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Thermoelectricity generation using BiTe alloys—a low temperature prototype
Heat Recovery Systems Vol. 6. No. 4, pp. 285-293, 1986 Printed in Great Britain.
0198-7593/86 $3.00+ .00 Pergamon Journals Ltd
THERMOELECTRICITY G E N E R A T I O N USING Bi-Te A L L O Y S - - A LOW TEMPERATURE PROTOTYPE C. DISPENZA, C. GIACONIA a n d L. PIGNATO Istituto di Fisica Tecnica Facolt~. di Ingegneria, Universit~i di Palermo, Viale delle Scienze, Palermo 90128, Italy (Received 15 November 1985) Abstract--The possibility of using thermocouples made from Bi-Te alloys in thermoelectric generation is investigated. A prototype has been assembled at the 'Istituto di Fisica Tecnica' in Palermo University using thermoelectric modules commercially available and normally used for thermoelectric refrigerators. Some experimental results are summarized; the hot source temperature during the test runs lies in the range 30-I 10° and ascertained efficiency is up to 2%.
1. I N T R O D U C T I O N In recent years there has been considerable interest in the scientific world in the development of systems capable of generating electric power from medium temperature resources. The main fields of application are the exploitation of geothermal sources and solar energy (e.g. solar ponds) and the utilization of energetic wastes. For the hot source temperature lying in the range 80-110 ° the overall efficiency reached using classical systems with 'non-conventional' working fluids (organic cycle power plants) is about 2% and the cost is very high. Therefore, it is very interesting to develop technologies for direct conversion of thermal into electrical energy. This work reports some results, obtained in the study of a small thermoelectric generator prototype assembled in Palermo at the 'Istituto di Fisica Tecnica', using commercially available thermoelectric modules employing Bi-Te alloys. The overall efficiency reached during the tests carried out is up to 2%. The results obtained with the prototype are very useful in the design of full-scale equipment. 2. T H E R M O E L E C T R I C GENERATORS Studies on the direct conversion of thermal energy into electricity using thermoelectric effects started about a century ago. First Rayleigh in 1885 thought of thermoelectric power generation based on Seebeck's effect. But the very small thermal efficiency reached with materials available at this time, did not allow the practical realization of a thermoelectric generator. The renewed interest in this field is due to the recent advances in development of special semiconducting materials which exhibit properties intermediate between metals and semiconductors of the type used in P - N junction transistor devices. The thermoelectric materials are prepared from semiconducting crystals more heavily doped than transistor devices to provide higher electrical conductivity. Such a material exhibits much lower thermal conductivity than metal does and a higher thermal e.m.f. With such materials a good improvement in efficiency is reached.
2.1. Outline of thermoelectrical power generation Figure ! shows the schematic diagram of a semiconductor thermoelectric generator: two P and N type semiconductor material ingots, with appropriate thermoelectrical properties, are joined at one end to a conductive bar. In the meanwhile the other ends are connected to a pure ohmic resistance. When the bar joining the P and N elements is maintained at a temperature Th and the other ends at a temperature To, a current flows from N to P on the hot side. The following phenomena are involved. Seebeck's effect. An e.m.f. (E) originates when the junctions of two different materials (conductors or semi-conductors) are maintained at two different temperatures: H.R.S.~/4-B
285
286
C. DISPENZA et al,
\
T, I
/
[[
['1
/ I/ 8/
Fig. 1. Basic thermoelectricgenerator circuit.
E =
~..p (T) dT
where %p(T), Scebeck's coefficient, represents the e.m.f, generated by the N-P couple in the case of an unitary temperature difference between the junctions. Peltier's effect. When a current flows across the isothermal junction of two different materials there is a heat absorption or rejection (depending from the versus of the current). With reference to the Fig. 1, when a current It flows in the circuit (both due to a Seebeck's e.m.f, or to the presence of an external generator) at the hot junction there is a heat absorption flow rate:
(t.~ = n.,,(Th) It %p(T) is the Peltier's coefficient for the couple N-P, At the cold junction there is a heat rejection flow rate:
q.. = %,(To)It. Thomson's effect. When along a homogeneous material (both conductor or semiconductor) there is a ternpexature difference and an electric current flowsalong it, there is an absorption or rejection of heat. For a differential element both of the P or N ingot in the unit of time there is: dT
dqr= T(T)It--~ dl T(T) is the Thomson's coefficient of the ingot material. Depending on the versus of the current, on the sign of the thermal gradient and of z, rejection or absorption of heat is possible. Peltier's and Thomson's effects take into account respectively the heat transferred to/from the external medium from/to the junction and the thermoelement as a consequence of the current flowing along it. The coefficients above defined, for the three differents thermoelectric effects, are linked by the two Kelvin's equations; for a temperature T in a section of the ingot there is: n..p = ~.,p T
d~n.p = r p - T.
