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Thermoacoustic travelling-wave cooler driven by a cascade thermoacoustic engine
Applied Thermal Engineering 59 (2013) 223e231
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Thermoacoustic travelling-wave cooler driven by a cascade thermoacoustic engine Huifang Kang a, *, Fan Jiang a, Hongfei Zheng a, Artur J. Jaworski b a b
Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK
h i g h l i g h t s Cascade thermoacoustic engine driving a cooler with linear topology is proposed. The best features of standing and travelling wave devices are used simultaneously. An acoustic absorption element is adopted to adjust the acoustic field. Principles and functionality demonstrated through modelling and experimentation.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 November 2012 Accepted 26 May 2013 Available online 5 June 2013
This paper proposes a novel configuration of a cooler driven by a cascade thermoacoustic engine. It consists of a standing-wave thermoacoustic engine, a travelling-wave thermoacoustic engine and a travelling-wave thermoacoustic cooler in series. The engines provide acoustic energy to drive the cooler. The three main components have a linear topology without the need for using feedback loops. Modelling and simulation of the cascade arrangement, together with the experimental results, are described in this paper. In the presented system, an acoustic absorption element is adopted to induce a higher acoustic power transfer, which increases the travelling-wave component in the acoustic field. It makes the regenerators of both the travelling-wave engine and cooler work in the travelling-wave phase region and allows the thermoacoustic performance offered by both the travelling-wave and the standing-wave to be utilized more effectively. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Thermoacoustic Engine Cooler Travelling-standing wave Cascade
1. Introduction Thermoacoustic energy conversion technologies have undergone a substantial development over the recent four decades thanks to the pioneering work of Rott [1e4], Ceperley [5,6] and subsequent demonstration projects undertaken at Los Alamos National Laboratory [7,8]. The thermoacoustic engine (TAE) converts thermal to acoustic energy and this can be used to drive the thermoacoustic cooler (TAC). The system combining the TAE and TAC is called a cooler driven by thermoacoustic engine [9,10]. In such arrangement, when a steep temperature gradient is set up along the regenerator of TAE, the acoustic wave with the oscillating pressure p1 ¼ j:p1 j:eiðutþ4z Þ and the oscillating velocity u1 ¼ j:u1 j:eiut is excited. Here u is the angular frequency and 4z is the leading phase of p1 relative to u1. When the acoustic wave
* Corresponding author. Tel.: þ86 10 68914303; fax: þ86 10 68949859. E-mail address: [email protected] (H. Kang). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.05.044
passes through the regenerator of TAC, a temperature gradient is established along its length corresponding to a certain coefficient of performance (COP). The acoustic wave drives gas parcels in the thermoacoustic regenerators to experience a certain thermodynamic cycle. Then, the conversion from thermal to acoustic energy and the heat pumping occurs without any moving parts in the system. Compared with traditional thermodynamic systems, the cooler driven by thermoacoustic engine has three main advantages: (1) It has a simple structure, no moving parts, low cost of manufacture, and high reliability; (2) By using inert gases as working fluids, this kind of machines is environmentally friendly; (3) The thermoacoustic devices can be driven by low quality energy source such as the exhausting thermal energy and the solar energy, so it is significant for remote rural areas where there may be no access to electricity grid. In thermoacoustic energy conversion processes, the key mechanism is a heat transfer interaction that takes place between the gas parcels undergoing oscillatory motion and a solid material along which the gas oscillations occur. In thermoacoustic engines, a
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spontaneous acoustic wave is excited which transports heat from the hotter to a cooler place of the solid by a cyclically compressing and expanding gas parcel; in thermoacoustic coolers the acoustically induced compression and expansion of gas parcels leads to heat pumping effects in the solid. However the exact nature of the thermodynamic cycle depends upon the phase difference between the oscillating pressure and the oscillating volume of the gas parcel [11], or in other words (using the equation of state for the gas) between the oscillating pressure p1 and the oscillating temperature T1. The relationship between the parameters of the oscillating gas parcel is shown in Fig. 1. The oscillating temperature T1 is determined by the thermo-relaxation and the oscillating displacement x which is controlled by u1. Thus, the type of the thermodynamic cycle is influenced by the thermo-relaxation and 4z. The early work concerned mainly a variety of standing wave devices [12,13] which were built based on the thermoacoustic theory. In the standing wave devices, gas parcels with 4z ¼ (2nþ1) 90 realize the conversion between thermal and acoustic energy using a thermodynamically irreversible process defined by an imperfect thermal contact between the working gas and the porous solid material, traditionally referred to as a stack.1 Although the standingwave devices are relatively simple to build, their efficiency is limited due to the irreversible thermodynamics on which their thermoacoustic conversion processes rely. The alternative to the standing-wave devices are travellingwave devices [5,6,8]. These are usually harder to control in terms of the acoustic wave properties, and traditionally have been more difficult to design and built. However, in such devices, gas parcels with 4z ¼ 2n 90 realize a reversible thermodynamic cycle due to a “perfect” thermal contact between the gas parcels and the porous solid material (traditionally referred to as a regenerator). In theory the “perfect” contact would require infinitesimally hydraulic radius of the regenerator, but this would inevitably lead to infinite viscous losses. Therefore in practice a finite hydraulic radius is chosen as a fraction (e.g. typically 0.2) of the thermal penetration depth, which gives acceptable viscous losses but at the same time sufficient thermoacoustic gain and improved efficiency. Subsequently, in practical travelling-wave devices, the oscillating temperature of gas parcels lags their oscillating displacement. Therefore, the phase difference between the oscillating temperature and pressure deviates from (2n þ 1) 90 because of the thermo-relaxation effects. Under such conditions, in order to improve the thermoacoustic gain and efficiency, the travelling-standing wave phase may be required to match the phase deviation due to the thermorelaxation. In practical thermoacoustic systems, there is neither pure travelling-wave mode nor pure standing-wave mode. The thermoacoustic effect is the result of the combined interaction of the travelling-wave component (TWC) and the standing-wave component (SWC) in the thermoacoustic system. The functions of the SWC are energy storage and energy conversion, while the functions of the TWC are energy transfer and energy conversion. In the thermoacoustic engine (TAE), the generated acoustic energy can be transferred by the TWC or stored as the SWC. In the thermoacoustic cooler (TAC), the consumed acoustic energy can be supplied by the TWC or compensated from the stored acoustic energy in the SWC. Biwa [14] demonstrated thermoacoustic energy conversions which make full use of the TWC and SWC of the acoustic field induced in the resonator. It is claimed that, in order to achieve high
1
In the context of subsequent discussion on the travelling-standing wave concept, and for simplicity this paper will use terminology “regenerator”, for both standing and travelling wave devices considered here.
Thermo-relaxation u
T
p
p
V
x
Thermodynamic cycle
Fig. 1. The relationship between the parameters of the oscillating gas parcel.
gain and efficiency, one has to choose an optimum 4z which can make both the TWC and SWC contribute to the amplification of the acoustic field intensity. However a new problem arises e namely, if the leading phase 4z can be chosen in the region of 180 4z 180 for the travelling-standing wave, then how to choose the optimum 4z for the regenerator. Kang et al. [15] investigated the thermoacoustic effect in the travelling-standing wave. The results of their analysis show that to gain a higher acoustic power and efficiency, the hot end of the regenerator in an engine should be close to the pressure anti-node (PAN), and the TWC should propagate from the ambient end to the hot end. To gain a higher cooling power and coefficient of performance, the ambient end of the regenerator in a cooler should be close to the PAN, and the TWC should propagate from the ambient end to the cold end. Furthermore, Kang et al. [16] analyzed the influence of the parameters of the acoustic field and the regenerator structure on the thermoacoustic conversion and identified the optimum condition for the thermoacoustic conversion. The optimal 4z depends on the hydraulic radius because 4z needs to balance the phase deviation generated by thermo-relaxation. Based on the analysis of the thermoacoustic performance in the travelling-standing wave, Kang et al. [17] designed a heat driven thermoacoustic cooler which utilized thermoacoustic effects of both the TWC and SWC. This device has the following advantages: (1) It utilizes simultaneously the thermoacoustic performance contributed by both the TWC and SWC; (2) The acoustic power produced by the engine drives the cooler directly; (3) The feedback tube realizes the recycling process of the residual acoustic power out of the cooler. However, the toroidal topology is more difficult to build than the linear one and also suffers from a circulating second-order mass flow, referred to as Gedeon streaming, which can reduce the efficiency. Gedeon streaming [8] has been successfully suppressed by exploiting the time-averaged pressure gradient developing in an oscillating flow through an asymmetric channel, however this consumes acoustic power. In addition, fabricating asymmetric channels adds complexity that is undesirable in commercial devices. Thus, this paper proposes a novel configuration of a cooler driven by a cascade thermoacoustic engine, as shown in Fig. 2. It consists of a standing-wave thermoacoustic engine (SWTAE), a travelling-wave thermoacoustic engine (TWTAE) and a travellingwave thermoacoustic cooler (TWTAC) in series. The two engines are the source of acoustic power to drive the cooler. In the device, an acoustic absorption element (AAE) is used to introduce a higher acoustic power transfer, which increases the TWC in the acoustic field. It makes the regenerators of both the TWTAE and the TWTAC work in the travelling-wave phase region and utilize effectively the thermoacoustic performance contributed by both the TWC and SWC, which improves the overall efficiency of the device. 2. Apparatus A prototype cooler driven by a cascade thermoacoustic engine has been constructed according to the present concept and the detailed modelling results. Fig. 3 is a photograph of the device. The pressure container elements are built out of 304 grade of stainless-
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Fig. 2. Schematic of the cascade system considered in this paper.
