International Journal of Thermal Sciences 88 (2015) 158e163

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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

Thermoacoustic sound generation under the influence of resonator curvature Konstantin Tourkov a, *, Florian Zink b, Laura Schaefer c a

University of Pittsburgh, Department of Mechanical Engineering and Material Science, 225 Benedum Hall, Pittsburgh, PA 15261, USA Volkswagen AG, D-38436 Wolfsburg, Germany c University of Pittsburgh, Department of Mechanical Engineering and Material Science, 153 Benedum Hall, Pittsburgh, PA 15261, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 December 2013 Received in revised form 12 September 2014 Accepted 15 September 2014 Available online 25 October 2014

This work discusses the effect of resonator curvature on the thermoacoustic effect. The introduction of curvature to the design of thermoacoustic devices has important implications to the packaging of future devices. Although some previous CFD studies have attempted to quantify the effect of this curvature, there are several mechanisms that occur in thermoacoustic engines that are difficult to model using CFD, so further work is needed. A standing wave engine design is utilized in the study with a square channel ceramic stack. The temperatures on both sides of the stack and the pressure at the antinode are examined under the influence of curvature. Increased curvature is shown to adversely effect sound pressure level and increase temperature difference across the stack at constant heat input. A close relationship is shown between the temperature variation across the stack and sound pressure level. © 2014 Elsevier Masson SAS. All rights reserved.

Keywords: Thermoacoustics Temperature distribution Resonator curvature

1. Background

1.1. Thermoacoustic energy conversion

Thermoacoustics, in its most basic form, is the use of a temperature difference to drive an acoustic pressure wave, creating a thermoacoustic engine (TAE). First noticed by Byron Higgins in 1777 [1,2] and subsequently examined by several others experimentally, the field did not develop the first accurate theory until 1969, when Rott proposed the general linear theory of thermoacoustics [3]. Since then, it has grown tremendously with significant progress in both standing and traveling wave devices. The thermoacoustic effect can also occur in the reverse with the use of an acoustic wave to create a temperature difference, most commonly used to achieve thermoacoustic refrigeration (TAR). The temperature difference is often generated across a porous regenerator, known as a stack. Stacks are typically made from ceramic monoliths and are designed to have a large surface area to volume ratio for maximum heat transfer between the gas and the stack. The two commonly found types of thermoacoustic engines are standing- and traveling-wave. As the names suggest, the time phasings of each type of engine are comparable to standing and traveling acoustic waves.

Standing-wave and traveling-wave engines operate under similar thermodynamic cycles. The traveling-wave cycle is identical to the Stirling cycle, while the standing-wave cycle can best be described as a modified version of the Stirling cycle. As stated above, in both types of engines, the primary motivative force is the bi-directional interaction of a solid and a gas to transfer heat, as driven by an acoustic wave and a temperature difference. However, it should be noted that secondary movements of heat can be present in standing wave devices due to Rayleigh streaming [4,5], as well as parasitic conduction [6,7]. A more detailed understanding of these phenomena is essential to improving the design and performance of thermoacoustic devices. Research into quantification of these phenomena is continuing, with focus on the use of CFD showing promise in the success of reducing these effects. For example, Yu et al. investigated a CFD model of a 300 Hz standing wave engine [8]. The model was examined for the behavior of pressure and flow vortices at the ends of the stack and resonator. Marx et al. used a similar approach to investigate a thin domain including a stack plate and two heat exchangers [9]. A similar evaluation of a domain containing a region within and close to stack plates was conducted by Tasnim et al. [10]. They concluded that the behavior at the edges of the stack is important for developing heat exchanger design. Zink et al. investigated thermal effects that occur in thermoacoustic engines and refrigerators in several works using

* Corresponding author. Tel.: þ1 412 526 3812. E-mail address: [email protected] (K. Tourkov). http://dx.doi.org/10.1016/j.ijthermalsci.2014.09.016 1290-0729/© 2014 Elsevier Masson SAS. All rights reserved.

