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Fast transient behavior of thermoelectric coolers with high current pulse and finite cold junction
~urgalll ~la P r c ~ l i d
It)79 P r m l c i l in (irc~tl B r i t a i n
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS WITH HIGH CURRENT PULSE AND FINITE COLD JUNCTION R I C H A R D L. F I E L D ~ and H A R O L D A. B L U M 2
~Texas A & M University, Mechanical Engineering Department, College Station, TX 77843 and :Departmenl of Civil and Mechanical Engineering, School of Engineering and Applied Science, Southern Methodist University, Dallas, TX 75275, U.S.A.
{Received 27 April 19791 Abstract Experimental, high speed temperature response data were taken on a single stage thermoelectric cooler as it was subjected to a high current, short duration, rectangular d.c. pulse. The pulse was imposed on the cooler as it was operating in its optimum, steady-state, cooled-down condition, After the cooler attained steady-state temperatures of about -40°C with the hot junction at 27c'C, pulse cooling down to about - 6 5 C was obtained with many combinations of current and pulse duration. Typical pulse current and duration were 10A for 30msec. The pulse could be repeated about every 15see. Average figure-of-merit of the cooler materials, bismuth and antimony tellurides, was 2.69 x 10 3 K t at 3'C. The cooler was of a practical, common size and configuration, being two elements, standing side-by-side, cormected at the top with a very thin silver bus bar. Element cross-sectional area was 0.0089 cm 2 and element height was 0.5 cm. Every effort was made to reduce the mass of the bus bar, solder, and thermocouple which was used to measure the temperature. Good correlation was obtained between the experimental data and a computer model solution by the Network Thermal Analyzer (NETHAN) program simulating the experimental conditions. Computer solutions of temperature were carried out for a wide range of cooler sizes, including the experimental model size. an approximately one-tenth size of the experimental model and sizes larger than the experimental model. Thermoelectric coupler Heat conduction, transient Refrigeration cooling Direct energy conversion Cold junction temperature.
INTRODUCTION
Peltier junctions
Solid state
this research we gratefully acknowledge. A detailed computer model was used to simulate the experiment and the results were correlated to the experimental data.
The fast transient effect is observed in thermoelectric coolers when the device is operating in its cooleddown, steady-state condition and is then subjected to a high current pulse of short duration. Instantly, additional Peltier cooling is developed at the cold junction, while the Joule or resistance heating developed in the elements requires a while to be conducted to the cold junction. This time lag gives rise to the pulse cooling phenomenon. Such a phenomenon could find application in any situation where extra cooling was needed for a short time, such as an infrared detector operating in a 'winking' mode, which needs to be supercold only during the wink. In the transient mode the smaller the mass of the object to be cooled, the colder it can be made to go. The bus bar joining the elements at the cold junction, the solder and any load mass must be kept to a minimum to achieve the maximum fast transient effect. The cold junction is defined as the interface between the thermoelectric material and the solder which joins it to the bus bar. The mass of an object times its specific heat is the thermal mass. The cooler studied experimentally had a combined cold surface thermal mass of 0.85 x 10-4cal/°C, Seven experimental models were built for this program by Nuclear Systems, Inc., Garland, Texas, whose contributions to
PREVIOUS WORK
The fast transient effect was first reported by Stil'bans and Fedorovitch [1], whose cooler consisted of two thermoelectric elements butt-soldered together to minimize cold junction mass. They did not report the size or dimensions of their cooler. The first extensive study of pulse cooling was made by Landecker and Findlay [2]. The configuration of their experimental model was ultrasonically-buttsoldered elements with essentially 'zero' mass at the cold surface. We were interested in the case with finite, known, cold surface mass. They report, for a cooler with infinitely-long elements: " . . . it is shown theoretically that for rectangular pulses the temperature of the cold junction is a function only of a parameter ~ = 1~/'t ( / = pulse current, t = pulse duration)." It is Jx/t (J - current/area) which will be used here to plot the computer and experimental data. The recent research on pulse cooling of Babin and Iordanishvili [3] involved a 'zero' mass butt-soldered cooler configuration. They also used the combination of variables J , t to present their analysis. 159
160
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRI(" ('OOLERS
Specific contact resistance (R,.) at a solder joint between the bus bar and the thermoelectric material is an important parameter. Mengali and Seiler [4] studied experimentally the resistance of solder joints between several different nickel-plated thermoelectric materials and copper. The range of values reported for bismuth telluride was 0.74 x 10 ~' 3.7 x 10 5 ohm-cm z with most values between 10 ~' and 10 s ohm-cm 2. Demonstration of a 'reduced variables' method of analyzing cooler designs by Bywaters and Blum [5] for finite difference solution of a one-dimensional heat conduction equation provided a simplified method for predicting transient temperature response. It was the goal of this study to (1) provide quantitative experimental data for the pulse cooling mode for coolers with finite cold surface mass and real contact resistance and (2) demonstrate a predictive method to design thermoelectric coolers utilizing the fast transient effect. EXPERIMENTAL INVESTIGATIONS The primary mode of pulse cooling of interest here was the application of a single square wave current pulse to a cooler operating already at its optimum steady-state current. A square wave is of interest because of the relative simplicity with which it may be produced electronically, as compared to a shaped pulse. The response to repeated pulses can be inferred from the response to a single pulse if the cooler is
allowed time to return to its equilibrium, s~eady-state condition. The variables were: cold surface thermal mass, specific contact resistance, current, pulse duration, element cross-sectional area and element height. Taken as constants were: type of thermoelectric material (bismuth and antimony tellurides), configuration (side-by-side elements standing vertically with a silver 'bus bar' soldered across the top of the elements), all specific heats, the absence of convective heat loading, and the neglecting of radiative heat loading (calculated as 0.04",, of Peltier cooling), and the baseplate temperature equal to 2 7 C _+ 1 C (300 K) so as to be comparable to other data in the literature. The following variables were taken as functions of temperature from laboratory measurements and from available literature: Seebeck coefficient, resistivity of bismuth and antimony tellurides, Thompson coefficient, and the thermal conductivity of bismuth and antimony telluride. Reference [6] presents details of materials properties. The experimental data of interest are the temperature of the top of the cold surface as a function of time and the current to the cooler as a function of time. The silver bus bar was weighed on a precision balance; the solder and thermocouple bead dimensions were measured under a microscope. The thickness of the solder joining the bus bar to the elements was estimated to be 0.0005 inch thick. The actual
Fig. 1. Experimental model, 10 4 cal/'C cooler.