Fig. 3. Photograph of the device.
steel for strength. Because the height of the laboratory room is less than 3.1 m which is the total length of the device, a 90 bend is used to reduce the height of the device. However, the 90 bend will increase the additional acoustic power dissipation. According to Ref. [7], the estimated loss of acoustic power due to bend is 0.21 W which is negligible compared to power levels described in the paper. In the following description of the apparatus, the length reported is along the acoustic axis, and diameters reported are inside diameters. The upper portion of the resonator located above SWTAE and shown in Figs. 2 and 3 is designed for the minimum dissipation of acoustic power without consideration for size. The upper compliance at the top consists of two flanged hemi-spherical end caps, the flanges connected with bolts. It has a volume of 0.014 m3. A 0.14 m long cone provides a smooth transition between the lower end of the upper compliance and the upper resonator. The cone lowers the acoustic velocity of the gas entering the upper compliance, reducing the minor-loss dissipation of acoustic power. The most important quantitative details of the construction of the three stages are presented in Table 1. The uppermost component, the AHE1 is a parallel plate-type heat exchanger shown in Fig. 4. The working gas oscillates vertically through the space between plates, while the ambient temperature water flows crosswise in the channels drilled perpendicular to the heat exchanger axis. Below this heat exchanger, there is a regenerator which is made out of stainless-steel screens disks with the mesh number 30 and the wire diameter of 0.305 mm. The electrically heated hot heat exchanger (HHE1) is located below the regenerator. Part of the cross sectional area of HHE1 is occupied by a parallel plate structure, while the remaining part is solid metal with holes prepared
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Table 1 Dimensions and other details of the three stages of the device.
SWTAE: AHE1 Reg1 HHE1 ST TBT1 TWTAE: AHE2 Reg2 HHE2 ST TBT2 TWTAC: AHE3 Reg3 CHE AAE
Length (mm)
Diameter (mm)
30 90 42
89 89 89 40 89e40e76
84 23 25 28 46 23 25 20
76 76 76 40 76e40e76 76 76 76 35
Mesh
Porosity
30
0.75
70
0.70
200
0.67
70
0.70
250
0.69
70
0.70
Number of screen
2
2
8
Material
Copper Stainless-steel Stainless-steel Stainless-steel Stainless-steel Copper Stainless-steel Stainless-steel Stainless-steel Stainless-steel Copper Stainless-steel Copper Stainless-steel Fig. 5. Detailed drawing of the hot heat exchanger.
for cartridge heaters, as shown in Fig. 5. The oscillating working gas passes through the space between plates, and the 6.35 mm diameter transverse holes hold electric cartridge heaters of various lengths corresponding to the lengths of holes. The taper angle of the 1st-stage thermal buffer tube (TBT1) was designed to suppress Rayleigh streaming, and the stainless-steelscreen flow straighteners (FS) at the end of the thermal buffer tube were designed to prevent jet-driven streaming. Together, these features are intended to encourage thermally stratified oscillating flow in the thermal buffer tube, without convection of heat from hot to ambient. The TWTAE and the TWTAC stages are similar in character to the SWTAE, with parallel plate-type ambient heat exchangers, electrically heated hot heat exchangers, parallel plate-type cold heat exchangers, and tapered thermal buffer tubes between stainlesssteel-screen flow straighteners. The acoustic absorption element (AAE) in the end of the lower resonator is in the form of a few layers of mesh screen. The lower compliance with a volume of 0.0027 m3 is similar in character to upper compliance. In experiments, the pressure data have been acquired and analyzed in real time by a computer. As illustrated in Fig. 2, eight calibrated pressure sensors, labelled P1 to P8, are installed in the system in order to obtain the distribution of the acoustic field. The pressure data acquisition system is comprised of the pressure
Fig. 4. Detailed drawing of the ambient heat exchanger.
sensors, a data acquisition board, a computer with the data acquisition program developed in-house. The pressure sensors are the piezoelectric type (CY-YD 208), supplied by Sinocera Piezotronics, Inc., China. The data acquisition board is AC1810, 12bit precision and 10 kHz sampling frequency. The output voltage from the piezoelectric transducer is amplified by a charge amplifier and then sent to the AC1810 board connected to the computer. The pressure signal can be displayed on the computer screen using the data acquisition program. Also four calibrated NiCreNiSi thermocouples, labelled T1, T2, Ta and Tc, are installed in the system as shown in Fig. 2. The thermocouple T1 is located at the hot end of the SWTAE regenerator; T2 is located at the hot end of the TWTAE regenerator; Ta is located at the ambient end of the TWTAC regenerator; and Tc is located at the cold end of the TWTAC regenerator. The temperature data are measured with 1 C accuracy. Heating power is adjusted by changing the supply voltage (V) to the heaters and is displayed by a digital voltmeter. The current (I) is measured by the ammeter, and then the heating power can be obtained as product of I and V. The cooling power is controlled and measured through the same method. 3. Simulation and analysis In order to perform a more detailed analysis, a specialized design tool referred to as DeltaEC (Design Environment for Lowamplitude ThermoAcoustic Energy Conversion) and developed by Los Alamos National Laboratory is employed [18]. Its calculation capabilities and precision in modelling thermoacoustic devices have been validated by many researchers [8,19]. DeltaEC solves the one-dimensional wave equation based on the usual low-amplitude acoustic approximation. It is suitable for the standing wave, the travelling wave and the complex acoustic field of standing-travelling wave. It can be used in the design process in order to optimize a thermoacoustic system, or to predict the performance of an existing build of a thermoacoustic device. DeltaEC integrates numerically the acoustic wave equation and energy equation segment by segment throughout the whole device based on the low amplitude acoustic approximation and the sinusoidal time dependence of the variables [18]. In the current work, DeltaEC is used to simulate the acoustic field and the acoustic power flow in the thermoacoustic device under study. In the system described in this paper, there are three energy conversion units, and each unit has its own efficiency. It is hard to
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make the three stages reach their highest efficiency at the same time. For convenience, the total performance effect (TPE) of the device is defined as the cooling power divided by the total heat input. In the device described here, it is can be expressed as:
TPE ¼
Qc Q1 þ Q2
(1)
where Qc is the cooling power, Q1 and Q2 are heat inputs delivered via resistive heating in the two engines. To obtain the highest TPE, the DeltaEC model is used to optimize the dimensions of each segment one by one. Because most of the parameters will influence the acoustic field, and subsequently influence the optimization results of the other parameters, all of the optimization steps are executed again and again, until the changes in the optimization results are negligible. The process of design and optimization is quite involved and would require a separate paper to describe all the detailed steps. Therefore, for convenience, the simulation results discussed in this section are based on the final design of the prototype, with dimensions given in the last section. Furthermore, the calculation was carried out under the condition as follows: Helium is used as working gas, the mean pressure is 2.5 MPa, the temperature of the two hot heat exchangers is maintained at 700 K, the temperature of the cold heat exchanger is 273 K, while the temperature of the three ambient heat exchangers is 300 K. In the calculation, it is found that it is impossible to realize the high efficient cooling by adjusting the lengths and radii of the device elements. The reason for this is that the TWC is too small. The region with high efficiency is too narrow [16] and the acoustic field in the TWTAC regenerator is similar to the standing-wave. Moreover, the AAE (in the form of a few layers of mesh screen) is installed in the lower resonator to absorb acoustic energy. When the AAE dissipates the acoustic energy due to viscosity and converts acoustic energy into heat, the balanced distribution of acoustic energy in the system is broken. Subsequently, the acoustic energy transfer happens. The acoustic power will be transported from the engine, where the acoustic energy is generated, to the AAE, where
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the acoustic energy is absorbed and dissipated. Then the TWC, on which the acoustic power transfer relies, increases. The influence of AAE on the acoustic power, the acoustic field and the thermoacoustic conversion performance is shown in Fig. 6. In Fig. 6(a), the acoustic power absorbed in by the AAE increases when the length LR of the AAE increases. Subsequently, the TWC increases and the length of the region with the travelling-wave phase increases [16]. According to Fig. 6(b), as LR increases, the location of 4z ¼ 0 moves to near the TWTAC, and 4z of the TWTAC regenerator comes closer to 0 . 4z of the TWTAE regenerator decreases close to 0 and then drops to the negative phase difference. 4z of the SWTAE changes a little, but the efficiency of the SWTAE decreases because the impedance increases. As illustrated in Fig. 6(c), the efficiency of TWTAE reaches its maximum (h2 ¼ 35.0%) when LR ¼ 6.33 mm. According to Fig. 6(b), the TWTAE regenerator is in the region of 39.7 < 4z < 3.84 . The coefficient-ofperformance of TWTAC reaches its maximum (COP ¼ 2.58) when LR ¼ 1.32 mm. According to Fig. 6(b), the TWTAC regenerator is in the region of 1.11 <4z < 23.0 . The TPE reaches its maximum (TPE ¼ 0.184) when LR ¼ 0.92 mm as shown in Fig. 6(d). Referring to Fig. 6(b) and (c), when LR ¼ 0.92 mm, the performance and 4z of the three stages can be obtained as follows: the efficiency of SWTAE is h1 ¼ 26.2% and its working phase region is 91.0 < 4z < 74.6 ; the efficiency of TWTAE is h2 ¼ 34.3% and its working phase region is 44.9 < 4z < 18.3 ; the COP of TWTAC is COP ¼ 2.67 and its working phase region is 20.0 < 4z < 41.8 . Therefore, the optimal system with LR ¼ 0.92 mm is selected to analyze the acoustic field and the work flow in the system which is illustrated in Fig. 7. Fig. 7(a) shows the pressure amplitude distribution along the device which is around 3.1 m long. The maximum of pressure amplitude jp1 j ¼ 1:12 105 Pa appears between the SWTAE and TWTAE. Although there is the flow resistance of the regenerator, the changing trends of the pressure amplitude in the SWTAE and TWTAE are different. The pressure amplitude grows along the SWTAE regenerator, but drops along the TWTAE regenerator. The reason for this is that the changing trend of the pressure amplitude without the flow resistance is determined by the boundary
Fig. 6. The acoustic power absorbed by the AAE, the acoustic field and the thermoacoustic conversion performance versus the length of the AAE LR. (a) the acoustic power absorbed by the AAE; (b) the phase difference at the ends of three regenerators; (c) the efficiency h1 of SWTAE, the efficiency h2 of TWTAE, and the coefficient-of-performance COP of TWTAC; (d) The total performance effect (TPE) of the device defined as the cooling power versus the total inputting heat power.
