AIR STANDARD CYCLE USING OTTO CYCLE IN MATLAB
OTTO CYCLE:
The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat. The mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system's effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.
PROCESS INVOLVED IN OTTO CYCLE:
The Otto cycle consists of;
- isentropic compression,
- heat addition at constant volume,
- isentropic expansion, and
- rejection of heat at constant volume.
THE PROCESSES ARE DESCRIBED AS:
- Process 0–1 a mass of air is drawn into piston /cylinder arrangement at constant pressure.
- Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead center (BDC) to top dead centre (TDC).
- Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead centre. This process is intended to represent the ignition of the fuel-air mixture and the subsequent rapid burning.
- Process 3–4 is an adiabatic (isentropic) expansion (power stroke).
- Process 4–1 completes the cycle by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead centre.
- Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.
DIAGRAM:
PROCESS REPRESENTATION USING VALVE DIAGRAM:
PROBLEMS GIVEN:
- Your code should create a PV diagram.
- You should output the thermal efficiency of the engine.
SOLUTIONS(1):
For plotting the pv diagram,we need to know how the volume changes in the piston.It depends upon the engine kinematics parameters.
THE ENGINE GEOMETRIC PARAMETERS:
- Bore,
- Stroke,
- Connecting rod length,
- Compression ratio.
SWEPT VOLUME AND CLEARANCE VOLUME:
Swept volume is the displacement of one cylinder. It is the volume between top dead center (TDC) and bottom dead center (BDC). As the piston travels from top to bottom, it "sweeps" its total volume. This measurement can be listed in cubic inches or cubic centimeters.
Swept Volume = (Pi/4) x [Bore] ^2 x Stroke
Clearance volume is a volume between the cylinder head and the piston top when the piston is at top dead center (TDC). It can also be defined as the volume of cylinder that is not swept by the piston. Each time the piston goes up, it compress the fuel air mixture in the clearance volume before ignition takes place.
Clearance volume=swept volume/(compression ratio-1)
FORMULAS USED:
IDEAL GAS EQUATION:
pv/t=constant
VOLUME TRACE:
v/vc =1+1/2(cr-1)[R+1-cos(theta)-(R^2-sin^2(theta))^0.5]
DIAGRAM:
ASSUMPTIONS FOR PROBLEM 1:
After calculation of p2 the output should be greater than the value of p1.This states the process is done correctly.
At the end point of combustion the output of p3 should be greater than the value of p2.
For finding the compression rate and expansion rate the special code program is used called FUNCTION [V].
FUNCTION:
Function is the piece of code calling it by name and passing it to the right parametre.
ex; Function [v]=engine_kinematics(bore,stroke);
PROGRAM CODE FOR PROBLEM 1:
clear all
close all
clc
%state variables
p1 = 101325
t1 = 500
%inputs
gamma = 1.4
t3 = 2300
%engine geometric parameters
bore = 0.1;
stroke = 0.1;
con_rod = 0.15;
cr = 12;
%calculation of sewft-volume and the clearence_volume
v_s = (pi/4)*bore^2*stroke
v_c = v_s/(cr-1)
v1 = v_s+v_c
v2 = v_c
%calculation of state point 2
%p2*v2^gamma = p1*v1^gamma
%p2 = p1*(v1/v2)^gamma
p2 = p1*cr^gamma
constant_c = p1*v1^gamma
V_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0)
P_compression = constant_c./V_compression.^gamma
%p1*v1/t1 = p2*v2/t2 / t2 = p2*v2*t2*t1/p1*v1
t2 = p2*v2*t1/(p1*v1)
%state variables at state point 3
v3 = v2
%p3*v3/t3 = p2*v2/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 variables at 4
v4 = v1
%p3*v3^gamma = p4*v4^gamma / p4 = p3*(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma
%to find t4
%p4*v4/t4 = p3*v3/t3 / t4 = t3*p4*v4/p3*v3
t4 = t3*p4*v4/p3*v3
figure(1)
hold on
plot(V_compression,P_compression);
plot(V_expansion,P_expansion);
plot([v2 v2],[p2 p3]);
plot([v1 v1],[p1 p4]);
OUTPUT DERIVATIVES AT WORK PLACE:
PRESSURE POINTS:
TEMPERATURE POINTS:
VOLUME POINTS:
CLEARACE VOLUME:
V_c = 7.139983303613168e-05
SWEPT VOLUME:
V_s = 7.853981633974484e-04
PLOT FOR PROBLEM 1:
SOLUTION FOR PROBLEM 2:
THERMAL EFFICIENCY=1-(cr)^(1-gamma)
IDEAL GAS EQUATION=pv/t=constant
For plotting the various points in the graph for thermal efficieny and compression ratio the linespace command is used.
PROGRAM CODE FOR PROBLEM 2:
clear all
close all
clc
%state variables
p1 = 101325
t1 = 500
%inputs
gamma = 1.4
t3 = 2300
%engine geometric parameters
bore = 0.1;
stroke = 0.1;
con_rod = 0.15;
cr = 12;
%calculation of sewft-volume and the clearence_volume
v_s = (pi/4)*bore^2*stroke
v_c = v_s/(cr-1)
v1 = v_s+v_c
v2 = v_c
%calculation of state point 2
%p2*v2^gamma = p1*v1^gamma
%p2 = p1*(v1/v2)^gamma
p2 = p1*cr^gamma
constant_c = p1*v1^gamma
V_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0)
P_compression = constant_c./V_compression.^gamma
%p1*v1/t1 = p2*v2/t2 / t2 = p2*v2*t2*t1/p1*v1
t2 = p2*v2*t1/(p1*v1)
%state variables at state point 3
v3 = v2
%p3*v3/t3 = p2*v2/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 variables at 4
v4 = v1
%p3*v3^gamma = p4*v4^gamma / p4 = p3*(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma
%to find t4
%p4*v4/t4 = p3*v3/t3 / t4 = t3*p4*v4/p3*v3
t4 = t3*p4*v4/p3*v3
%thermal_efficiency
thermal_eff = 1- (cr)^(1-gamma)
thermal_eff = 1- (12)^(1-1.4)
%compression_ratio
compression_ratio = linspace(0,10,25)
ther_eff = 1- (compression_ratio).^(1-gamma)
figure(2)
hold on
plot(compression_ratio,ther_eff,'color','r');PLOT FOR PROBLEM 2:
WORKSPACE VALUES:
v4 =8.5680e-04
p4 =1.7251e+05
t4 =4.3396e-06
thermal_eff =0.6299
CONCLUSION:
By using the function syntax the values of pv diagram are calculated respectively.
The thermal efficiency of the otto cycle is determined as 62%.