T-~ Let us assume: (1) (2) (3) (4) (5)
Heat transfer to/from external medium takes place only at hot and cold junctions. As the T h - Tc temperature difference is small, Thomson's effect can be neglected. Temperature gradient along each therrnoelement varies linearly. Thermal and electrical conductivity for the temperature range examined are both constant. Junction electrical resistances are negligible in respect to the distributed ingot r~istances.
With: 1,, lp S,, Sp
thermoelements length thermoelements cross section area
Thermoelectricitygeneration using Bi-Te alloys Zn, Zp
P., Pp
K.,K~
thermoelements thermoelements thermoelements thermoelements
287
thermal conductivity electrical conductivity thermal conductance electrical resistance
where
soz.
K" = - - U ' K' =
Spzp R =pol., R =p,l, s.
s,
The generator efficiency, when the circuit is closed on the load Rt, is given by:
P.
RiI~
RtI~
Qh
Qh
• I • On, -4- qcond - - [ q,
where 0.h is the heat flow rate absorbed from the hot source, due to the Peltier's effect, q~,.d is the heat flow rate, due to thermal conduction, transferred from the hot to the cold source along the thermoelements and q, is the 'thermal source strength' (referred to the unit of time) in the thermoelement due to the Joule's effect; this is equally shared--depending on condition (3)---between the hot and cold source
4.* = n..?It = o~..,( T,) I, Th #~o.d = (K. + Kt,)(T h - Tc) 4, = (R. +
Rp)#.
Defining, figure of merit: Z -~.
O~2'P
(K. + Kp) (R. + R,) with ~.,r mean value of ~..p(T) in the range Th, Tc and with:
r = RI/(R. + R,) the efficiency expression can be written in the form (6):
T , - T.. r/ =
Th
1+
r/(1 + r) 1 r+l 1 Th-Tc Z
Th
2
Th
1
(1)
r+l
this equation shows the relation between the efficiency r/and the figure of merit Z which depends both on electrical and thermal conductivity of the ingots. Deriving equation (1) with respect to the r factor and equating to zero, the r0 value at which the efficiency reaches the maximum, is obtained: 1 r 0 = (1 + ~Z(Th + To))'/2;
substituting this value in (1) we get: qmax
=
T h - T~ r0 - 1 (1 + 1/2Z(Th + T~)t/2- 1 Th Tc = qO,~ot T~" r0+~ (1 + 1/2Z(Th+ rc)'a+~h h
(2)
The maximum of the efficiency value (2) is given by the product of the Carnot efficiency of an ideal machine working between the temperatures Th and Tc and a factor, always less than the unity, representing the reduction factor due to the irreversibility linked to thermal conduction along the thermoeleetrodes and to the Joule's effect which originates with the flow of electric current into the same. The maximum of the power output from the thermoelectric generator corresponds to the case when: Rl = R. + Rp.
288
C. DISPENZA et al.
Table 1. Therrnoelectrical properties of bismuth,tel!uride (Bi2Te ~) Type N Seebeck ~<,0LV"C I)
Conduc.
(°C)
Resist, (mflcra)
(WoC-lcnl-i)
Resist. (mflcm-i)
Type P Scebeck %(laVOC-I)
Conduc. (WoC-!cm i t
20 40 60 80 100 120 140
0,83 0.91 0.99 1.07 1.16 1.24 1.29
183 188 139 197 198 199 198
0,0127 0.0133 0.0193 0.0144 0.0150 0.0156 0.0162
0.63 0.74 I).84 0.94 1.03 1.13 1.23
159 164 169 173 177 182 185
0.0127 0;0133 0.0139 0,0144 0.0150 0.0156 0.0162
Temp.
2.2. Thermoelectrical materials In the construction of thermoelectric modules the most used materials are: Bismuth telluride Lead telluride Selenides Si-Ge Alloys
Temperature range 0-300°C 0-600°C 150-850°C 0-1000°C
For use below 150°C bismuth-telluride alloys with suitable doping agents are preferred. Some properties of Bi2Te3 alloy are reported in Table t.
3. DESCRIPTION OF THE EXPERIMENTAL PROTOTYPE To construct the prototype 8 modules type CP2.8-32-06L Melcor Co. have been used. Each module has 32 thermoelectric couples of quaternary alloy bismuth, telturide, selenium and antimonium with a small amount of suitable doping agents. The field of use ranges from - 150 to 110°C. The module dimension are 40 x 40 mm and the thickness is 4.7 ram. Each dement of every couple has a cross section of 2.8 mm and a length of 0.06 in. Figure 2 shows the exploded view of the prototype. The components are showed in Fig. 3. Adopted geometry allows a thermally symmetric system. The heater, placed in the center of the system, is made by a copper-covered vetronite slab (copper thickness 70 tim); on each face is photoengraved the electrical resistance. This slab, fed by an alternative current line controlled by a rheostat, has the function of hot source. Two copper slabs 2.5 mm thick perform as temperature equalizators and were pressed against the hot source and electrically insulated with a paper stuck with special 10w thermal resistance grease (Thermalcote-Thermalloy). The ohmic resistance of each face o f the heater is 2.4 D at 25°C. The expected uniformity of temperature on the faces of copper slabs was experimentally verified
Fi t. 2. Mechanical parts layout.
