dana gilbert - second year lab report

School of Physics & Astronomy Optimizing a Thermoacoustic Heat Pump Dana May Ortmann Gilbert’s Second year lab project

Abstract The experiment aimed at creating and optimizing an acoustic heat pump by investigating the effects of changing various parameters. A standing wave was created in a tube with a stack made from kapton tape and PVC tubes allowing the air to travel through the stack whilst still exchanging heat with the material in the stack. Temperature differences of slightly more than 3°C across the stack were achieved at resonance frequencies after a few minutes of running the experiment after which the temperature difference would no longer increase significantly. by Dana May Ortmann Gilbert Student ID: 1453729 Lab Partner: Frances Redihough Supervisor: Ms M. B. Brunetti Deputy: Dr A. Romano Date: 24/3/2016

Dana May Ortmann Gilbert Page 1 of 14

Introduction A thermoacoustic heat pump aims at using standing sound waves to heat and cool certain parts of the system. The basic setup involves a closed tube with loudspeaker at an open end emitting sound according to a sine wave at resonance frequency. This creates pressure nodes and anti-nodes, which compress and expand the air in different areas of the tube. A “stack” of material is placed in the tube such that the displaced and compressed/expanded air may create a net heat flow from cold to warm. This will result in one end of the stack heating up and the other cooling down (depending on its position in relation to the nodes) from the same initial temperature. In this lab we have investigated the effects of altering the method used to create the stack, the size of the stack, the frequency and the position of the stack in the tube. Aim With this lab we have aimed to firstly create a functional heat pump and further investigate variable parameters that may optimize the heat difference across the stack. Theory Standing-wave heat pumps function by using a driver to inject acoustic power into the system and creating a standing sound wave. The standing sound wave may be represented as a pressure curve complemented by a displacement curve as seen in Figure 1.

Figure 1: Standing wave - from hyperphysics Figure 1 also illustrates how equal masses of air particles have a smaller volume at high pressure and higher volume at lower pressure regions. The cycle of a small mass of air in the standing wave may therefore also be illustrated as a combination of a PV-graph and a displacement diagram as in Figure 2(i) and 2(ii) respectively.


Figure 2(i): Reversed Brayton cycle Figure 2(ii): Displacement of air Figure 2 is a simplified approximation of the process occurring causing a temperature difference to the system[1]. The small mass of air starts at a. In step 1 the mass is displaced to b, during the process the mass is adiabatically compressed. The air is now warmer than the surroundings causing heat to flow from the air to the surroundings in step 2. This heat exchange causes the air to be isobarically compressed from b to c. In step 3 the air is adiabatically displaced from c to d. At d the air is now colder than its surroundings causing step 4 where heat flows from the surroundings to the air. The cycle has therefore caused the surroundings at a/d to cool and the surroundings at b/c to heat up. As the cycle repeats itself, a net heat flow is seen carrying heat from the cold a/d end to the warm b/c end, i.e. effectively up the temperature gradient. The standing wave heat pump may be used commercially by maintaining the warm end (or cold end) at constant temperature and connecting the cold end (or warm end) to an area that needs cooling (or heating). To do so heat exchangers must be used at either end. To optimise the temperature differences (or heat flow) a stack of material is placed in the standing wave allowing the heat to cascade along the material. The stack of material must allow the air to be displaced whilst still absorbing the heat from the air and radiating heat to the air at either end. This is best achieved by effectively creating several parallel tubes with a radius defined from the system’s penetration depth, δ[2]. The optimum distance between the layers in the stack is 4δ where δ is calculated from the material’s constant of conductivity, K, the frequency of the standing wave, f, the density of the gas in the system, ρ and the material’s specific heat capacity, Cp:

= . To be effective the stack should fulfil certain thermal properties[3]. One property of the material is it should have low thermal conductivity to minimize the heat flow down the


temperature gradient. Further the material should have a high specific heat capacity to allow a high heat transfer between the stack and the gas. An adequate way to measure the temperatures at each end of the stack would be with thermocouples. A simple thermocouple consists of three wires connected to a voltmeter. For a type T[4] thermocouple two copper wires are connected to the voltmeter at one end and connected to the same piece of nickel-copper alloy at the other end. One junction would be at a reference point where the absolute temperature is known and the other junction would be used as a thermometer of unknown temperatures. The temperature reading is achieved by measuring the potential difference created across the alloy and measured by the voltmeter. For a type T thermocouple at room temperature, this potential difference is converted to a temperature difference using the Seebeck coefficient 41µV/°C. The calculated temperature difference is then compared to the known temperature at the first junction and thus the temperature at the second junction is found. To investigate the acoustic heat pump and temperatures associated with the stack the absolute temperature is not needed, only the temperature difference across the stack is investigated. A modified type T thermocouple can therefore be compiled. Here the alloy would have the length of the stack and instead of a reference point, there would simply be a junction at each end of the stack. This way the potential difference across the stack due to the temperature difference across the stack can be directly measured and converted to the appropriate temperature difference to a precision of one 41st of a degree. Experimental procedure / equipment Main experimental setups: The experiment involved two different types of measurements. One examined the temperatures across the stack (type A) and the other examined the pressure variations in the tube from the sounds wave (type B). The experimental setup for type A measurements can be seen in Figure 3. The setup used an open tube with a loudspeaker at one end where blue tack was used to seal the gap between the speaker and the tube and used to block the other end while still allowing room for various thermocouples. The loudspeaker was connected to a wave generator adjusted to create a sinusoidal wave. Thermocouples from the second year lab equipment was secured to each end of the stack and connected to the digital thermometer. This would only display either T1, T2 or T1 – T2 (where T1 – T2 = ΔT) in 1°C steps.


