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The design of ARCTIC: A rotary compressor thermally insulated μcooler
Sensors and Actuators A 134 (2007) 47–56
The design of ARCTIC: A rotary compressor thermally insulated cooler Joshua D. Heppner ∗ , David C. Walther, Albert P. Pisano Berkeley Sensor and Actuator Center, University of California at Berkeley, Berkeley, CA 94720, United States Received 1 March 2006; received in revised form 2 June 2006; accepted 26 June 2006 Available online 5 September 2006
Abstract Microscale cooling to date relies largely on passive on-chip cooling in order to move heat from hot spots to alternate sites. Such passive cooling devices include capillary pump loops (CPL), heat pipes, and thermosiphons. Recent developments for active cooling systems include thermal electric coolers (TECs) for heat removal. This paper focuses on the design of an active microscale closed loop cooling system that utilizes the Rankine vapor compression cycle. In this design, a rotary compressor will generate the high pressure required for efficient cooling and will circulate the working fluid to move heat away from chip level hot spots to the ambient. The rotary compressor will leverage technology gained from the rotary engine power system (REPS) program at UC Berkeley, most specifically the 367 mm3 displacement platform. The advantage of a Wankel (Maillard) compressor is that it provides six compression strokes per revolution rather than a single compression stroke common to other popular compressors such as the rolling piston. The current Wankel compressor design will achieve a theoretical compression ratio of 4.7:1. The ARCTIC (a rotary compressor thermally insulated cooler) system will be a microscale hybrid system consisting of some microfabricated (or MEMS) components including microchannels, in plane MEMS valves, and MEMS temperature, pressure and flow sensors integrated with mesoscale, traditionally machined steel components, including the compressor itself. The system is designed to remove between 45 W of heat at 1000 rpm using R-134a but the system is easily scaleable through a speed increase or decrease of the compressor. Further, a vapor compression cycle using R-134a operating between 258 and 310 K has a theoretical coefficient of performance (C.O.P.) of approximately 4.6. While this calculation does not include pressure losses, compressor inefficiency, or heat transfer losses, it provides ample room for significant improvement over comparable TECs with C.O.P.s of approximately 0.1–0.2. Finally, a thermal circuit analysis determines that the time constant to achieve refrigeration temperature at the evaporator in 12 s is possible. © 2006 Elsevier B.V. All rights reserved. Keywords: MEMS; Compressor; Refrigeration; Electronic cooling; Vapor compression; Heat transfer; Rakine cycle
1. Introduction The vapor compression cycle is the most common mechanical-type refrigeration cycle. The cycle and its variants are found anywhere from the common household refrigerator to a vehicle’s air conditioning system. However, on the microscale, the cycle has not been employed as more often than not passive designs such as thermosiphons, heat pipes [1], and capillary pump loops (CPL) [2], have been developed. Active systems, such as thermoelectric coolers (TEC) [3], have been used as alternatives as well. These other options have found their way into the microscale in lieu of the vapor compression cycle for two
∗
Corresponding author. Tel.: +1 510 642 9753. E-mail addresses: [email protected] (J.D. Heppner), [email protected] (D.C. Walther). URL: http://www-bsac.eecs.berkeley.edu/. 0924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2006.06.072
reasons. The first reason applies only to the passive designs: the vapor compression cycle requires input power. Passive designs generally rely on a fluid’s phase change ability to remove heat and to also provide motion. However, these designs are temperature limiters in reality and are limited to the fluid’s thermal properties in regards to the final temperature of the cooled chip. The second reason vapor compression cycles have been limited on the microscale is the size of the system. Each of the previous designs, active or passive, have been minimized to some degree of success. While several pumps have been put to use on the microscale [4], they have been limited to the amount of pressure head which can be added to the fluid. Further, compressors have been limited on the microscale mostly due to entropy considerations [5]. However, success at UC Berkeley in the rotary engine power system (REPS) program has shown that engines can be operated at small scales [6]. This program has specifically demonstrated a 367 mm3 displacement engine is capable of combustion. The
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Nomenclature A cp C C.O.P. h i k K L m P Q rp rv R t T V V
cross-sectional area heat travels through (m2 ) specific heat for constant pressure (J/kg K) thermal capacitance (J/K) coefficent of performance heat transfer coefficient (W/m2 K) electrical current (A) thermal conductivity (W/m K) constant conducting length, length heat will travel (m) mass (kg) pressure (N/m2 , atm) heat (W) pressure ratio compression ratio Thermal resistance (W/K) time (s) temperature (K) volume (m3 ) voltage (V)
Greek symbols γ ratio of specific heats ε emissivity σ Stefan–Boltzman constant (W/m2 K4 ) Subscripts cond thermal conduction conv thermal convection in into the compressor out out of the compressor rad thermal radiation s surface of device sur surrounding air
cycle of this rotary engine is intake, compress, ignite, expand, and exhaust. A compressor only requires an intake, compression, and exhaust stroke. Therefore, the development of a rotary compressor driven design is ongoing [7]. Rotary compressor sealing has long been troublesome at the small scale for high compression applications [8]. Sealing at the small scale is difficult because the differential pressure across the seal is larger and as the scale is reduced the dimensions are small, making the pressure gradient large. Small scale refrigeration systems on the other hand, have two primary advantages: (1) the requisite pressure ratio is reduced and (2) the compression stage in vapor compression systems occurs near the liquid boundary and any liquid present enhances the sealing by reducing the effective leakage area. The wet compression process can offer some thermodynamic advantages, however in this particular example, it is not explicitly considered. The initial compressor design has a footprint of 25 mm × 30 mm or about the size of one Intel® Pentium® 4 chip. To enable a vapor compression cycle with an ideal coefficient of
performance (C.O.P.) around 4.6 a moderate pressure ratio of 4.7:1 is required, where C.O.P. is defined as C.O.P. =
heat lift power in
In this analysis, the processes are assumed to be isentropic and the performance of real systems will be lower. This isentropic approach was carried out rather than using polytropic compression because of a lack of experimental data. As such a sensitivity analysis has been carried out. Despite the reduction in performance due to leakage and entropy generation the theoretical C.O.P. is significantly greater than thermoelectric coolers. Thermoelectric coolers have seen rapid development advances with the introduction of enhanced nanostructures [9]. The current figure of merit (ZT) for one thermoelectric material, Bi2 Te3 /Sb2 Te3 , is 2.4, which is a significant increase. The figure of merit sets a maximum temperature across the TEC element. This maximum temperature drop is however, at the point of no heat pumping (i.e. Q = 0). The attained temperature drop decreases with increased thermal load (Q), and therefore, TECs are typically used in stacked modules to move significant quantities of heat. Furthermore, TEC’s suffer from parasitic conduction of heat back to the cool side of the device because the materials used are inherently conductive, both electrically and thermally, limiting their C.O.P. Vapor compression cycles can minimize this by using insulating layers to limit parasitic conduction losses while maintaining a high C.O.P. This paper will discuss the design of a complete vapor compression refrigeration cycle for the microscale which can theoretically achieve heat lifts of 45 W at 1000 rpm at a temperature change of 40 K from the ambient. This will include the design of individual parts as well as a thermal circuit analysis using lump capacitance modeling. The thermal circuit analysis will be developed not only to show the performance of the system but also analyze parameters which will lead to optimal performance of the system. 2. ARCTIC design The vapor compression cycle is composed of four essential steps. The active part of the system, the compressor, receives uncompressed refrigerant and does work on this vapor by compressing the gases to the desired pressure. The compressor releases the vapor into the passive part of the system, beginning with the condenser. In the condenser, the refrigerant goes through a phase change, transforming from a vapor to a liquid. In the process, the refrigerant releases heat to the environment. Once the refrigerant leaves the condenser it is in a high pressure, high temperature liquid state prepared to enter the expansion valve. The expansion valve expands the liquid into a low pressure, low temperature state. The refrigerant moves through the evaporator absorbing heat by again changing phases, this time from liquid to vapor. Then the cycle repeats [10]. A review of this cycle can be seen in Fig. 1. Work is ongoing to optimize the compressor design, however, the details of this work will not be discussed in detail here.
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Fig. 1. Vapor compression cycle.
