DEVELOPMENT OF SMALL-SCALE THERMOACOUSTIC ENGINE AND THERMOACOUSTIC COOLING DEMONSTRATOR

Transcription

1 DEVELOPMENT OF SMALL-SCALE THERMOACOUSTIC ENGINE AND THERMOACOUSTIC COOLING DEMONSTRATOR By NAJMEDDIN SHAFIEI-TEHRANY Mater in Mechanical Engineering Wahington State Univerity School of Mechanical and Material Engineering May 008

2 To the Faculty of Wahington State Univerity The member of the Committee appointed to examine the thei of Najmeddin Shafiei-Tehrany find it atifactory and recommend that it be accepted. Chair ii

3 Acknowledgement Many pecial thank go to my advior, Dr. Kontantin Matveev, for the guidance he gave me during my graduate tudie. Without hi help and patience I would not have ucceeded. I alo extend my gratitude to Mr. John Rutherford, machinit at The Science Shop, and Mr. Kurt Hutchinon, machinit at The Mechanical and Material Engineering Shop, for their profeionalim and the time they pent on manufacturing the component of the thermoacoutic engine and the refrigeration ytem. I am alo grateful for the aitance provided by Mr. Robert Lentz during the entire reearch. I alo would like to thank the Mechanical Shop for allowing me to ue their machine to manufacture neceary part at my convenience. I alo would like to thank Dr. Mike Anderon for all the help and upport he howed throughout my reearch. Finally I would like to thank my committee, Prof. Robert Richard and Prof. Cecilia Richard, for honoring me with their participation. iii

4 Development of Small-Scale Thermoacoutic Engine and Thermoacoutic Cooling Demontrator Chair: Kontantin Matveev Abtract By Najmeddin Shafiei-Tehrany, M.S. Wahington State Univerity May 008 Thermoacoutic i a cience and technology field that tudie heat and ound interaction. Sound wave in any fluid conit of coupled preure, motion, and temperature ocillation. When the ound travel through a narrow channel, an ocillating heat flow between the fluid and the channel wall become ignificant. The preent tudy deal with the effect of thermoacoutic cooling with cloed and open ended tube and alo invetigate the performance of a mall-cale thermoacoutic heat engine. The firt part of thi document preent the deign, contruction, and teting of a miniature tanding-wave thermoacoutic heat engine. The main objective wa to build and tet a miniature heat engine without moving part. Recorded parameter included the temperature difference acro the tack and the correponding acoutic preure amplitude of the ound produced by the engine. The ytem wa alo teted for different tack material and tube length. The mot efficient ytem i decribed in detail in thi document. The critical temperature difference acro the tack wa meaured to be approximately 350 C for the 5.8 cm engine and 50 C for the 9.3 cm engine. The average acoutic RMS preure of the ound produced wa about.7 Pa at 30 cm from the engine for both length and the frequency of the ound wa about.4 khz for the 5.8 cm engine and about khz for the 9.3 cm engine. The econd part of thi document preent the effect of thermoacoutic cooling with cloed and open ended tube. The poition of the tack and ound frequencie were varied to iv

5 etablih the mot effective configuration. For each configuration, the preure amplitude inide the tube and the ound frequency were the controlled parameter, and the temperature difference acro the tack wa meaured. The experimental reult of the thermoacoutic cooling ytem are compared to the theoretical reult. For the cloed-end ytem the temperature of the top of the tack wa higher than the bottom and for the open-end ytem the temperature of the top of the tack wa lower than the bottom. The maximum temperature difference wa about 3 C for the cloed-end and 6 C for the open-end. v

6 TABLE OF CONTENTS Acknowledgement Abtract Lit of Symbol Lit of Table Lit of Figure iii iv vii ix x. Introduction.. Background... Heat Engine 4... Refrigerator 5.. Objective 6. Methodology 8.. Theoretical Formulation 9... Heat Engine 9... Refrigerator 9.. Experimental Setup 3... Heat Engine 3... Refrigerator 5 3. Reult and Dicuion Heat Engine Cooling Demontrator Cloed-End Sytem Open-End Sytem 5 4. Concluion and Recommendation Bibliography 64 vi

7 a c p Lit of Symbol peed of ound iobaric heat capacity per unit ma D diameter of the tack D hx diameter of the heat exchanger h pacing between the tack plate h hx pacing between the heat exchanger plate k fluid thermal diffuivity K fluid thermal conductivity K S olid thermal conductivity l tack plate half-thickne l hx heat exchanger plate half-thickne L reonator length p acoutic preure waveform P A acoutic preure amplitude R radiu of the reonator R air ga contant g T m T m T crit mean temperature mean temperature gradient acro the tack ideal critical temperature gradient acro the tack Δ T temperature difference acro the tack u acoutic velocity waveform x coordinate along the reonator x S tack poition Δ x tack length Δ heat exchanger length y 0 x hx hx half-pacing between plate of the tack y 0 half-pacing between plate of the heat exchanger γ ratio of pecific heat ε tack plate heat capacity ratio σ Prandtl number Γ normalized temperature gradient Π cro-ectional perimeter of the tack urface Π hx cro-ectional perimeter of the heat exchanger urface ω angular frequency λ radian wavelength rad vii

8 λ β ρ m ν μ δ k δ δ ν acoutic wavelength thermal expanion coefficient mean denity kinetic vicoity dynamic vicoity thermal penetration depth of the fluid thermal penetration depth of the olid material vicou penetration depth of the fluid viii

9 Lit of Table. Tabulated Temperature Uncertainty Calculation 33. Tabulated Temperature Uncertainty Calculation Tabulated Reult of the Acoutic Preure RVC 00 PPI Tabulated Reult of the Acoutic Preure for RVC 80 PPI Tabulated Reult of the Acoutic Preure for Steel Wool Preure Uncertainty Calculation for 5.8 cm Engine at Different Angle 4 7. Tabulated experimental and theoretical reult for both 5.8 and 9.3 cm engine 4 8. Uncertainty Calculation for Different RMS Preure Uncertainty Calculation for Different Stack Poition Uncertainty Calculation for Different Stack Poition 57. Uncertainty Calculation for Different RMS Preure 58 ix

