Proceedings of of IMECE IMECE2008 Proceedings 2008 ASME 2008International InternationalMechanical MechanicalEngineering EngineeringCongress Congressand andExposition Exhibition 2008 ASME October/November 31-6, 2008, Boston, USA October 31-November 6, 2008, Boston, Massachusetts,

IMECE2008-66510

ADVANCING THERMOACOUSTICS THROUGH CFD SIMULATION USING FLUENT

Florian Zink Energy Systems Laboratory Dept. of Mechanical Engineering and Material Science University of Pittsburgh Pittsburgh, Pennsylvania 15261 Email: [email protected]

ABSTRACT From the time mechanical refrigeration was first introduced, its use has significantly increased. In general, cooling is achieved with vapor compression machines that use specific refrigerants (blends of hydrogen, carbon, fluorine and chlorine in various mixing ratios) that can be tailored to create cooling at any required temperature level. Each refrigerant exhibits a specific global warming potential and ozone depletion potential in the atmosphere by absorbing infrared radiation and breaking down of ozone molecules. Since the adverse effects of those substances have been discovered, the field of refrigeration has been moving away from conventional refrigerants, and searching for better alternatives. Thermoacoustic refrigeration is such an alternative that can provide cooling to essentially any required temperature level without using any environmentally harmful substances. It is presently a niche technology that can be expanded into a broader market, primarily if the sizing problem can be solved. Currently, the most efficient thermoacoustic refrigerators are used in industrial settings. This work explores the possibility of decreasing the footprint of these refrigerators by utilizing a coiled resonator. A CFD analysis has been developed and first results in regard to coiled resonators are shown and discussed.

Jeffrey S. Vipperman Laura A. Schaefer Energy Systems Laboratory Dept. of Mechanical Engineering and Material Science University of Pittsburgh Pittsburgh, Pennsylvania 15261

pump [1]. It wasn’t until 1834, however, that Perkins developed the first machine, that was able to sustain constant low temperatures. The first vapor compression cycles were invented in the 1860s and 1870s. At this point in time, refrigeration was primarily used in industry and to create ice which was then used in ice boxes to provide cooling in residential settings. In the first quarter of the 20th century, refrigeration finally bypassed the icebox and was established in homes [1; 2]. Today, refrigeration and air conditioning are vital parts of our daily routine. We expect to use perishable goods in our households. Before those reach their final destination, they have to be transported and stored, both under cooled conditions. We expect our homes, offices, and vehicles to be comfortable in any environment and outside temperature. Less obvious applications are cryogenic cooling of gases such as natural gas and hydrogen, which is of importance in the transport of gaseous fuels on trains, airplanes, and other vehicles (which is of increasing interest to manufacturers and policy makers). This large need for refrigeration on many different temperature levels has created a vast variety of technologies. Most notably, those are vapor compression cycles and absorption cycles. The latter are used for large scale applications, while the former are used widely in everyday applications. In recent times, the environmental concern of traditional refrigeration technology has increased, primarily because of the substances used to provide the cooling in refrigerators and air conditioning units. The following paragraphs explain these issues in detail. The purpose of this paper is to highlight thermoacoustic refrigeration as a viable alternative technology and

INTRODUCTION Mechanical refrigerators were developed close to 250 years ago, when William Cullen managed to freeze water with an air 1

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when the substance started to be used commercially is given. R12 is used in vehicle applications, but it is being replaced by R134a [5; 6]. CO2 (also referred to as R-744) is being considered again because of its low GWP value. R-22 is used in residential air conditioning systems [5], but will inevitably be phased out as well because of its chlorine content.

introduce one means of advancing thermoacoustics through CFD simulation. Science of Refrigeration Vapor compression refrigeration (VCR) utilizes the latent heat of vaporization to withdraw a cooling load from an object and deposits this heat to the environment via a condenser. The peripherals include pumps and secondary heat exchangers that influence the performance of the refrigeration system. The most important requirement for the working fluid is its volumetric cooling capacity (i.e. a measure for the material-specific heat of vaporization) and boiling point (which is pressure dependent). The boiling point, of course, determines the lowest achievable temperature. When large scale refrigeration was introduced in the 19th century, natural refrigerants such as carbon dioxide (CO2 ), ammonia (NH3 ), and sulphur dioxide (SO2 ) were used [3]. CO2 provided the safest option, but it requires a relatively high operating pressure to achieve a useful boiling point. The latter two refrigerants are toxic, which is one reason why replacements were required later, especially when refrigeration moved into residential applications. The breakthrough occurred when chlorofluorocarbons (CFCs) were developed (most notably CFC-11). They provided safe refrigeration because they were neither flammable, toxic, explosive, or corrosive. In addition, they were odorless [4].

