Experimental and numerical investigation of Helmholtz resonators and perforated liners as attenuation devices in industrial gas turbine combustors

This paper reports upon developments in the simulation of the passive control of combustion dynamics in industrial gas turbines using acoustic attenuation devices such as Helmholtz resonators and perforated liners. Combustion instability in gas turbine combustors may, if uncontrolled, lead to large-amplitude pressure fluctuations, with consequent serious mechanical problems in the gas turbine combustor system. Perforated combustor walls and Helmholtz resonators are two commonly used passive instability control devices. However, experimental design of the noise attenuation device is time-consuming and calls for expensive trial and error practice. Despite significant advances over recent decades, the ability of Computational Fluid Dynamics to predict the attenuation of pressure fluctuations by these instability control devices is still not well validated. In this paper, the attenuation of pressure fluctuations by a group of multi-perforated panel absorbers and Helmholtz resonators are investigated both by experiment and computational simulation. It is demonstrated that CFD can predict the noise attenuation from Helmholtz resonators with good accuracy. A porous material model is modified to represent a multi-perforated panel and this perforated wall representation approach is demonstrated to be able to accurately predict the pressure fluctuation attenuation effect of perforated panels. This work demonstrates the applicability of CFD in gas turbine combustion instability control device design

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length -- the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.Comment: 10 pages, 3 figures, In Proc. A4A5, Chester UK, Jul. 18-22 200

Adaptive Finite Element Simulation of Steady State Currents at Microdisc Electrodes to a Guaranteed Accuracy

We consider the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the "edge-effect". Our approach to overcoming this problem involves the derivation of an a posteriori bound on the error in the numerical approximation for the current which can be used to drive an adaptive mesh-generation algorithm. This allows us to calculate the current to within a prescribed tolerance. Here we demonstrate the power of the method for a simple model problem -- an E reaction mechanism at a microdisc electrode -- for which the analytical solution is known, then we extend the work to the case of a (pseudo) first order EC' reaction mechanism at both an inlaid and a recessed disc

Models for pattern formation in somitogenesis: a marriage of cellular and molecular biology

Somitogenesis, the process by which a bilaterally symmetric pattern of cell aggregations is laid down in a cranio-caudal sequence in early vertebrate development, provides an excellent model study for the coupling of interactions at the molecular and cellular level. Here, we review some of the key experimental results and theoretical models related to this process. We extend a recent chemical pre-pattern model based on the cell cycle Journal of Theoretical Biology 207 (2000) 305-316, by including cell movement and show that the resultant model exhibits the correct spatio-temporal dynamics of cell aggregation. We also postulate a model to account for the recently observed spatio-temporal dynamics at the molecular level

Adaptive Finite Element Simulation of Currents at Microelectrodes to a Guaranteed Accuracy. Application to Channel Microband Electrodes.

We extend our earlier work (see K. Harriman et al., Technical Report NA99/19) on adaptive finite element methods for disc electrodes to the case of reaction mechanisms to the increasingly popular channel microband electrode configuration. We use the standard Galerkin finite element method for the diffusion-dominated (low-flow) case, and the streamline diffusion finite element method for the convection-dominated (high-flow) case. We first consider the simple E reaction mechanism (convection-diffusion equation) and we demonstrate excellent agreement with previous approximate analytical results across the range of parameters of interest, on comparatively coarse meshes. We then consider ECE and EC2E reaction mechanisms (linear and nonlinear systems of reaction-convection-diffusion equations, respectively); again we are able to demonstrate excellent agreement with previous results.\ud \ud The authors are pleased to acknowledge the financial support of the following organisations: a research studentship for KH; a Career Development Fellowship from the Medical Research Council for DJG, which has allowed them to undertake this research

Long term variability of the cosmic ray intensity

In a previous paper Bhat, et al., assess the evidence for the continuing acceleration of cosmic rays in the Loop I supernova remnant. The enhanced gamma-ray emission is found consistent with the Blandford and Cowie model for particle acceleration at the remnant shock wave. The contributions of other supernovae remnants to the galactic cosmic ray energy density are now considered, paying anisotropy of cosmic rays accelerated by local supernovae ( 100 pc). The results are compared with geophysical data on the fluctuations in the cosmic ray intensity over the previous one billion years

Lunar surface engineering properties experiment definition Quarterly report, 1 Oct. - 31 Dec. 1968

Mechanical properties of simulated lunar soil

Active Nematic Multipoles: Flow Responses and the Dynamics of Defects and Colloids

We introduce a general description of localised distortions in active nematics using the framework of active nematic multipoles. We give the Stokesian flows for arbitrary multipoles in terms of differentiation of a fundamental flow response and describe them explicitly up to quadrupole order. We also present the response in terms of the net active force and torque associated to the multipole. This allows the identification of the dipolar and quadrupolar distortions that generate self-propulsion and self-rotation respectively and serves as a guide for the design of arbitrary flow responses. Our results can be applied to both defect loops in three-dimensional active nematics and to systems with colloidal inclusions. They reveal the geometry-dependence of the self-dynamics of defect loops and provide insights into how colloids might be designed to achieve propulsive or rotational dynamics, and more generally for the extraction of work from active nematics. Finally, we extend our analysis also to two dimensions and to systems with chiral active stresses.Comment: 24 pages, 10 figure

Colloids in Two-Dimensional Active Nematics: Conformal Cogs and Controllable Spontaneous Rotation

A major challenge in the study of active systems is to harness their non-equilibrium dynamics into useful work. We address this by showing how to design colloids with controllable spontaneous propulsion or rotation when immersed in active nematics. This is illustrated for discs with tilted anchoring and chiral cogs, for which we determine the nematic director through conformal mappings. Our analysis identifies two regimes of behaviour for chiral cogs: orientation-dependent handedness and persistent active rotation. Finally, we provide design principles for active nematic colloids to achieve desired rotational dynamics.Comment: 17 pages, 9 figure

Numerical modelling of MPA-CVD reactors with the discontinuous Galerkin finite element method

In this article we develop a fully self consistent mathematical model describing the formation of a hydrogen plasma in a microwave power assisted chemical vapour deposition (MPA-CVD) reactor employed for the manufacture of synthetic diamond. The underlying multi-physics model includes constituent equations for the background gas mass average velocity, gas temperature, electromagnetic field energy and plasma density. The proposed mathematical model is numerically approximated based on exploiting the discontinuous Galerkin finite element method. We demonstrate the practical performance of this computational approach on a variety of CVD reactor geometries for a range of operating conditions