The goal for the overall system design, which is shown in Fig. 3, is a flat device. By utilizing MEMS technology the system will be able to minimize height so that it resembles a TEC. This resemblance will also include the fact that there will be a hot side, the condenser, and a cold side, the evaporator. To minimize heat leakage between the components insulation will also be used. Furthermore, the system maybe controlled to vary the heat lift of the device using input from environmental factors. The system can vary the heat lift by a mere change in the rotational speed of the compressor. A graph showing the linear relationship of heat lift depending on rotational speed for a lossless system is shown in Fig. 2. As the rotational speed is increased pressure loss through the microchannels will undoubtedly increase, reducing system efficiency. Furthermore, compressor inefficiency, and heat transfer leaks from the evaporator to the compressor will affect system performance. 2.1. ARCTIC’s vapor compression cycle overview The initial ARCTIC vapor compression cycle will utilize a cycle similar to the macroscale designs as a method to determine the baseline capability of the system’s performance. This cycle requires the superheated fluid leaving the evaporator and entering the compressor to be 1.62 atm at 258 K. The compres-
Fig. 2. Heat lift vs. rotational speed for the ARCTIC system.
sor will then compress the gases to 7.6 atm at 310 K before it enters the condenser. The refrigerant will then condense on the condenser walls and will also cool down to 303 K. Next the fluid will expand adiabatically, theoretically, in the expansion valve before heading into the evaporator dropping to the evaporator pressure of 1.62 atm (Fig. 3). 2.2. Compressor design The design of the Wankel rotary compressor utilizes a 367 mm3 displacement while trying to maintain a small form factor. The compressor has a footprint of 25 mm × 30 mm and is 6.25 mm thick. This design used parameters set forth in previous papers [11]. The inherent advantage of the Wankel rotary compressor is its flat shape making it a good fit for the form factor required by ARCTIC. Further, the Wankel rotary compressor design requires two sets of ports: one inlet port and one exhaust port. The ports allow the rotary compressor to compress the vapor on both sides of the housing as the housing is symmetric, as shown in Fig. 4. Finally, the compressor may be composed of a variety of materials as it is not subjected to harsh temperatures. However, as the results will later show, it will be necessary to
Fig. 3. ARCTIC system schematic.
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ratio, rp , defined as rp =
Fig. 4. Schematic of Wankel compressor depicting the two sets of ports. Note that compressor ports are not optimized but shown in this manner for clarity.
manufacture the housing from a conducting material which can wear well. The ports shown in Fig. 4 are actually not optimal as they allow “cross-talking” between ports. Cross-talking occurs when the rotor allows a direct path for the fluid from the inlet port to the exhaust port. In order to design optimal ports one wants to cover the exhaust ports when the rotor opens the inlet ports. An optimal port design is shown in Fig. 5. This design minimizes crosstalking and allows the compressor to achieve a compression ratio, rv defined as rv =
Vin Vout
where V is the volume. This particular design achieves a compression ratio of 3.3. Assuming an isentropic compression process this will enable a high pressure of 3.6 atm as given from the refrigeration tables for R-134a. If the working fluid is air the high pressure would be 5.3 atm for a reversible adiabatic process. This is found using the following well-known relationship:
Pout Pin
To achieve this internal compression ratio the system must have adequate sealing. The Wankel compressor has two inherent leakage paths: around the rotor apexes and around the rotor faces. To minimize the effects of these two leakage paths the system uses a combination of sealing mechanisms. To reduce leakage around the rotor apexes, apex seals have been introduced into the design as shown in Fig. 5. These seals use a spring hidden behind the seal to push the sealing surface against the wall to minimize the distance between the rotor and the housing wall, effectively reducing the leakage gap. The second leakage path, the rotor face, does not have a sealing system but instead relies on machining tolerances to minimize the gap between the rotor face and the housing. In addition to these sealing mechanisms the refrigerant requires a lubricant to be added into the system. This lubricant should aid in the operation and sealing of the compressor. Further, using a model previously demonstrated [8], the system can achieve its desired compression ratio, if a design tolerance of 6 m is attained. Pressures of 3.6 atm are most often not enough to achieve the desired heat lift. This is because the pressure and the temperature are interrelated in a given state; by compressing the refrigerant the temperature raises. To allow the heat to be absorbed into the environment the temperature must be greater than that of the ambient. Due to these constraints, all positive displacement compressors and pumps require check valves, one-way fluid valves, to prevent back flows into the compressor and the Wankel compressor is no different. Thus, the check valves are designed so that they open at the desired pressure by using an adjustable preloaded spring to maintain contact between a precision bearing and seat. Check valves will allow the system to reach pressures up to 8 atm which is just above the necessary pressure required for a system pressure ratio of 4.7:1. 2.3. Design of the passive parts
γ
PV = K where P is the pressure, K the constant, and γ is the ratio of specific heats. Knowledge of the high pressure will set the pressure
The passive parts of the system include the condenser, expansion valve, and evaporator. Each of these parts can be made using microfabrication techniques. However, none of the parts have yet
Fig. 5. Optimal port design to eliminate cross-talking. (a) Shows inlet just closing with exhaust completely closed. (b) Shows exhaust just opening with inlet completely closed.
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Fig. 6. Conceptual design of ARCTIC condenser.
been optimally designed; thus, there is no discussion here about the correct number of turns or the size of the channels to reduce pressure drop. The condenser, shown in Fig. 6, is a serpentine structure with fins. This tubular structure takes advantage of the microscale’s large surface area to volume ratio in order to increase heat transfer to the environment. This device can be made either in a polymolding process [12] or by using an optimized silicon DRIE process [13] and capping the etched channels by bonding a second substrate to the device layer. A detailed thermal model will finalize the desired material properties and structure dimensions. The expansion valve can made using a simple MEMS device, the diffuser in Fig. 7 [14]. The expansion valve in a vapor compression system requires efficiency. An idealized vapor compression system assumes the enthalpy entering the expansion valve is the same going out. To achieve this, the entrance loss must be minimized. Work has been done to show that a half angle of 7◦ is the most effective in minimizing pressure loss and thus enthalpy drop loss across the expansion valve [15]. The expansion valve will be designed to utilize such characteristics. The evaporator, shown in Fig. 8, is very similar in design to the condenser. The only exception is that the material between the serpentine is not removed. This additional material increases the heat capacity of the evaporator and allows heat to be absorbed into the fluid from the sides as well as from the object to be cooled. Again the advantage of having microscale channels here allows the fluid to quickly absorb heat, minimizing the necessary size of the evaporator. The overall system performance is
Fig. 8. Conceptual design of ARCTIC evaporator and accompanying insulation layer.
strongly affected by the heat flow to the evaporator; therefore the value of the thermal resistance (K/W) across the insulating layer shown in Fig. 8 is imperative to the system design as the results will later show. A MEMS sensor suite of temperature and pressure sensors will be added to the package as well. In mesoscale systems and smaller, it is critical that sensor elements are closely integrated with the structure. Unoptimized temperature sensors provide a major source of heat loss as well as pressure drops for in line sense elements. Such integrated MEMS sensors can be used to enhance system performance by sensing heat fluxes and temperatures in the evaporator to provide control input parameters for the compressor speed. Further, the pressure going into the condenser will be monitored to ensure that the system is performing optimally and to provide feedback to the system’s check valves. 3. ARCTIC analysis In order to determine the performance of ARCTIC, a parametric analysis of the thermal network of the refrigeration cycle has been completed. The parameters investigated include thermal resistance across the evaporator insulation, thermal insulation of the compressor, and device layer thermal resistance. This analysis of the heat transfer was completed using a thermal circuit model. Such modeling splits the thermal system elements into their electrical analogs which allow one to use an electrical circuit model code such as SpiceTM by Cadence. From a thermal perspective this is the same as treating each element as a point with mass and utilizing a lumped capacitance model for each node. Thermal circuit modeling provides the added convenience of using industrial code for solving the system. 3.1. Refrigeration cycle
Fig. 7. MEMS expansion chamber.