289
Thermoelectricity generation using Bi-Te alloys _
Fig. 3. Disassembled view of the components.
I
Al A2 Fl Pl Rl V2 Vrl
= = = = = = =
1
I
Amperometera.c. 10Af.s. Cl. 0.5 Digital mutt. P.M. 2421 (Philips) Flowmeter KD4 (MeterFlux) Precision slide-wire patenriometer 2.4 Ohm/t5 A Strip-chart recorder 12 ch. TRANSOKOMP 299 [Philips) Digital mult. HP 3490A Variac
Fig, 4. Measurement setup.
up to 150°C. In the center of external faces of the equalizators there are two tin-brazed thermocouples (Cu-Const or type T). The 8 modules inserted, four for each face of the heater, are pressed with another two copper slabs 2Smm thick. Good thermal contact is assured with a special grease. Another two thermocouples are tin-brazed in the center of the equalizators. Then the package is faced with the cold source made by two anodized aluminium channels (120 x 20 mm) into which flows a cold water stream. Xnlet and outlet refrigerating water temperatures are measured by means of four T type thermocouples (Fig. 4).
290
C. DISPENZA et al. 10
. Test 1.6 mc/h ÷ Test 1.1 m d h o Test 1.6mc/h (with ins.)
98-
7
¢_
6-
¢D
a.
o/
543-
f..o. J
2-
~ 10
t
20
I 30
i 40
I 50
I 60
I 70
l 80
/ 90
I 100
DT (*'C) Fig, 5. Generated net power vs hot and cold sources temperature difference.
3.0
* Test 1.6 mc/h ÷ Test 1.1 mc/h o Test 1.6 rnc/h (with ins.)
--
2.5
J
2.0
o . S ÷*
"q% 1.5
1.0
0.5
0"00
1 10
I 20
I 30
I 40
L,, 50
t 60
I 70
I 80
~ 90
i I O0
DT (°C) Fig. 6. Prototype efficiency vs hot and cold sources temperature difference.
30-
.....
Carnot efficiency Prototype efficiency
25 2O /"
~%
15
.j.J" /
•m
1
/
.///"
10 20 30 40
50 60
'80 90 100
DT (°C) Fig. 7. Carnot ideal and prototype ef6cienc7 vs hot and cold sources temperature difference
Thermoelectricity generation using Bi-Te alloys
291
• , Test-1.6 mc/h * Test1.1 mc/h o Test 1.6 mc/h (with ins.)
3.0
2.5
2.0 1.5 o (£ 1.0
0.5 r 1
0.0 0
I 2
I 3
I 4
I 5
Pu (Watt)
Fig. 8. Optimum load resistance vs generated net power. 4. T E S T •
LOOP
\
The test loop is represented in Fig. 4. The measured parameters are: Power input into the heater Generated net power Hot and cold source temperatures Refrigerating water flow rate Refrigerating water input and output temperatures. Due to low frequency (50 Hz) of electric line, the load has been considered a pure ohmic load; so the net power generated by the equipment has been measured with the volt-amperometric method. For each run the power measured has been the maximum obtainable (corresponding to the optimum value of the load resistance). Hot and cold source temperatures are measured in the center of external faces of the two equalizators. For each run the value of load resistance is tried which allows the maximum power transfer rate. 5.
EXPERIMENTAL
RESULTS
The main results obtained are summarized in Figs 5-9. Tables 2 and 3 pertain to test runs performed with the equipment not-insulated for two different refrigerating water flow rates, 3.0-1~-3
• Test 1.6 mc/h • Test 1.1 mc/h o Test 1.6 mc/h (with ins.)
2.52.0
1.5
0o
*.o
I
I
^* o
N
1.0
0.5
0'00
I
I
I
I
I
I
i
I
10 20 30 40 50 50 70 80 90 100 Tm (°C)
Fig. 9. Figure of merit vs mean system temperature.
C. DISPENZA et aL
292
Table 2. Experimental results from test run no. I i
Refrigerating water flow rate -- 1.6 m 3 h th t~ V 1, ('C) (C) (V) /A) 40.3 49.9 60.9 70.2 79.9 89.0 101.9 110.2
40.3 49.5 60.5 70.0 79.8 89.6 101.2 109.6
24.7 28.5 33.0 33.2 39.8 42.6 44.1 48.0
24.4 28.8 32.8 32.5 38.9 41.7 43.0 46.0
8.26 10.49 12.70 14.30 16.00 17.40 19.90 21.10
6.32 7.71 8.92 9.75 10.05 11.00 12.00 12140
I:~ (V)
1,, (A)
g .... (tt)
0.654 0.9]0 1.265 1.540 1.820 1.990 2.500 2.653
0.333 0.556 0.763 0.949 1.143 1.286 1.547 1.684
1.964 1.637 1.657 1.623 1.593 1.547 1.616 1.575
Table 3. Experimental results from test run no. 2 Refrigerating water flow rate = I. I m 3 h th
t,
V,
I,
l'~
1=
go.
