Handbook of Mechanical Engineering Calculations P2

2.1
SECTION 2
STEAM CONDENSING
SYSTEMS AND AUXILIARIES
Design of Condenser Circulating-Water
Systems for Power Plants
2.1
Designing Cathodic-Protection Systems
for Power-Plant Condensers
2.7
Steam-Condenser Performance Analysis
2.12
Steam-Condenser Air Leakage
2.16
Steam-Condenser Selection
2.17
Air-Ejector Analysis and Selection
2.18
Surface-Condenser Circulating-Water
Pressure Loss
2.20
Surface-Condenser Weight Analysis
2.22
Weight of Air in Steam-Plant Surface
Condenser
2.23
Barometric-Condenser Analysis and
Selection
2.24
Cooling-Pond Size for a Known Heat
Load

2.26
DESIGN OF CONDENSER CIRCULATING-WATER
SYSTEMS FOR POWER PLANTS
Design a condenser circulating-water system for a turbine-generator steam station
located on a river bank. Show how to choose a suitable piping system and cooling
arrangement. Determine the number of circulating-water pumps and their capacities
to use. Plot an operating-point diagram for the various load conditions in the plant.
Choose a suitable intake screen arrangement for the installations.
Calculation Procedure:
1. Choose the type of circulating-water system to use
There are two basic types of circulating-water systems used in steam power plants
today—the once-through systems, Fig. 1a, and the recirculating-water system, Fig.
1b. Each has advantages and disadvantages.
In the once-through system, the condenser circulating water is drawn from a
nearby river or sea, pumped by circulating-water pumps at the intake structure
through a pipeline to the condenser. Exiting the condenser, the water returns to the
river or sea. Advantages of a once-through system include: (a) simple piping ar-
rangement; (b) lower cost where the piping runs are short; (c) simplicity of
operation—the cooling water enters, then leaves the system. Disadvantages of once-
through systems include: (a) possibility of thermal pollution—i.e., temperature in-
crease of the river or sea into which the warm cooling water is discharged; (b) loss
of cooling capacity in the event of river or sea level decrease during droughts; (c)
trash accumulation at the inlet, reducing water flow, during periods of river or sea
pollution by external sources.
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS
2.2
POWER GENERATION

River flow
River flow
FIGURE 1 a. Once-through circulating-water system discharges warm
water from the condenser directly to river or sea. Fig. 1b. Recirculating-
water system reuses water after it passes through cooling tower and sta-
tionary screen. (Power.)
Recirculating systems use small amounts of water from the river or sea, once
the system has been charged with water. Condenser circulating water is reused in
this system after passing through one or more cooling towers. Thus, the only water
taken from the river or sea is that needed for makeup of evaporation and splash
losses in the cooling tower. The only water discharged to the river or sea is the
cooling-tower blowdown. Advantages of the recirculating-water system include: (a)
low water usage from the river or sea; (b) little or no thermal pollution of the
supply water source because the cooling-tower blowdown is minimal; (c) remote
chance of the need for service reductions during drought seasons. Disadvantages
of recirculating systems include: (a) possible higher cost of the cooling tower(s)
compared to the discharge piping in the once-through system; (b) greater operating
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.3
complexity of the cooling tower(s), their fans, motors, pumps, etc.; (c) increased
maintenance requirements of the cooling towers and their auxiliaries.
The final choice of the type of cooling system to use is based on an economic
study which factors in the reliability of the system along with its cost. For the
purposes of this procedure, we will assume that a once-through system with an
intake length of 4500 ft (1372 m) and a discharge length of 4800 ft (1463 m) is
chosen. The supply water level (a river in this case) can vary between