10 Lit of Table. Two Type of Heat Engine 3. (a) Schematic of Thermoacoutic Engine 9 (b) Expanded View of the Stack Plate 9 (c) Preure and Velocity Waveform along the Reonator 9 3. Location of Recorded Temperature and Refrigerator Setting 4. (a) Schematic of 5.8 cm Engine 4 (b) Schematic of 5.8 cm Engine 4 5. Engine Structure 4 6. (a) Aembled 9.3 cm Engine With Cooling Jacket 4 (b) Photo of the 5.8 cm Engine 4 7. Heat Engine Experiment 6 8. (a) Schematic of Open-End Sytem 7 (b) Schematic of Cloed-End Sytem 7 9. (a) Open-End Sytem 8 (b) Cloed-End Sytem 8 0. (a) Open-Ended Refrigerator 9 (b) Cloed-Ended Refrigerator 9. Temperature Profile for 5.8 cm Engine 3. Preure Profile for 5.8 cm Engine 3 3. Variation of Temperature Difference for 5.8 cm Engine 3 4. Preure Variation for 5.8 cm Engine 3 5. Acoutic RMS Preure with the Change in Temperature Difference Acro the Stack Temperature Profile for Steel Wool Temperature Profile for RVC 00 PPI Temperature Profile for RVC 80 PPI 35 x

11 9. Temperature Difference for RVC 00 PPI, 80 PPI, and Steel Wool for 5.8 cm Engine Temperature Profile for 5.8 cm and 9.3 cm Engine with RVC 00PPI 39. Acoutic Preure Profile for 5.8 cm and 9.3 cm engine with RVC 00PPI 39. Acoutic Preure Error Meaurement at Different Angle for 5.8 cm Engine 4 3. Frequency Profile for Stack at 3 cm Temperature Difference for Stack Located at 7 cm Temperature Difference for Stack Located at 9 cm Temperature Difference for Stack Located at cm Temperature Difference for Stack Located at 3 cm Temperature Difference for Different Stack Location at 3.5 kpa of RMS Preure Temperature Difference for Different Stack Location at 8 Hz Repeatability Error for 8 Hz Signal and 3.5 kpa of RMS Preure Repeatability Error for 8 Hz Signal and Stack at 3 cm Temperature Difference for Different Stack Material at 3 cm Temperature Profile Recorded Every 5 Second Temperature Profile Recorded Every 5 Second Enthalpy Flow Acro the Tube for a Cloe-Ended Sytem Temperature Difference for Stack Located at 6 cm Temperature Difference for Stack Located at 7 cm Temperature Difference for Stack Located at 8 cm Frequency Profile for Stack at 6 cm Enthalpy Flow Acro the Tube for an Open-Ended Sytem 55 xi

12 4. Temperature Difference for Different Stack Poition at 0.35 kpa of RMS Preure Temperature Difference for Different Stack Poition at 330 Hz Repeatability Error for 330 Hz Signal and 0.5 kpa of RMS Preure Repeatability Error for 330 Hz Signal and Stack at 6 cm Temperature Difference for Different Stack Material at 6 cm 58 xii

13 Chapter Introduction

14 Introduction.. Background Thermoacoutic i a cience and technology field that tudie heat and ound interaction. Sound wave in any fluid conit of coupled preure, motion, and temperature ocillation. When ound travel through a narrow channel, an ocillating heat flow between the fluid and the channel wall become ignificant. Device in which heat-ound interaction play an important role are known a thermoacoutic ytem []. Audible ound temperature fluctuation are uually very mall and normally not important. In the cae of thermoacoutic engine, the combination of temperature gradient and pecial ytem geometry make thee temperature fluctuation important, ince they can ignificantly amplify ound []. Thermoacoutic effect have been tudied ince the 9 th century. One of the firt obervation wa made in 850 when Sondhau recorded ound appearance in glablower equipment [3]. The ound wave were produced when hot gla came in contact with a cool open ended gla tube. The frequency of the oberved tonal ound wa equal to the natural frequency of the tube [4]. Subequently, other thermoacoutic finding oon followed. In 859, Rijke noticed that placing hot gauze in the lower half of an open-ended tube created a imilar pure tone where ound ocillation were varied by changing the gauze location along the tube. Rijke potulated that the expanion of air at the gauze and the contraction of cooling air toward the open end of the tube explained the ound generation [5]. Soon after thee dicoverie, Lord Rayleigh came up with an explanation of the thermoacoutic intabilitie which caued thi phenomenon: If heat be given to the air at the moment of greatet condenation, or be taken from it at the moment

15 of greatet rarefaction, the vibration i encouraged. On the other hand, if heat be given at the moment of greatet rarefaction, or abtracted at the moment of greatet condenation, the vibration i dicouraged [6]. Thermoacoutic device can be made without moving part and uing variou gae a working fluid. The implicity of manufacturing uch engine reult in low cot and low maintenance and, therefore, i deirable in indutry [7]. Thermoacoutic engine can be divided into two major group. In the firt group, thermoacoutic prime mover convert ome fraction of heat upplied from a high temperature ource into acoutic power, rejecting the ret of the heat into a low temperature heat ink. In the econd group, thermoacoutic refrigerator and heat pump ue ound to pump heat againt a temperature gradient. The temperature gradient in a refrigerator i typically much lower than in the heat engine [6]. Figure how the two baic type of heat engine. Heat Pump - Refrigerator. W Q. H T H. Engine Q C Prime Mover. Q H Q C T H. Engine. W T C T C Figure : Two type of heat engine. There have been major development and advance in the thermoacoutic field in recent decade and ome thermoacoutic ytem have been teted for indutrial ue. One example i large cale commercial refrigeration uing thermoacoutic engine. The efficiency limitation in imple tanding wave engine motivated the development of cloed loop traveling wave engine, a few meter in ize, that produce approximately kw of acoutic power [3]. Other medium-cale ytem were built that produce up to 3

