Mark Kimber

Local Heat Transfer Coefficients Induced by Piezoelectrically Actuated Vibrating Cantilevers

Piezoelectric fans have been shown to provide substantial enhancements in heat transfer over natural convection while consuming very little power. These devices consist of a piezoelectric material attached to a flexible cantilever beam. When driven at resonance, large oscillations at the cantilever tip cause fluid motion, which in turn results in improved heat transfer rates. In this study, the local heat transfer coefficients induced by piezoelectric fans are determined experimentally for a fan vibrating close to an electrically heated stainless steel foil, and the entire temperature field is observed by means of an infrared camera. Four vibration amplitudes ranging from 6.35 to 10 mm are considered, with the distance from the heat source to the fan tip chosen to vary from 0.01 to 2.0 times the amplitude. The two-dimensional contours of the local heat transfer coefficient transition from a lobed shape at small gaps to an almost circular shape at intermediate gaps. At larger gaps, the heat transfer coefficient distribution becomes elliptical in shape. Correlations developed with appropriate Reynolds and Nusselt number definitions describe the area-averaged thermal performance with a maximum error of less than 12%.

Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low Keulegan-Carpenter numbers

Slender sharp-edged flexible beams such as flapping wings of micro air vehicles (MAVs), piezoelectric fans and insect wings typically oscillate at moderate-to-high values of non-dimensional frequency parameter β with amplitudes as large as their widths resulting in Keulegan–Carpenter (KC) numbers of order one. Their oscillations give rise to aerodynamic damping forces which vary nonlinearly with the oscillation amplitude and frequency; in contrast, at infinitesimal KC numbers the fluid damping coefficient is independent of the oscillation amplitude. In this article, we present experimental results to demonstrate the phenomenon of nonlinear aerodynamic damping in slender sharp-edged beams oscillating in surrounding fluid with amplitudes comparable to their widths. Furthermore, we develop a general theory to predict the amplitude and frequency dependence of aerodynamic damping of these beams by coupling the structural motions to an inviscid incompressible fluid. The fluid–structure interaction model developed here accounts for separation of flow and vortex shedding at sharp edges of the beam, and studies vortex-shedding-induced aerodynamic damping in slender sharp-edged beams for different values of the KC number and the frequency parameter β. The predictions of the theoretical model agree well with the experimental results obtained after performing experiments with piezoelectric fans under vacuum and ambient conditions.

Pressure and Flow Rate Performance of Piezoelectric Fans

A piezoelectric fan is a flexible cantilever beam whose vibration is actuated by means of a piezoelectric material. Such fans have been employed for the enhancement of heat transfer by increasing the fluid circulation in regions which are otherwise stagnant. The main focus of past studies has been to predict and describe the heat transfer achievable using these devices, as well as the flow field generated by vibrating cantilevers. In order to directly compare these fans with their traditional counterparts such as small axial fans, the present work casts the performance of piezofans in terms of a characteristic often used to represent conventional fans, namely the fan curve. The primary focus of this paper is to determine the relationship between the pressure and the flow rate generated by miniature piezoelectric fans. Experimental measurements are obtained for fans with operating frequencies of 60 and 113 Hz. The maximum flow rate conditions yield nearly 30 l/min, while the greatest static pressure generated is found to be 6 Pa. The performance is highly dependent on both the vibration amplitude and frequency. Predictive relationships are developed to describe the experimental trends and provide insight into the sensitivity of pressure and flow rate to these operating parameters. These fans are directly compared to two commercially available axial fans, both in terms of overall performance and efficiency with which energy is imparted to the fluid. Piezoelectric fans are found to compare quite favorably using either of these performance metrics with a nearly order-of-magnitude increase in fan efficiency. A secondary focus of this paper is to explore the effects of fan installation details on fan performance. The proximity of surrounding walls is considered through the use of three different enclosures within which the fan is mounted. Effective inlet areas from which the air enters the fan are also identified. This paper provides a practical framework for determining the optimal placement and configuration for these fans in prototypical applications.

