M/££rW WATER POLLUTION CONTROL RESEARCH SERIES • 16130—10/70
^WillWI^
THERMOELECTRIC GENERATORS
POWERED BY THERMAL WASTE
FROM ELECTRIC POWER PLANTS
ENVIRONMENTAL PROTECTION AGENCY • WATER QUALITY OFFICE
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the
results and progress in the control and abatement of pollution
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Environmental Protection Agency, Washington, D C 20242
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THERMOELECTRIC GENERATORS POWERED BY THERMAL WASTE
FROM ELECTRIC POWER PLANTS
Mostafa A. Shirazi
National Thermal Pollution Research Program
ENVIRONMENTAL PROTECTION AGENCY
Water Quality Office
Pacific Northwest Water Laboratory
Corvallis, Oregon 97330
October 1970
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, B.C., 20402 - Price 45 cents
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EPA Review Notice
This report has been reviewed by the Water Quality Office,
EPA, and approved for publication. Approval does not signi-
fy that the contents necessarily reflect the views and poli-
cies of the Environmental Protection Agency, nor does mention
of trade names or commercial products constitute endorsement
or recommendation for use.
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ABSTRACT
The feasibility of recovering electricity from the waste heat of elec-
tric power plants was assessed. Sources considered were: stack flue
gas, gas—turbine exhaust, and condensing steam. Typical 1600 MW fossil—
fuel steam plants and gas—turbine plants were used as examples. Flat
plate heat exchangers were designed with thermoelectric couples arranged
in series within the plates. Heat flux, conversion efficiencies, and
flow friction losses were calculated. Except for the condenser applica-
tion, the friction losses are several times the thermoelectric power
generated. Under favorable conditions, 3 to 9 MW is obtainable from the
thermoelectric condensers. The high material cost, however, precludes
all such applications today.
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CONTENTS
SECTION Page
I INTRODUCTION . 1
II THERMOELECTRIC HEAT EXCHANGER ANALYSIS 3
III THERMOELECTRICITY FROM CONDENSING STEAM 7
0-1 The Power Density, d 8
D-2 Power Intensity,
0-3 Net Power, net 13
0-4 The Effects of Turbine Back Pressure on
Power Generated 16
0-5 The Effects of a High Figure of Merit. . . . 18
IV THERMOELECTRICITY FROM COMBUSTION PRODUCTS 19
V COST ANALYSIS 21
VI CONCLUSION 25
VII REFERENCES 27
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LIST OF FIGURES
Figure Page
1 A Crossflow Thermoelectric Heat Exchanger Unit . . . . 4
2 Power Density for Several Thermoelectric Condensers. 10
3 The (net) Power Intensity for Geometries Indicated . 14
4 Power Generated from Thermoelectric Condenser lO.27T
From the Waste of a 1600 MW Steam Power Plant
Operating at 4”Hg abs 15
5 Maximum Thermoelectric Power Generated as a Function
of Turbine Back Pressure from the Waste of a 1600 MW
Steam Power Plant 17
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LIST OF TABLES
Table Page
1 Condenser Design Data for Three
Cooling Water Temperatures 8
2 Peak Performance Data for the Three
Thermoelectric Condensers Shown in Figure 2
(a) Geometric Data 11
(b) Heat Exchange and Flow Data 11
(c) Power Generation Data 12
3 Heat Transfer and Generating Performance
Characteristics of the Thermoelectric
Condenser 10.271 16
4 Comparative Cost of Thermoelectric Generation
(Plate Thickness .01”) with Steam-Electric
Generation both for 3.066 MWe 22
5 Comparative Cost of Thermoelectric
Generation/Steam Electric Generation 23
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SECTION I
I NTRODUCT ION
Thermoelectric generators are known to be inefficient. Their use in
direct energy conversion lead to several times greater fuel consumption
than conventional methods. Thermoelectric generators powered by the
waste heat would not suffer, at least, from this disadvantage. The high
material and development costs have rendered such generators commercially
unattractive, if not outright prohibitive today.
If the quest for a higher efficiency persists despite an economic penalty,
thermoelectric devices could be used to reduce the waste heat from con-
ventional power plants by converting a minute portion of it to electricity.
This, admittedly, is not the most efficient or least expensive way.
Against this background, we proceed to entertain the possibility of
applying thermoelectric materials to waste heat utilization, leaving its
economic feasibility aside for the moment. When we return to the dis-
cussion of the latter problem, we are able to present only a rough esti-
mate of the cost involved.
In a study by Embry and Tudor (1), thermoelectric generators were powered
by the exhaust heat of an auto engine. The generators were shown to supply
the entire electrical requirements of an automobile, thereby slightly in-
creasing the overall engine efficiency. Embry and Tudor presented several
references to earlier attempts concerning similar application of thermo-
electric devices.
The present study applies thermoelectric devices to the utilization of
waste heat from thermal power plants. In particular, the low pressure
steam from a steam power cycle could be condensed in a special “thermo-
electric condenser” that has thermocouple circuits embedded within its
walls. While conducting the latent heat from the condensing steam to
the cooling water, the couples convert a portion of this heat to elec-
tricity.
