Bruce F. Carroll

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.

Characteristics of multiple shock wave/turbulent boundary-layer interactions in rectangular ducts

Multiple shock wave/turbulent boundary-layer interactions in a rectangular duct have been investigated using wall pressure measurements, surface oil flow visualization, spark schlieren photography, and laser Doppler velocimetry. Two undisturbed incoming Mach numbers were considered, Mach 2.45 and Mach 1.6. At Mach 2.45 the shock structure was a neutrally stable pattern of oblique shocks followed by repeated normal shocks with the level of flow confinement having only a small effect in the interaction. A large, three-dimensional separation region was observed. At Mach 1.6 the pattern consisted of a bifurcated normal shock followed by weaker, unbifurcated normal shocks. The boundary layer under the bifurcated shock was incipiently separated. In contrast to the Mach 2.45 case, the lower Mach number interaction was much steadier with the length of the interaction scaling directly with the level of flow confinement.

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.

Rigid and Flexible Low Reynolds Number Airfoils

Issues related to the design of low Reynolds number airfoils, such as the thickness, camber, and surface proe les, are investigated. To contrast the issues involved, NACA 0012 and CLARK-Y, two well-known airfoils, a recently proposed low Reynolds number airfoil S1223, and a modie ed airfoil UF, are compared under varied Reynolds numbers and angles of attack. These airfoilsrange from 0% (NACA 0012)to 8.89%(S1223)camber, and from 6% (UF)to12.9%(CLARK-Y)thickness,and allowusto makea broadcomparison of thelift-and-drag characteristics with varying Reynolds numbers, from 7.5 £ 104 to 2.0 £ 106. Furthermore, the concept of a e exible airfoil is assessed in an unsteady, low Reynolds number environment. To facilitate the present study, we have employed techniques treating either inviscid or coupled inviscid/boundary-layer e ows around rigid airfoils, as well as a moving boundary technique to handle an elastic, massless membrane in a portion of the upper airfoil surface. The results show that within the range of Reynolds numbers and airfoil shapes, increased camber and reduced thickness provide more favorable lift-and-drag characteristics when the Reynolds number becomes lower. The results also indicate that a e exible proe le yields better overall performance than a similar rigid proe le in an oscillating freestream.

Temperature Dependence of Pressure Sensitive Paints

The photoluminescence properties of a typical pressure sensitive paint (PSP) formulation consisting of tris-(4,7-diphenylphenanthrollne)ruthenium(II) dichloride (RudpCl) dispersed in a polydimethylsiloxane (PDMS) binder were examined as a function of temperature. Thus, the temperature dependence of the luminescence intensity I em and emission decay lifetime τ em of the PSP formulation and for the photoluminescent RudpCl dye dissolved in ethanol solvent were determined for temperatures ranging from 5 to 50°C. Analysis of the experimental data indicates that under deoxygenated conditions the temperature dependence of I em and τ em for either the PSP formulation or ethanol solutions is dominated be the intrinsic temperature dependence of the nonradiative decay rate of the photoluminescent dye molecule. By contrast, for the PSP formulation at 1-atm air pressure the temperature dependence of I em and τ em is dominated by the temperature dependence of the diflusivity of oxygen in the PDMS binder. The implications of the experimental results on the design and application of PSP formulations are discussed.

Heat-Transfer Measurements in Hypersonic Flow Using Luminescent Coating Techniques

Thedevelopmentandapplicationofhigh-speedimagingandluminescentcoatingtechniquestomeasurefull-e eld surface heat-transfer rates in short-duration hypersonic e ow is presented. Tests were performed on an indented cone model at the 48-in. shock tunnel and the LENS I tunnel facilities at Calspan— University of Buffalo Research Center. Nominal test conditions ranged between Mach numbers of 9.5 and 11.1 and Reynolds numbers of 1:4 £ 10 5 and 3 £ 10 5 m ii 1 with run times of less than 10 ms. Processed submillisecond images show the threedimensional, time-dependent development of the embedded separated e ow and shock/boundary-layer interaction into a steady axisymmetric structure bounded by regions of laminar e ow. Conversion from processed image data to full-e eld heat-transfer measurements were performed using both an in situ calibration with thin-e lm platinum heat-transfer gauges as well as an a priori temperature calibration and transient heat-transfer theory. In situ calibrations displayed excellent correlation with surface-mounted gauges, whereas a priori calibrations showed a larger susceptibility to bias errors.

