Louis N. Cattafesta

Formation Criterion for Synthetic Jets

Af ormation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zero-net mass-flux device that imparts momentum to its surroundings. Je tf ormation is defined as the appearance of a time-averaged outward velocity along the jet axis and corresponds to the generation and subsequent convection or escape of a vortex ring. It is shown that over a wide range of operating conditions synthetic jet formation is governed by the jet Strouhal number Sr (or Reynolds number Re and Stokes number S). Both numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric synthetic jet formation data in the literature. The data support the jet formation criterion 1/Sr = Re/S 2 > K, where the constant K is approximately 1 and 0.16 for two-dimensional and axisymmetric synthetic jets, respectively. In addition, the dependence of the constant K on the normalized radius of curvature of a rounded orifice or slot is addressed. The criterion is expected to serve as a useful design guide for synthetic jet formation in flow control, heat transfer, and acoustic liner applications, in which a stronger jet is synonymous with increased momentum transfer, vorticity generation, and acoustic nonlinearities.

Lumped Element Modeling of Piezoelectric-Driven Synthetic Jet Actuators

Abstract : This paper presents a lumped element model of a piezoelectric-driven synthetic jet actuator. A synthetic jet, also known as a zero net mass-flux device, uses a vibrating diaphragm to generate an oscillatory flow through a small orifice or slot. In lumped element modeling (LEM), the individual components of a synthetic jet are modeled as elements of an equivalent electrical circuit using conjugate power variables. The frequency response function of the circuit is derived to obtain an expression for Q(sub out)/V(sub AC), the volume flow rate per applied voltage. The circuit is analyzed to provide physical insight into the dependence of the device behavior on geometry and material properties. Methods to estimate the model parameters are discussed, and experimental verification is presented. In addition, the model is used to estimate the performance of two prototypical synthetic jets, and the results are compared with experiment.

Mode-switching and nonlinear effects in compressible flow over a cavity

Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible flow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This article describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the short-time Fourier transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This is verified by instantaneous schlieren images acquired simultaneously with the unsteady pressures. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-fr...

Sparsity constrained deconvolution approaches for acoustic source mapping

Using microphone arrays for estimating source locations and strengths has become common practice in aeroacoustic applications. The classical delay-and-sum approach suffers from low resolution and high sidelobes and the resulting beamforming maps are difficult to interpret. The deconvolution approach for the mapping of acoustic sources (DAMAS) deconvolution algorithm recovers the actual source levels from the contaminated delay-and-sum results by defining an inverse problem that can be represented as a linear system of equations. In this paper, the deconvolution problem is carried onto the sparse signal representation area and a sparsity constrained deconvolution approach (SC-DAMAS) is presented for solving the DAMAS inverse problem. A sparsity preserving covariance matrix fitting approach (CMF) is also presented to overcome the drawbacks of the DAMAS inverse problem. The proposed algorithms are convex optimization problems. Our simulations show that CMF and SC-DAMAS outperform DAMAS and as the noise in the measurements increases, CMF works better than both DAMAS and SC-DAMAS. It is observed that the proposed algorithms converge faster than DAMAS. A modification to SC-DAMAS is also provided which makes it significantly faster than DAMAS and CMF. For the correlated source case, the CMF-C algorithm is proposed and compared with DAMAS-C. Improvements in performance are obtained similar to the uncorrelated case.

Acoustic energy harvesting using an electromechanical Helmholtz resonator.

This paper presents the development of an acoustic energy harvester using an electromechanical Helmholtz resonator (EMHR). The EMHR consists of an orifice, cavity, and a piezoelectric diaphragm. Acoustic energy is converted to mechanical energy when sound incident on the orifice generates an oscillatory pressure in the cavity, which in turns causes the vibration of the diaphragm. The conversion of acoustic energy to electrical energy is achieved via piezoelectric transduction in the diaphragm of the EMHR. Moreover, the diaphragm is coupled with energy reclamation circuitry to increase the efficiency of the energy conversion. Lumped element modeling of the EMHR is used to provide physical insight into the coupled energy domain dynamics governing the energy reclamation process. The feasibility of acoustic energy reclamation using an EMHR is demonstrated in a plane wave tube for two power converter topologies. The first is comprised of only a rectifier, and the second uses a rectifier connected to a flyback converter to improve load matching. Experimental results indicate that approximately 30 mW of output power is harvested for an incident sound pressure level of 160 dB with a flyback converter. Such power level is sufficient to power a variety of low power electronic devices.