The refrigeration cycle modeled using R-134a is a more conservative cycle than the optimized cycle presented above. This cycle is used because it drives the evaporator to the lowest likely temperature. The result of this will provide initial conservative
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estimates for the insulation of the evaporator. R-134a has a critical temperature of 247.08 K which determines the evaporator temperature. The compressor is modeled to achieve a maximum pressure ratio of 8:1. This pressure ratio will set the condenser temperature to vary between 304.94 and 315 K depending on the position of the fluid. Allowing the compressor to rotate at 1000 rpm, ARCTIC can lift approximately 27 W of heat across a temperature difference of 51 K from ambient using the prescribed cycle. It is necessary to note that applications requiring more heat lift can be handled by ARCTIC by increasing the rotation speed of the compressor. For example an application requiring 54 W of heat lift will require the ARCTIC compressor to rotate at 2000 rpm.
Table 1 Summary of electrical–thermal circuit analogs
3.2. Assumptions and equations for a thermal circuit model
The thermal circuit model analysis must begin with the determination of the circuit to be solved, shown in Fig. 9. This begins with the determination of what ground represents. In this thermal model, ground will represent the ambient temperature, 298 K. This temperature is chosen because the compressor is initially at ambient temperature. Thus, ground determines the initial condition of the system. The voltage sources dictate what temperature the fluid is within the element. In the evaporator the temperature is set to 247 K, in the compressor it is set to the highest condenser temperature, 315 K, and finally in the compressor it is set to 295 K. The capacitors linked to the voltage sources represent the capacitance of the fluid inside the element. The resistors linked to the voltage source represent the heat transfer from fluid to the element. The capacitors in the lower half of Fig. 9 linked to ground, represent the capacitance of the individual element while the resistor in parallel represents the heat being leaked to the ambient from the element. Finally, the power being introduced into the system through the dc motor is represented by the current source. The values for each of the circuit compo-
A lumped capacitance analysis requires that each of the elements in a system have a node which represents the average temperature across the device, thus no single element has a temperature gradient. Thermal circuit modeling requires turning each aspect of the thermal regime into its electrical circuit analog. Every mode of heat transfer, that is conduction, convection and radiation, become resistors. Each element also has a thermal capacitance due to its mass. Temperature and heat are analogous to voltage and current, respectively. These analogs are summarized in Table 1 [16,17]. The analysis assumes that the fluid immediately reaches its steady state temperature for each of the states of the thermodynamic cycle, Fig. 1. Thus, the fluid in the evaporator immediately reacts as if it has been compressed, expanded, and can now transform into a vapor. Also, the expansion valve is modeled as an adiabatic gas expansion, similar to the general literature treatment of the expansion process of refrigeration systems [10].
Electrical analog
Thermal analog
Representative equation
Voltage, V Current, i
Temperature, T Heat transfer rate, Q Conduction, Rcond Convection, Rconv Radiation, Rrad
L Rcond = kA 1 Rconv = hA Rrad = h 1 A , where
Resistor, R Capacitor, C
Thermal capacitance, C
rad
2 ) hrad = εσ(Ts + Tsur )(Ts2 + Tsur C = mcp
3.3. Analysis
Fig. 9. Thermal circuit model.
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Table 2 Values for circuit components and the necessary values for the calculation
Evaporator insulation Compressor to environment Condenser to environment Evaporator/compressor interface Compressor/condenser interface dc motor wire
Conduction resistors
Surface area
606.06 0.04 0.18 222.22 51.28 249.38
0.00055 0.00165 0.00055 0.00075 0.00075 4E−07
Evaporator Compressor Condenser Evaporator fluid Compressor fluid Condenser fluid
0.001 0.015 0.015 0.0005 0.001 0.04
h
1.78 13.33 2.50 148.15
A
1000 100 712 12
0.000563 0.00075 0.000563 0.000563
Capacitance
Density
Volume
Mass
cp
6.22 27.45 6.22 0.02 0.36 0.12
2330 2702 2330 5.2581 39.557 39.557
3.75E−06 1.13E−05 3.75E−06 2.81E−06 8.44E−06 2.81E−06
8.74E−03 3.04E−02 8.74E−03 1.48E−05 3.34E−04 1.11E−04
712 903 712 1280.5 1078.4 1078.4
nents and the values necessary to calculate them are shown in Table 2. The heat transfer coefficients for the two-phase flows in the evaporator and condenser transferring heat to the plate itself are determined using an analysis similar to that describe by Lou [18]. While heat transfer coefficients change as the quality of the vapor varies, the lowest heat transfer coefficient is included for the thermal circuit analysis. This ensures a worst case performance scenario for the analysis. The heat transfer coefficient for the heat transferred from the condenser to the environment is calculated using a free convection analysis for the upper surface of a heated plate [16]. The model is built using SpiceTM exactly as shown in Fig. 9. To enable a transient analysis, the voltage and current sources must introduce a step input to the system. The step input causes the capacitors to react as the heat transferred through the capacitor is defined as Q=C
L
0.003 237 148 0.003 0.026 401
Convection resistors Evaporator fluid Compressor fluid Condenser fluid Condenser to environment
k
dT dt
Thus, the capacitor will only react with a change in temperature over time. Using a transient Euler analysis, SpiceTM can output the systems response to the fluid instantly being changed to the steady state temperature.
of heat is transferred to the environment then the system will not have enough capacity remaining to cool an attached device. By varying the resistance of the evaporator insulation according to the thermal conductivity values of different insulation materials, the system performance was determined. The results of this analysis are shown in Table 3. From this analysis it is found the evaporator must be well insulated to achieve any meaningful performance. For the case with no insulation the evaporator loses its capability of lifting any heat as 26.3 W of the available 27 W heat lift is transferred to the environment. Higher end insulation materials such as the aluminum cryogenic insulation material can reduce the heat transferred to the environment to 0.2% of the total heat lift. However, less expensive insulation materials such as aerogel do nearly as well, reducing the heat leaked to 0.3% of the total. As Fig. 10 shows there is only slightly less heat loss when using reflective aluminum insulation. Materials such as foam and aerogel lie on the graph at the point of diminishing returns. To design the compressor it must be determined if insulation would be necessary for system effectiveness. From the model it was determined that insulation would not be useful. Table 4 shows that insulating the compressor would lead to high operating temperatures mainly due to the input power of the dc motor which would not be able to escape. Thus, heat would be absorbed
4. Results
Table 3 Insulating material and amount of heat lost to environment
In order to determine system performance, the individual parameters of the system were systematically varied while the remainder of the system values were fixed. As noted previously the thermal resistance of the insulation between the evaporator and the remainder of the system has the most significant impact on the refrigeration system performance. If a large percentage
Insulation material
Heat leaked (W)
No insulation Glass fiber Foam Aerogel 10 layer of reflective aluminum evacuated
26.3 1.22 0.704 0.083 0.044
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Fig. 11. Effect of interface resistance on system. Fig. 10. Evaporator insulation resistance vs. heat loss.
by the fluid traveling through the compressor, reducing the efficiency of the system. Considering this effect, the compressor must be made out of conducting material. Two such effective compressor materials are aluminum and ceramic which raise the temperature of the compressor to no higher that 305.6 K. The heat absorbed by the refrigerant at this temperature is negligible. In order to properly design the system, interface resistances must be considered. Interface resistances can cause difficulties when trying to transfer heat between two objects such as electronics and heat sinks. To reduce interface resistances in such systems thermal greases are often used. In the ARCTIC system, large interface resistances between the compressor and the evaporator can actually help system performance. Further, it is valuable to note that adding insulation between the compressor and evaporator will be imperative. The temperature gradient between the layers is large, 10,000 K/m, and thus a layer providing insulation is necessary to ensure that heat transferred from the evaporator to the compressor is minimized. System performance for this system is enhanced if the evaporator is able to utilize its total cooling capacity on the object being cooled. Although it has been shown that compressor efficiency can be enhanced by reducing the operating temperature of the compressor, this gain in compressor efficiency is counteracted by a loss in system efficiency, if there is heat leaked from the compressor to the evaporator [10]. In order to show the effect of interface resistance on system performance, the interface resistance between the compressor and evaporator was varied. The corresponding temperatures for the evaporator and compressor were recorded and shown in Fig. 11. It is clear that increased interface resistances enhance system performance in terms of temperature. Furthermore, typical thermal resistances do not vary above 10 K/W. As seen in the graph low thermal resistances Table 4 Compressor materials and insulation vs. operating temperature Compressor/insulating material
Temperature (K)
Aluminum Ceramic Teflon insulation Foam insulation
298.5 305.6 412 463
Fig. 12. Plot of temperature response time for ARCTIC components.
