Decay of geodesic acoustic modes due to the combined action of phase mixing and Landau damping

Geodesic acoustic modes (GAMs) are oscillations of the electric field whose importance in tokamak plasmas is due to their role in the regulation of turbulence. The linear collisionless damping of GAMs is investigated here by means of analytical theory and numerical simulations with the global gyrokinetic particle-in-cell code ORB5. The combined effect of the phase mixing and Landau damping is found to quickly redistribute the GAM energy in phase-space, due to the synergy of the finite orbit width of the passing ions and the cascade in wave number given by the phase mixing. When plasma parameters characteristic of realistic tokamak profiles are considered, the GAM decay time is found to be an order of magnitude lower than the decay due to the Landau damping alone, and in some cases of the same order of magnitude of the characteristic GAM drive time due to the nonlinear interaction with an ITG mode. In particular, the radial mode structure evolution in time is investigated here and reproduced quantitatively by means of a dedicated initial value code and diagnostics.Comment: Submitted to Phys. Plasma

Liquid-vapour asymmetry in pure fluids: A Monte Carlo simulation study

Monte Carlo simulations within the grand canonical ensemble are used to obtain the joint distribution of density and energy fluctuations $p_L(\rho,u)$ for two model fluids: a decorated lattice gas and a polymer system. In the near critical region the form of $p_L(\rho,u)$ is analysed using a mixed field finite-size-scaling theory that takes account of liquid-vapour asymmetry. Field mixing transformations are performed that map $p_L(\rho,u)$ onto the joint distribution of critical scaling operators \ptMEstar\ appropriate to the Ising fixed point. Carrying out this procedure permits a very accurate determination of the critical point parameters. By forming various projections of \ptMEstar , the full universal finite-size spectrum of the critical density and energy distributions of fluids is also obtained. In the sub-critical coexistence region, an examination is made of the influence of field mixing on the asymmetry of the density distribution.Comment: 19 pages Latex, 15 Figures available on request. Report Number #IP-94.15

Simulation studies of fluid critical behaviour

We review and discuss recent advances in the simulation of bulk critical phenomena in model fluids. In particular we emphasise the extensions to finite-size scaling theory needed to cope with the lack of symmetry between coexisting fluid phases. The consequences of this asymmetry for simulation measurements of quantities such as the particle density and the heat capacity are pointed out and the relationship to experiment is discussed. A general simulation strategy based on the finite-size scaling theory is described and its utility illustrated via Monte-Carlo studies of the Lennard-Jones fluid and a two-dimensional spin fluid model. Recent applications to critical polymer blends and solutions are also briefly reviewed. Finally we consider the outlook for future simulation work in the field.Comment: 35 pages Revtex, 11 eps figures. Review article to appear in J. Phys.: Condens. Matte

Colour in visualisation for computational fluid dynamics

Colour is used in computational fluid dynamic (CFD) simulations in two key ways. First it is used to visualise the geometry and allow the engineers to be confident that the model constructed is a good representation of the engineering situation. Once an analysis has been completed, colour is used in post-processing the data from the simulations to illustrate the complex fluid mechanic phenomena under investigation. This paper describes these two uses of colour and provides some examples to illustrate the key visualisation approaches used in CFD

Large Eddy Simulations of gaseous flames in gas turbine combustion chambers

Recent developments in numerical schemes, turbulent combustion models and the regular increase of computing power allow Large Eddy Simulation (LES) to be applied to real industrial burners. In this paper, two types of LES in complex geometry combustors and of specific interest for aeronautical gas turbine burners are reviewed: (1) laboratory-scale combustors, without compressor or turbine, in which advanced measurements are possible and (2) combustion chambers of existing engines operated in realistic operating conditions. Laboratory-scale burners are designed to assess modeling and funda- mental flow aspects in controlled configurations. They are necessary to gauge LES strategies and identify potential limitations. In specific circumstances, they even offer near model-free or DNS-like LES computations. LES in real engines illustrate the potential of the approach in the context of industrial burners but are more difficult to validate due to the limited set of available measurements. Usual approaches for turbulence and combustion sub-grid models including chemistry modeling are first recalled. Limiting cases and range of validity of the models are specifically recalled before a discussion on the numerical breakthrough which have allowed LES to be applied to these complex cases. Specific issues linked to real gas turbine chambers are discussed: multi-perforation, complex acoustic impedances at inlet and outlet, annular chambers.. Examples are provided for mean flow predictions (velocity, temperature and species) as well as unsteady mechanisms (quenching, ignition, combustion instabil- ities). Finally, potential perspectives are proposed to further improve the use of LES for real gas turbine combustor designs

