performance evaluation of thermoacoustic engines using different gases

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ICSV19, Vilnius, Lithuania, July 8-12, 2012 1

PERFORMANCE EVALUATION OF THERMOACOUSTICENGINE USING DIFFERENT GASES

A.H. Ibrahim1*

, M. Emam1, Hosny Omar

1, Karim Addas

1and Ehab Abdel-

Rahman1, 2+

1The American University in Cairo, School of Sciences and Engineering, Department of

Physics, 11835 New Cairo, Egypt.2The American University in Cairo, School of Sciences and Engineering, Youssef Jameel

Science and Technology Research Center (YJSTRC), 11835 New Cairo, Egypt.

*On Leave from Mechanical Power Department, Faculty of Engineering, Cairo University,

Giza, Egypt.+ Author for correspondence (e-mail: [email protected])

An advantage of thermoacoustic engines is the utilization of environmentally friendly gases.

In this work, guidelines for the selection of a working gas are presented and discussed.

Subsequently, the effect of using different gases as working fluid and different stack

porosities on the engines performance was evaluated. In each case, the onset temperature

difference, the generated acoustic power, working frequency and the excitation of higher

harmonics are quantified and used as performance indicators. These working gases scan a

range of sonic speeds from 374 m/s to 1101 m/s, a range of Prandtl number from 0.40 to

0.67, a range of density of 0.48 kg/m3

to 0.99 kg/m3

and a range of thermal conductivity from0.030 W/m K to 0.091 W/m K. It is shown that it is not possible to achieve the best values for

the performance indicators simultaneously, such as low onset temperature and reducedviscous losses. The results indicate that when operating at low mean pressures, the mixture

density plays a role as important as the sonic speed or the Prandtl number. It is shown that forlow pressure ratios, the square of the dynamic pressure amplitude of the fundamental is

proportional to the input heat power. The proportionality constant depends on the sonic

speed, the mixture density and the Prandtl number. On the other hand, the dynamic pressureamplitude of the first harmonic is proportional to the square of that of the fundamental mode

throughout the full studied pressure range. Remarkably, the proportionality constant is quite

the same for all gas mixtures and stack porosities used. Analysis of the transient profiles

shows that the transient overshoot in the dynamic pressure as well as the size of the dynamic

pressure-temperature hysteresis loop may be correlated to the thermal conductivity of the gas.

1. Introduction

Thermoacoustic engines (TAEs) operate by converting heat into acoustic power using thecomplex interactions between thermodynamics and acoustics. The working gas in a standing-wave

thermoacoustic engine undergoes a Brayton cycle through the proper phasing between the dynamic


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19th International Congress on Sound and Vibration, Vilnius, Lithuania, July 8-12, 2012

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pressure and the gas parcel velocity, allowing the energy conversion from thermal form into

acoustic form to take place without moving parts or sliding seals. Detailed description of

thermoacoustic engines can be found in[1-3]

. Prototypes of these engines have demonstrated first

and second law efficiencies of 18% and 30%, respectively [4,5]. Operation with solar energy as well

as waste heat was demonstrated[6,7]

.

The performance of thermoacoustic engines usually is characterized through several

indicators as follows:

- The first law efficiency, defined as the ratio of the acoustic power generated to the heatinput power supplied to the engine. The former is evaluated as half the dot product of the

dynamic pressure of the generated wave times the gas parcel velocity

- The second law efficiency, defined as the ratio of the first law efficiency to that of a Carnotcycle operating between the same temperature limits

- The onset temperature difference, defined as the minimum temperature difference across thesides of the stack at which the dynamic pressure is generated

- The frequency of the resultant pressure wave, since this frequency should match theresonance frequency required by the load device, either a thermoacoustic refrigerator/heat

pump or a linear alternator- The degree of harmonic distortion, indicating the ratio of higher harmonics to the

fundamental mode in the resulting dynamic pressure wave

- The variation of the resultant wave frequency with the TAE operating temperatureThe objectives of this work are: 1- to highlight the factors affecting the selection of a working

gas and 2- to experimentally quantify the effects of the selection on the overall engine performance.

