Handbook of Mechanical Engineering Calculations P1

P
•
A
•
R
•
T1
POWER GENERATION
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
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POWER GENERATION
1.3
SECTION 1
MODERN POWER-PLANT
CYCLES AND EQUIPMENT
CYCLE ANALYSES
1.4
Choosing Best Options for Boosting
Combined-Cycle Plant Output
1.4
Selecting Gas-Turbine Heat-Recovery
Boilers
1.10
Gas-Turbine Cycle Efficiency Analysis
and Output Determination
1.13

Determining Best-Relative-Value of
Industrial Gas Turbines Using a Life-
Cycle Cost Model
1.18
Tube Bundle Vibration and Noise
Determination in HRSGs
1.22
Determining Oxygen and Fuel Input in
Gas-Turbine Plants
1.25
Heat-Recovery Steam Generator
(HRSG) Simulation
1.28
Predicting Heat-Recovery Steam
Generator (HRSG) Temperature
Profiles
1.33
Steam Turbogenerator Efficiency and
Steam Rate
1.36
Turbogenerator Reheat-Regenerative
Cycle Alternatives Analysis
1.37
Turbine Exhaust Steam Enthalpy and
Moisture Content
1.42
Steam Turbine No-Load and Partial-
Load Steam Flow
1.43
Power Plant Performance Based on

Test Data
1.45
Determining Turbogenerator Steam
Rate at Various Loads
1.47
Analysis of Reheating-Regenerative
Turbine Cycle
1.48
Steam Rate for Reheat-Regenerative
Cycle
1.49
Binary Cycle Plant Efficiency Analysis
1.51
CONVENTIONAL STEAM CYCLES
1.53
Finding Cogeneration System
Efficiency vs a Conventional Steam
Cycle
1.53
Bleed-Steam Regenerative Cycle
Layout and T-S Plot
1.55
Bleed Regenerative Steam Cycle
Analysis
1.59
Reheat-Steam Cycle Performance
1.62
Mechanical-Drive Steam-Turbine
Power-Output Analysis
1.67

Condensing Steam-Turbine Power-
Output Analysis
1.69
Steam-Turbine Regenerative-Cycle
Performance
1.71
Reheat-Regenerative Steam-Turbine
Heat Rates
1.74
Steam Turbine-Gas Turbine Cycle
Analysis
1.76
Gas Turbine Combustion Chamber
Inlet Air Temperature
1.81
Regenerative-Cycle Gas-Turbine
Analysis
1.83
Extraction Turbine kW Output
1.86
STEAM PROPERTIES AND PROCESSES
1.87
Steam Mollier Diagram and Steam
Table Use
1.87
Interpolation of Steam Table Values
1.90
Constant-Pressure Steam Process
1.93
Constant-Volume Steam Process

1.95
Constant-Temperature Steam Process
1.97
Constant-Entropy Steam Process
1.99
Irreversible Adiabatic Expansion of
Steam
1.101
Irreversible Adiabatic Steam
Compression
1.103
Throttling Processes for Steam and
Water
1.105
Reversible Heating Process for Steam
1.107
Determining Steam Enthalpy and
Quality Using the Steam Tables
1.109
Maximizing Cogeneration Electric-
Power and Process-Steam Output
1.110
ECONOMIC ANALYSES OF
ALTERNATIVE ENERGY SOURCES
1.112
Choice of Most Economic Energy
Source Using the Total-Annual-Cost
Method
1.112
Seven Comparison Methods for

Energy Source Choice
1.115
Selection of Prime Mover Based on
Annual Cost Analyses
1.120
Determining If a Prime Mover Should
Be Overhauled
1.122
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
1.4
POWER GENERATION
Deaerator
H-p
turbine
H-p steam
Fuel
I-p turbine L-p turbine
I-p steam
Generator
Gas turbine
Air
H-p superheater
Blowdown Blowdown
H-p
evaporator
I-p
suprerheater

H-p
economizer
I-p
suprerheater
I-p
evaporator
I-p
economizer
L-p
evaporator
L-p
economizer
I-p pump
I-p pump
Reheater
Hot reheat
Cold
reheat
steam
Feedwater
pumps
L-p
steam
Generator
Cooling tower
Makeup water
Condensate
pumps
Deaerator
FIGURE 1 155-MW natural-gas-fired gas turbine featuring a dry low NO

x
combustor (Power).
Cycle Analyses
CHOOSING BEST OPTION FOR BOOSTING
COMBINED-CYCLE PLANT OUTPUT
Select the best option to boost the output of a 230-MW facility based on a 155-
MW natural-gas-fired gas turbine (GT) featuring a dry low NO
x
combustor (Fig.
1). The plant has a heat-recovery steam generator (HRSG) which is a triple-pressure
design with an integral deaerator. A reheat condensing steam turbine (ST) is used
and it is coupled to a cooling-tower/surface-condenser heat sink turbine inlet. Steam
conditions are 1450-lb /in
2
(gage)/1000
Њ
F (9991-kPa/538
Њ
C). Unit ratings are for
operation at International Standard Organization (ISO) conditions. Evaluate the var-
ious technologies considered for summer peaking conditions with a dry bulb (DB)
temperature of 95
Њ
F and 60 percent RH (relative humidity) (35
Њ
C and 60 percent
RH). The plant heat sink is a four-cell, counterflow, mechanical-draft cooling tower
optimized to achieve a steam-turbine exhaust pressure of 3.75 inHg absolute (9.5
cmHg) for all alternatives considered in this evaluation. Base circulating-water sys-
tem includes a surface condenser and two 50 percent-capacity pumps. Water-

treatment, consumption, and disposal-related O&M (operating & maintenance)
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.5
TABLE 1
Performance Summary for Enhanced-Output Options
Measured change from
base case
Case 1
Evap.
cooler
Case 2
Mech.
chiller
Case 3
Absorp.
chiller
Case 4
Steam
injection
Case 5
Water
injection
Case 6
1
Supp.-
fired

HRSG
Case 7
2
Supp.-
fired
HRSG
GT output, MW 5.8 20.2 20.2 21.8 15.5 0 0
ST output, MW 0.9 2.4
Ϫ
2.1
Ϫ
13 3.7 8 35
Plant aux. load, MW 0.05 4.5 0.7 400 0.2 0.4 1
Net plant output, MW 6.65 18.1 17.4 8.4 19 7.6 34
Net heat rate, Btu/kWh
3
15 55 70 270 435 90 320
Incremental costs
Change in total water
cost, $/h 15 35 35 115 85 35 155
Change in wastewater
cost, $/h 1 17 17 2 1 1 30
Change in capital cost /
net output, $ / kW 180 165 230 75 15 70 450
1
Partial supplementary firing.
2
Full supplementary firing.
3
Based on lower heating value of fuel.