will lead to poor system performance thus additional resistance can be added using thermal insulation to reach the required resistance between the two system elements. ARCTIC’s overall system performance based on temperature is shown in Fig. 12. This analysis uses all the optimal values found through the entire analysis and previously shown in Table 2. The plot shows how quickly the system responds with time. The time constant to cool the evaporator to operating temperature is 12 s. This can be dropped further though by operating the compressor at a higher speed which will drive more refrigerant through the evaporator in a given time. 5. Conclusions This paper has suggested a design for a vapor compression system, ARCTIC. The vapor compression cycle is minimized through the use of MEMS structures, most specifically the check valves, condenser, evaporator, expansion valve, and a sensor suite. The Wankel compressor design has enabled a flat design resembling a TEC device with a cold side and a hot side. The performance of this refrigeration unit is 45 W of heat lift at a temperature change of 40 K and a compressor operating at 1000 rpm. The heat lift is scaleable thru compressor speed allowing ARCTIC to be used for a variety of applications. The most intriguing aspect of the design is the efficiency of the system which theoretically can achieve C.O.P. of 4.6.
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Furthermore, a thermal network analysis has been carried out to determine nodal sensitivities. This analysis has assumed an isentropic compression process, an isenthalpic expansion process, and lumped capacitance assumptions. This analysis has determined the necessity of insulation around the evaporator and between the evaporator and compressor. The addition of simple insulation materials such as foam and aerogel can improve system performance by three orders of magnitude in terms of heat transferred to the environment. The system performs well dynamically with a time constant for cool down of 12 s which can be enhanced with startup sequences which initially flood the evaporator with more refrigerant than necessary. In the near future the system will be further developed. This will include the fabrication of the system and experimentation. Once complete the system will be further miniaturized to achieve a small form factor while simultaneously determining optimized performance solutions. Acknowledgments The authors would like to thank the members of the REPS team and BMAD at the University of California at Berkeley for their useful contributions. Most specifically Chris Hogue, Robert Azevedo, Fabian Martinez, and Mitchell Swanger for there suggestions and analytic help. References [1] B. Suman, N. Hoda, Effect of Variations in thermophysical properties and design parameters on the performance of a V-shaped microgrooved heat pipe, Int. J. Heat Mass Transfer 48 (2005) 2090. [2] K.I. Pettigrew, MEMS Based Capillary Pumped Loops for Integral Thermal Management, Masters Thesis, University of California at Berkeley, 2002. [3] R. Yang, G. Chen, J. Snyder, J.-P. Fleurial, Multistage thermoelectric microcoolers, in: Proceedings of the Eighth Intersociety Conference on Thermal and Thermomechanical phenomena in Electronic Systems, San Diego, May 30–June 1, 2002. [4] S.V. Garimella, V. Singhal, Single-phase flow and heat transport in microchannel heat sinks, in: Proceedings of the First International Conference on Microchannels and Minichannels, Rochester, April 24–25, 2003. [5] S. Jong, How difficult is it to make a microrefrigerator, Int. J. Refrigeration 27 (2004) 309–313. [6] S.B. Sprague, S.-W. Park, D.C. Walther, A.P. Pisano, A.C. Fernandez-Pello, Development and characterization of small-scale rotary engines, Int. J. Alt. Prop., in press. [7] J.D. Heppner, D.C. Walther, A.P. Pisano, ARCTIC: rotary compressor thermally insulated cooler, in: Proceedings of the International Mechancial Engineering Congress and Exposition (IMECE), Orlando, FL, November 6–11, 2005. [8] J.D. Heppner, D.C. Walther, A.P. Pisano, Leakage flow analysis for a MEMS rotary engine, in: Proceedings of the International Mechanical Engineering Congress and Exposition (IMECE), Washington, DC, November 15–22, 2003. [9] A. Majumdar, Thermoelectricity in seminconductor nanostructures, Science 303 (5659) (2004) 777–778. [10] Dossat, J. Roy, Principles of Refrigeration, Prentice Hall, Upper Saddle River, 1997. [11] K. Yamamoto, Rotary Engine, Toyo Kogyo Co., Hiroshima, 1981. [12] N.H. Talbot, Polysilicon micromolding of closed-flow passages for the fabrication of multifunctional microneedles, PhD Thesis, University of California at Berkeley, 1999.
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[13] F.C. Martinez, N. Chen, M. Wasilik, A.P. Pisano, Optimized ultra-DRIE for the MEMS rotary engine power system, in: Proceedings of the EMN04, Paris, October 20–21, 2004. [14] C.-L. Sun, et al., Dynamic modeling of a thermally-driven microdiffuser pump, in: Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition (IMECE), Washington, DC, November 16–21, 2003. [15] A. Olsson, G. Stemme, E. Stemme, Numerical and experimental studies of flat-walled diffuser elements for valve-less micropumps, Sens. Actuators 84 (1) (2000) 165. [16] F.P. Incropera, D.P. DeWitt, Introduction to Heat Transfer, 3rd ed., John Wiley & Sons, New York, 1996, pp. 74–81, 460–464. [17] S.D. Senturia, Microsystem Design, Kluwer Academic Publishers, Boston, 2001. [18] Z.D. Lou, A dynamic model of automotive air conditioning systems, in: Proceedings of the 2005 SAE World Congress, Detroit, April 11–14, 2005.
Biographies Joshua D. Heppner, in 2004, earned his master’s in mechanical engineering (MEMS) at the University of California, Berkeley, and is currently working towards his PhD. He finished his undergraduate work at Santa Clara University in mechanical engineering. During his stay at Santa Clara University, he researched and built a NanoSatellite funded by DARPA. At UC Berkeley, he has worked on numerous projects included leakage analysis of a rotary engine, rotary engine apex seal design, systems engineering, and a micro-refrigeration system. He has held research internships at NASAAmes, Hewlett Packard Laboratories, and Harris Communications. David C. Walther, in 1998, earned his doctorate in mechanical engineering (thermosciences) at the University of California, Berkeley. From 1999 to 2000, he served as a post-doctoral research engineer for the Combustion Processes Laboratory in Berkeley, overseeing two NASA Fire Safety Flight Programs, and a DARPA MEMS Program. In the spring of 2001, Dr. Walther served as an adjunct faculty at Santa Clara University, teaching advanced thermodynamics. Since 2001, Dr. Walther has served as the principal research engineer for several DARPA, Army Research Lab, State of California, and Industrial Sponsored Research Programs at the Berkeley Sensor and Actuator Center in the areas of PowerMEMS, BioMEMS, and RF MEMS. Exceptional PI status has been granted to Dr. Walther for many of these programs. Dr. Walther currently also serves as an advisory board member for micro/nanotechnology for MedCap Partners, a life sciences/healthcare related investment fund. Albert P. Pisano currently serves as professor and chair of the Department of Mechanical Engineering at the University of California at Berkeley. He was elected to the National Academy of Engineering in 2001. At UCB, Professor Pisano holds the FANUC Chair of Mechanical Systems in the Department of Mechanical Engineering, with a joint appointment to the Department of Electrical Engineering and Computer Science. He currently serves as a Director of the Berkeley Sensor & Actuator Center (BSAC). Professor Pisano received his BS, MS and PhD (1981) degrees from Columbia University in the City of New York in mechanical engineering. Prior to joining the faculty at UC Berkeley, he held research positions with Xerox Palo Alto Research Center, Singer Sewing Machines Corporate R&D Center, and General Motors Research Labs. From 1997 to 1999, he served as program manager for the MEMS program at the Defense Advanced Research Projects Agency
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(DARPA). His research interests and activities at UC Berkeley include MEMS for a wide variety of applications, including RF components, power generation, drug delivery, strain sensors, biosensors, and disk-drive actuators. Professor Pisano is the co-inventor listed on 20 patents in MEMS and has authored or
co-authored more than 190 archival publications. He is a co-founder in start-up companies in the area of transdermal drug delivery, transvascular drug delivery, sensorized catheters, MEMS manufacturing equipment, and MEMS RF devices.
