One of the major problems in computational aero-acoustics is the disparity in length scales between the flow field and the acoustic field. As a result, a mapping function is normally used to achieve a non-uniform grid distribution. In this paper, a B-spline collocation method with an arbitrary grid placement capability is proposed. This capability not only allows an optimum grid distribution but also avoids the numerical complexities associated with the mapping function. The B-spline collocation method is applied to the case of spinning co-rotating vortices. The result agrees well with the matched asymptotic solution. To cite this article: R. Widjaja et al., C. R. Mecanique 333 (2005).相似文献
Many problems in linear elastodynamics, or dynamic fracture mechanics, can be reduced to Wiener–Hopf functional equations defined in a strip in a complex transform plane. Apart from a few special cases, the inherent coupling between shear and compressional body motions gives rise to coupled systems of equations, and so the resulting Wiener–Hopf kernels are of matrix form. The key step in the solution of a Wiener–Hopf equation, which is to decompose the kernel into a product of two factors with particular analyticity properties, can be accomplished explicitly for scalar kernels. However, apart from special matrices which yield commutative factorizations, no procedure has yet been devised to factorize exactly general matrix kernels.
This paper shall demonstrate, by way of example, that the Wiener–Hopf approximant matrix (WHAM) procedure for obtaining approximate factors of matrix kernels (recently introduced by the author in [SIAM J. Appl. Math. 57 (2) (1997) 541]) is applicable to the class of matrix kernels found in elasticity, and in particular to problems in QNDE. First, as a motivating example, the kernel arising in the model of diffraction of skew incident elastic waves on a semi-infinite crack in an isotropic elastic space is studied. This was first examined in a seminal work by Achenbach and Gautesen [J. Acoust. Soc. Am. 61 (2) (1977) 413] and here three methods are offered for deriving distinct non-commutative factorizations of the kernel. Second, the WHAM method is employed to factorize the matrix kernel arising in the problem of radiation into an elastic half-space with mixed boundary conditions on its face. Third, brief mention is made of kernel factorization related to the problems of flexural wave diffraction by a crack in a thin (Mindlin) plate, and body wave scattering by an interfacial crack. 相似文献
This paper presents a numerical study of noise source term in non-isothermal flows in the context of an aeroacoustic hybrid technique at low Mach numbers. Asymptotic analysis applied to the fully compressible Navier–Stokes equations provides separated sets of equations for the dynamic of the flow and the production and propagation of acoustic waves. Comparisons with analytical dipole and quadrupole distributions are performed, confirming the dipole type of non-isothermal source distribution. This paper is a preliminary work for some more extensive studies on the topic. To cite this article: F. Golanski, C. Prax, C. R. Mecanique 333 (2005).相似文献
In this work, certain peculiarities of the dynamics of pressure waves in a liquid containing bubbles are studied. The specification of a model of bubbly liquids with regard to acoustic damping of the bubbles is considered. Our theoretical results are compared with experimental ones.Received: 30 June 2002, Accepted: 2 February 2003, Published online: 11 June 2003 相似文献
The nature of the instability governing the self-sustained tones produced by a low Mach number plane jet impinging on a slotted plate, known as slot-tone, is identified experimentally. For a given Reynolds number, the natural shear-layer and the jet column mode frequencies of the free jet delimit the values of the measured slot-tone operating frequencies. The oscillations at lower frequencies are the result of the amplification of the jet column mode, and those at higher frequencies correspond to the shear layer instabilities. To cite this article: A. Billon et al., C. R. Mecanique 332 (2004).相似文献
This Note presents an experimental vibro-acoustic set-up that aims to reproduce the energy pumping phenomenon between an acoustic medium and an essentially nonlinear oscillator. It shows a one-way irreversible transfer of energy between the first acoustic mode in a tube and a thin visco-elastic membrane. To cite this article: B. Cochelin et al., C. R. Mecanique 334 (2006).相似文献
In this paper a rigorous dual-porosity model is formulated, which accurately represents the coupling between large-scale fractures
and the micropores within dual porosity media. The overall structure of the porous medium is conceptualized as being blocks
of diffusion dominated micropores separated by natural fractures (e.g. cleats for coal) through which Darcy’s flow occurs.
In the developed model, diffusion in the matrix blocks is fully coupled to the pressure distribution within the fracture system.
Specific assumptions on the pressure behaviour at the matrix boundary, such as step-time function employed in some earlier
studies, are not invoked. The model involves introducing an analytical solution for diffusion within a matrix block, and the
resultant combined flow equation is a nonlinear integro-(partial) differential equation. Analyses to the equation in this
text, in addition to the theoretical development of the proposed model, include: (1) discussion on the “fading memory” of
the model; (2); one-dimensional perturbation solution subject to a specific condition; and (3) asymptotic analyses of the
“long-time” and “short-time” responses of the flow. Two previous models, the Warren-Root and the modified Vermeulen models,
are compared with the proposed model. The advantages of the new model are demonstrated, particularly for early time prediction
where the approximations of these other models can lead to significant error. 相似文献