Cooling Performance of Arrays of Vibrating Cantilevers

A piezoelectric fan is a cantilever beam whose vibration is actuated by means of a piezoelectric element. This element is typically bonded near the clamped end of the beam and induces a bending moment at the interface between the cantilever beam and the piezo element when a voltage is applied. For an alternating voltage, the beam is set into an oscillatory motion, which in turn creates motion in the surrounding fluid. This fluid motion has been shown to provide heat transfer enhancements with low power consumption in an otherwise quiescent region. These devices can also be configured to meet the geometric constraints of applications where the limited available volume might preclude the use of traditional cooling techniques. The fan design can be tailored to operate at frequencies, which are inaudible to the human ear. Due to these attractive features, piezoelectric fans have been investigated in the literature for practical cooling applications. Vibrating cantilever-type structures have been commonplace in engineering for decades. However, detailed studies of the motion induced in the surrounding fluid, and more importantly its effect on heat transfer, have only been recently undertaken. Flow field measurements around a cantilever vibrating in quiescent air at relatively small vibration amplitudes less than 3 mm peak-topeak tip vibration were obtained by Kim et al. 1. They observed a pair of counter-rotating vortices from each oscillation cycle. These vortices were shed from the fan tip as it passed the position of zero displacement. The maximum velocity occurred in the region between these two vortices and just beyond the cantilever tip, and was measured to be approximately four times the maximum tip velocity. Kimber et al. 2 experimentally measured the local heat transfer characteristics of piezoelectric fans and developed heat transfer correlations based on applicable dimensionless numbers. Numerical modeling of the fluid flow and heat transfer induced

Quantification of piezoelectric fan flow rate performance and experimental identification of installation effects

A piezoelectric fan is a flexible cantilever beam whose vibration is actuated by means of a piezoelectric material. Such fans have been employed for the enhancement of heat transfer by increasing the fluid circulation in regions which are otherwise stagnant. The main focus of past studies has been to describe the heat transfer achieved from these devices, as well as the flow field generated by vibrating cantilevers. In order to directly compare these fans with their traditional counterparts such as small axial fans, the present work casts the performance of piezofans in terms of a characteristic often used to represent conventional fans, namely the fan curve. The main thrust of this paper is to determine the relationship between the pressure and flow rate generated by miniature piezoelectric fans. Experimental measurements are obtained for two different fans with operating frequencies of 60 and 113 Hz. The maximum flow rate conditions yield nearly 30 1/min, while the greatest static pressure generated is found to be 6 Pa. The performance is highly dependent on both the vibration amplitude and frequency. Predictive relationships are developed to describe the experimental trends and provide insight into the sensitivity of pressure and flow rate to these operating parameters. A second thrust of this paper is to explore the effects of fan installation details on fan performance. The proximity of surrounding walls is considered through the use of three different enclosures within which the fan is mounted. Effective inlet areas from which the air enters the fan are also identified. This work provides a practical framework for determining the optimal placement and configuration for these fans in prototypical applications.

An Experimental Study of Fluidic Coupling Between Multiple Piezoelectric Fans

Piezoelectric fans have been shown to provide large enhancements in heat transfer over natural convection while consuming very little power. These fans consist of a piezoelectric material attached to a flexible cantilever. When driven at resonance, large oscillations at the cantilever tip cause fluid motion, which in turn, results in improved heat transfer rates. In this work, the performance of two fans operating simultaneously is analyzed. A coupling phenomenon is observed which, for a given input, causes an increase in vibration amplitude of as large as 40 percent compared to an isolated single fan. Understanding this coupling is essential in order to create design tools for implementing piezoelectric fans in practical cooling systems. Mylar fans are analyzed, and multiple experiments performed in air and within a vacuum chamber to isolate the source of coupling and determine its magnitude. The results suggest that coupling is almost entirely due to fluid-structure interaction, and the impact on the characteristic vibration parameters is explored. The collective motion of the fans decreases the fluidic damping, and the coupling magnitude is determined for a range of fan pitches

Experimental Mapping of Local Heat Transfer Coefficients Under Multiple Piezoelectric Fans

Piezoelectric fans have been shown to provide large enhancements in heat transfer over natural convection while consuming very little power. These fans consist of a piezoelectric material attached to a flexible cantilever. When driven at resonance, large oscillations at the cantilever tip cause fluid motion, which in turn, results in improved heat transfer rates. In this study, the local heat transfer coefficients are determined experimentally for piezoelectric fans vibrating close to an electrically heated stainless steel foil, and the entire temperature field is observed by means of an infrared camera. Various vibration amplitudes, distances from heater to fan tip (or gap), and fan pitches are considered for both single-fan and two-fan configurations in impinging orientations. Of particular interest is the increase in heat transfer performance with an additional fan present and the dependence of this increase on the variable parameters. Results show nearly uniform cooling within the envelope of vibration for single-fan experiments with small gaps, and the existence of an optimal gap distance which is dependent on vibration amplitude. The benefits of an additional fan include greater coverage area, but the resulting increase in peak convection coefficient is highly dependent on the fan pitch. Conditions exist where constructive interference is observed which causes a roughly 10% increase in peak convection coefficient while significantly increasing the coverage area. Understanding the local performance of piezoelectric fans provides an important tool to help implement these devices in practical cooling systems.Copyright