The design of ARCTIC: A rotary compressor thermally insulated cooler Joshua D. Heppner ∗ , David C. Walther, Albert P. Pisano Berkeley Sensor and Actuator Center, University of California at Berkeley, Berkeley, CA 94720, United States Received 1 March 2006; received in revised form 2 June 2006; accepted 26 June 2006 Available online 5 September 2006
Abstract Microscale cooling to date relies largely on passive on-chip cooling in order to move heat from hot spots to alternate sites. Such passive cooling devices include capillary pump loops (CPL), heat pipes, and thermosiphons. Recent developments for active cooling systems include thermal electric coolers (TECs) for heat removal. This paper focuses on the design of an active microscale closed loop cooling system that utilizes the Rankine vapor compression cycle. In this design, a rotary compressor will generate the high pressure required for efficient cooling and will circulate the working fluid to move heat away from chip level hot spots to the ambient. The rotary compressor will leverage technology gained from the rotary engine power system (REPS) program at UC Berkeley, most specifically the 367 mm3 displacement platform. The advantage of a Wankel (Maillard) compressor is that it provides six compression strokes per revolution rather than a single compression stroke common to other popular compressors such as the rolling piston. The current Wankel compressor design will achieve a theoretical compression ratio of 4.7:1. The ARCTIC (a rotary compressor thermally insulated cooler) system will be a microscale hybrid system consisting of some microfabricated (or MEMS) components including microchannels, in plane MEMS valves, and MEMS temperature, pressure and flow sensors integrated with mesoscale, traditionally machined steel components, including the compressor itself. The system is designed to remove between 45 W of heat at 1000 rpm using R-134a but the system is easily scaleable through a speed increase or decrease of the compressor. Further, a vapor compression cycle using R-134a operating between 258 and 310 K has a theoretical coefficient of performance (C.O.P.) of approximately 4.6. While this calculation does not include pressure losses, compressor inefficiency, or heat transfer losses, it provides ample room for significant improvement over comparable TECs with C.O.P.s of approximately 0.1–0.2. Finally, a thermal circuit analysis determines that the time constant to achieve refrigeration temperature at the evaporator in 12 s is possible. © 2006 Elsevier B.V. All rights reserved. Keywords: MEMS; Compressor; Refrigeration; Electronic cooling; Vapor compression; Heat transfer; Rakine cycle
1. Introduction The vapor compression cycle is the most common mechanical-type refrigeration cycle. The cycle and its variants are found anywhere from the common household refrigerator to a vehicle’s air conditioning system. However, on the microscale, the cycle has not been employed as more often than not passive designs such as thermosiphons, heat pipes [1], and capillary pump loops (CPL) [2], have been developed. Active systems, such as thermoelectric coolers (TEC) [3], have been used as alternatives as well. These other options have found their way into the microscale in lieu of the vapor compression cycle for two
∗
Corresponding author. Tel.: +1 510 642 9753. E-mail addresses: [email protected] (J.D. Heppner), [email protected] (D.C. Walther). URL: http://www-bsac.eecs.berkeley.edu/. 0924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2006.06.072
reasons. The first reason applies only to the passive designs: the vapor compression cycle requires input power. Passive designs generally rely on a fluid’s phase change ability to remove heat and to also provide motion. However, these designs are temperature limiters in reality and are limited to the fluid’s thermal properties in regards to the final temperature of the cooled chip. The second reason vapor compression cycles have been limited on the microscale is the size of the system. Each of the previous designs, active or passive, have been minimized to some degree of success. While several pumps have been put to use on the microscale [4], they have been limited to the amount of pressure head which can be added to the fluid. Further, compressors have been limited on the microscale mostly due to entropy considerations [5]. However, success at UC Berkeley in the rotary engine power system (REPS) program has shown that engines can be operated at small scales [6]. This program has specifically demonstrated a 367 mm3 displacement engine is capable of combustion. The
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Nomenclature A cp C C.O.P. h i k K L m P Q rp rv R t T V V
cross-sectional area heat travels through (m2 ) specific heat for constant pressure (J/kg K) thermal capacitance (J/K) coefficent of performance heat transfer coefficient (W/m2 K) electrical current (A) thermal conductivity (W/m K) constant conducting length, length heat will travel (m) mass (kg) pressure (N/m2 , atm) heat (W) pressure ratio compression ratio Thermal resistance (W/K) time (s) temperature (K) volume (m3 ) voltage (V)
Greek symbols γ ratio of specific heats ε emissivity σ Stefan–Boltzman constant (W/m2 K4 ) Subscripts cond thermal conduction conv thermal convection in into the compressor out out of the compressor rad thermal radiation s surface of device sur surrounding air
cycle of this rotary engine is intake, compress, ignite, expand, and exhaust. A compressor only requires an intake, compression, and exhaust stroke. Therefore, the development of a rotary compressor driven design is ongoing [7]. Rotary compressor sealing has long been troublesome at the small scale for high compression applications [8]. Sealing at the small scale is difficult because the differential pressure across the seal is larger and as the scale is reduced the dimensions are small, making the pressure gradient large. Small scale refrigeration systems on the other hand, have two primary advantages: (1) the requisite pressure ratio is reduced and (2) the compression stage in vapor compression systems occurs near the liquid boundary and any liquid present enhances the sealing by reducing the effective leakage area. The wet compression process can offer some thermodynamic advantages, however in this particular example, it is not explicitly considered. The initial compressor design has a footprint of 25 mm × 30 mm or about the size of one Intel® Pentium® 4 chip. To enable a vapor compression cycle with an ideal coefficient of
performance (C.O.P.) around 4.6 a moderate pressure ratio of 4.7:1 is required, where C.O.P. is defined as C.O.P. =
heat lift power in
In this analysis, the processes are assumed to be isentropic and the performance of real systems will be lower. This isentropic approach was carried out rather than using polytropic compression because of a lack of experimental data. As such a sensitivity analysis has been carried out. Despite the reduction in performance due to leakage and entropy generation the theoretical C.O.P. is significantly greater than thermoelectric coolers. Thermoelectric coolers have seen rapid development advances with the introduction of enhanced nanostructures [9]. The current figure of merit (ZT) for one thermoelectric material, Bi2 Te3 /Sb2 Te3 , is 2.4, which is a significant increase. The figure of merit sets a maximum temperature across the TEC element. This maximum temperature drop is however, at the point of no heat pumping (i.e. Q = 0). The attained temperature drop decreases with increased thermal load (Q), and therefore, TECs are typically used in stacked modules to move significant quantities of heat. Furthermore, TEC’s suffer from parasitic conduction of heat back to the cool side of the device because the materials used are inherently conductive, both electrically and thermally, limiting their C.O.P. Vapor compression cycles can minimize this by using insulating layers to limit parasitic conduction losses while maintaining a high C.O.P. This paper will discuss the design of a complete vapor compression refrigeration cycle for the microscale which can theoretically achieve heat lifts of 45 W at 1000 rpm at a temperature change of 40 K from the ambient. This will include the design of individual parts as well as a thermal circuit analysis using lump capacitance modeling. The thermal circuit analysis will be developed not only to show the performance of the system but also analyze parameters which will lead to optimal performance of the system. 2. ARCTIC design The vapor compression cycle is composed of four essential steps. The active part of the system, the compressor, receives uncompressed refrigerant and does work on this vapor by compressing the gases to the desired pressure. The compressor releases the vapor into the passive part of the system, beginning with the condenser. In the condenser, the refrigerant goes through a phase change, transforming from a vapor to a liquid. In the process, the refrigerant releases heat to the environment. Once the refrigerant leaves the condenser it is in a high pressure, high temperature liquid state prepared to enter the expansion valve. The expansion valve expands the liquid into a low pressure, low temperature state. The refrigerant moves through the evaporator absorbing heat by again changing phases, this time from liquid to vapor. Then the cycle repeats [10]. A review of this cycle can be seen in Fig. 1. Work is ongoing to optimize the compressor design, however, the details of this work will not be discussed in detail here.
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Fig. 1. Vapor compression cycle.
