ANALYSIS OF STACK GEOMETRY EFFECTS ON THERMOACOUSTIC WITH PARTICLE IMAGE VELOCIMETRY (PIV) IRWAN SHAH BIN ALI

Transcription

1 ANALYSIS OF STACK GEOMETRY EFFECTS ON THERMOACOUSTIC WITH PARTICLE IMAGE VELOCIMETRY (PIV) IRWAN SHAH BIN ALI A project report submitted in partial fulfilment of the requirements for the award of the degree of Master of Engineering (Mechanical) Faculty of Mechanical Engineering Universiti Teknologi Malaysia MAY 2011

2 This report writing is dedicated to my family, respectable supervisor and my supportive friends. iii

3 iv ACKNOWLEDGEMENT I would like to take this opportunity to express my deepest gratitude and thanks to my research supervisor, Assoc. Prof. Dr. Normah Mohd Ghazali. Without her guidance and constructive ideas, I would not able to complete this research work. She always gives me the idea and knowledge in helping me to carry out the research in a better way. Her knowledge is very useful for me to do the research appropriately. I would also want to express my gratitude for the assistance and cooperation provided by all the Thermoacoustic Project members and Aeronautic Lab member. Their guidance and patience is very much appreciated. Besides, sincere thanks to all my friends for helping me directly or indirectly in making these projects a success. Finally yet importantly, my research would not be carried out smoothly without the continuing supports and encouragements given by my family, coursemates, and friends. I would like to express my sincere gratitude to them especially during the time in need.

4 v ABSTRACT Thermoacoustic refrigerator system generates cooling from acoustic energy. Acoustic waves interact with stack plates in the resonator tube of a thermoacoustic refrigerator to induce a temperature difference the significance of which depends on the solid-fluid interactions. In this study, the flow field at the end of the stack plates was investigated using Particle Image Velocimetry (PIV) method. Results were obtained from three stack configurations with different plate geometry. Effects of plate thickness and separation gap were determined by comparison of the velocity profile obtained from different configuration; separation gaps of 1mm and 3mm, and thickness of 1mm and 3mm. The ratio of separation gaps to viscous penetration depth was also determined to see the effect. For 1mm separation gaps, the ratio is about 6.27 and for 3mm it is There are differences in the velocity within the separation gaps of stack plates. The velocity in the separation gap region for the 1mm is smaller compared to the 3mm separation gap due to the smaller ratio. A vortex is observed near the edge of the plate with thickness 3mm and there is no clear vortices seen near the stack for the 1mm thickness. The Reynolds number based on the plate thickness of 1mm and 3mm are and respectively. Wakes were observed behind the 3mm thickness stack plates but none behind the 1mm plate.

5 vi ABSTRAK Sistem penyejukan termoakustik menghasilkan penyejukan dari tenaga akustik. Gelombang akustik berinteraksi dengan plat stack dalam tiub resonator pada sistem penyejukan termoakustik untuk menghasilkan perbezaan suhu yang bergantung kepada interaksi antara pepejal-cecair. Dalam tesis ini, medan aliran pada hujung plat stack dikaji menggunakan kaedah Particle Image Velocimetry (PIV). Keputusan diperoleh daripada tiga tatarajah stack dengan geometri plat yang berbeza. Kesan ketebalan plat dan jarak pemisah plat ditentukan dengan perbandingan profil kelajuan yang diperoleh daripada tatarajah berbeza; jarak pemisah 1mm dan 3mm, dan ketebalan 1mm dan 3mm. Nisbah jarak pemisah kepada kedalaman penembusan kelikatan juga dikira untuk melihat kesan. Untuk jarak pemisah 1mm, nilai nisbah adalah 6.27 dan untuk 3mm Terdapat perbezaan dalam halaju di antara jarak pemisah plat stack. Halaju pada kawasan jarak pemisah untuk 1mm adalah lebih rendah berbanding dengan 3mm jarak pemisah disebabkan oleh nisbah yang rendah. Vorteks kelihatan pada hujung plat untuk ketebalan 3mm dan tiada vortex jelas kelihatan berdekatan stack 1mm ketebalan. Nombor Reynolds berdasarkan pada ketebalan plat untuk 1mm dan 3mm adalah masing-masing dan Keracak kelihatan pada belakang 3mm ketebalan plat stack tetapi tiada pada belakang 1mm plat.

6 vii TABLE OF CONTENTS CHAPTER TITLE PAGE TITLE PAGE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF ABBREVIATIONS i ii iii iv v vi vii ix x xii 1 INTRODUCTION 1.1 Background of the Study 1.2 Literature Review 1.3 Problem Statement 1.4 Research Objective 1.5 Scope of Study THEORY 2.1 Introduction 2.2 Thermoacoustic Effects Standing wave Principle of Thermoacoustic Effect 2.3 Main Components of a Thermoacoustic Refrigerator Thermoacoustic Core

7 viii Resonator Tube Acoustic Driver Heat Exchangers METHODOLOGY 3.1 Introduction 3.2 Thermoacoustic Component Resonator Stack configuration Acoustic driver 3.3 PIV Measurement Setup Smoke Generator Optical Setup Flow Manager Software RESULTS AND DISCUSSION 4.1 Introduction 4.2 Velocity Profiles The Single Plate Effects of Time Effects of the Plate separation gap, h Effects of the Plate thickness, t CONCLUSION AND RECOMMENDATIONS 5.1 Conclusion 5.2 Recommendations REFERENCES 47

8 ix LIST OF TABLES TABLE NO. TITLE PAGE 1.1 Summary of literature review on PIV method Stack geometry for single and multiple plates Oscillating flow parameters at T Oscillating flow parameters at T1. 45