Table 1: MATERIAL PROPERTIES OF SEVERAL RELEVANT REFRIGERANTS ADAPTED FROM KIM ET AL. [3] AND DOE BUILDING ENERGY DATA HANDBOOK 2007 [5]. Refrigerant

R-12

R-22

R-134a

R-744

ODP/GWP

1/8500

0.05/1700

0/1300

0/1

TBP [◦C]

-29.8

-40.8

-26.2

-78.4

[kJ/m3 ]

2734

4356

2868

22545

Introduced in

1931

1936

1990

1869

Cre f r

TBP and Cre f r are the boiling point and refrigeration capacity of the substance, respectively. The large numbers corresponding to the GWP represent the amount of (reference) CO2 would have to be emitted to achieve the same greenhouse effect as one unit amount (commonly measured in tons) of that refrigerant emitted. The ODP is measured using CFC-11 as the reference value (thus CFC-22 has an ODP 20 times smaller than CFC-12).

Global Warming and Ozone Depletion Potential. In 1974, it was discovered that the ozone layer was being depleted and also that the use of CFCs was responsible for this phenomenon. Specifically, it is the chlorine component of these refrigerants that is responsible for ozone depletion. One chlorine molecule can break down 100,000 ozone molecules (O3 ) [4]. In addition to exhibiting an ozone depletion potential (ODP), CFCs also act as greenhouse gases in the atmosphere. Greenhouse gases are capable of absorbing infrared radiation, which results in a rise in temperature. Every gas exhibits this to a different degree; a measure for this behavior is provided by the global warming potential (GWP). In 1987, the Montreal Protocol started requiring nations to decrease their production and emission of CFCs and prompted a sharp increase in the development of alternatives. The first step was to develop hydrochlorofluorocarbons (HCFCs) and more recently, hydrofluorocarbons (HFCs). The former still utilizes chlorine molecules and thus has an ODP, while the latter does not contain chlorine and exhibits a zeroODP. Both types of refrigerants, however, maintain a relatively large global warming potential.

Reducing Refrigerants in Cooling Applications The 2007 Buildings Energy Data Handbook (DOE) illustrates that CFC-12 is the single most emitted refrigerant in the U.S. R-134a is also emitted in significant amounts. Together, both substances contribute almost half of the total emitted halocarbons (data ranging until 2001). Both are used primarily in vehicle air conditioning (AC) systems. The other major contributing substance is HCFC-22 (R-22). Since the implementation of the Montreal Protocol, the use of harmful refrigerants has been decreasing significantly. While already smaller than the GWP of CFC-12 (10600), the GWP of R-134a (1300) is still very high compared to carbon dioxide [5]. As R-134a is a hydrofluorocarbon (HFC) and thus contains no chlorine, its ODP is zero, which is the primary reason for its use. Regardless, the high GWP remains, and, for this reason, R-134a is phased out in Europe beginning 2011 and carbon dioxide (R-744) and R152 (GW P = 140) are considered as one of the possible replacements. The latter substance is flammable, illustrating how, ironically, toxicity and flammability are starting to become accepted

Properties of Commonly Used Refrigerants. Table 1 lists ODP, GWP, normal boiling point TBP and refrigeration capacity Cre f r of several different refrigerants. Also, the year 2

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which stores heat between cycle segments [8]. It is noteworthy that this externally heated, closed cycle uses the same gas for all stages, as opposed to the internal combustion engine, which has a constant throughput of working gas and fuel. The transition to thermoacoustic technology occurred when Ceperley recognized that sound waves could replace pistons for gas compression and displacement [9].

again, as long as the GWP of the substance can be decreased [6]. Other “natural refrigerants” such as ammonia are also being considered for alternatives as well, although toxicity remains an issue. One technology that can provide refrigeration without using any chemically designed refrigerants is the thermoacoustic refrigerator (TAR). Ideally, this device can be powered by a thermoacoustic Stirling heat engine (TASHE), which results in a system that can run on waste heat and does not contain refrigerants or moving parts. Below, thermoacoustics will be introduced in detail, and the “Total Equivalent Warming Potential” section will show why the ability to run on waste heat is an important attribute of TASHEs and thermoacoustic refrigerators (TARs).

Thermoacoustic Stirling Engines There are two main approaches to thermoacoustic engines, namely standing wave and traveling wave devices. Both contain a regenerative unit (called a stack or regenerator, respectively) sandwiched between two heat exchangers, one to supply heat at high temperature, the other to withdraw heat from the system at near ambient temperature. The regenerator is placed inside a resonance tube. This temperature gradient across this porous section results in amplification of pressure disturbances and results in loud noise being emitted once a steady state has been achieved. Figure 2 shows a demonstration engine. The porous section is located close to the closed end of the resonance tube. It is heated with heating wire. Active cooling with a second heat exchanger is not necessary because of the low thermal conductivity of the used ceramic regenerator.