Turbulence phenomena in a multiple normal shock wave/turbulent boundary-layer interaction

An experimental investigation of a Mach 1.61 multiple normal shock wave/turbulent boundary-layer interaction in a rectangular, nearly constant area duct is discussed with an emphasis on the turbulence phenomena. The two-component laser Doppler velocimeter measurements reveal a large amplification of the turbulence kinetic energy and Reynolds stress through the interaction. The leading shock in the multiple shock pattern causes a significant distortion of the turbulent stress tensor. Partial recovery occurs immediately downstream of the first shock. The trailing shocks in the system are much weaker than the first shock and tend to maintain the nonequilibrium turbulence structure, with complete recovery occurring well downstream of the interaction.

Temperature- and Pressure-Sensitive Paint Measurements in Short-Duration Hypersonic Flow

Surface temperatures and pressures were measured on an elliptic cone lifting body in a hypersonic e owe eld using thin-e lm (» 5πm) temperature- and pressure-sensitive paints (TSPs and PSPs ). The tests were conducted in the 48-inch hypersonic shock tunnel (48-inch HST) at Calspan‐University of Buffalo Research Center and were part of a more comprehensive experimental study examining the three-dimensional characteristics of laminar, transitional, and turbulent e ow over the model. Measurement opportunity in the 48-inch HST was limited by the short duration of steady freestream conditions of the driven gas; image acquisition times were » 3 ms. Images of the coatings applied to the broad side of the symmetric elliptic cone were calibrated with in situ static pressure and surface-e lm temperature measurements. The TSP results illustrate the higher heat transfer rates and change in boundary-layer transition over the model surface caused by the nose geometry, and the PSP results show a mild pressure gradient over the interrogated surface region. Submillisecond TSP acquisition using a high-speed imager demonstrated the feasibility of measuring the surface temperature rise.

Computations and experiments for a multiple normal shock/boundary-layer interaction

Results from a numerical investigation of a Mach 1.61 multiple normal shock wave/turbulent boundary-layer interaction are compared to wall static pressure and laser Doppler velocimeter measurements. The computations used the explicit, time-dependent, second-order accurate MacCormack scheme to solve the mass-averaged Navier-Stokes equations. Turbulence was modeled by means of the Baldwin-Lomax algebraic model and the Wilcox-Rubesin two-equation model. The computation with the Wilcox-Rubesin model was able to capture the major features of the normal shock train and accurately predicted the flow reacceleration mechanisms which occur between shocks. However, this computation failed to accurately predict the level of flow separation under the first shock. The Baldwin-Lomax computation displayed a more limited ability to capture the features of this shock train flow.

Model Development and Analysis of the Dynamics of Pressure-Sensitive Paints

Two models for the dynamic behavior of pressure-sensitive paints are developed. The e rst of the two models is a purely empirical approach to designing a model and compensator. The second model presented encompasses the physics of the process by which an unsteady pressure e eld over the paint layer affects the layer and causes an intensity of e uorescence that is e uctuating in time. Within this second model, two different forms for the static calibration are chosen. The effect of the calibration on the system dynamics is demonstrated. Nomenclature A = amplitude a = pressure-sensitive paint thickness b = intercept of linear Stern ‐Volmer static calibration c = calibration constants D = diffusivity E = activation energy f = calibration function from pressure to intensity g = calibration function from intensity to pressure H = transfer function I = integrated intensity J = intensity per unit thickness j = the complex number, p i1 K = intensity error per unit thickness relative to surface condition M = model order m = oxygen concentration difference relative to surface condition n = oxygen concentration P = pressure T = temperature t = time x = distance from substrate ® = modal states ¸ = eigenvalues ae = solubility ? = time constant A = phase 9 = spatial eigenfunctions ! = frequency