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Influence of resonator length on the performance of standing wave thermoacoustic
prime mover
Wahyu Nur Achmadin, Ikhsan Setiawan, Agung Bambang Setio Utomo, and Makoto Nohtomi
Citation: AIP Conference Proceedings 1755, 110006 (2016);
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Published by the American Institute of Physics
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Influence of Resonator Length on the Performance of
Standing Wave Thermoacoustic Prime Mover
Wahyu Nur Achmadin1, a), Ikhsan Setiawan1, Agung Bambang Setio Utomo1, and
Makoto Nohtomi2
Department of Physics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada,
Sekip Utara BLS 21, Yogyakarta, 55281 Indonesia
Graduate School of Environment and Energy Engineering, Waseda University,
Nishi-tomita 1101, Honjo City, Saitama pref., Japan.
Abstract. A research on the influence of resonator length on the performance of a standing wave thermoacoustic prime
mover has been conducted. The thermoacoustic prime mover consists of an electric heater, a resonator tube filled with
atmospheric air, and a stack. The stack was made of stainless steel wire mesh screens with mesh number of #14. The
stack had a length of 5 cm and placed 13 cm from resonator hot-end. The resonator tube was made of stainless steel pipe
with 6.8 cm inner diameter. The electric heater which has a maximum power capability of 299 W was attached to the hot
side of the stack. We varied the resonator length from 105 cm until 205 cm. It was found that the thermoacoustic prime
mover with a resonator length of 155 cm generated the sound with the smallest onset temperature difference and shortest
time to reach the onset condition, those are 252 qC and 401 s, respectively. Also, the prime mover with a resonator length
of 105 cm produced the highest frequency that is 174 Hz. On the other hand, by using resonator length of 180 cm, the
prime mover generated the highest pressure amplitude of 0.0041 MPa, and the thermoacoustic device delivered the
highest acoustic power of 2.8 W and efficiency of 0.9%.
Thermoacoustics is a study concerned mainly with the interaction between heat and acoustic wave, namely with
the conversion of thermal energy to acoustic energy and vice versa. Based on the heat flowing direction, the
thermoacoustic device is divided into two categories; they are a thermoacoustic prime mover and thermoacoustic
refrigerator. The thermoacoustic prime mover is transferring heat from a high-temperature reservoir to a lowtemperature reservoir to produce acoustic work, and conversely, thermoacoustic refrigerator is removing heat from a
low-temperature reservoir to a high-temperature reservoir by absorbing acoustic work from an external agent. The
simplicity and potentially offers low cost, and high reliability makes the thermoacoustic devices attractive for
researchers. The thermoacoustic prime mover is environmentally friendly as they can utilize waste heat as heat
sources for their operation and do not emit any exhaust gases[1-3].
Hariharan et al. have conducted research about the influences of stack geometry and resonator length on the
performance of their thermoacoustic engine [4]. Other examples of the recent publications on standing-wave
thermoacoustic prime mover were written by Hao et al. [5] and Setiawan et al. [6]. The former studied
experimentally the influence of difference working gases on the performance of thermoacoustic prime mover while
the latter made a numerical study on the effect various compositions of helium-based binary mixture working gases.
This paper describes the influence of resonator length on the performance of thermoacoustic prime mover. In the
next sections, it is presented the theory, experimental method, result, and discussion, and finally, some conclusions
are provided.
Advances of Science and Technology for Society
AIP Conf. Proc. 1755, 110006-1–110006-7; doi: 10.1063/1.4958540
Published by AIP Publishing. 978-0-7354-1413-6/$30.00
The hydraulic radius, porosity, and
ZW parameter of the stack made of wire mesh screens are calculated as [7]
d wire
I 1
4(1 I )
Z W ¨¨ h
rh is the hydraulic radius of the stacking channel, d wire is the diameter of the wire, I is porosity, n is the
mesh number (number of meshes per inch),
the thermal penetration depth is roughly the distance that heat can
diffuse through the medium during the time interval related to the period of the acoustic oscillation.
The thermal penetration depth is given by:
SfU m c p
Where k is the thermal conductivity, Um is the mean density, cp is the isobaric specific heat of the gas, f is the sound
frequency. In this research, these equations have been calculated and shown in Table.1.