costs for the zero-discharge facility are assumed to be $3/1000 gal ($3/3.8 m
3
)of
raw water, $6/1000 gal ($6/3.8 m
3
) of treated demineralized water, and $5/1000
gal ($5/3.8 m
3
) of water disposal. The plant is configured to burn liquid distillate
as a backup fuel.
Calculation Procedure:
1. List the options available for boosting output
Seven options can be developed for boosting the output of this theoretical reference
plant. Although plant-specific issues will have a significant effect on selecting an
option, comparing performance based on a reference plant, Fig. 1, can be helpful.
Table 1 shows the various options available in this study for boosting output. The
comparisons shown in this procedure illustrate the characteristics, advantages, and
disadvantages of the major power augmentation technologies now in use.
Amidst the many advantages of gas turbine (GT) combined cycles (CC) popular
today from various standpoints (lower investment than for new greenfield plants,
reduced environmental impact, and faster installation and startup), one drawback is
that the achievable output decreases significantly as the ambient inlet air tempera-
ture increases. The lower density of warm air reduces mass flow through the GT.
And, unfortunately, hot weather typically corresponds to peak power loads in many
areas. So the need to meet peak-load and power-sales contract requirements causes
many power engineers and developers to compensate for ambient-temperature-
output loss.
The three most common methods of increasing output include: (1) injecting
water or steam into the GT, (2) precooling GT inlet air, and/or (3) supplementary
firing of the heat-recovery steam generator (HRSG). All three options require sig-

nificant capital outlays and affect other performance parameters. Further, the options
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.6
POWER GENERATION
may uniquely impact the operation and / or selection of other components, including
boiler feedwater and condensate pumps, valves, steam turbine/generators, con-
densers, cooling towers, and emissions-control systems.
2. Evaluate and analyze inlet-air precooling
Evaporative cooling, Case 1, Table 1, boosts GT output by increasing the density
and mass flow of the air entering the unit. Water sprayed into the inlet-air stream
cools the air to a point near the ambient wet-bulb temperature. At reference con-
ditions of 95
Њ
F (35
Њ
C) DB and 60 percent RH, an 85 percent effective evaporative
cooler can alter the inlet-air temperature and moisture content to 85
Њ
F (29
Њ
C) and
92 percent RH, respectively, using conventional humidity chart calculations, page
16.79. This boosts the output of both the GT and—because of energy added to the
GT exhaust—the steam turbine/generator. Overall, plant output for Case 1 is in-
creased by 5.8 MW GT output
ϩ
0.9 MW ST output—plant auxiliary load of 0.9

MW
ϭ
6.65 MW, or 3.3 percent. The CC heat rate is improved 0.2 percent, or 15
Btu/kWh (14.2 kJ/kWh). The total installed cost for the evaporative cooling sys-
tem, based on estimates provided by contractors and staff, is $1.2-million. The
incremental cost is $1,200,000/6650 kW
ϭ
$180.45/kW for this ambient condition.
The effectiveness of the same system operating in less-humid conditions—say
95
Њ
F DB (35
Њ
C) and 40 percent RH—is much greater. In this case, the same evap-
orative cooler can reduce inlet-air temperature to 75
Њ
F DB (23.9
Њ
C) by increasing
RH to 88 percent. Here, CC output is increased by 7 percent, heat rate is improved
(reduced) by 1.9 percent, and the incremental installed cost is $85/ kW, computed
as above. As you can clearly see, the effectiveness of evaporative cooling is directly
related to reduced RH.
Water-treatment requirements must also be recognized for this Case, No. 1. Be-
cause demineralized water degrades the integrity of evaporative-cooler film media,
manufacturers may suggest that only raw or filtered water be used for cooling
purposes. However, both GT and evaporative-cooler suppliers specify limits for
turbidity, pH, hardness, and sodium (Na) and potassium (K) concentrations in the
injected water. Thus, a nominal increase in water-treatment costs can be expected.
In particular, the cooling water requires periodic blowdown to limit solids buildup

and system scaling. Overall, the evaporation process can significantly increase a
plant’s makeup-water feed rate, treatment, and blowdown requirements. Compared
to the base case, water supply costs increase by $15/h of operation for the first
approach, and $20 /h for the second, lower RH mode. Disposal of evaporative-
cooler blowdown costs $1 /h in the first mode, $2/h in the second. Evaporative
cooling has little or no effect on the design of the steam turbine.
3. Evaluate the economics of inlet-air chilling
The effectiveness of evaporative cooling is limited by the RH of the ambient air.
Further, the inlet air cannot be cooled below the wet-bulb (WB) temperature of the
inlet air. Thus, chillers may be used for further cooling of the inlet air below the
wet-bulb temperature. To achieve this goal, industrial-grade mechanical or absorp-
tion air-conditioning systems are used, Fig. 2. Both consist of a cooling medium
(water or a refrigerant), an energy source to drive the chiller, a heat exchanger for
extracting heat from the inlet air, and a heat-rejection system.
A mechanical chilling system, Case 2, Table 1, is based on a compressor-driven
unit. The compressor is the most expensive part of the system and consumes a
significant amount of energy. In general, chillers rated above 12-million Btu/h (3.5
MW) (1000 tons of refrigeration) (3500 kW) employ centrifugal compressors. Units
smaller than this may use either screw-type or reciprocating compressors. Overall,
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.7
Ambient air
(95F, 60% RH)
Chilled air
(60F, 100% RH)
Gas turbine/

generator
Cooling
water
Cooling
tower
Condensate
return
25-psia
steam
from
HRSG
Chilled-water loop
2-stage
lithium
bromide
adsorption
chiller
Electric-
driven
centrifugal
chiller
Cooling tower
HRSG
Chilled-
water coils
Circulating
water pump
Chilled
water
FIGURE 2 Inlet-air chilling using either centrifugal or absorption-type chillers, boosts the

achieveable mass flow and power output during warm weather (Power).
compressor-based chillers are highly reliable and can handle rapid load changes
without difficulty.
A centrifugal-compressor-based chiller can easily reduce the temperature of the
GT inlet air from 95
Њ
F (35
Њ
C) to 60
Њ
F (15.6
Њ
C) DB—a level that is generally ac-
cepted as a safe lower limit for preventing icing on compressor inlet blades—and
achieve 100 percent RH. This increases plant output by 20.2 MW for GT
ϩ
2.4
MW for ST
Ϫ
4.5 MW plant auxiliary load
ϭ
18.1 MW, or 8.9 percent. But it
degrades the net CC heat rate by 0.8 percent and results in a 1.5-in-(3.8-cm)-H
2
O
inlet-air pressure drop because of heat-exchanger equipment located in the inlet-air
stream.
Cooling requirements of the chilling system increase the plant’s required cir-
culating water flow by 12,500 gal/min (47.3 m
3

/min). Combined with the need for
increased steam condensing capacity, use of a chiller may necessitate a heat sink
25 percent larger than the base case. The total installed cost for the mechanical
chilling system for Case 2 is $3-million, or about $3,000,000 /18,100 kW
ϭ
$165.75/kW of added output. Again, costs come from contractor and staff studies.
Raw-water consumption increase the plant’s overall O&M costs by $35/h when
the chiller is operating. Disposal of additional cooling-tower blowdown costs $17/
h. The compressor used in Case 2 consumes about 4 MW of auxiliary power to
handle the plant’s 68-million Btu/h (19.9 MW) cooling load.
4. Analyze an absorption chilling system
Absorption chilling systems are somewhat more complex than mechanical chillers.
They use steam or hot water as the cooling motive force. To achieve the same inlet-
air conditions as the mechanical chiller (60
Њ
F DB, 100 percent RH) (15.6
Њ
C, 100
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.8
POWER GENERATION
percent RH), an absorption chiller requires about 111,400 lb /h (50,576 kg/h) of
10.3-lb/in
2
(gage) (70.9-kPa) saturated steam, or 6830 gal /min (25.9 m
3
/min) of