9 x LIST OF FIGURES FIGURE NO. TITLE PAGE 2.1 Schematic diagram of a standing wave (a) Schematic of resonance tube of thermoacoustic 14 refrigerator, (b) Pressure, velocity and temperature distributions along the resonance tube, (c) Heat pumping cycle in the magnified stack region visualized by considering the oscillation of one gas parcel (Wetzel and Herman, 2000). 2.3 Four steps thermoacoustic refrigeration cycle occurring for 15 one gas parcel with existence of stack (Tijani, 2001). 2.4 Overall heat transfer in stack plate of gas parcels in 15 thermoacoustic refrigerator (Nurudin, 2008). 2.5 Sketch of a thermoacoustic refrigerator Space between stack plate and plate thickness The flow chart of the study Resonator and resonator base Loudspeaker Function generator Power amplifier Connection between function generator, power amplifier 27 and loudspeaker. 3.7 Schematic illustration of the thermoacoustic refrigerator with 28 magnified view. 3.8 Smoke generator Camera Laser. 30

10 xi 3.11 Arrangement of camera and laser on the measurement field Experimental setup Block diagram of the experimental setup Velocity profile for 1mm thickness single plate Velocity profile for 3mm thickness single plate Velocity profile for configuration A Graph velocity against time interval at point 1-3 for 36 configuration A. 4.5 Velocity profile for configuration B Graph velocity against time interval at point 1-3 for 38 configuration B. 4.7 Velocity profile for configuration C Graph velocity against time interval at point 1-3 for 40 configuration C. 4.9 Comparison of velocity profile at T Graph of velocity against time intervals at point 1 and 2 for 42 configuration A and B Comparison of velocity profile at T Graph of velocity against time intervals at point 1 and 2 for 44 configuration A and C.

11 xii LIST OF ABBREVIATIONS BR - Blockage ratio C - Sound speed CCD - Charge coupled device CFC - Chlorofluorocarbons c p - Isobaric specific heat of the gas D r - Drive ratio f - Frequency HWA - Hot-wire anemometry 2y o - Separation gap K - Thermal conductivity L - Length LDA - Laser doppler anemometry UTM - Universiti Teknologi Malaysia PhD - Doctor of philosophy PIV - Particle image velocimetry Pr - Prandtl number P A - Peak pressure P m - Mean pressure p A - Pressure distribution Re d - Reynolds number SHM - Simple harmonic motion 2l - Thickness u A - Velocity distribution v - Velocity w - Width x - Distance x c - Stack center position

12 xiii x td - Tidal displacement λ - Wavelength λ ac - Wavelength of the standing wave Δx - Stack of plates of length ΔT - Temperature difference ω - Angular frequency δ α - Thermal penetration depth δ v - Viscous penetration depth ρ m - Density μ - Dynamic viscosity β - Thermal expansion coefficient

13 CHAPTER 1 INTRODUCTION 1.1 Background of the Study Recently, considerations on the environmental aspects have become important issues in design and development of new systems. The refrigeration industry has been pointed as one of the main causes of ozone crisis, due to the production of chlorofluorocarbons (CFC) which also contributes to greenhouse effect. CFC is any organic compounds composed of carbon, fluorine and chlorine which were originally developed as refrigerants during the 1930s, and also found use as aerosol-spray propellants, solvents, and foam-blowing agents. They are well suited for these and other applications because they are nontoxic and non-flammable and can be readily converted from a liquid to a gas and vice versa. CFCs were eventually discovered to pose a serious environmental threat. Studies indicated that CFCs, once released into atmosphere, accumulate in the stratosphere, where they contribute to the depletion of the ozone layer. Stratospheric ozone shields life on Earth from the harmful effects of the sun s ultraviolet radiation, even relatively small decrease in the stratospheric ozone concentration can result in an increase incident of skin cancer in humans and genetic damage in many organisms. Thus, thermoacoustic refrigerator a system without CFC but uses inert gases instead is an alternative to this conventional refrigeration system that has caused much destruction to the ozone layer due to the production of CFCs.

14 2 Thermoacoustic is a combined phenomenon of acoustic and thermodynamics. Thermoacoustic effects are produced when pressure oscillations or acoustics generate a temperature gradient or vice versa. Thermal energy is moved through an elastic medium that is typically a compressible working fluid. Thermoacoustic effects will occur when temperature oscillations accompany the pressure oscillations and when there are spatial gradients in the temperature oscillation. Thermoacoustic engine can be classified into two basic kinds which are thermoacoustic prime mover and thermoacoustic refrigerator or thermoacoustic heat pump. A system that converts heat energy into acoustics is called a thermoacoustic prime mover while a system that converts acoustics into heat energy difference is called a thermoacoustic refrigerator. In general, thermoacoustic engines can be divided into standing wave and travelling wave devices. In standing wave devices, the wave will remain at a constant position. The standing wave phenomena occurs when the reflecting wave traveling in the opposite direction with the same frequency meet up with the incoming wave. The interference between these two waves from opposite directions and at the same frequency will produce the stationary medium in devices. Whereas for traveling wave devices there are no reflecting wave occurrences and there is no stationary medium produced. This study will focus on the standing wave thermoacoustic refrigeration system. Particle Image Velocimetry (PIV) is a particle tracer method of fluid visualization technique used to make flow patterns visible, in order to get qualitative or quantitative information on them. Typical PIV apparatus consists of a camera (normally a digital camera), a high power laser, an optical arrangement to convert the laser output light to a thin light sheet (normally using cylindrical lens and spherical lens), and a synchronizer to act as an external trigger to control the camera and laser while the seeding particles and the fluid is still under investigation. PIV is an important experimental tool in fluid mechanics and aerodynamics. The basic principle involves photographic recording of the motion of microscopic particles that follow the fluid or gas flow. Image processing methods are then used to determine the particle motion, and hence the flow velocity, from the photographic