16 00 W of acoutic power. One example of uch a thermoacoutic engine wa built by NASA with a total length of 6 cm and weight of about 900 g []. Becaue manufacturing macro-cale thermoacoutic engine i relatively imple, mot of the work and tudie done ue large or medium engine. Some of the thermoacoutic project are aimed at converting acoutic power into electric power. A project attempting to facilitate thi converion wa originally deigned for a pace generator which produced 00 W of electrical power at 0% efficiency. Thi engine ha a total length of 6 cm, but the generated power i much larger in comparion to previou deign [4]. Another cae tudy wa done at Lo Alamo National Laboratory that coupled a thermoacoutic engine to an electric alternator, which wa part of a NASA pace project [6].... Heat Engine A imple thermoacoutic engine conit of a tube (reonator) with one end cloed and the other end open to the atmophere with a porou material, referred to a a tack, placed inide the tube at a fixed location. The ytem produce ound only when the temperature difference acro the tack exceed a critical value. Thermoacoutic heat engine can be divided in two major categorie: tanding-wave and traveling-wave engine. In a tanding-wave thermoacoutic heat engine, heat i upplied to the ocillating ga at high preure and i removed at a low preure upporting preure and velocity fluctuation. Thee elf-utained ocillation atify Rayleigh criterion; in other word, heat i added to the ga in phae with preure fluctuation, imilar to the Stirling cycle [6]. For thermoacoutic pump or refrigerator thi proce i revered. 4

17 In a traveling-wave heat engine, the preure and velocity component of an acoutic traveling wave are inherently phaed to caue the fluid in the tationary temperature gradient to undergo a Stirling thermodynamic cycle. Thi cycle reult in amplification or attenuation of the wave depending on the wave direction relative to the direction of the gradient. Thi cycle pump heat in the direction oppoite the direction of wave propagation through the device [9]. Variou thermoacoutic ytem have been built in the pat, uually in large or medium cale. The main motivation for our reearch i to build a miniature engine with a relatively imple deign for eae of manufacturing. An example of a relatively mall thermoacoutic engine previouly developed i a 4 cm Hofler tube [7]. The Hofler tube ha a contant bore capped at one end, and imilar to other engine, open on the other end. The open end i made of aluminum and funnel haped with a tack of reticulated vitreou carbon (RVC). Smaller engine, down to few centimeter in length, were alo built [7], but their deign wa not documented in detail ufficient for reproduction.... Refrigerator A imple thermoacoutic refrigerator conit of a reonator with one end attached to a peaker. The other end i open or cloed, and porou material (tack) i placed at a certain location inide the reonator [6]. The tack uually conit of a large number of cloely paced urface aligned with the reonator tube. The primary contraint in electing the tack i the fact that tack layer need to be placed a few thermal penetration depth apart. About four thermal penetration depth i the recommended plate eparation in tanding-wave ytem. Thermal penetration depth i the ditance, or thickne, of the 5

18 layer where unteady heat propagate during one ocillation cycle []. In a refrigerator, externally applied work tranfer heat from the lower temperature reervoir to the higher temperature reervoir. In thi cae the external work i upplied by the tanding ound wave produced by a peaker in the reonator. The tanding ound wave force the ga particle to ocillate parallel to the wall of the tack. The alternating compreion and rarefaction of the ga caue the local temperature of the ga to fluctuate. If the local temperature of the ga become higher than that of the nearby tack wall, heat i tranferred from the ga to the tack wall. However, if the local temperature of the ga drop below that of the tack wall, heat i tranferred from the wall to the ga. Depending on the ytem configuration, the mean temperature of each tack end will differ. In the cloed-end configuration, the temperature of the tack end cloe to the cap i higher than the other end of the tack, where a cooling effect i achieved. The heat i pumped from the cold end to the hot end... Objective The main objective of thi tudy i to build and tet a miniature thermoacoutic engine and quantify it performance. The development proce included everal different model that were built and teted. The heat engine wa teted with different tack material in order to find the bet material for the tack. The value meaured in our tudie are the critical temperature acro the tack and the preure amplitude of the ound produced. Thee value are compared with theoretical value obtained from numerical analyi. 6

19 The econd part of our effort deal with a contruction of a cooling model with a peaker a a ound ource. Thi ytem i built and then teted with different tack material and two different geometry configuration: cloed- and open-ended. The frequency of the acoutic ignal and the preure amplitude inide the reonator were controlled parameter, and the meaured parameter wa the temperature difference acro the tack. Thee tudie are done to identify the difference between a cloed and open ytem and alo to find the mot effective ytem. The experimental reult were compared with the theoretical value. Some reult of thee activitie were preented at conference [8, 9]. 7

20 Chapter Methodology 8

21 . Methodology.. Theoretical Formulation... Heat Engine The goal of thi ection i to theoretically obtain the critical temperature difference acro the tack, the acoutic power produced, and the acoutic preure amplitude. In order to formulate neceary equation to calculate thee parameter, the conervation of energy in the ytem i analyzed. Figure how a configuration of our acoutic engine and the acoutic preure and velocity waveform. The acoutic preure i maximized at the cloed-end and zero at the open end. The acoutic velocity ditribution tart at zero at the cloed end and reache a maximum value at the open end. Figure (a) and (b) how the mot important dimenion of the thermoacoutic heat engine. Δ x R y 0 x L l Figure. (a) Schematic of thermoacoutic engine (b) Expanded view of the tack plate P P A U ρ a P A 0 x L X (c) Preure and velocity waveform along the reonator. 9

22 The preure and velocity component of the tanding acoutic wave in the reonator are function of time t and ditance x : i t p = ω p ( x) e, () u i t u = ω ( x) e i, () The patial component of the acoutic tanding wave preure and velocity are approximated a follow: x p = ( x) PA co, (3) λrad P A x u = ( x) in. (4) ρma λrad The cloed end location i elected to be at zero and the x-axi i directed toward the open end. In figure the pacing and the thickne of the plate are hown. Half-pacing between the plate i y 0 and half-plate thickne i l. In figure, X S i the ditance from cloed end to the middle of the tack. The preure and velocity waveform are function of x and vary along the engine. The radian wavelength of the fundamental acoutic wave in the open-cloed tube i approximated a follow: λ rad = a λ L ω = π = π. (5) 0

