Synthetic Jet Cooling Part I: Overview of Heat Transfer and Acoustics

Transcription

1 Synthetic Jet Cooling Part I: Oeriew of Heat Transfer and Acoustics Clemens J.M. Lasance 1, Ronald M. Aarts 1,2 1 Philis Research Laboratories, 2 Eindhoen Uniersity of Technology High Tech Camus 4, 5656 AE Eindhoen, The Netherlands clemens.lasance@hilis.com Abstract The aer deals with an oeriew of the rinciles of heat transfer and acoustics related to a romising alternatie for fans: synthetic jet cooling. After a short discussion of the benefits, the background and the rinciles underlying the hysics are treated. The roblems with otimisation through numerical analysis are highlighted. An accomanying aer discusses the exerimental results in terms of heat transfer and noise for a secial embodiment: an acoustic diole cooler. 1. Introduction Many current and future consumer roducts suffer from thermal roblems due on the one hand to miniaturisation and more features leading to increased temeratures, while on the other hand the customer exects higher reliability and less noise. Natural or forced cooling with air will be the referred choice for a long time to come for many consumer roducts with the excetion of comuters. Unfortunately, the cooling otential of natural conection is reaching its hysical limits in today s roducts. Howeer, there is a certain reluctance to switch to fans due to the disadantages usually associated with them. A cooling technology that could significantly enhance natural conection while at the same time relaxing many of the drawbacks of a fan would be an interesting otion for many electronic roducts. One of the most romising otions is to use jets, in articular synthetic jets. Basically, the technology requires only a small loudseaker and some electronics. The benefits are somewhat deendent on the alication, but in general the following imroements are exected when comaring synthetic jet cooling with fans, for the same heat transfer erformance: (much) lower noise leel better (thermodynamic) efficiency, half the ower or less design-friendly because of much better form factor intrinsic higher reliability less fouling roblems, the ibrating art can be rotected from the ambient miniaturisation easier than with fans relatiely simle noise cancellation ossible 2. Physical rinciles of synthetic jets It is well known that a jet generates sound, conersely the oosite is also true: sound can generate jets. This henomenon is known as acoustic streaming. Acoustic streaming is essentially a net mean flow generated by a sound field. Basically, the sound wae is attenuated by the iscosity and the inertia of the medium, resulting in a ressure gradient along the wae roagation direction exerting a body force on the medium leading to induced flow. Faraday, in 1831, was the first to describe emirically the flow that deelos near a ibrating surface. Just oer 1 years ago, Rayleigh was the first to roide a theoretical descrition that is still alid today to a first aroximation. From a theoretical oint of iew a major roblem is that acoustic streaming is drien by nonlinear effects and hence cannot be analysed using linear acoustics. Noteworthy are the arious classifications in literature, all with their own simlifications of the full Naier- Stokes equations: boundary-layer-drien streaming, outer streaming, inner streaming, Rayleigh streaming, Eckert streaming, Stuart streaming, Gedeon streaming, jet-drien streaming, traelling-wae streaming, small-scale or largescale streaming, slow or fast streaming. This is one of the reasons that the henomenon is difficult to understand. One of the results is that it is rather comlicated to exlain the hysics to eole who are not exerts in fluid dynamics. Two oeriews hae been ublished: by Lighthill in , and by Boluriaan and Morris in One of the most imortant alications that motiated research in this field is the use of acoustic streaming for aerodynamic flow control deices resulting in drag reduction, lift enhancement, mixing augmentation and flow-induced noise suression. The interaction of synthetic jets with an external cross flow oer the surface in which they are mounted can effect flow changes on length scales that are one to two orders of magnitude larger than the characteristic scale of the jets. A reiew coering this alication field has been ublished by Glezer and Amitay in Some other alications are: roulsion, microums, non-contact surface cleaning and heat transfer enhancement. Focusing on cooling, already in the late 193 s Marthelli and Boelter 4 reorted enhancement oer natural conection from a ibrating horizontal cylinder. Vainshtein et al, 5 analysed the heat transfer between two lates at different temeratures and showed that the heat transfer could be enhanced by an order of magnitude using high-frequency, high-amlitude sound fields. Contrary to a traditional jet, a synthetic jet oerates without net mass injection and is constructed from the surrounding fluid, see Figure /8/$ IEEE 2 24th IEEE SEMI-THERM Symosium