Large eddy simulation of a lifted ethylene flame using a dynamic nonequilibrium model for subfilter scalar variance and dissipation rate

Accurate prediction of nonpremixed turbulent combustion using large eddy simulation(LES) requires detailed modeling of the mixing between fuel and oxidizer at scales finer than the LES filter resolution. In conserved scalar combustion models, the small scale mixing process is quantified by two parameters, the subfilter scalar variance and the subfilter scalar dissipation rate. The most commonly used models for these quantities assume a local equilibrium exists between production and dissipation of variance. Such an assumption has limited validity in realistic, technically relevant flow configurations. However, nonequilibrium models for variance and dissipation rate typically contain a model coefficient whose optimal value is unknown a priori for a given simulation. Furthermore, conventional dynamic procedures are not useful for estimating the value of this coefficient. In this work, an alternative dynamic procedure based on the transport equation for subfilter scalar variance is presented, along with a robust conditional averaging approach for evaluation of themodel coefficient. This dynamic nonequilibrium modeling approach is used for simulation of a turbulent lifted ethylene flame, previously studied using DNS by Yoo et al. (Proc. Comb. Inst., 2011). The predictions of the new model are compared to those of a static nonequilibrium modeling approach using an assumed model coefficient, as well as those of the equilibrium modeling approach. The equilibrium models are found to systematically underpredict both subfilter scalar variance and dissipation rate. Use of the dynamic procedure is shown to increase the accuracy of the nonequilibrium modeling approach. However, numerical errors that arise as a consequence of grid-based implicit filtering appear to degrade the accuracy of all three modeling options. Thus, while these results confirm the usefulness of the new dynamic model, they also show that the quality of subfilter model predictions depends on several factors extrinsic to the formulation of the subfilter model itself

A global study of enhanced stretching and diffusion in chaotic tangles

A global, finite-time study is made of stretching and diffusion in a class of chaotic tangles associated with fluids described by periodically forced two-dimensional dynamical systems. Invariant lobe structures formed by intersecting global stable and unstable manifolds of persisting invariant hyperbolic sets provide the geometrical framework for studying stretching of interfaces and diffusion of passive scalars across these interfaces. In particular, the present study focuses on the material curve that initially lies on the unstable manifold segment of the boundary of the entraining turnstile lobe.A knowledge of the stretch profile of a corresponding curve that evolves according to the unperturbed flow, coupled with an appreciation of a symbolic dynamics that applies to the entire original material curve in the perturbed flow, provides the framework for understanding the mechanism for, and topology of, enhanced stretching in chaotic tangles. Secondary intersection points (SIP's) of the stable and unstable manifolds are particularly relevant to the topology, and the perturbed stretch profile is understood in terms of the unperturbed stretch profile approximately repeating itself on smaller and smaller scales. For sufficiently thin diffusion zones, diffusion of passive scalars across interfaces can be treated as a one-dimensional process, and diffusion rates across interfaces are directly related to the stretch history of the interface.An understanding of interface stretching thus directly translates to an understanding of diffusion across interfaces. However, a notable exception to the thin diffusion zone approximation occurs when an interface folds on top of itself so that neighboring diffusion zones overlap. An analysis which takes into account the overlap of nearest neighbor diffusion zones is presented, which is sufficient to capture new phenomena relevant to efficiency of mixing. The analysis adds to the concentration profile a saturation term that depends on the distance between neighboring segments of the interface. Efficiency of diffusion thus depends not only on efficiency of stretching along the interface, but on how this stretching is distributed relative to the distance between neighboring segments of the interface

Turbulent mixing

The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field