t2
   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 variable at state point 4
   v4 = v1
   
   %p3v3^gamma = p4v4^gamma | p4 = p3(v3/v4)^gamma
   p4 = p3*(v3/v4)^gamma
   
   
   figure(1)
   hold on
   plot(v1,p1,'*','color','r')
   plot(v_compression,p_compression)
   plot(v2,p2,'*','color','r')
   plot(v3,p3,'*','color','r')
   plot(v_expansion,p_expansion)
   plot(v4,p4,'*','color','r')
   plot([v2 v3],[p2 p3],[v4 v1],[p4 p1])
   xlabel('voloume')
   ylabel('pressure')
   
   % calculating thermal efficieny in%
   thermal_efficiency = (1-1/(cr^(gamma-1)))*100
   

result:

plot: PV diagram

thermal efficiency = 60.1893%

Conclution: thus we calculated the thermal efficiency and ploted pv diagram