The goal for the overall system design, which is shown in Fig. 3, is a flat device. By utilizing MEMS technology the system will be able to minimize height so that it resembles a TEC. This resemblance will also include the fact that there will be a hot side, the condenser, and a cold side, the evaporator. To minimize heat leakage between the components insulation will also be used. Furthermore, the system maybe controlled to vary the heat lift of the device using input from environmental factors. The system can vary the heat lift by a mere change in the rotational speed of the compressor. A graph showing the linear relationship of heat lift depending on rotational speed for a lossless system is shown in Fig. 2. As the rotational speed is increased pressure loss through the microchannels will undoubtedly increase, reducing system efficiency. Furthermore, compressor inefficiency, and heat transfer leaks from the evaporator to the compressor will affect system performance. 2.1. ARCTIC’s vapor compression cycle overview The initial ARCTIC vapor compression cycle will utilize a cycle similar to the macroscale designs as a method to determine the baseline capability of the system’s performance. This cycle requires the superheated fluid leaving the evaporator and entering the compressor to be 1.62 atm at 258 K. The compres-
Fig. 2. Heat lift vs. rotational speed for the ARCTIC system.
sor will then compress the gases to 7.6 atm at 310 K before it enters the condenser. The refrigerant will then condense on the condenser walls and will also cool down to 303 K. Next the fluid will expand adiabatically, theoretically, in the expansion valve before heading into the evaporator dropping to the evaporator pressure of 1.62 atm (Fig. 3). 2.2. Compressor design The design of the Wankel rotary compressor utilizes a 367 mm3 displacement while trying to maintain a small form factor. The compressor has a footprint of 25 mm × 30 mm and is 6.25 mm thick. This design used parameters set forth in previous papers [11]. The inherent advantage of the Wankel rotary compressor is its flat shape making it a good fit for the form factor required by ARCTIC. Further, the Wankel rotary compressor design requires two sets of ports: one inlet port and one exhaust port. The ports allow the rotary compressor to compress the vapor on both sides of the housing as the housing is symmetric, as shown in Fig. 4. Finally, the compressor may be composed of a variety of materials as it is not subjected to harsh temperatures. However, as the results will later show, it will be necessary to
Fig. 3. ARCTIC system schematic.
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ratio, rp , defined as rp =
Fig. 4. Schematic of Wankel compressor depicting the two sets of ports. Note that compressor ports are not optimized but shown in this manner for clarity.
manufacture the housing from a conducting material which can wear well. The ports shown in Fig. 4 are actually not optimal as they allow “cross-talking” between ports. Cross-talking occurs when the rotor allows a direct path for the fluid from the inlet port to the exhaust port. In order to design optimal ports one wants to cover the exhaust ports when the rotor opens the inlet ports. An optimal port design is shown in Fig. 5. This design minimizes crosstalking and allows the compressor to achieve a compression ratio, rv defined as rv =
Vin Vout
where V is the volume. This particular design achieves a compression ratio of 3.3. Assuming an isentropic compression process this will enable a high pressure of 3.6 atm as given from the refrigeration tables for R-134a. If the working fluid is air the high pressure would be 5.3 atm for a reversible adiabatic process. This is found using the following well-known relationship:
Pout Pin
To achieve this internal compression ratio the system must have adequate sealing. The Wankel compressor has two inherent leakage paths: around the rotor apexes and around the rotor faces. To minimize the effects of these two leakage paths the system uses a combination of sealing mechanisms. To reduce leakage around the rotor apexes, apex seals have been introduced into the design as shown in Fig. 5. These seals use a spring hidden behind the seal to push the sealing surface against the wall to minimize the distance between the rotor and the housing wall, effectively reducing the leakage gap. The second leakage path, the rotor face, does not have a sealing system but instead relies on machining tolerances to minimize the gap between the rotor face and the housing. In addition to these sealing mechanisms the refrigerant requires a lubricant to be added into the system. This lubricant should aid in the operation and sealing of the compressor. Further, using a model previously demonstrated [8], the system can achieve its desired compression ratio, if a design tolerance of 6 m is attained. Pressures of 3.6 atm are most often not enough to achieve the desired heat lift. This is because the pressure and the temperature are interrelated in a given state; by compressing the refrigerant the temperature raises. To allow the heat to be absorbed into the environment the temperature must be greater than that of the ambient. Due to these constraints, all positive displacement compressors and pumps require check valves, one-way fluid valves, to prevent back flows into the compressor and the Wankel compressor is no different. Thus, the check valves are designed so that they open at the desired pressure by using an adjustable preloaded spring to maintain contact between a precision bearing and seat. Check valves will allow the system to reach pressures up to 8 atm which is just above the necessary pressure required for a system pressure ratio of 4.7:1. 2.3. Design of the passive parts
γ
PV = K where P is the pressure, K the constant, and γ is the ratio of specific heats. Knowledge of the high pressure will set the pressure
The passive parts of the system include the condenser, expansion valve, and evaporator. Each of these parts can be made using microfabrication techniques. However, none of the parts have yet
Fig. 5. Optimal port design to eliminate cross-talking. (a) Shows inlet just closing with exhaust completely closed. (b) Shows exhaust just opening with inlet completely closed.
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Fig. 6. Conceptual design of ARCTIC condenser.
been optimally designed; thus, there is no discussion here about the correct number of turns or the size of the channels to reduce pressure drop. The condenser, shown in Fig. 6, is a serpentine structure with fins. This tubular structure takes advantage of the microscale’s large surface area to volume ratio in order to increase heat transfer to the environment. This device can be made either in a polymolding process [12] or by using an optimized silicon DRIE process [13] and capping the etched channels by bonding a second substrate to the device layer. A detailed thermal model will finalize the desired material properties and structure dimensions. The expansion valve can made using a simple MEMS device, the diffuser in Fig. 7 [14]. The expansion valve in a vapor compression system requires efficiency. An idealized vapor compression system assumes the enthalpy entering the expansion valve is the same going out. To achieve this, the entrance loss must be minimized. Work has been done to show that a half angle of 7◦ is the most effective in minimizing pressure loss and thus enthalpy drop loss across the expansion valve [15]. The expansion valve will be designed to utilize such characteristics. The evaporator, shown in Fig. 8, is very similar in design to the condenser. The only exception is that the material between the serpentine is not removed. This additional material increases the heat capacity of the evaporator and allows heat to be absorbed into the fluid from the sides as well as from the object to be cooled. Again the advantage of having microscale channels here allows the fluid to quickly absorb heat, minimizing the necessary size of the evaporator. The overall system performance is
Fig. 8. Conceptual design of ARCTIC evaporator and accompanying insulation layer.
strongly affected by the heat flow to the evaporator; therefore the value of the thermal resistance (K/W) across the insulating layer shown in Fig. 8 is imperative to the system design as the results will later show. A MEMS sensor suite of temperature and pressure sensors will be added to the package as well. In mesoscale systems and smaller, it is critical that sensor elements are closely integrated with the structure. Unoptimized temperature sensors provide a major source of heat loss as well as pressure drops for in line sense elements. Such integrated MEMS sensors can be used to enhance system performance by sensing heat fluxes and temperatures in the evaporator to provide control input parameters for the compressor speed. Further, the pressure going into the condenser will be monitored to ensure that the system is performing optimally and to provide feedback to the system’s check valves. 3. ARCTIC analysis In order to determine the performance of ARCTIC, a parametric analysis of the thermal network of the refrigeration cycle has been completed. The parameters investigated include thermal resistance across the evaporator insulation, thermal insulation of the compressor, and device layer thermal resistance. This analysis of the heat transfer was completed using a thermal circuit model. Such modeling splits the thermal system elements into their electrical analogs which allow one to use an electrical circuit model code such as SpiceTM by Cadence. From a thermal perspective this is the same as treating each element as a point with mass and utilizing a lumped capacitance model for each node. Thermal circuit modeling provides the added convenience of using industrial code for solving the system. 3.1. Refrigeration cycle
Fig. 7. MEMS expansion chamber.