23 The wavelength λ i a function of length of the reonator. In our cae, ince one end of the engine i open, the wave length i equal to about 4 L. The peed of ound i a function of temperature and for ideal ga can be written a follow: a = γ RT, (6) where T i the ga temperature. Therefore the natural frequency of the open-cloed tube become a function of temperature and tube length: f ω γ RT = =, (7) π 4L In order to find the critical temperature difference acro the tack we ue the energy balance of the ytem [3]: W & = E& + E& + E& rad re hx, (8) where W & i the acoutic power produced, E & rad i the radiated acoutic power, re E & i the acoutic power aborbed by the wall of the reonator, and E & hx i the acoutic power aborbed by thermovicou effect in heat exchanger. Acoutic ocillation occurring in the vicinity of a plate reult in two important effect: the generation and aborption of acoutic power W &, and alo a time-average heat flow Q & near the urface of the plate, both effect occurring along the direction of acoutic ocillation. Now each term in the energy balance equation will be analyzed. The acoutic power produced in the preence of thermovicou loe can be written a follow [3]:

24 ( ) ( ) ( ) ( ) ( ) ( ) ) ( 4 y y x u x y y a x p x W m v m S k ν ν ν ν δ δ ωρ δ δ δ σ ε ρ ω γ δ + Δ Π + + Γ + Δ Π = &, (9) The flow velocity through the tack will be different due to finite thickne of tack plate. In order to have continuou flowrate throughout the ytem, a correction factor mut be added to the velocity component throughout the tack. The velocity ditribution along the tack become: + = rad m A x y l a P x u λ ρ in ) ( 0. (0) All ymbol in equation (9) are explained below or given in nomenclature. Since the preure amplitude and temperature difference are the target parameter. Thi way the acoutic power equation can be written in implified form a follow [3]: ( ) 3 A A P C C T C P W Δ = &. () where C, C, and 3 C are the contant. Since the working pace in the engine i bounded by the wall of the reonator and the air i a vicou fluid, the vicou penetration depth and the thermal penetration depth play a critical role in our calculation. The thermal penetration depth i the ditance through which the heat can be diffued through the working fluid, in our cae air, during time interval equal to ω π. On the other hand, the air will move without heat tranfer when it i ufficiently far from the wall. The acoutic ocillation of the air in the engine reult in vicou hear tree that lead to attenuating lo mechanim that occur in the volume

25 of air generally within a vicou penetration depth. The vicou penetration depth in the fluid can be written a follow: ν δ ν =, () ω where kinematic vicoity i: μ ν =. (3) ρ m Here the mean denity ρ m i a function of temperature that for the ideal ga become: P ρ m =, (4) R T g where for air kj R g = kg K The dynamic vicoity of the working fluid, in our cae the air, alo varie with temperature [3]. The thermal penetration depth of the olid i k δ k =, (5) ω where thermal diffuivity i K k =. (6) ρ m c p The Prandtl number i one of the parameter ued, which can be written a: cpμ ν δ ν σ = = =. (7) K k δ k 3

26 The plate heat capacity ratioε ue the propertie of the fluid, in our cae the air, and the propertie of the olid. Conidering y >> δ 0 k and l >> δ, the implified expreion for ε i: air mcpδ k olid cδ ρ ε =, (8) ρ The perimeter in equation (9) can be approximated auming parallel plate tack geometry: πd Π =, (9) h where h = y0, if l << y0, or with the finite plate thickne, h = y0 + l0. The next term that appear in the equation i the normalized temperature gradient. Normalized temperature gradient i the ratio of to the actual and ideal critical temperature gradient. T m Γ =, (0) Tcrit where f df i defined a ince we conider a one-dimenional problem. dx In thi cae Tm i the mean temperature gradient of the tube in the x-direction, which can be repreented a follow: ΔT T m =, () Δx where ΔT i the difference temperature of two ide of the tack and Δx i the tack length. 4

27 The Tcrit i the critical mean temperature gradient that can be obtained uing the following equation [3]: T βωp x m ( S ) Tcrit =. () ρ mc pu ( x ) The thermal expanion coefficient β for an ideal ga i β =. (3) T Now we conider individual term on the right hand ide of equation (8). The firt term i the radiated acoutic power E & rad. The acoutic power radiating away from the open end of a mall-diameter 4 λ reonator []: 4 P A R E& π = rad 8, (4) ρmaλrad Where P A i the acoutic preure amplitude at the cloed end of the reonator and R i the radiu of the reonator. The implified form of radiated acoutic power i: E & = C P, (5) rad 4 A where C 3 4 π R 3ρ m al 4 =. (6) Acoutic power adorbed by the reonator wall E & re i obtained by integrating the local power attenuation per urface area over 4 λ of ide wall: ( p ) ω( γ ) ρ ( ) δ ω δ k e & re = + m u ν, (7) 4ρ a + ε 4 m 5

28 where p and u were defined by equation (3) and (4). We integrate e& re over the urface area of the reonator. E& re 0 L ( e & ) π R dx + π R e& 0 =. (8) re Performing the integration we obtain: RLπωP γ R E& A = δ + + δ re k ν. (9) 4a ρm + ε L The implified equation of the acoutic power adorbed i: E & = C P, (30) re 5 A where RLπω γ R C = δ + + k δν. (3) 5 4a ρm + ε L We obtain the acoutic power aborbed by vicou effect in the heat exchanger E & uing the ame equation that the acoutic power aborbed but thi time it will be multiplied the urface area of the firt and the econd heat exchanger. Acoutic power aborbed: ( p ) ( ) ω γ + ρ m ( u ) δν Π hxδxhx k E& δ hx = ω, (3) 4ρ ma + ε 4 where the urface area can be expreed a follow: hx by Π hx Δx hx π D = π D hx Δxhx = hhx y0hx hx + l hx Δx hx. (33) In thi cae the preure and velocity amplitude can be etimated from equation (3) and (4) at heat exchanger location. The total energy aborbed by both heat exchanger (on each ide of tack) i: 6

29 7 hx hx hx E E E & & & + =, (34) Finally the energy aborbed by the heat exchanger can be written a follow: 6 A hx P E = C &, (35) where ( ) + + Δ Π = ν δ ε γ δ ρ ω B A a x C k m hx hx 4 6, (36) where A and B are parameter that include the acoutic preure and velocity: Δ + + Δ = L x x L x x A co co π π, (37) Δ + + Δ = L x x L x x B in in π π. (38) Combining equation (), (5), (30), and (35) the critical temperature difference acro the tack T Δ can be written a follow: C C C C C C T = Δ. (39) It i important to note that the temperature difference i a function of geometry and material property of the tack. Material propertie relate to thermo-phyical propertie of the material ued in the tack (air, copper, tainle teel). The geometrie relate to the reonator length L and radiu R, tack poition x and length x Δ, plate thickne l and pacing 0 y, and heat exchanger thickne hx l, pacing hx y, and length hx x Δ.