FII!LD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS Power
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cross-sectional area at the elements was 0.0089 cm 2, rather than the design value of 0.0079 cm 2. Figure 1 is a photograph of one of the models. A 0.002 inch diameter copper-constantan thermocouple was mounted atop the cold surface above the center of an element, nearer the end of the bus bar. This was done because, when mounted in the ,,'enter, a large undesirable time lag occurred between the development of the pulse cooling at the cold junction and the sensing of it by the thermocouple. A t~me lag of less than 2 msec was observed between the onset of the current pulse and the movement of the temperature trace when the thermocouple was mounted above the element. A 24 gauge Chromel-Alumel thermocouple sensed the temperature of the copper baseplate. A beryllium oxide (BeO) plate insulated electrically the current-carrying copper 'feet' of the elements from the copper baseplate. BeO is a good conductor of heat. The 0.0025 in. thick silver bus bar joined the thermoelectric elements at the top. Silver was used rather than copper because of silver's lower specific heat. EXPERIMENTAL APPARATUS The main apparatus consisted of: an evacuated chamber and vacuum system, a d.c. power supply for the steady-state current, an electrical square pulse source, high-speed recording instruments for current and temperature, and thermocouple circuits. For the steady current to the cooler a laboratorygrade d.c. power supply (0-20 V at 0-1.5 A) was used. Steady-state current was measured by the voltage drop across a precision 0.1 ohm resistor, registered on a d.c. digital voltmeter. The precision resistor was removed from the pulsing circuit before the pulse was initiated to increase the current to the cooler. A safety switch forced all current to go to a dummy cooler (a length of Chromel wire, 0.2 ohm resistance) unless the switch was thrown, :in which case the current was
allowed to go to the cooler. As may be seen in Fig. 2, the current circuit schematic, the pulse current adds to the steady-state current, it does not replace it. An oscillograph registered total current to the cooler as a function of time. The pulse source consisted of one or more car batteries and an amplifier which were turned on by the pulse-initiate switch and were turned off by a monastable multivibrator circuit ('one-shot'), so that a single rectangular pulse of current of controllable amplitude and duration was sent to the cooler. The schematic of the one-shot and amplifier is given in Ref. [6]. Pulse amplitude was determined by the stateof-charge of the car batteries and by the amount of resistance added to the cooler pulse circuit. For some runs a single 12 V battery was used: for others a 12 V and 6 V were used in series. Two 6 V lantern batteries in series were used to drive the one-shot. Pulse duration was controlled by a variable resistor and a variable capacitor in the one-shot. Exact values of resistance and capacitance used for each run are tabulated in Ref. [6]. The pulse-initiate switch was a double pole-double throw, spring-loaded switch. In one position, steady-state current could flow to the cooler (or dummy). As the switch was thrown, a circuit was completed in the one-shot to initiate the pulse. The one-shot turned itself off. In the 'dead' state after the pulse the output terminals of the one-shot were shorted, so that steady-state current continued to flow in a complete circuit to the cooler after the one-shot had shut off'. A 0 3 ohm variable resistor (a length of Chromel wire) was put in the pulsing circuit to limit current for low current runs. A 3 A safety fuse was installed in the pulse circuit; it did not blow with a 13 A pulse of 30 msec duration. Two channels of the oscillograph were utilized, one for the temperature of the cold surface and one for the pulse current. Large series resistances limited current on the pulse current channel, since only 32#A was
162
FIELD AND BLUM: FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
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required for full-scale deflection of the galvanometers in the oscillograph. Timing lines 10msec apart were impressed on the paper for a time reference. The oscillograph was calibrated by passing a known current through each galvanometer circuit with the particular arrangement of resistors to be used in the experiments. The current appeared on a strip-chart recorder (SCR) which was calibrated with a standard cellpotentiometer combination. Calibration for current versus oscillograph deflection was made both before and after the data-taking. Calibration of thermocouples was also made both before and after data-taking. The top thermocouple was installed in the thermocouple circuits in the position it would have in service, only it was not attached to the upper surface of a cooler. It was calibrated with a mercury-dry ice bath, using an ASTM thermometer vs oscillograph deflection. The baseplate thermocouple was calibrated in much the same way. Optimum T,~ (temperature of cold surface in steady-state) did not vary greatly from about - 4 0 ° C at 0.81 A (90 A/cm2). The test procedure is given in detail in Ref. [6]. Figure 3 shows actual oscillograph output from run no. 2/18/71-7. In this figure the first event is steadystate temperature recording, then the pulse, showing simultaneity of current and temperature response. Paper speed during this pulse (and all pulses) was 10 in/sec. This was one of the longest duration pulses. The pulse is quite rectangular, except for a tail-off at the end which occurred after the temperature trace had begun flattening out. Recorder overshoot is visible at the initiation of the pulse. This is a result of the damping and frequency response characteristics of the galvanometer in the oscillograph. After current shut-off we see a rather slow decay of temperature
back above the steady-state temperature, this being a characteristic of a relatively low current pulse. Eventually (after several seconds) the steady-state will be resumed. Higher current pulses have a longer recovery time. Figure 4 represents the same kind of data for a high current run. Note that about the same temperature is attained, only faster and post-pulse heat-up is greater (more energy has been input to cooler). Note also that the temperature trace flattens out before current shutoff. The 60 Hz noise seen on all traces was probably due to currents in the room, although everything was shielded and grounded to a copper stake driven in the ground. The very high sensitivity of the oscillograph made total elimination of noise virtually impossible. See Ref. [6] for additional discussion and justification of this procedure.