THERMOACOUSTICS The thermodynamic cycle occurring in the thermoacoustic Stirling heat engine (TASHE) as well as TARs is the Stirling cycle, which was developed in 1816 by Robert Stirling [7]. The original mechanical Stirling engine utilized two pistons and a regenerative heat exchanger [8]. Figure 1 shows such an engine.

Figure 2: PICTURE OF A SIMPLE STANDING WAVE ENGINE DEMONSTRATOR.

Under oscillating conditions, the working gas experiences displacement and pressure variations (compression and expansion). Specifically, this temperature gradient has to be larger than the critical temperature gradient for thermoacoustic engines. The expression for this critical temperature gradient was derived by Swift [10] and is given in Equation 1:

Figure 1: SCHEMATIC OF A STIRLING ENGINE [8]

Over the course of one cycle, the working gas is compressed, and it then gives off heat to the heat sink, thus maintaining a constant temperature. Afterwards, the gas is heated at constant volume by the regenerator and then is heated further at the heat source. This heat supply occurs while the gas is allowed to expand and driving the power piston, again at constant temperature. After expansion, the gas is displaced to the heat sink, while cooling off at constant volume by depositing heat to the regenerator,

∇Tcrit =

ωps1 ρm c p us1

(1)

The critical temperature gradient thus depends on the operat3

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ing frequency ω, and the first order pressure and velocity in the standing wave ps1 and us1 , as well as the mean gas density ρm and specific heat c p . Depending on the ratio of the temperature gradient and critical temperature gradient, acoustic work is either cre/dx ated (a thermoacoustic engine) when dTdT/dx| < 1 or transformed crit /dx into heat energy (a refrigerator) when dTdT/dx| > 1 or vice versa crit [11]. For refrigerators, the critical temperature gradient results in the physical limit of a smallest reachable temperature given a finite length of the refrigeration regenerator. The difference between the standing wave and traveling wave engine lies in the phasing between velocity and pressure. In standing wave engines, the phasing is such that we need to artificially delay the transfer of heat by utilizing a porous structure with large channels [12]. In the traveling wave engine, the phasing is such that the heating can inherently occur after the compression and the cooling can occur after the expansion. Here, the flow channels can be designed much smaller [12]. Consequently, the temperature of the gas is almost always the same as the wall temperature, resulting in heat transfer over very small temperature differences. This process produces inherently less entropy, and is thus more efficient than the standing wave engine [13; 14]. To illustrate this phenomenon, we can draw parallels to optics. The amplification of the acoustic wave is similar to an optical laser, where light waves travel between a mirror and a partially silvered mirror in a standing wave fashion. The light waves are amplified through resonance and released through the partially mirrored side as a high power laser beam. The amplified sound waves can also be extracted from the resonance tube to power external devices [15]. Since the original discovery, many different designs have been conceived. Simple demonstration devices are usually standing wave engines, while the more efficient traveling wave engine has been utilized to drive TARs. The (advantageous) traveling wave phasing between pressure and velocity can be achieved in two ways. One can use a looped tube as the compliance or one can utilize an annular so-called feedback inertance. The latter has been utilized by Bastyr et al. (refer to [16] and [17]) and is very similar to a standing wave device in appearance. Backhaus et al. introduced a large scale traveling wave engine that achieved a thermal efficiencies of 30%, corresponding to 41% of Carnot efficiency [18]. In any engine, the resonator determines the operating frequency. Even the efficient traveling wave engine utilizes a superimposed standing wave engine to increase the pressure amplitude in the regenerator region of the looped tube [19].

Figure 3: REGENERATIVE COOLERS THAT CAN BE DRIVEN BY TASHEs [21]