15 3 recordings. Provided there are enough particles within the area of flow under investigation, the entire velocity field of the flow can be determined. The use of PIV technique is very attractive in modern aerodynamics. Examples of current applications are aircraft wake (measurement of the wake vortices of a lifting aircraft wing), helicopter aerodynamics (investigation of rotor aerodynamics with respect to noise emission of various noise sources such as blade or vortex interactions), and transonic flow over airfoils. Besides studies in aerodynamics, PIV is increasingly used in the investigation of liquid flows (vortex-free-surface interaction, thermal convection and Couette flow between concentric spheres). A flow is visualized by seeding the fluid with small particles that follow the changes of the flow instantaneously. The light-sheet which is generated by a laser and a system of optical components is not continuous or permanent but pulsed to produce a stroboscopic effect, freezing the movement of the seeding particles. To detect the position of the illuminated seeding particles, a CCD-camera (CCD = Charge Coupled Device) is positioned at right angle to the light-sheet and the particle positions will appear as light specks on a dark background on each camera frame. The pulsing lightsheet and the camera are synchronized so that the particle positions of particular light pulse number 1 are registered on frame 1 of the camera and particle positions from pulse number 2 are on frame Literature Review The stack is considered as the heart of a thermoacoustic system. Development and continuous improvement of it can better the overall performance of a thermoacoustic system. The heat transfer process crucial to thermoacoustic effects occurs in and near the stack region and current technology of the stack material and geometry has room for improvement based on the background studies completed. Various researchers have recommended various stack gaps using latest discovery of the best performance stack material.

16 4 It was Carter et al. (1962) who were responsible for introducing the stack in the thermoacoustic system. Starting from here, the stack was used to increase the thermoacoustic effects. Then Rott (1980) studied the circular and parallel stack. His study on the stack was put into the Rott s Function diagram, a diagram which is important in determining the stack boundary layers (Swift, 1988). Wheatley et al. (1986) then used tungsten as a stack with parallel plate geometry for his patented thermoacoustic device. In the same year, Hofler (1986) then used a camera film as a stack with spiral geometry for his PhD work. His geometry was considered simple to fabricate. Arnott et al. (1991) then studied square, rectangular and triangular pores for the stack. The studies of these stacks were added into the Rott s function diagram in the year In 1992, STAR thermoacoustic refrigeration system was developed using Mylar with spiral roll as the stack. This was the big turning point in stack development, as many researchers after that used Mylar as stack because of its success. Keolian and Swift (1995) and Hayden and Swift (1997) mentioned the pin array stack. They proved that the pin-array is the best geometry for the stack. The main problem is the difficulties in fabricating the stack. Poese and Garret (1998) and Tijani (2001) then used parallel plates with Mylar as the stack. Literature on acoustic flow field is generally extensive among the researchers. The flow fields were measured using various techniques and for thermoacoustic refrigerator investigation, optical method is more preferred due to its non-intrusive characteristic. Previous studies on thermoacoustic refrigerator show that the visualization flow field techniques that have been used are Holographic Interferometry, Laser Doppler Anemometry (LDA) and Particle Image Velocimetry (PIV). Herman et al. (1998) used Holographic Interferomany for the visualization of the flow near the stack plate. Taylor (1976) was the first to measure the acoustic velocity in an acoustic resonator using LDA. And also Baillet et al. (2000) measure the acoustic power flow in a thermoacoustic resonator using this technique. These techniques only yield data for a single point in the measurement volume. Meanwhile, PIV is more preferred since it allows obtaining velocity data over a large area.

17 5 Besides, few researchers have ventured into PIV measurement technique to obtain the flow field around an acoustic stack of the thermoacoustic refrigerator. Philippe Blance-Benon and his colleagues from the John Hopkins University, (2003) have visualized the oscillating flow field in a thermoacoustic stack using PIV measurement and compared the results with computational predictions obtained under similar condition. The author focused on stacks operating at low drive ratios, and presented results obtained with two stack configurations which are characterized by ratios of the plate thickness to the viscous penetration depths. For the thick-plate configuration, both experimental computational results revealed the presence of concentrated vortices near the edge of the plate. This is because the ratio of plate spacing to the viscous penetration depth is large and also the plate Reynolds number was high enough to permit vortex generation. As for the thin-plate configuration, the result did not show the formation of well-defined eddies that contrasted with the observation of the thick-plate configuration. Mao et al. from the University of Manchester (2005) completed PIV measurement of coherent structures and turbulence created by an oscillating flow at the end of a thermoacoustic stack. The author s objective was to identify the flow morphology and turbulence characteristics in the vicinity of the parallel-plate thermoacoustic stack. Two stack models were tested; thin and thick stack with area of the stack kept constant. The results showed that there were significant differences between the low drive ratio (D r <1%) for thick stack and high drive ratio (D r >1%) for thin stack. Drive ratio is the ratio between peak pressure (P A ) amplitude to mean pressure (P m ) in the resonator,. The flow on the thick stack is dominated by laminar-like features. The vortices formed at the edges of the plates in the ejection phase and finally the vortices that formed were sucked back between the plates when the velocity changed its direction. And for the thin stack the high vorticity regions were much more elongated. During the ejection phase coherent vortex structures were being shed from the edges of the plates.

18 6 Berson and his colleagues (2008) also used PIV technique to address the characterization of the flow inside a thermoacoustics refrigerator and the measurement technique was validated by comparing the velocity fields obtained in the resonator without stack to a simple plane wave model. The oscillating boundary layers between two plates of the stack were investigated and the generation of vortices at the edges of the stack plate was precisely described. Effect of the acoustic pressure level on the vortices was also investigated by the author. Although validated, results had some limitations on the linear model at higher acoustic pressure level when nonlinearities appeared. The acoustic velocity fields behind the stack plate were characterized and showed vortices appearing during half periods of the acoustic cycle when the fluid flowed out of the stack. For the effect of acoustic pressure level, counter-rotating vortices were generated at the edges of the plates at low pressure level and they were symmetrical and remain attached to the plates. With increasing acoustic pressure level, structures detached and developed a symmetrical street of vortices. A recent study by Shi et al. (2009) investigated vortex shedding processes occurring at the end of the stack of parallel plates due to an oscillating flow induced by an acoustic standing wave. PIV and also Hot-Wire Anemometry (HWA) were used. PIV were used to quantify the vortex shedding processes within an acoustic cycle phase-by-phase, in particular during the ejection of the fluid out of the stack. Meanwhile, HWA was applied to detect the velocity fluctuations near the end of the stack. Combination of these two measurement techniques provided a detailed analysis of the vortex shedding phenomena. Impact of the plate thickness and the Reynolds number on the vortex shedding pattern also had been discussed by the author in this study. Table 1.1 list out past studies completed with PIV method.