A second source of waste heat in a conventional fossil-fueled electric
power plant is the hot stack gases released into the atmosphere. A
third source is the hot exhaust gases from a gas turbine electric power
system. The hot gases from these sources, too, could be passed through
special (thermoelectric) heat exchangers for generating electricity
while conducting heat through the couples to the ambient air on the
cold side.
The condenser application receives the primary emphasis. The gas-turbine
exhaust and the stack gas applications will be discussed briefly, show-
ing in each case some of the results without presenting the details.
While reasonable designs will be sought in the course of this study to
enable meaningful estimates, no attempt will be made to find the most
optimum situations.
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SECTION II
THERMOELECTRIC HEAT EXCHANGER ANALYSIS
It is convienent for the purpose of this discussion to specify a feasible
heat exchanger geometry. Consider as a possible arrangement the plate-
fin surface geometry shown in Figure 1-a. The heat exchanger is of the
cross-flow type. The plates (or modules) separating the hot fluid from
the cold fluid contain the thermoelectric elements. Such plates lend
themselves easily to the current manufacturing techniques for thermo-
electric modules. The module surfaces are protected on each side by a
sheet of stainless steel plate, 0.005-inch thick. The elements within
the plates are connected in series as shown in Figure 1-b. The plates
themselves are arranged in pairs in such a way that the hot (or cold)
junctions of their couples face one another. For condensers, the plates
are finned only on the water side. For gas-to-gas exchangers, the
plates are finned on both sides. The spacing between the plates on the
cold side is held equal to that on the hot side for all cases considered
here. The heat exchangers are made in the shape of cubes - 12-feet on
each side. The plate module thickness is varied between 0.004-inch to
0.2—inch. The packing density of the couples is not specified, but the
calculations assume very dense packing.
The convective heat transfer coefficient is calculated from:
—2 , 2/
h = (c /D Npr 3 ) (N tNpr 3) NR (1)
where NR is the Reynolds Number, N 5 t is the Stanton Number, Npr the
Prandt] Number, 0 the hydraulic diameter, i the viscosity coefficient,
and c the specific heat. The friction power expended per unit surface
areais evaluated from:
E = (2p 2 gY’(p/D) 3 f N 3 (2)
where pis the density, and f the friction factor. The heat transfer and
flow friction performance data are found in Reference 2.
To enable calculation of the thermoelectric conversion efficiencies, surface
temperatures on the hot and cold sides of the modules will be evaluated by
allowing a linearly proportionate temperature drop for all the fluid and
material thermal resistances across the plate. The effect of the fluid
temperature changes along the heat exchanger path is accounted for by
taking a simple arithmetic average of the inlet and outlet fluid tempera-
tures. The maximum thermal conversion efficiency is evaluated from:
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P1.ATE (OR
MODULE)
THICKNESS
PLATE
SPACING
12’
HOT
c .o auto
FLUID
a) HEAT EXCHANGER UNIT SHOWING PLATE ARRANGDLNT
AND DIIIENSIOIIS.
ri ___
Ii U LI I I Ii II [ T [ It
/ vvwvvvwcwvvvvvvc -r
b) CROSS-SECTION OF A flODlIE SHO •:I7:5 IflE THER OELECTRIC
ELEI ENTS, STAINLESS STEEL PROTECTII G SHEll AflD n tiS.
FIGURE 1. A CROSSFLOW THERMOELECTRIC HEAT EXCHAIGER UNIT.
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T 1 _ T 0 m 0 1 (3)
where
(1 + Z (T + Ti)/2)” (4)
T 1 is the hot junction and T 0 the cold junction temperatures both measured
in the absolute scale, and Z is the figure of merit for the thermoelectric
material.
The thermoelectric material properties were evaluated at the mean tempera-
tures of the hot and cold fluids. The alloys considered in this study
were Bi 2 Te 3 -Bi 2 Se 3 (n-type) and Bi 2 Te 3 —Sb 2 Te 3 (p-type).
5
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SECTION III
THERMOELECTRICITY FROM CONDENSING STEAM
In this application, the condenser cooling water serves as the heat sink
and the condensing steam as the heat source. The “thermoelectric con-
denser” has the general features just described and it serves the usual
function of condensing steam and maintaining the appropriate turbine back
pressure in a steam power cycle. In addition, it converts a fraction of
the latent heat of the steam to electricity. The magnitude of electric
power so generatedis governed by the temperature of the cooling water,
the turbine back pressure, and the steam rate. In order to fix our
ideas, we choose the three power plants listed in Table 1. The steam
flow delivered to the condensers is assumed equal to 7 x 106 lb/hr. The
temperature of the cooling water available to the first power plant is
40°F and the corresponding back pressure is 0.5-inches of mercury abso-
lute. The second and third power plants have access to cooling waters
at temperatures of 65°F and 80°F, respectively. The corresponding turbine
back pressures are 1.5” Hg and 4” Hg, absolute. The second power plant
is an example of a typical modern generating system. The other two are
examples of somewhat extreme pressure and temperature conditions. The
latter could conceivably represent two off-design operating conditions
of the second power plant. The terminal temperature difference between
the condensate and the cooling water exit temperature is 5°F or more.
