Week 2 Air standard Cycle

Aim:   To write a program in python to calculate thermal efficiency and PV diagram of otto cycle

Equation used to solve thermal efficiency and otto cycle and volume relationship:`v/v_c =1+1/2*(r_c-1)*[R+1-cosθ-〖(R^2-〖sinθ〗^2)]〗^(1/2)`

`ηthermal=1-1/〖cr〗^(Υ-1)`

Introduction:

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

Ratio of power output to that of energy supplied by the fuel is known as thermal efficiency. 

The Otto cycle consists of isentropic compression, heat addition at constant volume, isentropic expansion, and rejection of heat at constant volume which are represented in PV diagram.

Objectives:

1. To find the thermal efficiency of otto cycle
2. To plot the P-V diagram of otto cycle

Solution procedure:

Code to plot PV diagram

import math
import matplotlib.pyplot as plt 
import numpy as np
def engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank): # defining function 
	a=stroke/2 
	R=con_rod/a
	sc= math.radians(start_crank) # starting crank angle 
	ec=math.radians(end_crank)    # ending crank angle 
	num_value=50                  # number of divisions to be made 
	dtheta=(ec-sc)/(num_value-1)  # interval values 
	v=[]                          # Empty array for storing volume values 
	for i in range (0,num_value):  # for loop for 
		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))*v2)      # appending the value of v for i values 
	return v                                      # returning value of v to array 
# Geometric specifications 
bore=0.16# bore diameter in m  
stroke= 0.2# stroke length in m 
con_rod=0.25 # length of connecting rod in m
cr=12 # compression ratio 
# volume parameters 
v_s=math.pi*(1/4)* pow(bore,2)* stroke # v_s 
v2=v_s/(cr-1) # v_c 
v1=v2+v_s
gama=1.4
# Input thermal parameters 
p1= 101325 # inlet pressure in pascal 
t1=500 # temperature at inlet 
t3=3000 # peak temperature 
# parameters at state point 2 
p2=(p1*pow(v1,gama))/(pow(v2,gama))
t2=(t1/pow((v2/v1),gama-1))
v_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0) # function values during compression 
constant=p1*pow(v1,gama)
p_compression=[]
for v in v_compression:
	p_compression.append(constant/pow(v,gama))
# parameters at state point 3
v3=v2
p3=(p2*t3)/t2
v_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180) # function values during expansion 
constant=p3*pow(v3,gama)
p_expansion=[]            # array for storing p expansion values 
for v in v_expansion:     
	p_expansion.append(constant/pow(v,gama))
# state point 4 
v4=v1
t4=((t3)/pow((v4/v3),gama-1))
p4=((p3)/pow((t3/t4),3.5))
# plotting of PV diagram 
plt.plot((v_compression),(p_compression))
plt.plot((v2,v3),(p2,p3))
plt.plot((v_expansion),(p_expansion))
plt.plot((v4,v1),(p4,p1))
plt.legend(['ad_compression','cv_heat addition','ad_expansion','cv_heat regection'])
plt.xlabel('volume')
plt.ylabel("pressure")
plt.title("Pressure volume diagram ")
plt.savefig("Pressure volume diagram")
plt.show()

Code to calculate thermal efficiency 

Th_efficiency=1-((1)/pow(cr,gama-1))
print(Th_efficiency)