Experimental Design and Analysis of Bimorphs as Synthetic Jet Diaphragms

Synthetic jet actuators are promising Active Flow Control (AFC) devices which could lead to saving millions of dollars in fuel consumption each year. The Bimorph piezoelectric actuators are an attractive alternative to other type of actuators as active diaphragms and are the focus of this work. Among the properties of a Bimorph actuator, a number of geometrical and physical external factors may have an effect on its performance as a synthetic jet actuator. Using statistical tools some of the physical and geometrical factors are evaluated as independent variables that may have an effect on the synthetic jet peak velocity, the dependent variable. Among the factors studied are the geometry of the synthetic jet cavity, the driving signal used to operate the active diaphragm, and the effect of a pressure gradient on the device. Among the six factors considered, the driving signal was found to have the highest effect on the peak jet velocity, and the factor of frequency proved to have a smaller effect. The cavity geometrical parameters were also relevant, a smaller orifice and a smaller cavity produce higher peak jet velocities. An adverse pressure gradient was also found to have a significant effect on peak jet velocity, diminishing its magnitude with increasing pressure. NOMENCLATURE CH cavity height Do orifice diameter E voltage FZ driving signal PB passive cavity pressure Xi factors Yi responses f frequency i factor no. j run no. n number of runs ro orifice radius xi individual factor yj response per run (j) j y + high level responses j y − low level responses ∆xi effect estimate per factor (i) INTRODUCTION Methods that attempt to control the motion of fluids have been extensively explored in the past. These methods can be passive or active or both (Gad-el-Hak 2000). Passive flow control is usually achieved through careful modifications to the existing system using steady state tools such as wing flaps, spoilers and vortex generators, among others. These techniques, though effective, have marginal power efficiency and are not capable of adjusting to the instantaneous flow 1 Copyright © 2006 by ASME conditions experienced during flight. Active flow control (AFC) methods however, are much more efficient. Through AFC, the flow field around a body can be modified to match the constantly changing conditions of an unsteady flow field by introducing small amounts of energy locally to achieve nonlocal changes in the flow field with large performance gains (Amitay et al. 1998, Kral et al. 1997, Smith & Glezer 1998). The feasibility of increasing the efficiency and simplifying fluid related systems is very appealing considering that a one percent saving in world consumption of jet fuel is worth about 1.25 million dollars a day of direct operating costs (Collis et al. 2004). Likewise, such fuel savings would lead to reduced environmental impact, although such environmental effects are difficult to quantify. Mclean et al. evaluated different AFC concepts and applications were considered for civil jet transports (McLean et al. 1999). The simplification of conventional high lift systems by AFC was identified as a prime candidate, possibly providing 0.3% airplane cost reduction, up to 2% weight reduction and about 3% cruise drag reduction. Also the advent of MEMS (Micro Electro Mechanical Systems) technology in the last two decades has provided a new impetus to the field of active control (Ho & Tai 1996). In spite of all the advantages, using active flow control devices usually adds complexity in design, increases manufacturing and operation cost, which prevents their use. For this reason, many researchers have focused on designing better active flow control devices that are easy to manufacture, are small in size and require little power to operate. One of the devices that fulfill all of these qualities is called synthetic jets. Synthetic jets consist of a cavity with an oscillating diaphragm. When the diaphragm oscillates air is pushed out an orifice forming a jet (Smith 1999). The jets are so called because they are synthesized from a train of vortex rings or pairs, formed from the external fluid, without net mass addition. This is one attractive feature of these devices since no hardware is required to obtain mass and flow from a separate source. The jets are formed from the working fluid of the flow system from which they are deployed. The interaction of the jets with an external flow leads to the formation of closed recirculating flow regimes near the surface. This interaction can act as a “virtual surface” and consequently is an apparent modification of the flow boundary (Amitay et al. 1997). An array of such microfabricated devices can produce a large jet velocity if the orifices are at the correct spacing and the driving signals are in phase. The oscillating diaphragm used in the synthetic jet cavity is usually driven using electrical or mechanical power. In the past, researchers have used compressed air or regulated blowers as a means of supplying steady or oscillating flow (Seifert et al. 1993, Seifert et al. 1996). This adds to the complexity and weight of the system. Piezoelectric disks that oscillate in the same manner as a piston or a shaker when driven with an AC electric signal seem like an attractive alternative if the shaker or a piston can be eliminated to reduce the number of moving parts. Because of these advantages, several investigators have adopted piezoelectric disks as oscillating diaphragms in synthetic jets to attempt to make the systems lighter, increase efficiency and save resources (Crook et al. 1999, Rathnasingham & Breuer 1997, Smith & Glezer 1998). The most commonly used piezoelectric diaphragm consists of a Lead Zirconate Titanate (PZT) disk bonded to a metal shim using a conductive epoxy, a Unimorph. Although these piezoelectric disks have been successful in generating high velocities capable of altering the flow fields, the devices operate best at high resonance frequencies, limiting the range of operation of the synthetic jet. Also, after a period of time, the PZT disk would start to delaminate and/or the output of the device would drop and the resonant frequency would change. Part of the degradation of performance of the device with time may be due to a combination of small cracks appearing in the bond line and the growth of a thin oxide layer between the brass and the conductive electrode (Bryant 1996). The ideal piezoelectric synthetic jet is unobtrusive, consumes low power, is light, and depending on the flow conditions, can be adjusted by changing frequency of operation. In the current study a piezoelectric laminate, Bimorph, is used as the active diaphragms in the jet cavity. Besides being lightweight, and having low power consumption, this laminate has the ability to produce micro scale displacements and provide a wide bandwidth response. Such advantages make the Bimorphs suitable for flow control purposes as demonstrated by Mossi et al. (Mossi & Bryant 2004a & b, Mossi et al. 2005a). The promising potential of piezoelectric synthetic jets for flow control has motivated researchers at various universities, industrial laboratories and government institutions to continue to invest time and effort into their further development since synthetic jets have potential applications ranging from jet vectoring (Smith & Glezer 1997), mixing enhancement (Chen et al. 1999, Davis & Glezer 1999), to active control of separation and turbulence in boundary layers (Amitay et al. 1998, Crook et al. 1999). Although numerical investigations are capable of providing insight into the operation of a synthetic jet, a parametric study of the flow configuration through experiments is necessary to validate the results. Experimentation however is a time consuming and expensive proposition. Design of experiments theory provides an alternative. Through a series of screening experiments, this study aims at identifying the important factors on the operation of a synthetic jet driven with a Bimorph device. The selected factors are then used in developing a regression model that quantifies the dependence of the desired response on the existing factors. Through screening experiments, statistics, and regression models a response surface of the relevant factors can be created to optimize the performance of the jet. These factors can then be incorporated on numerical models of the entire flow field for optimization. 2 Copyright © 2006 by ASME + Poled for series operation