DEVELOPMENT OF AN ADAPTIVE WEAPONS-BAY SUPPRESSION SYSTEM

This paper describes our recent efforts towards the development of an adaptive weapons-bay suppression system. The system is comprised of piezoelectric flap actuators at the leading edge of the cavity, unsteady pressure sensors inside the cavity, and a real-time, adaptive, feedback control system. Results are presented in which High Technology Corporation tested a prototype suppression system on a DERA-supplied, l/10*-scale model in the Aircraft Research Association Ltd. Transonic Wind Tunnel Facility in Bedford, UK. The piezoelectric actuators degraded in the initial part of the test, leading to a reduction in their resonance frequency and deflection amplitude. As a result, the test matrix was restricted to Mach numbers of 0.4, 0.6, and 0.85. The results were disappointing, in that reductions in the peaks of only a few dB were achieved for single modes at Mach 0.4 and 0.6. At Mach 0.85, the system had no effect. In order to show the potential performance of the system, successful results of an earlier wind-tunnel test are also presented. We conclude that the failure of the suppression system is due to the poor performance of the actuators. Possible factors responsible for their inadequacy are discussed.

Dynamics of Airfoil Separation Control using Zero-Net Mass-Flux Forcing

Zero-net mass-flux jet based control of flow separation over a stalled airfoil is examined using numerical simulations. Two-dimensional simulations are carried out for a NACA 4418 airfoil at a chord Reynolds number of 40,000 and angle of attack of 18 deg. Results for the uncontrolled flow indicate the presence of three distinct natural time scales in the flow corresponding to the shear layer, separation bubble, and wake regions. The natural frequencies are used to select appropriate forcing frequencies, and it is found that forcing frequencies closer to the separation bubble frequency elicit the best response in terms of reduction of separation extent and an improvement in aerodynamic performance. In contrast, higher forcing frequencies closer to the natural shear layer frequency tend to enhance separation. The vortex dynamics and frequency response of flow are examined in detail to gain insight into mechanisms underlying the observed behavior.

Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate

This paper presents an analytical two-port, lumped-element model of a piezoelectric composite circular plate. In particular, the individual components of a piezoelectric unimorph transducer are modeled as lumped elements of an equivalent electrical circuit using conjugate power variables. The transverse static deflection field as a function of pressure and voltage loading is determined to synthesize the two-port dynamic model. Classical laminated plate theory is used to derive the equations of equilibrium for clamped circular laminated plates containing one or more piezoelectric layers. A closed-form solution is obtained for a unimorph device in which the diameter of the piezoelectric layer is less than that of the shim. Methods to estimate the model parameters are discussed, and model verification via finite-element analyses and experiments is presented. The results indicate that the resulting lumped-element model provides a reasonable prediction (within 3%) of the measured response to voltage loading and the natural frequency, thus enabling design optimization of unimorph piezoelectric transducers.

A Jet Formation Criterion for Synthetic Jet Actuators

This paper proposes and validates a jet formation criterion for synthetic jet actuators. The synthetic jet is a zero net mass flux device, adding additional momentum but no mass to its surroundings. Jet formation is defined as a mean outward velocity along the jet axis and corresponds to the clear formation of shed vortices. It is shown that the synthetic jet formation is governed by the Strouhal number (or Reynolds number and Stokes number). Numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric jet formation data in the literature. The data support the jet formation criterion , where the constant 2 Re/ S K > K is approximately 2 and 0.16 for two dimensional and axisymmetric synthetic jets, respectively. This criterion is valid for relatively thick orifice plates with thickness-to-width ratios greater than approximately 2. This result is expected to be useful for the design of flow-control actuators and engine nacelle acoustic liners.

Development of Piezoelectric Actuators for Active Flow Control

The development of piezoelectric actuators for active e ow control is discussed. The type of actuators considered consists of a single sheet of piezoceramic material bonded to the underside of a shim: a “ unimorph” e ap design. Existing theoretical beam models are extended to incorporate a linear strain distribution in the composite unimorph beam structure. This model is combined with an optimization scheme to design a e ap that maximizes the tip dee ection per unit voltage for a given bandwidth. The optimization model is then used to design a piezoelectric actuator. The model predictions compare favorably to measurements of the actuator frequency response function. A sample application to control of separated e ow from a backward-facing step is also described, in which the actuator is installed at the origin of the free shear layer. Detailed hot-wire measurements, together with dimensional analysis, reveal the physical mechanism responsible for the e uid-structure coupling. A quasi-static model based on the solid-body displacement of the incoming shear layer accurately describes the peak streamwise velocity perturbations produced by the actuator. This model leads to a proportional relationship between the e ap tip displacement, the incoming boundary-layer proe le parameters, and the streamwise velocity e uctuations produced by the actuator.