370
Њ
F (188
Њ
C) hot water.
Cost-effective supply of this steam or hot water requires a redesign of the ref-
erence plant. Steam is extracted from the low-pressure (l-p) steam turbine at 20.3
lb/in
2
(gage) (139.9 kPa) and attemperated until it is saturated. In this case, the
absorption chiller increases plant output by 8.7 percent or 17.4 MW but degrades
the plant’s heat rate by 1 percent.
Although the capacity of the absorption cooling system’s cooling-water loop
must be twice that of the mechanical chiller’s, the size of the plant’s overall heat
sink is identical—25 percent larger than the base case—because the steam extracted
from the l-p turbine reduces the required cooling capacity. Note that this also re-
duces steam-turbine output by 2 MW compared to the mechanical chiller, but has
less effect on overall plant output.
Cost estimates summarized in Table 1 show that the absorption chilling system
required here costs about $4-million, or about $230/ kW of added output. Compared
to the base case, raw-water consumption increases O&M costs by $35/h when the
chiller is operating. Disposal of additional cooling-water blowdown adds $17/h.
Compared to mechanical chillers, absorption units may not handle load changes
as well; therefore they may not be acceptable for cycling or load-following oper-
ation. When forced to operate below their rated capacity, absorption chillers suffer
a loss in efficiency and reportedly require more operator attention than mechanical
systems.
Refrigerant issues affect the comparison between mechanical and absorption
chilling. Mechanical chillers use either halogenated or nonhalogenated fluorocar-
bons at this time. Halogenated fluorocarbons, preferred by industry because they

reduce the compressor load compared to nonhalogenated materials, will be phased
out by the end of the decade because of environmental considerations (destruction
of the ozone layer). Use of nonhalogenated refrigerants is expected to increase both
the cost and parasitic power consumption for mechanical systems, at least in the
near term. However, absorption chillers using either ammonia or lithium bromide
will be unaffected by the new environmental regulations.
Off-peak thermal storage is one way to mitigate the impact of inlet-air chilling’s
major drawback: high parasitic power consumption. A portion of the plant’s elec-
trical or thermal output is used to make ice or cool water during off-peak hours.
During peak hours, the chilling system is turned off and the stored ice and /or cold
water is used to chill the turbine inlet air. A major advantage is that plants can
maximize their output during periods of peak demand when capacity payments are
at the highest level. Thermal storage and its equipment requirements are analyzed
elsewhere in this handbook—namely at page 18.70.
5. Compare steam and water injection alternatives
Injecting steam or water into a GT’s combustor can significantly increase power
output, but either approach also degrades overall CC efficiency. With steam injec-
tion, steam extracted from the bottoming cycle is typically injected directly into the
GT’s combustor, Fig. 3. For advanced GTs, the steam source may be extracted from
either the high-pressure (h-p) turbine exhaust, an h-p extraction, or the heat recovery
steam generator’s (HRSG) h-p section.
Cycle economics and plant-specific considerations determine the steam extrac-
tion point. For example, advanced, large-frame GTs require steam pressures of 410
to 435 lb /in
2
(gage) (2825 to 2997 kPa). This is typically higher than the econom-
ically optimal range of h-p steam turbine exhaust pressures of 285 to 395 lb /in
2
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.9
Water-injection
power sugmentation
Steam-injection
power sugmentation
Attemperating
stationWater
injection
skid
HRSG
Gas turbine/
generator
High-pressure
superheater
Demin.
storage
FIGURE 3 Water or steam injection can be used for both power augmentation and NO
x
control
(Power).
(gage) (1964 to 2722 kPa). Thus, steam must be supplied from either the HRSG
or an h-p turbine extraction ahead of the reheat section.
Based on installed-cost considerations alone, extracting steam from the HRSG
is favored for peaking service and may be accomplished without altering the reheat
steam turbine. But if a plant operates in the steam-injection mode for extended
periods, extracting steam from the turbine or increasing the h-p turbine exhaust
pressure becomes more cost-effective.

Injecting steam from the HRSG superheat section into the GT increases unit
output by 21.8 MS, Case 4 Table 1, but decreases the steam turbine /generator’s
output by about 12.8 MW. Net gain to the CC is 8.4 MW. But CC plant heat rate
also suffers by 4 percent, or 270 Btu/kWh (256.5 kJ/kWh).
Because the steam-injection system requires makeup water as pure as boiler
feedwater, some means to treat up to 350 gal/min (22.1 L / s) of additional water
is necessary. A dual-train demineralizer this size could cost up to $1.5-million.
However, treated water could also be bought from a third party and stored. Or
portable treatment equipment could be rented during peak periods to reduce capital
costs. For the latter case, the average expected cost for raw and treated water is
about $130/h of operation.
This analysis assumes that steam- or water-injection equipment is already in
place for NO
x
control during distillate-fuel firing. Thus, no additional capital cost
is incurred.
When water injection is used for power augmentation or NO
x
control, the rec-
ommended water quality may be no more than filtered raw water in some cases,
provided the source meets pH, turbidity, and hardness requirements. Thus, water-
treatment costs may be negligible. Water injection, Case 5 Table 1, can increase
the GT output by 15.5 MW.
In Case 5, the bottoming cycle benefits from increased GT-exhaust mass flow,
increasing steam turbine /generator output by about 3.7 MW. Overall, the CC output
increases by 9.4 percent or 19 MW, but the net plant heat rate suffers by 6.4 percent,
or 435 Btu /kWh (413.3 kJ /kWh). Given the higher increase in the net plant heat
rate and lower operating expenses, water injection is preferred over steam injection
in this case.
6. Evaluate supplementary-fired HRSG for this plant

The amount of excess O
2
in a GT exhaust gas generally permits the efficient firing
of gaseous and liquid fuels upstream of the HRSG, thereby increasing the output
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.10
POWER GENERATION
from the steam bottoming cycle. For this study, two types of supplementary firing
are considered—(1) partial supplementary firing, Case 6 Table 1, and (2) full sup-
plementary firing, Case 7 Table 1.
There are three main drawbacks to supplementary firing for peak power en-
hancement, including 910 lower cycle efficiency, (2) higher NO
x
and CO emissions,
(3) higher costs for the larger plant equipment required.
For this plant, each 100-million Btu /h (29.3 MW) of added supplementary firing
capacity increases the net plant output by 5.5 percent, but increases the heat rate
by 2 percent. The installed cost for supplementary firing can be significant because
all the following equipment is affected: (1) boiler feed pumps, (2) condensate
pumps, (3) steam turbine/generator, (4) steam and water piping and valves, and (5)
selective-catalytic reduction (SCR) system. Thus, a plant designed for supplemen-
tary firing to meet peak-load requirements will operate in an inefficient, off-design
condition for most of the year.
7. Compare the options studied and evaluate results
Comparing the results in Table 1 shows that mechanical chilling, Case 2, gives the
largest increase in plant output for the least penalty on plant heat rate—i.e., 18.1
MW output for a net heat rate increase of 55 Btu/kWh (52.3 kJ/ kWh). However,

this option has the highest estimated installed cost ($3-million), and has a relatively
high incremental installed cost.
Water injection, Case 5 Table 1, has the dual advantage of high added net output
and low installed cost for plants already equipped with water-injection skids for
NO
x
control during distillate-fuel firing. Steam injection, Case 4 Table 1, has a
significantly higher installed cost because of water-treatment requirements.
Supplementary firing, Cases 6 and 7 Table 1, proves to be more acceptable for
plants requiring extended periods of increased output, not just seasonal peaking.
This calculation procedure is the work of M. Boswell, R. Tawney, and R. Narula,
all of Bechtel Corporation, as reported in Power magazine, where it was edited by
Steven Collins. SI values were added by the editor of this handbook.
Related Calculations. Use of gas turbines for expanding plant capacity or for
repowering older stations is a popular option today. GT capacity can be installed
quickly and economically, compared to conventional steam turbines and boilers.
Further, the GT is environmentally acceptable in most areas. So long as there is a
supply of combustible gas, the GT is a viable alternative that should be considered
in all plant expansion and repowering today, and especially where environmental
conditions are critical.
SELECTING GAS-TURBINE HEAT-RECOVERY
BOILERS
Choose a suitable heat-recovery boiler equipped with an evaporator and economizer
to serve a gas turbine in a manufacturing plant where the gas flow rate is 150,000
lb/h (68,040 kg/h) at 950
Њ
F (510
Њ
C) and which will generate steam at 205 lb/in
2