THEORETICAL ANALYSIS A full discussion of the attempts at analytical solution is to be found in Ref. [6]. A closed form solution was not obtained and the fact that approximations would have been required led us to the computer model where non-linear functions could be included, and we could get as close as we liked to the physical model. We used an explicit (finite difference) computer solution [7] by Reynard and Billerbeck [8] (Nethan) to determine the temperature history for all nodes (subdivisions). It is possible to include radiation and convection effects if needed as well as temperaturedependent properties for the solutions. Bywaters and Blum's 'reduced properties" [5] approach, based on the assumption that the elements are in parallel ther-
FIELD
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FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
BLUM:
163
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really, makes it possible and practical to convert a multi-element stage to a single equivalent element. A trade-off was required between the excessive amount of computer time for a large number of nodes in the solution and the improvement in the solution accuracy given by a large number of nodes. The practical criterion that evolved was: we will increase the number of nodes until the improvement in the transient solution is less than 2°C for a doubling of the number of nodes. Then we will use the error formula of Ref. [-6, Appendix E] to compute the temperature for an infinite number of nodes. In most cooler designs studied, 20 nodes for a 0.5 cm high element gave a solution of such accuracy. But the number of nodes required to get the desired accuracy was dependent on the pulse current. Forty nodes were required for the 1270amp/cm 2 pulse and greater current pulses. Four sizes of cooler were studied; two, extensively. The two cooler sizes studied in detail were the 10-4cal/°C and the 10-Scal/°C size thermal mass coolers. Theoretically, the smaller the mass to be cooled, the colder it can be made in the transient case, if it were not for contact resistance heating between the elements and the bus bar at the solder joints. We made all computer runs for R~ = 10 -s, 5 x 10 -6, 10 -6 and 0 ohm-cm 2. The 10 -4cal/°C cooler is of a size readily constructed in the laboratory. A 10 -5 cooler would be more difficult to build because of its very small size. A large 5 x 10-4 cal/°C size cooler was examined and it appears that colder temperatures can be obtained with this cooler but the height of the cooler elements would need to be impractically large, on the order of 10 cm.
In designing a 10 4cal/°C cooler, we wanted the largest cross-sectional area of elements obtainable, since the Joule and contact resistance heating would be smallest and therefore the coldest temperatures could be obtained. A limit on big area was the fact that a given cold surface thermal mass (10-4cal/°C) can be spread just so thin over the end surfaces of the thermoelectric elements, due to the practical state-ofthe-art design limits in making metal thin without being too fragile. It is with these criteria that designs for 10 -4 and 10 5 cal/OC coolers were made and from which the 10-4cal/°C coolers were constructed. The height of the elements was determined from computer results using the arbitrary criterion for selection that when a given height was doubled the increased cooling would be less than 2°C. See Ref. [6] for detailed discussion of cooler height design. RESULTS After the cooler was operating in the steady-state, from steady-state temperatures of -38-40°C and with steady-state current densities of about 90 A/cm 2, high current pulses produced pulse cooling down to about -61°C, for a AT of pulse cooling ranging from 18 to 21°C. Some pulse cooling could be obtained with any current surge or small pulse (like 466 A/cm 2 to get 19°C AT), but it was found that about 1270 A/cm 2 for the size cooler studied was required to get the maximum AT. Thus about 14 times the steady-state current density is required to get maximum AT. However, the longest time at near-maximum AT occurred for the lowest current density pulse (466A/cm2), and the greatest heat removal occurs with low current densities, also. Plotted in
164
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS M,.:O85x
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Fig. 5. Pulse cooling, temperature vs J\/t, 10 4 cal/:C cooler.
Fig. 5 are computer model curves, each labeled with a specific contact resistance and one curve labeled 'experimental'. The experimental points are the coldest temperature attained for a given current density, one point for each current density. Both computer and experimental data include thermocouple (T/C) heat loss effects, For applications, one must know performance without T/C effects. See Ref. [6] for details on correction for T/C effects. Figure 6 shows one curve corrected for estimated T/C effects. The 'uncertain' properties, referred to on the figures, are a set of materials property data used in the computer runs in which each material parameter has been allowed to deviate from its measured value to the limit of uncertainty in the variable. The uncertainties were combined as the "square root of the sum of the squares" following the technique of Ref. [9]. If any object is installed on the cold surface, then heat gain from it must be considered in the computer model. In the case of large current pulses, the thermal contact resistance of any object on the surface can produce a very large time lag to maximum AT, as sensed by the object. For instance, with the thermocouple it took 0.052 sec to maximum AT; without T/C effect, 0.033 sec. We found that a thermal contact resistance of 12,000 sec K/cal produced the best correlation. Rth = 1/Ahc = 12,000; hc = 0.00925 cal/seccm2K. This would vary according to T/C installation. For any pulse current, say 1090A/cm 2, some optimum pulse length exists. This optimum is equal to the time to m i n i m u m temperature. In other words, there is no benefit to be obtained from leaving the high current on very much past the maximum AT point. The time coordinate in Fig. 5 is the time to maximum AT. If a larger current is used, say 1270A/cm ~, no more cooling will be obtained, but the time to maximum AT will be much shorter. It is seen in Fig. 5 that
current densities of 1090, 1270 and 1420A/cm 2 all produced cold surface temperatures of -60.3°C, approx. The slenderness ratio, ). = height of elements,,' cross sectional area, was 56 cm 1. If maximum heat removal is desired, it will be advantageous to leave the pulse on as long as temperature is near its coldest point, In some cases, if, for example, the pulse is left on as much as 25 msec past maximum AT time, additional 'time at temperature', or energy removal will take place. Additional energy removal by lengthening 'time at temperature' is made at the expense of recovery time before the next pulse can be made. Figure 5 shows satisfactory correlation of 'cold surface temperature attainable' between the experiments and the assumed computer model if uncertainties in material properties are allowed to go to the limits of the assumed uncertainty simultaneously. It appears from this figure that the specific contact resistance of the experimental model was about 10-Vohm-cm z (10 -~ and 0 o h m - c m 2 produce almost exactly the I
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Fig. 6. Temperature response with time. 1270 A/cm 2.