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Fig. 7. Pressure amplitude (a), volumetric velocity (b), acoustic impedance (c), phase difference (d) and acoustic power flow (e) distribution along the system.
conditions. The pressure amplitude reaches the peaks at the stagnation points of the standing-wave where the oscillating velocity reaches its minimum. There are three stagnation points in the system. Two stagnation points are the two ends of the device, while the third one is located between the TWTAE and TWTAC. In the SWTAE, the flow resistance of the regenerator just makes the pressure amplitude increase more slowly than that without the flow resistance. In the TWTAE, TWTAC and AAE, the flow resistance makes the pressure amplitude drop more steeply than that without the flow resistance. The pressure amplitude changes smoothly along all other parts. Fig. 7(b) shows the distribution of the volumetric velocity along the device. There are two maxima and three minima along the system. One maximum of the volumetric velocity is in the upper resonator, while the other is in the lower resonator. Two minima are located at the two ends of the system, while the third one is in the thermal buffer tube (TBT1) between the SWTAE and TWTAE where the maximum of the pressure amplitude is located. The fact that the velocity amplitude approaches zero near the regenerators will contribute to reducing the viscous loss, which will help to improve their efficiency. The small volumetric velocity within the regenerator is preferred to avoid high viscous dissipation. It can also be seen that the volumetric velocity increases significantly along the regenerator of the TWTAE. This is due to the sharp temperature gradient along the regenerator and the acoustic power generated by the TWTAE. Furthermore, at the location of the TWTAC, there is a sudden decrease of the volumetric velocity because the temperature drops along the regenerator and the acoustic power is consumed to pump heat from the cold heat exchanger. Along all other parts, the volumetric velocity changes smoothly. Fig. 7(c) shows the acoustic impedance along the system. It can be seen that the acoustic impedance is highest ðjZj ¼ 19r0 c=Ag Þ at
the ambient end of the TWTAE. The three stages are located in the high acoustic impedance region which will decrease the viscous dissipation. The impedance drops quickly because the pressure amplitude decreases (see Fig. 7(a)) while the volumetric velocity increases sharply in the regenerator of the TWTAE (see Fig. 7(b)). The impedance increases slightly because the volumetric velocity decreases in the regenerator of TWTAC (see Fig. 7(b)). Fig. 7(d) illustrates the phase difference 4z along the system. There are three points where 4z ¼ 0 . Two points are in the upper and lower resonators where the pressure amplitude approaches zero, while the third one is in TBT1 where the maximum of the pressure amplitude is located. It can be found that the regenerators of both the TWTAE and the TWTAC are in the near travelling wave phase region which will benefit the thermoacoustic conversion. The TWTAE regenerator works in the region of 44.9 < 4z < 18.3 , and the TWTAC regenerator works in the region of 20.0 < 4z < 41.8 . According the analysis of Ref. [12], it is indicated that the TWTAE regenerator realizes the conversion from heat to acoustic energy and the TWTAC regenerator pumps heat from the cold end, the functions which are achieved by both the standingwave and travelling-wave. Fig. 7(e) shows the acoustic power flow along the system. It can be seen that the acoustic power flow changes its direction at x ¼ 1.3 m where the regenerator of the SWTAE is located. This means that the acoustic energy generated in the SWTAE is divided into two parts: one part is transferred along x direction to feed the acoustic power dissipation in the upper compliance, the upper resonator and the ambient heat exchanger (AHE1); the other part is transferred along þ x direction. The calculation data shows that the SWTAE can produce a net acoustic power of about 313 W at an inputting heat power of 1195 W, corresponding to a thermoacoustic conversion efficiency of h1 ¼ 26.2%. The acoustic power of 31 W enters the AHE1 and decreases along x direction. After the AHE1
H. Kang et al. / Applied Thermal Engineering 59 (2013) 223e231
which dissipates around 11 W, the remaining 20 W is dissipated in the upper resonator and compliance. The acoustic power of 282 W flows out from regenerator of SWTAE, and is transferred along þ x direction. After being slightly dissipated in the TBT1 and the ambient heat exchanger (AHE2) of the TWTAE, the acoustic power of 265 W enters the ambient end of the TWTAE regenerator and increases along the regenerator with a positive temperature gradient established by the externally supplied heat through the hot heat exchanger (HHE2). Then, an acoustic power of 570 W is gained at the hot end of the TWTAE regenerator. The calculation data shows that the TWTAE can produce a net acoustic power of about 305 W at the inputting heat power of 888 W, corresponding to a thermoacoustic conversion efficiency of h2 ¼ 34.3%. After being slightly dissipated in the TBT2 and the ambient heat exchanger (AHE3) of the TWTAC, the acoustic power of 543 W is fed into the ambient end of the TWTAC regenerator and pumps heat directly. It is reduced gradually due to the consumption of acoustic power for heat pumping from the cold end of the regenerator. When it comes out of the cold heat exchanger (CHE) with a value of 406 W, the acoustic power consumed by the TWTAC is 137 W. The net cooling power of the TWTAC given by the calculation is about 366 W. It implies that the TWTAC achieves COP ¼ 2.67 at the cooling temperature of 0 C. 406 W of the residual acoustic power enters the lower resonator. The lower resonator, the AAE and the lower compliance dissipate acoustic power of around 6 W, 398 W, and 2 W respectively. These calculation results show that the TPE reaches TPE ¼ 0.184 at the cooling temperature of 0 C when the AAE absorbs the acoustic power of 398 W. Fig. 7(d) shows that 4z changes sharply in the region of 0.38 m < x < 0.46 m, and the travelling wave phase region is relatively narrow. This is due to the fact that the acoustic power flowing along x direction is small and the TWC is small. Hence the acoustic field in the region of 0 < x < 1.3 m is similar to the standing wave. Moreover, 4z changes sharply [16] in the region of 0.38 m < x < 0.46 m. 4z decreases slowly at first and then sharply in the region of 2.1 m < x < 2.73 m. The reason for this is that the acoustic power is dissipated strongly in the AAE. Firstly, the acoustic power is about 406 W. The intensity of travelling wave is sufficiently high to transfer the acoustic power which causes a slow change of 4z. After the AAE with acoustic power absorption of 398 W, the residual acoustic power is small. So the TWC is small, and the acoustic field in the region of 2.5 m < x < 3.1 m is similar to the standing wave. Subsequently, 4z changes sharply in the region of 2.5 m < x < 2.6 m.