(gage) (1413.5 kPa). Feedwater enters the boiler at 227
Њ
F (108.3
Њ
C). Determine if
supplementary firing of the exhaust is required to generate the needed steam. Use
an approach temperature of 20
Њ
F (36
Њ
C) between the feedwater and the water leav-
ing the economizer.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.11
Top Numbers: Example 1
Bottom Numbers: Example 2
Approach point
Pinch point
T
1
950
1,550
T
2
415
440

T
3
317
296
T
w
370
325
T
t
227
227
T
l
390
390
950˚F (510˚C) 1550˚F (843˚C) 390˚F (199˚C) 390˚F (199˚C)
415˚F (213˚C) 440˚F (227˚C) 370˚F (188˚C) 325˚F (163˚C)
317˚F (158˚C) 296˚F (147˚C) 227˚F (108˚C) 227˚F (108˚C)
FIGURE 4 Gas/ steam profile and data (Chemical Engineering).
Calculation Procedure:
1. Determine the critical gas inlet-temperature
Turbine exhaust gas (TEG) typically leaves a gas turbine at 900–1000
Њ
F
(482–538
Њ
C) and has about 13 to 16 percent free oxygen. If steam is injected into
the gas turbine for NO
x

control, the oxygen content will decrease by 2 to 5 percent
by volume. To evaluate whether supplementary firing of the exhaust is required to
generate needed steam, a knowledge of the temperature profiles in the boiler is
needed.
Prepare a gas/steam profile for this heat-recovery boiler as shown in Fig. 4.
TEG enters on the left at 950
Њ
F (510
Њ
C). Steam generated in the boiler at 205 lb/
in
2
(gage) (1413.5 kPa) has a temperature of 390
Њ
F (198.9
Њ
C), from steam tables.
For steam to be generated in the boiler, two conditions must be met: (1) The ‘‘pinch
point’’ temperature must be greater than the saturated steam temperature of 390
Њ
F
(198.9
Њ
C), and (2) the temperature of the saturated steam leaving the boiler econ-
omizer must be greater than that of the feedwater. The pinch point occurs some-
where along the TEG temperature line, Fig. 4, which starts at the inlet temperature
of 950
Њ
F (510
Њ

C) and ends at the boiler gas outlet temperature, which is to be
determined by calculation. A pinch-point temperature will be assumed during the
calculation and its suitability determined.
To determine the critical gas inlet-temperature, T
1
, get from the steam tables the
properties of the steam generated by this boiler: t
s
ϭ
390
Њ
F (198.9
Њ
C); h
l
, heat of
saturated liquid
ϭ
364 Btu /lb (846.7 kJ/kg); h
s
, total heat of saturated vapor
ϭ
1199.6 Btu/ lb (2790.3 kJ/kg; h
w
, heat of saturated liquid of feedwater leaving the
economizer at 370
Њ
F (187.8
Њ
C)

ϭ
342 Btu/lb (795.5 kJ /kg); and heat of satu-h ,
ƒ
rated liquid of the feedwater at 227
Њ
F (108.3
Њ
C)
ϭ
196.3 Btu/lb (456.6 kJ/kg).
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.12
POWER GENERATION
Writing an energy balance across the evaporator neglecting heat and blowdown
losses, we get: (T
1
Ϫ
T
2
)/(T
1
Ϫ
T
3
)
ϭ
(h

s
Ϫ
h
w
)/
ϭ
X, where T
1
ϭ
gas(h
Ϫ
h )
sƒ
temperature in boiler,
Њ
F(
Њ
C); T
2
ϭ
pinch-point gas temperature,
Њ
F(
Њ
C); T
3
ϭ
outlet gas temperature for TEG,
Њ
F(

Њ
C); enthalpy, h, values as listed above; X
ϭ
ratio of temperature or enthalpy differences. Substituting, X
ϭ
(1199.6
Ϫ
342)/
(1199.9
Ϫ
196.3)
ϭ
0.855, using enthalpy values as given above.
The critical gas inlet-temperature, T
1c
ϭ
(t
s
Ϫ
/(1
Ϫ
X), where t
s
ϭ
tem-Xt )
ƒ
perature of saturated steam,
Њ
F(
Њ

C);
ϭ
temperature of feedwater,
Њ
F(
Њ
C); othert
ƒ
symbols as before. Using the values determined above, T
1c
ϭ
[390
Ϫ
(0.855)(227)]/(1
Ϫ
0.855)
ϭ
1351
Њ
F (732.8
Њ
C).
2. Determine the system pinch point and gas / steam profile
Up to a gas inlet temperature of approximately 1351
Њ
F (732.8
Њ
C), the pinch point
can be arbitrarily selected. Beyond this, the feedwater inlet temperature limits the
temperature profile. Let’s then select a pinch point of 25

Њ
F (13.9
Њ
C), Fig. 4. Then,
T
2
, the gas-turbine gas temperature at the pinch point,
Њ
F(
Њ
C)
ϭ
t
ϩ
pinch-point
ƒ
temperature difference, or 390
Њ
F
ϩ
25
Њ
F
ϭ
415
Њ
F (212.8
Њ
C).
Setting up an energy balance across the evaporator, assuming a heat loss of 2

percent and a blowdown of 3 percent, leads to: (1
Ϫ
heat loss)(TEGQ
ϭ
W
evap e
heat capacity, Btu/
Њ
F) (T
1
Ϫ
T
2
), where W
e
ϭ
TEG flow, lb/h; heat capacity of
TEG
ϭ
0.27 Btu /
Њ
F; T
1
ϭ
TEG inlet temperature,
Њ
F(
Њ
C). Substituting,
ϭ

Q
evap
150,000(0.98)(0.27)(950
Ϫ
415)
ϭ
21.23
ϫ
10
6
Btu/h (6.22 MW).
The rate of steam generation,
ϩ
blowdown percent
ϫ
W
ϭ
Q /[(h
Ϫ
h )
s evap sw
(h
l
Ϫ
h
w
)], where the symbols are as given earlier. Substituting, W
s
ϭ
21.23

ϫ
10
6
/[(1199.6
Ϫ
342)
ϩ
0.03
ϫ
(364
Ϫ
342)]
ϭ
24,736 lb/h (11,230 kg/h).
Determine the boiler economizer duty from
ϭ
(1
ϩ
blowdown)(W
s
)Q
econ
where symbols are as before. Substituting,
ϭ
1.03(24,736)(342
Ϫ
(h
Ϫ
h ), Q
wƒ econ

196.3)
ϭ
3.71
ϫ
10
6
Btu/h (1.09 MW).
The gas exit-temperature, T
3
ϭ
T
2
Ϫ
/TEG gas flow, lb /h)(1
Ϫ
heatQ
econ
loss)(heat capacity, Btu /lb
Њ
F). Since all values are known, T
3
ϭ
415
Ϫ
3.71
ϫ
10
6
/(150,000
ϫ

0.98
ϫ
0.27)
ϭ
317
Њ
F (158
Њ
C). Figure 4 shows the temperature
profile for this installation.
Related Calculations. Use this procedure for heat-recovery boilers fired by
gas-turbine exhaust in any industry or utility application. Such boilers may be un-
fired, supplementary fired, or exhaust fired, depending on steam requirements.
Typically, the gas pressure drop across the boiler system ranges from 6 to 12 in
(15.2 to 30.5 cm) of water. There is an important tradeoff: a lower pressure drop
means the gas-turbine power output will be higher, while the boiler surface and the
capital cost will be higher, and vice versa. Generally, a lower gas pressure drop
offers a quick payback time.
If
⌬
P
e
is the additional gas pressure in the system, the power, kW, consumed in
overcoming this loss can be shown approximately from P
ϭ
5
ϫ
10
Ϫ
8

(W
e
⌬
P
e
T
/E, where E
ϭ
efficiency of compression).
To show the application of this equation and the related payback period, assume
W
e
ϭ
150,000 lb / g (68,100 kg /h), T
ϭ
1000
Њ
R (average gas temperature in the
boiler,
⌬
P
e
ϭ
4 in water (10.2 cm), and E
ϭ
0.7. Then P
ϭ
5
ϫ
10