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
same result). We see this in the experimental versus computer data with the 'uncertain' properties. The uncertainty in the computer model of 4-6°C and in the experimental data of about 1.5°C means that data overlap to a very great extent. Also, apparently, the amount of pulse cooling obtainable does not depend on the steady-state temperature from which the pulse cooling is initiated, T,~. This is true only if the steady-state temperature is near its optimum: for pulses from room temperature will not even attain --40 C, the T¢~[10]. In other words, if the T,.~ is - 38 C, a pulse will take the temperature down to - 6 1 C, for a total AT of 23'C. If the T,~ is --41' C, the pulse will take the temperature down to the same - 6 1 C, for a AT of 20°C. Thus there seems to be a limiting temperature for this cooler to which a large number of current density values will drive it. Due to this, since Tc~~ varied slightly from run to run, a plot of AT vs d,v/t would not be expected to correlate the data as well as a plot of pulse temperature vs J,/t. With the promising results from the 1 0 - 4 c a l / C cooler, a computer study of a smaller 1.14 x 10 5 c a l / C cooler was undertaken. Unfortunately, the expected contact resistance would limit the performance of this design, and the cold surface mass could not be spread thinly enough over a large area to produce colder temperatures than the 10 -4 cal/~C cooler. The results are presented in Ref. [6]. Temperatures of about - 5 8 C could be expected for this cooler, were i~ built, representing ~t AT of about 14'C. Computer runs without T/C were made to determine the length of time to return to the steady-state if the pulse were shut off at the point of maximum AT. For a 466A,.'cm 2 pul:~e to a 10 '*cal/°C cooler, the pulse temperature was - 5 9 C , achieved 0.140 sec after pulse initiation. At this point the current was returned to 90 A/cm 2, the steady-state current density. The cold surface returned to within 5°C of the steadystate temperature of - 4 3 C in 8 sec, within I°C in 15 sec. and within 0.2 C in 17sec. In the 1270A/cm 2 case, temperature returned within 5°C of steady-state value in 10.4see, within 1 C in 17sec, and within {).2' C in 19.8 sec. Temperature vs time curves for a 1270 A/cm 2 pulse to a I0 ¢ 4 c a l / C cooler are given in Fig. 6 for the computer model and the experiments. If uncertainties in computer model and experiment are considered, the correlation is acceptable. Note the large effect of the thermocouple in the high current runs. The computer curve without T/C effects is 'about what would be expected in an experiment with no thermocouple. From this we estimate that the experimental data without thermocouple effects wouM show a coldest temperature of - 6 5 . 8 ° C at 0.033 sec. U N C E R T A I N T Y ANALYSIS The complete uncertainty analysis is given in
165
Ref. [6]. The experimental uncertainty in temperature of pulse cooling was _+1.5°C. If individual uncertainties in the computer model were combined with equal weight, a total uncertainty in temperature of pulse cooling of + 3.3°C would result.
CONCLUSIONS 1. It has been demonstrated that a practical thermoelectric cooler can be built utilizing the fast transient effect. The full range of temperature response was obtained experimentally showing the capabilities of such a cooler. Single stage fast transient coolers with steady-state temperatures of - 4 f f C can be pulsed down to -60"C, and this temperature can be maintained (_+2C) for about 55 msec if low current density pulses are used. Pulses can be repeated about every 15 sec. 2. A finite difference model can be used to simulate fast transient response. When the uncertainty in the computer model solution is considered, the same absolute limit of pulse temperature ( - 6 0 ° C , approx.) is seen for this cooler as in the experiments. The computer model can be used to include the effect of heat loads, as from thermocouple lead wires, can show the effect of specific contact resistance and can illustrate the effect of varying any parameters, without the expense of building a cooler for each problem. It was also discovered that, because of Re, temperature solutions depend on J and J,v/i, not on J \ / t alone, as some theoretical investigators have said [2, 3].
REFERENCES [1] L. S. Stil'bans and N. A. Fedorovitch, Soviet Phys. tech. Phys. 3, 460 (1958). [2] K. Landecker and A. W. Findlay, Solid-St. Electrons 3, 239 (1961). [3] V. P. Babin and E. K. lordanishvili, Soviet Phv~s, tech. Phys. 14, 293 (1969). [4] O. J. Mengali and M. R. Seller, Adv. Ener,qy Comersion 2, 59 (1962). [5] R. P. Bywaters and H. A. Blum, Enerqy Conversion 10, (1971). [6] R. L. Field, A Study of the Fast Transient Behavior of Pulsed Thermoelectric Coolers, Ph.D. Dissertation, Southern Methodist University, Dallas, Texas (1971). Available from University Microfilms. Ann Arbor, Michigan 48106, U.S.A. [7] P. J. Schneider, Conduction Heat Tran.st~'r. AddisonWesley, MA (1957). [8] P. C. Reynard and W. J. Billerbeck, NETHAN IllThermal Network Analyzer Program, Report No. TRDS/165, Communications Satellite Corp., Washington, D.C. (Feb. 28, 1967). [9] S.J. Kline and F. A. McClintock, Mech. Engng 75, 3 (19531. [10] A. D. Reich and J. R. Madigan, J. appl. Phys. 32, 294 (1961).
It)79 P r m l c i l in (irc~tl B r i t a i n
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS WITH HIGH CURRENT PULSE AND FINITE COLD JUNCTION R I C H A R D L. F I E L D ~ and H A R O L D A. B L U M 2
~Texas A & M University, Mechanical Engineering Department, College Station, TX 77843 and :Departmenl of Civil and Mechanical Engineering, School of Engineering and Applied Science, Southern Methodist University, Dallas, TX 75275, U.S.A.