Thermoacoustic engines employ non-toxic, non ozone-depleting or global warming gases

making them immune from global warming environmental legislations. These are usually inert

gases or mixtures of inert gases. The selection of the proper working gas or gas mixture has to take

into consideration several factors. An idealworking gas should [1] have high speed of sound, a,

since the power density of the device is proportional to the speed of sound [8]. It should be noted that

for fixed engine geometry and operating conditions, the working frequency is proportional to thesquare root of the sound speed of the working gas; [2] have low thermal conductivity, k, to reduce

the heat transfer from the hot side of the stack to the cold side across the working gas. A large

thermal conductivity, however, increases the thermal penetration depth (defined as (2k/cp),where is the gas density, cp is the isobaric specific heat and is the angular frequency), whichfacilitates the manufacturing of the stack; [3] have a specific-heat ratio close to one, because thenumerical results of Belcheret al.

[9]showed that if all losses outside the stack are negligible (in the

heat exchangers and resonator), then this condition leads to a minimum onset temperature; [4] have

low Prandtl number, to allow thick thermal penetration depth (to increase the thermal interactionsbetween the gas and the stack) together with a thin viscous penetration depth (to reduce viscous

losses by viscous shear in the viscous penetration depth). However, numerical results [9] showed that

large Prandtl numbers are preferred for low onset temperatures although they cause large viscous

losses; [5] be leak tight. Light gases are more difficult to seal than heavy gases and this difficulty

increases as the mean pressure increases and should not be underestimated in the design and

assembly of the different resonator modules, or during the welding of heat exchangers or flanges or

thorough the fittings of the engine accessories. Several arrangements of effective flange sealing are

presented by Jens et al[10].

These contradicting requirements indicate that the optimum mixture of gases in a

thermoacoustic engine should be selected according to the particular design objective with careful

consideration of the temperature of the available heat source.

Helium, for example, enjoys large sonic speed but its high specific-heat ratio requires large

onset temperature difference which eliminates several potential heat sources, its high thermalconductivity increases the conduction heat losses and makes it more difficult to maintain thetemperature gradient across the stack, its small molecule is harder to seal than other inert gases and


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its low density makes the power density very low unless operating at high mean gas pressure. In

this work, a mixture of air and helium at a mean pressure of 1 bar is studied and the interplay

between these factors is highlighted.

The estimation of thermodynamic and transport properties for selected binary gas mixtures is

presented by several authors[11,12]

. It was estimated that a Prandtl number of 0.12 can be obtained at

a helium/xenon composition of a xenon molar fraction of 0.975 [12]. However, because of its low

abundance, xenon is much more expensive than other light noble gases. To avoid the high cost of

Xenon, another alternative occurs with a mixture of Helium and Nitrogen with a Nitrogen molar

fraction of 0.76 that leads to a Prandtl number of 0.48. In all mixtures, it should be noted that the

larger the molecular mass of the heavier gas the smaller the amount needed to decrease the Prandtl

number[9].

Figure 1 shows how a gas mixture of two gases (air and helium in this case) enjoys a widerange of speeds of sound, thermal conductivity, density and a minimum Prandtl number at a certain

mixture composition. The bottom part of the figure shows the onset temperature and acoustic powerfor the mixtures used.

Figure 1:Upper part: Density, speed of sound, Prandtl number and

thermal conductivity for air/helium gas mixtures. Bottom part: Onsettemperature difference and generated acoustic power as a function of

the helium molar fraction increases

2. Experimental SetupThe experimental setup was described in details in

[13,14]. Only additional information related

to this work is stated here. To fill the engine with gases other than air, the atmospheric air is first

pumped out using a vacuum pump, and then the required gas or gas mixture is filled using helium

or argon cylinders (of purity 99.99 % and 99.0 %, respectively). The gases then are purged using

the vacuum pump and fresh helium/argon gas is refilled again. The purging process is repeated

three times to fully remove the air traces inside the engine and then the required gas mixture finally

is introduced in the engine.