(°C)
("C)
(V)
(A)
(V)
(A)
(fl)
8.37 10.35 12.30 13.80 15.60 17.60 19.10 21.00
6.40 7.60 8.65 9.35 10.10 IIA0 11.60 12.40
0,664 0,889 1.280 1.456 1~737 2.053 2.340 2.643
0.341 0.519 0.670 0.833 1.023 1.288 1.467 1.665
1.947 1.713 1.910 1.748 1:698 1.594 1.595 1.587
40.6 51.2 62.2 70.8 81.7 89.0 99.5 110.7
40.3 52.1 63.5 71.4 82.2 87.9 99.2 109.5
25.9 31.8 36.3 39.0 43.3 42.3 44.5 50.0
25.4 31.4 35.3 38.2 42.0 40.6 42.8 47.8
Table 4. Experimental r ~ u l t s from test run no. 3 Refrigerating water flow rate = 1.6 m 3 h -I (with insulation)
t,
t,
v,
/,
v.
t.
no,,
('~C)
(C)
(V)
(A)
(V)
(A)
(fl)
8.24 10.78 12.54 14.50 16.20 18.10 19.70 21.40
6.32 7.80 8,90 9.85 10.50 11.40 12.00 12.50
0.607 0.968 1.265 1.626 1.860 2:190 Z560 Z847
0:359 0.574 0.757 0.945 1.159 1.384 1.512 1.694
1.691 1,686 1.671 1.721 1,605 1.582 1.693 1.680
39.9 50.3 59.6 70.0 80.0 90.1 100.1 110.5
39.6 50.0 58.9 69.4 79.3 89.6 99,8 109.6
26.2 29.3 33.0 35.1 37.6 41.8 44,7 48.3
25.5 28.4 31.5 34.0 36.0 39.6 42.3 45.6
Table 5. Theoretical figure of merit calculated for the chips employed Mean temp. ('C) l0 20 30 40 50 60 70 80 90 100 110 120
Zeta (l/K) 3.27 3.15 3.02 2.89 2.77 2.64 2.51 2.39 2.26 2.14 2.01 1.88
x × x × × × × × x x x ×
l0 -3 l0 -3 l0 3 t0 3 10 `-3 10 -3 10 r 10 10 10 ~ 10 3 10
Table 4 refers to test runs with the equipment insulated (Figs 5-9). The values of both Th and To, report~! in the tables, indicate the good symmetry of the prototype. As far as it pertains to the performance parameters (Pu, rt) bctw~n the values for the insulated and not-insulat~l corresponding ease there are no significant differences, so all data points have been r ~ o r t ~ l in the graph in Fig. 5. This shows the trend of Pu vs D T (the temperature difference bctw~n the hot and cold sources. Versus the aforesaid parameter (DT) in Fig. 6 is r ~ o r t ~ l the overall ettieiency of the prototype and in Fig. 7. also, is reported Carnot's effaeiency for an ideal cycle working between the same temperatures. Figure 8 reports the values of the optimum load resistance referring to each experimental datum as a function of Pu. Figure 9 reports the values of the figure of merit, Z, estimated by means of (2) with the results obtained during the test runs and in Table 5 are reported some values obtained theoretically using data of Table 1.
Thermoelectricity generation using Bi-Te alloys
293
6. C O N C L U S I O N S F o r the hot source t e m p e r a t u r e range (40-110°C) explored, the overall efficiency m a y reach a figure o f a b o u t 2 % , though this value is not obtained due to the fact that the value of D T has been limited to not m o r e than 63°C to not exceed absolute m a x i m u m rating for the selected chips. But, the value o f the ascertained efficiency is similar to that obtainable with m o r e complex systems (organic cycle power plants, M H D ) . With respect to this latter case the thermoelectric generator is m o r e a d v a n t a g e o u s due to it compactness, no moving parts and no sophisticated control devices. REFERENCES 1. J. Kestin et al. Sourcebook on the Production of Electricity from Geothermal Energy, U.S. Dept. of Energy, DOE/RA/4051-1 (1980). 2. H. J. Goldsmid, J. E. Giutronich and M. M. Kaila, Solar thermoelectric generation using Bi-Te alloys, Solar Energy, Sept. (1980). 3. T. C. Harman, Special techniques for measurement of thermoelectric properties, J. Appl. Phys. Sept. (1985). 4. R. W. Fritts, Design parameters for optimizing the efficiency of thermoelectric generators utilizing P-type and N-type lead-telluride. A.I.E.E. Paper n.59-909-1959. 5. J. Kaye and J. A. Welsh, Direct Conversion of Heat to Electricity, J. Wiley, New York (1960). 6. L. S. Chang, Conversion de renergie, Dunod, Paris (1966).