30 8 The acoutic preure amplitude A P in the exited region i another parameter that can be determined by modeling. The T Δ will be eliminated in order to olve for A P, which i a function of geometry of the tack, material property, and the temperature difference outide heat exchanger ext T Δ. ( ) geometry material property T P P ext A A,, Δ = Heat flux through the tack i a follow [3]: ( )( ) ( ) ( ) x T lk K y y y y x u x p T H v S S v Δ Δ + Π + + Γ Π = ) ( ) ( 4 σ σ σ δ σε δ δ ε σ β δ ν ν &, (40) After inerting the value for preure and velocity the equation become: B A P H A + = &. (4) where ( ) ( )( )( ) ΠΓ = in co y y a L x L x y l y T A v v δ ν δ ν ε σ σ ρ π π σ σ δ σε β δ, (4) ( ) x lk K y T B Δ + ΠΔ = 0, (43) In order to calculate the acoutic preure amplitude we equate the heat flux through the tack H & with the heat flux through either heat exchanger: Δ Δ = d S T T K H ext ) ( &, (44) where H & i the energy flux through either heat exchanger, cu K i thermal conductivity of copper, S effective area, and d i the effective ditance.

31 Thee parameter can be etimated a follow: R hx D d = = hx, 4 (45) S = nl hx Δx hx, (46) where n = π R ( l + y ) hx hx 0hx. (47) The heat flow through the heat exchanger can now be written a: ( ΔT ΔT ) H & = C, (48) hx where C nk ext l cu hx hx = 4. (49) D hx Δx Preure amplitude can be calculated equating the heat tranfer equation: P A ( ΔT ΔT ) C ext B =. (50) A... Refrigerator In the cae of the cooling demontrator, the main parameter are the temperature difference acro the tack and acoutic preure amplitude inide the reonator. In thi ection, conervation of energy i ued to develop all the formula neceary for both open-end and cloed-end ytem. The reult will be different ince the boundary condition are different. Therefore, not only the temperature of each end of the tack will be different, but alo the acoutic preure and velocity ditribution will have different form. 9

32 0 The preure and velocity component of the acoutic wave in the reonator for an openend cylindrical tube are function of timet, ditance x, frequency of the ignal []: ( ) = = a fl a x l f e P e p p t i A t i π π ω ω in in, (5) where a f a k ω π = =, (5) ( ) = = a fl a x l f iz e P e iu u t i A t i π π ω ω in co 0, (53) Z aira = ρ 0, (54) where a i the peed of ound, k i the wave number, and 0 Z i the acoutic impedance. For the refrigeration ytem the equation for thermoacoutic heat pumping can be written a follow []: ( )( ) Π = y y u p T H m k δ ν δ ν σ ε β δ & Γ 0 y ν δ σ σ σε σ σ, (55) where p and u can be etimated uing equation (5) and (53), crit m T T = Γ, (56)

33 Tt Tb Tm =, (57) Δx where T b i the temperature of the bottom of the tack cloe to the peaker, T t i the temperature of the top of the tack cloe to end of the reonator, and x i the ditance from the ource to the center of the tack. The poition of microphone depend of the configuration. For the cloed- and open-end ytem thi parameter i different. In figure 3 the configuration of the refrigerator i repreented: X T t L dx x T b Figure 3: Location of recorded temperature and refrigerator etting. Uing equation (5) we olve for P A, the preure amplitude inide the reonator. P A = πfl p ( xm ) in a πf ( l x) in a, (59) where ( x ) p m i the preure amplitude at the microphone location x m. We aim at the qualitative comparion of tet data and theoretical reult. Since the direction of the heat pumping i our main objective, the above formula can be implified a follow:

34 H ~ h, (60) ( x ) u ( x ) h = p. (6) For a cloed ended ytem patial variation of acoutic preure and velocity are: ( ) ( ρa) PA πf ( l x) p x = co, (6) πfl a in a ( l x) πf in ( ) a u x = ρap, (63) A πfl in a For etimating the thermoacoutic enthalpy flow, equation (60) and (6) can be ued for the cloed-end ytem a well.

35 .. Experimental Setup... Heat Engine The reonator of the engine conit of three part. The firt part i the tube with one end cloed acting a the hot heat exchanger in the ytem. It i made of olid copper tubing, which wa machined down to appropriate dimenion. The econd part i the ceramic tack holder that contain a cavity with the ame inner diameter a the copper tube. The third part i the open-end tube made of copper and imilarly machined to the right dimenion. Flange were added to each part, which were connected with each by long crew tightened with nut for the integrity of aembly. The heat exchanger were two layer of thin copper meh placed on each ide of the tack. The aembled engine i chematically hown in figure 5. The material ued for the tack were imilar to the Hofler tube [7]: Reticulated Vitreou Carbon foam (RVC) with two different denitie and a teel wool. RVC i a porou tructure or open-celled foam coniting of an interconnected network of olid fiber. RVC can be pecified with two different characteritic: the number of pore per inch (PPI) and volumetric poroity [8]. The RVC ued in our tet are 00 PPI and 80 PPI. The main dimenion of the two engine ued in thi experiment are identical except for the total length, which are 5.8 and 9.3 cm. Since the geometry and material propertie of each part of the engine are the variable that could change the reult, the two arbitrary length were choen to invetigate the change in reult with the change in geometry. The inner diameter of the copper tube and the tack holder i.4 cm. The copper tube have a 0.05 cm wall thickne. The tack length i 0.7 cm and i located.6 cm away from the cloed end. In figure 4 (a) and (b) the two engine are hown with their repective dimenion. 3

