Analysis of the commutation error of filtering operators for the double-averaged equations of flows in porous media in a LES formalism

The continuum approach employing porous media models is an attractive solution method in the area of Computational Fluid Dynamics (CFD) simulation of fixed-bed reactors due to its robustness and efficiency. This paper applies the double-averaging methodology to refine the mathematical basis for the continuum approach, opening a way to alleviate its main limitations: space-invariant averaging volume and inaccurate treatment of the porous/non-porous interface. The averaging operator is recast as a general space-time filter and a detailed analysis of commutation errors is performed, using a classic Large Eddy Simulation (LES) formalism. An explicit filtering framework has been implemented in the open-source CFD library OpenFOAM to carry out an a-posteriori evaluation of the unclosed terms appearing in the Double-Averaged Navier-Stokes (DANS) equations also considering a space-varying filter width. Two resolved simulations have been performed. First, the flow around a single, stationary particle has been considered and used to validate derived equations and the filtering procedure. Second, an LES of the turbulent flow in a channel partly occupied with a porous medium has been conducted. The results have been filtered, and the commutation error at the porous-fluid interface has been evaluated and compared to the prediction of two models. The significance of the commutation error terms is also discussed and assessed. Finally, the solver for DANS equations has been developed and used to simulate both of the studied geometries. The magnitude of the error associated with neglecting the commutation errors has been investigated and an LES simulation combined with a porous drag model was performed. Very encouraging results have been obtained indicating that the inaccuracy of the drag closure overshadows the error related to the commutation of operators.Comment: This material has been submitted to Physics of Fluids. It contains 33 pages and 21 Figure

Fast calculation of real fluid properties for steam turbine CFD analysis with the new IAPWS standard on the spline-based table look-Up method (SBTL)

Workshop byl částečně podpořen projektem CZ.1.07/2.3.00/20.0139. Tento projekt je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky

Generalization of particle impact behavior in gas turbine via non-dimensional grouping

Fouling in gas turbines is caused by airborne contaminants which, under certain conditions, adhere to aerodynamic surfaces upon impact. The growth of solid deposits causes geometric modifications of the blades in terms of both mean shape and roughness level. The consequences of particle deposition range from performance deterioration to life reduction to complete loss of power. Due to the importance of the phenomenon, several methods to model particle sticking have been proposed in literature. Most models are based on the idea of a sticking probability, defined as the likelihood a particle has to stick to a surface upon impact. Other models investigate the phenomenon from a deterministic point of view by calculating the energy available before and after the impact. The nature of the materials encountered within this environment does not lend itself to a very precise characterization, consequently, it is difficult to establish the limits of validity of sticking models based on field data or even laboratory scale experiments. As a result, predicting the growth of solid deposits in gas turbines is still a task fraught with difficulty. In this work, two nondimensional parameters are defined to describe the interaction between incident particles and a substrate, with particular reference to sticking behavior in a gas turbine. In the first part of the work, historical experimental data on particle adhesion under gas turbine-like conditions are analyzed by means of relevant dimensional quantities (e.g. particle viscosity, surface tension, and kinetic energy). After a dimensional analysis, the data then are classified using non-dimensional groups and a universal threshold for the transition from erosion to deposition and from fragmentation to splashing based on particle properties and impact conditions is identified. The relation between particle kinetic energy/surface energy and the particle temperature normalized by the softening temperature represents the original non-dimensional groups able to represent a basis of a promising adhesion criterion

Evaluation of the flame propagation within an SI engine using flame imaging and LES

This work shows experiments and simulations of the fired operation of a spark ignition engine with port-fuelled injection. The test rig considered is an optically accessible single cylinder engine specifically designed at TU Darmstadt for the detailed investigation of in-cylinder processes and model validation. The engine was operated under lean conditions using iso-octane as a substitute for gasoline. Experiments have been conducted to provide a sound database of the combustion process. A planar flame imaging technique has been applied within the swirl- and tumble-planes to provide statistical information on the combustion process to complement a pressure-based comparison between simulation and experiments. This data is then analysed and used to assess the large eddy simulation performed within this work. For the simulation, the engine code KIVA has been extended by the dynamically thickened flame model combined with chemistry reduction by means of pressure dependent tabulation. Sixty cycles have been simulated to perform a statistical evaluation. Based on a detailed comparison with the experimental data, a systematic study has been conducted to obtain insight into the most crucial modelling uncertainties

Encoding simplicial quantum geometry in group field theories

We show that a new symmetry requirement on the GFT field, in the context of an extended GFT formalism, involving both Lie algebra and group elements, leads, in 3d, to Feynman amplitudes with a simplicial path integral form based on the Regge action, to a proper relation between the discrete connection and the triad vectors appearing in it, and to a much more satisfactory and transparent encoding of simplicial geometry already at the level of the GFT action.Comment: 15 pages, 2 figures, RevTeX, references adde

Effective Hamiltonian Constraint from Group Field Theory

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the group field theory action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions. We apply our procedure to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of group field theories.Comment: 14 page

The complete 1/N expansion of colored tensor models in arbitrary dimension

In this paper we generalize the results of [1,2] and derive the full 1/N expansion of colored tensor models in arbitrary dimensions. We detail the expansion for the independent identically distributed model and the topological Boulatov Ooguri model