229
Fig. 8. The pressure amplitude comparison between the experiments and the simulation. Points are measured values, and lines are calculations.
measured frequency of 175 Hz and calculated frequency of 173 Hz is about 1.3%. Fig. 9 gives the hot end temperatures of the regenerators of the two engines, the cooling power and the pressure amplitude measured by P4 as a function of the number of screens in the AAE. The experiment was carried out under the following conditions: the mean pressure pm ¼ 25 bar, the working gas is helium, the heat power inputted into the HHE1 is Q1 ¼ 1400 W, the heat power inputted into the HHE2 is Q2 ¼ 1100 W, and the temperature difference in the regenerator of TWTAC is DT ¼ 0 C. As shown in Fig. 9(a), the hot end temperature T1 of the SWTAE regenerator increases as the number of screens in the AAE increases. The reason for this is that the thermoacoustic conversion efficiency h1 of the SWTAE decreases as shown in Fig. 6(c). So an increased inputting heat cannot be transformed into acoustic
4. Experimental results and discussion To test the practical performance of the whole system, a series of experiments have been conducted. Under the condition of Q1 ¼ 600 W and Q2 ¼ 500 W, an acoustic oscillation starts spontaneously when the hot end temperature of regenerators rises above the critical value T1 ¼ 297 C and T2 ¼ 312 C, respectively. As a first step, the comparison between the measurement and calculations is provided in order to acquire the confidence in the calculation. In particular, the acoustic pressure will form the basis for trying to understand the velocity, the leading phase 4z, and the acoustic power levels within the device. Fig. 8 shows the pressure amplitude measured by the pressure sensors under the condition of the mean pressure of 25 bar, helium as working gas, the HHE1’s temperature of 420 C, the HHE2’s temperature of 435 C, and the CHE’s temperature of 0 C. The disagreement between measured and calculated pressures in Fig. 8 is smaller than 6%. The operating frequency of 175 Hz was measured by a Stanford Research model SR-830 DSP lock-in amplifier. The disagreement between the
Fig. 9. The hot end temperatures of regenerators, the cooling power and the pressure amplitude measured by P4 as the function of the number of screens in the AAE.
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power and accumulates in the HHE1 leading to the increase of T1. Similarly, with the increase of the number of screens, the hot end temperature T2 of the TWTAE regenerator decreases at first and then increases, which is similar to the behaviour of h2. According to Fig. 9(b), the maximum cooling power is 282 W when the AAE made out of 8 pieces of screens were added in the end of the lower resonator. However, the measured cooling power is much lower than that calculation, because the DeltaEC model just considers the heat involved in the thermoacoustic conversion, and doesn’t consider the heat losses (such as the heating load introduced by acoustic dissipation in the resonators, the thermal radiation loss, the heat conduction loss along the tube wall, and so on) that decrease the measured cooling power. As shown in Fig. 9(b), the pressure amplitude decreases with the increase of the number of screens in the AAE, which can be explained by the acoustic dissipation in the system. In most parts of the thermoacoustic system, dTm/dx ¼ 0 and the acoustic power produced by the engines is dissipated in the system. According to Eq. (8) of Ref. [15], the acoustic power dissipation is expressed as dE2 dx
¼ 12 urm Im½fv2ju1 j2 12 g1 g j1fv j (
¼
1 Im½fv jZN j2 j1fv j2
uIm½fk ~ 2 pm jp1 j
ðg 1ÞIm½fk
)
ujp1 j2 2pm g
(2)
where g is the ratio of isobaric specific heat to isochoric specific heat, pm is the mean pressure of the fluid, rm is the mean density of the working gas, and fv, fk are the cross-sectional averaged Rott’s functions which depend on the specific channel geometry under consideration, ZN is the normalized impedance defined as,
ZN ¼
p1 =u1 rm c
Fig. 10. The temperatures measured by the thermocouples and the pressure amplitude measured by P4 with different heat power inputted into HHE2 when the heat power inputted into the HHE1 is Q1 ¼ 1400 W.
(3)
According to Eq. (2), the acoustic power dissipation is proportional to jp1 j2 . With the increase of the number of screens, there is more acoustic power dissipated in the AAE and the acoustic power dissipated in the other elements of the system decreases. Subsequently, the pressure amplitude will decrease to maintain the balance between the generated and dissipated acoustic power in the system. Fig. 10 gives the temperatures measured by the thermocouples and the pressure amplitude measured by P4 with different heat power Q2 supplied into the HHE2. The experiment was carried out under the following conditions: the mean pressure pm ¼ 25 bar, the working gas is helium, the heat power inputted into the HHE1 is Q1 ¼ 1400 W, and the cooling power is Qc ¼ 0 W. According to Fig. 10(a), the pressure amplitude and the hot end temperature T2 of the TWTAE regenerator increases with the increase of Q2. However, the hot end temperature T1 of the SWTAE regenerator decreases with the increase of Q2. The reason for this is that the thermoacoustic conversion effect increases as the oscillation becomes stronger. Hence, more heat power will be transformed into acoustic power and be extracted from the HHE1 leading to the decrease of the T1. Similarly, the cold end temperature Tc of the TWTAC regenerator decreases with the increase of Q2 in Fig. 10(b) because the oscillation becomes stronger. According to Fig. 10(b), the ambient end temperature Ta of the TWTAC regenerator increases as Q2 increases. There are three main reasons for the increase of Ta: (1) the increase of T2 leads to higher radiation heat losses as well as higher heat conduction losses along the wall of TBT2, from the HHE2 to the AHE3; (2) the stronger oscillation will pump more heat from the cold end to the AHE3; (3) the heat exchange capacity of the AHE3 is limited, and so the increase of the thermal load will lead to the increase of Ta.
5. Conclusion This paper proposes a novel configuration of a travelling-wave cooler driven by a cascade thermoacoustic engine. It consists of a standing-wave thermoacoustic engine, a travelling-wave thermoacoustic engine and a travelling-wave thermoacoustic cooler in series. The engines are source of acoustic power to drive the cooler. The novelty lies in four aspects: (1) it is more efficient in its simultaneous utilization of the thermoacoustic performance provided by both of the TWC and SWC; (2) acoustic power transfer determines the travelling-wave distribution within the system; (3) the TWC can influence the phase difference in the acoustic field; (4) the linear topology (in-series configuration) is easy to build and prevents the occurrence of Gedeon streaming. Modelling and simulation of the cascade arrangement, together with the experimental results, are described in this paper. In the device, an acoustic absorption element is adopted to introduce a higher acoustic power transfer, which increases the TWC in the acoustic field. It makes the regenerators of both the TWTAE and the TWTAC work in the travelling-wave phase region. The TWTAE regenerator works in the region of 44.9 < 4z < 18.3 , and the TWTAC regenerator works in the region of 20.0 < 4z < 41.8 . It is indicated that the regenerator of the TWTAE realized the conversion from thermal to acoustic energy and the TWTAC regenerator pumps heat from the cold end, which are achieved by both the standing-wave and the travelling-wave. The total efficiency of the thermoacoustic device is improved. According to the calculation, the thermoacoustic conversion efficiencies of the three stages can reach h1 ¼ 26.2%, h2 ¼ 34.3%, and COP ¼ 2.67, respectively. It can also obtain a cooling power of 366 W when the AAE absorbs the acoustic power of 406 W. Based on the new idea of system configuration and the results of numerical analysis, a cascade thermoacoustic engine driving cooler
H. Kang et al. / Applied Thermal Engineering 59 (2013) 223e231
has been designed, manufactured and tested. The total length of the device is about 3.1 m. It uses helium as working gas and operates at frequency of 175 Hz. At the operating point with the mean pressure of 25 bar and the total inputting heat power of 2500 W, the experimental cooler provides a no-load temperature difference of 103 C and a cooling power of 282 W at the cooling temperature difference of 0 C. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant no. 51006009 and 51076016), the Natural Science Foundation of Beijing, China (Grant No. 3112021), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101101120009). References [1] N. Rott, Damped and thermally driven acoustic oscillations in wide and narrow tubes, Z. Angew. Math. Phys. 20 (1969) 230e243. [2] N. Rott, Thermally driven acoustic oscillations, part II: stability limit for helium, Z. Angew. Math. Phys. 24 (1973) 54e59. [3] N. Rott, Thermally driven acoustic oscillations, part III: second-order heat flux, Z. Angew. Math. Phys. 26 (1975) 43e49. [4] N. Rott, G. Zouzoulas, Thermally driven acoustic oscillations, part IV: tubes with variable cross section, Z. Angew. Math. Phys. 27 (1976) 197e224.