19 7 Table 1.1: Summary of literature review on PIV method. Author Resonator Stack Blance- Benon, P. et al. (2003) Mao, X. et al. (2005) Berson, A. et al. (2008) Shi, L. et al. (2009) 86cm long 7.4m long, 136x136m m 2 Plexiglass 86cm long, 80x80mm 2 Metal Tube 7.4m long, 134x134m m 2 Parallel plate Glass plate Thickness: 0.15mm,1mm Separation gap: 1mm, 2mm Parallel plate 200mm long, 136mm wide. Thickness: 1mm, 5mm Separation gap: 5mm, 10mm Parallel plate Glass 25mm long Thickness: 1mm Separation gap: 1mm Parallel plate 200mm long, 132mm wide. Thickness: 0.5-5mm Separation gap: 1.2mm- 10.8mm Working Fluid Air Air, atmospheric pressure Air, atmospheric pressure Air, atmospheric pressure, room temperature Remark thick-plate configuration revealed the presence of concentrated vortices near the edge of the plate, thinplate configuration result does not show the formation of well-defined eddies The flow on the thick stack is dominated by laminar-like features - the vortices formed at the edges of the plates, for the thin stack the high vorticity regions are much more elongated vortices appearing during half periods of the acoustic cycle when the fluid flowed out of the stack, counterrotating vortices were generated at the edges of the plates at low pressure level, symmetrical street of vortices develop with increasing acoustic pressure level At thin stack a pair of attached vortex structures at the end of the plate form and elongated as the velocity gradually increases, when thickness increase the attached symmetrical vortex structures are no longer elongated but begin to break up early and into discrete vortices

20 8 1.3 Problem Statement In the high-intensity acoustic field, the flow structures at the end of the stack are very complex due to discontinuities of the cross section and the oscillatory nature of the flow. The energy transfer taking place within the thermoacoustic stack will be affected by entrance/exit effects, vortex shedding and generation of the turbulence over different parts of the acoustic cycle (Mao et al., 2008). In order to optimize the stack which form the heart of the cooler in a thermoacoustic refrigerator, the coefficient of stack performance, defined as the ratio of heat pumped by the stack to the acoustic power used by stack, has to be maximized (Tijani, 2001). Thus, to improve thermoacoustic refrigeration system, a better understanding on the flow field around the component of stack is important. This study involves an experimental analysis of a flow around the thermoacoustic stack and also the effects of the stack geometry on this flow field. The flow around the stack is visualized experimentally using PIV. 1.4 Research Objectives Objective of this research is to investigate the effect of the stack geometry (thickness and separation gaps) on thermoacoustic effects using Particle Image Velocimetry (PIV).

21 9 1.5 Scope of the Study The scopes of this research are to: 1. Design appropriate thermoacoustic resonator geometry and associated stack for the resonator tube for a PIV experimental set-up. 2. Fabricate stack geometry of different thickness and separation gaps. 3. Complete experiments with PIV to investigate the effects of the stack geometry and space beyond the stack on velocity profiles.

22 CHAPTER 2 THEORY 2.1 Introduction The last 20 years have seen theoretical, experimental and numerical studies completed in order to establish the theories behind thermoacoustic. The exercise involves fundamental theories behind acoustics, thermodynamics and heat transfer with additional generation of thermoacoustic theory itself. Basic concepts and theories relevant to the current study are discussed here, in particular those that relate to the standing wave thermoacoustic resonator. 2.2 Thermoacoustic Effect The thermoacoustic effect of interest in thermoacoustic refrigeration is the results of the interaction of acoustic waves and a solid wall. This effect occurs in the stack region and requires the presence of two thermodynamic media, the stack plate and the working fluid in the resonator tube. Under adequate conditions, a high amplitude standing wave creates a temperature gradient along the stack of plates. A heat flux was then transferred from the cold side to the hot side of the plate. This heat flux results from the adequate phasing between the compression-expansion cycle and the oscillatory motion imposed on fluid particles by the acoustic standing wave.

23 Standing wave A standing wave or stationary wave is the interference of two waves of equal frequency travelling along the same straight line in opposite directions. Consider two equal amplitude simple harmonic motion (SHM) waves, y 1 and y 2, each with amplitude a: (2.1) (2.2) where λ is the wavelength, v is the velocity, t is time and x is distance. Therefore, the interface produces (2.3) where (2.4) Equation (2.3) is a standing wave, where R is the amplitude of the new wave which does not vary with time. At certain points (n is odd), the amplitude is permanently zero, so that there is no any disturbance at those points. Such points are called nodes. At points midway between the nodes such as (n is even), the amplitude reaches a maximum value of 2a. These points are called antinodes. A schematic of a standing wave is shown in Figure 2.1. For thermoacoustic refrigeration system, a pressure node is also a displacement of anti-node and vice versa.

24 12 NODE 0 λ/2 λ ANTI-NODE Figure 2.1: Schematic diagram of a standing wave Principle of Thermoacoustic Effect In a thermoacoustic refrigerator, shown in Figure 2.2a, an acoustic standing wave is generated in the working fluid in a resonance tube with an acoustic driver. The length of the resonance tube can correspond to half or quarter wavelength of the standing wave, λ ac /L. The pressure distribution is given by (2.5) and the velocity distribution by (2.6) along the resonance tube as indicated in Figure 2.2b. When introducing a densely spaced stack of plates of length, Δx at a location specified by the stack center position, x c into the acoustic field, a temperature difference, ΔT develops along the stack. This temperature difference is caused by the thermoacoustic effect, and the temperature distribution within the resonance tube is shown in Figure 2.2b.