0198-7593/86 $3.00+ .00 Pergamon Journals Ltd
THERMOELECTRICITY G E N E R A T I O N USING Bi-Te A L L O Y S - - A LOW TEMPERATURE PROTOTYPE C. DISPENZA, C. GIACONIA a n d L. PIGNATO Istituto di Fisica Tecnica Facolt~. di Ingegneria, Universit~i di Palermo, Viale delle Scienze, Palermo 90128, Italy (Received 15 November 1985) Abstract--The possibility of using thermocouples made from Bi-Te alloys in thermoelectric generation is investigated. A prototype has been assembled at the 'Istituto di Fisica Tecnica' in Palermo University using thermoelectric modules commercially available and normally used for thermoelectric refrigerators. Some experimental results are summarized; the hot source temperature during the test runs lies in the range 30-I 10° and ascertained efficiency is up to 2%.
1. I N T R O D U C T I O N In recent years there has been considerable interest in the scientific world in the development of systems capable of generating electric power from medium temperature resources. The main fields of application are the exploitation of geothermal sources and solar energy (e.g. solar ponds) and the utilization of energetic wastes. For the hot source temperature lying in the range 80-110 ° the overall efficiency reached using classical systems with 'non-conventional' working fluids (organic cycle power plants) is about 2% and the cost is very high. Therefore, it is very interesting to develop technologies for direct conversion of thermal into electrical energy. This work reports some results, obtained in the study of a small thermoelectric generator prototype assembled in Palermo at the 'Istituto di Fisica Tecnica', using commercially available thermoelectric modules employing Bi-Te alloys. The overall efficiency reached during the tests carried out is up to 2%. The results obtained with the prototype are very useful in the design of full-scale equipment. 2. T H E R M O E L E C T R I C GENERATORS Studies on the direct conversion of thermal energy into electricity using thermoelectric effects started about a century ago. First Rayleigh in 1885 thought of thermoelectric power generation based on Seebeck's effect. But the very small thermal efficiency reached with materials available at this time, did not allow the practical realization of a thermoelectric generator. The renewed interest in this field is due to the recent advances in development of special semiconducting materials which exhibit properties intermediate between metals and semiconductors of the type used in P - N junction transistor devices. The thermoelectric materials are prepared from semiconducting crystals more heavily doped than transistor devices to provide higher electrical conductivity. Such a material exhibits much lower thermal conductivity than metal does and a higher thermal e.m.f. With such materials a good improvement in efficiency is reached.
2.1. Outline of thermoelectrical power generation Figure ! shows the schematic diagram of a semiconductor thermoelectric generator: two P and N type semiconductor material ingots, with appropriate thermoelectrical properties, are joined at one end to a conductive bar. In the meanwhile the other ends are connected to a pure ohmic resistance. When the bar joining the P and N elements is maintained at a temperature Th and the other ends at a temperature To, a current flows from N to P on the hot side. The following phenomena are involved. Seebeck's effect. An e.m.f. (E) originates when the junctions of two different materials (conductors or semi-conductors) are maintained at two different temperatures: H.R.S.~/4-B
285
286
C. DISPENZA et al,
\
T, I
/
[[
['1
/ I/ 8/
Fig. 1. Basic thermoelectricgenerator circuit.
E =
~..p (T) dT
where %p(T), Scebeck's coefficient, represents the e.m.f, generated by the N-P couple in the case of an unitary temperature difference between the junctions. Peltier's effect. When a current flows across the isothermal junction of two different materials there is a heat absorption or rejection (depending from the versus of the current). With reference to the Fig. 1, when a current It flows in the circuit (both due to a Seebeck's e.m.f, or to the presence of an external generator) at the hot junction there is a heat absorption flow rate:
(t.~ = n.,,(Th) It %p(T) is the Peltier's coefficient for the couple N-P, At the cold junction there is a heat rejection flow rate:
q.. = %,(To)It. Thomson's effect. When along a homogeneous material (both conductor or semiconductor) there is a ternpexature difference and an electric current flowsalong it, there is an absorption or rejection of heat. For a differential element both of the P or N ingot in the unit of time there is: dT
dqr= T(T)It--~ dl T(T) is the Thomson's coefficient of the ingot material. Depending on the versus of the current, on the sign of the thermal gradient and of z, rejection or absorption of heat is possible. Peltier's and Thomson's effects take into account respectively the heat transferred to/from the external medium from/to the junction and the thermoelement as a consequence of the current flowing along it. The coefficients above defined, for the three differents thermoelectric effects, are linked by the two Kelvin's equations; for a temperature T in a section of the ingot there is: n..p = ~.,p T
d~n.p = r p - T.