Figure 3: Type A measurements investigating the temperature difference across the stack. Later only one thermocouple was secured to stack allowing us to measure the absolute temperature of T1. In addition to the absolute temperature, a homemade type T thermocouple was created and a digital voltmeter was used to display T1- T2. This improved setup can be seen in Figure 4. The copper wires were wired through a PVC tube each to provide additional insulation, ease of identification and protection from the blue tack. The copper wire was connected to a Eureka (copper-nickel alloy) wire the length of the longest stack used such that the temperature of each end could be compared. The temperature difference was measured in microvolts where 41 µV = 1°C temperature difference.

Figure 4: Diagram illustrating the areas measured by the thermocouples. Typical type A measurements were taken by placing the stack at the end of the tube opposite of the loudspeaker. The standing wave would then be formed by the loudspeaker and sine wave generator. The stack would be exposed to the wave for 5 minutes where the relevant temperatures were noted down every 10 seconds. The stack would then be moved towards the loudspeaker (moved a distance approximately equal to the length of the stack). Here the measurements would be repeated until measurements were taken noting the relevant temperature readings across the entire tube. The equipment used for the experiments had the following specifications. The tube used had inner diameter 18.695 +/- 0.004mm and length 60cm. The loudspeaker used had a snug


fit to the tube allowing for good sound insulation and could emit sound at a frequency of minimum 160Hz. The stacks used are described in the results and data analysis. The experimental setup for type B measurements can be seen in Figure 5. The setup was similar to type A measurements, but instead of thermocouplers attached to the stack a microphone was inserted into the tube. The microphone was connected to an oscilliscope allowing us to measure the maximum voltage recorded which was used as a representation of pressure. Measurements were taken both in an empty tube and with the stack close to the loudspeaker to investigate whether the stack would interfere with the standing wave.

Figure 5: Type B experimental setup measuring the pressure in the tube with a microphone. The parameter x is used to define the position of any measurements taken in the tube. X is the distance from the open (right hand side) of the tube to the right hand end of the stack. This definition is illustrated in Figure 6.

Figure 6: The definition of x for both type A and type B measurements. Results and data analysis Frequency dependence: The theory predicts maximum temperature at resonance frequency. To confirm this the stack was placed at x = 42.5cm and the frequency was then altered while measuring the temperature difference achieved after several minutes at each frequency.


Frequencies in the range 160Hz to 400Hz was measured for 2 minutes and all other frequencies were measured for 4 minutes. In the range 160Hz to 700Hz the temperature difference was measured with the initial type A setup and at frequencies 960Hz to 1040Hz this was measured with the homemade thermocouple. From these measurements (seen in figure 7) maximum temperature differences was found at 455Hz and 680Hz, both within 40Hz of the resonance frequencies of n= 3 and 5, but no maximum was found at 1000Hz (n = 7).

Figure 7: ΔT depending on the frequency, stack used was of type C1 (see below) Building and optimizing the stack: The first stack (stack A) was built by lining duct tape with regular drinking straws approximately 8cm long and then rolling the lined tape up to a spiral. The length was chosen such that it would be equal to a fourth of the wavelength corresponding to the frequency used to try to create a temperature difference across the stack. Unfortunately no temperature difference was found using stack A. From the theory, it was realized that the penetration depth had to be smaller than what was provided by the straws and the thermal properties needed to be optimized. Kapton tape[5] (Cp = 1150 J kg-1K-1 and K = 0.19 Wm-1K-1) and PVC tubes[6] (C =1400 Jkg-1K-1, K =0.17 Wm-1K-1 and outer diameter =1.560 ± 0.004mm) were therefore used and assembled in a similar fashion (to create stack B). With this material the penetration depth was calculated using the above K and Cp values for kapton and PVC, the density of air[7] = 1.204 kgm-3, and the smallest resonance frequency found 455Hz.