25 13 Figure 2.2c illustrates the thermoacoustic heat pumping mechanism; this can be explained by considering the oscillation of a single gas parcel of the working fluid along a stack plate. The cycle begins with the gas parcel at a temperature T. Under the influence of the acoustic standing wave, the gas parcel moves to the left, towards the pressure antinodes. The magnitude of the displacement is called the tidal displacement, x td 2u A (x)/ω where ω are angular frequency. Meanwhile, the gas parcel is subjected to adiabatic compression, which causes its temperature to rise by two arbitrary units to T ++. At this state, the gas parcel is warmer than the stack plate, irreversible heat transfer into the stack plate taken place denoted by dq h in the schematic in Figure 2.2c. The resulting temperature of the gas parcel after this step is T +. After that, the gas parcel experiences adiabatic expansion and cools down by two arbitrary units, to reach the temperature T - on its way back to the initial location. At this state it is colder than the stack plate, and then the irreversible heat transfer from the stack plate towards the gas parcel taken place, shown as dq c in Figure 2.2c. Those steps show that the gas parcel has completed one thermodynamic and acoustic cycle, it has reached its initial location and temperature T, and the cycle is then repeated. Since many gas parcels along the stack plate are subjected to this thermodynamic cycle, the heat delivered to the stack plate by one gas parcel is transported further by the adjacent parcel, so that an overall temperature gradient will develop along the stack plates. Figure 2.3 shows the thermoacoustic refrigeration cycle occurring for one gas parcel with the existence of a stack, and Figure 2.4 shows the overall heat transfer in stack plate of gas parcels in a thermoacoustic refrigerator.

26 14 Figure 2.2: (a) Schematic of resonance tube of thermoacoustic refrigerator, (b) Pressure, velocity and temperature distributions along the resonance tube, (c) Heat pumping cycle in the magnified stack region visualized by considering the oscillation of one gas parcel (Wetzel and Herman, 2000).

27 15 Figure 2.3: Four steps thermoacoustic refrigeration cycle occurring for one gas parcel with existence of stack (Tijani, 2001). Figure 2.4: Overall heat transfer in stack plate of gas parcels in thermoacoustic refrigerator (Nurudin, 2008). In thermoacoustic refrigerators two characteristic length scales, the thermal penetration depth, δ α and the viscous penetration depth, δ v are important for a heat transfer analysis. The thermal penetration depth is also known as the thermal boundary layer. It describes the thickness of the fluid layer around the stack plate where the thermoacoustic effect occurs. It represents the distance that heat can

28 16 diffuse through the working fluid during the time interval corresponding to one cycle of oscillations (Swift, 1988), 1/ω. The viscous penetration depth describes the thickness of the layer of fluid around the stack plates that is restrained in its movement under the influence of viscous forces. Viscous dissipation is responsible for the loss of kinetic energy, so that the fluid layer of thickness δ v in the vicinity of each stack plate contributes less to the thermoacoustic effect (Wetzel and Herman, 1996). Thermal penetration depth is given by (2.7) K is thermal conductivity, ρ m is the density, and c p is the isobaric specific heat of the gas. Viscous penetration depth is given by (2.8) (μ is dynamic viscosity). The exact theoretical expressions of the acoustic power and cooling power in the stack are complicated. To simplify this problem, the short stack and boundarylayer approximations are used. The boundary-layer and short-stack approximations assume the following (Swift, 1988): The reduced acoustic wavelength is larger than the stack length: λ/2π» L s, so that the pressure and velocity can considerer as constant over the stack and that the acoustic field is not significantly disturbed by the presence of the stack. The termal and viscous penetration depths are smaller than the spacing in the stack: δ α, δ v «y o. This assumption leads to the simplification of Rott s functions, where the complex hyperbolic tangents can be set equal to one. The temperature difference is smaller than the average temperature: ΔT m «T m, so that the thermophysical properties of the gas can be considered as constant within the stack.

29 Main Components of a Thermoacoustic Refrigerator For design purposes, the thermoacoustic refrigerator can be divided into four main components: (i) thermoacoustic core (stack), (ii) resonance tube, (iii) acoustic driver, and (iv) the heat exchangers (Wetzel and Herman, 1996). Figure 2.5: Sketch of a thermoacoustic refrigerator Thermoacoustic Core Since the termoacoustic effect takes place in the termoacoustic core, the design of a thermoacoustic refrigerator starts with the thermoacoustic core. To evaluate the performance and to find the optimum design for the thermoacoustic core, Wetzel and Herman (1996) developed a design algorithm for the thermoacoustic core based on the short-stack and boundary-layer approximation introduced by Swift (1988). Suitable working fluids for thermoacoustic refrigerators are ideal gas or liquids close to their critical point. The reason for this is the fact that such working fluids have a large thermal expansion coefficient, β (Swift, 1988). Another requirement relevant for the selection of the working fluid is a low Prandtl number, Pr. This is easily understood by considering the relation between viscous and thermal penetration depths, (2.9)

30 18 A low Prandtl number result in a small viscous penetration depth, δ v. Therefore, the difference between thermal and viscous penetration depths increase and more working fluid contributes to the thermoacoustic heat pumping cycle. The requirement for the stack plate is a low thermal conductivity material, because conduction along the stack plate has a negative impact on the performance of the thermoacoutic core (Swift, 1988). Furthermore, a heat capacity larger than the heat capacity of the working gas is required in order that the temperature of the stack plate remain steady. Stack plate geometry design chosen involves several specific parameters that should be considered. Geometry specific parameters defined by Wetzel and Herman (1996) are discussed here. A schematic is shown in Figure 2.6. Δx h = 2y o (separation gap) Plate t = 2l (thickness) Plate Plate Figure 2.6: Space between stack plate and plate thickness. The stack length, Δx is normalized according to, (2.10) where the value for ξ c is between 0.1 and 0.3. The normalized stack center position is given by, (2.11)

