Solving Galbrun’s Equation with a Discontinuous galerkin Finite Element Method

© S. Hirzel Verlag · EAA Over many years, scientists and engineers have developed a broad variety of mathematical formulations to investigate the propagation and interactions with flow of flow-induced noise in early-stage of product design and development. Beside established theories such as the linearized Euler equations (LEE), the linearized Navier–Stokes equations (LNSE) and the acoustic perturbation equations (APE) which are described in an Eulerian framework, Galbrun utilized a mixed Lagrange–Eulerian framework to reduce the number of unknowns by representing perturbations by means of particle displacement only. Despite the advantages of fewer degrees of freedom and the reduced effort to solve the system equations, a computational approach using standard continuous finite element methods (FEM) suffers from instabilities called spurious modes that pollute the solution. In this work, the authors employ a discontinuous Galerkin approach to overcome the difficulties related to spurious modes while solving Galbrun’s equation in a mixed and pure displacement based formulation. The results achieved with the proposed approach are compared with results from previous attempts to solve Galbrun’s equation. The numerical determination of acoustic modes and the identification of vortical modes is discussed. Furthermore, case studies for a lined-duct and an annulus supporting a rotating shear-flow are investigated

Measuring monopole and dipole polarizability of acoustic meta-atoms

We present a method to extract monopole and dipole polarizability from experimental measurements of two-dimensional acoustic meta-atoms. In contrast to extraction from numerical results, this enables all second-order effects and uncertainties in material properties to be accounted for. We apply the technique to 3D-printed labyrinthine meta-atoms of a variety of geometries. We show that the polarizability of structures with shorter acoustic path length agrees well with numerical results. However, those with longer path lengths suffer strong additional damping, which we attribute to the strong viscous and thermal losses in narrow channels

An Abridged Review of Blast Wave Parameters

In case of blast loading on structures, analysis is carried out in two stages, first the blast loading on a particular structure is determined and second, an evaluation is made for the response of the structure to this loading. In this paper, a review of the first part is presented which includes various empirical relations available for computation of blast load in the form of pressure-time function resulting from the explosion in the air. Different empirical techniques available in the form of charts and equations are reviewed first and then the various blast wave parameters are computed using these equations. This paper is providing various blast computation equations, charts, and references in a concise form at a single place and to serve as base for researchers and designers to understand, compare, and then compute the blast wave parameters. Recommendations are presented to choose the best suitable technique from the available methods to compute the pressure-time function for obtaining structural response.Defence Science Journal, 2012, 62(5), pp.300-306, DOI:http://dx.doi.org/10.14429/dsj.62.114

Computation of conservation laws in optimal control

Making use of a computer algebra system, we define computational tools to identify symmetries and conservation laws in optimal control

Prediction of the intramembranous tissue formation during perisprosthetic healing with uncertainties. Part 2. Global clinical healing due to combination of random sources

This work proposes to examine the variability of the bone tissue healing process in the early period after the implantation surgery. The first part took into account the effect of variability of individual biochemical factors on the solid phase fraction, which is an indicator of the quality of the primary fixation and condition of its long-term behaviour. The next issue, addressed in this second part, is the effect of cumulative sources of uncertainties on the same problem of a canine implant. This paper is concerned with the ability to increase the number of random parameters to assess the coupled influence of those variabilities on the tissue healing. To avoid an excessive increase in the complexity of the numerical modelling and further, to maintain efficiency in computational cost, a collocation-based polynomial chaos expansion approach is implemented. A progressive set of simulations with an increasing number of sources of uncertainty is performed. This information is helpful for future implant design and decision process for the implantation surgical act

Metahouse: noise-insulating chamber based on periodic structures

Noise pollution remains a challenging problem requiring the development of novel systems for noise insulation. Extensive work in the field of acoustic metamaterials has led to occurrence of various ventilated structures which, however, are usually demonstrated for rather narrow regions of the audible spectrum. In this work, we further extend the idea of metamaterial-based systems developing a concept of a metahouse chamber representing a ventilated structure for broadband noise insulation. Broad stop bands originate from strong coupling between pairs of Helmholtz resonators constituting the structure. We demonstrate numerically and experimentally the averaged transmission -43 dB within the spectral range from 1500 to 16500 Hz. The sparseness of the structure together with the possibility to use optically transparent materials suggest that the chamber may be also characterized by partial optical transparency depending on the mutual position of structural elements. The obtained results are promising for development of novel noise-insulating structures advancing urban science