DIFFRACTION OF AN ACOUSTIC WAVE BY A PLATE IN A UNIFORM FLOW: A NUMERICAL APPROACH

We study the diffraction in time harmonic regime of an acoustic wave by a rigid plate in the presence of a uniform flow in a duct. Contrary to prior analytical studies, using Wiener–Hopf techniques and thus restricted to semi-infinite plates, we use a finite elements method which allows us to deal with plates of finite length. To take into account irrotational perturbations induced by the trailing edge of the plate, a potential formulation requires the introduction of a vortex sheet behind the plate. The key point of the method is to get access at the singular coefficient of the velocity potential near the trailing edge, in order to cancel it using the so-called Kutta–Joukowski condition. This approach leads to an efficient finite elements method, and numerical computations are presented: we show the amplitude of the vortex sheet versus the Mach number and the plate length and the dissipated acoustic power versus the Mach number and the frequency. This method is extended to the case of two aligned plates to analyze the influence of the choice of the boundary condition on the downstream plate which interacts with a vortex sheet.

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Finite-wavelength scattering of incident vorticity and acoustic waves at a shrouded-jet exit

Journal of Fluid Mechanics ◽

10.1017/s0022112008003212 ◽

2008 ◽

Vol 612 ◽

pp. 407-438 ◽

Cited By ~ 15

Author(s):

ARNAB SAMANTA ◽

JONATHAN B. FREUND

Keyword(s):

Mach Number ◽

Acoustic Waves ◽

Vortex Sheet ◽

Acoustic Mode ◽

Uniform Flow ◽

Sharp Edge ◽

Potential Mechanism ◽

Ambient Flow ◽

Acoustic Modes ◽

Cylindrical Vortex

As the vortical disturbances of a shrouded jet pass the sharp edge of the shroud exit some of the energy is scattered into acoustic waves. Scattering into upstream-propagating acoustic modes is a potential mechanism for closing the resonance loop in the ‘howling’ resonances that have been observed in various shrouded jet configurations over the years. A model is developed for this interaction at the shroud exit. The jet is represented as a uniform flow separated by a cylindrical vortex sheet from a concentric co-flow within the cylindrical shroud. A second vortex sheet separates the co-flow from an ambient flow outside the shroud, downstream of its exit. The Wiener–Hopf technique is used to compute reflectivities at the shroud exit. For some conditions it appears that the reflection of finite-wavelength hydrodynamic vorticity modes on the vortex sheet defining the jet could be sufficient to reinforce the shroud acoustic modes to facilitate resonance. The analysis also gives the reflectivities for the shroud acoustic modes, which would also be important in establishing resonance conditions. Interestingly, it is also predicted that the shroud exit can be ‘transparent’ for ranges of Mach numbers, with no reflection into any upstream-propagating acoustic mode. This is phenomenologically consistent with observations that indicate a peculiar sensitivity of resonances of this kind to, say, jet Mach number.

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ACOUSTIC DIFFRACTION BY A PLATE IN A UNIFORM FLOW

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202502001829 ◽

2002 ◽

Vol 12 (05) ◽

pp. 625-647 ◽

Cited By ~ 7

Author(s):

A. S. BONNET-BENDHIA ◽

L. DAHI ◽

E. LUNEVILLE ◽

V. PAGNEUX

Keyword(s):

Velocity Potential ◽

Vortex Sheet ◽

Uniform Flow ◽

Mathematical Framework ◽

Trailing Edge ◽

Singular Functions ◽

Acoustic Diffraction ◽

Potential Representation

We present a mathematical framework for the problem of the acoustic diffraction by a plate located in a duct, in the presence of a uniform flow. The model is based on a velocity potential representation outside a vortex sheet which is induced by the trailing edge of the plate. Using limiting absorption techniques and singular functions decompositions, we show how to get a theoretical and numerical well-suited formulation.

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MECHANICAL BEHAVIOR OF DISTAL RADIUS FRACTURE FIXATION PLATE BY THE FINITE ELEMENTS METHOD

10.26678/abcm.enebi2018.eeb18-0134 ◽

2018 ◽

Author(s):

Leonardo Battaglion ◽

Antonio Shimano ◽

Ana Paula MACEDO

Keyword(s):

Finite Elements ◽

Mechanical Behavior ◽

Distal Radius Fracture ◽

Distal Radius ◽

Fracture Fixation ◽

Finite Elements Method ◽

Radius Fracture ◽

Fixation Plate

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Finite element modeling of multiple density materials of bone specimens for biomechanical behavior evaluation

SN Applied Sciences ◽

10.1007/s42452-021-04760-9 ◽

2021 ◽

Vol 3 (9) ◽

Author(s):

Sebastián Irarrázaval ◽

Jorge Andrés Ramos-Grez ◽

Luis Ignacio Pérez ◽

Pablo Besa ◽

Angélica Ibáñez

Keyword(s):