to force a reverse Stirling cycle: the pressure amplitude of the sound wave created in a TASHE decreases across the second stack, and just like the addition of heat to the driving stack amplified the sound waves, we can now withdraw heat energy from the surroundings. Refrigerators and chillers driven by TASHEs are a reality today; however they are limited to few, specialized uses, for example in gas liquefaction. There are several advanced models of TARs used for these specialized applications. The National Institute of Standards and Technology (NIST) in collaboration with Radebaugh (Los Alamos National Laboratory) have built a TAR with 5W of cooling power at 120K and a low temperature at no load of 90K [20]. The main benefit is the lack of moving parts (such as seals), thus reducing maintenance costs. It is noteworthy that TARs can achieve these low temperatures in a single stage, whereas VCRs can only achieve approximately 230K in a single stage [20]. Cryogenic cooling is not the only application for TARs. A practical example of this design was given by Poese with a freezer for ice cream storage. This small scale chiller featured an annular space around the regenerative unit to achieve traveling wave phasing [17] Figure 3 illustrates the range of regenerative coolers found today [21]. In the figure, all coolers are driven by mechanical drivers, but all can be driven by thermoacoustic engines. The main reason, why TARs have not been implemented on a large scale is based on their inherently low coefficient of performance (COP), which is the ratio of input energy over cooling capacity. Note that it is not an efficiency in the classical sense and thus not bounded by 1. One benchmark of cooling illustrates a spread of COP of traditional refrigeration between 2 and 6, varying with different working fluids and compressor efficiencies. [22]. On the other hand, TARs are still operating at COPs of less than one [23]. One reason for this limitation is that the compression of the gas in TARs is more energy intensive than

Thermoacoustic Refrigerators without Moving Parts As mentioned before, the primary application for TASHEs is in refrigeration. For a simple demonstration of the TAR-concept, we can use a second stack sandwiched between a second set of heat exchangers placed in the same resonator as the driving stack 4

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shown that powering all AC units in vehicles is responsible for 107 tons CO2 /year. In addition to this amount is the direct TEWI contribution of the refrigerant, which can be estimated at 50% of the indirect contribution and is thus 1.675 · 107 tons CO2 /year [28]. These TEWI considerations show that the additional fuel consumed by current VC refrigeration units in vehicles are the largest contributer to their GWP. Thus, replacing this technology is only useful where this indirect contribution can be eliminated. This renders locations with availability of waste heat as a primary target market of TARs. Vehicles are such a target application. Zoontjens et al. have conducted an initial feasibility study on this subject and concluded that the mobile application can indeed be a target for TARs [29]. To achieve this goal, TARs have to be significantly smaller and more efficient than present technology. The required cooling capacity will drive overall TAR size, and the size of engine compartment and packaging will drive the research towards alternative resonator shapes. In addition, the temperature level of the waste heat available will also contribute to the design of TARs. The exhaust temperature before the vehicles exhaust aftertreatment system is on the order of several hundred degrees Celsius and is certainly high enough. However, we must consider the temperature drop caused by the heat utilization of the TAR, and make sure that the temperature level after the TAR is high enough to ensure proper performance of the after treatment system.

the compression of the liquid working fluid in VC refrigerators. Issues with Introduction of TARs At first glance, this introduction shows TARs as the solution to many environmental problems that refrigeration causes. However, their inherently lower COP requires a higher heat input to provide the same cooling load as a comparable VC refrigerator. As a consequence, additional carbon dioxide (CO2 ) is emitted, which is, of course, also a strong greenhouse gas. Worse, its emission is continuous, as the heat input is necessary during operation (as opposed to the refrigerant in conventional refrigerators and chillers that is only emitted slowly over time through leaks or when the system is disposed of). The goal must be then to drive TARs with waste heat so as to actually significantly decrease the GWP of refrigeration. To illustrate this issue, the Alternative Fluorocarbons Environmental Acceptability Study (AFEAS) has introduced the Total Equivalent Warming Impact (TEWI) which considers the direct warming impact of the utilized working fluid (zero for TARs) and the indirect impact on warming by the operation of the device (higher for TARs than VCRs when driven by electricity) [24]. This figure of merit has previously not been considered with respect to thermoacoustic refrigeration. Total Equivalent Warming Impact (TEWI) As mentioned above, thermoacoustic refrigeration is based on the (externally heated) Stirling cycle, and as a consequence the TAR can be driven by waste heat. Locations with large waste heat production are industrial processes and vehicles. McCulloch has illustrated that residential refrigerators only account for about 10% of refrigerant emissions into the atmosphere. Also, since these systems are hermetically sealed, they only pose a problem when they are improperly disposed of at the end of their life cycle (which is approximately 20 years). Mobile applications, primarily vehicle air conditioning (AC) units on the other hand, pose a much larger problem because of leakage and accidental spills. The average life cycle of the refrigerant in this application is only 6 years [25]. The Energy Information Agency published information on the number of vehicles used in the US, with a detailed breakdown of total miles driven and fuel consumed [26]. Assuming the same percentage of fuel used for air conditioning vs. total average fuel consumption provided by Bhatti (23.5 gallons/year and 707 gallons/year, respectively, is 3.3% [27]), this yields a total fuel consumption solely for air conditioning of 3.7 · 109 gallons/year (based on 113.1 billion gallons total consumption [26]). According to Bhatti, there are approximately 170 million vehicles in use in the U.S. alone [27]. Thus, approximately 28 million vehicles have to replace their entire refrigerant volume every year. In addition to this direct effect, we have to consider the amount of CO2 emitted by powering 170 million AC systems. It can be