{Received 27 April 19791 Abstract Experimental, high speed temperature response data were taken on a single stage thermoelectric cooler as it was subjected to a high current, short duration, rectangular d.c. pulse. The pulse was imposed on the cooler as it was operating in its optimum, steady-state, cooled-down condition, After the cooler attained steady-state temperatures of about -40°C with the hot junction at 27c'C, pulse cooling down to about - 6 5 C was obtained with many combinations of current and pulse duration. Typical pulse current and duration were 10A for 30msec. The pulse could be repeated about every 15see. Average figure-of-merit of the cooler materials, bismuth and antimony tellurides, was 2.69 x 10 3 K t at 3'C. The cooler was of a practical, common size and configuration, being two elements, standing side-by-side, cormected at the top with a very thin silver bus bar. Element cross-sectional area was 0.0089 cm 2 and element height was 0.5 cm. Every effort was made to reduce the mass of the bus bar, solder, and thermocouple which was used to measure the temperature. Good correlation was obtained between the experimental data and a computer model solution by the Network Thermal Analyzer (NETHAN) program simulating the experimental conditions. Computer solutions of temperature were carried out for a wide range of cooler sizes, including the experimental model size. an approximately one-tenth size of the experimental model and sizes larger than the experimental model. Thermoelectric coupler Heat conduction, transient Refrigeration cooling Direct energy conversion Cold junction temperature.
INTRODUCTION
Peltier junctions
Solid state
this research we gratefully acknowledge. A detailed computer model was used to simulate the experiment and the results were correlated to the experimental data.
The fast transient effect is observed in thermoelectric coolers when the device is operating in its cooleddown, steady-state condition and is then subjected to a high current pulse of short duration. Instantly, additional Peltier cooling is developed at the cold junction, while the Joule or resistance heating developed in the elements requires a while to be conducted to the cold junction. This time lag gives rise to the pulse cooling phenomenon. Such a phenomenon could find application in any situation where extra cooling was needed for a short time, such as an infrared detector operating in a 'winking' mode, which needs to be supercold only during the wink. In the transient mode the smaller the mass of the object to be cooled, the colder it can be made to go. The bus bar joining the elements at the cold junction, the solder and any load mass must be kept to a minimum to achieve the maximum fast transient effect. The cold junction is defined as the interface between the thermoelectric material and the solder which joins it to the bus bar. The mass of an object times its specific heat is the thermal mass. The cooler studied experimentally had a combined cold surface thermal mass of 0.85 x 10-4cal/°C, Seven experimental models were built for this program by Nuclear Systems, Inc., Garland, Texas, whose contributions to
PREVIOUS WORK
The fast transient effect was first reported by Stil'bans and Fedorovitch [1], whose cooler consisted of two thermoelectric elements butt-soldered together to minimize cold junction mass. They did not report the size or dimensions of their cooler. The first extensive study of pulse cooling was made by Landecker and Findlay [2]. The configuration of their experimental model was ultrasonically-buttsoldered elements with essentially 'zero' mass at the cold surface. We were interested in the case with finite, known, cold surface mass. They report, for a cooler with infinitely-long elements: " . . . it is shown theoretically that for rectangular pulses the temperature of the cold junction is a function only of a parameter ~ = 1~/'t ( / = pulse current, t = pulse duration)." It is Jx/t (J - current/area) which will be used here to plot the computer and experimental data. The recent research on pulse cooling of Babin and Iordanishvili [3] involved a 'zero' mass butt-soldered cooler configuration. They also used the combination of variables J , t to present their analysis. 159
160
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRI(" ('OOLERS
Specific contact resistance (R,.) at a solder joint between the bus bar and the thermoelectric material is an important parameter. Mengali and Seiler [4] studied experimentally the resistance of solder joints between several different nickel-plated thermoelectric materials and copper. The range of values reported for bismuth telluride was 0.74 x 10 ~' 3.7 x 10 5 ohm-cm z with most values between 10 ~' and 10 s ohm-cm 2. Demonstration of a 'reduced variables' method of analyzing cooler designs by Bywaters and Blum [5] for finite difference solution of a one-dimensional heat conduction equation provided a simplified method for predicting transient temperature response. It was the goal of this study to (1) provide quantitative experimental data for the pulse cooling mode for coolers with finite cold surface mass and real contact resistance and (2) demonstrate a predictive method to design thermoelectric coolers utilizing the fast transient effect. EXPERIMENTAL INVESTIGATIONS The primary mode of pulse cooling of interest here was the application of a single square wave current pulse to a cooler operating already at its optimum steady-state current. A square wave is of interest because of the relative simplicity with which it may be produced electronically, as compared to a shaped pulse. The response to repeated pulses can be inferred from the response to a single pulse if the cooler is
allowed time to return to its equilibrium, s~eady-state condition. The variables were: cold surface thermal mass, specific contact resistance, current, pulse duration, element cross-sectional area and element height. Taken as constants were: type of thermoelectric material (bismuth and antimony tellurides), configuration (side-by-side elements standing vertically with a silver 'bus bar' soldered across the top of the elements), all specific heats, the absence of convective heat loading, and the neglecting of radiative heat loading (calculated as 0.04",, of Peltier cooling), and the baseplate temperature equal to 2 7 C _+ 1 C (300 K) so as to be comparable to other data in the literature. The following variables were taken as functions of temperature from laboratory measurements and from available literature: Seebeck coefficient, resistivity of bismuth and antimony tellurides, Thompson coefficient, and the thermal conductivity of bismuth and antimony telluride. Reference [6] presents details of materials properties. The experimental data of interest are the temperature of the top of the cold surface as a function of time and the current to the cooler as a function of time. The silver bus bar was weighed on a precision balance; the solder and thermocouple bead dimensions were measured under a microscope. The thickness of the solder joining the bus bar to the elements was estimated to be 0.0005 inch thick. The actual
Fig. 1. Experimental model, 10 4 cal/'C cooler.
