Application of Ultrasonic Beam Modeling to Phased Array Testing of Complex Geometry Components

For several years, the French Atomic Energy Commission (CEA) has developed phased array techniques to improve defect characterization and adaptability to various inspection configurations [1]. Such techniques allow to steer and focus the ultrasonic beam radiated by a transducer split into a set of individually addressed elements, using amplitude and delay laws. For most conventional systems, those delay laws are extracted from geometric ultrasonic paths between each element of the array and a geometric focusing applied to perform beam-forming abilities [2] for simple geometry components (e.g. beam- steering over a plane specimen), whereas experimental delays can be supplied to the array at transmission and reception to optimally adapt the ultrasonic beam to the detected defect, in a so-called self-focusing process [3,4]. This method, relevant for complex material or geometry leading to phase distortion or complex paths that cannot be predicted by simple geometrical calculations, obviously requires the existence of a reflector and the ultrasonic beam radiated by the experimental delay law cannot be known. Therefore this technique is used to improve defect detection (optimal sensibility) rather than defect characterization. To assess complex geometry components inspection with an adaptive system, the CEA has developed new modeling devoted to predict the ultrasonic field radiated by arbitrary transducers through complex geometry and material specimen [5]. A model allows to compute optimized delay laws to preserve the characteristics of the beam through the complex surface, as well as the actual radiated field using those delays. This paper presents two applications of this model : the inspection of a misaligned specimen, and the inspection of an irregular surface

Cooperation and Competition Strategies in Multi-objective Shape Optimization - Application to Low-boom/Low-drag Supersonic Business Jet

International audienceCooperation and competition are natural laws that regulate the interactions between agents in numerous physical, or social phenomena. By analogy, we transpose these laws to devise e cient multi-objective algorithms applied to shape optimization problems involving two or more disciplines. Two e cient strategies are presented in this paper: a multiple gradient descent algorithm (MGDA) and a Nash game strategy based on an original split of territories between disciplines. MGDA is a multi-objective extension of the steepest descent method. The use of a gradient-based algorithm that exploits the cooperation principle aims at reducing the number of iterations required for classical multi-objective evolutionary algorithms to converge to a Pareto optimal design. On the other hand side, the Nash game strategy is well adapted to typical aeronautical optimization problems, when, after having optimized a preponderant or fragile discipline (e.g. aerodynamics), by the minimization of a primary objective-function, one then wishes to reduce a secondary objective-function, representative of another discipline, in a process that avoids degrading excessively the original optimum. Presently, the combination of the two approaches is exploited, in a method that explores the entire Pareto front. Both algorithms are rst analyzed on analytical test cases to demonstrate their main features and then applied to the optimum-shape design of a low-boom/low-drag supersonic business jet design problem. Indeed, sonic boom is one of the main limiting factors to the development of civil supersonic transportation. As the driving design for low-boom is not compliant with the low-drag one, our goal is to provide a trade-o between aerodynamics and acoustics. Thus Nash games are adopted to de ne a low-boom con guration close to aerodynamic optimality w.r.t. wave drag

UN NOUVEAU MODÈLE POUR LE CALCUL DU CHAMP DE PRESSION PARAMÉTRIQUE

a new method for obtaining the parametric sound field is performed, which combines the parabolic approximation and the expansion of the source condition in a sum of Gaussians. This leads to a single integral easy to compute numerically. The main features of the parametric sound field are studied afterwards

Numerical simulation of shock wave focusing at fold caustics, with application to sonic boom

International audienceWeak shock wave focusing at fold caustics is described by the mixed type elliptic/hyperbolic nonlinear Tricomi equation. This paper presents a new and original numerical method for solving this equation, using a potential formulation and an ``exact'' numerical solver for handling nonlinearities. Validation tests demonstrate quantitatively the efficiency of the algorithm, which is able to handle complex waveforms as may come out from ``optimized'' aircraft designed to minimize sonic booms. It provides a real alternative to the approximate method of the hodograph transform. This motivated the application to evaluate the ground track focusing of sonic boom for an accelerating aircraft, by coupling CFD Euler simulations performed around the mock-up on an adaptated mesh grid, atmospheric propagation modeling, and the Tricomi algorithm. The chosen configuration is the European Eurosup mock-up. Convergence of the focused boom at the ground level as a function of the matching distance is investigated to demonstrate the efficiency of the numerical process. As a conclusion, it is indicated how the present work may pave the way towards a study on sonic superboom (focused boom) mitigation

Variability of Focused Sonic Booms from Accelerating Supersonic Aircraft in Consideration of Meteorological Effects.

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Meteorologically Induced Variability of Sonic-Boom Characteristics of Supersonic Aircraft in Cruising Flight

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CHARACTERISTIC FAST MARCHING METHOD FOR MONOTONICALLY PROPAGATING FRONTS IN A MOVING MEDIUM

International audienceThe fast marching method is computationally efficient in approximating the viscosity solution of the eikonal equation in the case of unidirectional wavefront propagation through a medium at rest. The main assumption of this method is that the front propagates only in its normal direction, which is the case when the medium of propagation is at rest. In many real-time applications, the medium may be occupied with a moving fluid. In such cases, the governing equation is a generalized (anisotropic) eikonal equation. The main assumption of the fast marching method may not hold in this case, since the front may propagate in both the tangential and the normal direction. This leads to instability in the fast marching method due to violation of the upwind criterion. In this work, we develop a fast marching method for the generalized eikonal equation, called the characteristic fast marching method, where the upwind criterion is achieved using the characteristic direction of the propagating wavefront at each grid point. We suitably modify the narrow band algorithm of the fast marching method so that the anisotropic nature of the medium is incorporated in the method. We compare the numerical results obtained from our method with the solution obtained using the ray theory (geometrical optics theory) to show that the method accurately captures the viscosity solution of the generalized eikonal equation. We apply the method to study the propagation of a wavefront in a medium with a cavity and also study the merging of two wavefronts from different sources. The method can easily be generalized to higher order approximations. We develop a method with second order finite difference approximation and study the rate of convergence numerically

A re-analysis of Carancas meteorite seismic and infrasound data based on sonic boom hypothesis

International audienceMeteoroids entering the Earth atmosphere at high hypersonic velocities are a source of sonic boom that is recorded as infrasound signal at the ground level. The Carancas meteorite (Peru, 2007) is re-examined in this way as a reference case with ground crater and nearby seismic and infrasonic recordings. A new trajectory is proposed for this meteorite by minimizing the difference between computed and observed times of arrivals for geometrical arrivals. A scenario based on diffraction is proposed to explain non-geometrical arrivals. Model frequency spectra show a reasonable agreement with data, which allows estimation of the meteorite diameter in a narrow range compatible with crater observations

Nonlinear focusing of acoustic shock waves at a caustic cusp (vol 117, pg 566, 2005)

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