REQUIREMENTS FOR NEXT-GENERATION TARs History has shown that in certain technologies, a small change in a component’s design, a new idea, can revolutionize that device’s utility. Consider for example the computer during the transition from room sized systems to ubiquitous calculators and computers using (microfabricated) transistors. It resulted in a significant decrease in size and power consumption, thus opening the door to a wide market penetration. Today, of course, computer technology is an integral part of daily life. Thermoacoustics can be considered as being in the “tube” stage, but it can be significantly advanced by improving simple components. Design Considerations Above, it was shown that TARs can only provide environmental benefits when driven on waste heat. This limits their application to locations where this heat is readily available. The temperature level at which this heat is available remains an important factor. The heat exchanging capability depends primarily on the two flows of mediums exchanging heat. Heat is rejected by the hot stream and accepted by the cold stream. In a thermoacoustic driver, we aim to heat the hot end of the regenerator which in turn heats the working gas throughout the cycle. The maximum achievable temperature is the temperature with 5

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which the waste heat stream enters the heat exchanger, and thus is the highest achievable hot side temperature for the regenerator. Given this temperature, we can calculate the maximum achievable temperature gradient for a given regenerator length. This value then has to be larger than the critical temperature gradient shown in Equation 1 for successful engine operation. Conversely, with the critical temperature gradient and temperature level of waste heat given, the length of the regenerator can be determined, which in turn determines the overall device size and cooling capacity. For example flared flue gases at a steel plant supplies heat at much higher temperature than the operation of servers in a large scale computing center. Regardless, just as an engine of a vehicle, both scenarios are potential heat sources for thermoacoustic refrigeration. Once the device size is determined, we have to consider several other issues, such as packaging and efficiency of the TAR. If placed inside an engine compartment of a vehicle, the device may be required to fit inside existing layouts around the engine block and peripheral devices. To achieve useful incorporation in engine compartments, a straight resonator may not be a feasible solution, thus requiring curvature to be incorporated in the resonator. This consideration has not been seen in the literature.

Figure 4: THE CFD MESH USED FOR OUR FIRST THERMOACOUSTIC ENGINE MODEL.

Gambit. The grid dimensions are 15 mm wide and 150 mm long. The stack of the engine is represented by several walls spaced 500 µm apart. These walls are given a non-zero thickness in order to participate in a heat exchange with the surrounding fluid. The grid is built using triangular cells, with a total cell count of approximately 25000 cells. Triangular cells were chosen because it allowed to gradually increase the cell density (i.e. the node spacing on the walls by the stack is much smaller than on the closed wall boundary on the left) towards the stack region, where high accuracy in the representation of the flow behavior is most important. The mesh was was modeled after the engine shown in Figure 2 and is shown in Figure 4. Boundary Conditions. The model includes an open end (a 0 Pa gauge pressure “pressure outlet”) and a “pressure inlet” (for the initial disturbance) of a positive gauge pressure of 10 Pa. This creates a pressure gradient across the device and a non-zero velocity distribution throughout the model. In the present setup, the simulation uses adiabatic walls at the compliance, resonator and stack. The horizontal walls in the stack section are given a constant (with respect to time) temperature with a gradient from 700 K down to 300 K over a distance of 10 mm utilizing a user defined function (UDF). The heat transfer coefficient between the stack walls and the fluid is set to be 50 W /m2 K. The equation of state used for the working gas is the ideal gas equation, which allows for temperature and pressure dependent variation of the gas’ density. Viscous effects are accounted for using the k − ε model. The time advancement is firstorder, the pressure-velocity coupling uses the PISO scheme, and the discretization for all variables (pressure, density, momentum and energy) is second-order upwind. For the unsteady solution the pressure inlet condition on the compliance side was replaced by another adiabatic wall, to mimic the real engine.

SOLUTION STRATEGY In order to investigate different resonator shapes quickly, we have developed a computational fluid dynamics (CFD) simulation of a standing wave engine in Fluent. The simulation is capable of recreating self-sustained oscillations. It generally follows the ideas introduced by Nijholt et al. [30] and Hanschke et al. [31]. Nijholt used ANSYS CFX to simulate a traveling wave engine inside a Helmholtz resonator, mimicking the design built by Bastyr et al. [16]. They used a very coarse grid, and a time step that was just large enough to resolve the expected oscillations. Hanschk et al. used Fluent 4.4.4 to simulate a Rijke tube (which is similar to a classic thermoacoustic engine, except that the oscillations are created with one heated wire screen rather than a stack). Their boundary conditions are questionable, as they use a thermal conductivity for the gas that is 10 times higher than the realistic value for room temperature [31]. This corresponds to a Prandtl Number that is 10 times lower than the real value for their gas at room temperature (which equals approximately 0.7).