2 Figure 1: Sketch of synthetic jet formed by an actuator in a caity roided with an orifice 1 In more technical terms, it is a deice that requires zero mass inut yet roduces non-zero momentum outut. They are synthesized from the coalescence of a train of ortices as a result of a time-harmonic motion of a diahragm drien by whateer means, iezoelectric, mechanical or magnetic, roided the amlitude is large enough to induce flow searation at the orifice. In this case a shear layer is formed between the exelled fluid and the surrounding fluid. This layer of orticity rolls u to form a ortex ring (axisymmetric) or ortex air (two-dimensional slot). A synthetic jet is nothing more than a sequence of ortex rings created one after another. Without the time-harmonic motion, the henomenon of ortex ring creation is actually a well-known daily occurrence, many eole hae tried at one oint or another to blow smoke rings. A design known as a smokeortex launcher is ery oular in undergraduate hysics demonstrations, see Figure 2. focusing on a lane two-dimensional jet formed by the motion of a circular diahragm drien at resonance (nominally 114 Hz) in a sealed caity with a rectangular orifice measuring.5*75 mm. One of the obsered differences with conentional 2D jets is that the net entrained olume flow rate is substantially larger. Smith and Swift 11 showed the difference between steady and oscillatory flow losses caused by bends, exansion and entrance effects, mainly for understanding the acoustic streaming losses for thermoacoustic engines. The interaction of adjacent synthetic jets has been studied by Smith and Glezer 12. Recent aers coering ractical alications are 13, 14, 15, 16, 17, 18, 19, 2, 21, Synthetic jet design: acoustic considerations The inestigation of reroduction of low frequency sound signals by means of small transducers with an accetable efficiency has recently led to resonant loudseaker systems 23. These systems consist of a loudseaker connected to a tube that acts as a resonator. In the otimal condition the ie length must be of the order of λ/4, with λ the acoustical waelength. It was obsered that the sound waes roduced by these systems generate ulsating air streams near the outlet of the tube. Ideally we want to use a small loudseaker with large amlitude to generate the jet. Small cabinet loudseakers are quite inefficient. Fortunately we are not concerned with achieing a flat Sound Pressure Leel (SPL) resonse and therefore we can roide a system with greater usable efficiency. Such a non-flat design can be constructed with a ery comact housing 24, 25, but small driers usually require a relatiely large cone excursion to obtain a high SPL. In 23 a new solution is resented that uses a resonant combination of a couling olume and a long ie-shaed ort. The efficient resonant couling of the drier to the acoustic load by this construct enables small driers with modest cone dislacement to achiee a high SPL. Figure 2: Tyical ortex launcher Jet formation associated with oscillating solid boundaries hae been the subject of numerous inestigations. As early as 195 Ingard and Labate 6 used standing waes in an acoustically drien circular tube to induce an oscillating elocity field of an orifice late laced near a ressure node and obsered the formation of jets from trains of ortex rings on both sides of the orifice. In 1975, Medniko and Noitskii 7 reorted jet formation without net mass flux and aerage elocities u to 17 m/s by inducing a low-frequency elocity field with a mechanical iston. In 198, Lebedea 8 created a round jet with elocities u to 1 m/s by transmitting high amlitude sound waes through an orifice laced at the end of a tube. A major contribution to the theory and alication