The approximate relationship between the cooling water temperature is
5°F or more. The approximate relationships between the cooling water
temperature and the most economical condenser pressure are assumed in
accordance with the data presented in References 3 and 4. The total heat
carried away by the cooling water decreases slightly with condensing
pressure because of the corresponding decrease in the latent heat of
vaporization. The efficiency of the power plant increases at lower back
pressures with the corresponding increase in the power plant output. For
a station efficiency of 40 percent, the electric output from power plant
II is roughly 1640 MW.
The third power plant represents the most favorable conditions for thermo-
electric power generation for it has the highest condenser temøerature.
Detailed thermoelectric condenser design calculations are carried out for
this case alone. The other two cases are treated in a general way only.
The design procedure followed is briefly outlined below.
The cooling water rate was estimated for a specific surface geometry and
an initial plate thickness. The flow velocity and the Reynolds Number
were calculated to be used in Equations (1) and (2). With the aid of
experimental performance data from Reference 2 and these equations, the
convective heat transfer coefficient and the friction power on the water
side were evaluated. The convective heat transfer coefficient was then
used in evaluating the fin efficiency, the overall unit heat transfer
conductance, the number of heat transfer unit (NTU), and the heat ex-
changer effectiveness. From the last item, the total heat transfer for
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a single condenser unit was calculated. More units were added to achieve
a total heat transfer equal to 2063 MW - a quantity equal to the latent
heat released by the incoming steam in the third power plant. At this
point, if the outlet water temperature was equal to 98°F or slightly
below, the heat transfer calculation was considered complete and Equation
(3) was used to evaluate the thermoelectric conversion efficiency and the
power generated. This procedure was repeated for several plate thicknesses
and heat exchanger surface geometries. In all calculations, an attempt was
made to find the minimum number of condenser units that would condense the
incoming steam without raising the outlet water temperature above 98°F.
For the convenience in calculation, the convective heat transfer coefficient
on the steam side was held at an arbitrary, but a reasonable, magnitude of
3000 Btu/hr ft 2 °F.
TABLE 1
CONDENSER DESIGN DATA FOR THREE
COOLING WATER TEMPERATURES
Plant I
Plant II
Plant III
Cooling water in t 1 , °F
Steam pressure, °Hg abs
40
.5
65
1.5
80
4.
Steam temperature t 5 , °F
Cooling water out t 2 , °F
Steam rate 106 lb/hr
58.9
53
7
91.7
85
7
125.4
98
7
Heat to cooling water, MW
2176
2137
2063
Many important parameters were calculated for each design. Among these,
three quantities were of particular significance. They were: (1) the
power density, d’ expressed in net kilowatts generated per cubic foot
of thermoelectric material; (2) the power density, P expressed in watts
per square foot of generating surface; and (3) the net power, 1 ’net’ ex-
pressed in megawatts.
D-l The Power Density, Pd :
The total thermoelectric power generated in all units less the total power
expended in flow friction was divided by the total volume of the thermo-
electric material used in the plate modules to find the (net) power density
The plots of d against the plate thickness for the three heat transfer
8
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surfaces is shown in Figure 2. For each surface geometry, the power density
curve peaks at an optimum plate thickness td The power density maxima for
the surfaces examined are seen to occur between 0.003-inch to 0.01-inch.
The magnitudes of d at these points vary between 10.23 KW/ft 3 to 16.67
KW/ft 3 .
A physical explanation for the peaking behavior of these curves may be as
follows: when the plate is thick, the thermal resistance is great and
the heat flux is low. Hence, the surface area and thus the material
volume must be increased to allow the required heat transfer to take
place. The conversion efficiency is relatively large, but with a small
heat flux, only a small amount of power per unit volume can be generated.
As the plate thickness is reduced, the heat flux increases, too. This
trend continues up to a certain point, td where the plate is still thick
enough to maintain a relatively large differential temperature between
the hot and cold sides. At this point, the maximum power density occurs.
As the plate thickness is further reduced, it becomes progressively more
difficult to maintain an adequately large differential temperature across
the plate. From there on, the conversion efficiency is drastically re-
duced and the power density eventually drops to zero.
For the convenience in presenting the condenser performance data, three
separate tables are provided. Table 2—a contains the geometric data in-
cluding the unit and passage dimensions, the number of plate modules per
unit, the total number of units, and the optimum plate thickness, td of
the power density curve. Table 2-b contains the heat transfer and flow
data including the outlet water temperature, water velocity, the Reynolds
Number, the heat transfer coefficients, the heat exchanger effectiveness,
the total heat transfer and the flow friction. Particular reference
should be made in this table to the small magnitudes of the fin effective-
ness (18 to 35 percent) and the heat exchanger effectiveness (about 38
percent). These quantities could stand much improvement. Practical heat
exchangers have better than 70 percent fin and heat transfer effectiveness.
