ENGINE KINEMATICS

OTTO CYCLE

1.OBJECTIVE: To create a PV plot of the engine process and to calculate thermal efficiency.

2.PROGRAM:

• The engine parameters such as engine bore dia, compression ratio, stroke length, and connecting rod length are given as input.
• Initial conditions such as temperature and pressure at first state point and temperature at state point 3 are given and constant gamma is specified.
• Using the above input volume is calculated.
• State 2, state 3 and state 4 variables are calculated, using conditions and formulas.
• To visualize the actual variation of volume with pressure between state 1 to 2 and state 3 to 4, Functions \'engine_kinematics\' is created.In function start_angle, end_angle are the crank angles( it defines the piston position in the cylinder and hence also defines volume).
• volume relation `V/Vc = (1)+(0.5)*(cr-1)((r+1-cos(theta)-(r^2-sin(theta)^2)^0.5)`
• State points, process path are defined plotted using \'PLT.plot()\'
• Thermal efficiency calculated using relation thermal efficiency = 1-(1/cr^(gamma-1))

3.CODE

# OTTO CYCLE ENGINE

import math
import matplotlib.pyplot as PLT

# FUNCTION TO TRACE VOLUME VS PRESSURE DURING COMPRESSION AND EXPANSION

def engine_kinematics(stroke,conrod,cr,start_angle,end_angle):

	# ENGINE PARAMETERS AND INITIAL CONDITIONS
	# a = stroke/2 ; R = conrod/a

	R = 2*conrod/stroke

	# EQUATION OF V = (1+term1+term2+term3)*clearance volume

	initial_theta = math.radians(start_angle)
	final_theta = math.radians(end_angle)
	num_values = 50
	point_theta = (initial_theta-final_theta)/(num_values-1)
	VOLUME = []

	for i in range(0,num_values):

		theta = initial_theta+(i*point_theta)
		term1 = 0.5*(cr-1)
		term2 = R+1-math.cos(theta)
		term3 = pow(pow(R,2)-pow(math.sin(theta),2),0.5)

		VOLUME.append((1+term1*(term2-term3))*v_clr)

	return VOLUME

# FUNCTION ENDS
# ENGINE PARAMETERS AND INITIAL CONDITIONS

bore = 0.1
stroke = 0.1
conrod = 0.15
cr = 10
gamma = 1.4
p1 = 101325
t1 = 500 
t3 = 2300

# VOLUME CALUCLATIONS

v_swept = math.pi/4*pow(bore,2)*stroke
v_clr = v_swept/(cr-1)
v_total = v_clr + v_swept

# STATE POINTS 1

v1 = v_total

# STATE POINTS 2

v2 = v_clr
p2 = p1*pow(v1/v2,gamma)
constant = p1*v1/t1
t2 = p2*v2/constant
constant_value1 = p1*pow(v1,gamma)

v_compression = engine_kinematics(stroke,conrod,cr,180,0)
p_compression = []

for x in v_compression:

	p_compression.append(constant_value1/pow(x,gamma))


# STATE POINTS 3

v3 = v_clr
p3 = constant*t3/v3

# STATE POINTS 4

v4 = v_total
p4 = p3*pow(v3/v4,gamma)
t4 = p4*v4/constant
constant_value2 = p3*pow(v3,gamma)

v_expansion = engine_kinematics(stroke,conrod,cr,0,180)
p_expansion = []

for y in v_expansion:

	p_expansion.append(constant_value2/pow(y,gamma))

# PLOT

PLT.plot([v1,v2,v3,v4],[p1,p2,p3,p4],\'*\')

PLT.plot(v_compression,p_compression,label=\'compression\')
PLT.plot([v2,v3],[p2,p3],label=\'heat addition\')
PLT.plot(v_expansion,p_expansion,label=\'expansion\')
PLT.plot([v4,v1],[p4,p1],label=\'heat rejection\')

PLT.xlabel(\'volume [meter cube]\')
PLT.ylabel(\'pressue [pascals]\')
PLT.title(\'OTTO CYCLE\')
PLT.legend(loc=\'best\')

PLT.show()

# THERMAL EFFICIENCY
# thermal efficieny = work done/ heat supplied.
# derived equation, thermal efficieny= 1 -(1/cr^(gamma-1))

power = gamma-1

n_therm = 1-(1/pow(cr,power))

#n_therm in percentage

n_therm100 = n_therm*100


print(\'THERMAL EFFICIENCY\',n_therm100)

4.RESULT:

1. PV plot for the otto cycle is obtained.

2. output of thermal efficiency is shown.

THANK YOU