Luc Mongeau

Extremum seeking control of a tunable thermoacoustic cooler

In this paper, the performance of a prototype standing wave thermoacoustic cooler is optimized using an extremum seeking control (ESC) algorithm. A tunable Helmholtz resonator was developed for a thermoacoustic cooler to change the boundary condition of the standing wave tube. The volume of the resonator is changed by changing the location of a piston on a ball-screw assembly driven by a dc motor. Multiparameter ESC was applied to optimize the cooling power via tuning both the boundary condition (piston location) and the driving frequency. Experiments were conducted for the online optimization under both fixed and varying operating conditions. The experimental results demonstrated the effectiveness of using ESC for maintaining maximum achievable performance. The effect of changing parameters in the ESC algorithm on the transient behavior was also investigated.

Effects of trailing jet instability on vortex ring formation

Numerical simulations of an impulsively started jet were performed in order to investigate the effects of trailing jet instability on axisymmetric vortex ring formation. The predictions were compared to experimental results reported in the literature and to recently published numerical results. The total and vortex ring circulations were found to be in good agreement with both the experimental and the numerical results. The presence of a universal formation time scale was confirmed. The results also highlighted an important interaction between an instability which develops in the trailing jet for large discharge times and the dynamics of the head vortex ring. This interaction accelerates the process by which the vortex ring detaches from the trailing jet and has a significant effect on the vortex ring circulation.

Influence of support properties on the sound radiated from the vibrations of rectangular plates

Abstract The control of the forced vibration response of structures through the optimal tuning of its supports is desirable in many applications. Tuning may enhance the dissipation of vibration energy within the supports, thereby reducing fatigue and structure-borne noise. Two different models were developed to calculate the optimal support stiffness that minimizes the velocity response of homogeneous plates. The first model, based on the wave propagation at the edge, yields a good first cut approximation of the optimal properties. The optimal viscous and viscoelastic support stiffness for minimal reflection at the edge was calculated. Maximum absorption of the incident waves occurs when the viscous support stiffness matches the characteristic mechanical impedances of the plate. The second model, based on the Rayleigh–Ritz method, yields more accurate estimates of the optimal support stiffness required to minimize the forced velocity response of the finite rectangular plate. The optimal support properties calculated from the two different methods were in good agreement. This suggested that the modal response of the plate is strongly influenced by the wave reflections at the edges. Finally, the effects of support properties on the sound radiated from the plate were investigated. The optimal support stiffness that minimizes the radiated sound power was found to be smaller than the value that minimizes the velocity response. The results show that both the velocity response and sound radiation are strongly influenced by dissipation of vibration energy at the edges, and demonstrate that support tuning can yield significant noise and vibration reduction.

Sensitivity of a continuum vocal fold model to geometric parameters, constraints, and boundary conditions

The influence of key dimensional parameters, motion constraints, and boundary conditions on the modal properties of an idealized, continuum model of the vocal folds was investigated. The Ritz method and the finite element method were used for the analysis. The models vibratory modes were determined to be most sensitive to changes in the anterior-posterior length of the vocal fold model, due to the influence of three-dimensional stress components acting in the transverse plane. Anterior/ posterior boundary conditions were found to have a significant influence on the vibratory response. Overestimation of modal frequencies resulted when vibration of the structure was restricted to the transverse plane. The overestimation of each modal frequency was proportional to the ratio of longitudinal to transverse Youngs modulus, and was significant for ratio values less than 20.

Analysis of the flow-induced vibrations of viscoelastically supported rectangular plates

Abstract The purpose of this study was to develop a theoretical model for the flow-induced vibration of viscoelastically supported rectangular plates. In particular, the influence of the dynamic mechanical properties of the elements supporting the plate was investigated. The case of a homogeneous rectangular plate supported along all four edges by a complex viscoelastic element was treated. The Rayleigh–Ritz method was used applying beam functions as the trial functions. This approach ensured a fast convergence rate, which is advantageous for vibration analysis of high order modes. The flow-induced vibration of the plate was calculated using the Corcos model for the surface pressure loading. The results suggest that there is an optimal support stiffness that minimizes the flow-induced vibration response of the plate.

Instantaneous orifice discharge coefficient of a physical, driven model of the human larynx.

The quasisteady approximation is often made in the study of phonatory aerodynamics to facilitate the modeling of time-varying air flows through the self-oscillating vocal folds. The unsteady, pulsating flow is approximated by a sequence of steady flows through representative configurations of the vocal folds at rest. Previous studies have discussed the accuracy of this approximation for a range of orifice geometries, and flow conditions. The purpose of the present study was to further evaluate the quasisteady approximation experimentally using an improved procedure, from a direct comparison between the discharge coefficients of steady jets through fixed orifices and unsteady jets through modulated orifices of identical shape, area, and transglottal pressures at a given time. Life-scale convergent and divergent glottis-shaped rubber orifices were used in a rigid-walled tube and a low Mach number flow representative of human phonation. It was found that the quasisteady approximation is valid during 70% of the duty cycle, when the Reynolds number was above 3000, for a frequency of oscillations of 100 Hz. The steady form of Bernoullis equation along a streamline, and Bernoullis flow obstruction theory were found to be reasonably accurate for the unsteady flows. These models break down at low Reynolds numbers, near the beginning and the end of the duty cycle, due to viscous effects and to the influence of flow displaced by the motion of the walls.