Ϫ
8
(150,000
ϫ
4
ϫ
1000/0.7)
ϭ
42 kW.
If the gas turbine output is 4000 kW, nearly 1 percent of the power is lost due
to the 4-in (10.2-cm) pressure drop. If electricity costs 7 cent /kWh, and the gas
turbine runs 8000 h /yr, the annual loss will be 8000
ϫ
0.07
ϫ
42
ϭ
$23,520. If
the incremental cost of a boiler having a 4-in (10.2-cm) lower pressure drop is, say
$22,000, the payback period is about one year.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.13
Burner
Fuel
TEG
W

e
, T
1
´(W
e
ϩ W
f
),T
1
´
(W
e
h
1
´ ϩ LHV ϫ W
t
) ϭ (W
e
ϩ W
f
)h
1
F, W
f
FIGURE 5 Gas/ steam profile for fired mode (Chemical Engineering).
If steam requirements are not stated for a particular gas inlet condition, and
maximum steaming rate is desired, a boiler can be designed with a low pinch point,
a large evaporator, and an economizer. Check the economizer for steaming. Such
a choice results in a low gas exit temperature and a high steam flow.
Then, the incremental boiler cost must be evaluated against the additional steam

flow and gas-pressure drop. For example, Boiler A generates 24,000 lb/h (10,896
kg/h), while Boiler B provides 25,000 lb /h (11,350 kg/h) for the same gas pres-
sure-drop but costs $30,000 more. Is Boiler B worth the extra expense?
To answer this question, look at the annual differential gain in steam flow. As-
suming steam costs $3.50 /1000 lb (3.50/454 kg), the annual differential gain in
steam flow
ϭ
1000
ϫ
3.5
ϫ
8000/1000
ϭ
$28,000. Thus, the simple payback is
about a year ($30,000 vs $28,000), which is attractive. You must, however, be
certain you assess payback time against the actual amount of time the boiler will
operate. If the boiler is likely to be used for only half this period, then the payback
time is actually two years.
The general procedure presented here can be used for any type industry using
gas-turbine heat-recovery boilers—chemical, petroleum, power, textile, food, etc.
This procedure is the work of V. Ganapathy, Heat-Transfer Specialist, ABCO In-
dustries, Inc., and was presented in Chemical Engineering magazine.
When supplementary fuel is added to the turbine exhaust gas before it enters
the boiler, or between boiler surfaces, to increase steam production, one has to
perform an energy balance around the burner, Fig. 5, to evaluate accurately the gas
temperature increase that can be obtained.
V. Ganapathy, cited above, has a computer program he developed to speed this
calculation.
GAS-TURBINE CYCLE EFFICIENCY ANALYSIS
AND OUTPUT DETERMINATION

A gas turbine consisting of a compressor, combustor, and an expander has air
entering at 60
Њ
F (15.6
Њ
C) and 14.0 lb /in
2
(abs) (96.5 kPa). Inlet air is compressed
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.14
POWER GENERATION
FIGURE 6 Ideal gas-turbine cycle, 1-2-3-4-1. Actual compression takes place along 1-2
Ј
; actual
heat added 2
Ј
-3
Ј
; ideal expansion 3
Ј
-4
Ј
.
to 56 lb/in
2
(abs) (385.8 kPa); the isentropic efficiency of the compressor is 82
percent. Sufficient fuel is injected to give the mixture of fuel vapor and air a heating

value of 200 Btu /lb (466 kJ/kg). Assume complete combustion of the fuel. The
expander reduces the flow pressure to 14.9 lb/in
2
(abs), with an engine efficiency
of 85 percent. Assuming that the combustion products have the same thermody-
namic properties as air, c
p
ϭ
0.24, and is constant. The isentropic exponent may
be taken as 1.4. (a) Find the temperature after compression, after combustion, and
at the exhaust. (b) Determine the Btu /lb (kJ/kg) of air supplied, the work delivered
by the expander, the net work produced by the gas turbine, and its thermal effi-
ciency.
Calculation Procedure:
1. Plot the ideal and actual cycles
Draw the ideal cycle as 1-2-3-4-1, Figs. 6 and 7. Actual compression takes place
along 1-2
Ј
. Actual heat added lies along 2
Ј
-3
Ј
. The ideal expansion process path is
3
Ј
-4
Ј
. Ideal work
ϭ
c

p
(ideal temperature difference). Actual work
ϭ
c
p
(actual
temperature difference).
2. Find the temperature after compression
Use the relation (T
2
/T
1
)
ϭ
where T
1
ϭ
entering air temperature,
Њ
R;
(
k
Ϫ
1
)
/ k
(P /P ),
21
T
2

ϭ
temperature after adiabatic compression,
Њ
R; P
1
ϭ
entering air pressure, in
units given above; P
2
ϭ
pressure after compression, in units given above; k
ϭ
isentropic exponent
ϭ
1.4. With an entering air temperature, T
1
of 60
Њ
F (15.6
Њ
C),
or 60
ϩ
460
ϭ
520
Њ
R, and using the data given,
ϭ
(1.4

Ϫ
1) / 1.4
T
ϭ
520[(56/14)]
2
772.7
Њ
R, or 772.7
Ϫ
520
ϭ
252.7
Њ
F (122.6
Њ
C).
(a) Here we have isentropic compression in the compressor with an effi-
ciency of 85 percent. Using the equation, Efficiency, isentropic
ϭ
(c
p
)(T
2
Ϫ
T
1
)/
(c
p

) and solve for the temperature after isentropic compression. Solv-(T
Ϫ
T ), T ,
2
Ј
12
Ј
ing,
ϭ
0.82
ϭ
0.24(772.7
Ϫ
520)/0.24
ϭ
828.4
Њ
R, or 368
Њ
F. ThisT (T
Ϫ
520)
2
Ј
2
Ј
is the temperature after compression.
3. Determine the temperature after combustion
To find the temperature after combustion, use the relation Heating value of fuel
ϭ

Q
ϭ
c
p
where
ϭ
temperature after combustion,
Њ
R. Substituting,(T
Ϫ
T ), T
3
Ј
2
Ј
3
Ј
200
ϭ
0.24 Solving,
ϭ
1661.3
Њ
R; 1201.3
Њ
F (649.6
Њ
C).(T
Ϫ
828). T

3
Ј
3
Ј
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.15
FIGURE 7 Ideal gas-turbine cycle T-S diagram with the same processes as in Fig. 6; complete-
cycle gas turbine shown below the T-S diagram.
4. Find the temperature at the exhaust of the gas turbine
Using an approach similar to that above, determine T
4
from
ϭ
(T / T )
4
Ј
3
Ј
Substituting and solving for
ϭ
1661
ϭ
k
Ϫ
1/k. (1.4
Ϫ

1) / 1.4
[(P / P )] T [(14.9/56)]
4
Ј
3
Ј
4
Ј
1137.9
Њ
R, or 677.8
Њ
F (358.8
Њ
C).
Now use the equation for gas-turbine efficiency, namely, Turbine efficiency
ϭ
c
p
ϭ
0.85, and solve for the temperature after expan-(T
Ϫ
T )/c (T
Ϫ
T ) T ,
3
Ј
4
؆
p 3

Ј
4
Ј
4
؆
sion, at the exhaust. Substituting as earlier,
ϭ
1218.2
Њ
R, 758.2
Њ
F (403.4
Њ
C). ThisT
4
؆
is the temperature after expansion, i.e., at the exhaust of the gas turbine.
5. Determine the work of compression, expander work, and thermal efficiency
(b) The work of compression
ϭ
c
p
ϭ
0.24(828
Ϫ
520)
ϭ
74.16 Btu (78.23(T
Ϫ
T )