ϩ
5 ft (1.5
m) and
ϩ
45 ft (13.7 m).
2. Plot the operating-point diagram for the pumping system
The maximum cooling-water flow rate required, based on full-load steam flow
through the turbine-generator, is 314,000 gpm (19,813 L /s). Intermediate flow rates
of 283,000 gpm (17,857 L/s) and 206,000 gpm (12,999 L/ s) for partial loads are
also required.
To provide for safe 24-hour, 7-day-per-week operation of a circulating-water
system, plant designers choose a minimum of two water pumps. As further safety
step, a third pump is usually also chosen. That will be done for this plant.
Obtaining the pump characteristic curve from the pump manufacturer, we plot
the operating-point diagram, Fig. 2, for one-pump, two-pump, and three-pump op-
eration against the system characteristic curve for river (weir) levels of
ϩ
5 ft (1.5
m) and
ϩ
45 ft (13.7 m). We also plot on the operating-point diagram the seal-well
weir curve.
The operating-point diagram is a valuable tool for both plant designers and
operators because it shows the correct operating range of the circulating-water
pumps. Proper use of the diagram can extend pump reliability and operating life.
3. Construct the energy-gradient curves for the circulating-water system
Using the head and flow data already calculated and assembled, plot the energy-
gradient curve, Fig. 3, for several heads and flow rates. The energy-gradient curve,
like the operating-point diagram, is valuable to both design engineers and plant
operators. Practical experience with a number of actual circulating-water installa-

tions shows that early, and excessive, circulating-pump wear can be traced to the
absence of an operating-point diagram and an energy-gradient curve, or to the lack
of use of both these important plots by plant operating personnel.
In the once-through circulating-water system being considered here, the total
conduit (pipe) length is 4500
ϩ
4800
ϭ
9300 ft (2835 m), or 1.76 mi (2.9 km).
This conduit length is not unusual—some plants may have double this length of
run. Such lengths, however, are much longer than those met in routine interior plant
design where 100 ft (30.5 m) are the norm for ‘‘long’’ pipe runs. Because of the
extremely long piping runs that might be met in circulating-water system design,
the engineer must exercise extreme caution during system design—checking and
double-checking all design assumptions and calculations.
4. Analyze the pump operating points
Using the operating-point diagram and the energy-gradient curves, plot the inter-
section of the system curves for each intake water level vs. the characteristic curves
for the number of pumps operating, Fig. 3. Thus, we see that with one pump
operating, the circulating-water flow is 120,000 gpm (7572 L/s) at 48.2 ft (14.7 m)
total dynamic head.
With a weir level of
ϩ
5 ft (1.5 m), and two pumps operating, the flow is 206,000
gpm (12,999 L /s) at 79 ft (24.1 m) total dynamic head. When three pumps are
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.4

POWER GENERATION
FIGURE 2 Operating-point diagram shows the correct operating range of the circulating-water
pumps. (Power.)
used at the 5-ft (1.5 m) level, the flow is 225,000 gpm (14,198 L/ s) at 79 ft (24.1
m) total dynamic head.
Using the sets of curves mentioned here you can easily get a complete picture
of the design and operating challenges faced in this, and similar, plants. The various
aspects of this are discussed under Related Calculations, below.
5. Choose the type of intake structure and trash rack to use
Every intake structure must provide room for the following components: (a) cir-
culating-water or makeup-water pumps; (b) trash racks; (c) trash-removal
screens—either fixed or traveling; (c) crane for handling pump removal or instal-
lation; (d) screen wash pump; (e) access ladders and platforms.
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.5
FIGURE 3 Energy-gradient diagram shows the actual system pressure values and is valuable in
system design and operation. (Power.)
A typical intake structure having these components is shown in Fig. 4. This
structure will be chosen for this installation because it meets the requirements of
the design.
Trash-rack problems are among the most common in circulating-water systems
and often involve unmanageable weed entanglements, rather than general debris.
The type of trash rack and rack-cleaning facilities used almost exclusively in the
United States and many international plants, is shown in Fig. 4. Usually, the trash
rack is inclined and bars are spaced at about 3-in (76.2-mm). The trash rake may
be mechanical or manual.