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Nomenclature R SPL T

resistance sound pressure level temperature

Subscripts ambient ambient side temperature H heating wire hot hot side temperature

two-dimensional CFD models of standing wave devices [11e14]. Two of those studies, further discussed below, evaluated the effect of curvature by modeling curved resonators of a standing wave engine [11,13]. The models showed that, as would be expected, curvature adversely affects pressure, velocity, and temperature, reducing the net energy transfer between the walls and the gas. As mentioned, streaming can be a significant source of energy loss in thermoacoustic devices. Oosterhuis et al. investigated Rayleigh streaming using CFD by modeling a vibrating resonator [15]. Experimental studies have also been conducted on the effects of Rayleigh streaming by Yazaki et al. [16]. Other experimental investigations were conducted on losses, such as the experiment by Olson et al. using oscillating fluid under influence of gravity in a vertical coiled pipe [17]. 1.2. Motivation for resonator curvature One of the main reasons why TAEs/TARs have not been implemented on a large scale is based on their inherently low coefficient of performance (COP), which is the ratio of useful energy output over input energy. This limitation can be somewhat mitigated by the ability of TAEs to use low-grade waste heat. If a given source of input energy would otherwise not be utilized, and if alternative cycles (such as vapor compression and some absorption cycles) with higher COPs cannot be operated using low-quality heat, the low COP is not as important. However, given this rather specialized application, another limiting factor for widespread implementation of thermoacoustics is the physical size of TARs [18]. While prototypes have achieved power densities of 1.3 W/L [19], most thermoacoustic devices are still too prohibitively large to be used in the small spaces available around regular generators of underutilized waste heat, such as vehicles and electronics. There are two ways to achieve this - reducing the diameter of the overall device, and reducing the length of the device's footprint. For the former method, Benavides has outlined a theoretical lower limit [20,21]. For the latter method, one way to achieve this would be through coiling of the resonator. While theoretical models for curvature behavior in relation to the thermoacoustic effect have previously been proposed [20], there has been a lack of computational models, as well as experimental tests, that accurately predict the resulting interrelated phenomena. Previously, our group has investigated the effect of curvature on the thermoacoustic effect through a CFD simulation [11,13]. Fig. 1 shows the two-dimensional meshes examined in the investigation, while Fig. 2 shows the results for the various parameters used to describe the behavior of the engine in relation to curvature. As stated above, there is an increasing amount of research in modeling the thermoacoustic effect using CFD. However, several mechanisms that occur in thermoacoustic engines are difficult to model in the computational environment, such as conduction along the stack and resonator, and streaming. Several works, mentioned above,

Fig. 1. TAEs with differently curved resonators [11].

have modeled these separately, with accurate results. However, it is important to investigate the limitations of the simplified models to further develop accurate ones. To this end, the work presented in this paper evaluates the thermoacoustic effect in a standing wave engine with curved resonators, as part of examining the accuracy of the results reported in the models used in the CFD investigations described above [11,13]. In the following sections, we discuss the experimental setup upon which the present study is based, and illustrate the effect of resonator curvature on thermoacoustic oscillations. Note that the frequency is not affected by the curvature. 2. Experimental setup The goal for the present study was to extend the results found in CFD simulations to an experimental setup. We determined: (a) How curvature affects the total temperatures on the hot and cold side, and (b) How curvature affects the oscillation behavior (i.e. does sound pressure level decrease as curvature increases?). In order to accomplish this, a quarter-wavelength, standing wave TAE was constructed using a stainless steel stack housing and a flexible PVC tubing resonator of 3.9 mm thickness (the inner diameter of both was 52.5 mm). The two components were joined by a flange with the stainless steel portion closed at the end and the flexible tubing left open. The flexible PVC tubing was used to acquire the proper curvatures (0 , 15 , 30 , and 45 ), as shown in Fig. 3. To prevent deformation of the flexible tubing while bending, the maximum curvature was limited to 45 . The assembly was mounted such that the open end would face an unimpeded volume of air at atmospheric conditions of at least 1 m in radius from the open end. The total length of the TAE is 1000 mm, with the curved section having a length 500 mm. The stack was built from a ceramic diesel particle filter, and was 50 mm long. During operation, it was placed 100 mm away from the closed end of the resonator tube,

Fig. 2. Results of the CFD investigation by Zink et al. [11].

