Lecture 12
Lecture 12
Lecture 12
Thermodynamics II
Level 1: Carnot power cycle
Heat Transfer issues:
Energy of boiler hot gases can not be
extracted below TH. the Boiler thermal
efficiency.
two-phase systems limits TH ( <
374 C for water) => the thermal
efficiency.
Turbine issues:
Steam with high moisture content.
The impingement of liquid droplets on the turbine
blades causes erosion and is a major source of wear Carnot cycle is not a
realistic model for vapor
Steam with x < 90 percent power cycles
h2 = h1 − t (h1 − h2 s )
h4 = h3 + v( p4 − p3 ) / p
Modeling the Ideal Rankine Cycle the working fluid undergoes series of internally reversible processes
(a) Determine for the cycle the thermal efficiency (c) The 𝑚ሶ 𝑠𝑡𝑒𝑎𝑚 in kg/h
= 0.371
Tsat (8 kpa)
State 1: = 41.51 C
sat. vapor => h1 = 2758.0 kJ/kg, s1 = 5.7432 kJ/kg.K
State 2: (f) 𝑚ሶ 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑤𝑎𝑡𝑒𝑟 in the condenser (kg/h) if
P2=0.008 mpa, s2=s1 => sat. liq. Vap. mix. Tcooling water, in =15 C and Tcooling water, out = 35 C.
h2s = hf + x2hfg
(e) 𝑄ሶ 𝑜𝑢𝑡 rejected in condenser, in MW,
s2s = sf + x2sfg
Effect of irreversibilities within the turbine and pump can be gauged by comparing values from Example 8.2 with their
counterparts in Example 8.1
(TH)avg_new
(TH)avg_old
2. Lowering the Condenser Pressure
By inspection, what is the (TL)avg_old ?
By inspection, what is the (TH)avg_new ?
(TL)avg_old
TL_new
reheater
(TH)avg_reheat
(TH)avg_Superheat
(TH)avg_simple
Example 8.3 Steam is the working fluid in an
ideal Rankine cycle with superheat and reheat.
Steam enters the first-stage turbine at 8.0 MPa,
480 C, and expands to 0.7 MPa. It is then
reheated to 440 C before entering the second-
stage turbine, where it expands to the condenser
pressure of 0.008 MPa. The net power output is
100 MW. Determine ,
(a) the thermal efficiency of the cycle
m extracted m2
Define: y= =
m main m1
W m1 wt1 + (1 − y ) wt 2 − [(1 − y ) w p1 + w p 2 ]
=
Qin m1 h1 − h7
v4 ( P5 − P4 )
(h1 − h2 ) + (1 − y )(h2 − h3 ) − [(1 − y )( h5 − h4 ) + ( h7 − h6 )]
=
(h1 − h7 )
v6 ( P7 − P6 )
Example 8.5: Steam enters the turbine at P1= Fix state 3s: P3= 0.008 MPa and s3= s2 => SLVM
8.0 MPa, T1= 480 C and expands to P2 = 0.7
MPa, where some of the steam is extracted to x3s = 0.8208; => h3s = 2146.3 kJ/kg.
OFWH operating at 0.7 MPa. The remaining
steam expands through the 2nd turbine to the Fix state 3:
condenser pressure of P3= 0.008 MPa.
Saturated liquid exits the OFWH at 0.7 MPa. The
h3 = 2832.8 – 0.85*(2832.8 – 2146.3)
isentropic efficiency of each turbine stage is 85%
= 2249.3 kJ/kg
and each pump operates isentropically. If the net
power output of the cycle is 100 MW, determine State 4: sat liq at 0.008 Mpa h4 = 173.88 kJ/kg
a) the thermal efficiency
State 5:
Fix State 1: P1= 8.0 MPa and T1= 480 C => SHV P5 = 0.7 Mpa & s5 = s4 (isen.) => Com. Liq.
h1 = 3348.4 kJ/kg and s1 = 6.6586 kJ/kg.K
= 181.94 kJ/kg
Fix state 2s: P2= 0.7 MPa and s2s= s1 => SLVM
State 6: sat liq at 0.7 Mpa h6 = 697.22 kJ/kg.
x2s = 0.9895 => h2s = 2741.8 kJ/kg
State 7: P7 = 8 Mpa & s7 = s6 (isen.) => Com. Liq.
Fix state 2: P2= 0.7 MPa
= 705.3 kJ/kg
100 MW 1000kW kg
m1 = = 3.69 105
984.4 − 9.7 MW h
MEE220
Lecture 13
Thermodynamics II
8.4.2 Closed Feedwater Heaters
2 --
-- 7
Apply energy balance
over the CFWH
8
m2 (h2 − h7 ) + m5 (h5 − h6 ) = 0
Apply energy balance over the CFWH
m2 (h2 − h7 ) = m5 (h6 − h5 )
m 2 ( h 2 − h 7 ) + m 5 ( h5 − h 6 ) = 0 9
divide by m1
m2 (h2 − h7 ) = m5 (h6 − h5 )
y (h2 − h7 ) = (h6 − h5 )
y (h2 − h7 ) = (1 − y )(h6 − h5 ) 6
h6 − h5 y (h2 − h7 ) = (h6 − h5 ) − y (h6 − h5 ) h6 − h5
y= y=
h2 − h7 (h2 − h7 ) + (h6 − h5 )
y[(h2 − h7 ) + (h6 − h5 )] = (h6 − h5 )
State 1 same as in Ex 8.3, h1 = 3348.4 kJ/kg State 11 p11= 8.0 Mpa and 205 C =>CL
and s1 = 6.6586 kJ/kgK. h11 = hf_205 + vf_205 (p11 - psat_at_205)
Example 8.6 :
Steam enters the 1st turbine at
8.0 MPa, 480 C and expands
to 0.7 MPa. The steam is
reheated to 440 C before
entering the 2nd turbine, where
it expands to the condenser
pressure of 0.008 MPa.
h5 = 3101.5 kJ/kg.
feedwater heater, which operates at
0.3 MPa. The stream exiting the
open feedwater heater is saturated
liquid at 0.3 MPa. The net power
output of the cycle is 100 MW. There
is no stray heat transfer from any
component to its surroundings.
(1-y`)h8+y`h13–h9
y`` = y`` = 0.0941
h8 -h5
wt1 + wt 2 - w p1 - w p1
Wt1 =
= (h1 -h 2 ) + (1-y`) (h 2 -h 3 ) = 572.9 kJ/kg qin
m1
= 0.43
Wt 2
= (1-y`) (h 4 -h 5 )+ (1-y`-y`) (h 5 -h 6 )
m1 Wnet
m1 =
=720.7 kJ/kg wt1 + wt 2 - w p1 - w p1
m1
extracted from the 1st turbine at 2
MPa and fed to the closed feedwater
heater. Feedwater leaves the closed
heater at 205 C and 8.0 MPa, and
condensate exits as saturated liquid
at 2 MPa. The condensate is trapped
into the open feedwater heater.
Steam extracted from the 2nd turbine
at 0.3 MPa is also fed into the open
feedwater heater, which operates at
0.3 MPa. The stream exiting the
open feedwater heater is saturated
liquid at 0.3 MPa. The net power
output of the cycle is 100 MW. There
is no stray heat transfer from any
component to its surroundings.
9.9 Gas Turbine–Based Combined Cycles
9.9.2 Cogeneration
h2s=f(Pr2)
Pr2 =(P2/P1)Pr1
h8 = h 7 -
h1 = h(T1) 0.9(h7-h8s)
No condenser for
the top-cycle! All
Qout heats bottom
cycle from d to e