Chapter 8: VAPOR POWER AND REFRIGERATION SYSTEMS

Example 8.01, page: 190

In [2]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 8E6 #Pa
P2 = 0.008E6 #Pa
Wtdot = 100E6 #W
T1 = 15 #degC
T2 = 35 #degC

#Calculations:
#from Table T-3
h1 = 2758.0 #kJ/kg
s1 = 5.7432 #kJ/kg-K
sf = 0.5926 #kJ/kg-K
sg = 8.2287 #kJ/kg-K
s2 = s1
hf = 173.88 #kJ/kg
hfg = 2403.1 #kJ/kg
#qualty at 2
x2 = (s2 - sf)/(sg - sf)
#enthalpy at 2
h2 = hf + x2*hfg
#from Table T-3
h3 = 173.88 #kJ/kg
v3 = 1.0084E-3 #specific vol in m3/kg
P4 = P1
P3 = P2
#enthalpy at 4
h4 = h3 + v3*(P4 - P3)/1000

#thermal Efficiency
n = ((h1-h2)-(h4-h3))/(h1-h4)
#back work ratio
bwr = (h4-h3)/(h1-h2)
#mass flow rate of steam
mdot = Wtdot*3.600/((h1-h2)-(h4-h3))
#heat transfer rate in to the working fluid through the boiler
Qindot = mdot*(h1-h4)/3600000
#heat transfer rate fromom the condensing steam as it passes through the condenser
Qoutdot = mdot*(h2 - h3)/3600000
#mass flow rate of the condenser cooling water
#from Table T-2
hcwout = 146.68 #kJ/kg
hcwin = 62.99 #kJ/kg
#
mcwdot = mdot*(h2 - h3)/(hcwout - hcwin)

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"
print  "b)back  work  ratio  is", round(bwr*100,2),"%"
print  "c)mass  flow  rate  of steam is", round(mdot,0),"kg/h"
print  "d)energy  inflow  rate  is",round(Qindot,2),"MW"
print  "e)energy  outflow  rate  is",round(Qoutdot,2),"MW"
print  "f)mass  flow  rate  of cooling water is",round(mcwdot,0),"kg/h"

a)thermal  efficiency  is 37.1 %
b)back  work  ratio  is 0.84 %
c)mass  flow  rate  of steam is 376903.0 kg/h
d)energy  inflow  rate  is 269.7 MW
e)energy  outflow  rate  is 169.7 MW
f)mass  flow  rate  of cooling water is 7299844.0 kg/h

Example 8.02, page: 196

In [3]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 8E6 #Pa
P2 = 0.008E6 #Pa
Wtdot = 100E6 #W
T1 = 15 #degC
T2 = 35 #degC
nt = 0.85

#Calculations:
#from Table T-3
h1 = 2758.0 #kJ/kg
s1 = 5.7432 #kJ/kg-K
h2s = 1794.8 #kJ/kg
#specific enthalpy at 2
h2 = h1 - nt*(h1 - h2s)
#from Table T-3
h3 = 173.88 #kJ/kg
v3 = 1.0084E-3 #specific vol in m3/kg
P4 = P1
P3 = P2
#enthalpy at 4
h4 = h3 + v3*(P4 - P3)/(1000*nt)

#thermal Efficiency
n = ((h1-h2)-(h4-h3))/(h1-h4)
#mass flow rate of steam
mdot = Wtdot*3.600/((h1-h2)-(h4-h3))
#heat transfer rate in to the working fluid through the boiler
Qindot = mdot*(h1-h4)/3600000
#heat transfer rate fromom the condensing steam as it passes through the condenser
Qoutdot = mdot*(h2 - h3)/3600000
#mass flow rate of the condenser cooling water
#from Table T-2
hcwout = 146.68 #kJ/kg
hcwin = 62.99 #kJ/kg
#
mcwdot = mdot*(h2 - h3)/(hcwout - hcwin)

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"
print  "b)mass  flow  rate  of steam is", round(mdot,0),"kg/h"
print  "c)energy  inflow  rate  is",round(Qindot,1),"MW"
print  "d)energy  outflow  rate  is",round(Qoutdot,1),"MW"
print  "e)mass  flow  rate  of cooling water is",round(mcwdot,0),"kg/h"

a)thermal  efficiency  is 31.4 %
b)mass  flow  rate  of steam is 444863.0 kg/h
c)energy  inflow  rate  is 318.2 MW
d)energy  outflow  rate  is 218.2 MW
e)mass  flow  rate  of cooling water is 9384161.0 kg/h