Also, the ratio of the friction power to the heat. transfer for these cal-
culations is at least an order of magnitude greater than the corresponding
values found in a shell and tube condenser. Some of this is attributed
to the poor thermal conductivity of the thermoelectric material as com-
pared with copper alloys and the consequent effect this has on reducing
the heat flux and increasing the surface area. Friction is also increased
by the presence of fins in these designs.
Finally, the power generation data are shown listed in Table 2-c. These
include surface temperatures, Carnot cycle efficiency, conversion efficiency,
the ratio of net power to heat transfer, and the flow friction power. The
Carnot cycle efficiency is between 0.5 to 2 percent, the conversion effi-
ciency is about ten times less than the latter, and the ratio of net power
to heat transfer is slightly less than the conversion efficiency.
9
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•17
16
15
14
13
12
U
4J
‘ 10
It
0 1 11111
.001 .01 .1
PLATE THICKNESS, t, INCH
FIGURE 2. POWER DENSITY FOR SEVERAL. THERMOELECTRIC COM)E SERS
I I
S
I I 11111
SURFACE GEOMETRY
dA 10.271
o 3.97
0 9.03
I
S
S
1 I ii i I ] I
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TABLE 2
PEAK PERFORMANCE DATA FOR THE THREE
THERMOELECTRIC CONDENSERS SHOWN IN FIGURE 2
(a) Geometric Data
Unit Designation
1O.27T
9.03
3.97
Plate spacing (in.)
.544
.823
.75
Hydraulic diameter (in.)
.151
.1828
.338
Frontal area, ft 2
144
144
144
Unit volume, ft 3
1728
1728
1728
Fin area/Total area
.863
.888
.766
Water side area, Million ft 2
1.450
2.676
1.115
Plate thickness (in.)
.01
.01
.003
Number of plates per unit
256
266
189
Number of units
6
13
11
(b) Heat
Exchange & Flow Data
Unit Designation
10.27T
9.03
3.97
Outlet water temperature, °F
97.5
96.6
97.0
Water velocity, ft/sec
4.75
2.24
2.83
Reynolds Number
8080
4620
10800
Water side h, Btu/hr ft 2 °F
1174
562
715
Steam side h, Btu/hr ft 2 °F
3000
3000
3000
Fin effectiveness, %
.216
.18
.350
Total thermal resistance,
hr ft 2 °F/Btu
.00741
.0139
.00576
Heat exchanger effectiveness
.385
.365
.374
Flow Friction, Watt/ft 2
1.061
.1307
.211
Total Heat Transfer, MW
2060
2064
2059
Friction/heat Transfer, %
.0746
.0169
.0114
11
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TABLE 2 (CONT.)
PEAK PERFORMANCE DATA FOR THE THREE
THERMOELECTRIC CONDENSERS SHOWN IN FIGURE 2
Cc) Power Generation Data
Unit Designation
1O.27T
9.03
3.97
Hot junction temperature, °K
321.1
322.4
321.4
Cold junction temperature, °K
314.9
318.3
319.7
Carnot cycle efficiency, %
1.924
1.279
.532
Conversion efficiency, %
.2235
.1490
.0618
Net power/heat transfer, %
.1488
.1321
.0504
Friction power, MW
1.538
.350
.236
Net power, MW
3.066
2.726
1.04
Friction power/electric power
.3340
.1137
.1851
Power intensity, Watt/ft 2
13.89
8.526
3.47
Maximum power density, KW/ft 3
16.67
10.23
13.9
Thermoelectric material
volume, ft 3
184.0
266.4
74.74
It appears from the comparison of these data
formance with the highest electrical output.
smallest hydraulic radius and plate spacing.
tion, other selections should be made. There
improvements could not be introduced in these
D-2 Power Intensity, P :
that 10.27T has the best per-
This configuration has the
To find a better configura-
is no reason why further
designs.
The power density curve has a logical design appeal for it maximizes the
power output per unit volume. However, the peak of this curve occurs at
a very small plate thickness and it may become too costly to slice very
thin couples. The designer then may choose a thicker module to avoid the
high manufacturing cost. The power intensity curve can be used as a guide-
line in this situation. The power intensity curve is obtained from dividing
the net power output per module by the total module surface area. A design
that is based on maximizing power intensity relaxes some of the emphasis
that might be unduly placed on the saving of material in return for a
possible gain in the total power generated.
12
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The plots of P against the material volume is seen in Figure 3. These
plots, too, exhibit definite peaks but the peaks occur at optimum plate
thicknesses ti>td as indicated by the markers on the curves.
It is interesting to note that t. and td could be used in a design to
define two limits for a possible module thickness, t. If t is made more
nearly equal to td then the greatest power per unit volume of the thermo-
electric material is obtained. Alternately, if t is made more nearly
equal to t , maximum power per unit module area is obtained.