FII!LD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS Power
oaltery
16~
[2-I~ • Fuse
~
1ia2nterr, V~ battery
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(Tec~
i[
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Pulse-initiate Switch j
Fig. 2. Current schematic.
cross-sectional area at the elements was 0.0089 cm 2, rather than the design value of 0.0079 cm 2. Figure 1 is a photograph of one of the models. A 0.002 inch diameter copper-constantan thermocouple was mounted atop the cold surface above the center of an element, nearer the end of the bus bar. This was done because, when mounted in the ,,'enter, a large undesirable time lag occurred between the development of the pulse cooling at the cold junction and the sensing of it by the thermocouple. A t~me lag of less than 2 msec was observed between the onset of the current pulse and the movement of the temperature trace when the thermocouple was mounted above the element. A 24 gauge Chromel-Alumel thermocouple sensed the temperature of the copper baseplate. A beryllium oxide (BeO) plate insulated electrically the current-carrying copper 'feet' of the elements from the copper baseplate. BeO is a good conductor of heat. The 0.0025 in. thick silver bus bar joined the thermoelectric elements at the top. Silver was used rather than copper because of silver's lower specific heat. EXPERIMENTAL APPARATUS The main apparatus consisted of: an evacuated chamber and vacuum system, a d.c. power supply for the steady-state current, an electrical square pulse source, high-speed recording instruments for current and temperature, and thermocouple circuits. For the steady current to the cooler a laboratorygrade d.c. power supply (0-20 V at 0-1.5 A) was used. Steady-state current was measured by the voltage drop across a precision 0.1 ohm resistor, registered on a d.c. digital voltmeter. The precision resistor was removed from the pulsing circuit before the pulse was initiated to increase the current to the cooler. A safety switch forced all current to go to a dummy cooler (a length of Chromel wire, 0.2 ohm resistance) unless the switch was thrown, :in which case the current was
allowed to go to the cooler. As may be seen in Fig. 2, the current circuit schematic, the pulse current adds to the steady-state current, it does not replace it. An oscillograph registered total current to the cooler as a function of time. The pulse source consisted of one or more car batteries and an amplifier which were turned on by the pulse-initiate switch and were turned off by a monastable multivibrator circuit ('one-shot'), so that a single rectangular pulse of current of controllable amplitude and duration was sent to the cooler. The schematic of the one-shot and amplifier is given in Ref. [6]. Pulse amplitude was determined by the stateof-charge of the car batteries and by the amount of resistance added to the cooler pulse circuit. For some runs a single 12 V battery was used: for others a 12 V and 6 V were used in series. Two 6 V lantern batteries in series were used to drive the one-shot. Pulse duration was controlled by a variable resistor and a variable capacitor in the one-shot. Exact values of resistance and capacitance used for each run are tabulated in Ref. [6]. The pulse-initiate switch was a double pole-double throw, spring-loaded switch. In one position, steady-state current could flow to the cooler (or dummy). As the switch was thrown, a circuit was completed in the one-shot to initiate the pulse. The one-shot turned itself off. In the 'dead' state after the pulse the output terminals of the one-shot were shorted, so that steady-state current continued to flow in a complete circuit to the cooler after the one-shot had shut off'. A 0 3 ohm variable resistor (a length of Chromel wire) was put in the pulsing circuit to limit current for low current runs. A 3 A safety fuse was installed in the pulse circuit; it did not blow with a 13 A pulse of 30 msec duration. Two channels of the oscillograph were utilized, one for the temperature of the cold surface and one for the pulse current. Large series resistances limited current on the pulse current channel, since only 32#A was
162
FIELD AND BLUM: FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
PulseinlhOte
O°C
2
--
Zera current ~
~ o
/v',/vV',z,.A~
~0
.1
163 sec Pulse length
~ O 147sec~l I • Time~to maxA II
Paper l ln Isec
speed lO in/sec
V"" '~
~
Jn/sec
<~
-i
%2
',~Tline irlcreaslNg Fig. 3. Oscillograph sample data, run 2/'18/71-7.
required for full-scale deflection of the galvanometers in the oscillograph. Timing lines 10msec apart were impressed on the paper for a time reference. The oscillograph was calibrated by passing a known current through each galvanometer circuit with the particular arrangement of resistors to be used in the experiments. The current appeared on a strip-chart recorder (SCR) which was calibrated with a standard cellpotentiometer combination. Calibration for current versus oscillograph deflection was made both before and after the data-taking. Calibration of thermocouples was also made both before and after data-taking. The top thermocouple was installed in the thermocouple circuits in the position it would have in service, only it was not attached to the upper surface of a cooler. It was calibrated with a mercury-dry ice bath, using an ASTM thermometer vs oscillograph deflection. The baseplate thermocouple was calibrated in much the same way. Optimum T,~ (temperature of cold surface in steady-state) did not vary greatly from about - 4 0 ° C at 0.81 A (90 A/cm2). The test procedure is given in detail in Ref. [6]. Figure 3 shows actual oscillograph output from run no. 2/18/71-7. In this figure the first event is steadystate temperature recording, then the pulse, showing simultaneity of current and temperature response. Paper speed during this pulse (and all pulses) was 10 in/sec. This was one of the longest duration pulses. The pulse is quite rectangular, except for a tail-off at the end which occurred after the temperature trace had begun flattening out. Recorder overshoot is visible at the initiation of the pulse. This is a result of the damping and frequency response characteristics of the galvanometer in the oscillograph. After current shut-off we see a rather slow decay of temperature
back above the steady-state temperature, this being a characteristic of a relatively low current pulse. Eventually (after several seconds) the steady-state will be resumed. Higher current pulses have a longer recovery time. Figure 4 represents the same kind of data for a high current run. Note that about the same temperature is attained, only faster and post-pulse heat-up is greater (more energy has been input to cooler). Note also that the temperature trace flattens out before current shutoff. The 60 Hz noise seen on all traces was probably due to currents in the room, although everything was shielded and grounded to a copper stake driven in the ground. The very high sensitivity of the oscillograph made total elimination of noise virtually impossible. See Ref. [6] for additional discussion and justification of this procedure.
