Gennaro Coppola

Modeling and Experimental Validation of the Frequency Response of Synthetic Jet Actuators

A lumped-element mathematical model of the operation of a synthetic jet actuator driven by a thin piezoelectric disk is both analytically and numerically investigated to obtain information about the frequency response of the device. It is shown that the actuator behaves as a two-coupled oscillator system, and simple relationships are given to predict the two peak frequencies, corresponding to the modified Helmholtz and first-mode structural resonance frequencies. The model is validated through experimental tests carried out on three devices having different mechanical and geometrical characteristics, designed primarily to achieve an increasing coupling strength. A strict agreement between overall theoretical scaling laws and numerical computations is also found.

Insights on the impact of a plane drop on a thin liquid film

Numerical simulations of early and intermediate instants of a plane two-dimensional drop impact on a preexisting thin film of the same liquid are performed. The evolution of the phenomenon is analyzed by solving the free-surface Navier–Stokes equations by means of a volume of fluid (VOF) method. Viscous, inertial and surface tension forces are taken into account; gravity is neglected. The so-called splashing regime is emphasized, where the emergence of an initial horizontal ejecta sheet is followed by the formation of an almost vertical lamella sheet, which is the planar counterpart of the well known splashing-crown of spherical geometry. Overall velocity and pressure fields as well as detailed interface shapes are presented, and several insights on the relevant scaling laws are furnished. In the ejecta sheet (jet) regime a major result is the finding of a deviation from the standard square root behavior for the dependence on time of the contact length of sheet first emergence, which is proved to be cruci...

LEM Characterization of Synthetic Jet Actuators Driven by Piezoelectric Element: A Review

In the last decades, Synthetic jet actuators have gained much interest among the flow control techniques due to their short response time, high jet velocity and absence of traditional piping, which matches the requirements of reduced size and low weight. A synthetic jet is generated by the diaphragm oscillation (generally driven by a piezoelectric element) in a relatively small cavity, producing periodic cavity pressure variations associated with cavity volume changes. The pressured air exhausts through an orifice, converting diaphragm electrodynamic energy into jet kinetic energy. This review paper considers the development of various Lumped-Element Models (LEMs) as practical tools to design and manufacture the actuators. LEMs can quickly predict device performances such as the frequency response in terms of diaphragm displacement, cavity pressure and jet velocity, as well as the efficiency of energy conversion of input Joule power into useful kinetic power of air jet. The actuator performance is also analyzed by varying typical geometric parameters such as cavity height and orifice diameter and length, through a suited dimensionless form of the governing equations. A comprehensive and detailed physical modeling aimed to evaluate the device efficiency is introduced, shedding light on the different stages involved in the process. Overall, the influence of the coupling degree of the two oscillators, the diaphragm and the Helmholtz frequency, on the device performance is discussed throughout the paper.

On transient growth oscillations in linear models

The study of oscillating norm behavior in linear systems is addressed. The analysis is carried out by considering a model equation that naturally arises in the context of the linearized formulation of some convection-dominated systems over finite length domains. The occurrence of oscillating patterns in the energy evolution of the solutions is linked to the structure of the spectrum and to the non-normal character of the linear operator involved. A distinction between transient and asymptotic oscillations is made and some relations between the frequency signatures shown in both cases and global characteristics of the spectrum are highlighted. The physical importance of such oscillating behaviors is stressed by reconsidering a model for the linear stability of a falling liquid curtain studied by other authors in a previous work.

Explicit Runge-Kutta schemes for incompressible flow with improved energy-conservation properties

The application of pseudo-symplectic Runge-Kutta methods to the incompressible Navier-Stokes equations is discussed in this work. In contrast to fully energy-conserving, implicit methods, these are explicit schemes of order p that preserve kinetic energy to order q, with q p . Use of explicit methods with improved energy-conservation properties is appealing for convection-dominated problems, especially in case of direct and large-eddy simulation of turbulent flows. A number of pseudo-symplectic methods are constructed for application to the incompressible Navier-Stokes equations and compared in terms of accuracy and efficiency by means of numerical simulations.

Surface tension effects on the motion of a free-falling liquid sheet

The stationary motion of a liquid curtain falling under the effects of inertia, gravity, and surface tension is analyzed. An original equation governing the streamwise distribution of thickness and velocity is derived by means of a Taylor expansion in the lateral distance from the mean line of the sheet. Approximate solutions are obtained by means of perturbation approaches involving the two parameters governing the problem, namely, the slenderness ratio ɛ and the Weber number We. The numerical procedure employed in order to integrate the non-linear equation is discussed and a parametric study is presented, together with a comparison with the approximate asymptotic solutions valid for small ɛ and We.

Generalization of the Spline Interpolation Based on the Principle of the Compact Schemes

In this work the authors extend the high order compact difference schemes to the matching technique to develop a Local Matched Reconstruction theory that can be also considered as a generalization of the spline theory. The problem of the high order reconstructions correlated to an optimal matching in overlapping regions for contiguous expansions in one or more dimensions is stressed; some new generalized matched interpolations and their related numerical schemes are presented together with Fourier analysis of errors. Finally, some relevant aspects of the computational efforts associated to the various approaches are discussed.

Global eigenmodes of free-interface vertical liquid sheet flows

The global dynamics of unsteady free-interface vertical liquid sheet flows is studied, where the dynamics is termed global because it refers to the whole fluid system. The formal development of a proper mathematical model is presented initially, which accounts for pressure disturbances produced by the compliant interface in an air enclosure adjacent to the sheet. The linear spectral analysis (here restricted to sinuous disturbances only) shows that the surface tension is globally stabilizing, the spectrum exhibiting two typical branches related to the two characteristics curves of the governing equations. This basic finding is confirmed by means of both computations of the optimal amplifications (i.e. the greatest amplifications over all initial perturbations) of the relevant system energy and direct numerical simulations of the spatio-temporal evolution of an initial disturbance having the form of an interface Gaussian perturbation.

The VOF Method Applied To The NumericalSimulation Of A 2D Liquid Jet Under Gravity

Numerical simulations of a two-dimensional gravitational liquid sheet injected in another immiscible fluid are performed. The steady state of the liquid sheet has been calculated by solving the two-dimensional Navier-Stokes equations for variable density incompressible flows and the interface between the two fluids has been determined by using the Volume of Fluids method . The analysis takes into account viscous, inertial, gravitational and surface tension forces and different regimes of motion are identified according to the values of Reynolds and Stokes numbers. Velocity, pressure and shape of the sheet are investigated and the results are in well agreement with previous numerical and experimental results.

Characterization of Synthetic Jet Resonant Cavities

The acoustic properties of piezo-electric driven resonant cavities usually employed to generate the so-called synthetic jets are analytically and numerically investigated in order to characterize the performances of such devices. It is shown that the actuator behaves as a two-coupled oscillators system and the dimensionless form of the governing equations allows one to identify various particular operating conditions. The theoretical predictions are validated through experimental tests carried out on devices having different mechanical and geometrical characteristics, designed in order to achieve an increasing coupling strength. Practical design implementations are discussed as well.