= = 0.19∗ 455 ∗ 1.204 ∗ 1150 = 0.31

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= = 0.17∗ 455 ∗ 1.204 ∗ 1400 = 0.27

The ideal distance between the layers was therefore deduced to be = 4 ∗ +

2 = 1.16 , which is just below the outer diameter of the PVC tubes. For stack B it was assumed that the thickness of the tubes combined with the idea of the air being able to move through the tubes would approximate the effective distance between the material to the ideal depth of 1.16mm. Unfortunately this did not appear to be the case and stack B rendered no temperature difference. It was hypothesised that the air could not move through the tubes freely, hence the next stack (stack C) was assembled with the PVC tubes approximately 1cm apart. Thus the penetration depth was equal to the outer diameter of the pvc tubes and the air was capable of getting displaced by the standing wave. Although the distance between the layers was slightly bigger than the ideal distance stack C allowed us to measure a temperature difference across the stack. The design of stack C was therefore used to construct 3 different stacks at lengths 4.5cm, 3cm and 1.5cm named C1, C2 and C3 respectively.

General behaviour of the temperature difference: By investigating the temperature differences achieved across the various stacks at different frequencies, a clear behaviour is found. Initially there is a rapid increase in ΔT, but after approximately a minute, the ΔT value almost stabilises and only very slightly continues to increase. This behaviour may be seen in figure 8, but can be investigated more by comparing all stacks and frequencies investigated in appendix 1.

Figure 8: General behaviour of ΔT for various positions of stack C3 at 455Hz.

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Comparing pressure with temperature difference across stack: A type B experimental setup was used to find the pressure across stack C1 at 455Hz. The microphone was used to measure the pressure at various positions in the tube (where pressure is represented by the voltage measured from the sound wave), both without the stack and with the stack placed near the microphone. As can be seen in Figure 9 the stack did not alter the standing wave, but only the magnitude of the sound wave measured. The microphone was not capable of precisely recording sound above 280mV, but unfortunately the loudspeaker emitted sound above 280mV despite being at the lowest amplitude setting. It was therefore decided to use the pressure measurements found with the stack in the tube for further analysis as only the whereabouts of pressure nodes and anti-nodes is needed.

Figure 9: Pressure measured as voltage by a microphone in the tube. Figure 10 allows for a comparison between the pressure measurements from above and those gathered in a type A experimental setup with stack C1 at 455Hz (using the initial thermocouple provided by the lab). The figure shows that the highest magnitudes of ΔT occurs at high pressure magnitudes, but not at the anti-nodes. Additional, the ΔT = 0 points occur at the pressure nodes and anti-nodes. This may be explained in accordance with theory as a temperature difference only occurs if the air particles are both displaced and experience a variation in pressure. Displacement of the air particles is 45° out of phase with the pressure wave, meaning the maximum temperature differences occur at a location allowing a certain compromise between high pressure and large displacement.

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Figure 10: Comparison of pressure and ΔT. Please note, the pressure is represented as the sound wave measured in the range [0 mV, 280 mV] and the temperature differences are in the range [-3°C, 3°C]. Size dependence: An important part of the optimisation of the system was to examine how the size of the stack would affect the temperature difference measured. Stacks C1, C2 and C3 were therefore all investigated at 455Hz (using a type A experimental setup with the year 2 lab thermocouple for C1 and homemade type T thermocouple for C2 and C3). Between each measurement the stacks were moved a distance approximately equal to the length of it (I.e. C1 was moved 5cm, C2 3cm and C1 2cm). From Figure 11 it can be seen that the length of the stack has no significant effect on the system as similar ΔTs are achieved at the same positions in the tube regardless of the stack used.

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Pressure and temperature difference - Stack C1, 455Hz,

Pressure at thecentre of thestackAverage acrossstackC1, 455Hz,averageC1, 455Hz, lastmeasurement


Figure 11: Illustrating ΔT in the tube at 455Hz for stacks of different lengths. Frequency dependence of stack C1: Stack C1 was used to investigate where the magnitude of ΔT was a maximum and where it was a minimum as the frequency was altered from one resonance frequency to another. It should be noted that the measurements at 455Hz were taken with the initial thermocouple setup (where the digital display only showed integer temperature differences) and the measurements at 680Hz were taken with the type T thermocouple. Figure 12 shows more minima and maxima temperature differences for the higher frequency (680Hz) than for the lower frequency (455Hz). This corresponds to the above interpretation of the pressure and temperature difference as a higher frequency would result in a standing wave with lower wavelength and hence shorter distance between each position with an optimal combination of displacement and pressure. The figure also indicates a greater temperature difference at the lower frequency (455Hz). This may be disregarded due to the uncertainty of the thermocouple, but as the difference in the maximum ΔT achieved at 455Hz and 680Hz is greater than the uncertainty at 455Hz it may be concluded that the lower frequency is more effective at creating temperature differences. The temperature difference across the stack appear to be approximately equal for all the stacks at frequency 455Hz (as deduced in Figure 11), so the above temperature differences across stack C1 at 455Hz may be more adequate than represented by the error bars.

