Week 2 Air standard Cycle

INTRODUCTION

A thermodynamic cycle consists of a linked sequence of the thermodynamic processes that involve the transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid (system) may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump. At every point in the cycle, the system is in thermodynamic equilibrium, so the cycle is reversible.

OBJECTIVE

To write a program for determining various state points of an air standard cycle and plot those points. Also to find the thermal efficiency of the cycle.

PROGRAM

import math
import matplotlib.pyplot as plt

def engine_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank):

	#geomentric parameters
	a= stroke/2
	R = con_rod/a

	#Volume parameters
	v_s= (math.pi/2)*pow(bore,2)*stroke
	v_c= v_s/(cr-1)

	sc= math.radians(start_crank)
	ec= math.radians(end_crank)

	num_values = 50

	dtheta = (ec - sc)/(num_values-1)

	V= []

	for i in range (0,num_values):
		theta = sc + i*dtheta
		term1 = 0.5*(cr-1)
		term2 = R + 1 - math.cos(theta)
		term3 = pow(R,2) - pow(math.sin(theta),2)
		term3 = pow(term3,0.5)

		V.append((1 + term1*(term2 - term3))*v_c)
	return V

#inputs
p1= 101325
t1= 500
gamma= 1.4
t3= 2300

#geometric parameters
bore= 0.1
stroke= 0.1
con_rod= 0.15
cr= 12

#Volume computation
v_s= (math.pi/2)*pow(bore,2)*stroke
v_c= v_s/(cr-1)
v1= v_s + v_c

#state points 2
v2 = v_c

# p2v2^gamma = p1v1^gamma
p2 = p1*pow(v1,gamma)/pow(v2,gamma)

#p1v1/t1 = p2v2/t2 | rhs = p2v2/t2 | rhs = p1v1/t1
rhs = (p1*v1)/t1
t2 = (p2*v2)/rhs

V_compression= engine_kinematics(bore, stroke, con_rod, cr, 180, 0)
constant= p1*pow(v1,gamma)
P_compression=[]

for v in V_compression:
	P_compression.append(constant/pow(v,gamma))

#state point3
v3 = v2

#p3v3/t3 = p2v2/t2 | rhs = p2v2/t2 | rhs = p3v3/t3
p3= (rhs*t3)/v3

V_expansion= engine_kinematics(bore, stroke, con_rod, cr, 0, 180)
constant= p3*pow(v3,gamma)
P_expansion=[]

for v in V_expansion:
	P_expansion.append(constant/pow(v,gamma))


#state point 4
v4 = v1

#p4v4^gamma = p3v3^gamma
p4 = p3*pow(v3,gamma)/pow(v4,gamma)


#p4v4/t4 = rhs
tr= (p4*v4)/rhs

#plotting
plt.plot([v2,v3],[p2,p3])
plt.plot(V_compression, P_compression)
plt.plot(V_expansion, P_expansion)
plt.plot([v4,v1],[p4,p1])
plt.show()

#Thermal_Efficiency
te= 1-pow((v2/v1), (gamma-1))
print(te)

EXPLANATION

• The required libraries are imported to the program.
• A function called engine_kinematics is defined with parameters like bore, stroke, con_rod, cr, start_crank, end_crank.
• Geometric parameters are declared and volumetric parameters are calculated.
• The volume ratio formula is separated into terms to make the code easy and finally the V is appended.
• Then the state parameters at various points are determined using ideal gas equations.
• In between the points 1-2 and 3-4, the compression and expansion volumes are calculated for each theta value.
• Finally, all the points are plotted and thermal efficiency is calculated.

PLOT

Thermal_ Efficiency

CONCLUSION

Thus the program is created to obtain the various state points of an air standard cycle and plot them in the graph. Thermal efficiency is also calculated using those values.