2
Ј
1
J).
The work delivered by the expander
ϭ
c
p
ϭ
0.24 (1661
Ϫ
1218)
ϭ
(T
Ϫ
T )
2
Ј
1
106.32 Btu (112.16 J).
The net work
ϭ
106.3
Ϫ
74.2
ϭ
32.1 Btu (33.86 J). Then, the thermal
efficiency
ϭ
net work/ heat supplied

ϭ
32.1/200
ϭ
0.1605, 16.6 percent thermal
efficiency.
Related Calculations. With the widespread use today of gas turbines in a va-
riety of cycles in industrial and central-station plants, it is important that an engineer
be able to analyze this important prime mover. Because gas turbines can be quickly
installed and easily hooked to heat-recovery steam generators (HRSG), they are
more popular than ever before in history.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.16
POWER GENERATION
FIGURE 8 With further gas-turbine cycle refinement, the specific fuel consumption declines.
These curves are based on assumed efficiencies with T
3
ϭ
1400 F (760 C).
Further, as aircraft engines become larger—such as those for the Boeing 777
and the Airbus 340—the power output of aeroderivative machines increases at little
cost to the power industry. The result is further application of gas turbines for
topping, expansion, cogeneration and a variety of other key services throughout the
world of power generation and energy conservation.
With further refinement in gas-turbine cycles, specific fuel consumption, Fig. 8,
declines. Thus, the complete cycle gas turbine has the lowest specific fuel con-
sumption, with the regenerative cycle a close second in the 6-to-1 compression-
ratio range.

Two recent developments in gas-turbine plants promise much for the future. The
first of these developments is the single-shaft combined-cycle gas and steam turbine,
Fig. 9. In this cycle, the gas turbine exhausts into a heat-recovery steam generator
(HRSG) that supplies steam to the turbine. This cycle is the most significant electric
generating system available today. Further, its capital costs are significantly lower
than competing nuclear, fossil-fired steam, and renewable-energy stations. Other
advantages include low air emissions, low water consumption, smaller space re-
quirements, and a reduced physical profile, Fig. 10. All these advantages are im-
portant in today’s strict permitting and siting processes.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.17
Stack
H-p I-p L-p
HRSG
L-p I-p H-p
Steam turbine
Generator
Inlet air
Gas turbine
Fuel
Synchronous
clutch
FIGURE 9 Single-shaft combined-cycle technology can reduce costs and increase thermal effi-
ciency over multi-shaft arrangements. This concept is popular in Europe (Power).
68.5 ft (20.9 m)
(51.9 m)

170.6 ft
29.5 ft 95 ft
152 ft
(8.99 m) (46.33 m) (28.95 m)
FIGURE 10 Steam turbine, electric generator, and gas turbine fit into one compact building when
all three machines are arranged on a single shaft. Net result: Reduced site footprint and civil-
engineering work (Power).
Having the gas turbine, steam turbine, and generator all on one shaft simplifies
plant design and operation, and may lower first costs. When used for large reheat
cycles, as shown here, separate high-pressure (h-p), intermediate-pressure (i-p), and
low-pressure (l-p) turbine elements are all on the same shaft as the gas turbine and
generator. Modern high-technology combined-cycle single-shaft units deliver a
simple-cycle net efficiency of 38.5 percent for a combine-cycle net efficiency of
58 percent on a lower heating value (LHV) basis.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.18
POWER GENERATION
The second important gas-turbine development worth noting is the dual-fueled
turbine located at the intersection of both gas and oil pipelines. Being able to use
either fuel gives the gas turbine greater opportunity to increase its economy by
switching to the lowest-cost fuel whenever necessary. Further developments along
these lines is expected in the future.
The data in the last three paragraphs and the two illustrations are from Power
magazine.
DETERMINING BEST-RELATIVE-VALUE OF
INDUSTRIAL GAS TURBINES USING A
LIFE-CYCLE COST MODEL

An industrial application requires a 21-MW continuous electrical output year-round.
Five different gas turbines are under consideration. Determine which of these five
turbines is the best choice, using a suitable life-cycle cost analysis.
Calculation Procedure:
1. Assemble the cost data for each gas turbine being considered
Assemble the cost data as shown below for each of the five gas turbines identified
by the letters A through E. Contact the gas-turbine manufacturers for the initial
cost, $/ kW, thermal efficiency, availability, fuel consumption, generator efficiency,
and maintenance cost, $/kWh. List these data as shown below.
The loan period, years, will be the same for all the gas turbines being considered,
and is based on an equipment life-expectancy of 20 years. Interest rate on the capital
investment for each turbine will vary, depending on the amount invested and the
way in which the loan must be repaid and will be provided by the accounting
department of the firm considering gas-turbine purchase.
Equipment Attributes for Typical Candidates*
Parameter
Gas-turbine candidates
ABCDE
Initial cost, $ /kW 205 320 275 320 200
Thermal efficiency, % 32.5 35.5 34.0 36.5 30.0
Loan period, yr 20 20 20 20 20
Availability 0.96 0.94 0.95 0.94 0.96
Fuel cost, $ / million Btu 4 4 4 4 4
Interes, % 6.5 8.0 7.0 8.5 7.5
Generator efficiency, % 98.0 98.5 98.5 98.0 98.5
Maintenance cost, $ /kWh 0.004 0.005 0.005 0.005 0.004
*Assuming an equipment life of 20 years, an output of 21 MW.
2. Select a life-cycle cost model for the gas turbines being considered
A popular and widely used life-cycle cost model for gas turbines has three parts:
(1) the annual investment cost, C

p
; (2) annual fuel cost, (3) annual maintenanceC ;
ƒ
cost, C
m
. Summing these three annual costs, all of which are expressed in mils /
kWh, gives C
T
, the life-cycle cost model. The equations for each of the three
components are given below, along with the life-cycle working model, C
T
:
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.19
The life-cycle cost model (C
T
) consists of annual investment cost (C
p
)
ϩ
annual
fuel cost
ϩ
annual maintenance cost (C
m
). Equations for these values are:(C )

ƒ
Ϫ
n
l{i /[1
Ϫ
(1
Ϫ
i)]}
C
ϭ
p
(A)(kW)(8760)(G )
where l
ϭ
initial capital cost of equipment, dollars
i
ϭ
interest rate
n
ϭ
number of payment periods
A
ϭ
availability (expressed as decimal)
kW
ϭ
kilowatts of electricity produced
8760
ϭ
total hours in year

G
ϭ
efficiency of electric generator
C
ϭ
E(293)
ƒ
where E
ϭ
thermal efficiency of gas turbine
293
ϭ
conversion of Btu to kWh
C
ϭ
M/kW
m
where M
ϭ
maintenance cost, dollars per operating (fired) hour.
Thus, the life-cycle working model can be expressed as
Ϫ
n
l{i/[1
Ϫ
(1
Ϫ
i)]}
C
ϭϩ