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C2, EndC3, EndC1, End


Figure 12: Comparison of ΔT achieved across C1 at the two investigated resonance frequencies 455Hz and 680Hz. Please note only the 455Hz error bars are big enough to be seen in the figure. Relative temperature changes: Both the absolute temperature at the right end of the stack (T1) and the temperature difference across the stack was measured using a type A experimental setup with the homemade type T thermocouple to measure ΔT and the digital thermometer to measure T1. Unfortunately the digital thermometer could only display integer temperatures so the absolute temperature is not very accurate. In Figure 13 the change in T1 and the change in T2 (calculated from the change in T1 minus the temperature difference across the stack) for stack C2, frequency = 455Hz and x = 3cm is plotted. On the figure there is also plotted an educated estimate of the trend line. From the above investigation of the general behaviour of ΔT across the stack it is known that the temperature reaches a relatively constant value within the first minute, hence it is estimate that T1 only reached just above 1.5°C, but with a maximum temperature difference of 3°C that resulted in T2 reaching approximately -1.5°C. Hence the temperature of the cold and warm end of stack seems to be equally affected.

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Figure 13: T1 and T2 estimated from T1 and ΔT readings. Conclusion In accordance with theory, peaks in the magnitude of the temperature difference across the stack were found at resonance frequencies. The loudspeaker could not produce frequencies small enough to produce the first odd harmonic, clear peaks were seen at the second and third odd harmonics (at the predicted frequencies for n= 3 and n = 5, +/- 40Hz), but no peak was found at the fourth harmonic (n = 7). When the stack is exposed to the second and third odd harmonic the temperature difference is slightly larger for the lower frequency. The standing wave for the higher frequency has a smaller period and therefore more peaks in ΔT. A working stack was built by creating a spiral out of kapton tape and separating the layers with PVC tubes. This way the layers were separated by a distance close to the desired 4δ allowing the air to be displaced from one region of the stack to another whilst still exchanging heat with the stack. The length of the stack was examined and showed no effect on the temperature differences achieved across the stack. Generally (independently of the stack and frequency) ΔT increases within the first minimum and then almost stabilises, i.e. it still increases by small increments. This almost stabile temperature difference may be caused due to the batural heat flow down the temperature gradient increasing as the temperature difference increases, thus after a short while the heat flow up the temperature gradient caused by the standing wave cancels out with the natural heat flow from warm to cold.


The peaks in ΔT seem to occur at a position where neither displacement nor pressure is a minimum as both these characteristics need to be as high as possible, but cannot both be at maximum due to them being out of phase. By investigating the absolute temperature difference at one end of the stack combined with the temperature difference across the stack it was found that both ends were equally affected by the standing wave. In other words, the cold end cooled approximately the same amount as the warm end heated. Acknowledgements Thank you to all who have helped us with our experiment. Thank you to the second year lab technician for helping us find any equipment we may have needed. Thank you to Dr Mark Colclough for your advice, especially concerning the type T thermocouple. Thank you to our supervisor Maria Brunetti and our Deputy Dr Angela Romano for your help and advice along our project. Finally a special thank you to my lab partner Frances for enduring the many hours of constantly listening to a sine wave and taking measurements with me. Bibliography References [1] Rossing, T. D. & Dunn, F. (2007). Springer Handbook of Acoustics. New York: Springer, p. 250-251. [2] Russell, D. A. & Weibull, P. (2001). Tabletop Thermoacoustic Refrigerator for Demonstrations.

Kettering University, p. 1231. [3] Minner, B. L. & Braun, J. E. & Mongeau, L. (1996). Optimizing the Design of a Thermoacoustic

Refrigerator. International Refrigeration and Air Conditioning Conference, p. 316-317. [4] L, F. (2016, Feb). analog.com. Retrieved from Two Ways to Measure Temperature:

http://www.analog.com/library/analogDialogue/archives/44-10/thermocouple.pdf, p. 1. [5] Minner, B. L. & Braun, J. E. & Mongeau, L. (1996). Optimizing the Design of a Thermoacoustic

Refrigerator. International Refrigeration and Air Conditioning Conference, p. 317. [6] Make It From . (2016, Jan 25). Retrieved from http://www.makeitfrom.com/material-

properties/Plasticized-Flexible-Polyvinyl-Chloride-PVC-P/ [7] About Education. (2016, Jan 25). Retrieved from http://chemistry.about.com/od/gases/f/What-Is-The-Density-Of-Air-At-Stp.htm Figures

1) From http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html


Appendix 1 The general behaviour of all stacks at 455Hz and 680Hz (where measured). Each line represents a different position x in the tube at which the five minutes measurements were taken.

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dana gilbert - second year lab report

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