of synthetic jets has been realised by Glezer s grou at Georgia Tech in Atlanta. The first aer on synthetic jet cooling aeared in Smith and Glezer 1 resented a useful oeriew of the formation and eolution of synthetic jets Figure 3: Schematic construction of loudseakers. (a) Bandass enclosure with long ort. (b) Bass-reflex enclosure with long ort We define the frequency f for the configuration of Figure 3a as the resonance frequency of the box with closed olume V lus the drier, in the absence of olume V 1 and the ie. In the case of Figure 3b f = f b, where f b is the free air resonance frequency of the drier. With a band-ass box design, f usually coincides with the Helmholtz frequency f H. Howeer, for long ies f can differ considerably from f H. For examle, the enclosure of Figure 3(b) may look like a 24th IEEE SEMI-THERM Symosium

3 Helmholtz resonator, but the ie is so long that it does not act like one. This can be clarified by calculating the Helmholtz resonance frequency of a simle Helmholtz resonator, gien as: c S f H = (1) 2π L V 1 where L is the effectie ie length that includes an end correction needed to account for the comlex acoustic radiation imedance of the ie. If the arameters of Table 1 are used in Eq. (1), then we get f H = 3Hz whereas the system has an anti-resonance frequency of f b = 277Hz. Helmholtz frequency f H 3 (Hz) Resonance frequency f b 277 (Hz) Front Volume V 1 8 (cm 2 ) Port length L 12 (mm) Effectie Port length L ' (mm) Port radius r 3 (mm) Port Area S 28.3 (mm 2 ) Port losses R.31 (Ns/m) Port losses Q 3 (-) Table 1: Fitted arameters of rototye ie 2 = Z 2 j ρ c S 1 sin kl + cos kl Looking at Eq. (3), we see that at frequencies such that Z 2 «ρ c S and sin kl ~1, 2 can be much larger than 1. For these frequencies we get a gain of 2 1 ρcs = jz It is this gain that we want to exloit. 2 (3) (4) Aarently the ie is so long that we must use a transmission-line model, rather than alying Eq. (1). In the following we continue to denote the working frequency f work by f b, which alies for any length of ie, in contrast to f H, which together with Eq. (1) alies only to a system using a short ie. We refer to a long ie, somewhat arbitrarily, if L > λ/1, where λ = c/f is the waelength of the signal at the working frequency f. Mounting the ie to a front olume V 1 has the adantages that the ie length can be traded for the front olume without affecting efficiency at resonance, and that the drier diameter may be of a larger size than the ie diameter, as shown schematically in Figure 3. Figure 4 gies the imedances and elocities occurring in the system s ie of cross-sectional area S and length L. The band-ass system is modelled by a lumed-element model according to Figure. It is the combination of this front olume, the long ie-shaed ort, and the drier itself that enables an efficient resonant couling between the drier and the acoustic load. We will discuss in the following the acoustics of the long ort, which form an integral art of the resonating system. If the air is ibrating harmonically with a frequency corresonding to the wae number k=ω/c and elocity 1, then the inut mechanical imedance Z 1 is gien by 26 : Z 1 = ρ c S Z2 cos kl + j sin kl ρcs Z 2 j sin kl + cos kl ρ c S The elocity at the end of the ie is (2) Figure 4: Mechanical imedances Z and elocities in system ie Figure 5: Lumed element model of system according to Figure 4 A loudseaker in a ie can be noisy. To reduce the noise a sound source of oosite hase can be used to cancel the original signal. Here it is assumed that the hase relating to the linear art of the acoustic field (the tonal sound) is of oosite hase with resect to both orifices of the ies, like a diole 26. In the simlest form one ie is acoustically connected to one side of the loudseaker cone, and the other ie to the other side of the cone, see Figure 6. The assumtion is that the blowing art does not add coherently and een contributes to the jet. 24th IEEE SEMI-THERM Symosium