In an ideal situation, the surface geometry is so selected that for a
given application the power density curve and the power intensity curve
both peak at the same plate thickness, that is,
t td = t. (for the most optimum design).
D-3 Net Power, Pnet :
The plots for the total power generated and the net power for lO.27T
alone are shown in Figure 4. The deviation between these plots are
due to the friction losses on the water side. It is seen that the
power output increases with thickness. From a 1640 MW electric power
plant operating under the third conditions in Table 1, more than 12 MW
can be generated with a thermoelectric condenser having a plate thick-
ness equal to 0.2-inch. It was shown earlier that a better condenser
design has a plate thickness as small as 0.01” and no greater than 0.05”.
The net power generated for these limits are between 3.066 MW and 8.79
MW and the material volume between 184 ft 3 and 1575 ft 3 , respectively.
Additional performance data of interest on l0.27T are presented in
Table 3. The data are listed for plate thicknesses ranging from 0.004”
to 0.2”. The items included in this table are the heat flux per unit
area, net power to heat transfer ratio, conversion efficiency, friction
power to heat transfer ratio, and the Carnot cycle efficiency. Attention
is drawn to the five-fold variations in the heat flux, conversion and
Carnot cycle efficiencies for the range of plate thicknesses indicated.
The conversion efficiency approaches the net power to heat transfer
ratio at large plate thicknesses. The Carnot cycle efficiency is nearly
ten times the conversion efficiency and it varies between 1.058 percent
at t = 0.004” to 5.015 percent at t = 0.2”. The friction to heat transfer
ratio varies with the plate thickness, but in a subtle way. It is most
affected by the flow Reynolds Number and the associated heat transfer
coeffi ci ent.
13
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I I I I III
.005”
.0075 1 1
01
01
I I I I I I I
SURFACE GEOMETRY
.02”
1
0 .27T
SURFACE GEOMETRY
3.97
I
I I I I III
075”
.05h 1
1”
MARKERS REFER TO
PLATE THICKNESS
1000
TEM VOLUME, ft 3
I
I
N
4,
‘4-
>-
‘I )
w
L&J
0
0
24
22
20
18
16
14
12
10
8
6
4
2
2”
0
004”
20
100
10,000
FIGURE 3. THE (NET) POWER INTENSITY FOR GEOMETRIES INDICATED
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TOTAL POWER
MARKERS REFER TO PLATE THICKNESS
1 OCO
THERMOELECTRIC MATERIAL VOLUME, Ft 3
FIGURE 4.
POWER GENERATED FROM THERMOELECTRIC CONDENSER 10.271 FROM THE WASTE OF A
1600 MW STEAM POWER PLANT OPERATING AT 4” Hg abs
Is
12
11
10
9
8
7
6
5
4
3
2
1
0
.
I
.0075”
‘0
100
10,000
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TABLE 3
HEAT TRANSFER AND GENERATING PERFORMANCE CHARACTERISTICS
OF THE THERMOELECTRIC CONDENSER 1O.27T
Plate
Thickness
in.
Heat Flux
Q
KW/ft 2
Net
Power/Q
%
Conversion
Efficiency
%
Friction/Q
Carnot
Efficiency
%
.004
11.169
.0097
.1224
.1127
1.058
.005
11.105
.0304
.1484
.1180
1.282
.0075
9.328
.1101
.1754
.0653
1.511
.01
9.333
.1488
.2235
.0746
1.924
.015
9.426
.2085
.3113
.1028
2.678
.02
8.185
.2700
.3400
.0700
2.919
.05
5.461
.4259
.4459
.0333
3.926
.075
4.461
.4875
.5138
.0263
4.388
.1
3.623
.5122
.5285
.0163
4.510
.2
2.271
.5803
.5885
.0082
5.015
D-4 The Effects of Turbine Back Pressure on Power Generated :
The foregoing calculations were all carried out for the third power
plant with 4” Hg abs back pressure. A rough comparison of the relative
magnitude of the thermoelectric power generated with back pressures 0.5”
and 1.5” Hg abs can be established if the flow friction is not considered
and if some arbitrary but reasonable values are assumed for the heat
transfer coefficients. Accordingly, we let the water side convective
heat transfer coefficient equal 750 Btu/hr ft 2 °F and that for the steam
side equal 3000 Btu/hr ft 2 °F. The hot and cold side surface temperatures
are then calculated and inserted in Equation (3) to find the appropriate
conversion efficiencies and the related maximum power obtainable in each
case. The results of these calculations are shown plotted in Figure 5.
It is found that the plot for the 4” Hg back pressure closely approximates
the similar plot shown in Figure 4. It is also seen that the power
generated increases with back pressure. The maximum power obtainable
with 4” Hg abs back pressure is 1304 MW. With back pressures 1.5” Hg,and 0.5”Hg
the maximum power is 6.28 and 4.81 MW, respectively.