36 6 mm 35 mm 6 mm 70 mm 9.5 mm 5 mm 0.5 mm 4 mm 9.5 mm 5 mm 0.5 mm 4 mm mm mm 7 mm 7 mm 58 mm Figure 4: (a) Schematic of 5.8 cm engine. 93 mm (b) Schematic of 9.3 cm engine. The following figure how the engine tructure emphaizing all the part in the heat engine. End cap (Heat ource) Flange Bolt Open End Stack Hot Heat Exchanger Cold Heat Exchanger Ceramic Stack Holder Figure 5: Engine tructure. Figure 6 (a) and (b) how picture of the heat engine with and without the cooling jacket. In order to create a tight veel with the exception of the open end, graphite gaket that reit temperature up to 455 C were placed between flange of the engine part. Figure 6: (a) Aembled 9.3 cm engine with the cooling jacket. (b) Photo of the 5.8 cm engine. 4

37 To achieve the critical temperature difference acro the tack, the cloed end i heated uing a butane torch, and the oppoite end of the tack i cooled with the cooling water. A cooling jacket wa fabricated to fit over the open-end tube. Uing a cold-water bath and a circulator, water at approximately C i pumped through the jacket. The deign of the tack holder wa choen to reduce it cro-ectional area and heat tranfer between the hot and cold ection. Two K-type thermocouple were inerted between the flange and gaket on each ide of the tack for recording the temperature of the hot and cold end of the tack. A LinearX M5 microphone wa placed outide the engine for meauring the acoutic preure amplitude. Thi particular microphone i a high-performance low-voltage condener type. It i pecifically deigned for the meaurement of high ound preure level. The microphone conform to the external dimenion of indutry tandard / inch meaurement microphone. It ha 70dB SPL capability, wide frequency repone, low voltage power upply requirement, and a enitivity of.. The acoutic preure P wa meaured uing a microphone 30 cm away from the open end. The reaon for meauring at thi ditance wa to avoid change in boundary condition at the open end of the engine, and to provide an approximation to treat the open end a a point acoutic ource. A ound level meter wa alo ued at the ame ditance for comparion. Figure 7 how the etting of the experiment. Since under thee condition the ound produced will be reflected from other urface preent in the room, uch a the wall, ceiling, the table, and other object, the meaured value may contain a large margin of error. The microphone i 7 cm away from the left wall, about 400 cm away from the right wall, and about 80 cm away from the back wall. The ditance from ceiling to the microphone i 5

38 about 5 m and from the microphone to the ground i about 30 cm. The ditance to the table i about 6 cm where oft foam wa placed on for acoutic damping. Under thee pecific condition the acoutic preure wa meaured. Figure 7: Heat engine experimental etup.... Refrigerator The refrigerator i driven by a 00 W RCA 4 -way full range peaker made by Smart Mobile Technology. The peaker i mounted to a 5 cm thick platic plate. Thi plate ha a hole with the ize of the peaker to allow vertical movement of air. A cm thick platic plate, with a hole in the center the ame ize a the reonator, i crewed to the 5 cm plate, and an acrylic tube i inerted in the thinner plate. For the open end, the reonator i 7.5 cm long with an internal diameter of 3 cm. In the cae of the cloed end, the length of the tube i 9 cm o that a cap can be crewed on top, but the inner diameter wa machined to be the ame. Figure 8 how a repreentation of both ytem with all part and main dimenion. 6

39 30 mm 30 mm 75 mm 35 mm 90 mm x 0 mm x 0 mm 50 mm Figure 8: (a) Schematic of open-end ytem. 50 mm (b) Schematic of cloed-end ytem For each configuration, different type of tack were teted in order to find the mot efficient tack for each ytem. The tack material included cotton wool, teel wool with two different denitie, and ceramic with two different poroitie. The teel wool i a bundle of trand of very fine oft teel filament with a fiber diameter of 50 µm for uper-fine and 80 µm for fine wool. Thi particular teel wool i a production of Rhode American Steel Wool. The two grade that reponded to our ytem were the uper fine and extra fine. The Celcor cellular ceramic ubtrate ued in our experiment are made by Corning Incorporated and they have been widely ued at the core of the catalytic converter. The ceramic ubtrate have high temperature durability and can effectively operate at temperature up to 00 C. Their ingle piece tructure and cellular geometry enure tiffne and mechanical durability. The particular ceramic ued in thee experiment ha a poroity of 35% [0]. The ceramic tructure i parallel plate that are placed vertically, creating quare haped gap. Thee quare have a ide length of approximately mm. For our ytem the bet reult were obtained uing the uper-fine 7

40 teel wool. The following figure 9 (a) and (b) how the tructure of both cloed- and open-end refrigerator with all the component. Preure Tranducer End Cap Preure Tranducer Platic Tube (Reonator) Platic Tube (Reonator) Stack Stack Screw Screw Platic Plate 00 W Speaker Platic Plate 00 W Speaker Figure 9: (a) Open-end ytem. (b) Cloed-end ytem. Signal from a function generator i amplified and delivered to a peaker that produce ound. Since the reonator are detachable from the bae, the ame peaker i ued for both cloed and open ended ytem. In order to meaure the preure amplitude inide the reonator during operation, a preure tranducer i mounted to the reonator tube at a et location hown in figure 9. The tranducer i an 850C-5 Endevco Piezoreitive preure tranducer with a enitivity of.04 V P and a range from 0 to 03.4 kpa. Becaue of the different etting the location of the tranducer i different. The preure tranducer capture the ignal and end it to an amplifier, which i connected to an ocillocope. Utilizing the graphical reult of a 0B BK Preciion dual trace ocillocope, the ignal can be analyzed to determine the frequency and the preure amplitude during operation. In figure 0 (a) and (b) how a picture of both ytem during operation. 8