First Results. Figure 5 illustrates a section of the oscillations attained by the simulation in Fluent. It shows the transition from amplification to a steady state over the course of 60,000 timesteps or 0.6 seconds. The final amplitude is approximately 5125Pa, which corresponds to a sound pressure level of ≈ 120 dB. These values are very high considering the simple design of the engine. However, the simulation currently does not consider any loss mechanisms. Therefore, it is not surprising to achieve high sound levels. The highest sound pressure level re-

CFD representation of Engine Given this gap in our detailed understanding of thermoacoustic phenomena, we have created a thorough CFD model of a TASHE in Fluent using realistic parameters and boundary conditions. Mesh. For the initial models, a very simple standing wave engine with a quarter wavelength resonator was replicated in 6

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ported in the literature is 190 dB [7], which was achieved in an advanced traveling wave engine and not a simple standing wave demonstration device. This sound pressure level corresponds to a (root mean squared) pressure amplitude of

(2)

which is approaching the highest achievable SPL (in standard conditions, as the peak pressure cannot exceed one atmosphere). The theoretical operating frequency of an engine with a total length of L = 150 mm is

104000

102000

100000

98000

λ → λ = 0.6 m 4 c 350 m/s →f = = = 580 s−1 = 580 Hz λ 0.6 m L = 0.15 m =

60000

50000

40000

where c is the speed of sound (and used as a rough estimate for air and sea level pressure) and λ is the wavelength.. This frequency corresponds well with the extracted frequency from the simulations. Measuring peak to peak time difference (in Figure 5) , we can see that the simulation also resulted in oscillations of approximately 600 Hz. Under steady operation, the simulation shows some significant vortice development inside the compliance section. Figure 6 illustrates this vortice in a temperature plot. This simple model shows that Fluent is capable of simulating the operation of a thermoacoustic device and sets important boundary conditions for future simulations. The following section will illustrate an elaboration on this initial model.

30000

0

96000 20000

) · 20 µPa ≈ 63000Pa

10000

190dB 20

106000

Absolute Pressure

10(

108000

Time Step

Figure 5: OSCILLATIONS TRANSITIONING FROM THE INITIAL DISTURBANCE TO A STEADY STATE (CALLED LIMIT CYCLE BY HANSCHKE ET AL. [31]).

ferent pressure behavior is a result of the curvature and not from mesh-specific differences. As a result of the introduced curvature, we can show that the total amplitude of the pressure oscillations is decreased. Figure 7 shows the oscillation’s behavior for both cases, the straight resonator and the right angle bend. A close-up of the fully developed region is shown in Figure 8. Also, the frequency seems to be affected by the curved resonator. With the 0◦ case as a baseline, the frequency of the pressure oscillations in the curved cases is higher. A possible explanation is that the effective resonator length is decreased by the curved resonator; the tube behaves as if the resonator was shorted. This effect can also be seen when the distance over which the curvature is applied is varied.

Consideration of Resonator Curvature As mentioned above, the resonator of TARs has to exhibit curvature in order to comply with space requirements in tight engine compartments. It is currently not understood how curvature influences the performance of thermoacoustic engines or refrigerators. Variation of Degree of Curvature. The basic TASHE design serves as a starting point for the curvature investigation. We utilized a modified grid that was curved 90◦ over a distance of 80mm, measured from the open end. Thus, the total length of the engine remained constant, in order to ensure equal resonance conditions and operating frequencies. The resonator was the only section that was modified for this investigation, and the node count on the sides of the resonator was maintained as constant for all cases, which ensured a close to identical mesh count between the straight and curved geometry. As a result, the dif-

Variation of Severity of Curvature. In the first set of curvature simulations, we varied the angle over which a constant length of resonator was curved. In this subsequent investigation, we investigated the effect of varying the length over which a constant curvature angle (90◦ ) was applied. While the initial 90◦ case applied this curvature over a distance of 80mm, we also investigated a length of 40mm. The goal of this investigation is to determine how sharper bends affect the oscillations inside a 7

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112000 straight resonator

90 degrees bend

Abs. Pressure [Pa]

108000 104000 100000

4

2.9 10

4

2.9 10

4

2.9 10

4

2.8 10

Figure 6: TEMPERATURE CONTOURS IN THE COMPLIANCE AND STACK. THE GAS IS STREAMING THROUGH THE STACK INTO THE COMPLIANCE.