16
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“4
FIWRE 5. MAXIPIJ4 THERMOELECTRIC POWER GENERATED AS A FU?CTION OF
TURBINE BACK PRESSURE FROM THE WASTE OF A 1600 W STEAII
POWER PLANT.
4” Hg abs
10
B
hwater
B
750 Btu/hr ft 2 °F
a
3000 Btu/hr ft 2 F
C
I-
LI
1.5 Hg abs
4
0.5” Hg abs
.05
PLATE THICK? ESS, I? CH
.15
.2
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D-5 The Effects of a High Figure of Merit :
The figure of merit used in the previous calculations was equal to
1.85 x 01(1. It is difficult to assess the effects of a better
thermoelectric material on the condenser power generation merely from
the knowledge of the figure of merit. The thermal conductivity of the
material also must be known in order to carry out the heat transfer
calculations. However, if we ignore this fact for the sake of argument,
we find that if Z _factor is doubled, a 166 percent improvement in the
conversion efficiency is obtained. If we triple the factor, the improve—
ment will be 215 percent. Presumably, similar increases could be ex-
pected for the power output. This is a rough estimate, but the agrument
shows that using better materials that are available with today’s tech-
nology, one expects at least 20 i V 4 power output. This is equal to 1.2
percent of the plant capacity.
18
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SECTION IV
THERMOELECTRICITy FROM COMBUSTION PRODUCTS
There is a substantial quantity of heat released to the atmosphere as a
result of burning fossil fuels for power generation. Usually, air at an
ambient temperature enters the process to enable combustion, but when
released, the exhaust is inadequately cooled and thus carries with it
a portion of the combustion energy. Consider a typical 1000 MW fossil-
fueled steam power plant. The stack gas temperature ranges between 250°F
and 300°F. It can be shown that the waste heat carried away through the
stack is between 100 MW and 150 MW. An open cycle gas turbine power
plant of the same capacity releases as much as 780 MW through the exhaust
at a temperature of the order of 750°F. It appears, therefore, that the
hot exhaust could be passed through thermoelectric heat exchangers for
generating electricity as the heat is conducted through the thermocouples
to the ambient air on the cold side of the exchanger.
Let us assume an ambient air temperature of 70°F and calculate the maximum
conversion efficiency based on the inlet temperature conditions from
Equation (3). The efficiencies so obtained are 5.7 percent and 10.8 per-
cent for the stack gas and gas turbine conditions, respectively. Clearly,
these relatively high efficiencies are impossible to realize in a thermo-
electric heat exchanger. The major difficulty is maintaining a high dif-
ferential junction temperature across the module. Since the fluid film
resistance is much greater than the plate resistance, the principal temper-
ature drop occurs across the film and not the plate. Unless the plate is
made extremely thick, it will offer only a minor resistance to the passage
of heat, thereby maintaining only a small temperature differential between
the hot and cold junctions. This reduces the conversion efficiency
drastically. A sample calculation was carried out for platethicknesses
between 0.01-inch and 0.5-inch. At a plate thickness equal to 0.01, the
efficiency dropped two orders of magnitude from the theoretical limit.
It dropped to within one-half of this limit at a plate thickness equal to
0.5”. In these calculations, the convective heat transfer coefficients
on both air and gas sides were equal to 45 Btu/hr ft 2 °F. Initial pressures
equal to 15 psia were assumed for both fluids. Under these conditions, the
friction power was at least an order of magnitude greater than the thermo-
electric power generated.
Several calculations were carried out at higher inlet air and gas pressures.
Progressively better results were obtained as the initial pressure was in-
creased. The pressure at which the friction power and the generated power
became of the same order of magnitude was about 100 psia for the stack gas
conditions and somewhat below that for the gas turbine exhaust conditions.
The plate thickness in these calculations was held at 0.05-inch. Better
results are expected with thicker plates. It is of some interest to note
that the friction power to heat transfer ratios in the latter calculations
were less than 0.5 percent. This is a reasonable number for conventional
regenerators.
19
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SECTION V
COST ANALYSIS
An attempt is made to compare the cost of generating electricity by
conventional methods with the cost of generation by thermoelectric
condensers. Only a rough estimate of the latter cost is possible,
primarily because thermoelectric material supplies in large quantities
have not been in demand and thus are not presently available. The
cost of manufacturing large quantities must be extrapolated from the
present level of availability of the raw materials and the processing
technology. The manufacturing cost of large scale modular units to
fit thermoelectric condensers must be estimated in a similar way. The
cost estimate presented here is furthermore biased by the particular
choice of the heat exchanger geometry. It may be possible to select
other surface geometries that combine effectiveness for heat transfer
with the ease in manufacturing.
The capital cost, the annual fixed charges, and the annual operating
costs for conventional steam power generation systems were obtained
from Reference 5. The capital cost of $l50/KW based on 1970 estimates
was used. Other cost items were 13.55 percent fixed charges and 2.97
Mills/KWH operating cost with 2.5 Mills/KWH for fuel. A thirty-year
operating life with 6000 hours of operation per year was assumed. An
interest rate of 8 percent was charged as a part of annual fixed costs.
