Search

The work describes the wave propagation in a periodic structure formed by a linear spring-mass chain with local Duffing non-linear resonators. The wave propagation is studied using the Floquet-Bloch theorem combined with a perturbation approach to identify the dispersion relations in the nonlinear periodic structure. The theoretical model is benchmarked by a numerical model that considers an analogous finite resonant spring-mass system. The numerical nonlinear model provides an apparent dispersion relation of the structure obtained from an inverse identification method, the latter based on imposing a wave number as an initial condition, and then obtaining the corresponding frequency from the analysis of the chain amplitude in the time domain. The perturbation and the numerical methods are compared to discuss the behaviour of the wave propagation in the nonlinear resonators periodic chain. The perturbation is then compared with the Harmonic Balance Method previously used in the literature. Keywords: Periodic structures, Resonators, Non-linearities

International audience; At supercritical conditions, thermodynamics may become strongly nonlinear which is reflected by large thermodynamic Jacobian values. This means that small variations in density, momentum or energy can result in large pressure perturbations. Because of such nonlinearities, simulations of high-pressure flows are subject to stability issues when the conservative form of the Navier-Stokes system is employed. In high-Reynolds number simulations, transported quantities are altered by numerical scheme errors, stabilization methods and filtering procedures. These alterations affect density and energy independently and may lead to significant pressure oscillations due to the nonlinear behavior of the equation of state. The objective of the present work is to compare three methods based on different sets of transport equations, to measure their impact on pressure and mixing temperature. A classical fully-conservative approach based on the transport of internal energy is compared to two quasi-conservative methods: a pressure-based and an enthalpy-based formulation. A suite of test cases of increasing complexity is employed to expose the main differences between these approaches, at conditions relevant for engineering applications. The analysis first confirmed that the energy-based formulation is prone to artificial pressure fluctuations caused by the interaction between thermodynamic nonlinearities and the numerical dissipation introduced by the stabilization scheme. It is also demonstrated that despite the stability properties of the pressure-based formulation, the mixing temperature is not properly captured since the pressure equation is not used in its conservative form. The enthalpy-based approach however, offers an improved representation of the mixing thermodynamic state while avoiding non-physical pressure variations.

International audience; The computational burden of Large-eddy Simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, would greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, we show how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. We also demonstrate how the improved statistical model adds critical insight to the performance of the model.

International audience; The influence of vortical structures on the transport and mixing of passive scalars is investigated. Initial conditions are taken from a direct numerical simulation database of forced homogeneous isotropic turbulence, with passive scalar fluctuations, driven by a uniform mean gradient, are performed for Taylor microscale Reynolds numbers (R λ) of 140 and 240, and Schmidt numbers 1/8 and 1. For each R λ, after reaching a fully developed turbulent regime, which is statistically steady, the Coherent Vorticity Extraction is applied to the flow. It is shown that the coherent part is able to preserve the vortical structures with only less than 4% of wavelet coefficients while retaining 99.9% of energy. In contrast, the incoherent part is structureless and contains negligible energy. By taking the total, coherent and incoherent velocity fields in turn as initial conditions, new simulations were performed without forcing while the uniform mean scalar gradient is maintained. It is found that the results from simulations with total and coherent velocity fields as initial conditions are very similar. In contrast, the time integration of the incoherent flow exhibits its primarily dissipative nature. The evolutions of passive scalars at Schmidt numbers 1/8 and 1 advected by the total, coherent or incoherent velocity suggest that the vortical structures retained in the coherent part play a dominant role in turbulent transport and mixing. Indeed, the total and coherent flows give almost the same time evolution of the scalar variance, scalar flux and mean scalar dissipation, while the incoherent flow only gives rise to weak scalar diffusion.

Preliminary mission design for planetary satellite orbiters requires a deep knowledge of the long term dynamics that is typically obtained through averaging techniques. The problem is usually formulated in the Hamiltonian setting as a sum of the principal part, which is given through the Kepler problem, plus a small perturbation that depends on the specific features of the mission. It is usually derived from a scaling procedure of the restricted three body problem, since the two main bodies are the Sun and the planet whereas the satellite is considered as a massless particle. Sometimes, instead of the restricted three body problem, the spatial Hill problem is used. In some cases the validity of the averaging is limited to prohibitively small regions, thus, depriving the analysis of significance. We find this paradigm at Enceladus, where the validity of a first order averaging based on the Hill problem lies inside the body. However, this fact does not invalidate the technique as perturbation methods are used to reach higher orders in the averaging process. Proceeding this way, we average the Hill problem up to the sixth order obtaining valuable information on the dynamics close to Enceladus. The averaging is performed through Lie transformations and two different transformations are applied. Firstly, the mean motion is normalized whereas the goal of the second transformation is to remove the appearance of the argument of the node. The resulting Hamiltonian defines a system of one degree of freedom whose dynamics is analyzed. © 2010 Springer Science+Business Media B.V.