2.8 10

2.8 10

4

92000

4

96000

Time Steps [1e-5 s]

Figure 8: DETAILED VIEW OF THE CURVATURE EFFECT (0◦ AND 90◦ ).

112000 straight resonator 90 degrees bend

Abs. Pressure [Pa]

108000

tube, thus increasing the frequency. The actual tube length now does not directly correspond to the operating frequency. On the other hand, the amplitude is far less affected as the severity of curvature increases. As a conclusion, we can see that curvature in the resonator influences both the amplitude and the frequency of the pressure waves. Both effects have to be considered when thermoacoustic refrigerators are designed, because a small change in operating conditions can result in drastic changes in performance. Table 2 summarizes the results of this investigation.

104000 100000

4

3 10

4

2.5 10

4

2 10

4

1.5 10

4

1 10

3

5 10

92000

0

96000

CONCLUSION AND OUTLOOK This work summarized the motivations for an advancement of thermoacoustic refrigeration past niche industrial applications. We illustrated the arguments for a switch from conventional vapor compression technologies based on the total equivalent (global) warming potential (TEWI) of these established technologies. The TEWI considerations showed that the switch to thermoacoustic refrigeration and air conditioning is only useful when these new devices are driven by waste heat and not powered by electricity or heat provided by burning additional fuel. Vehicle air conditioning has been identified as a primary target market because of its abundance of waste heat to drive TARs. In order to comply with the stringent space requirements inside a vehicle’s (internal combustion) engine compartment, the thermoacoustic device has to move beyond the standard straight resonators. To investigate the effect of curvature on the performance of a ther-

Time Steps [1e-5 s]

Figure 7: EFFECT OF A CURVED RESONATOR ON THERMOACOUSTIC OSCILLATIONS, COMPARISON BETWEEN 0◦ AND 90◦ .

resonance tube with constant length. As mentioned before, the introduction of curvature causes a decrease of pressure amplitude achieved in the engine. Figure 9 shows a detailed view of the steady oscillations. The transition from the initial state to the sustained oscillations is irrelevant. We can see that a change in the severity changes the frequency of the oscillations. It seems to mimic a shorter resonance 8

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112000

fering insights into the solid-fluid interactions. The CFD study can also be expanded to account for traveling wave behavior as well as refrigerator designs. For the curvature investigation, we will simulate engines with longer resonators, that will eventually allow for higher degrees of curvature, than the current model allows.

Lc=40 Lc=80

Abs. Pressure [Pa]

108000 104000 100000

ACKNOWLEDGEMENT This work is supported by the National Science Foundation under the grant CBET-0729905.

4

2.9 10

4

2.88 10

4

2.84 10

2.86 10

4

2.8 10

2.82 10

4

92000

4

96000

REFERENCES [1] Anderson, O., 1972. Refrigeration in America. JKennikat Press, Port Washington, NY. [2] Schaefer, L. A., 2000. “Single pressure absorption heat pump analysis”. PhD thesis, Georgia Institue of Technology. [3] Kim, M.-H., Pettersen, J., and Bullard, C. W., 2004. “Fundamental process and system design issues in co2 vapor compression systems”. Progress in Energy and Combustion Science. [4] Anderson, S. O., Sarma, K. M., and Taddino, K. N., 2007. Technology Transfer for the Ozone Layer. Earthscan, London. [5] US Department of Energy, 2007. 2007 building energy data handbook, chapter 3.2. http://buildingsdatabook.eere.energy.gov/default.asp. [6] Weissler, P., 2007. “Cooling off gloabal warming potential”. SAE International, 115(10), pp. 57–59. [7] Garrett, S. L., 1999. “Reinventing the engine”. Nature, 339. [8] Kaushik, S. C., and Kumar, S., 2000. “Finite time thermodynamic analysis of endoreversible stirling heat engine with regenerative losses”. Energy, 25, pp. 989–1003. [9] Ceperley, P. H., 1985. “Gain and efficiency of a short traveling wave heat engine”. Journal of the Acoustical Society of America, 77(3), pp. 1239–1244. [10] Swift, G. W., 2002. Thermoacoustics: A unifying perspective for some engines and refrigerators. Acoustical Society of America, Melville NY. [11] Xiao, J. H., 1995. “Thermoacoustic heat transportation and energy transformation, part 3: Adiabatic wall thermoacoustic effects”. Cryogenics, 35(1), pp. 27–29. [12] Ceperley, P. H., 1978. Us pat. no. 4114380. [13] Garrett, S. L., 2004. “Resource letter: Ta-1: Thermoacoustic engines and refrigerators”. American Journal of Physics, 72(1), pp. 11–17. [14] Ceperley, P. H., 1979. “A pistonless stirling engine - the traveling wave heat engine”. Journal of the Acoustical Society of America, 66(5), pp. 1508–1513.