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Fig. 3. TAEs with differently curved resonators.

measured from the end of the stack. The stack was heated with 22WG nickel-chrome wire and an DC power source, mounted as shown in Fig. 4. Its resistance was RH ¼ 2.25 U (measured at room temperature). During testing, the wire was heated to identical conditions each time. This constant-heat flux boundary condition would show results in differing hot and ambient side temperatures, depending on the curvature. 2.1. Data acquisition To record temperatures, four K-type thermocouples were inserted and cemented into each end of the stack, positioned as shown in Fig. 4. Sound output was recorded with a PCB 130D20 array microphone. The data acquisition was performed in LabView. The tests were performed after the engine reached steady state performance at a voltage level of 15 V. The sound pressure level was recorded simultaneously with the temperature to observe any potential correlation. The output of each curvature was recorded in three separate 300 s (5 min) spans. Each curvature was tested three times to increase the confidence in the temperature and sound pressure level readings. 3. Results: temperature behavior In order to show the effect of resonator curvature on the thermoacoustic effect, we averaged the recorded readings of the four hot and ambient thermocouples. Figs. 5 and 6 show histograms of the averaged readings for the individual runs of the 0 curvature on the hot and ambient sides, respectively. Figs. 7 and 8 show the time lapsed respective hot and ambient side temperatures for each curvature. The behavior through each run for both the hot and ambient side appears to follow a normal distribution relationship, allowing for the error to be estimated using a normal distribution assumption. Figs. 9 and 10 show the time averages of each run for

Fig. 4. TAEs with differently curved resonators.

Fig. 5. Hot side individual run histogram for 0 curvature.

all curvatures examined with the error estimated at 95% confidence. The error for each run spanned a range of 0.5355  C to 1.5185  C. The temperature trends are discussed below. 3.1. Hot side behavior The range of the individual hot side run averages spans approximately 18  C. The individual runs also show a general trend of increase in temperature with curvature. While this general trend is visible, there is obvious overlap in the averages of the individual runs, particularly between the 0 curvature and 15 curvature. The spacing between the averages stays fairly equal, and thus, a linear relationship can be predicted. The results of a linear regression analysis are discussed in Section 3.3. 3.2. Ambient side behavior The ambient side individual runs fail to show any meaningful pattern, spanning a range of approximately 7  C. A possible reason for this could be the gradual heating of the stack and the steel housing, due to the leaching of heat from the hot side. A weak trend can be predicted based on the 15 , 30 , and 45 curvatures of

Fig. 6. Ambient side individual run histogram for 0 curvature.

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Fig. 7. Individual hot side run data averaged over four thermocouples displayed for each curvature.

Fig. 8. Individual ambient side run data averaged over four thermocouples displayed for each curvature.

decreasing temperature with respect to an increase in curvature. As discussed below, this trend is further evaluated using a regression analysis. While these results fail to show a trend, the overall magnitude of variation is small for the whole range, implying that observing the effect of curvature from the ambient side is not as effective as from the hot side, and as is later discussed, from the measurements of the sound pressure level.

between curvature and temperature. The average value for the 0 curvature appears to be significantly lower than that of the other curvatures. Fig. 10 shows little noticeable variation in the behavior of the individual run temperatures with respect to curvature, suggesting no correlation in the behavior. It should be noted that the overall spread of the averages is similar in magnitude to the hot side.

3.3. Trends between temperature and curvature

4. Results: acoustic behavior

Using the data shown in Fig. 9, a correlation was acquired between the curvature and the average hot side temperature with an R-squared value for the relationship of 0.9428. A similar analysis was performed on the ambient side average temperatures. However, unlike the hot side, the ambient side showed little correlation

Above, we discussed the effect of resonator curvature on the temperature throughout the stack. Next we must discuss the effect of curvature on the pressure behavior of the TAE, as the sound output is the primary metric in the characterization of thermoacoustic devices.

Fig. 9. Hot side individual run averages for each curvature.

Fig. 10. Ambient side individual run averages for each curvature.

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158.5 Run 1 Run 2 Run 3

SPL (dB)

158 157.5 157 156.5 156

Fig. 11. Hot side individual run histogram for 0 curvature.