Materials that used in this research is a stack, which is made of a tight pile of stainless steel wire mesh screens
with mesh number of #14 and arranged in stack length of 5 cm. Gasket carbon material with an outer diameter of
17.5 cm and width of 1.55 mm as to indicate the leakage. The resonator is made of stainless steel pipes with an inner
diameter of 6.8 cm, whereas the total length is varied from 105 cm to 205 cm.
The equipment used in this research is an electric heater system with maximum heat power of 299 W. Type-K
thermocouples sensor produced by Sakaguchi E.H Voc Corp and dynamic pressure transducers of the PGM-10KH
model from Kyowa Electronic Instruments Co., LTD, which connected the WE7000 Ethernet software with data
logger types of Yokogawa models 707821. Then, the heat exchanger system consists of the cold heat exchanger and
hot heat exchanger.
Data retrieval
The stack placed 13 cm from resonators closed-ends, between the cold heat exchanger and hot heat exchanger.
The temperatures sensor and dynamic pressures were connected to the data logger and calibration constants on the
pressure transducer are inserted. The operation of the thermoacoustic prime mover is done by providing the
electrical input power to the heater. The data were recorded every second at temperature sensor and every 10 oC at
dynamic pressure sensor. If the temperature difference has been constant, so we turn off the electric heater. This
measurement repeated with variation of length tube resonator which was 105 cm, 130 cm, 255 cm, 180 cm, and 205
Data processing
The analysis of output data was done by interpreting the graph of the time history of temperature measurement
and dynamic pressure measurement. The output data from dynamic pressure analyzed by fast Fourier transform to
know the dominant frequency and amplitude for every measurement. This measurement is used to calculate the
acoustic power and efficiency. The maximum results will be seen when it occurred at a difference temperature
indicator of 350 oC in this research. The present experimental apparatus is schematically illustrated in Fig. 1.
FIGURE 1. Schematic diagram of the standing wave TAPM. TH, TC, and TRHE are thermocouples. P1-P3 are dynamic
pressures and TC, TH; TRHE is a thermocouple. The length unit is centimeter.
About the measurement of acoustic power, Fusco et al. [8] and Swift [7] present a reliable method known as the
two-microphone method, in which two sensors P1 and P3 of are placed with a known distance between them as
shown in the following equation:
­° G v
¨ Im ª¬ P1 A P1B
1B ¼ ®1 °¯ 4rh
§Z ·
2 Um a sin ¨ ¸ ¨ G v P 2 P 2
© 'x ¹ ¨ 8r 1 A
Where A is the cross-sectional area,
is the mean gas density, a is the speed of sound,
is the viscous penetration depth,
Prandtl number,
ª J 1 § J 1 · Z'x
§ Z'x · º ½° ·
¨1 «1 ¸ a cot ¨ a ¸ » ¾ ¸
V ©
V ¹
¹ ¼ °¿ ¸
ª J 1 § J 1 · Z'x
§ Z'x · º ¸
¨1 csc ¨
«1 ¸
V ©
V ¹ a
© a ¹ ¼ ¸¹
is the angular
rh is the hydraulic radius, J is the specific heat ratio, V is the
'x is the distance between the two sensors. Moreover, the efficiency of the engine is defined as:
Where E is power output acoustic,
Ein is electric power input.
Onset temperature difference is a minimum temperature difference between cold side and hot side of the stack
that causes existence the sound wave the thermoacoustic prime mover. Determination of onset temperature
difference can be done by observing the behavior of temperature like Fig.2.
Figure 2 shows time history of temperatures measurement when prime mover heated by 299 W electric input
power. We can see that temperature of the hot end of stack Th increases rapidly, likewise slow increases in the
temperature of the resonators hot-end Trhe. The onset condition could be reached by increases the Trhe. Interpretation
data like Fig. 2 with length resonator of 105 cm, 130 cm, 155 cm, 180 cm, and 205 cm is done too, that so obtain
onset difference temperature as shown Fig.3.
Based on the results obtained (Fig. 3), the tube resonator length of 155 cm has the lowest onset temperature
difference at operation with electric input power 299 W. The onset temperature difference decrease at the tube
resonator length of 105 to 155 cm, and then the onset increased with increasing of length tube resonator.