THEORETICAL ANALYSIS A full discussion of the attempts at analytical solution is to be found in Ref. [6]. A closed form solution was not obtained and the fact that approximations would have been required led us to the computer model where non-linear functions could be included, and we could get as close as we liked to the physical model. We used an explicit (finite difference) computer solution [7] by Reynard and Billerbeck [8] (Nethan) to determine the temperature history for all nodes (subdivisions). It is possible to include radiation and convection effects if needed as well as temperaturedependent properties for the solutions. Bywaters and Blum's 'reduced properties" [5] approach, based on the assumption that the elements are in parallel ther-
FIELD
AND
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
BLUM:
163
L Z er o curren~
I
r
3
- popet
- -
¢~
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o
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~
T ime increasing
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Fig. 4. Oscillograph sample data, run 2, 19/71-8.
really, makes it possible and practical to convert a multi-element stage to a single equivalent element. A trade-off was required between the excessive amount of computer time for a large number of nodes in the solution and the improvement in the solution accuracy given by a large number of nodes. The practical criterion that evolved was: we will increase the number of nodes until the improvement in the transient solution is less than 2°C for a doubling of the number of nodes. Then we will use the error formula of Ref. [-6, Appendix E] to compute the temperature for an infinite number of nodes. In most cooler designs studied, 20 nodes for a 0.5 cm high element gave a solution of such accuracy. But the number of nodes required to get the desired accuracy was dependent on the pulse current. Forty nodes were required for the 1270amp/cm 2 pulse and greater current pulses. Four sizes of cooler were studied; two, extensively. The two cooler sizes studied in detail were the 10-4cal/°C and the 10-Scal/°C size thermal mass coolers. Theoretically, the smaller the mass to be cooled, the colder it can be made in the transient case, if it were not for contact resistance heating between the elements and the bus bar at the solder joints. We made all computer runs for R~ = 10 -s, 5 x 10 -6, 10 -6 and 0 ohm-cm 2. The 10 -4cal/°C cooler is of a size readily constructed in the laboratory. A 10 -5 cooler would be more difficult to build because of its very small size. A large 5 x 10-4 cal/°C size cooler was examined and it appears that colder temperatures can be obtained with this cooler but the height of the cooler elements would need to be impractically large, on the order of 10 cm.
In designing a 10 4cal/°C cooler, we wanted the largest cross-sectional area of elements obtainable, since the Joule and contact resistance heating would be smallest and therefore the coldest temperatures could be obtained. A limit on big area was the fact that a given cold surface thermal mass (10-4cal/°C) can be spread just so thin over the end surfaces of the thermoelectric elements, due to the practical state-ofthe-art design limits in making metal thin without being too fragile. It is with these criteria that designs for 10 -4 and 10 5 cal/OC coolers were made and from which the 10-4cal/°C coolers were constructed. The height of the elements was determined from computer results using the arbitrary criterion for selection that when a given height was doubled the increased cooling would be less than 2°C. See Ref. [6] for detailed discussion of cooler height design. RESULTS After the cooler was operating in the steady-state, from steady-state temperatures of -38-40°C and with steady-state current densities of about 90 A/cm 2, high current pulses produced pulse cooling down to about -61°C, for a AT of pulse cooling ranging from 18 to 21°C. Some pulse cooling could be obtained with any current surge or small pulse (like 466 A/cm 2 to get 19°C AT), but it was found that about 1270 A/cm 2 for the size cooler studied was required to get the maximum AT. Thus about 14 times the steady-state current density is required to get maximum AT. However, the longest time at near-maximum AT occurred for the lowest current density pulse (466A/cm2), and the greatest heat removal occurs with low current densities, also. Plotted in
164
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS M,.:O85x
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X - 56. crn ' C r o s s - sectional area • 0 0 0 8 9 c m 2
-70 -
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o D 0
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A/cm z A/crnZ A/cm z Experimental - ~ [ "Uncer rain" pc'operties, R c =0 A/cm 2 ~ -,. ~.~ A/cm 2
Symbols with toils ore ~ experimental data points
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=
~ "
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-30 50
L IOO
t
i 2oo
15o
J¢~
L____L 250 300
amp s e c J ~ / c m 2
Fig. 5. Pulse cooling, temperature vs J\/t, 10 4 cal/:C cooler.
Fig. 5 are computer model curves, each labeled with a specific contact resistance and one curve labeled 'experimental'. The experimental points are the coldest temperature attained for a given current density, one point for each current density. Both computer and experimental data include thermocouple (T/C) heat loss effects, For applications, one must know performance without T/C effects. See Ref. [6] for details on correction for T/C effects. Figure 6 shows one curve corrected for estimated T/C effects. The 'uncertain' properties, referred to on the figures, are a set of materials property data used in the computer runs in which each material parameter has been allowed to deviate from its measured value to the limit of uncertainty in the variable. The uncertainties were combined as the "square root of the sum of the squares" following the technique of Ref. [9]. If any object is installed on the cold surface, then heat gain from it must be considered in the computer model. In the case of large current pulses, the thermal contact resistance of any object on the surface can produce a very large time lag to maximum AT, as sensed by the object. For instance, with the thermocouple it took 0.052 sec to maximum AT; without T/C effect, 0.033 sec. We found that a thermal contact resistance of 12,000 sec K/cal produced the best correlation. Rth = 1/Ahc = 12,000; hc = 0.00925 cal/seccm2K. This would vary according to T/C installation. For any pulse current, say 1090A/cm 2, some optimum pulse length exists. This optimum is equal to the time to m i n i m u m temperature. In other words, there is no benefit to be obtained from leaving the high current on very much past the maximum AT point. The time coordinate in Fig. 5 is the time to maximum AT. If a larger current is used, say 1270A/cm ~, no more cooling will be obtained, but the time to maximum AT will be much shorter. It is seen in Fig. 5 that
current densities of 1090, 1270 and 1420A/cm 2 all produced cold surface temperatures of -60.3°C, approx. The slenderness ratio, ). = height of elements,,' cross sectional area, was 56 cm 1. If maximum heat removal is desired, it will be advantageous to leave the pulse on as long as temperature is near its coldest point, In some cases, if, for example, the pulse is left on as much as 25 msec past maximum AT time, additional 'time at temperature', or energy removal will take place. Additional energy removal by lengthening 'time at temperature' is made at the expense of recovery time before the next pulse can be made. Figure 5 shows satisfactory correlation of 'cold surface temperature attainable' between the experiments and the assumed computer model if uncertainties in material properties are allowed to go to the limits of the assumed uncertainty simultaneously. It appears from this figure that the specific contact resistance of the experimental model was about 10-Vohm-cm z (10 -~ and 0 o h m - c m 2 produce almost exactly the I
-50,~
M,h =0 8 5 x I0 ~ 00~/(
J
Iss ~0 8 f cmDs
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~
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60 :/'x'x _ L_ ~ C ~ , . ~ i n : c : r ? nr L//__ "--y p i entoI data IL Computer case 4A2MXS,"Uneertain" .70 L properties, no T/C, R c = 0 0 02 04 06 08 rrrne seconds
Fig. 6. Temperature response with time. 1270 A/cm 2.
