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 outAC QV, 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. IntroductionSynthetic jet actuators have been the focus of significant research activity for the past decade (Smith and Glezer 1998). The interest in synthetic jets is primarily due to their utility in flow control applications, such as separation control, mixing enhancement, etc. Chen et al. 1999;Honohan et al. 2000;Chatlynne et al. 2001).A schematic of a synthetic jet actuator is shown in Figure 1. A typical synthetic jet, also known as a zero net mass-flux device, uses a vibrating diaphragm to drive oscillatory flow through a small orifice or slot. Although there is no source, a mean jet flow is established a few diameters from the orifice due to In addition to studies that emphasize applications, there are numerous others that have concentrated on the design, visualization, and/or measurements of synthetic jets (Crook et al. 1999;Chen et al. 2000;Crook and Wood, 2001;Gilarranz and Rediniotis, 2001).Furthermore, several computational studies also have focused on fundamental aspects of these devices (Kral et al. 1997; Rizzeta et al. 1998;Mallinson et al. 2000;Utturkar et al. 2002). Crook and Wood (2001) emphasize the importance of understanding the scaling and operational characteristics of a synthetic jet. Clearly, this information is required for a user to design an appropriate device for a particular application.In addition, feedback control applications require the actuator transfer function that relates the input voltage to the output property of interest (e.g., volumetric flow rate) in the control system.The design itself represents an electromechanical-acoustic coupled system with frequency dependent properties determined by device dimensions and material properties. The analysis and design of coupled-domain transducer systems are commonly performed using lumped element models (Fisher 1955;Hunt 1982;Rossi 1988).The main assumption employed in LEM is that the characteristic length scales of the governing AIAA-2002-0125Lumped Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching exis...

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 outAC QV, 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. IntroductionSynthetic jet actuators have been the focus of significant research activity for the past decade (Smith and Glezer 1998). The interest in synthetic jets is primarily due to their utility in flow control applications, such as separation control, mixing enhancement, etc. Chen et al. 1999;Honohan et al. 2000;Chatlynne et al. 2001).A schematic of a synthetic jet actuator is shown in Figure 1. A typical synthetic jet, also known as a zero net mass-flux device, uses a vibrating diaphragm to drive oscillatory flow through a small orifice or slot. Although there is no source, a mean jet flow is established a few diameters from the orifice due to In addition to studies that emphasize applications, there are numerous others that have concentrated on the design, visualization, and/or measurements of synthetic jets (Crook et al. 1999;Chen et al. 2000;Crook and Wood, 2001;Gilarranz and Rediniotis, 2001).Furthermore, several computational studies also have focused on fundamental aspects of these devices (Kral et al. 1997; Rizzeta et al. 1998;Mallinson et al. 2000;Utturkar et al. 2002). Crook and Wood (2001) emphasize the importance of understanding the scaling and operational characteristics of a synthetic jet. Clearly, this information is required for a user to design an appropriate device for a particular application.In addition, feedback control applications require the actuator transfer function that relates the input voltage to the output property of interest (e.g., volumetric flow rate) in the control system.The design itself represents an electromechanical-acoustic coupled system with frequency dependent properties determined by device dimensions and material properties. The analysis and design of coupled-domain transducer systems are commonly performed using lumped element models (Fisher 1955;Hunt 1982;Rossi 1988).The main assumption employed in LEM is that the characteristic length scales of the governing AIAA-2002-0125Lumped Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching exis...

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 lumpedelement 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.

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The flow field generated by a zero-net mass-flux (ZNMF) actuator is investigated via both numerical simulations and experiments to augment the current understanding of the flow physics of the orifice. The results aid in improving the accuracy of low dimensional lumped element ZNMF models suitable for design. Dimensional analysis yields a number of key parameters that govern the characteristics of this flow. Among them for a sharp rectangular slot or circular orifice are the Reynolds number, the dimensionless stroke length, and the orifice height-to-diameter ratio. Variation of these parameters shows that the flow field differs appreciably from the exact linear solution of pipe flow driven by an oscillatory pressure gradient. In particular, depending on the stroke length and the orifice geometry, the pressure drop in the orifice may be dominated by nonlinear "minor" losses due to entrance/exit effects, or linear "major" losses associated with the presence of a nominally fully-developed region in the central region of the orifice/slot.