41 Figure 0: (a) Cloed-ended refrigerator. (b) Open-ended refrigerator. 9

42 Chapter 3 Reult and Dicuion 30

43 3. Reult and Dicuion In thi ection all the experimental reult for both heat engine and refrigerator are preented, dicued and compared to theoretical reult. 3.. Heat Engine It wa very important to reach the critical temperature difference in order for the ytem to repond and produce ound. The following figure are the reult of the 5.8 cm engine and RVC 00 PPI. In figure the recorded temperature over a period of time are preented. A we can ee the engine produced a ound in approximately one minute after the torch wa turned on, when the temperature difference acro the tack ound appear in the range ΔT = C Cold Temp Hot Temp Temperature Diff Temperature ( C) C 355 C C Time () Figure : Temperature profile for 5.8 cm. Another important meaurement in our heat engine wa the ound preure produced, which i preented in figure. 3

44 3 0.5 db Preure (Pa) Time () Figure : Preure profile for 5.8 cm engine. Uncertainty analyi wa done for thi configuration in order to identify the repeatability error. In figure3 the repeatability error for the temperature difference acro the tack after 60 and 50 i hown. In figure 4 the uncertainty for the preure meaurement i repreented. The uncertainty calculation made in thi ection i pecific for the etup and environment that the tet were carried. Thee uncertaintie do not apply in any other condition and configuration. 500 Temperature ( C) C 433. C Time () Figure 3: Variation of temperature difference for 5.8 cm engine. 4 RMS Preure(Pa) 3.76 Pa 0. Pa Time () Figure 4: Preure variation for 5.8 cm engine. 3

45 Time () T ( C) T ( C) T 3 ( C) T 4 ( C) T 5 ( C) T 6 ( C) T 7 ( C) T 8 ( C) T 9 ( C) T 0 ( C) Avg. Temp. ( C) Linearity ( C) Thermocouple Senitivity ( C) Thermometer Senitivity ( C) Zero Shift ( C) Standard Dev. ( C) Standard Dev. of Mean ( C).9.78 Total Bia ( C).6.48 Total Uncertainty ( C) Table : Tabulated temperature uncertainty calculation. Time () P (Pa) 0..8 P (Pa) 0..8 P 3 (Pa) P 4 (Pa) P 5 (Pa) P 6 (Pa) P 7 (Pa) 0..8 P 8 (Pa) 0..8 P 9 (Pa) P 0 (Pa) Avg. Acoutic Preure (Pa) Ocillocope Readability error (Pa) Microphone Senitivity (Pa) Standard Dev. (Pa) Standard Dev. of Mean (Pa) Total Bia (Pa) Total Uncertainty (Pa) Table : Tabulated preure uncertainty calculation. In figure 5 the preure amplitude of the ytem i plotted againt temperature difference acro the tack. Here we can ee that after reaching certain temperature at the hot end of the engine, in thi cae 500 C, the ytem reache teady tate and the change in preure amplitude i not dratic. From the time the ound produced to the time the ound reache maximum amplitude i about 35. The recorded temperature of the heat 33

46 ource, at the cloed end wa about 398 C when the ound wa produced, and it increaed up to 500 C when the ytem wa in teady tate. The cold-open end wa about 36 C and in teady tate reached approximately 65 C. A a reult, the temperature difference acro the tack wa 350 C at the tart and reached 430 C in equilibrium. In thee condition, the RMS acoutic preure for the 5.8 cm engine wa about.7 Pa, which i equivalent to 0 db ound preure level. The frequency of the ound produced wa about.4 khz at equilibrium. In thi cae the tack ued wa RVC 00 PPI. 3 Preure (Pa) Temperature ( C) Figure 5: Acoutic RMS preure with the change in temperature difference acro the tack. The ame proce wa repeated for the 5.8 cm engine with different tack. A mentioned before, the only other tack that reponded where the RVC 80 PPI and teel wool. When the engine produced ound, the acoutic preure amplitude and the frequency of the ytem were relatively imilar. The only difference wa in the time required for the engine to produce ound and the critical temperature difference acro the tack. In figure 6, 7 and 8 the temperature profile between the 5.8 cm engine with RVC 00 PPI, RVC 80 PPI and uper fine teel wool are preented. The temperature difference at which the engine tarted to produce ound are marked in the following figure: 34

47 500 Cold and Differential Temperature ( C) Temp. Diff. 400 Cold Temp C Time () Figure 6: Temperature profile for teel wool. 500 Cold and Differential Temperature ( C) Temp. Diff. Cold Temp. 355 C Time () Figure 7: Temperature profile for RVC 00 PPI. 500 Cold and Differential Temperature ( C) Temp. Diff. Cold Temp. 355 C Time () Figure 8: Temperature profile for RVC 80 PPI. 35

48 The ound preure level in all three cae reached a maximum of approximately 03 db. In figure 9 the reult for 5.8 cm engine with three different tack material are hown. In thi cae the temperature difference wa recorded over 80 time period. We can ee that the RVC PPI 00 and PPI 80 have very imilar reult. Both material require approximately 60 econd and a temperature difference acro the tack at about 350 C in order to produce ound. In the cae of teel wool the ound wa produced after about 90 econd and a temperature difference of about 380 C wa required for the engine to repond. Temperature Difference ( C) C 374 C RVC 00 PPI RVC 80 PPI Steel Wool Time () Figure 9: Temperature difference for RVC 00 PPI, 80 PPI, and teel-wool for 5.8 cm engine. The following reult repreent the temperature difference and the preure ditribution for RVC 00 PPI tack in the 5.8 cm and 9.3 cm engine. In figure 0 and, the temperature difference acro the tack and acoutic preure ditribution were plotted over 80 econd time period in order to ee how long it take for the engine to produce ound and reach equilibrium. The reult how that for the 5.8 cm engine we require about 60 econd in order to produce ound, but for the 9.3 cm engine, after only 45 econd, ound wa produced. Alo, a lower temperature difference acro the tack wa required for the longer engine to perform. The experimental reult were compared to the 36