The capital cost for thermoelectric power generation is estimated below.
There were no fuel charges in this case, but all other cost items were
computed at the rates just mentioned for the conventional steam power
generation.
The capital cost estimate for the construction of thermoelectric conden-
sers was based on the cost of Bismuth Telluride Alloy. An order of
magnitude estimate of the cost of this material as obtained from Refer-
ence 6 was $16 per pound, or $6,912 per cubic foot. In the process of
cutting very thin slices, some material may be lost, but since very
large quantities are involved, such losses could be subjected to re-
cycling. There is some manufacturing cost penalty for slicing very thin
pieces that is difficult to assess and is not included in the cost esti-
mate. Plate thicknesses of 0.05” are relatively easy to achieve (6).
The cost of producing thinner plates could have penalty factors approach-
ing the cost of the material itself for each 0.01” reduction.
If we arbitrarily allow a uniform cost factor equal to the material cost
for manufacturing the modules (i.e., cutting, bonding, etc.) and an
additional factor for constructing the condenser, the condenser would
cost $20,736 for each cubic foot of thermoelectric material that goes
into it.
21
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In the previous analysis, we have shown the thermoelectric power output
as a function of the thermoelectric material volume that goes into the
condenser. A capital cost estimate based on these data and for three
plate module thicknesses of 0.01”, 0.02”, and 0.05” are thus estimated
at $1250/KW, $1560/KW, and $3720/KW, respectively.
Detailed cost estimates for a condenser of a plate module thickness equal
to 0.01” are listed in Table 4. In this table, the annual fixed charges
do not include the 8 percent interest rate. The present worth cost was
obtained from the amortized 30 years annual fixed and operating charges.
Mote the relatively low annual operating cost of thermoelectric genera-
tion from waste heat due to the absence of fuel requirements. Based on
its present worth cost, the latter is nearly five times costlier than
the steam electric generation despite the low annual operating cost just
mentioned.
TABLE 4
COMPARATIVE COST OF THERMOELECTRIC GENERATION
(Plate Thickness .01”) WITH STEAM-ELECTRIC
GENERATION BOTH FOR 3.066 MWe
Cost (106$)
Fossil
$l50/KW
Thermoelectric
$1250/KW
Annual fixed charges
0.026
0.218
Annual operating charges
0.055
0.009
Present worth estimate
0.912
2.56
Capital cost
0.460
3.83
Total present worth
1.37
6.39
The cost of thermoelectric generation with plate module thicknesses equal
to 0.02” and 0.05” were also calculated and the results together with those
for plate thicknesses of 0.01” are listed in Table 5. The cost items in
this table are plant capital cost and investment, present worth cost and
the total present worth, all given for thermoelectric/steam-electric
generation. It is shown that this cost ratio increases with plate thick-
ness. In particular, the ratio of the total present worth costs for a
plate thickness of 0.05” is as high as 14.
22
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TABLE S
COMPARATIVE COST OF THERMOELECTRIC
GENERATION/STEAM ELECTRIC GENERATION
Plate thickness (in.) (Plant capacity, MWe)
Cost 01” (3.066 MWe) .02” (5.607 MWe) .05” (8.787 MWe)
Capital cost 1250 / 150 1560 / 150 3750 / 150
($1 KW)
Present worth
cost (106$) 2.56 / 0.912 5.79 / 1.67 21.3 / 2.61
Capital invest-
ment (106$) 3.83 / 0.460 8.75 / 0.841 32.7 / 1.32
Total present
worth (} 6$) 6.39 / 1.37 14.5 / 2.51 54.0 / 3.93
23
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SECTION VI
CONCLUSION
The foregoing analysis was a demonstration of a method that can be
applied to designing thermoelectric heat exchangers for generating
electricity from waste heat. No attempt was made to select the most
suitable surface geometry for the applications considered; neither
was a serious attempt made to optimize the designs. We have presented
order of magnitude estimates of the cost involved. Based on these
estimates, at the present time, it is uneconomical to use thermoelectric
devices to generate electricity from waste heat.
25
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SECTION VII
REFERENCES
1. Embry, Bertes L. and James R. Tudor. “A Thermoelectric Generator
Powered by Engine Exhaust Heat.” Intersociety for Energy Conversion
Engineering Conference, p. 995. 1968.
2. Kays, W. M. and A. L. London. Compact Heat Exchangers . 2nd Edition,
McGraw-Hill. 1964.
3. Skrotzki, B. G. A. and W. A. Vopat. Power Station Engineering and
Economy , pp. 14, 23, 55. 1960.
4. Barmeister, T. and L. S. Marks. Mechanical Engineering Handbook.
McGraw-Hill, pp. 9-96, 97. 1958.
5. Swengel, F. M. “A New Era of Power Supply Economics.” Power
Engineering , pp. 30-38. March 1970.