The refrigeration cycle modeled using R-134a is a more conservative cycle than the optimized cycle presented above. This cycle is used because it drives the evaporator to the lowest likely temperature. The result of this will provide initial conservative
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estimates for the insulation of the evaporator. R-134a has a critical temperature of 247.08 K which determines the evaporator temperature. The compressor is modeled to achieve a maximum pressure ratio of 8:1. This pressure ratio will set the condenser temperature to vary between 304.94 and 315 K depending on the position of the fluid. Allowing the compressor to rotate at 1000 rpm, ARCTIC can lift approximately 27 W of heat across a temperature difference of 51 K from ambient using the prescribed cycle. It is necessary to note that applications requiring more heat lift can be handled by ARCTIC by increasing the rotation speed of the compressor. For example an application requiring 54 W of heat lift will require the ARCTIC compressor to rotate at 2000 rpm.
Table 1 Summary of electrical–thermal circuit analogs
3.2. Assumptions and equations for a thermal circuit model
The thermal circuit model analysis must begin with the determination of the circuit to be solved, shown in Fig. 9. This begins with the determination of what ground represents. In this thermal model, ground will represent the ambient temperature, 298 K. This temperature is chosen because the compressor is initially at ambient temperature. Thus, ground determines the initial condition of the system. The voltage sources dictate what temperature the fluid is within the element. In the evaporator the temperature is set to 247 K, in the compressor it is set to the highest condenser temperature, 315 K, and finally in the compressor it is set to 295 K. The capacitors linked to the voltage sources represent the capacitance of the fluid inside the element. The resistors linked to the voltage source represent the heat transfer from fluid to the element. The capacitors in the lower half of Fig. 9 linked to ground, represent the capacitance of the individual element while the resistor in parallel represents the heat being leaked to the ambient from the element. Finally, the power being introduced into the system through the dc motor is represented by the current source. The values for each of the circuit compo-
A lumped capacitance analysis requires that each of the elements in a system have a node which represents the average temperature across the device, thus no single element has a temperature gradient. Thermal circuit modeling requires turning each aspect of the thermal regime into its electrical circuit analog. Every mode of heat transfer, that is conduction, convection and radiation, become resistors. Each element also has a thermal capacitance due to its mass. Temperature and heat are analogous to voltage and current, respectively. These analogs are summarized in Table 1 [16,17]. The analysis assumes that the fluid immediately reaches its steady state temperature for each of the states of the thermodynamic cycle, Fig. 1. Thus, the fluid in the evaporator immediately reacts as if it has been compressed, expanded, and can now transform into a vapor. Also, the expansion valve is modeled as an adiabatic gas expansion, similar to the general literature treatment of the expansion process of refrigeration systems [10].
Electrical analog
Thermal analog
Representative equation
Voltage, V Current, i
Temperature, T Heat transfer rate, Q Conduction, Rcond Convection, Rconv Radiation, Rrad
L Rcond = kA 1 Rconv = hA Rrad = h 1 A , where
Resistor, R Capacitor, C
Thermal capacitance, C
rad
2 ) hrad = εσ(Ts + Tsur )(Ts2 + Tsur C = mcp
3.3. Analysis
Fig. 9. Thermal circuit model.
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Table 2 Values for circuit components and the necessary values for the calculation
Evaporator insulation Compressor to environment Condenser to environment Evaporator/compressor interface Compressor/condenser interface dc motor wire
Conduction resistors
Surface area
606.06 0.04 0.18 222.22 51.28 249.38
0.00055 0.00165 0.00055 0.00075 0.00075 4E−07
Evaporator Compressor Condenser Evaporator fluid Compressor fluid Condenser fluid
0.001 0.015 0.015 0.0005 0.001 0.04
h
1.78 13.33 2.50 148.15
A
1000 100 712 12
0.000563 0.00075 0.000563 0.000563
Capacitance
Density
Volume
Mass
cp
6.22 27.45 6.22 0.02 0.36 0.12
2330 2702 2330 5.2581 39.557 39.557
3.75E−06 1.13E−05 3.75E−06 2.81E−06 8.44E−06 2.81E−06
8.74E−03 3.04E−02 8.74E−03 1.48E−05 3.34E−04 1.11E−04
712 903 712 1280.5 1078.4 1078.4
nents and the values necessary to calculate them are shown in Table 2. The heat transfer coefficients for the two-phase flows in the evaporator and condenser transferring heat to the plate itself are determined using an analysis similar to that describe by Lou [18]. While heat transfer coefficients change as the quality of the vapor varies, the lowest heat transfer coefficient is included for the thermal circuit analysis. This ensures a worst case performance scenario for the analysis. The heat transfer coefficient for the heat transferred from the condenser to the environment is calculated using a free convection analysis for the upper surface of a heated plate [16]. The model is built using SpiceTM exactly as shown in Fig. 9. To enable a transient analysis, the voltage and current sources must introduce a step input to the system. The step input causes the capacitors to react as the heat transferred through the capacitor is defined as Q=C
L
0.003 237 148 0.003 0.026 401
Convection resistors Evaporator fluid Compressor fluid Condenser fluid Condenser to environment
k
dT dt
Thus, the capacitor will only react with a change in temperature over time. Using a transient Euler analysis, SpiceTM can output the systems response to the fluid instantly being changed to the steady state temperature.
of heat is transferred to the environment then the system will not have enough capacity remaining to cool an attached device. By varying the resistance of the evaporator insulation according to the thermal conductivity values of different insulation materials, the system performance was determined. The results of this analysis are shown in Table 3. From this analysis it is found the evaporator must be well insulated to achieve any meaningful performance. For the case with no insulation the evaporator loses its capability of lifting any heat as 26.3 W of the available 27 W heat lift is transferred to the environment. Higher end insulation materials such as the aluminum cryogenic insulation material can reduce the heat transferred to the environment to 0.2% of the total heat lift. However, less expensive insulation materials such as aerogel do nearly as well, reducing the heat leaked to 0.3% of the total. As Fig. 10 shows there is only slightly less heat loss when using reflective aluminum insulation. Materials such as foam and aerogel lie on the graph at the point of diminishing returns. To design the compressor it must be determined if insulation would be necessary for system effectiveness. From the model it was determined that insulation would not be useful. Table 4 shows that insulating the compressor would lead to high operating temperatures mainly due to the input power of the dc motor which would not be able to escape. Thus, heat would be absorbed
4. Results
Table 3 Insulating material and amount of heat lost to environment
In order to determine system performance, the individual parameters of the system were systematically varied while the remainder of the system values were fixed. As noted previously the thermal resistance of the insulation between the evaporator and the remainder of the system has the most significant impact on the refrigeration system performance. If a large percentage
Insulation material
Heat leaked (W)
No insulation Glass fiber Foam Aerogel 10 layer of reflective aluminum evacuated
26.3 1.22 0.704 0.083 0.044
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Fig. 11. Effect of interface resistance on system. Fig. 10. Evaporator insulation resistance vs. heat loss.
by the fluid traveling through the compressor, reducing the efficiency of the system. Considering this effect, the compressor must be made out of conducting material. Two such effective compressor materials are aluminum and ceramic which raise the temperature of the compressor to no higher that 305.6 K. The heat absorbed by the refrigerant at this temperature is negligible. In order to properly design the system, interface resistances must be considered. Interface resistances can cause difficulties when trying to transfer heat between two objects such as electronics and heat sinks. To reduce interface resistances in such systems thermal greases are often used. In the ARCTIC system, large interface resistances between the compressor and the evaporator can actually help system performance. Further, it is valuable to note that adding insulation between the compressor and evaporator will be imperative. The temperature gradient between the layers is large, 10,000 K/m, and thus a layer providing insulation is necessary to ensure that heat transferred from the evaporator to the compressor is minimized. System performance for this system is enhanced if the evaporator is able to utilize its total cooling capacity on the object being cooled. Although it has been shown that compressor efficiency can be enhanced by reducing the operating temperature of the compressor, this gain in compressor efficiency is counteracted by a loss in system efficiency, if there is heat leaked from the compressor to the evaporator [10]. In order to show the effect of interface resistance on system performance, the interface resistance between the compressor and evaporator was varied. The corresponding temperatures for the evaporator and compressor were recorded and shown in Fig. 11. It is clear that increased interface resistances enhance system performance in terms of temperature. Furthermore, typical thermal resistances do not vary above 10 K/W. As seen in the graph low thermal resistances Table 4 Compressor materials and insulation vs. operating temperature Compressor/insulating material
Temperature (K)
Aluminum Ceramic Teflon insulation Foam insulation
298.5 305.6 412 463
Fig. 12. Plot of temperature response time for ARCTIC components.
will lead to poor system performance thus additional resistance can be added using thermal insulation to reach the required resistance between the two system elements. ARCTIC’s overall system performance based on temperature is shown in Fig. 12. This analysis uses all the optimal values found through the entire analysis and previously shown in Table 2. The plot shows how quickly the system responds with time. The time constant to cool the evaporator to operating temperature is 12 s. This can be dropped further though by operating the compressor at a higher speed which will drive more refrigerant through the evaporator in a given time. 5. Conclusions This paper has suggested a design for a vapor compression system, ARCTIC. The vapor compression cycle is minimized through the use of MEMS structures, most specifically the check valves, condenser, evaporator, expansion valve, and a sensor suite. The Wankel compressor design has enabled a flat design resembling a TEC device with a cold side and a hot side. The performance of this refrigeration unit is 45 W of heat lift at a temperature change of 40 K and a compressor operating at 1000 rpm. The heat lift is scaleable thru compressor speed allowing ARCTIC to be used for a variety of applications. The most intriguing aspect of the design is the efficiency of the system which theoretically can achieve C.O.P. of 4.6.