The two usual rake designs are the unguided rake, which rides on the trash bars,
and the guided rake, which runs in guides on the two sides of the water channel.
If the trash bars are vertical, the guided rake is almost a necessity to keep the rake
on the bars. But neither solves all the problems.
If seaweed or grass loads are particularly severe, alternative trash rakes, such as
the catenary or other moving-belt rakes, should be considered. These are rarely put
into original domestic installations. There are many other alternative types of trash
racks and rakes in use throughout the world that are successful in handling heavy
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.6
POWER GENERATION
FIGURE 4 Intake structure has trash rack, traveling screen, pumps, and crane for dependable
operation of the circulating-water system. (Power.)
loads. Log booms, skimmer walls, channel modifications, and specialized raking
equipment can sometimes alleviate raking problems.
Traveling screens follow the trash racks. These usually are of the vertical flow-
through type. European practice uses alternative screens, such as center-flow, dual-
flow, and drum screens. Traveling screens may be one- or two-speed. Most two-
speed screens operate in the range of 3 to 12 fpm (0.9 to 3.7 m /min) but speeds
as high as 30 fpm (9.1 m /min) have been used. Wear is much greater at higher
speeds.
Depending on the type of piping used in the circulating-water system—concrete
or steel—some form of cathodic protection may be needed, in addition to the trash
racks and rakes. Cathodic protection is needed primarily when steel pipe is used
for the circulating water system. Concrete pipe does not, in general, require such
protection. Since the piping in once-through systems can be 10 to 12 ft ( 3 to 3.7
m) in diameter, use of the cathodic protection is an important step in protecting an

expensive investment. Cathodic protection methods are discussed elsewhere in this
handbook.
Related Calculations. Designing a condenser circulating-water system can be
a complex task when the water supply is undependable. With a fixed-level supply,
the design procedure is simpler. The above procedure covers the main steps in such
designs. Head loss, pipe size, and other considerations are covered in detail in
separate procedures given elsewhere in this handbook.
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.7
Construction of the operating-point diagram and the energy-gradient chart are
important steps in the system design. Further, these two plots are valuable to op-
erating personnel because they give the design assumptions for the system. When
pressures or flow rates change, the operator will know that the system requires
inspection to pinpoint the cause of the change.
The design procedure given here can be used for other circulating-water ap-
plications, such as those for refrigeration condensers, air-conditioning systems,
internal-combustion-engine plants, etc.
Data given here are the work of R. T. Richards, Burns & Roe Inc., as reported
in Power magazine. SI values were added by the handbook editor.
DESIGNING CATHODIC-PROTECTION SYSTEMS
FOR POWER-PLANT CONDENSERS
Design a cathodic-protection system for an uncoated 10,000-tube steam condenser
having an exposed waterbox/tubesheet surface area of 1000 ft
2
(92.9 m
2

). Deter-
mine the protective current needed for this condenser if the design current density
is 0.2 amp/ft
2
(2.15 amp/ m
2
) and 95 percent effective surface coverage will be
maintained. How many anodes of magnesium, zinc, and aluminum would be needed
in seawater to supply 50 amp for protection? Compare the number of anodes that
would be needed in fresh water to supply 50 amp for protection.
Calculation Procedure:
1. Determine the required protective current needed
Cathodic protection of steam condensers is most often used to reduce galvanic
corrosion of ferrous waterboxes coupled to copper-alloy tubesheets and tubes. Sys-
tems are also used to mitigate attack of both iron-based waterboxes and copper-
alloy tubesheets in condensers tubed with titanium or stainless steel.
Cathodic protection is achieved by forcing an electrolytic direct current to flow
to the structure to be protected. The name is derived from the fact that the protected
structure is forced to be the cathode in a controlled electrolytic circuit.
There are two ways this current may be generated: (1) Either an external direct-
current power source can be used, as in an impressed-current system, Fig. 5a,or
(2) a piece of a more eletronegative metal can be electrically coupled to the struc-
ture, as in a sacrificial anode system, Fig. 5b.
The first step in the design of a cathodic-protection system is to estimate the
current requirement. The usual procedure is to calculate the exposed waterbox and
tubesheet area, and then compute the total current needed by assuming a current
density. In practice, current needs are often estimated by applying a test current to
the structure and measuring the change in structure potential.
Table 1 lists actual current densities used by utilities to protect condensers made
of several different combinations of metals. The values given were taken from a