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[5] P.H. Ceperley, A pistonless stirling engine-the travelling wave heat engine, J. Acoust. Soc. Am. 66 (1979) 1508e1513. [6] P.H. Ceperley, Gain and efficiency of a short traveling wave heat engine, J. Acoust. Soc. Am. 77 (1985) 1239e1244. [7] G.W. Swift, Thermoacoustics: A Unifying Perspective for Some Engines and Refrigerators, Acoustical Society of America, New York, 2002. [8] S. Backhaus, G.W. Swift, A thermoacoustic-Stirling heat engine, Nature 399 (1999) 335e338. [9] Y. Ueda, T. Biwa, U. Mizutani, Experimental studies of a thermoacoustic Stirling prime mover and its application to a cooler, J. Acoust. Soc. Am. 115 (2004) 1134(3). [10] B. Yu, E.C. Luo, S.F. Li, Experimental study of a thermoacoustically-driven traveling wave thermoacoustic refrigerator, Cryogenics 51 (2011) 49e54. [11] F.Z. Zhang, Thermodynamics Cycle Mode Analysis of Thermoacoustic Engine and Design of Miniaturization Thermoacoustic Refrigerator, Dissertation for the Degree of Doctor of Engineering, Harbin, 2005. [12] G.W. Swift, Thermoacoustic engines, J. Acoust. Soc. Am. 84 (1988) 1145e1180. [13] J. Wheatley, T. Hofler, G.W. Swift, An intrinsically irreversible thermoacoustic heat engine, J. Acoust. Soc. Am. 74 (1983) 153e170. [14] T. Biwa, Y. Tashiro, U. Mizutani, Experimental demonstration of thermoacoustic energy conversion in a resonator, Phys. Rev. E 69 (2004) 066304(6). [15] H.F. Kang, Q. Li, G. Zhou, Thermoacoustic effect of travellingestanding wave, Cryogenics 49 (2009) 112e119. [16] H.F. Kang, Q. Li, G. Zhou, Optimizing hydraulic radius and acoustic field of the thermoacoustic engine, Cryogenics 50 (2010) 450e458. [17] H.F. Kang, Q. Li, G. Zhou, Heat driven thermoacoustic refrigerator based on travelling-standing wave, Energy Conversion Manag. 51 (2010) 2103e2108. [18] W.C. Ward, C. John, G.W. Swift, Design Environment for Low-amplitude Thermoacoustic Energy Conversion (DELTAEC) (2008). Software and users guide are available online from: http://www.lanl.gov/thermoacoustics/. [19] D.L. Gardner, G.W. Swift, A cascade thermoacoustic engine, J. Acoust. Soc. Am. 114 (2003) 1905e1919.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Thermoacoustic travelling-wave cooler driven by a cascade thermoacoustic engine Huifang Kang a, *, Fan Jiang a, Hongfei Zheng a, Artur J. Jaworski b a b
Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China Department of Engineering, University of Leicester, University Road, Leicester LE1 7RH, UK
h i g h l i g h t s Cascade thermoacoustic engine driving a cooler with linear topology is proposed. The best features of standing and travelling wave devices are used simultaneously. An acoustic absorption element is adopted to adjust the acoustic field. Principles and functionality demonstrated through modelling and experimentation.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 November 2012 Accepted 26 May 2013 Available online 5 June 2013
This paper proposes a novel configuration of a cooler driven by a cascade thermoacoustic engine. It consists of a standing-wave thermoacoustic engine, a travelling-wave thermoacoustic engine and a travelling-wave thermoacoustic cooler in series. The engines provide acoustic energy to drive the cooler. The three main components have a linear topology without the need for using feedback loops. Modelling and simulation of the cascade arrangement, together with the experimental results, are described in this paper. In the presented system, an acoustic absorption element is adopted to induce a higher acoustic power transfer, which increases the travelling-wave component in the acoustic field. It makes the regenerators of both the travelling-wave engine and cooler work in the travelling-wave phase region and allows the thermoacoustic performance offered by both the travelling-wave and the standing-wave to be utilized more effectively. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Thermoacoustic Engine Cooler Travelling-standing wave Cascade
1. Introduction Thermoacoustic energy conversion technologies have undergone a substantial development over the recent four decades thanks to the pioneering work of Rott [1e4], Ceperley [5,6] and subsequent demonstration projects undertaken at Los Alamos National Laboratory [7,8]. The thermoacoustic engine (TAE) converts thermal to acoustic energy and this can be used to drive the thermoacoustic cooler (TAC). The system combining the TAE and TAC is called a cooler driven by thermoacoustic engine [9,10]. In such arrangement, when a steep temperature gradient is set up along the regenerator of TAE, the acoustic wave with the oscillating pressure p1 ¼ j:p1 j:eiðutþ4z Þ and the oscillating velocity u1 ¼ j:u1 j:eiut is excited. Here u is the angular frequency and 4z is the leading phase of p1 relative to u1. When the acoustic wave
* Corresponding author. Tel.: þ86 10 68914303; fax: þ86 10 68949859. E-mail address: [email protected] (H. Kang). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.05.044
passes through the regenerator of TAC, a temperature gradient is established along its length corresponding to a certain coefficient of performance (COP). The acoustic wave drives gas parcels in the thermoacoustic regenerators to experience a certain thermodynamic cycle. Then, the conversion from thermal to acoustic energy and the heat pumping occurs without any moving parts in the system. Compared with traditional thermodynamic systems, the cooler driven by thermoacoustic engine has three main advantages: (1) It has a simple structure, no moving parts, low cost of manufacture, and high reliability; (2) By using inert gases as working fluids, this kind of machines is environmentally friendly; (3) The thermoacoustic devices can be driven by low quality energy source such as the exhausting thermal energy and the solar energy, so it is significant for remote rural areas where there may be no access to electricity grid. In thermoacoustic energy conversion processes, the key mechanism is a heat transfer interaction that takes place between the gas parcels undergoing oscillatory motion and a solid material along which the gas oscillations occur. In thermoacoustic engines, a
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spontaneous acoustic wave is excited which transports heat from the hotter to a cooler place of the solid by a cyclically compressing and expanding gas parcel; in thermoacoustic coolers the acoustically induced compression and expansion of gas parcels leads to heat pumping effects in the solid. However the exact nature of the thermodynamic cycle depends upon the phase difference between the oscillating pressure and the oscillating volume of the gas parcel [11], or in other words (using the equation of state for the gas) between the oscillating pressure p1 and the oscillating temperature T1. The relationship between the parameters of the oscillating gas parcel is shown in Fig. 1. The oscillating temperature T1 is determined by the thermo-relaxation and the oscillating displacement x which is controlled by u1. Thus, the type of the thermodynamic cycle is influenced by the thermo-relaxation and 4z. The early work concerned mainly a variety of standing wave devices [12,13] which were built based on the thermoacoustic theory. In the standing wave devices, gas parcels with 4z ¼ (2nþ1) 90 realize the conversion between thermal and acoustic energy using a thermodynamically irreversible process defined by an imperfect thermal contact between the working gas and the porous solid material, traditionally referred to as a stack.1 Although the standingwave devices are relatively simple to build, their efficiency is limited due to the irreversible thermodynamics on which their thermoacoustic conversion processes rely. The alternative to the standing-wave devices are travellingwave devices [5,6,8]. These are usually harder to control in terms of the acoustic wave properties, and traditionally have been more difficult to design and built. However, in such devices, gas parcels with 4z ¼ 2n 90 realize a reversible thermodynamic cycle due to a “perfect” thermal contact between the gas parcels and the porous solid material (traditionally referred to as a regenerator). In theory the “perfect” contact would require infinitesimally hydraulic radius of the regenerator, but this would inevitably lead to infinite viscous losses. Therefore in practice a finite hydraulic radius is chosen as a fraction (e.g. typically 0.2) of the thermal penetration depth, which gives acceptable viscous losses but at the same time sufficient thermoacoustic gain and improved efficiency. Subsequently, in practical travelling-wave devices, the oscillating temperature of gas parcels lags their oscillating displacement. Therefore, the phase difference between the oscillating temperature and pressure deviates from (2n þ 1) 90 because of the thermo-relaxation effects. Under such conditions, in order to improve the thermoacoustic gain and efficiency, the travelling-standing wave phase may be required to match the phase deviation due to the thermorelaxation. In practical thermoacoustic systems, there is neither pure travelling-wave mode nor pure standing-wave mode. The thermoacoustic effect is the result of the combined interaction of the travelling-wave component (TWC) and the standing-wave component (SWC) in the thermoacoustic system. The functions of the SWC are energy storage and energy conversion, while the functions of the TWC are energy transfer and energy conversion. In the thermoacoustic engine (TAE), the generated acoustic energy can be transferred by the TWC or stored as the SWC. In the thermoacoustic cooler (TAC), the consumed acoustic energy can be supplied by the TWC or compensated from the stored acoustic energy in the SWC. Biwa [14] demonstrated thermoacoustic energy conversions which make full use of the TWC and SWC of the acoustic field induced in the resonator. It is claimed that, in order to achieve high
1
In the context of subsequent discussion on the travelling-standing wave concept, and for simplicity this paper will use terminology “regenerator”, for both standing and travelling wave devices considered here.