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Furthermore, a thermal network analysis has been carried out to determine nodal sensitivities. This analysis has assumed an isentropic compression process, an isenthalpic expansion process, and lumped capacitance assumptions. This analysis has determined the necessity of insulation around the evaporator and between the evaporator and compressor. The addition of simple insulation materials such as foam and aerogel can improve system performance by three orders of magnitude in terms of heat transferred to the environment. The system performs well dynamically with a time constant for cool down of 12 s which can be enhanced with startup sequences which initially flood the evaporator with more refrigerant than necessary. In the near future the system will be further developed. This will include the fabrication of the system and experimentation. Once complete the system will be further miniaturized to achieve a small form factor while simultaneously determining optimized performance solutions. Acknowledgments The authors would like to thank the members of the REPS team and BMAD at the University of California at Berkeley for their useful contributions. Most specifically Chris Hogue, Robert Azevedo, Fabian Martinez, and Mitchell Swanger for there suggestions and analytic help. References [1] B. Suman, N. Hoda, Effect of Variations in thermophysical properties and design parameters on the performance of a V-shaped microgrooved heat pipe, Int. J. Heat Mass Transfer 48 (2005) 2090. [2] K.I. Pettigrew, MEMS Based Capillary Pumped Loops for Integral Thermal Management, Masters Thesis, University of California at Berkeley, 2002. [3] R. Yang, G. Chen, J. Snyder, J.-P. Fleurial, Multistage thermoelectric microcoolers, in: Proceedings of the Eighth Intersociety Conference on Thermal and Thermomechanical phenomena in Electronic Systems, San Diego, May 30–June 1, 2002. [4] S.V. Garimella, V. Singhal, Single-phase flow and heat transport in microchannel heat sinks, in: Proceedings of the First International Conference on Microchannels and Minichannels, Rochester, April 24–25, 2003. [5] S. Jong, How difficult is it to make a microrefrigerator, Int. J. Refrigeration 27 (2004) 309–313. [6] S.B. Sprague, S.-W. Park, D.C. Walther, A.P. Pisano, A.C. Fernandez-Pello, Development and characterization of small-scale rotary engines, Int. J. Alt. Prop., in press. [7] J.D. Heppner, D.C. Walther, A.P. Pisano, ARCTIC: rotary compressor thermally insulated cooler, in: Proceedings of the International Mechancial Engineering Congress and Exposition (IMECE), Orlando, FL, November 6–11, 2005. [8] J.D. Heppner, D.C. Walther, A.P. Pisano, Leakage flow analysis for a MEMS rotary engine, in: Proceedings of the International Mechanical Engineering Congress and Exposition (IMECE), Washington, DC, November 15–22, 2003. [9] A. Majumdar, Thermoelectricity in seminconductor nanostructures, Science 303 (5659) (2004) 777–778. [10] Dossat, J. Roy, Principles of Refrigeration, Prentice Hall, Upper Saddle River, 1997. [11] K. Yamamoto, Rotary Engine, Toyo Kogyo Co., Hiroshima, 1981. [12] N.H. Talbot, Polysilicon micromolding of closed-flow passages for the fabrication of multifunctional microneedles, PhD Thesis, University of California at Berkeley, 1999.
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[13] F.C. Martinez, N. Chen, M. Wasilik, A.P. Pisano, Optimized ultra-DRIE for the MEMS rotary engine power system, in: Proceedings of the EMN04, Paris, October 20–21, 2004. [14] C.-L. Sun, et al., Dynamic modeling of a thermally-driven microdiffuser pump, in: Proceedings of the ASME 2003 International Mechanical Engineering Congress and Exposition (IMECE), Washington, DC, November 16–21, 2003. [15] A. Olsson, G. Stemme, E. Stemme, Numerical and experimental studies of flat-walled diffuser elements for valve-less micropumps, Sens. Actuators 84 (1) (2000) 165. [16] F.P. Incropera, D.P. DeWitt, Introduction to Heat Transfer, 3rd ed., John Wiley & Sons, New York, 1996, pp. 74–81, 460–464. [17] S.D. Senturia, Microsystem Design, Kluwer Academic Publishers, Boston, 2001. [18] Z.D. Lou, A dynamic model of automotive air conditioning systems, in: Proceedings of the 2005 SAE World Congress, Detroit, April 11–14, 2005.
Biographies Joshua D. Heppner, in 2004, earned his master’s in mechanical engineering (MEMS) at the University of California, Berkeley, and is currently working towards his PhD. He finished his undergraduate work at Santa Clara University in mechanical engineering. During his stay at Santa Clara University, he researched and built a NanoSatellite funded by DARPA. At UC Berkeley, he has worked on numerous projects included leakage analysis of a rotary engine, rotary engine apex seal design, systems engineering, and a micro-refrigeration system. He has held research internships at NASAAmes, Hewlett Packard Laboratories, and Harris Communications. David C. Walther, in 1998, earned his doctorate in mechanical engineering (thermosciences) at the University of California, Berkeley. From 1999 to 2000, he served as a post-doctoral research engineer for the Combustion Processes Laboratory in Berkeley, overseeing two NASA Fire Safety Flight Programs, and a DARPA MEMS Program. In the spring of 2001, Dr. Walther served as an adjunct faculty at Santa Clara University, teaching advanced thermodynamics. Since 2001, Dr. Walther has served as the principal research engineer for several DARPA, Army Research Lab, State of California, and Industrial Sponsored Research Programs at the Berkeley Sensor and Actuator Center in the areas of PowerMEMS, BioMEMS, and RF MEMS. Exceptional PI status has been granted to Dr. Walther for many of these programs. Dr. Walther currently also serves as an advisory board member for micro/nanotechnology for MedCap Partners, a life sciences/healthcare related investment fund. Albert P. Pisano currently serves as professor and chair of the Department of Mechanical Engineering at the University of California at Berkeley. He was elected to the National Academy of Engineering in 2001. At UCB, Professor Pisano holds the FANUC Chair of Mechanical Systems in the Department of Mechanical Engineering, with a joint appointment to the Department of Electrical Engineering and Computer Science. He currently serves as a Director of the Berkeley Sensor & Actuator Center (BSAC). Professor Pisano received his BS, MS and PhD (1981) degrees from Columbia University in the City of New York in mechanical engineering. Prior to joining the faculty at UC Berkeley, he held research positions with Xerox Palo Alto Research Center, Singer Sewing Machines Corporate R&D Center, and General Motors Research Labs. From 1997 to 1999, he served as program manager for the MEMS program at the Defense Advanced Research Projects Agency
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(DARPA). His research interests and activities at UC Berkeley include MEMS for a wide variety of applications, including RF components, power generation, drug delivery, strain sensors, biosensors, and disk-drive actuators. Professor Pisano is the co-inventor listed on 20 patents in MEMS and has authored or
co-authored more than 190 archival publications. He is a co-founder in start-up companies in the area of transdermal drug delivery, transvascular drug delivery, sensorized catheters, MEMS manufacturing equipment, and MEMS RF devices.