Chapter 15: Gas cycles

Exa 15.1

In [ ]:
#Find the efficiency, and the work per pound of fluid circulated, for a 
#Baryton cycle working between pressures of 15 psia and 75 psia, if the 
#minimum temp. in the cycle is 550 R and the max. temp is 1700R?
import math
#initialisation of variables
p= 15.									#psia
p1= 75.									#psia
T= 550. 								#R
T1= 1700. 								#R
k= 1.4
#CALCULATIONS
Ta= T*math.pow((p1/p),((k-1)/k))		#Temperature at A
Tc= T1/(math.pow((p1/p),((k-1)/k))) 	#Temperature at C
cp= 0.24 
Q1= cp*(T1-Ta) 							#Heat in 1
Q2= cp*(Tc-T) 							#Heat in 2
Wnet= Q1-Q2 							#Work done
n= Wnet/Q1 								#efficiency
hb= 422.59 								#Btu/lb
hc= 269.27 								#Btu/lb
ha= 208.41	 							#Btu/lb
hd= 131.46 								#btu/lb
Q1i= hb-ha								#Heat in 1 case 2
Q2i= hc-hd 								#Heat in 2 case 2
Wnet1= Q1i-Q2i 							#work in case 2
n1= Wnet1/Q1i 							#efficiency 2
#RESULTS
print '%s %.2f' %('Efficiency = ',n)
print '%s %.3f' %( 'Efficiency in case 2= ',n1)
raw_input('press enter key to exit')

Efficiency =  0.37
Efficiency in case 2=  0.357

Exa 15.2

In [1]:
#Repeat for example 1 for a cycle using a regenerator of 75% effectiveness
#initialisation of variables
import math
p= 15. 								#psia
p1= 75. 							#psia
T= 550 								#R
T1= 1700 							#R
k= 1.4
n= 75.
cp= 0.24
#CALCULATIONS
Ta= T*math.pow((p1/p),((k-1)/k))	#Temperature at A
Tc= T1/(math.pow((p1/p),((k-1)/k)))	#Temperature at C
Ta1= (n/100.)*(Tc-Ta)+Ta 			#Temperature at A in case 2
Tc1= Ta+Tc-Ta1 						#Temperature at C in case 2
Q1= cp*(T1-Ta1) 					#Heat in 1
Q2= cp*(Tc1-T) 						#heat in 2
Wnet= Q1-Q2 						#Net work done
n1= Wnet/Q1 						#Efficiency
#CALCULATIONS
print '%s %.2f' %('Efficiency = ',n1)
raw_input('press enter key to exit')

Efficiency =  0.45
press enter key to exit
Out[1]:
''

Exa 15.3

In [2]:
#Find the efficiency, air rate and back work ratio for a gas turbine plant
#of the following description. T=60 F, p1=15. p2/p1=6; macchine efficiences
#of compressor and turbine both 60%. LHV=18500. Turbine inlet temp=1450 F.
#initialisation of variables
h1= 124.27 			#Btu/lb
Pr1= 1.2147 		#psia
r= 6
p4= 15. 			#psia
p1= 15. 			#psia
h2s= 197.5 			#Btu/lb
Wnet= 48.9 			#Btu/lb air
hs= 18500 			#Btu/lb
wfbywa= 0.0146 		#lb fuel/lb sir
W= 2545 			#Btu/lb air
dh=-91.5 			#Btu/lb
Wc= 91.5 			#Btu/lb air
#CALCULATIONS
n= Wnet/(wfbywa*hs)	#Efficiency
n1= W/Wnet			#Air rate
n2= Wc/Wnet 		#Back work ratio
#RESULTS
print '%s %.3f' %('Efficiency = ',n)
print '%s %.2f' %(' \n air rate  (lb air/hphr) = ',n1)
print '%s %.2f' %(' \n back work ratio = ',n2)
raw_input('press enter key to exit')

Efficiency =  0.181
 
 air rate  (lb air/hphr) =  52.04
 
 back work ratio =  1.87
press enter key to exit
Out[2]:
''