Otto Cycle of Engine Kinematics for Honda g200

OTTO CYCLE OF ENGINE KINEMATICS

AIM:

The program in matlab to simulate honda g200 engine kinematics of otto cycle.

PROCEDURE:

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.

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 center (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 center. 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 center.

Process 1–0 the mass of air is released to the atmosphere in a constant pressure process.

The Otto cycle consists of isentropic compression, heat addition at constant volume, isentropic expansion, and rejection of heat at constant volume. In the case of a four-stroke Otto cycle, technically there are two additional processes: 1) for the exhaust of waste heat and combustion products at constant pressure (isobaric), and 2) for the intake of cool oxygen-rich air also at constant pressure; however, these are often omitted in a simplified analysis. Even though those two processes are critical to the functioning of a real engine, wherein the details of heat transfer and combustion chemistry are relevant, for the simplified analysis of the thermodynamic cycle, it is more convenient to assume that all of the waste-heat is removed during a single volume change.

Honda g200 engine geometric parameters,

Bore = 67 mm

Stroke length = 56 mm

Compression ratio (cr) = 6.5

connecting rod length = 136 mm

R = connecting rod/a

crank stroke (a) = stroke/2

Program to find engine kinematics,

As per the given parameters we are writing a program for otto cycle engine kinematics.

% otto_cycle_of_piston_engine_of_honda_g200

% inputs
gamma=1.4;
t3=2300;

% state_variables
p1=101325;
t1=500;

% honda_g200_engine_geometric_parameters
bore=67;
stroke=56;
connecting_rod=136;
cr=6.5;

% calcularing_swept_volume_&_clearance_volume
v_swept=(pi/4)*bore^2*stroke;
v_clearance=v_swept/(cr-1);
v1=v_swept+v_clearance
v2=v_clearance

% state_variables_at_state_point_2
% p2v2^gamma = p1v1^gamma
% p2=p1*(v1/v2)^gamma=p1*cr^gamma
p2=p1*cr^gamma

constant_c=p1*v1^gamma
V_compression=otto_cycle_of_piston_engine_kinematics(bore,stroke,connecting_rod,cr,180,0)
P_compression=constant_c./V_compression.^gamma;


% p1v1/t1 = p2v2/t2 | t2=p2*v2*t1/(p1*v1)
t2=p2*v2*t1/(p1*v1);

% 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=otto_cycle_of_piston_engine_kinematics(bore,stroke,connecting_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','g')
plot(V_compression,P_compression,'color','g')
plot(v2,p2,'*','color','g')
line([v2,v3],[p2,p3],'color','r')
plot(v3,p3,'*','color','g')
plot(V_expansion,P_expansion,'color','g')
plot(v4,p4,'*','color','g')
line([v4,v1],[p4,p1],'color','r')

xlabel('volume')
ylabel('pressure')

% thermal_efficiency_of_engine
TE=1-1/cr^(gamma-1)

Swept Volume :

Swept volume can be defined as the volume swept by the engine piston during one stroke. Swept volume is also the product of piston area and stroke.

swept volume = (pi/4) * bore^2 * stroke.

Clearance Volume :

Clearance volume can be defined as the volume that remains in the cylinder when the engine piston is in the top centre position.

clearance volume = swept volume/(cr-1).

By using the swept & clearance volume we can find the volume of stroke 1 & 2, v1 = swept + clearance volume ; v2 = clearance volume.

As per the ideal gas law, pv/t = 0 , and pv^gamma = 0. with this equation we can find pressure & temperature of each strokes.

The efficiency of a heat engine measured by the ratio of the work done by it to the heat supplied to it.

(thermal efficiency) TE = 1-1/(cr)^(gamma-1)

We cant plot the graph perfectly by the above code, so to plot volume & pressure we using another formula which determine the volume inside the combusion chamber change.

V/v_clearance = 1+ 0.5(cr-1)[R+1-cos(theta)-(R^2-sin^2(theta))^0.5]

Program to find volume,

function[V] = otto_cycle_of_piston_engine_kinematics(bore, stroke, connecting_rod, cr, start_crank, end_crank)


a=stroke/2;
R=connecting_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;

end

As per the above program we created code template by using function code, The above code which shows the traces of volume. After we can executed the code in the first program by using name of code template.

The final plotting will takes place after we run the program and the result is shown below,

CONCLUSION:

Hence the program in matlab to simulate honda g200 engine kinematics of otto cycle is successfully concluded.