4 Figure 6: Diole with noise cancellation 4. Numerical analysis of synthetic jets: challenges From a design oint of iew it would be ery aluable if numerical modelling could be used with confidence. Unfortunately, accurate numerical analysis of acoustic streaming henomena is difficult due to the following reasons: Moing boundaries: non-linear diahragm modelling required Very dense mesh required Microsecond to second temoral scales Large solution domain, much larger than the caity From fully comressible to fully incomressible There are many arameters that hae to be otimised and we need numerically efficient methods to simulate these flows. A number of methods are described in literature, of which a selection of releant aers is listed below Introduction The traditional aroach in Comutational Fluid Dynamics (CFD) is to start with the Naier-Stokes (NS) equations. A major roblem is turbulence modelling because it turns out that eery aroximation based on statistically aeraging introduces a new aroximation, the so-called closure roblem. One way out is to sole the equations directly without any assumtion about turbulence modelling (Direct Numerical Simulation (DNS)), howeer, because this inoles the solution of all turbulence scales the grid requirements limit alications to the most simle of models. A oular method, certainly with the increased comuter ower right on one s desk, is Large Eddy Simulation (LES) that differs from DNS in resoling only the larger scales and assuming a model for the smallest scales. More comutationally efficient but also less accurate are methods called Reynolds Aerage Naier Stokes (RANS). All these methods are based on soling continuum hysics. Increasingly oular for multi-scale simulation aroaches are methods that use the dynamics of article density functions. Usually a distinction is made between Molecular Dynamics (MD) models and seudo-article models. The first grou soles the interatomic forces and is obiously not ery suited for the ery large number of articles that occur in a dense gas. The second grou is usually diided in off-lattice models and lattice-based models. Off-lattice models don t make use of a lattice, instead they use Monte-Carlo methods. A combination of MD and Direct Simulation Monte Carlo has been deeloed 27. Lattice-based models include the older lattice gas automata and, more recently, lattice Boltzmann automata methods, of which the Lattice Boltzmann Method (LBM) is becoming quite oular, mainly because they are more numerically stable and comutationally more efficient than Finite Volume or Finite Element solers, in fact, orders of magnitude faster. An LBM comrises a set of nodes arranged on a Cartesian grid. The nodes are connected by links. Links are occuied by articles moing from one node to the next according to certain rules determined by density functions and scattering mechanisms. Reeated alication of local rules for the motion, collision and re-distribution of seudo-articles generates the resulting flow field. It can be roen that an LBM solution is also a solution of the NS equations. Howeer, days of CPU time are still required! 4.2. Lower-order and hybrid models Yamalee and Carenter 28 discussed a reduced-order model for simulation of synthetic jet actuators combining the accuracy of full numerical simulation methods with the efficiency of zero-order models. They demonstrated that the jet elocity strongly deends on the diahragm frequency, due to fluid comressibility effects. Some faourable results hae also been reorted by Gallas et al. using a low-dimensional modelling aroach 29, 3 and by Li using a reduced-order model and LES 31, 32. Holman et al., 33 showed that the generally used dimensionless stroke length for estimating the goerning arameters of a synthetic jet can be imroed and formulated a general jet formation criterion based on the Strouhal number and the geometry of the orifice. They also erformed a numerical study using a Cartesian grid soler for the NS equations. The adantage is that eerything is modelled on a stationary mesh. A romising aroach seems to be a hybrid solution using Euler equations for the caity and full Naier-Stokes for the exterior 34. Lower-order and analytically-based solutions are ery useful for getting a feeling which arameter combinations goern the hysics Traditional CFD LES and Unsteady Reynolds Aeraged Naier-Stokes (URANS) simulations of the interaction of synthetic jets with a turbulent boundary layer are studied by a French grou 35. Fugal, et al., 36 used a commercially aailable CFD-code to study the influence of the exit geometry for a 2D lanar jet using an incomressible, unsteady URANS-based solution strategy with a standard k-ε model. They concluded among others that the ower required to form a synthetic jet is 24th IEEE SEMI-THERM Symosium