Finite Elements ◽

Computational Models ◽

Reaction Force ◽

Elastic Stiffness ◽

Finite Elements Method ◽

Mechanical Resistance ◽

Assessment Procedure ◽

Axial Tomography ◽

Biomechanical Behavior ◽

Ct Data

AbstractThe finite elements method allied with the computerized axial tomography (CT) is a mathematical modeling technique that allows constructing computational models for bone specimens from CT data. The objective of this work was to compare the experimental biomechanical behavior by three-point bending tests of porcine femur specimens with different types of computational models generated through the finite elements’ method and a multiple density materials assignation scheme. Using five femur specimens, 25 scenarios were created with differing quantities of materials. This latter was applied to computational models and in bone specimens subjected to failure. Among the three main highlights found, first, the results evidenced high precision in predicting experimental reaction force versus displacement in the models with larger number of assigned materials, with maximal results being an R2 of 0.99 and a minimum root-mean-square error of 3.29%. Secondly, measured and computed elastic stiffness values follow same trend with regard to specimen mass, and the latter underestimates stiffness values a 6% in average. Third and final highlight, this model can precisely and non-invasively assess bone tissue mechanical resistance based on subject-specific CT data, particularly if specimen deformation values at fracture are considered as part of the assessment procedure.

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Auto and Cross Correlation Measurements in a Turbine Cascade Using a Digital Correlator

Volume 1: Turbomachinery ◽

10.1115/82-gt-132 ◽

1982 ◽

Cited By ~ 3

Author(s):

P. J. Bryanston-Cross ◽

J. J. Camus

Keyword(s):

Mach Number ◽

High Speed ◽

Cross Correlation ◽

Turbine Blades ◽

Image Plane ◽

Strongly Correlated ◽

Trailing Edge ◽

Number Range ◽

Cross Correlations ◽

Digital Correlator

A simple technique has been developed which samples the dynamic image plane information of a schlieren system using a digital correlator. Measurements have been made in the passages and in the wakes of transonic turbine blades in a linear cascade. The wind tunnel runs continuously and has independently variable Reynolds and Mach number. As expected, strongly correlated vortices were found in the wake and trailing edge region at 50 KHz. Although these are strongly coherent we show that there is only limited cross-correlation from wake to wake over a Mach no. range M = 0.5 to 1.25 and variation of Reynolds number from 3 × 105 to 106. The trailing edge fluctuation cross correlations were extended both upstream and downstream and preliminary measurements indicate that this technique can be used to obtain information on wake velocity. The vortex frequency has also been measured over the same Mach number range for two different cascades. The results have been compared with high speed schlieren photographs.

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The Effect of Pulsed Blowing on the Boundary Layer of a Highly Loaded Low Pressure Turbine Blade

Volume 6A: Turbomachinery ◽

10.1115/gt2013-94566 ◽

2013 ◽

Cited By ~ 3

Author(s):

Marion Mack ◽

Roland Brachmanski ◽

Reinhard Niehuis

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Mach Number ◽

Suction Side ◽

Reynolds Numbers ◽

Low Pressure ◽

Trailing Edge ◽

Low Pressure Turbine ◽

Wide Range ◽

Highly Loaded

The performance of the low pressure turbine (LPT) can vary appreciably, because this component operates under a wide range of Reynolds numbers. At higher Reynolds numbers, mid and aft loaded profiles have the advantage that transition of suction side boundary layer happens further downstream than at front loaded profiles, resulting in lower profile loss. At lower Reynolds numbers, aft loading of the blade can mean that if a suction side separation exists, it may remain open up to the trailing edge. This is especially the case when blade lift is increased via increased pitch to chord ratio. There is a trend in research towards exploring the effect of coupling boundary layer control with highly loaded turbine blades, in order to maximize performance over the full relevant Reynolds number range. In an earlier work, pulsed blowing with fluidic oscillators was shown to be effective in reducing the extent of the separated flow region and to significantly decrease the profile losses caused by separation over a wide range of Reynolds numbers. These experiments were carried out in the High-Speed Cascade Wind Tunnel of the German Federal Armed Forces University Munich, Germany, which allows to capture the effects of pulsed blowing at engine relevant conditions. The assumed control mechanism was the triggering of boundary layer transition by excitation of the Tollmien-Schlichting waves. The current work aims to gain further insight into the effects of pulsed blowing. It investigates the effect of a highly efficient configuration of pulsed blowing at a frequency of 9.5 kHz on the boundary layer at a Reynolds number of 70000 and exit Mach number of 0.6. The boundary layer profiles were measured at five positions between peak Mach number and the trailing edge with hot wire anemometry and pneumatic probes. Experiments were conducted with and without actuation under steady as well as periodically unsteady inflow conditions. The results show the development of the boundary layer and its interaction with incoming wakes. It is shown that pulsed blowing accelerates transition over the separation bubble and drastically reduces the boundary layer thickness.

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