LES of an Isothermal High Reynolds Number Turbulent Round Jet

Round turbulent jets have fundamental relevance in various engineering applications and are also of practical interest in the lower plenum of the High Temperature Gas-Cooled Reactors (HTGR). In the direction of developing an experimentally validated computational model for the lower plenum flow, a Large Eddy Simulation (LES) of an isothermal high Reynolds number confined jet has been studied. The enclosure within which the jet is confined has been selected large enough so that the results can be compared with well-known experimental studies available in the literature. The Sub-Grid Scale (SGS) model chosen within the LES framework is a variant of the dynamic Smagorinsky model. The effect of inlet flow profile and turbulent fluctuations on the evolution of the jet have been analyzed in detail. The mesh distribution was found to play a vital role in the magnitude and profile of the Reynolds stresses throughout the computational domain. Additionally, it is critically important to properly specify the turbulent fluctuations at the jet inlet in order to accurately predict key near field characteristics such as the potential core length. We perform a separate discrete eddy simulation of the flow in the nozzle upstream of the jet inlet to accurately determine the inlet turbulent fluctuations. The LES results of this study include both first order statistics (mean velocity field) and second order statistics (components of the Reynolds stresses). For each of these quantities, excellent agreement is obtained between our LES predictions and experimental measurements. This research lays the groundwork needed to develop a high-fidelity computational model of the complex mixing flow in the HTGR lower plenum.Copyright

Thrust Force Characterization of Oscillating Cantilevers Operating Near Resonance

Harmonic oscillations from cantileverlike structures have found use in applications ranging from thermal management to atomic force microscopy and propulsion, due to their simplicity in design and ease of implementation. In addition, making use of resonance conditions, a very energy efficient solution is achievable. This paper focuses on the application of providing thrust through cantilever oscillations at or near the first mode of resonance. This method of actuation provides a balance between full biomimicry and ease of fabrication. Previous studies have shown promise in predicting the propulsion performance based on the operating parameters, however, they have only considered a single cantilever geometry. Here, additional cantilever sizes and materials are included, yielding a much larger design space to characterize the thrust trends. The thrust data is experimentally captured and is assembled into two sets of predictive correlations. The first is based on Reynolds and Strouhal numbers, while the second only employs the Keulegan–Carpenter number. Both correlations are proven to predict the experimental data and can be shown to yield nearly identical proportional relationships after accounting for the cantilever frequency response. The findings presented in this research will aid in further understanding and assessing the capabilities of thrust generation for oscillating cantilevers, but also provides a foundation for other applications such as convection heat transfer and fluid transport.

Characterization of the Behavior of Confined Laminar Round Jets

Confined laminar fluid jets have many practical applications in industry. Several examples include expansions in pipes and flow of gas into a large plenum. While much consideration has been given experimentally to heat transfer and pressure gradients within the confinement, little attention has been paid to quantify the velocity profiles and transitions between various flow behaviours. Using a finite volume CFD code, OpenFOAM ®, the Navier-Stokes equations were solved for varying expansion ratio, 1/e = renclosure/rj, and varying Reynolds numbers. In the present analysis, Reynolds number based on the inlet jet diameter is varied from 30 to 70, well within the accepted range for laminar jet behavior. The expansion ratio, 1/e is varied from 20–200. Of primary focus in the current study are compact correlations for the jet centreline velocity as a function of jet Reynolds number, Rej and expansion ratio. Similar functional dependences for the “linear” decay region of the jet, and the location of the stagnation point on the enclosure wall, are also investigated. These are all important features of the global flow field for the confined jet. Results suggest that initially, the flow characteristics are identical to a free jet. At some downstream location, the presence of the enclosure is felt by the jet and deviations begin to be seen from free jet behavior. This transition region continues until at a sufficiently large downstream location, the flow becomes fully developed, internal Poiseuille flow. In this paper, we analyse these transition regions and offer explanations and practical correlations to successfully predict the important flow physics that occur between free jet behavior and Poiseuille flow. Key dimensionless parameters are identified, the magnitude of which can be used to classify the flow conditions.Copyright