Thermo-relaxation u
T
p
p
V
x
Thermodynamic cycle
Fig. 1. The relationship between the parameters of the oscillating gas parcel.
gain and efficiency, one has to choose an optimum 4z which can make both the TWC and SWC contribute to the amplification of the acoustic field intensity. However a new problem arises e namely, if the leading phase 4z can be chosen in the region of 180 4z 180 for the travelling-standing wave, then how to choose the optimum 4z for the regenerator. Kang et al. [15] investigated the thermoacoustic effect in the travelling-standing wave. The results of their analysis show that to gain a higher acoustic power and efficiency, the hot end of the regenerator in an engine should be close to the pressure anti-node (PAN), and the TWC should propagate from the ambient end to the hot end. To gain a higher cooling power and coefficient of performance, the ambient end of the regenerator in a cooler should be close to the PAN, and the TWC should propagate from the ambient end to the cold end. Furthermore, Kang et al. [16] analyzed the influence of the parameters of the acoustic field and the regenerator structure on the thermoacoustic conversion and identified the optimum condition for the thermoacoustic conversion. The optimal 4z depends on the hydraulic radius because 4z needs to balance the phase deviation generated by thermo-relaxation. Based on the analysis of the thermoacoustic performance in the travelling-standing wave, Kang et al. [17] designed a heat driven thermoacoustic cooler which utilized thermoacoustic effects of both the TWC and SWC. This device has the following advantages: (1) It utilizes simultaneously the thermoacoustic performance contributed by both the TWC and SWC; (2) The acoustic power produced by the engine drives the cooler directly; (3) The feedback tube realizes the recycling process of the residual acoustic power out of the cooler. However, the toroidal topology is more difficult to build than the linear one and also suffers from a circulating second-order mass flow, referred to as Gedeon streaming, which can reduce the efficiency. Gedeon streaming [8] has been successfully suppressed by exploiting the time-averaged pressure gradient developing in an oscillating flow through an asymmetric channel, however this consumes acoustic power. In addition, fabricating asymmetric channels adds complexity that is undesirable in commercial devices. Thus, this paper proposes a novel configuration of a cooler driven by a cascade thermoacoustic engine, as shown in Fig. 2. It consists of a standing-wave thermoacoustic engine (SWTAE), a travelling-wave thermoacoustic engine (TWTAE) and a travellingwave thermoacoustic cooler (TWTAC) in series. The two engines are the source of acoustic power to drive the cooler. In the device, an acoustic absorption element (AAE) is used to introduce a higher acoustic power transfer, which increases the TWC in the acoustic field. It makes the regenerators of both the TWTAE and the TWTAC work in the travelling-wave phase region and utilize effectively the thermoacoustic performance contributed by both the TWC and SWC, which improves the overall efficiency of the device. 2. Apparatus A prototype cooler driven by a cascade thermoacoustic engine has been constructed according to the present concept and the detailed modelling results. Fig. 3 is a photograph of the device. The pressure container elements are built out of 304 grade of stainless-
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225
Fig. 2. Schematic of the cascade system considered in this paper.
Fig. 3. Photograph of the device.
steel for strength. Because the height of the laboratory room is less than 3.1 m which is the total length of the device, a 90 bend is used to reduce the height of the device. However, the 90 bend will increase the additional acoustic power dissipation. According to Ref. [7], the estimated loss of acoustic power due to bend is 0.21 W which is negligible compared to power levels described in the paper. In the following description of the apparatus, the length reported is along the acoustic axis, and diameters reported are inside diameters. The upper portion of the resonator located above SWTAE and shown in Figs. 2 and 3 is designed for the minimum dissipation of acoustic power without consideration for size. The upper compliance at the top consists of two flanged hemi-spherical end caps, the flanges connected with bolts. It has a volume of 0.014 m3. A 0.14 m long cone provides a smooth transition between the lower end of the upper compliance and the upper resonator. The cone lowers the acoustic velocity of the gas entering the upper compliance, reducing the minor-loss dissipation of acoustic power. The most important quantitative details of the construction of the three stages are presented in Table 1. The uppermost component, the AHE1 is a parallel plate-type heat exchanger shown in Fig. 4. The working gas oscillates vertically through the space between plates, while the ambient temperature water flows crosswise in the channels drilled perpendicular to the heat exchanger axis. Below this heat exchanger, there is a regenerator which is made out of stainless-steel screens disks with the mesh number 30 and the wire diameter of 0.305 mm. The electrically heated hot heat exchanger (HHE1) is located below the regenerator. Part of the cross sectional area of HHE1 is occupied by a parallel plate structure, while the remaining part is solid metal with holes prepared
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Table 1 Dimensions and other details of the three stages of the device.
SWTAE: AHE1 Reg1 HHE1 ST TBT1 TWTAE: AHE2 Reg2 HHE2 ST TBT2 TWTAC: AHE3 Reg3 CHE AAE
Length (mm)
Diameter (mm)
30 90 42
89 89 89 40 89e40e76
84 23 25 28 46 23 25 20
76 76 76 40 76e40e76 76 76 76 35
Mesh
Porosity
30
0.75
70
0.70
200
0.67
70
0.70
250
0.69
70
0.70
Number of screen
2
2
8
Material
Copper Stainless-steel Stainless-steel Stainless-steel Stainless-steel Copper Stainless-steel Stainless-steel Stainless-steel Stainless-steel Copper Stainless-steel Copper Stainless-steel Fig. 5. Detailed drawing of the hot heat exchanger.
for cartridge heaters, as shown in Fig. 5. The oscillating working gas passes through the space between plates, and the 6.35 mm diameter transverse holes hold electric cartridge heaters of various lengths corresponding to the lengths of holes. The taper angle of the 1st-stage thermal buffer tube (TBT1) was designed to suppress Rayleigh streaming, and the stainless-steelscreen flow straighteners (FS) at the end of the thermal buffer tube were designed to prevent jet-driven streaming. Together, these features are intended to encourage thermally stratified oscillating flow in the thermal buffer tube, without convection of heat from hot to ambient. The TWTAE and the TWTAC stages are similar in character to the SWTAE, with parallel plate-type ambient heat exchangers, electrically heated hot heat exchangers, parallel plate-type cold heat exchangers, and tapered thermal buffer tubes between stainlesssteel-screen flow straighteners. The acoustic absorption element (AAE) in the end of the lower resonator is in the form of a few layers of mesh screen. The lower compliance with a volume of 0.0027 m3 is similar in character to upper compliance. In experiments, the pressure data have been acquired and analyzed in real time by a computer. As illustrated in Fig. 2, eight calibrated pressure sensors, labelled P1 to P8, are installed in the system in order to obtain the distribution of the acoustic field. The pressure data acquisition system is comprised of the pressure
Fig. 4. Detailed drawing of the ambient heat exchanger.
sensors, a data acquisition board, a computer with the data acquisition program developed in-house. The pressure sensors are the piezoelectric type (CY-YD 208), supplied by Sinocera Piezotronics, Inc., China. The data acquisition board is AC1810, 12bit precision and 10 kHz sampling frequency. The output voltage from the piezoelectric transducer is amplified by a charge amplifier and then sent to the AC1810 board connected to the computer. The pressure signal can be displayed on the computer screen using the data acquisition program. Also four calibrated NiCreNiSi thermocouples, labelled T1, T2, Ta and Tc, are installed in the system as shown in Fig. 2. The thermocouple T1 is located at the hot end of the SWTAE regenerator; T2 is located at the hot end of the TWTAE regenerator; Ta is located at the ambient end of the TWTAC regenerator; and Tc is located at the cold end of the TWTAC regenerator. The temperature data are measured with 1 C accuracy. Heating power is adjusted by changing the supply voltage (V) to the heaters and is displayed by a digital voltmeter. The current (I) is measured by the ammeter, and then the heating power can be obtained as product of I and V. The cooling power is controlled and measured through the same method. 3. Simulation and analysis In order to perform a more detailed analysis, a specialized design tool referred to as DeltaEC (Design Environment for Lowamplitude ThermoAcoustic Energy Conversion) and developed by Los Alamos National Laboratory is employed [18]. Its calculation capabilities and precision in modelling thermoacoustic devices have been validated by many researchers [8,19]. DeltaEC solves the one-dimensional wave equation based on the usual low-amplitude acoustic approximation. It is suitable for the standing wave, the travelling wave and the complex acoustic field of standing-travelling wave. It can be used in the design process in order to optimize a thermoacoustic system, or to predict the performance of an existing build of a thermoacoustic device. DeltaEC integrates numerically the acoustic wave equation and energy equation segment by segment throughout the whole device based on the low amplitude acoustic approximation and the sinusoidal time dependence of the variables [18]. In the current work, DeltaEC is used to simulate the acoustic field and the acoustic power flow in the thermoacoustic device under study. In the system described in this paper, there are three energy conversion units, and each unit has its own efficiency. It is hard to
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make the three stages reach their highest efficiency at the same time. For convenience, the total performance effect (TPE) of the device is defined as the cooling power divided by the total heat input. In the device described here, it is can be expressed as:
TPE ¼
Qc Q1 þ Q2
(1)