This study proves that the ratio hydraulic radius with thermal penetration depth rh G k to the most appropriate
onset temperature difference to generated the thermal contact is the tube resonator length of 155 cm. Setiawan had
done the numerical calculate the effect of hydraulic radius to the onset of difference temperature which shown the
value optimum ratio rh G k 2.1 to every tested gas [6]. While in this research, the tube resonator length of 155 cm
had value optimum ratio 2.0, so it could be concluded that value of the ratio in this experiment approached the
numerical and experimental value ratio rh G k as shown in Table 1.
Figure 4 shows influence resonator length time to reach onset condition. From Fig. 4, the optimum value of time
to reach onset condition and onset temperature difference is the resonator tube length of 155 cm, this condition
caused by the influence of ratio rh G k to thermoacoustic prime mover. The frequency at the closed resonator
tube just influenced by air velocity at the tube resonator v and the tube resonator length. So the longer length of tube
resonator the lower value of its frequency and the conversely, as shown in Fig. 5. In all the cases the experimental
value is more than that of theoretical resonance frequency due to the variable cross-sectional area of the stack and
non-uniform temperature distribution of gas in the system, which leads to lower values of sound velocity than
assumed a value in the calculations [4].
FIGURE 2. Time history of temperature measurements for 299 W input electric power. Th and Tc are the
temperatures of the hot and cold ends of the stacks. Trhe is the temperature of the resonator’s hot-end, Tr is the
temperature in the room, and Tdiff is the temperature difference between both ends of the stack.
FIGURE 3. Influence resonator length on the onset temperature difference with electric input power 299 W
FIGURE 4. Influence resonator length on time to reach onset condition with electric input power 299 W
TABLE 1. Stack parameter in thermoacoustic
rh G k Resonator
Length (cm)
Frequency (Hz)
The pressure amplitude value decreased at resonator length of 205 cm as shown in Fig. 6. The decreasing
possibility happened when thermal contact value with generated frequency less corresponding, so the pressure
amplitude value is decreasing. Therefore, the optimum amplitude pressure on the thermoacoustic prime mover
engine this research generated by the length of tube resonator 180 cm. The research result similar to the studies has
been conducted by Biwa [9]. Biwa has conducted research to know energy conversion performance thermoacoustic
with two types of the stack. Biwa used to stack with the value thermal contact ZW is 0.13 and 3.5. It was found that
the value of the thermal contact stack ZW is 3.5 with the ratio hydraulic radius rh G k 1.87, It is the best stack
because it could generate the large amplitude, the acoustic power, and the efficiency. In the following, stack with
optimum amplitude ZW is 3.4, and the ratio is rh G k 1.84 (Table 1).
FIGURE 5. Influence resonator length on the sound frequency at temperature difference 350 oC with electric input power 299
FIGURE 6. Influence resonator length pressure amplitude at temperature difference 350 oC with electric input power 299 W
FIGURE 7. Influence resonator length acoustic power at temperature difference 350 oC with electric input power 299 W
FIGURE 8. Influence resonator length efficiency at temperature difference 350 oC with electric input power 299
Influence resonator length on the acoustic power and efficiency at temperature difference 350 oC as shown in Fig.
7 and Fig. 8. From Fig. 7 shows the best acoustic power is 2.78 W and from Fig. 8 shows the best efficiency is
0.93%. We can see that resonator length of 180 cm in Fig. 8 was decreased.
In this case, the addition resonator length suspected would make the velocity of air gaseous in the stack
decreases. The value of energy dissipation expands at work medium with high rate. The small dissipation value
indicates that the thermal energy is used to move the thermal from a heat point to a cold point a bit wasted so the
movement of heat will optimum.
This research has been carried out by varying the resonator length. The experimental results show that the
resonator length affects the performance of the standing wave thermoacoustic prime mover. The best resonator
length found in this research is 155 – 180 cm as it gives the lowest onset temperature difference, shortest the time to
reach onset condition, and the highest pressure amplitude. We also found that the resonator length variation is
altering the acoustic power and efficiency. The best acoustic power and efficiency in this research are 2.8 W and
0.9%, respectively.
A part of this work was supported by Department of Physics, Faculty of Mathematics and Natural Science
Universitas Gadjah Mada.
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