Hamiltonian discontinuous Galerkin FEM for linear, rotating incompressible Euler equations: inertial waves

A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions. The numerical challenges concern: (i) discretisation of a divergence-free velocity field; (ii) discretisation of geostrophic boundary conditions combined with no-normal flow at solid walls; (iii) discretisation of the conserved, Hamiltonian dynamics of the inertial-waves; and, (iv) large-scale computational demands owing to the three-dimensional nature of inertial-wave dynamics and possibly its narrow zones of chaotic attraction. These issues have been resolved: (i) by employing Dirac’s method of constrained Hamiltonian dynamics to our DGFEM for linear, compressible flows, thus enforcing the incompressibility constraints; (ii) by enforcing no-normal flow at solid walls in a weak form and geostrophic tangential flow —along the wall; (iii) by applying a symplectic time discretisation; and, (iv) by combining PETSc’s linear algebra routines with our high-level software. We compared our simulations with exact solutions of three-dimensional compressible and incompressible flows, in (non)rotating periodic and partly periodic cuboids (Poincar´e waves). Additional verifications concerned semi-analytical eigenmode solutions in rotating cuboids with solid walls

Aeronautical Engineering. A continuing bibliography with indexes, supplement 156

This bibliography lists 288 reports, articles and other documents introduced into the NASA scientific and technical information system in December 1982

Hybrid Noise Simulation for Enclosed Configurations

Future air traffic regulations are going to further limit the noise and pollutant emissions of aero engines in a way that can only be met by the comprehensive migration towards lean premixed combustion based aero engine designs. Compared to conventional rich-quench-lean setups, these next generation combustion systems are more prone to thermoacoustic instabilities caused by combustion noise. For this reason, improved methods for the prediction and investigation of combustion noise and thermoacoustic instabilities are required. Consequently, a hybrid Computational Aeroacoustics (CAA) method is devised, implemented and applied to two enclosed, reactive configurations in this work. The method comprises a low Mach number flow solver, a dedicated acoustics tool and a coupling layer, which bridges the different numerical schemes and physical phenomena. In addition to traditional aeroacoustic problems, the method is applicable to enclosed configurations with complex geometries, while maintaining the favorable computational efficiency of common hybrid methods. Its key components are the newly developed acoustics solver and the corresponding coupling layer. For the description of the reacting flow field, an established, finite volume based flow solver is equipped with the coupling interface. By employing the high order spectral/hp element method in a discontinuous Galerkin formulation, the CAA solver efficiently accounts for acoustic wave propagation in complex, three-dimensional geometries. Its implementation is focused on stability and flexibility to allow for an easy adaption to industrial applications, such as combustion noise. This is achieved by solving the unconditionally stable Acoustic Perturbation Equations (APE) and using a set of Riemann solvers that can operate on variable density base flows. The developed coupling layer enables bi-directional communication of both solvers at run-time, without limiting their spatial and temporal resolutions, even when applied to coinciding domains. Their different length scales and discretization methods are overcome by a linear interpolation in time and a spatial, implicit low pass filter, that operates on an intermediate representation of the flow fields. The applicability of the hybrid CAA method is investigated by means of two laboratory scale combustors of increasing complexity. The first setup features a half-dump combustor, that facilitates a basic validation of the CAA solver and the coupling. It is shown that the short length scale base flow fields are sufficiently represented in terms of the CAA expansion by the coupling layer. In the obtained acoustic fields, the behavior of the system's first eigenmode is well reproduced. The instigation of a second eigenmode was not observed in the experimental noise spectrum but is in agreement with a similar hybrid CAA simulation. The second configuration is a pressurized burner, operated by a swirl stabilized, premixed flame. It is already beyond the capabilities of most available CAA tools and features most phenomena present in industry scale combustion systems. In the considered frequency range, the prevalent eigenmode is very well predicted. Independent of the acoustic governing equations, the developed method is estimated to require less than a fifth of the computational effort of a direct noise simulation for the considered configuration

Nonlinear self-excited thermoacoustic oscillations of a ducted premixed flame: Bifurcations and routes to chaos

AbstractThermoacoustic systems can oscillate self-excitedly, and often non-periodically, owing to coupling between unsteady heat release and acoustic waves. We study a slot-stabilized two-dimensional premixed flame in a duct via numerical simulations of a $G$-equation flame coupled with duct acoustics. We examine the bifurcations and routes to chaos for three control parameters: (i) the flame position in the duct, (ii) the length of the duct and (iii) the mean flow velocity. We observe period-1, period-2, quasi-periodic and chaotic oscillations. For certain parameter ranges, more than one stable state exists, so mode switching is possible. At intermediate times, the system is attracted to and repelled from unstable states, which are also identified. Two routes to chaos are established for this system: the period-doubling route and the Ruelle–Takens–Newhouse route. These are corroborated by analyses of the power spectra of the acoustic velocity. Instantaneous flame images reveal that the wrinkles on the flame surface and pinch-off of flame pockets are regular for periodic oscillations, while they are irregular and have multiple time and length scales for quasi-periodic and aperiodic oscillations. This study complements recent experiments by providing a reduced-order model of a system with approximately 5000 degrees of freedom that captures much of the elaborate nonlinear behaviour of ducted premixed flames observed in the laboratory.This is the author's accepted manuscript. The final version is available from CUP in the Journal of Fluid Mechanics at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9441088&fulltextType=RA&fileId=S002211201400601

Ferroelectrics

Ferroelectric materials exhibit a wide spectrum of functional properties, including switchable polarization, piezoelectricity, high non-linear optical activity, pyroelectricity, and non-linear dielectric behaviour. These properties are crucial for application in electronic devices such as sensors, microactuators, infrared detectors, microwave phase filters and, non-volatile memories. This unique combination of properties of ferroelectric materials has attracted researchers and engineers for a long time. This book reviews a wide range of diverse topics related to the phenomenon of ferroelectricity (in the bulk as well as thin film form) and provides a forum for scientists, engineers, and students working in this field. The present book containing 24 chapters is a result of contributions of experts from international scientific community working in different aspects of ferroelectricity related to experimental and theoretical work aimed at the understanding of ferroelectricity and their utilization in devices. It provides an up-to-date insightful coverage to the recent advances in the synthesis, characterization, functional properties and potential device applications in specialized areas