3. Results

The captured pressure wave is decomposed into a fundamental mode and higher harmonics,

according to the form


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! ! = !! !"#(!"!!! + !!)+ !! !"#(!"!!!+ !!)+ !! !"#(!"!!!+ !!)+!! !"#(!"!!!+ !!)This decomposition is performed using non-linear best fitting to reduce the sum of squared-

deviations between the measured signal and the above numerical form. This form fits the signalreasonably with a typical R2 value of 0.99 or higher [14]. The use of this form allows determination

of the pressure magnitudes of the fundamental mode and the first three harmonics (P 0, P1, P2, andP3) and their corresponding phases (0, 1, 2 and 3). In turn, this allows estimation of the average

acoustic power between any two microphones using the two-microphone method [15] for the

fundamental mode and the first harmonic.

First, it is beneficial to analyse the data shown in figure 1 above. As the helium molar fraction

increases from zero to 20%, the onset temperature is reduced, from 515 K to 481 K, due to the

increase of the specific heat ratio from 1.4 to 1.435. The increase of the sonic speed from 375 m/s to

417 m/s causes an increase in the generated acoustic power from 3.97 W to 4.24 W. Further

increase in molar helium concentration from 40% to 60%, however, does not bring additionalbenefits and quickly cause deterioration in the acoustic power due to the drop in density (from

0.653 kg/m3

at a molar helium concentration of 40% to 0.48 kg/m3

at molar helium concentration of

60%). The onset temperature increases from 537 K at 40% to 643 K at 60% and the acoustic powerdecreases from 4.11 W at 40% to 0.21 W at 60%.

Certain features for the best gas mixture above (80% air, 20% helium, 1 bar mean pressure)

are analysed in figures 2 and 3 before the same features are compared amongst all gas mixtures. The

properties of all mixtures used are summarized in Table 1.

Table1: Gas mixture properties and corresponding engine performance

Gas

mix

ture

Mo

lecular

We

ight,

Kg/Kmol

Pra

ndtl

Number

Density,

kg/m

3

Thermal

con

ductivity,

W/mK

Isobaric

spe

cific

Heat,J/kgK

Spe

cific-

hea

t

ratio

Laurett

num

ber

Onset

tem

perature

difference,

C

Fre

quency,

Hz

Acou

stic

power

outp

ut

at

150

Volt

80%air,

20%He,

400CPSI

24 0.52 0.82 0.046 1144 1.44 4.70 198 211 4.2

90 % air,

10%He,

400CPSI

26.5 0.59 0.91

0.038

1067

1.42 4.37

239 189

3.5

100%air,

400CPSI

29

0.69

0.99

0.030

1004

1.40

5.00

247

189

4.0

60%air,40%He,

400CPSI

19

0.43

0.65

0.066

1356

1.48

4.17

265 228

4.1

70%air,

30%He,

600CPSI

21.5

0.47

0.74

0.055 1238

1.45

3.37

290 219

4.4

100%air,

600CPSI

29

0.69

0.99

0.030

1004

1.40 4.33

309 191

0.7

40%air,

60%He,

400CSPI

14

0.40

0.48

0.091

1722

1.52

4.23

371

308

0.2

100%air,

200CPSI

29

0.69

0.99

0.030

1004

1.4

6.88

418

188

2.3


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The Rotts linear theory predicts a linear relationship between the square of the pressure

amplitude and the input heater power. Because of the linear approximation, this prediction is valid

only at low pressure ratios. The measurements presented in figure 2 show this linear trend followed

by deviations from linearity as the heater power increases. The deviation from linearity first is

observed at about 600 W in all three microphones. This deviation is proportional to the additional

heat power in all three microphones.