T-~ Let us assume: (1) (2) (3) (4) (5)
Heat transfer to/from external medium takes place only at hot and cold junctions. As the T h - Tc temperature difference is small, Thomson's effect can be neglected. Temperature gradient along each therrnoelement varies linearly. Thermal and electrical conductivity for the temperature range examined are both constant. Junction electrical resistances are negligible in respect to the distributed ingot r~istances.
With: 1,, lp S,, Sp
thermoelements length thermoelements cross section area
Thermoelectricitygeneration using Bi-Te alloys Zn, Zp
P., Pp
K.,K~
thermoelements thermoelements thermoelements thermoelements
287
thermal conductivity electrical conductivity thermal conductance electrical resistance
where
soz.
K" = - - U ' K' =
Spzp R =pol., R =p,l, s.
s,
The generator efficiency, when the circuit is closed on the load Rt, is given by:
P.
RiI~
RtI~
Qh
Qh
• I • On, -4- qcond - - [ q,
where 0.h is the heat flow rate absorbed from the hot source, due to the Peltier's effect, q~,.d is the heat flow rate, due to thermal conduction, transferred from the hot to the cold source along the thermoelements and q, is the 'thermal source strength' (referred to the unit of time) in the thermoelement due to the Joule's effect; this is equally shared--depending on condition (3)---between the hot and cold source
4.* = n..?It = o~..,( T,) I, Th #~o.d = (K. + Kt,)(T h - Tc) 4, = (R. +
Rp)#.
Defining, figure of merit: Z -~.
O~2'P
(K. + Kp) (R. + R,) with ~.,r mean value of ~..p(T) in the range Th, Tc and with:
r = RI/(R. + R,) the efficiency expression can be written in the form (6):
T , - T.. r/ =
Th
1+
r/(1 + r) 1 r+l 1 Th-Tc Z
Th
2
Th
1
(1)
r+l
this equation shows the relation between the efficiency r/and the figure of merit Z which depends both on electrical and thermal conductivity of the ingots. Deriving equation (1) with respect to the r factor and equating to zero, the r0 value at which the efficiency reaches the maximum, is obtained: 1 r 0 = (1 + ~Z(Th + To))'/2;
substituting this value in (1) we get: qmax
=
T h - T~ r0 - 1 (1 + 1/2Z(Th + T~)t/2- 1 Th Tc = qO,~ot T~" r0+~ (1 + 1/2Z(Th+ rc)'a+~h h
(2)
The maximum of the efficiency value (2) is given by the product of the Carnot efficiency of an ideal machine working between the temperatures Th and Tc and a factor, always less than the unity, representing the reduction factor due to the irreversibility linked to thermal conduction along the thermoeleetrodes and to the Joule's effect which originates with the flow of electric current into the same. The maximum of the power output from the thermoelectric generator corresponds to the case when: Rl = R. + Rp.
288
C. DISPENZA et al.
Table 1. Therrnoelectrical properties of bismuth,tel!uride (Bi2Te ~) Type N Seebeck ~<,0LV"C I)
Conduc.
(°C)
Resist, (mflcra)
(WoC-lcnl-i)
Resist. (mflcm-i)
Type P Scebeck %(laVOC-I)
Conduc. (WoC-!cm i t
20 40 60 80 100 120 140
0,83 0.91 0.99 1.07 1.16 1.24 1.29
183 188 139 197 198 199 198
0,0127 0.0133 0.0193 0.0144 0.0150 0.0156 0.0162
0.63 0.74 I).84 0.94 1.03 1.13 1.23
159 164 169 173 177 182 185
0.0127 0;0133 0.0139 0,0144 0.0150 0.0156 0.0162
Temp.
2.2. Thermoelectrical materials In the construction of thermoelectric modules the most used materials are: Bismuth telluride Lead telluride Selenides Si-Ge Alloys
Temperature range 0-300°C 0-600°C 150-850°C 0-1000°C
For use below 150°C bismuth-telluride alloys with suitable doping agents are preferred. Some properties of Bi2Te3 alloy are reported in Table t.
3. DESCRIPTION OF THE EXPERIMENTAL PROTOTYPE To construct the prototype 8 modules type CP2.8-32-06L Melcor Co. have been used. Each module has 32 thermoelectric couples of quaternary alloy bismuth, telturide, selenium and antimonium with a small amount of suitable doping agents. The field of use ranges from - 150 to 110°C. The module dimension are 40 x 40 mm and the thickness is 4.7 ram. Each dement of every couple has a cross section of 2.8 mm and a length of 0.06 in. Figure 2 shows the exploded view of the prototype. The components are showed in Fig. 3. Adopted geometry allows a thermally symmetric system. The heater, placed in the center of the system, is made by a copper-covered vetronite slab (copper thickness 70 tim); on each face is photoengraved the electrical resistance. This slab, fed by an alternative current line controlled by a rheostat, has the function of hot source. Two copper slabs 2.5 mm thick perform as temperature equalizators and were pressed against the hot source and electrically insulated with a paper stuck with special 10w thermal resistance grease (Thermalcote-Thermalloy). The ohmic resistance of each face o f the heater is 2.4 D at 25°C. The expected uniformity of temperature on the faces of copper slabs was experimentally verified
Fi t. 2. Mechanical parts layout.