survey prepared for the Electric Power Research Institute ‘‘Current Cathodic Pro-
tection Practice in Steam Surface Condensers,’’ CS-2961, Project 1689-3, on which
this procedure and its source are based.
With a design current density of 0.2 amp /ft
2
(2.15 amp /m
2
), the total protective
current need
ϭ
0.2 (1000)
ϭ
200 amp. With the 95 percent effective surface cov-
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.8
POWER GENERATION
Power Supply
Auxiliary
anode
Protected
structure
(cathode)
Sacrificial
anode
Protected
structure
(a)

(b)
FIGURE 5 a. Impressed-current cathodic protection system uses exter-
nal source to provide protective current. Fig. 5b. Sacrificial-anode cathodic
protection uses piece of metal more electronegative than the structure for
protection. (Power.)
erage, 5 percent of the surface will be exposed through coating faults. Hence, the
required protective current will be 0.05(200)
ϭ
10 amp. Clearly, gross miscalcu-
lations are possible if the effectiveness of the coating is incorrectly estimated. The
value of 0.2 amp /ft
2
(2.15 amp/ m
2
) is taken from the table mentioned above.
Another problem in estimating protective-current requirements occurs when con-
densers are tubed with noble alloy tubing such as stainless steel or titanium. In this
case, a significant length of tubing (up to 20 ft—6.1 m) may be involved in the
galvanic action, depending on the water salinity, temperature, and the tube material.
This length dictates the anode /cathode area ratio and, thus, the rate of galvanic
corrosion. Protective-current needs for this type of condenser can be unusually high.
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.9
TABLE 1
Current Densities Used for Various Condenser Materials*
Condenser materials

Waterbox Tubesheet Tubes
Design
current density
amp/ft
2
amp/m
2
Average
water salinity
ppm
Carbon steel Aluminum
bronze
90-10 Cu Ni 0.05 0.54 1000
Cast iron Muntz AL-6X stainless
steel
0.1 1.08 35,000
Epoxy-coated
carbon steel
Epoxy-coated
copper-nickel
Titanium 0.07 0.75 35,000
Carbon steel Muntz Aluminum brass 0.06 0.65 1000
Carbon steel Muntz 90-10 Cu Ni 0.06 0.65 1000
Carbon steel Muntz Aluminum brass 0.2 2.2 30,000
*Power
TABLE 2
Current Output that can be Expected from Typical Sacrificial Anodes Materials*
Current range
seawater, amp
Current range