31 19 the value for ξ c is between 0.1 and 0.3. The normalized plate spacing is given by, (2.12) the value for δ kh is between 0.25 and 0.5. The blockage ratio is defined as, (2.13) where the value of BR is almost 0.8 (Wetzel and Herman, 1996). The blockage ratio or porosity of the stack determines the oscillating gas flow. A high value of blockage ratio indicates the ability of smooth flow during heat pumping process. The gap between stack plates must allow the flow of the gas parcel without interrupting the oscillation of the standing wave. The optimum stack spacing according to Arnott (1991) is about 2.2. According to Tijani (2001) the optimal stack spacing is about 3, while Swift (1988) stated that it is 4. The reason for this uncertainty is because the Arnott s is based on theory and numerical study while Tijani made the conclusion based on his experimental result and for Swift based his on ease of fabrication. But the values proposed are still in the range of 2 to 4 which is recommended by Swift (1995). Also, it is desirable to have a significant temperature difference across the plate. When a stack is placed at a velocity node and pressure antinode, there are no displacements of gas parcel with no heat transfer occurring. The gas parcels are also not able to heat up due to zero pressure amplitude if the stack is placed at a pressure node and velocity antinode (Wetzel and Herman, 1996). Pressure in a gas is directly proportional to the absolute temperate stated by the Ideal Gas Law. If the pressure in a gas increases, the temperature also increases. Therefore, a stack plate should be placed between a pressure antinode and velocity antinode to get the optimum thermoacoustic effect.

32 Resonator Tube The resonator tube encloses the stack, working fluid and the standing wave. It should be transparent for visibility in using PIV. The resonator is designed in order that the length, weight, shape and the losses are optimal. The resonator has to be compact, light, and strong enough. The resonator lengths are determined by the wavelength, λ. The wavelength is the distance between repeating units of a propagating wave of a given frequency. Wetzel and Herman (1996) stated that the length of the resonance tube should be half or quarter wavelength. The optimization of resonator shape will not be considered and also half wave length resonators are used here. To obtain the wavelength and the resonator length, the following parameters need to be considered, The wave length is given by, (2.14) where, C is the sound speed, given by and f = frequency. Then the total length of a resonator for half wavelength is defined as, (2.15) Acoustic Driver Normally, in a thermoacoustic refrigerator a loudspeaker is used as the acoustic driver. The purpose of a loudspeaker is to convert electrical energy into

33 21 mechanical energy and radiate it as acoustic energy. There are two design requirements for an acoustic driver: (i) (ii) It has to supply the acoustic work required to pump the desired cooling load through the thermoacoustic core. It has to provide the force to achieve the required peak pressure amplitude of the acoustic standing wave. This work can be estimated using the design algorithm for a thermoacoustic refrigerator given by Wetzel and Herman (1996) Heat Exchangers Heat exchangers are necessary to transfer the heat of the thermoacoustic cooling process. The design of the heat exchangers is a critical task in thermoacoustics. Little is known about heat transfer in oscillatory flow with zero mean velocity. The standard steady flow design methodology for heat exchangers cannot be applied directly. There are two design requirements for heat exchangers in a thermoacoustic refrigerator (Wetzel and Herman, 1996). First, heating load at the cold and hot exchangers must be determined respectively. And second, the length of the heat exchangers in axial direction should correspond to two times the particle displacement of the acoustic standing wave at the cold and hot side of the stack respectively. However in this study, the model is built without heat exchangers because investigations are focused into the nature of the oscillating flow in the stack region and its neighbourhood.

34 CHAPTER 3 METHODOLOGY 3.1 Introduction This chapter will elaborate about methodology used along this study and the summary of the methodology was shown in a flow chart (Figure 3.1). The purpose of this study is to obtain the velocity profile at the thermoacoustic stack using Particle Image Velocimetry (PIV). This chapter describes the experimental setup that has been used in order to complete this study which divided into two parts, the first part involves the construction of the thermoacoustic components and second part is the PIV measurement setup.

35 23 Parameter Identification Analytical Study Resonator Tube Fabrication Stack Fabrication PIV Measurement Analysis and Conclusion Figure 3.1: The flow chart of the study. 3.2 Thermoacoustic Component The scope of this study is to design a suitable thermoacoustic resonator for a PIV experimental setup and fabricate stack geometry with different thickness and separation gaps. The thermoacoustic components include: 1. Resonator 2. Stack configuration 3. Acoustic driver

36 Resonator In this thermoacoustic refrigeration setup, a rectangular tube was selected as the resonator tube. The purpose of using rectangular tube instead of cylindrical tube was to reduce the effect of laser light reflection by PIV setup. The material used to build this resonator was acrylic since PIV measurement needs a transparent material, and it is easily found in a local factory. In order to attach the resonator tube to an acoustic driver, the base for the resonator will be fabricated with the same material. This study follows the experimental work done by Berson et al. (2008), which used air as the working fluid at atmospheric pressure and half wavelength resonator tube in their experiment. The length of the resonator in this investigation is 86cm with internal cross area 80 x 80 mm 2. Figure 3.2 shows the resonator with the resonator base. Resonator Resonator Base Figure 3.2: Resonator and resonator base.

37 Stack configuration Berson et al. (2008) had used a glass plate as the stack because this material is non-conducting and has a low thermal conductivity. Different set of geometry of the stack has been fabricated to analyze the effect of thickness and separation gap in this thermoacoustic refrigeration system. For separation gap, the dimension recommended by Swift (1995) is in the range of 2 to 4 for the optimization of stack performance. However in this study the thermoacoustic refrigerator fabricated is not optimized to achieve high thermal effect, therefore the separation gap applied does not follow Swift s (1995) recommendation. The thickness range about 1-5mm and the separation gap about 1-10mm was applied which follows Mao et al. (2005). In this study two different cases were analysed; single plate and multiple plates. For the single plate, two different thickness of stack plate was used which is 1mm and 3mm. And for multiple plates there are 3 sets of configurations were used. Each configuration has different thickness and separation gaps. The set of stack geometry that have been fabricated is shown in Table 3.1. Based on the literature review, Berson et al. (2008) used a stack with configuration of 25mm long and 80mm wide. The fabricated stack was located at the amplitudes where both pressure and velocity fluctuations are high enough for thermoacoustic effects to take place. Meanwhile, the centre of the stack is placed about 21.5cm from the acoustic driver. Table 3.1: Stack geometry for single and multiple plates. Thickness, t Separation gap, h Stack Geometry (mm) Length, x Width, w Centre position, x c Single plate 1, Configuration of multiple plates Config. A Config. B Config. C