5 significantly smaller for a rounded exit comared to a sharedged exit Lattice Boltzmann Methods Useful oeriews can be found in Chen and Doolen 37 and two web-based sites 38, 39. Haydock and Yeomans 4 described Lattice Boltzmann simulations of acoustic streaming as a steady flow field suerimosed uon the oscillatory motion of a sound wae roagating in a fluid. An alication of LBM to simulating the mechanism of sound generation in flutes was treated by Kuehnelt 41. He discusses among others the roblems with tracking both the sound field and the aerodynamic field, which roagate with disarate elocities and are weakly couled. Wang and Menon 42 describe a hybrid aroach couling LBM for the jet formation and LES for the far field. In an extensie reort Menon and Soo 43, 44 discuss DNS and LES of three-dimensional jets using LBM. One of their results was that in search for grid indeendence it was found that the solution beyond the caity is highly sensitie to the resolution at the orifice. Unfortunately, desite significant imroements in solution time comared to DNS they quote multile days of CPU time on a Cray multirocessor massiely arallel comuter system. The imortance of synthetic jet numerical simulation is also demonstrated by the creation of a synthetic jet flow field database for CFD alidation uroses 45. Unfortunately, after reading this study one tends to become rather essimistic about a useful aroach for the foreseeable future due to oerwhelming roblems with sufficiently accurate exerimental and numerical analyses related to a synthetic jet. Conclusions The aer discusses the rinciles of heat transfer and acoustics underlying synthetic jet technology for cooling uroses. Comared to fans, the benefits are highlighted and it is concluded that significant imroements can be exected in terms of heat transfer, acoustics, reliability and design freedom. A loudseaker in a secial enclosure yields a resonant system enabling a large form factor design freedom cooling system. In addition it can be a comact, sensitie, and relatiely efficient requiring a relatiely low cone excursion, which makes the system ery suitable for low-noise actie cooling. It is argued that numerical analysis is a must for future design otimization and seeral otions are discussed. Unfortunately, it must be concluded that the state-of-the-art techniques are not suited outside uniersity enironments. A romising way to circument the numerical roblems associated with synthetic jets is to adat the theory of continuous jets. Finally, if this technology takes off, it is obious that the designer needs a comact model of a synthetic jet to be used in system leel CFD analysis, akin to the way fans are currently handled. References 1. Lighthill J., Acoustic streaming, J. of Sound and Vibration ol.61, (1978) 2. Boluriaan S. and Morris P., Acoustic streaming: from Rayleigh to today, Aeroacoustics ol (23) 3. Glezer A. and Amitay M., Synthetic Jets, Annu. Re. Fluid Mech. ol.34, (22) 4. Marthelli R. and Boelter L., The effect of ibration on heat transfer by free conection from a horizontal cylinder, Proc. 5th Int. Congr. Al. Mechanics, (1939) 5. Vainshtein P., Fichman M., Gutfinger C., Acoustic enhancement of heat transfer between two arallel lates, Int. JHMT ol.38, (1995) 6. Ingard U. and Labate S., Acoustic circulation effects and the nonlinear imedance of orifices, J. Acoust. Soc. Am. ol.22,.211 (195) 7. Medniko E. and Noitskii B., Exerimental study of intense acoustic streaming, So. Phys. Acoust. ol.21,.152 (1975) 8. Lebedea I., Exerimental study of acoustic streaming in the icinity of orifices, So. Phys. Acoust. ol.26,.331 (198) 9. Thomson, M. R., Denny, D. L., Black, W. Z., Hartley, J. G., Glezer, A., Cooling of Microelectronic Deices using Synthetic Jet Technology, 11th Euroean Microelectronics Conference, Venice, Italy, (1997) 1. Smith B. and Glezer A., The formation and eolution of synthetic jets, Physics of Fluids, ol.1, (1998) 11. Smith B. and Swift G., Power dissiation and timeaeraged ressure in oscillating flow through a sudden area change, J. Acoust. Soc. Am. ol.113, (23) 12. Smith B. and Glezer A., Vectoring of adjacent synthetic jets, AIAA Journal, ol.43, (25) 13. Beratlis N. and Smith M., Otimization of synthetic jet cooling for microelectronics alications, 19th SEMITHERM San Jose, (23) 14. Gerty