Example 8.03, page: 199

In [20]:
from __future__ import division
import math
%pylab inline

# Initialization  of  Variable
P1 = 8 #MPa
T1 = 480 #degC
P2 = 0.7 #MPa
T2 = 480 #degC
Pcond = 0.008 #Mpa
T3 = 440 #degC
Wtdot = 100 #MW
nt = 0.85

#calculations:
##from Table T-4
h1 = 3348.4 #kJ/kg
s1 = 6.6586 #kJ/kg-K
s2 = s1
sf2 = 1.9922 #kJ/kg-K
sg2 = 6.708 #kJ/kg-K
hf2 = 697.22 #kJ/kg
hfg2 = 2066.3 #kJ/kg
#quality at 2
x2 = (s2 - sf2)/(sg2 - sf2)
#Enthalpy at 2
h2 = hf2 + x2*hfg2

#from Table T-4
h3 = 3353.3 #kJ/kg
s3 = 7.7571 #kJ/kg-K
s4 = s3
sf4 = 0.5926 #kJ/kg-K
sg4 = 8.2287 #kJ/kg-K
hf4 = 173.88 #kJ/kg
hfg4 = 2403.1 #kJ/kg
#quality at 4
x4 = (s4 - sf4)/(sg4 - sf4)
#enthalpy
h4 = hf4 + x4*hfg4

#from table T-4
h5 = 173.88 #kJ/kg
h6 = 181.94 #kJ/kg

#thermal eff
n1 = (h1 - h2 + h3 - h4 - h6 + h5)/(h1 - h6 + h3 - h2)
#mass flow rate of steam
mdot = Wtdot*3600*1000/(h1 - h2 + h3 - h4 - h6 + h5)
#rate of heat transfer from the condensing steam to the cooling water
Qoutdot = mdot*(h4 - h5)/(3600*1000)

h2s = h2
h4s = h4
#specific enthalpy at the exit of the first-stage turbine
h2 = h1 - nt*(h1 - h2s)
#specific enthalpy at the exit of the second-stage turbine
h4 = h3 - nt*(h3 - h4s)

#thermal efficiency
n2 = (h1 - h2 + h3 - h4 - h6 + h5)/(h1 - h6 + h3 - h2)

#creating empty lists for plotting
cte = []
ite = []

for t in range(0, 16):
    ite.append((t+85)/100)
    k=(t+85)/100
    h2 = h1 - k*(h1 - h2s)
    h4 = h3 - k*(h3 - h4s)
    cte.append((h1 - h2 + h3 - h4 - h6 + h5)/(h1 - h6 + h3 - h2))
    
# plots
fig  = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot(ite,cte)
xlabel('Isentropic Turbine Efficiency')
ylabel('Cycle thermal efficiency')
title('Thermal efficiency vs Turbine stage efficiency')
show()

#Results
print  "a)thermal  efficiency  is", round(n1*100,1),"%"
print  "b)mass  flow  rate  of steam is", round(mdot,0),"kg/h"
print  "c)energy  outflow  rate  is", round(Qoutdot,0),"MW"
print  "d)thermal  efficiency  is", round(n2*100,1),"%"

Populating the interactive namespace from numpy and matplotlib

a)thermal  efficiency  is 40.3 %
b)mass  flow  rate  of steam is 236345.0 kg/h
c)energy  outflow  rate  is 148.0 MW
d)thermal  efficiency  is 35.1 %

Example 8.04, page: 204

In [5]:
from __future__ import division
import math

# Initialization  of  Variable
P1 = 8 #MPa
T1 = 480 #degC
P6 = 0.7 #MPa
Pcond = 0.008 #Mpa
Wtdot = 100 #MW
nt = 0.85

#calculations:
#from example 8.3,
h1 = 3348.4 #kJ/kg
s1 = 6.6586 #kJ/kg-K
s2 = 6.8606 #kJ/kg-K
h2 = 2832.8 #kJ/kg
h4 = 173.88 #kJ/kg
s3s = s2
#from Table T-4
x3s = 0.8208
h3s = 2146.3 #kJ/kg
h6 = 697.22 #kJ/kg
#enthalpy at 3, 5 and 7
h3 = h2 - nt*(h2 - h3s)
#
P5 = P6
P4 = Pcond
P7 = P1
v4 = 1.0084E-3 #specific vol in m3/kg
v6 = 1.1080E-3 #in m3/kg
#
h5 = h4 + v4*(P5 - P4)*1000
h7 = h6 + v6*(P7 - P6)*1000