289
Thermoelectricity generation using Bi-Te alloys _
Fig. 3. Disassembled view of the components.
I
Al A2 Fl Pl Rl V2 Vrl
= = = = = = =
1
I
Amperometera.c. 10Af.s. Cl. 0.5 Digital mutt. P.M. 2421 (Philips) Flowmeter KD4 (MeterFlux) Precision slide-wire patenriometer 2.4 Ohm/t5 A Strip-chart recorder 12 ch. TRANSOKOMP 299 [Philips) Digital mult. HP 3490A Variac
Fig, 4. Measurement setup.
up to 150°C. In the center of external faces of the equalizators there are two tin-brazed thermocouples (Cu-Const or type T). The 8 modules inserted, four for each face of the heater, are pressed with another two copper slabs 2Smm thick. Good thermal contact is assured with a special grease. Another two thermocouples are tin-brazed in the center of the equalizators. Then the package is faced with the cold source made by two anodized aluminium channels (120 x 20 mm) into which flows a cold water stream. Xnlet and outlet refrigerating water temperatures are measured by means of four T type thermocouples (Fig. 4).
290
C. DISPENZA et al. 10
. Test 1.6 mc/h ÷ Test 1.1 m d h o Test 1.6mc/h (with ins.)
98-
7
¢_
6-
¢D
a.
o/
543-
f..o. J
2-
~ 10
t
20
I 30
i 40
I 50
I 60
I 70
l 80
/ 90
I 100
DT (*'C) Fig, 5. Generated net power vs hot and cold sources temperature difference.
3.0
* Test 1.6 mc/h ÷ Test 1.1 mc/h o Test 1.6 rnc/h (with ins.)
--
2.5
J
2.0
o . S ÷*
"q% 1.5
1.0
0.5
0"00
1 10
I 20
I 30
I 40
L,, 50
t 60
I 70
I 80
~ 90
i I O0
DT (°C) Fig. 6. Prototype efficiency vs hot and cold sources temperature difference.
30-
.....
Carnot efficiency Prototype efficiency
25 2O /"
~%
15
.j.J" /
•m
1
/
.///"
10 20 30 40
50 60
'80 90 100
DT (°C) Fig. 7. Carnot ideal and prototype ef6cienc7 vs hot and cold sources temperature difference
Thermoelectricity generation using Bi-Te alloys
291
• , Test-1.6 mc/h * Test1.1 mc/h o Test 1.6 mc/h (with ins.)
3.0
2.5
2.0 1.5 o (£ 1.0
0.5 r 1
0.0 0
I 2
I 3
I 4
I 5
Pu (Watt)
Fig. 8. Optimum load resistance vs generated net power. 4. T E S T •
LOOP
\
The test loop is represented in Fig. 4. The measured parameters are: Power input into the heater Generated net power Hot and cold source temperatures Refrigerating water flow rate Refrigerating water input and output temperatures. Due to low frequency (50 Hz) of electric line, the load has been considered a pure ohmic load; so the net power generated by the equipment has been measured with the volt-amperometric method. For each run the power measured has been the maximum obtainable (corresponding to the optimum value of the load resistance). Hot and cold source temperatures are measured in the center of external faces of the two equalizators. For each run the value of load resistance is tried which allows the maximum power transfer rate. 5.
EXPERIMENTAL
RESULTS
The main results obtained are summarized in Figs 5-9. Tables 2 and 3 pertain to test runs performed with the equipment not-insulated for two different refrigerating water flow rates, 3.0-1~-3
• Test 1.6 mc/h • Test 1.1 mc/h o Test 1.6 mc/h (with ins.)
2.52.0
1.5
0o
*.o
I
I
^* o
N
1.0
0.5
0'00
I
I
I
I
I
I
i
I
10 20 30 40 50 50 70 80 90 100 Tm (°C)
Fig. 9. Figure of merit vs mean system temperature.
C. DISPENZA et aL
292
Table 2. Experimental results from test run no. I i
Refrigerating water flow rate -- 1.6 m 3 h th t~ V 1, ('C) (C) (V) /A) 40.3 49.9 60.9 70.2 79.9 89.0 101.9 110.2
40.3 49.5 60.5 70.0 79.8 89.6 101.2 109.6
24.7 28.5 33.0 33.2 39.8 42.6 44.1 48.0
24.4 28.8 32.8 32.5 38.9 41.7 43.0 46.0
8.26 10.49 12.70 14.30 16.00 17.40 19.90 21.10
6.32 7.71 8.92 9.75 10.05 11.00 12.00 12140
I:~ (V)
1,, (A)
g .... (tt)
0.654 0.9]0 1.265 1.540 1.820 1.990 2.500 2.653
0.333 0.556 0.763 0.949 1.143 1.286 1.547 1.684
1.964 1.637 1.657 1.623 1.593 1.547 1.616 1.575
Table 3. Experimental results from test run no. 2 Refrigerating water flow rate = I. I m 3 h th
t,
V,
I,
l'~
1=
go.