where Qc is the cooling power, Q1 and Q2 are heat inputs delivered via resistive heating in the two engines. To obtain the highest TPE, the DeltaEC model is used to optimize the dimensions of each segment one by one. Because most of the parameters will influence the acoustic field, and subsequently influence the optimization results of the other parameters, all of the optimization steps are executed again and again, until the changes in the optimization results are negligible. The process of design and optimization is quite involved and would require a separate paper to describe all the detailed steps. Therefore, for convenience, the simulation results discussed in this section are based on the final design of the prototype, with dimensions given in the last section. Furthermore, the calculation was carried out under the condition as follows: Helium is used as working gas, the mean pressure is 2.5 MPa, the temperature of the two hot heat exchangers is maintained at 700 K, the temperature of the cold heat exchanger is 273 K, while the temperature of the three ambient heat exchangers is 300 K. In the calculation, it is found that it is impossible to realize the high efficient cooling by adjusting the lengths and radii of the device elements. The reason for this is that the TWC is too small. The region with high efficiency is too narrow [16] and the acoustic field in the TWTAC regenerator is similar to the standing-wave. Moreover, the AAE (in the form of a few layers of mesh screen) is installed in the lower resonator to absorb acoustic energy. When the AAE dissipates the acoustic energy due to viscosity and converts acoustic energy into heat, the balanced distribution of acoustic energy in the system is broken. Subsequently, the acoustic energy transfer happens. The acoustic power will be transported from the engine, where the acoustic energy is generated, to the AAE, where
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the acoustic energy is absorbed and dissipated. Then the TWC, on which the acoustic power transfer relies, increases. The influence of AAE on the acoustic power, the acoustic field and the thermoacoustic conversion performance is shown in Fig. 6. In Fig. 6(a), the acoustic power absorbed in by the AAE increases when the length LR of the AAE increases. Subsequently, the TWC increases and the length of the region with the travelling-wave phase increases [16]. According to Fig. 6(b), as LR increases, the location of 4z ¼ 0 moves to near the TWTAC, and 4z of the TWTAC regenerator comes closer to 0 . 4z of the TWTAE regenerator decreases close to 0 and then drops to the negative phase difference. 4z of the SWTAE changes a little, but the efficiency of the SWTAE decreases because the impedance increases. As illustrated in Fig. 6(c), the efficiency of TWTAE reaches its maximum (h2 ¼ 35.0%) when LR ¼ 6.33 mm. According to Fig. 6(b), the TWTAE regenerator is in the region of 39.7 < 4z < 3.84 . The coefficient-ofperformance of TWTAC reaches its maximum (COP ¼ 2.58) when LR ¼ 1.32 mm. According to Fig. 6(b), the TWTAC regenerator is in the region of 1.11 <4z < 23.0 . The TPE reaches its maximum (TPE ¼ 0.184) when LR ¼ 0.92 mm as shown in Fig. 6(d). Referring to Fig. 6(b) and (c), when LR ¼ 0.92 mm, the performance and 4z of the three stages can be obtained as follows: the efficiency of SWTAE is h1 ¼ 26.2% and its working phase region is 91.0 < 4z < 74.6 ; the efficiency of TWTAE is h2 ¼ 34.3% and its working phase region is 44.9 < 4z < 18.3 ; the COP of TWTAC is COP ¼ 2.67 and its working phase region is 20.0 < 4z < 41.8 . Therefore, the optimal system with LR ¼ 0.92 mm is selected to analyze the acoustic field and the work flow in the system which is illustrated in Fig. 7. Fig. 7(a) shows the pressure amplitude distribution along the device which is around 3.1 m long. The maximum of pressure amplitude jp1 j ¼ 1:12 105 Pa appears between the SWTAE and TWTAE. Although there is the flow resistance of the regenerator, the changing trends of the pressure amplitude in the SWTAE and TWTAE are different. The pressure amplitude grows along the SWTAE regenerator, but drops along the TWTAE regenerator. The reason for this is that the changing trend of the pressure amplitude without the flow resistance is determined by the boundary
Fig. 6. The acoustic power absorbed by the AAE, the acoustic field and the thermoacoustic conversion performance versus the length of the AAE LR. (a) the acoustic power absorbed by the AAE; (b) the phase difference at the ends of three regenerators; (c) the efficiency h1 of SWTAE, the efficiency h2 of TWTAE, and the coefficient-of-performance COP of TWTAC; (d) The total performance effect (TPE) of the device defined as the cooling power versus the total inputting heat power.
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Fig. 7. Pressure amplitude (a), volumetric velocity (b), acoustic impedance (c), phase difference (d) and acoustic power flow (e) distribution along the system.
conditions. The pressure amplitude reaches the peaks at the stagnation points of the standing-wave where the oscillating velocity reaches its minimum. There are three stagnation points in the system. Two stagnation points are the two ends of the device, while the third one is located between the TWTAE and TWTAC. In the SWTAE, the flow resistance of the regenerator just makes the pressure amplitude increase more slowly than that without the flow resistance. In the TWTAE, TWTAC and AAE, the flow resistance makes the pressure amplitude drop more steeply than that without the flow resistance. The pressure amplitude changes smoothly along all other parts. Fig. 7(b) shows the distribution of the volumetric velocity along the device. There are two maxima and three minima along the system. One maximum of the volumetric velocity is in the upper resonator, while the other is in the lower resonator. Two minima are located at the two ends of the system, while the third one is in the thermal buffer tube (TBT1) between the SWTAE and TWTAE where the maximum of the pressure amplitude is located. The fact that the velocity amplitude approaches zero near the regenerators will contribute to reducing the viscous loss, which will help to improve their efficiency. The small volumetric velocity within the regenerator is preferred to avoid high viscous dissipation. It can also be seen that the volumetric velocity increases significantly along the regenerator of the TWTAE. This is due to the sharp temperature gradient along the regenerator and the acoustic power generated by the TWTAE. Furthermore, at the location of the TWTAC, there is a sudden decrease of the volumetric velocity because the temperature drops along the regenerator and the acoustic power is consumed to pump heat from the cold heat exchanger. Along all other parts, the volumetric velocity changes smoothly. Fig. 7(c) shows the acoustic impedance along the system. It can be seen that the acoustic impedance is highest ðjZj ¼ 19r0 c=Ag Þ at
the ambient end of the TWTAE. The three stages are located in the high acoustic impedance region which will decrease the viscous dissipation. The impedance drops quickly because the pressure amplitude decreases (see Fig. 7(a)) while the volumetric velocity increases sharply in the regenerator of the TWTAE (see Fig. 7(b)). The impedance increases slightly because the volumetric velocity decreases in the regenerator of TWTAC (see Fig. 7(b)). Fig. 7(d) illustrates the phase difference 4z along the system. There are three points where 4z ¼ 0 . Two points are in the upper and lower resonators where the pressure amplitude approaches zero, while the third one is in TBT1 where the maximum of the pressure amplitude is located. It can be found that the regenerators of both the TWTAE and the TWTAC are in the near travelling wave phase region which will benefit the thermoacoustic conversion. The TWTAE regenerator works in the region of 44.9 < 4z < 18.3 , and the TWTAC regenerator works in the region of 20.0 < 4z < 41.8 . According the analysis of Ref. [12], it is indicated that the TWTAE regenerator realizes the conversion from heat to acoustic energy and the TWTAC regenerator pumps heat from the cold end, the functions which are achieved by both the standingwave and travelling-wave. Fig. 7(e) shows the acoustic power flow along the system. It can be seen that the acoustic power flow changes its direction at x ¼ 1.3 m where the regenerator of the SWTAE is located. This means that the acoustic energy generated in the SWTAE is divided into two parts: one part is transferred along x direction to feed the acoustic power dissipation in the upper compliance, the upper resonator and the ambient heat exchanger (AHE1); the other part is transferred along þ x direction. The calculation data shows that the SWTAE can produce a net acoustic power of about 313 W at an inputting heat power of 1195 W, corresponding to a thermoacoustic conversion efficiency of h1 ¼ 26.2%. The acoustic power of 31 W enters the AHE1 and decreases along x direction. After the AHE1
H. Kang et al. / Applied Thermal Engineering 59 (2013) 223e231
which dissipates around 11 W, the remaining 20 W is dissipated in the upper resonator and compliance. The acoustic power of 282 W flows out from regenerator of SWTAE, and is transferred along þ x direction. After being slightly dissipated in the TBT1 and the ambient heat exchanger (AHE2) of the TWTAE, the acoustic power of 265 W enters the ambient end of the TWTAE regenerator and increases along the regenerator with a positive temperature gradient established by the externally supplied heat through the hot heat exchanger (HHE2). Then, an acoustic power of 570 W is gained at the hot end of the TWTAE regenerator. The calculation data shows that the TWTAE can produce a net acoustic power of about 305 W at the inputting heat power of 888 W, corresponding to a thermoacoustic conversion efficiency of h2 ¼ 34.3%. After being slightly dissipated in the TBT2 and the ambient heat exchanger (AHE3) of the TWTAC, the acoustic power of 543 W is fed into the ambient end of the TWTAC regenerator and pumps heat directly. It is reduced gradually due to the consumption of acoustic power for heat pumping from the cold end of the regenerator. When it comes out of the cold heat exchanger (CHE) with a value of 406 W, the acoustic power consumed by the TWTAC is 137 W. The net cooling power of the TWTAC given by the calculation is about 366 W. It implies that the TWTAC achieves COP ¼ 2.67 at the cooling temperature of 0 C. 406 W of the residual acoustic power enters the lower resonator. The lower resonator, the AAE and the lower compliance dissipate acoustic power of around 6 W, 398 W, and 2 W respectively. These calculation results show that the TPE reaches TPE ¼ 0.184 at the cooling temperature of 0 C when the AAE absorbs the acoustic power of 398 W. Fig. 7(d) shows that 4z changes sharply in the region of 0.38 m < x < 0.46 m, and the travelling wave phase region is relatively narrow. This is due to the fact that the acoustic power flowing along x direction is small and the TWC is small. Hence the acoustic field in the region of 0 < x < 1.3 m is similar to the standing wave. Moreover, 4z changes sharply [16] in the region of 0.38 m < x < 0.46 m. 4z decreases slowly at first and then sharply in the region of 2.1 m < x < 2.73 m. The reason for this is that the acoustic power is dissipated strongly in the AAE. Firstly, the acoustic power is about 406 W. The intensity of travelling wave is sufficiently high to transfer the acoustic power which causes a slow change of 4z. After the AAE with acoustic power absorption of 398 W, the residual acoustic power is small. So the TWC is small, and the acoustic field in the region of 2.5 m < x < 3.1 m is similar to the standing wave. Subsequently, 4z changes sharply in the region of 2.5 m < x < 2.6 m.