F/E(293)
ϩ
M/kW
T
(A)(kW)(8760)(G )
where F
ϭ
fuel cost, dollars per million Btu (higher heating value)
To evaluate the comparative capital cost of a gas-turbine electrical generating
package the above model uses the capital-recovery factor technique. This approach
spreads the initial investment and interest costs for the repayment period into an
equal annual expense using the time value of money. The approach also allows for
the comparison of other periodic expenses, like fuel and maintenance costs.
3. Perform the computation for each of the gas turbines being considered
Using the compiled data shown above, compute the values for C
p
, and C
m
, andC ,
ƒ
sum the results. List for each of the units as shown below.
Results from Cost Model
Unit Mils/ kWh produced
A 48.3
B 47.5
C 48.3
D 46.6
E 51.9
4. Analyze the findings of the life-cycle model
Note that the initial investment cost for the turbines being considered ranges be-

tween $200 and $320 /kW. On a $/ kW basis, only unit E at the $200 level, would
be considered. However, the life-cycle cost model, above, shows the cost per kWh
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.20
POWER GENERATION
produced for each of the gas-turbine units being considered. This gives a much
different perspective of the units.
From a life-cycle standpoint, the choice of unit E over unit D would result in
an added expenditure of about $975,000 annually during the life span of the equip-
ment, found from [(51.9
Ϫ
46.6)/1000](8760 hr/yr)(21,000 kW)
ϭ
$974,988; this
was rounded to $975,000. Since the difference in the initial cost between units D
and E is $6,720,000
Ϫ
$4,200,000
ϭ
$2,520,000, this cost difference will be re-
covered in $2,520,000 /974,988
ϭ
2.58 years, or about one-eighth of the 20-year
life span of the equipment.
Also, note that the 20-year differential in cost/ kWh produced between units D
and E is equivalent to over 4.6 times the initial equipment cost of unit E. When
considering the values output of a life-cycle model, remember that such values are

only as valid as the data input. So take precautions to input both reasonable and
accurate data to the life-cycle cost model. Be careful in attempting to distinguish
model outputs that vary less than 0.5 mil from one another.
Since the predictions of this life-cycle cost model cannot be compared to actual
measurements at this time, a potential shortcoming of the model lies with the va-
lidity of the data and assumptions used for input. For this reason, the model is best
applied to establish comparisons to differentiate between several pieces of com-
peting equipment.
Related Calculations. The first gas turbines to enter industrial service in the
early 1950s represented a blend of steam-turbine and aerothermodynamic design.
In the late 1950s /early-1960s, lightweight industrial gas turbines derived directly
from aircraft engines were introduced into electric power generation, pipeline com-
pression, industrial power generation, and a variety of other applications. These
machines had performance characteristics similar to their steam-turbine counter-
parts, namely pressure ratios of about 12
Ϻ
1, firing temperatures of 1200–1500
Њ
F
(649–816
Њ
C), and thermal efficiencies in the 23–27 percent range.
In the 1970s, a new breed of aeroderivative gas turbines entered industrial ser-
vice. These units, with simple-cycle thermal efficiencies in the 32–37 percent
bracket, represented a new technological approach to aerothermodynamic design.
Today, these second-generation units are joined by hybrid designs that incor-
porate some of the aeroderivative design advances but still maintain the basic struc-
tural concepts of the heavy-frame machines. These hybrid units are not approaching
the simple-cycle thermal-efficiency levels reached by some of the early second-
generation aeroderivative units first earmarked for industrial use.

Traditionally, the major focus has been on first cost of industrial gas-turbine
units, not on operating cost. Experience with higher-technology equipment, how-
ever, reveals that a low first cost does not mean a lower total cost during the
expected life of the equipment. Conversely, reliable, high-quality equipment with
demonstrated availability will be remembered long after the emotional distress as-
sociated with high initial cost is forgotten.
The life-cycle cost model presented here uses 10 independent variables. A sin-
gle-point solution can easily be obtained, but multiple solutions require repeated
calculations. Although curves depicting simultaneous variations in all variables
would be difficult to interpret, simplified diagrams can be constructed to illustrate
the relative importance of different variables.
Thus, the simplified diagrams shown in Fig. 11, all plot production cost, mils/
kWh, versus investment cost. All the plots are based on continuous operation of
8760 h/yr at 21-MW capacity with an equipment life expectancy of 20 years.
The curves shown depict the variation in production cost of electricity as a
function of initial investment cost for various levels of thermal efficiency, loan
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.21
FIGURE 11 Economic study plots for life-cycle costs (Power).
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.22
POWER GENERATION
repayment period, gas-turbine availability, and fuel cost. Each of these factors is
an element in the life-cycle cost model presented here.

This procedure is the work of R. B. Spector, General Electric Co., as reported
in Power magazine.
TUBE BUNDLE VIBRATION AND NOISE
DETERMINATION IN HRSGs
A tubular air heater 11.7 ft (3.57 m) wide, 12.5 ft (3.81 m) deep and 13.5 ft (4.11
m) high is used in a boiler plant. Carbon steel tubes 2 in (5.08 cm) in outer diameter
and 0.08 in (0.20 cm) thick are used in inline fashion with a traverse pitch of 3.5
in (8.89 cm) and a longitudinal pitch of 3 in (7.62 m). There are 40 tubes wide
and 60 tubes deep in the heater; 300,000 lb (136,200 kg) of air flows across the
tubes at an average temperature of 219
Њ
F (103.9
Њ
C). The tubes are fixed at both
ends. Tube mass per unit length
ϭ
1.67 lb/ft (2.49 kg/m). Check this air heater
for possible tube vibration problems.
Calculation Procedure:
1. Determine the mode of vibration for the tube bundle
Whenever a fluid flows across a tube bundle such as boiler tubes in an evaporator,
economizer, HRSG, superheater, or air heater, vortices are formed and shed in the
wake beyond the tubes. This shedding on alternate sides of the tubes causes a
harmonically varying force on the tubes perpendicular to the normal flow of the
fluid. It is a self-excited vibration. If the frequency of the Von Karman vortices, as
they are termed, coincides with the natural frequency of vibration of the tubes, then
resonance occurs and the tubes vibrate, leading to possible damage of the tubes.
Vortex shedding is most prevalent in the range of Reynolds numbers from 300
to 200,000, the range in which most boilers operate. Another problem encountered
with vortex shedding is acoustic vibration, which is normal to both the fluid flow

and tube length observed in only gases and vapors. This occurs when the vortex
shedding frequency is close to the acoustic frequency. Excessive noise is generated,
leading to large gas pressure drops and bundle and casing damage. The starting
point in the evaluation for noise and vibration is the estimation of various frequen-
cies.
Use the listing of C values shown below to determine the mode of vibration.
Note that C is a factor determined by the end conditions of the tube bundle.
End conditions
Mode of vibration
123
Both ends clamped 22.37 61.67 120.9
One end clamped, one end hinged 15.42 49.97 104.2
Both hinged 9.87 39.48 88.8
Since the tubes are fixed at both ends, i.e., clamped, select the mode of vibration
as 1, with C
ϭ
22.37. For most situations, Mode 1 is the most important case.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.23
FIGURE 12 Strouhl number, S, for inline tube banks. Each curve
represents a different longitudinal pitch / diameter ratio (Chen).
2. Find the natural frequency of the tube bundle
Use the relation, ƒ
n
ϭ
90C[ Substituting, with C

ϭ
22.37,
442 0.5
d
Ϫ
d ]/(L
Ϫ
M ).
oi
ƒ
n
ϭ
(90)(22.37)[2
4
Ϫ
1.84
4
]
0.5
/(13.5
2
Ϫ
1.67
0.5
)
ϭ
18.2 cycles per second (cps).
In Mode 2, ƒ
n
ϭ

50.2, as C
ϭ
61.67.
3. Compute the vortex shedding frequency
To compute the vortex shedding frequency we must know several factors, the first
of which is the Strouhl Number, S. Using Fig. 12 with a transverse pitch /diameter
of 1.75 and a longitudinal pitch diameter of 1.5 we find S
ϭ
0.33. Then, the air
density
ϭ
40/(460
Ϫ
219)
ϭ
0.059 lb /ft
3
(0.95 kg /m
3
); free gas area
ϭ
40(3.5
Ϫ
2)(13.5/12)
ϭ
67.5 ft
2
(6.3 m
2
); gas velocity, V