(°C)
("C)
(V)
(A)
(V)
(A)
(fl)
8.37 10.35 12.30 13.80 15.60 17.60 19.10 21.00
6.40 7.60 8.65 9.35 10.10 IIA0 11.60 12.40
0,664 0,889 1.280 1.456 1~737 2.053 2.340 2.643
0.341 0.519 0.670 0.833 1.023 1.288 1.467 1.665
1.947 1.713 1.910 1.748 1:698 1.594 1.595 1.587
40.6 51.2 62.2 70.8 81.7 89.0 99.5 110.7
40.3 52.1 63.5 71.4 82.2 87.9 99.2 109.5
25.9 31.8 36.3 39.0 43.3 42.3 44.5 50.0
25.4 31.4 35.3 38.2 42.0 40.6 42.8 47.8
Table 4. Experimental r ~ u l t s from test run no. 3 Refrigerating water flow rate = 1.6 m 3 h -I (with insulation)
t,
t,
v,
/,
v.
t.
no,,
('~C)
(C)
(V)
(A)
(V)
(A)
(fl)
8.24 10.78 12.54 14.50 16.20 18.10 19.70 21.40
6.32 7.80 8,90 9.85 10.50 11.40 12.00 12.50
0.607 0.968 1.265 1.626 1.860 2:190 Z560 Z847
0:359 0.574 0.757 0.945 1.159 1.384 1.512 1.694
1.691 1,686 1.671 1.721 1,605 1.582 1.693 1.680
39.9 50.3 59.6 70.0 80.0 90.1 100.1 110.5
39.6 50.0 58.9 69.4 79.3 89.6 99,8 109.6
26.2 29.3 33.0 35.1 37.6 41.8 44,7 48.3
25.5 28.4 31.5 34.0 36.0 39.6 42.3 45.6
Table 5. Theoretical figure of merit calculated for the chips employed Mean temp. ('C) l0 20 30 40 50 60 70 80 90 100 110 120
Zeta (l/K) 3.27 3.15 3.02 2.89 2.77 2.64 2.51 2.39 2.26 2.14 2.01 1.88
x × x × × × × × x x x ×
l0 -3 l0 -3 l0 3 t0 3 10 `-3 10 -3 10 r 10 10 10 ~ 10 3 10
Table 4 refers to test runs with the equipment insulated (Figs 5-9). The values of both Th and To, report~! in the tables, indicate the good symmetry of the prototype. As far as it pertains to the performance parameters (Pu, rt) bctw~n the values for the insulated and not-insulat~l corresponding ease there are no significant differences, so all data points have been r ~ o r t ~ l in the graph in Fig. 5. This shows the trend of Pu vs D T (the temperature difference bctw~n the hot and cold sources. Versus the aforesaid parameter (DT) in Fig. 6 is r ~ o r t ~ l the overall ettieiency of the prototype and in Fig. 7. also, is reported Carnot's effaeiency for an ideal cycle working between the same temperatures. Figure 8 reports the values of the optimum load resistance referring to each experimental datum as a function of Pu. Figure 9 reports the values of the figure of merit, Z, estimated by means of (2) with the results obtained during the test runs and in Table 5 are reported some values obtained theoretically using data of Table 1.
Thermoelectricity generation using Bi-Te alloys
293
6. C O N C L U S I O N S F o r the hot source t e m p e r a t u r e range (40-110°C) explored, the overall efficiency m a y reach a figure o f a b o u t 2 % , though this value is not obtained due to the fact that the value of D T has been limited to not m o r e than 63°C to not exceed absolute m a x i m u m rating for the selected chips. But, the value o f the ascertained efficiency is similar to that obtainable with m o r e complex systems (organic cycle power plants, M H D ) . With respect to this latter case the thermoelectric generator is m o r e a d v a n t a g e o u s due to it compactness, no moving parts and no sophisticated control devices. REFERENCES 1. J. Kestin et al. Sourcebook on the Production of Electricity from Geothermal Energy, U.S. Dept. of Energy, DOE/RA/4051-1 (1980). 2. H. J. Goldsmid, J. E. Giutronich and M. M. Kaila, Solar thermoelectric generation using Bi-Te alloys, Solar Energy, Sept. (1980). 3. T. C. Harman, Special techniques for measurement of thermoelectric properties, J. Appl. Phys. Sept. (1985). 4. R. W. Fritts, Design parameters for optimizing the efficiency of thermoelectric generators utilizing P-type and N-type lead-telluride. A.I.E.E. Paper n.59-909-1959. 5. J. Kaye and J. A. Welsh, Direct Conversion of Heat to Electricity, J. Wiley, New York (1960). 6. L. S. Chang, Conversion de renergie, Dunod, Paris (1966).