Figure 3 compares the pressure amplitude of the first harmonic to the square of the

fundamental. This is indicative of the strength of the harmonic generation. Remarkably, the

relationship is linear throughout the whole range of input heat power suggesting that the pressure

amplitude of the first harmonics scales with the input heater power to the fourth power. The

microphone located closer to the pressure node (e.g., Mic #3) experiences higher harmonicamplitude than those located closer to the pressure antinode (e.g., Mic #1). This is because the

pressure antinode of the first harmonic corresponds to the pressure node of the fundamental.It is now suitable to compare the features observed above for a certain gas mixture with the

same features in different gases.

Figure 2: Square of the pressure amplitude of the

fundamental mode at different axial locations

along the resonator versus the heater power. Datafor a gas mixture made of 80% air, 20% helium

and a 400 CPSI stack.

Figure 3: First harmonic amplitude versus

square of fundamental amplitude. Same

conditions as in Figure 2.

Figure 4 shows the square of the pressure amplitude of the fundamental mode measured by

microphone #1 versus the heater power for different gases and different stack porosities. The linearrelationship up to a certain input heater power is observed for all gases. The proportionality constant

between the square of the pressure amplitude and the input heater power varies according to the gastype or stack CPSI. The largest pressure amplitude for any given input heater power occurs for a

mixture of 80% air and 20% helium (400 CPSI). This mixture enjoys relatively large density andlow Prandtl number. Higher helium concentrations cause an increase in the speed of sound, a

decrease in the Prandtl number but the decrease in density overcomes the benefits of these

advantages. The lowest pressure amplitude occurs for helium gas (200 CPSI). The reason is the low

density of the working gas at the mean operating pressure of 1 bar.

As observed in Figure 5, the amplitude of the first harmonic is proportional to the square of

that of the fundamental. This indicates that the generation of the harmonics arises from nonlinear

phenomena, usually in the aerodynamics or the thermodynamics. The proportionality constant

appears to be quite the same for a broad range of gases or stack CPSIs.

The relationship between the temperatures at the stack sides and the dynamic pressure as

measured by microphone #1 are plotted during start-up, operation and shutdown in figure 6 for

x 10-4


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different helium molar fractions in an air-helium mixture using a 600-cpsi stack. The left column

shows the dynamic pressure amplitude versus time where the dynamic pressure amplitude increases

after the onset and experiences an overshoot before it settles to a lower quasi-steady value. The

results indicate that as the helium fraction increases, the overshoot decreases until it disappears at

high helium fraction.

Figure 4: Square of the pressure amplitude of

the fundamental mode measured by Mic#1

versus the heater power. Data for different gases

mixtures and stacks. Same legend as in figure 5

Figure 5: First harmonic amplitude versus

square of fundamental amplitude. Both are

normalized by mean pressure.

The right column in figure 6 shows the hysteresis loop plotted as the variation between the

dynamic pressure amplitude versus the temperature difference across the stack. This reflects

evidence of hysteresis where the onset temperature difference at start-up is always higher than at

shut down, and the size of the hysteresis loop clearly decreases as the helium molar fraction

increases.

Figure 6: The relationships between the temperature at the hot

and cold stack sides and the dynamic pressure amplitude

measured by microphone # 1.

Both columns in the figure imply that the dynamic pressure overshoot and the size of the

hysteresis loop may be related to the non-uniform temperature distribution inside the stack and are

reduced as the gas thermal conductivity increases with the increase in the helium fraction.


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4. Summary and conclusions

The selections parameters of a working gas in a thermoacoustic engine are studied. The bestvalues for the performance indicators can not be achieved simultaneously (e.g. lowest onset

temperature and very low viscous losses can not be achieved for the same gas or gas mixture). It isshown that high specific heat ratio correspond to high onset temperatures and that at low gas

mixture densities, gains obtained by high sonic speeds and low Prandtl numbers can be offset by

low mixture densities. The excitation of harmonics is evaluated and quantified for all gases used

through the evaluation of the pressure of the fundamental mode and the pressure of the first

harmonics. The relationship between these two variables and the input heater power is discussed.