38 Acoustic driver In this study, a loudspeaker was used as an acoustic driver which converts electrical energy into acoustic energy. The conversion of electrical energy to acoustic energy takes place in two steps. First, the electrical signal causes mechanical motion of the speaker cone or diaphragm and finally causes the pressure waves in the air called sound. Besides that, the loudspeaker chosen should provide a low frequency range because this study is only focused on the frequency of 200Hz. Figure 3.3 shows a sample of the loudspeaker to be used. Figure 3.3: Loudspeaker. In order to generate a sinusoidal wave signal at the frequency of 200Hz, a function generator and power amplifier were used. The function generator was functioned to generate electrical waveform at the desired frequency. In this study, a sinusoidal waveform at 200Hz was set as the signal. Meanwhile, a power amplifier was used to increase the amplitude of the signal. The function generator and power amplifier used in this study is shown in Figure 3.4 and 3.5 respectively, whereas the connection between the function generator, power amplifier and loudspeaker is shown in Figure 3.6. Aschematic illustration of the thermoacoustic refrigerator with a magnified view is shown in Figure 3.7.

39 27 Figure 3.4: Function generator. Figure 3.5: Power amplifier. Figure 3.6: Connection between function generator, power amplifier and loudspeaker.

40 28 Resonator Tube Stack Plates Acoustic Driver x c L t h Measurement Area x Figure 3.7: Schematic illustration of the thermoacoustic refrigerator with a magnified view. 3.3 PIV Measurement Setup PIV measurement is the technique chosen to investigate the effects of stack geometry that has been fabricated. This setup consists of, 1. Smoke generator, 2. Optical setup, 3. Flow manager software. Smoke generator produced seeding particles or smoke that is injected into the resonator which was directly attached to the loudspeaker. An optical setup consists of a laser and cameras were used to detect the flow patterns of seeding particles. The area of the velocity field was illuminated by a piece of light sheet in order to detect the movement while the camera was used to record the position of illuminated seeding particles. All data obtained was finally analyzed using the flow manager

41 29 software. Thus, it can be concluded that PIV involved five stages; seeding, illuminating, recording, processing, and analyzing of flow field Smoke Generator PIV it is not actually measuring the velocity of the flow but the velocity of the particles suspended in the flow. Thus, the seeding considerations are important in PIV measurement. Particle should be able to follow the flow, with good light scatter, and clean. In this study, the resonator is seeded with smoke that generated by EXEROTECH smoke generator shown in Figure 3.8. The smoke is fed inside the resonator through a hole in the acrylic wall of the resonator near the measurement area and injected before the loudspeaker was turned on. Figure 3.8: Smoke generator Optical Setup The Dantec Dynamic camera with Nikon 60mm lens and Solo PIV Nd-YAG laser with 532nm wavelength used in this study was shown in Figure 3.9 and The camera distance is approximately 10cm from the measurement field. The measurement zone is restricted around the cold side of the stack plate (the edge further away from the loudspeaker) where multi-dimensional phenomena dominate

42 30 the flow. The camera was located perpendicular to the direction of oscillations and also perpendicular to the light sheet produced by the laser. Figure 3.11 shows the arrangement of the camera and laser near the measurement field. The pulsing light sheet and the camera were synchronized by using a flow manager software. Figure 3.9: Camera. Figure 3.10: Laser. Figure 3.11: Arrangement of camera and laser on the measurement field.

43 Flow Manager Software All data obtained from the PIV measurement were processed and analyzed using a flow manager software. In this study, the Dantec Dynamics Flow Manager Software version was used. The images of the velocity profile were sent to a computer after being captured by the camera to give a raw vector map. The raw vector map was then processed to produce an analyzed vector map. However, almost all PIV measurements may give incorrect vectors resulting from noise peak in the correlation function called outlier. Therefore, PIV raw vector map was validated to recognize, reject and remove this outlier. Also the vector map was filtered out to reduce the effect of noise which gives rise to small errors. Figure 3.12 below shows the experimental setup with thermoacoustic component and PIV measurement setup. The experiment was done at the Aeronautic Laboratory, Faculty of Mechanical Engineering UTM Skudai. And Figure 3.13 shows the block diagram of the experimental setup. Flow Manager Laser Thermoacoustic resonator Loudspeaker Camera Function generator and power amplifier Figure 3.12: Experimental setup.

44 32 Laser Thermoacoustic Refrigerator Power Amplifier Function Generator Camera Flow Manager Figure 3.13: Block diagram of the experimental setup.

45 CHAPTER 4 RESULTS AND DISCUSSION 4.1 Introduction Particle Image Velocimetry (PIV) is a measurement technique for obtaining instantaneous whole field velocities. It is based on the well known equation, speed = distance/time. In PIV, the property actually measured is the distance travelled by particles in the resonator within a known time interval. And also, the PIV technique is based on determining the displacement of a group of particle correlation technique. Image maps from the camera are processed into velocity vector maps using the flow manager software. The camera image is subdivided into a number of interrogation areas and within each of these, the first and second camera frames are correlated to estimate an average displacement vector. This does not require the tracking of individual particle but on the other hand demands several particles within each interrogation region to produce reliable results. 4.2 Velocity Profiles Velocity profiles in this study were divided into two parts; for a single stack plate and for different stack geometry configurations. The results focussed only on one side of the stack which is far from the acoustic driver. This is due to the limitation of the light sheet generated by the laser to illuminate the velocity field.

46 The Single plate In this section, there were two experiments performed with different thickness of stack plate which are 1mm and 3mm. The stack geometry for this single plate is shown in Table 3.1. Figure 4.1 and Figure 4.2 show the velocity profiles behind a single plate with 1mm and 3mm thickness at the same time interval, respectively. Figure 4.1: Velocity profile for 1mm thickness single plate. Figure 4.2: Velocity profile for 3mm thickness single plate.