FIELD AND BLUM:
FAST TRANSIENT BEHAVIOR OF THERMOELECTRIC COOLERS
same result). We see this in the experimental versus computer data with the 'uncertain' properties. The uncertainty in the computer model of 4-6°C and in the experimental data of about 1.5°C means that data overlap to a very great extent. Also, apparently, the amount of pulse cooling obtainable does not depend on the steady-state temperature from which the pulse cooling is initiated, T,~. This is true only if the steady-state temperature is near its optimum: for pulses from room temperature will not even attain --40 C, the T¢~[10]. In other words, if the T,.~ is - 38 C, a pulse will take the temperature down to - 6 1 C, for a total AT of 23'C. If the T,~ is --41' C, the pulse will take the temperature down to the same - 6 1 C, for a AT of 20°C. Thus there seems to be a limiting temperature for this cooler to which a large number of current density values will drive it. Due to this, since Tc~~ varied slightly from run to run, a plot of AT vs d,v/t would not be expected to correlate the data as well as a plot of pulse temperature vs J,/t. With the promising results from the 1 0 - 4 c a l / C cooler, a computer study of a smaller 1.14 x 10 5 c a l / C cooler was undertaken. Unfortunately, the expected contact resistance would limit the performance of this design, and the cold surface mass could not be spread thinly enough over a large area to produce colder temperatures than the 10 -4 cal/~C cooler. The results are presented in Ref. [6]. Temperatures of about - 5 8 C could be expected for this cooler, were i~ built, representing ~t AT of about 14'C. Computer runs without T/C were made to determine the length of time to return to the steady-state if the pulse were shut off at the point of maximum AT. For a 466A,.'cm 2 pul:~e to a 10 '*cal/°C cooler, the pulse temperature was - 5 9 C , achieved 0.140 sec after pulse initiation. At this point the current was returned to 90 A/cm 2, the steady-state current density. The cold surface returned to within 5°C of the steadystate temperature of - 4 3 C in 8 sec, within I°C in 15 sec. and within 0.2 C in 17sec. In the 1270A/cm 2 case, temperature returned within 5°C of steady-state value in 10.4see, within 1 C in 17sec, and within {).2' C in 19.8 sec. Temperature vs time curves for a 1270 A/cm 2 pulse to a I0 ¢ 4 c a l / C cooler are given in Fig. 6 for the computer model and the experiments. If uncertainties in computer model and experiment are considered, the correlation is acceptable. Note the large effect of the thermocouple in the high current runs. The computer curve without T/C effects is 'about what would be expected in an experiment with no thermocouple. From this we estimate that the experimental data without thermocouple effects wouM show a coldest temperature of - 6 5 . 8 ° C at 0.033 sec. U N C E R T A I N T Y ANALYSIS The complete uncertainty analysis is given in
165
Ref. [6]. The experimental uncertainty in temperature of pulse cooling was _+1.5°C. If individual uncertainties in the computer model were combined with equal weight, a total uncertainty in temperature of pulse cooling of + 3.3°C would result.
CONCLUSIONS 1. It has been demonstrated that a practical thermoelectric cooler can be built utilizing the fast transient effect. The full range of temperature response was obtained experimentally showing the capabilities of such a cooler. Single stage fast transient coolers with steady-state temperatures of - 4 f f C can be pulsed down to -60"C, and this temperature can be maintained (_+2C) for about 55 msec if low current density pulses are used. Pulses can be repeated about every 15 sec. 2. A finite difference model can be used to simulate fast transient response. When the uncertainty in the computer model solution is considered, the same absolute limit of pulse temperature ( - 6 0 ° C , approx.) is seen for this cooler as in the experiments. The computer model can be used to include the effect of heat loads, as from thermocouple lead wires, can show the effect of specific contact resistance and can illustrate the effect of varying any parameters, without the expense of building a cooler for each problem. It was also discovered that, because of Re, temperature solutions depend on J and J,v/i, not on J \ / t alone, as some theoretical investigators have said [2, 3].
REFERENCES [1] L. S. Stil'bans and N. A. Fedorovitch, Soviet Phys. tech. Phys. 3, 460 (1958). [2] K. Landecker and A. W. Findlay, Solid-St. Electrons 3, 239 (1961). [3] V. P. Babin and E. K. lordanishvili, Soviet Phv~s, tech. Phys. 14, 293 (1969). [4] O. J. Mengali and M. R. Seller, Adv. Ener,qy Comersion 2, 59 (1962). [5] R. P. Bywaters and H. A. Blum, Enerqy Conversion 10, (1971). [6] R. L. Field, A Study of the Fast Transient Behavior of Pulsed Thermoelectric Coolers, Ph.D. Dissertation, Southern Methodist University, Dallas, Texas (1971). Available from University Microfilms. Ann Arbor, Michigan 48106, U.S.A. [7] P. J. Schneider, Conduction Heat Tran.st~'r. AddisonWesley, MA (1957). [8] P. C. Reynard and W. J. Billerbeck, NETHAN IllThermal Network Analyzer Program, Report No. TRDS/165, Communications Satellite Corp., Washington, D.C. (Feb. 28, 1967). [9] S.J. Kline and F. A. McClintock, Mech. Engng 75, 3 (19531. [10] A. D. Reich and J. R. Madigan, J. appl. Phys. 32, 294 (1961).