The acquired data shows evidence that the overshoot in the dynamic pressure and the size of

the hysteresis loop are reduced as the helium fraction in an air/helium mixture increases suggesting

that they may be related to the non-uniformity in the stack temperature and the mixture thermal

conductivity.

5. REFERENCES1 G. W. Swift, Thermo-acoustic Engines, J. Acoust. Soc. Am., 84, 114680, (1988).2 J. Wheatley, An intrinsically irreversible thermoacoustic heat engine, J. Acoust. Soc. Am., 74, 153-

170, (1983).3 G. Swift, Thermoacoustics: A unifying perspective for some engines and refrigerators (2001).4 K. M. Godshalk, C. Jin, Y. K. Kwong, E. L. Hershberg, G. W. Swift, R. Radebaugh, Characterization

of 350 Hz thermoacoustic driven orificepulse tube refrigerator with measurements of the phase of the

mass flow and pressure,Adv. Cryo. Eng., 41, 1411-1418, (1996).5 D. L. Gardner, G.W. Swift, A cascade thermoacoustic engine, J. Acoust. Soc. Am., 114, 1905 -1919,

(2003).6 C. Shen, Y. He, Y. Li, H. Ke, D. Zhang, Y. Liu. Performance of solar powered thermoacoustic engine

at different tilted angles.Applied Thermal Engineering, 29, 27452756, (2009).7 M. Hatazawa, H. Sugita, T. Ogawa, Y. Seo, Performance of a thermoacoustic sound wave generatordriven with waste heat of automobile gasoline engine, Transactions of the Japan Society of

Mechanical Engineers, Part B, 70, 292 - 299, (2004).8 J. R. Olson and G. W. Swift. Similitude in thermoacoustics, J. Acoust. Soc. Am., 95, 1405-1412,

(1994).9 J. R. Belcher, W. V. Slaton, R. Raspet, H. E. Bass and J. Lightfoot, Working Gases in Thermo-

acoustic Engines,J. Acoust. Soc. Am., 105, 2677-2684, (1999).10 L. Z. Jens, C. Q. Howard, and A. C Zander. Development of a low-cost loudspeaker-driven

thermoacoustic refrigerator,Proceedings of acoustics 2005. Busselton, Western australia (2005).11 F. W. Giacobbe. Estimation of Prandtl numbers in binary mixtures of helium and other noble gases.J.

Acoust. Soc. Am. 96, 3568-3580, (1994).12 A. Campo, M. M. Papari and E. Abu-Nada, Estimation of the minimum Prandtl number for binary gas

mixtures formed with light Helium and certain heavier gases: Application to thermoacoustic

refrigerators,Applied Thermal Engineering, 31, 3142-3146, (2011).13 A. H. Ibrahim and E. Abdel-Rahman, Innovative Solar-Energy-Driven Power Converter: Efficient

Operation of Thermo-acoustic Engines, The 2nd

International Conference on Renewable Energy:

Generation and Applications, AlAin, UAE, 4 - 7 March 2012.14 A. H. Ibrahim, A. Elbeltagy, M. Emam and E. Abdel-Rahman, Development and Analysis of Non-

linearity in the Pressure Waves Resulting from Thermo-acoustic Heat Engines, Acoustics 2012,

Nantes, France, 23-27 April 2012.15 T. Biwa, Y. Tashiro, H. Nomura, Y. Ueda and T. Yazaki, Experimental Verification of a Two-sensor

Acoustic Intensity Measurement in Lossy Ducts,J. Acoust. Soc. Am., 124(3), (2008).

performance evaluation of thermoacoustic engines using different gases

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