6. Jensen, R. and M. Levine. Private Coniiiunication. Materials
Electronic Product Corporation, Trenton, New Jersey. 1970.
27
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BIBLIOGRAPHIC: Mostafa A. Shirazi, USD1/Federal Water Quality Administration, ACCESSION NO.
National Thermal Pollution Research Program, “Thermoelectric Generators Powered
by Thermal Waste from Electric Power Plants,” 16130---1O/70.
ABSTRACT: The feasibility of recovering electricity from the waste heat of electric KEY WORDS:
power plants was assessed. Sources considered were: stack flue gas, gas-
turbine exhaust, and condensing steam. Typical 1600 MW fossil-fuel steam Thermodynamics
plants and gas-turbine plants were used as examples. Flat plate heat exchangers
Heat Transfer
were designed with thermoelectric couples arranged in series within the plates.
Heat flux, conversion efficiencies, and flow friction losses were calculated. (Waste) Heated Water
Except for the condenser application, the friction losses are several times Thermoelectric Condenser
the thermoelectric power generated. Under favorable conditions, 3 to 9 MW is
obtainable from the thermoelectric condensers. The high material cost, however,
precludes all such applications today.
BIBLIOGRAPHIC: Mostafa A. Shirazi, USD1/Federal Water Quality Administration, ACCESSION NO.
National Thermal Pollution Research Program, “Thermoelectric Generators Powered
by Thermal Waste from Electric Power Plants,” 16130---10/70.
ABSTRACT: The feasibility of recovering electricity from the waste heat of electric KEY WORDS:
power plants was assessed. Sources considered were: stack flue gas, gas-
turbine exhaust, and condensing steam. Typical 1600 MW fossil-fuel steam Thermodynamics
plants and gas-turbine plants were used as examples. Flat plate heat exchangers Heat Transfer
were designed with thermoelectric couples arranged In series within the plates.
Heat flux, conversion efficiencies, and flow friction losses were calculated. (Waste) Heated Water
Except for the condenser application, the friction losses are several times Thermoelectric Condenser
the thermoelectric power generated. Under favorable conditions, 3 to 9 MW is
obtainable from the thermoelectric condensers. The high material cost, however,
precludes all such applications today.
BIBLIOGRAPHIC: Mostafa A. Shirazi, USD1/Federal Water Quality Administration, ACCESSION NO.
National Thermal Pollution Research Program, “Thermoelectric Generators Powered
by Thermal Waste from Electric Power Plants,” 16130---1O/70.
ABSTRACT: The feasibility of recovering electricity from the waste heat of electric KEY WORDS
power plants was assessed. Sources considered were: stack flue gas, gas-
turbine exhaust, and condensing steam. Typical 1600 MW fossil-fuel steam Thermodynamics
plants and gas-turbine plants were used as examples. Flat plate heat exchangers
Heat Transfer
were designed with thermoelectric couples arranged in series within the plates.
Heat flux, conversion efficiencies, and flow friction losses were calculated. (Waste) Heated Water
Except for the condenser application, the friction losses are several times Thermoelectric Condenser
the thermoelectric power generated. Under favorable conditions, 3 to 9 MW is
obtainable from the thermoelectric condensers. The high material cost, however,
precludes all such applications today.
-------
Acce. ion Number - Je rFR?d&c,rouP
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization
Ju. S. Department of the Interior, Federal Water Quality Administration, National
Thermal Pollution Research Program, Pacific Northwest Water Laboratory
Title
“Thermoelectric Generators Powered by Thermal Waste from Electric Power Plants.”
10] Author(s)
Mostafa A. Shirazi
16 Project Designation
Note
22 Citation
Descriptors (Starred First)
*Thermodynamjcs, *Heat Transfer, (Waste) Heated Water
25 identifiers (Starred First)
Thermoelectric condenser
_ j Abstract
The feasibility of recovering electricity from the waste heat 0 f electric power
plants was assessed. Sources considered were: stack flue gas, gas-turbine exhaust,
and condensing steam. Typical 1600 MW fossil-fuel steam plants and gas-turbine
plants were used as examples. Flat plate heat exchangers were designed with
thermoelectric couples arranged in series within the plates. Heat flux, conversion
efficiencies, and flow friction losses were calculated. Except for the condenser
application, the friction losses are several times the thermoelectric power
generated. Under favorable conditions, 3 to 9 MW is obtainable from the thermo-
electric condensers. The high material cost, however, precludes all such
applications today. (Shirazi-FWQA)
Abstractor Institution
M st f&A. Shirazj USDI/FWQA/Pacific’ Northwest Wat rJ.abor . tpry !fl PRP
WR 0 (REV JULY 969) SEND TO V ATER RESOURCES 5CIENTiFI PNPORMATION C ENTER
WRSIC U.5. DEPARTMENT OP TNE INTERIOR
WAS1-IINOTON. 0. C 20240
* 5PO 1962—359239
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