D. Mahalingam R., Glezer A., Design and characterization of a heat sink cooled by an integrated synthetic jet matrix, ITHERM 6, (26) 15. Gerty D., Gerlach D., Joshi Y., Glezer A., Deeloment of a rototye thermal management solution for -3D-stacked chi electronics by interleaed solid sreaders and synthetic jets, Therminic 27, Budaest (27) 16. Kercher D., Lee J-B., Brand O., Allen M., Glezer A., Microjet cooling deices for thermal management of electronics, IEEE CPT ol.26, (23) 17. Mahalingam R. and Glezer A., Air-cooled heat sinks integrated with synthetic jets, Proc. ITHERM2, , (22) 18. Mahalingam R. and Glezer A., Low-rofile synthetic jet cooling for ortable comuters, OIPACK3, Maui, aer # 3569 (23) 24th IEEE SEMI-THERM Symosium

6 19. Mahalingam R., Rumigny N., Glezer A., Thermal management using synthetic jet ejectors, IEEE CPT ol.27, (24) 2. Mahalingam R., Heffington S., Jones L., Schwickert M., Newisys serer rocessor cooling augmentation using synthetic jet ejectors, ITHERM 6, (26) 21. Mahalingam R. and Glezer A., Design and thermal characteristics of a synthetic jet ejector heat sink, ASME JEP ol.127, (25) 22. Mahalingam R., Heffington S., Jones L., Williams R., Synthetic jets for forced air cooling of electronics, Electronics Cooling, ol.13, no.2 (27) 23. Aarts R.M., Nieuwendijk J.A.M., Ouweltjes O., Efficient Resonant Loudseakers with Large Form-Factor Design Freedom, J. Audio Eng. Soc., 54(1), October, (26) 24. Larsen E. and Aarts R.M., Audio Bandwidth extension. Alication of Psychoacoustics, Signal Processing and Loudseaker Design., J. Wiley, ISBN (24) 25. Aarts R.M., High-Efficiency Low-Bl Loudseakers, J. Audio Eng. Soc., 53(7), (25) 26. Kinsler L.E., Frey A.R., Coens A.B., Sanders J.V., Fundamentals of acoustics, Wiley (1982) 27. Nedea S., Frijns A., Steenhoen A. Van, Hybrid method couling molecular dynamics and Monte Carlo simulations to study the roerties of gases in microchannels and nanochannels, Phys. Re. E ol.72, 1675 (25) 28. Yamalee N., Carenter M., Ferguson F., A reducedorder model for efficient simulation of synthetic jet actuators, AIAA Journal ol.43, (25) 29. Gallas Q., Holman R., Nishida T., Carroll B., Shelak M., Cattafeta L., Lumed element modeling of iezoelectric drien synthetic jet actuators, AIAA Journal ol.41, , (23) 3. Gallas Q., Holman R., Raju R., Mittal R., Shelak M., Cattafesa L., Low Dimensional Modeling of Zero-Net Mass-Flux Actuators, 2nd AIAA Flow Control Conference, Portland, OR, AIAA (24) 31. Li S. and Smith M., A reduced-order model of an axis symmetric synthetic jet caity, 56th APS Meeting of the Diision of Fluid Dynamics, Noember 23-25, New Jersey (23) 32. Li S., A Numerical Study of Micro Synthetic Jet and Its Alications in Thermal Management, PhD Thesis, GATech Atlanta (25) 33. Holman R., Utturkar Y., Mittal R., Smith B., Cattafesta L., Formation criteria for synthetic jets, AIAA Journal, ol.43, (25) 34. Yamalee N. and Carenter M., A Reduced-Order Model for Efficient Simulation of Synthetic Jet Actuators, NASA/TM (23) 35. Dandois J. and Garnier E., Unsteady simulation of a synthetic jet in a crossflow, AIAA Journal ol.44,.225 (26) 36. Fugal S., Smith B., Sall R., Dislacement amlitude scaling of a two-dimensional synthetic jet, Phys. of Fluids ol.17, 4513 (25) 37. Chen S. and Doolen D., Lattice Boltzmann method for fluid flows, Annual Reiew of Fluid Mechancis, ol.3, (1998) 38. Raabe D., Oeriew on the LBM for nano and microscale fluid dynamics, htt:// 39. htt:// 4. Haydock D. and Yeomans J., Lattice Boltzmann simulations of acoustic streaming, J. Phys. A ol.34, (21) 41. Kuehnelt H., Simulating the mechanism of sound generation in flutes using the lattice Boltzmann method, Proc. Stockholm Music Acoustics Conf., SMAC3, (23) 42. Wang H. and Menon S., Fuel-Air mixing enhancement by synthetic microjets, AIAA Journal ol.39,.238 (21) 43. Menon S. and Soo J., Direct and large-eddy simulations of three-dimensional jets using the lattice-boltzmann method, Final Reort submitted to Army Research Office (22) 44. Menon S. and Soo J., Simulation of ortex dynamics in three-dimensional synthetic and free jets using the largeeddy lattice Boltzmann method, J. of Turbulence, ol.5, N32 (24) 45. Yao C., Chen F., Neuhart D., Harris J., Synthetic Jet Flow Field Database for CFD Validation, 2nd AIAA Flow Control Conference, Portland, OR, AIAA (24) 24th IEEE SEMI-THERM Symosium