fresh water, amp
Magnesium 1.4–2.3 0.014–0.023
Zinc 0.5–0.8 0.005–0.008
Aluminum 0.5–0.8 0.005–0.008
*Power
2. Select the type of protective system to use
Protective-current needs generally determine whether an impressed-current or sac-
rificial-anode system should be used. For a surface condenser, the sacrificial-anode
system generally become impractical at current levels over 50 amp.
For a sacrificial-type system, the current output can be estimated by determining
the effective voltage and the resistance between anode and structure. The effective
voltage between anode and structure is defined as the anode-to-structure open-
circuit voltage minus the back-emf associated with polarization at both anode and
structure. This voltage depends primarily on the choice of materials, as shown in
Table 2.
Resistance of the metallic path is usually negligible for an uncoated structure
and the electrolytic resistance is dominant. For a coated structure, this resistance
may become significant. The maximum achievable current output can be estimated
by considering the case of an uncoated structure.
3. Determine the number of anodes needed for various sacrificial materials
Table 2 gives a range of current outputs estimated for different sacrificial materials
with an anode of the dimensions shown in Fig. 6. Thus, for any sacrificial material,
number of anodes needed
ϭ
(required protective-current output, amp)/ (current out-
put for the specific sacrificial material, amp).
Since the condenser being considered here is cooled by seawater, we will use
the values in the first column in Table 1. For magnesium, number of anodes required
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.10
POWER GENERATION
6 IN. (152 CM)
10 IN. (254 CM)
1 1/4 IN. (32 CM)
FIGURE 6 Typical sacrificial anode consists
of a flat slab of the consumable metal into which
fastening straps are cast. (Power.)
ϭ
50/ 2.3
ϭ
21.739; say 22 anodes. For zinc, number of anodes required
ϭ
50/
0.8
ϭ
62.5; say 63 anodes. For aluminum, number of anodes required
ϭ
50/ 0.8
ϭ
62.5; say 63. From a practical standpoint, 63 sacrificial anodes is an excessive
number to install in most condenser waterboxes.
The respective service of these anodes at 50 amp are about three months for
magnesium, six months for zinc and aluminum. This short service further reduces
the practicality of sacrificial anodes at high protective current levels.
However, in fresh water, the current output is lower and is limited by the higher
resistance of the water. Corresponding service lives are 5 to 10 years for magne-
sium, and 40 to 60 years for zinc and aluminum. Protective coating further reduces

the effective wetted surface area and lowers the required protective current at the
same time as it limits the current output of the anodes.
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STEAM CONDENSING SYSTEMS AND AUXILIARIES
STEAM CONDENSING SYSTEMS AND AUXILIARIES
2.11
FIGURE 7 Bayonet-type impressed-current
anode is located for optimum current throw
onto the condenser tubesheet. (Power.)
4. Choose the type of anode material to use
Several different factors affect the choice of anode material in both sacrificial and
impressed-current systems. Choice of a sacrificial-anode material is largely deter-
mined by the current density needed, but the efficiency of the material is also
important. In an anode material that is 50 percent efficient, half the material dete-
riorates without providing any useful current. Typical electrochemical efficiencies
are: magnesium, 40–50 percent; zinc, 90 percent; aluminum, 80 percent.
Here are brief features of several important anode materials: Magnesium anodes
provide a high driving voltage, but are not as efficient as zinc or aluminum. Zinc
anodes are excellent as sacrificial material; at temperatures above 140
Њ
F (60
Њ
C),
zinc may passivate, providing almost no protective current. Aluminum anodes are
not widely used to protect surface condensers because of performance problems.
Steel anodes are used in a few power plants to protect copper-alloy tubesheets, but
they are less efficient than traditional materials.
Impressed-current systems, Fig. 5a, use anodes of platinized alloy, lead alloy, or

iron alloy. Platinized- and lead-alloy anodes are favored in seawater, while iron-
alloy anodes are favored in low-salinity water. Platinized- and lead-alloy anodes
can be operated at higher current density than those of iron alloy, so fewer anodes
are needed in the waterbox.
Platinized-titanium anodes can be operated at current densities up to 1000
amp/ft
2
(10,764 amp/m
2
) and voltages up to about 8 V in seawater. Such anodes
should have a service life of 10 to 20 years, depending on the current density and
the platinum plating thickness.
Lead-alloy anodes are widely used in seawater applications. These anodes can
be operated at current densities as high as 10 to 20 amp/ ft
2
(107.6 to 215.3 amp/
m
2
) with a life expectancy of more than 10 years.
Related Calculations. This procedure outlines the essentials of sizing anodes
for protecting steam surface condensers. For more detailed information, refer to the
report mentioned in step 1 of this procedure. Data for this procedure were compiled
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STEAM CONDENSING SYSTEMS AND AUXILIARIES