ϭ
300,000/(67.5)(0.059)(3600)
ϭ
21 ft/s (6.4 m/s).
Use the relation, ƒ
c
ϭ
12(S)(V)/d
o
ϭ
12(0.33)(21)/2
ϭ
41.6 cps, where ƒ
c
ϭ
vortex shedding frequency, cps.
4. Determine the acoustic frequency
As with vortex frequency, we must first determine several variables, namely: ab-
solute temperature
ϭ Њ
R
ϭ
219
ϩ
460
ϭ
679
Њ
R; sonic velocity, V
s

ϭ
49(679)
0.5
ϭ
1277 ft/s (389.2 m/s); wave length,
␭
ϭ
2(w)/n, where w
ϭ
width of tube bank,
ft (m); n
ϭ
mode of vibration
ϭ
1 for this tube bank; then
␭
ϭ
2(11.7)/1
ϭ
23.4
ft (7.13 m).
The acoustic frequency, ƒ
a
ϭ
(V
s
)/
␭
, where V
s

ϭ
velocity of sound at the gas
temperature in the duct or shell, ft/s (m/s); V
s
ϭ
[(g)(
␳
)(RT)]
0.5
, where R
ϭ
gas
constant
ϭ
1546/molecular weight of the gas; T
ϭ
gas temperature,
Њ
R;
␳
ϭ
ratio
of gas specific heats, typically 1.4 for common flue gases; the molecular weight
ϭ
29. Simplifying, we get V
s
ϭ
49(T)
0.5
, as shown above. Substituting, ƒ

a
ϭ
1277/
23.4
ϭ
54.5 cps. For n
ϭ
2; ƒ
a
ϭ
54.4(2)
ϭ
109 cps. The results for Modes 1 and
2 are summarized in the tabulation below.
Mode of vibration
n
12
ƒ
n
, cps 18.2 50.2
ƒ
c
, cps 41.6 41.6
ƒ
a
(without baffles) 54.5 109
ƒ
a
(with baffles) 109 218
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.24
POWER GENERATION
Moment-connected corners
Main wall beams
Main roof beams
Roof cross-tie beams
Main frame
Tube-bundle
support beam
Suspension
bolt
Vibration
stopper
Heat-
transfer
tube bundle
Casing
Vibration
stopper
Insulation
Liner
Roof
pressure-part
supports
Pressure-part
expansion
guides

Upper header
Tube restraint
Tubes
Lower header
Lower header
cradle
Floor
pressure-part
supports
Main floor
beams
Floor cross-tie
beams
Moment-connected corners
Gas flow
Wall cross-tie
beams
1
/
2
-in. dia.
liner stud
Tube
restraint
supports
1
/
4
-in. casing
FIGURE 13 Tube bundles in HRSGs require appropriate support mechanisms; thermal cycling

in combined-cycle units makes this consideration even more important (Power).
The tube natural frequency and the vortex shedding frequency are far apart.
Hence, the tube bundle vibration problem is unlikely to occur. However, the vortex
shedding and acoustic frequencies are close. If the air flow increases slightly, the
two frequencies will be close. By inserting a baffle in the tube bundle (dividing the
ductwork into two along the gas flow direction) we can double the acoustic fre-
quency as the width of the gas path is now halved. This increases the difference
between vortex shedding and acoustic frequencies and prevents noise problems.
Noise problems arise when the acoustic and vortex shedding frequencies are
close—usually within 20 percent. Tube bundle vibration problems arise when the
vortex shedding frequency and natural frequency of the bundle are close—within
20 percent. Potential noise problems must also be considered at various turndown
conditions of the equipment.
Related Calculations. For a thorough analysis of a plant or its components,
evaluate the performance of heat-transfer equipment as a function of load. Analyze
at various loads the possible vibration problems that might occur. At low loads in
the above case, tube bundle vibration is likely, while at high loads acoustic vibration
is likely without baffles. Hence, a wide range of performance must be reviewed
before finalizing any tube bundle design, Fig. 13.
This procedure is the work of V. Ganapathy, Heat Transfer Specialist, ABCO
Industries, Inc.
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MODERN POWER-PLANT CYCLES AND EQUIPMENT
MODERN POWER-PLANT CYCLES AND EQUIPMENT
1.25
DETERMINING OXYGEN AND FUEL INPUT IN
GAS-TURBINE PLANTS
In a gas-turbine HRSG (heat-recovery steam generator) it is desired to raise the

temperature of 150,000 lb/h (68,100 kg /h) of exhaust gases from 950
Њ
F (510
Њ
C)
to 1575
Њ
F (857.2
Њ
C) in order to nearly double the output of the HRSG. If the
exhaust gases contain 15 percent oxygen by volume, determine the fuel input and
oxygen consumed, using the gas specific-heat method.
Calculation Procedure:
1. Determine the air equivalent in the exhaust gases
In gas-turbine based cogeneration/combined-cycle projects the HRSG may be fired
to generate more steam than that produced by the gas-turbine exhaust gases. Typ-
ically, the gas-turbine exhaust gas contains 14 to 15 percent oxygen by volume. So
the question arises: How much fuel can be fired to generate more steam? Would
the oxygen in the exhaust gases run out if we fired to a desired temperature? These
questions are addressed in this procedure.
If 0 percent oxygen is available in W
g
lb/h (kg/h) of exhaust gases, the air-
equivalent W
a
in lb /h (kg/h) is given by: W
a
ϭ
100(W
g

)(32O
x
)/[23(100)(29.5)]
ϭ
0.0417 W
g
(O). In this relation, we are converting the oxygen from a volume basis
to a weight basis by multiplying by its molecular weight of 32 and dividing by the
molecular weight of the exhaust gases, namely 29.5. Then multiplying by (100/
23) gives the air equivalent as air contains 23 percent by weight of oxygen.
2. Relate the air required with the fuel fired using the MM Btu (kJ) method
Each MM Btu (kJ) of fuel fired (HHV basis) requires a certain amount of air, A.
If Q
ϭ
amount of fuel fired in the turbine exhaust gases on a LHV basis (calcu-
lations for turbine exhaust gases fuel input are done on a low-heating-value basis)
then the fuel fired in lb/ h (kJ/h)
ϭ
W
ϭ
Q /LHV.
ƒ
The heat input on an HHV basis
ϭ
(HHV)/(10
6
)
ϭ
(Q /LHV)(HHV)/10
6

W
ƒ
Btu/h (kJ/ h). Air required lb/h (kg /h)
ϭ
(Q /LHV)(HHV)(A), using the MM Btu,
where A
ϭ
amount of air required, lb (kg) per MM Btu (kJ) fired. The above
quantity
ϭ
air available in the exhaust gases, W
a
ϭ
0.0417 W
g
(O).
3. Simplify the gas relations further
From the data in step 2, (Q / LHV)(HHV)(A)/10
6
ϭ
0.0417 W
g
(O). For natural gas
and fuel oils it can be shown that (LHV/A
x
HHV)
ϭ
0.00124. For example, LHV
of methane
ϭ

21,520 Btu/lb (50,055.5 kJ/kg); HHV
ϭ
23,879 Btu/lb (55,542.6
kJ/kg), and A
ϭ
730 lb (331.4 kg). Hence, (LHV/A
x
HHV)
ϭ
21,520/(730
ϫ
23,879)
ϭ
0.00124. By substituting in the equation in step 1, we have Q
ϭ
58.4
(W
g
)(O). This is an important equation because it relates the oxygen consumption
from the exhaust gases to the burner fuel consumption.
4. Find the fuel input to the HRSG
The fuel input is given by W
g
ϩ
h
g 1
ϩ
Q
ϭ
(W

g
ϩ
)(h
g 2
), where h
g 1
and h
g 2
W
ƒ
are the enthalpies of the exhaust gas before and after the fuel burner;
ϭ
fuelW
ƒ
input, lb/h (kg/h); Q
ϭ
fuel input in Btu/h (kJ /h).
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MODERN POWER-PLANT CYCLES AND EQUIPMENT