#fraction y of the flow extraced at 2
y = (h6 - h5)/(h2 - h5)
#total turbine work output
Wtm1dot = (h1 - h2) + (1 - y)*(h2 - h3)
#total pump work per unit of mass passing through the first-stage turbine
Wpm1dot = (h7 - h6) + (1 - y)*(h5 - h4)
#heat added in the steam generator per unit of mass passing through the first-stage turbine
Qinm1dot = h1 - h7
#thermal eff
n = (Wtm1dot - Wpm1dot)/Qinm1dot
#mass flow rate
m1dot = Wtdot*3600*1000/(Wtm1dot - Wpm1dot)

#Results
print  "a)thermal  efficiency  is", round(n*100,1),"%"
print  "b)mass  flow  rate is", round(m1dot,0),"kg/h" 

a)thermal  efficiency  is 36.9 %
b)mass  flow  rate is 368948.0 kg/h

Example 8.05, page: 211

In [6]:
from __future__ import division
import math

# Initialization  of  Variable
Tc = 0 #degC
Th = 26 #degC
mdot = 0.08 #kg/s

#calculations:
#from Table T-6
h1 = 247.33 #kJ/kg
s1 = 0.9190 #kJ/kg-K
P2 = 6.853 #bar
h2s = 264.7 #kJ/kg
h3 = 85.75 #kJ/kg
h4 = h3
#compressor work input
Wcdot = mdot*(h2s - h1)
#heat transfer rate to the refrigerant passing through the evaporator
Qindot = mdot*60*(h1 - h4)/211
#coeff of performance
b = (h1 - h4)/(h2s - h1)
bmax = (Tc + 273)/(Th - Tc)

#Results
print  "a) compressor work input is", round(Wcdot,1),"kW"
print  "b) refrigration  capacity  is", round(Qindot,2),"ton"
print  "c) coefficient  of  performanceis", round(b,2)
print  "d) maximum  coefficient  of  performance is", round(bmax,1)

a) compressor work input is 1.4 kW
b) refrigration  capacity  is 3.68 ton
c) coefficient  of  performanceis 9.3
d) maximum  coefficient  of  performance is 10.5

Example 8.06, page: 214

In [7]:
from __future__ import division
import math

# Initialization  of  Variable
Tc = 0 #degC
Th = 26 #degC
mdot = 0.08 #kg/s
P2 = 9 #bar
T1 = -10 #degC

#calculations:
#from Table T-6
h1 = 241.35 #kJ/kg
s1 = 0.9253 #kJ/kg-K
h2s = 272.39 #kJ/kg
h3 = 99.56 #kJ/kg
h4 = h3
#compressor work input
Wcdot = mdot*(h2s - h1)
#heat transfer rate to the refrigerant passing through the evaporator
Qindot = mdot*60*(h1 - h4)/211
#coeff of performance
b = (h1 - h4)/(h2s - h1)

#Results
print  "a) compressor work input is", round(Wcdot,2),"kW"
print  "b) refrigration  capacity  is", round(Qindot,2),"ton"
print  "c) coefficient  of  performanceis", round(b,2)

a) compressor work input is 2.48 kW
b) refrigration  capacity  is 3.23 ton
c) coefficient  of  performanceis 4.57

Example 8.07, page: 215

In [8]:
from __future__ import division
import math

# Initialization  of  Variable
Tc = 0 #degC
Th = 26 #degC
mdot = 0.08 #kg/s
P2 = 9 #bar
nc = 0.8
T1 = -10 #degC
T3 = 30 #degC

#calculations:
#from Table T-6
h1 = 241.35 #kJ/kg
s1 = 0.9253 #kJ/kg-K
h2s = 272.39 #kJ/kg
#enthalpy at 2
h2 = (h2s - h1)/nc + h1

#from table T-6
hf = 91.49 #kJ/kg
h3 = hf
h4 = h3
#compressor work input
Wcdot = mdot*(h2 - h1)
#heat transfer rate to the refrigerant passing through the evaporator
Qindot = mdot*60*(h1 - h4)/211
#coeff of performance
b = (h1 - h4)/(h2 - h1)

#Results
print  "a) compressor work input is", round(Wcdot,2),"kW"
print  "b) refrigration  capacity  is", round(Qindot,2),"ton"
print  "c) coefficient  of  performanceis", round(b,2)

a) compressor work input is 3.1 kW
b) refrigration  capacity  is 3.41 ton
c) coefficient  of  performanceis 3.86