47 35 From Figure 4.1 and 4.2, the differences in velocity profiles near the stack plate were observed. For 1mm thickness, the velocity profile does not show any formation of vortices at the end of stack. Meanwhile, for the 3mm plate, there was a vortex formation near the end of stack (in red circle). These phenomena will be discussed in detail in the second part of the velocity profile results where the geometry configurations of stack plate are varied Effects of Time Three sets of stack plate configurations with different geometry (thickness and separation gap) were done in this study. The summary of geometry for each stack plate configuration for multiple plates is given in Table 3.1. In order to perform a comparison between the configurations, it is necessary to properly synchronize the time axes. For all three configurations, data collection was performed at the same time. The PIV measurement was started 6seconds after the acoustic driver was turned on. For each configuration, 20 sets of data at equally spaced time were obtained and labelled as T1-T20. Figure 4.3 shows 4 sets of data at different time intervals for configuration A. And Figure 4.4 shows the velocity distribution for each time interval at point 1-3. Point 1 is located at the end of the plate and at the centre of the separation gap. 3 4m m 2 4m m 1 (a) T1 (b) T7

48 Velocity (m/s) 36 (c) T14 (d) T20 Figure 4.3: Velocity profile for configuration A Point 1 Point 2 Point T1 T7 T14 T20 Time Interval Figure 4.4: Graph velocity against time interval at point 1-3 for configuration A. From Figure 4.3, we can see that the flow between the stack is not too clear. Also from the 4 time intervals there was no clear vortex generated, except for a little bend on the flow at the edges of the stack plates. And from Figure 4.4 it shows that there were differences in velocity as time increases, whereas the velocity at time T7

49 37 was higher at all three positions. Besides that we can see that the velocity increases at the position farther from the end of the stack. As for configuration B, Figure 4.5 shows the velocity profile also at 4 time intervals with Figure 4.6 showing the velocity distribution at point 1-3 for every time interval. For point 1, positions are at the end of plate and at the centre of the separation gap. 3 4m m 2 4m m 1 (a) T1 (b) T7 (c) T14 (d) T20 Figure 4.5: Velocity profile for configuration B.

50 Velocity (m/s) Point 1 Point 2 Point T1 T7 T14 T20 Time Interval Figure 4.6: Graph velocity against time interval at point 1-3 for configuration B. From Figure 4.5, the flow between the stack plates are quite clear. The velocity profiles show a clear vector direction as well as the magnitude. Magnitudes of the velocity vector at the middle of the channel are higher compared to that near the surface of the stack plates. Besides that, there were changes in velocity value for time changes as shown in Figure 4.6. With increments of time, the velocity will decrease at time T7 and then increases after that. And finally, for configuration C, the velocity profile at time interval T1-T20 is shown in Figure 4.7. Velocity distribution for each time interval at point 1-3 for configuration C is shown in Figure 4.8 and also point 1 located at the end of plate and at the centre of the separation gap.

51 39 3 4m m 2 4m m 1 (a) T1 (b) T7 (c) T14 (d) T20 Figure 4.7: Velocity profile for configuration C.

52 Velocity (m/s) Point 1 Point 2 Point T1 T7 T14 T20 Time Interval Figure 4.8: Graph velocity against time interval at point 1-3 for configuration C. Figure 4.7 shows that the flow between the stack plates is not too clear. Only near the edge of the stack, the direction and magnitude of the velocity vector can clearly be seen. The vortices were generated at the edges of the stack plate. This can be seen at the velocity profile for all 4 time intervals but the position of the vortices changes with time. Meanwhile, from Figure 4.8 it can be seen that the velocity decreases as time increases Effects of the Plate separation gap, h In order to investigate the effect of stack separation gap, h, on the velocity profile (flow) of thermoacoustic phenomena, results from configuration A were compared with the results from configuration B. The time intervals for both configurations are the same so that the differences and similarities of the flow are analyzed under the same condition. For this comparison, the time interval T7 is used. Figure 4.9 shows the comparison of velocity profile at T7 for configuration A and B.

53 41 And Figure 4.10 shows the graph of velocity comparison at point 1 and 2 for both configurations where point 1 is located at the centre of the separation gap of the stack plate m m 4m m (a) Configuration A: t = 1mm, h = 1mm (b) Configuration B: t = 1mm, h = 3mm Figure 4.9: Comparison of velocity profile at T7.

54 Velocity (m/s) Point 1 (config. A) Point 1 (config. B) Point 2 (config. A) Point 2 (config. B) T1 T7 T14 T20 Time Interval Figure 4.10: Graph of velocity against time intervals at point 1 and 2 for configuration A and B. Table 4.2 shows the oscillating flow parameters for configurations A and B at time interval T7. The value for δ v is obtained from Equation (2.8) with the value of ν at room temperature and atmospheric pressure being 1.6 x 10-5 m 2 s -1. The Reynolds number, Re d is defined as ut / ν, where u is the velocity at the entrances of the stack. Table 4.1: Oscillating flow parameters at T7. u (m/s) h/δ v Re d Configuration A Configuration B From Figure 4.9 both velocity profiles do not show the formation of well defined vortices. This is because both configurations used the same thickness. Table 4.1 shows that the Reynolds number for both configuration are almost equal, therefore the flow pattern is almost the same at the edge of the stack plates.

55 43 There are differences in the velocity within the separation gaps and after the separation gaps of stack plates for both configurations as shown in Figure 4.10 (red circle). For configuration A, the velocity in the separation gap region is smaller compared to configuration B. The difference is due to the ratios of h/δv for both configurations which are not equal. From Table 4.1, we can see that the ratio of h/δ v for configuration B is higher than A. Based on the definition of δ v, therefore there are more particles that can move freely which is not influenced by the viscous forces for configuration B than configuration A. Thus, the velocities at the centre of the separation gap for configuration B are longer than A Effects of the Plate thickness, t Results from configuration A were compared with results from configuration C to study the effects of stack thickness, t on flow of thermoacoustics. For configuration A, the thickness of each stack plate is 1mm while for configuration B it is 3mm, three times larger than A. The time interval T1 is used for this comparison. Figure 4.11 shows the comparison of velocity profile at T1 for configurations A and C. Comparison of velocity magnitudes is shown in Figure m m 1 4m m (a) Configuration A: t = 1mm, h = 1mm