Timestep [1e-5s]

Figure 9: EFFECT OF SEVERITY OF RESONATOR BENDING ON THERMOACOUSTIC OSCILLATIONS (90◦ BEND APPLIED TO 80mm AND 40mm).

Table 2: ILLUSTRATION OD THE EFFECT OF BOTH THE DEGREE OF CURVATURE (TOP) AND THE LENGTH OF THE CURVED SECTION (FOR CONSTANT CURVATURE OF 90◦ , BOTTOM) ON MAXIMUM PRESSURE (pmax , ROOT MEAN SQUARED PRESSURE pRMS AND FREQUENCY f . Curvature

pmax [Pa]

pRMS [Pa]

f [Hz]

0

109909

101703

590

90

109023

101597

590

80mm

109020

101598

590

40mm

108950

101574

620

Length

moacoustic engine, we have developed a successful simulation of said engine in Fluent. Using a small pressure disturbance and a driving temperature gradient across the modeled stack, we were able to replicate the amplification of pressure waves. Results from this first model were shown, as well as elaboration on the investigation in regard to resonator curvature. Further advances of this subject may include a refinement of the simulation technique to allow for faster simulations. Also, the stack area may be modeled as a solid region, potentially of9

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Society of America, 118(4), pp. 2265–2270. [31] Hantschk, C.-C., and Vortmeyer, D., 1999. “Numerical simulation of self-excited thermoacoustic instabilities in a rijke tube”. Journal of Sound and Vibration, 277(9), pp. 758–763.

[15] Garrett, S. L., 2000. “The power of sound”. American Scientist, 88(6), pp. 516–526. [16] Bastyr, K. J., and Keolian, R. M., 2003. “High-frequency thermoacoustic-stirling heat engine demonstration device”. Acoustics Research Letters Online, 4(2), pp. 37–40. [17] Poese, M. E., Smith, R. W., Garrett, S. L., van Gerwen, R., and Gosselin, P., 2004. “Thermoacoustic refrigeration for ice cream sales”. In Proceedings of 6th IIR Gustav Lorentzen Conference. [18] Backhaus, S., and Swift, G. W., 2000. “A thermoacoustic stirling heat engine: Detailed study”. Journal of the Acoustical Society of America, 107(6), pp. 3148–66. [19] Ceperley, P. H., 1982. Us pat. no. 4355517. [20] Kagawa, N., 2000. Regenerative Thermal Machines. International Institute for Refrigeration, Paris. [21] Radebaugh, R., 2000. “Development of the pulse tube refrigerator as an efficient and reliable cryocooler”. Institue of Refrigeration. [22] Phelan, P. E., Swanson, J., Chiriac, F., and Chiriac, V., 2004. “Designing a mesoscale vapor-compression refrigerator for cooling high-power microelectronics”. Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM’04). [23] Herman, C., and Travnicek, Z., 2006. “Cool sound: The future of refrigeration? thermodynamic and heat transfer issues in thermoacoustic refrigeration”. Heat and Mass Transfer, 42, pp. 492–500. [24] Alternative Fluorocarbons Environmental Acceptability Study (AFEAS). http://www.afeas.org/tewi. [25] McCulloch, A., Midgley, P. M., and Ashford, P., 2003. “Releases of refrigerant gases (cfc-12, hcfc-22 and hfc-134a) to the atmosphere”. Atmospheric Environment, 37, pp. 889– 902. [26] Energy Information Administration/Household Vehicles Energy Use, 2001. Table a1. u.s. number of vehicles, vehicle-miles, motor fuel consumption and expenditures, 2001. www.eia.doe.gov/emeu/rtecs... /nhts survey/2001/tablefiles/table-a01.pdf. as of 4/2008. [27] Bhatti, M. S., 1999. “Enhancement of r-134a automotive air conditioning system”. In SAE International Congress and Exposition. [28] Schwarz, W., 2000. “Forecasting r-134a emissions from car air conditioning systems until 2020 in germany (translation of the german lecture)”. In DKV Deutsche KaelteKlima-Tagung Bremen, 22.-24. November 2000, OekoRecherche, Buero fuer Umweltforschung. [29] Zoontjens, L., Howard, C., Zander, A., and Cazzolato, B., 2005. “Feasibility study of an automotive thermoacoustic refrigerator”. [30] a Nijeholt, J. A. L., Tijani, M. E., and Spoelstra, S., 2005. “Simulation of traveling wave thermoacoustic engine using computational fluid dynamics”. Journal of the Acoustical 10

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