10 20 30 40 Curvature (degrees)

As mentioned above, the SPL was recorded simultaneously with the temperature behavior. A histogram of the data for the 0 curvature was generated to evaluated the behavior across each run. Fig. 11 shows that the data approximately follow a normal distribution for each run and the error can be approximated using this assumption. The error of the individual runs varied between 0.0562 dB to 0.2548 dB (approximately 3% to 13% of the recorded range). Fig. 12 shows the individual recorded levels for each run. While an overall decrease in the pressure level is present, there is significant overlap between the 0 and the 15 curvatures. The overlap between other curvatures is minimal. The SPL data spanned a range of z2 dB, with a minimum of approximately 156.4 dB. Averaging the runs for each curvature produces a better defined pattern of decreasing SPL with increasing curvature, shown in Fig. 13. While the relative spacings between the 15 and 30 curvatures and 30 and 45 curvatures appear approximately equal, the spacing between the 0 and 15 curvatures is significantly smaller. This behavior presents a difficulty in predicting a relationship between SPL and curvature, which is discussed below. 4.2. Trends between SPL and curvature No immediate linear relationship was clear, and thus both linear and quadratic predictions were tested. The linear prediction

showed a good correlation of 0.9154. However, the quadratic prediction shown in Fig. 13 resulted in an improved value of 0.9539, thus implying a quadratic relationship between curvature and SPL, at least for this limited data set. This data has been collected only on a limited span of curvatures and so this relationship cannot be extrapolated to increased curvatures, such as 90 or more. Also, the amount of error present in the data suggests that the relationship, however well defined, may prove unreliable, due to the large amount of overlap of the error. 4.3. Experimental results and CFD model The overall linear trend of rising hot side temperature with increase in curvature is in agreement with the qualitative predictions of the CFD model, as the efficiency of the engine is reduced and less heat energy is transferred to the ambient side. Additionally, the general trend of decrease in sound intensity agrees with the CFD simulation predictions. As is shown in the predictions for sound pressure, the decrease, while noticeable, is not of a large magnitude. The overall decrease in the experimental results was approximately 2 dB, corresponding to 200 Pa, similar in magnitude to the numerical predictions. These results are in agreement with the physical context of the model. Curvature of a resonator will increase acoustic losses [21], which will translate to reduced amplitude of the pressure wave. Since temperature, pressure, and velocity are inherently related in a thermoacoustic device, the reduced pressure amplitude will reduce the heat transfer across the

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Fig. 13. SPL averages for each run for each curvature.

4.1. General oscillation behavior

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Fig. 12. Individual run sound pressure levels color coded for each run. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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decreases due to curvature, significant SPL levels are maintained through increasing curvature, allowing for operation of coiled resonators to be viable. This could allow for the footprint of the devices to be reduced without causing a significant drop in performance, making their implementation easier when faced with limited space. A possible use for these findings is for TARs on mobile platforms, such as vehicles that run on or transport supercooled fluids. Acknowledgment This material is based upon work supported by the National Science Foundation under Grant CBET 0729905.

Fig. 14. Temperature difference across stack vs SPL.

stack, observed with a high temperature difference across the stack at constant heat input. 4.4. Relationship between SPL and temperature drop across the stack The above results showed conclusive evidence that, unsurprisingly, curvature negatively influenced the thermoacoustic effect. This effect was measured using temperature and SPL. The consistency of the results for the two measurement schemes was analyzed, as shown in Fig. 14, by measuring the temperature difference between the hot and ambient sides against the SPL. A very strong negative relationship (R-squared value of 0.9855) can be seen, implying that as the thermoacoustic effect weakens, less heat is transported to the ambient side, thereby increasing the difference in temperature across the stack, and decreasing the acoustic pressure [22]. 5. Conclusion We have analyzed the temperature and acoustic behavior of a standing wave thermoacoustic engine, and the way that this behavior changes as the curvature of the resonator of the engine is increased from an initial 0 to a final 45 position in four increments. By recording the performance of the engine three times for a period of 5 min each, at each curvature, we were able to acquire reliable average values for the hot and ambient side temperatures of the engine, as well as similarly reliable values for the sound pressure level. Using this data, we were able to acquire overall average values that presented a very strong positive linear relationship between hot side stack temperature and curvature. The SPL averages produced a strong negative quadratic relationship between curvature and SPL, with the peak of the quadratic function close to the 0 position. The ambient side behavior did not produce any meaningful relationship over all four curvatures. An analysis of the temperature drop across the stack against SPL showed a very strong relationship, implying accurate measurement of the thermoacoustic effect. The overall data agrees with the CFD predictions given in Refs. [11,13]. The results described above prove that it is feasible to design thermoacoustic devices with curved resonators. While the thermoacoustic effect

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