49 theoretical analyi from ection... The tack ued in our ytem wa an RVC with non-uniform geometry, therefore the urface area needed to be recalculated. The RVC of 00 PPI and 80 PPI have 97% poroity. In order to calculate the urface area of the RVC it wa aumed that the tack i a olid material with uniform hole acro it. Thi aumption neglect the empty pace between the hole and ue the poroity of the RVC to determine the approximated perimeter. Making thee aumption the urface area determined to be a follow: S = Π Δx.8π ΔxR = r. (64) where R i the inner radiu of the tack holder, r i the radiu of the mall cylinder, and Δx i the length of the tack. Uing the new urface area formula for the 5.8 cm engine, the required temperature difference calculated i about C; and for the 9.3 cm it i about 73 C. However, the theoretical calculation contain idealized aumption becaue of irregularitie in the tack geometry and the aumption made to calculate the urface area. Alo, the theoretical reult do not take into account the heat lo to the environment and aume perfect condition; therefore the theoretical reult are ignificantly lower than the meaured value. The preure wa calculated for different temperature to compare with the acoutic preure meaured 30 cm away from the open end. In order to calculate the acoutic preure we aume that the open end of the engine i a point ource located in the center of a phere with a radiu of 30 cm (the ditance between the engine and the microphone). We calculate the radiated energy from the point ource to the phere uing equation (4) from ection... Since energy i conerved the radiated energy from 37

50 point ource to the phere mut equal the radiated energy from the phere to the urrounding environment. The equation ued to determine the radiated energy from the phere to the environment i a follow: m Pm E& 4π urr =. (65) ρa where m i the radiu of the phere, Pm i the RMS preure meaured, ρ i the denity of air, and a i the peed of ound in air. Setting equation (4) and (65) equal we can olve for P m which i determined to be a follow: P m π R PA =. (66) 8 L m The preure P m wa determined to be approximately.3 Pa for the 5.8 cm engine and.8 Pa for the 9.3 cm engine for Δ Text at about 0 C. 38

51 Temperature Difference ( C) C C cm RVC 00 PPI cm RVC 00 PPI Time () Figure 0: Temperature profile for 5.8 cm and 9.3 cm engine with RVC 00 PPI. RMS Preure (Pa) cm RVC 00 PPI 9.3 cm RVC 00 PPI 03 db 0 db Time () Figure : Acoutic preure profile for 5.8 cm and 9.3 cm engine with RVC 00 PPI. In order to find the average acoutic preure amplitude the microphone wa moved around the engine 80 and the effect were recorded for the RVC 00 PPI and 5.8 cm engine. In table 3 the reult are tabulated. Angle ( ) RMS Preure (Pa) SPL Uing Microphone (db) SPL Uing Souldlevel Meter (db) Table 3: Tabulated reult of the acoutic preure for RVC 00 PPI. 39

52 The ame meaurement were taken for the RVC 80 PPI and teel wool. The reult are tabulated in table 4 and 5. Angle ( ) RMS Preure (Pa) SPL Uing Microphone (db) SPL Uing Souldlevel Meter (db) Table 4: Tabulated reult of the acoutic preure for RVC 80 PPI. Angle ( ) RMS Preure (Pa) SPL Uing Microphone (db) SPL Uing Souldlevel Meter (db) Table 5: Tabulated reult of the acoutic preure for teel-wool. Thee reult how that the tronget ignal for all three cae take place at an angle of about 30. The SPL meaured at different angle uing the ound-level meter were much larger than the SPL meaured uing the microphone. The reaon for that could be the fact that the ound-level meter i not very enitive and capture all the noie from urrounding. The repeatability error of thee meaurement were alo calculated by repeating the meaurement taken at each angle multiple time. The reult are tabulated in table 6 and hown in figure. The total intrumental uncertainty i about % for the microphone. 40

53 RMS Preure(Pa) Pa 0 0. Pa Angle ( ) Figure : Acoutic preure error meaurement at different angle for 5.8 cm engine. Angle ( ) P (Pa) P (Pa) P 3 (Pa) P 4 (Pa) P 5 (Pa) P 6 (Pa) P 7 (Pa) P 8 (Pa) Avg. Acoutic Preure (Pa) Ocillocope Readability error (Pa) Microphone Senitivity (Pa) Standard Dev. (Pa) Standard Dev. of Mean (Pa) Total Bia (Pa) Total Uncertainty (Pa) Table 6: Preure uncertainty calculation for 5.3 cm engine at different angle. Even though the reult are very cloe for all three tack material, we can conclude that for 5.8 cm engine the RVC 00 PPI wa the mot uitable tack, reulting to the highet acoutic preure amplitude at all angle. Uing thi aumption and equation (65) the acoutic power W & can be determined, which wa 0.0 W and 0.04 W for the 5.8 cm and 9.3 cm engine repectively. Becaue of the uncertaintie in the preure and dimenion meaurement error the uncertaintie of the calculated acoutic 4

54 power for thee particular configuration were about 4%. The acoutic preure meaurement were obtained by averaging the preure amplitude obtained for the ame engine condition but different microphone poition. The rate of heat upplied to the tack Q & in can be determined uing equation (40). The reult were about W and.4 W for 5.8 cm and 9.3 cm engine repectively; therefore the thermoacoutic efficiency of the ytem can be calculated uing the thermoacoutic efficiency formula a follow: W& η =. (67) & Q in Uing equation (67) the efficiency of the thermoacoutic heat engine for 5.8 cm engine i about % and for the 9.3 cm engine i determined to be about.%. The reult for both engine length are tabulated in table 7. Reonator length, L 5.8 cm 9.3 cm Meaured parameter: Temperature difference acro tack, Δ T 398 C 35 C Radiated acoutic power, E & 0.0 W 0.0 W rad Frequency, f.4 khz.0 khz Calculated parameter: Acoutic preure amplitude in the engine, P.0 kpa 3.9 kpa A Acoutic power generated in the tack, W & 0.0 W 0.04 W Rate of heat upply to the tack, Q &.00 W.40 W in Thermoacoutic efficiency, η = W & / Q &.0%.% in Table 7: Tabulated experimental and theoretical reult for both 5.8 and 9.3 cm engine. 4