229
Fig. 8. The pressure amplitude comparison between the experiments and the simulation. Points are measured values, and lines are calculations.
measured frequency of 175 Hz and calculated frequency of 173 Hz is about 1.3%. Fig. 9 gives the hot end temperatures of the regenerators of the two engines, the cooling power and the pressure amplitude measured by P4 as a function of the number of screens in the AAE. The experiment was carried out under the following conditions: the mean pressure pm ¼ 25 bar, the working gas is helium, the heat power inputted into the HHE1 is Q1 ¼ 1400 W, the heat power inputted into the HHE2 is Q2 ¼ 1100 W, and the temperature difference in the regenerator of TWTAC is DT ¼ 0 C. As shown in Fig. 9(a), the hot end temperature T1 of the SWTAE regenerator increases as the number of screens in the AAE increases. The reason for this is that the thermoacoustic conversion efficiency h1 of the SWTAE decreases as shown in Fig. 6(c). So an increased inputting heat cannot be transformed into acoustic
4. Experimental results and discussion To test the practical performance of the whole system, a series of experiments have been conducted. Under the condition of Q1 ¼ 600 W and Q2 ¼ 500 W, an acoustic oscillation starts spontaneously when the hot end temperature of regenerators rises above the critical value T1 ¼ 297 C and T2 ¼ 312 C, respectively. As a first step, the comparison between the measurement and calculations is provided in order to acquire the confidence in the calculation. In particular, the acoustic pressure will form the basis for trying to understand the velocity, the leading phase 4z, and the acoustic power levels within the device. Fig. 8 shows the pressure amplitude measured by the pressure sensors under the condition of the mean pressure of 25 bar, helium as working gas, the HHE1’s temperature of 420 C, the HHE2’s temperature of 435 C, and the CHE’s temperature of 0 C. The disagreement between measured and calculated pressures in Fig. 8 is smaller than 6%. The operating frequency of 175 Hz was measured by a Stanford Research model SR-830 DSP lock-in amplifier. The disagreement between the
Fig. 9. The hot end temperatures of regenerators, the cooling power and the pressure amplitude measured by P4 as the function of the number of screens in the AAE.
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H. Kang et al. / Applied Thermal Engineering 59 (2013) 223e231
power and accumulates in the HHE1 leading to the increase of T1. Similarly, with the increase of the number of screens, the hot end temperature T2 of the TWTAE regenerator decreases at first and then increases, which is similar to the behaviour of h2. According to Fig. 9(b), the maximum cooling power is 282 W when the AAE made out of 8 pieces of screens were added in the end of the lower resonator. However, the measured cooling power is much lower than that calculation, because the DeltaEC model just considers the heat involved in the thermoacoustic conversion, and doesn’t consider the heat losses (such as the heating load introduced by acoustic dissipation in the resonators, the thermal radiation loss, the heat conduction loss along the tube wall, and so on) that decrease the measured cooling power. As shown in Fig. 9(b), the pressure amplitude decreases with the increase of the number of screens in the AAE, which can be explained by the acoustic dissipation in the system. In most parts of the thermoacoustic system, dTm/dx ¼ 0 and the acoustic power produced by the engines is dissipated in the system. According to Eq. (8) of Ref. [15], the acoustic power dissipation is expressed as dE2 dx
¼ 12 urm Im½fv2ju1 j2 12 g1 g j1fv j (
¼
1 Im½fv jZN j2 j1fv j2
uIm½fk ~ 2 pm jp1 j
ðg 1ÞIm½fk
)
ujp1 j2 2pm g
(2)
where g is the ratio of isobaric specific heat to isochoric specific heat, pm is the mean pressure of the fluid, rm is the mean density of the working gas, and fv, fk are the cross-sectional averaged Rott’s functions which depend on the specific channel geometry under consideration, ZN is the normalized impedance defined as,
ZN ¼
p1 =u1 rm c
Fig. 10. The temperatures measured by the thermocouples and the pressure amplitude measured by P4 with different heat power inputted into HHE2 when the heat power inputted into the HHE1 is Q1 ¼ 1400 W.
(3)
According to Eq. (2), the acoustic power dissipation is proportional to jp1 j2 . With the increase of the number of screens, there is more acoustic power dissipated in the AAE and the acoustic power dissipated in the other elements of the system decreases. Subsequently, the pressure amplitude will decrease to maintain the balance between the generated and dissipated acoustic power in the system. Fig. 10 gives the temperatures measured by the thermocouples and the pressure amplitude measured by P4 with different heat power Q2 supplied into the HHE2. The experiment was carried out under the following conditions: the mean pressure pm ¼ 25 bar, the working gas is helium, the heat power inputted into the HHE1 is Q1 ¼ 1400 W, and the cooling power is Qc ¼ 0 W. According to Fig. 10(a), the pressure amplitude and the hot end temperature T2 of the TWTAE regenerator increases with the increase of Q2. However, the hot end temperature T1 of the SWTAE regenerator decreases with the increase of Q2. The reason for this is that the thermoacoustic conversion effect increases as the oscillation becomes stronger. Hence, more heat power will be transformed into acoustic power and be extracted from the HHE1 leading to the decrease of the T1. Similarly, the cold end temperature Tc of the TWTAC regenerator decreases with the increase of Q2 in Fig. 10(b) because the oscillation becomes stronger. According to Fig. 10(b), the ambient end temperature Ta of the TWTAC regenerator increases as Q2 increases. There are three main reasons for the increase of Ta: (1) the increase of T2 leads to higher radiation heat losses as well as higher heat conduction losses along the wall of TBT2, from the HHE2 to the AHE3; (2) the stronger oscillation will pump more heat from the cold end to the AHE3; (3) the heat exchange capacity of the AHE3 is limited, and so the increase of the thermal load will lead to the increase of Ta.
5. Conclusion This paper proposes a novel configuration of a travelling-wave cooler driven by a cascade thermoacoustic engine. It consists of a standing-wave thermoacoustic engine, a travelling-wave thermoacoustic engine and a travelling-wave thermoacoustic cooler in series. The engines are source of acoustic power to drive the cooler. The novelty lies in four aspects: (1) it is more efficient in its simultaneous utilization of the thermoacoustic performance provided by both of the TWC and SWC; (2) acoustic power transfer determines the travelling-wave distribution within the system; (3) the TWC can influence the phase difference in the acoustic field; (4) the linear topology (in-series configuration) is easy to build and prevents the occurrence of Gedeon streaming. Modelling and simulation of the cascade arrangement, together with the experimental results, are described in this paper. In the device, an acoustic absorption element is adopted to introduce a higher acoustic power transfer, which increases the TWC in the acoustic field. It makes the regenerators of both the TWTAE and the TWTAC work in the travelling-wave phase region. The TWTAE regenerator works in the region of 44.9 < 4z < 18.3 , and the TWTAC regenerator works in the region of 20.0 < 4z < 41.8 . It is indicated that the regenerator of the TWTAE realized the conversion from thermal to acoustic energy and the TWTAC regenerator pumps heat from the cold end, which are achieved by both the standing-wave and the travelling-wave. The total efficiency of the thermoacoustic device is improved. According to the calculation, the thermoacoustic conversion efficiencies of the three stages can reach h1 ¼ 26.2%, h2 ¼ 34.3%, and COP ¼ 2.67, respectively. It can also obtain a cooling power of 366 W when the AAE absorbs the acoustic power of 406 W. Based on the new idea of system configuration and the results of numerical analysis, a cascade thermoacoustic engine driving cooler
H. Kang et al. / Applied Thermal Engineering 59 (2013) 223e231
has been designed, manufactured and tested. The total length of the device is about 3.1 m. It uses helium as working gas and operates at frequency of 175 Hz. At the operating point with the mean pressure of 25 bar and the total inputting heat power of 2500 W, the experimental cooler provides a no-load temperature difference of 103 C and a cooling power of 282 W at the cooling temperature difference of 0 C. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant no. 51006009 and 51076016), the Natural Science Foundation of Beijing, China (Grant No. 3112021), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101101120009). References [1] N. Rott, Damped and thermally driven acoustic oscillations in wide and narrow tubes, Z. Angew. Math. Phys. 20 (1969) 230e243. [2] N. Rott, Thermally driven acoustic oscillations, part II: stability limit for helium, Z. Angew. Math. Phys. 24 (1973) 54e59. [3] N. Rott, Thermally driven acoustic oscillations, part III: second-order heat flux, Z. Angew. Math. Phys. 26 (1975) 43e49. [4] N. Rott, G. Zouzoulas, Thermally driven acoustic oscillations, part IV: tubes with variable cross section, Z. Angew. Math. Phys. 27 (1976) 197e224.
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