Broadband sound generation by confined turbulent jets

Sound generation by confined stationary jets is of interest to the study of voice and speech production, among other applications. The generation of sound by low Mach number, confined, stationary circular jets was investigated. Experiments were performed using a quiet flow supply, muffler-terminated rigid uniform tubes, and acrylic orifice plates. A spectral decomposition method based on a linear source-filter model was used to decompose radiated nondimensional sound pressure spectra measured for various gas mixtures and mean flow velocities into the product of (1) a source spectral distribution function; (2) a function accounting for near field effects and radiation efficiency; and (3) an acoustic frequency response function. The acoustic frequency response function agreed, as expected, with the transfer function between the radiated acoustic pressure at one fixed location and the strength of an equivalent velocity source located at the orifice. The radiation efficiency function indicated a radiation efficiency of the order (kD)2 over the planar wave frequency range and (kD)4 at higher frequencies, where k is the wavenumber and D is the tube cross sectional dimension. This is consistent with theoretical predictions for the planar wave radiation efficiency of quadrupole sources in uniform rigid anechoic tubes. The effects of the Reynolds number, Re, on the source spectral distribution function were found to be insignificant over the range 20002.5. The influence of a reflective open tube termination on the source function spectral distribution was found to be insignificant, confirming the absence of a feedback mechanism.

Compressible large eddy simulations of wall-bounded turbulent flows using a semi-implicit numerical scheme for low Mach number aeroacoustics

Large eddy simulations (LES) of low-speed, wall-bounded turbulent flows were conducted by numerically integrating the compressible Navier-Stokes equations in a generalized curvilinear coordinate system. An efficient numerical scheme based on a third-order additive semi-implicit Runge-Kutta method for time advancement and a sixth-order accurate, compact finite-difference scheme for spatial discretization were used. The convective terms in the wall-normal direction were treated implicitly to remove the time-step limitation associated with the use of fine meshes in the near-wall region for high Reynolds number viscous flows. The dynamic Smagorinsky subgrid-scale eddy viscosity model was used to close the filtered equations. Generalized characteristic-based non-reflecting boundary conditions were used together with grid stretching and enhanced damping in the exit zone. The accuracy and efficiency of the numerical scheme was assessed by simple acoustic model problems and by comparing LES predictions for fully developed turbulent channel flow and turbulent separated flow in an asymmetric diffuser to previous direct numerical simulation (DNS) and experimental data, respectively. LES predictions for both flows were in reasonable agreement with the DNS and experimental mean velocity and turbulence statistics. The findings suggest that the numerical approach employed here offers comparable accuracy to similar recent studies at approximately one-third of the computational cost and may provide both an accurate and efficient way to conduct computational aeroacoustics studies for low Mach number, confined turbulent flows.

Adaptive tuning of an electrodynamically driven thermoacoustic cooler

The commercial development of thermoacoustic coolers has been hampered in part by their low efficiencies compared to vapor compression systems. A key component of electrodynamically driven coolers is the electromechanical transducer, or driver. The drivers electroacoustic transduction efficiency, defined as the ratio of the acoustic power delivered to the working gas by the moving piston and the electrical power supplied, must be maintained near its maximum value if a high overall system efficiency is to be achieved. Modeling and experiments have shown that the electroacoustic efficiency peaks sharply near the resonance frequency of the electro-mechano-acoustic system. The optimal operating frequency changes as the loading condition changes, and as the properties of the working gas vary. The driver efficiency may thus drop significantly during continuous operation at a fixed frequency. In this study, an on-line driver efficiency measurement scheme was implemented. It was found that the frequency for maximum electroacoustic efficiency does not precisely match any particular resonance frequency, and that the efficiency at resonance can be significantly lower than the highest achievable efficiency. Therefore, a direct efficiency measurement scheme was implemented and validated using a functional thermoacoustic cooler. An adaptive frequency-tuning scheme was then implemented. Experiments were performed to investigate the effectiveness of the control scheme to maintain the maximum achievable driver efficiency for varying operating conditions.

Dual-driver standing wave tube: acoustic impedance matching with robust repetitive control

In some acoustic applications, it may be desirable to make a shorter standing wave tube operate like a longer tube at the same driving frequency. The basic idea is to reduce the length of a long tube, and replace the removed section with a secondary driver. The problem is then to match the acoustic impedance at the boundary where the secondary driver is installed to that of the original system. Two control formulations were investigated for this problem: a two-input-two-output (TITO) and a single-input-single-output (SISO) formulation. The TITO formulation directly tracks the two acoustic variables associated with the desired acoustic impedance, while the SISO formulation minimizes the impedance matching error. The desired impedance containing a very lightly damped mode is embedded in the augmented plant for feedback control design. In addition to the balance realization method, the Schur method was used for model reduction for the high-order plant. Since the standing wave tubes are driven by tonal signals, repetitive control was incorporated into the control frameworks to achieve the desired performance. Good performance of impedance matching was obtained for both formulations. The SISO formulation yielded slightly wider bandwidth of good impedance matching than the TITO. The TITO formulation offered additional control to individual signals related to the acoustic impedance of interest.