A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and non-intrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic methods such as parametric studies and Monte Carlo based techniques.     

Large eddy simulation of a slot jet impinging on a convex surface

A large eddy simulation is used to simulate flow and heat transfer in a turbulent plane jet with two distances from the jet-exit to impingement corresponding to twice and ten times the slot nozzle width. The resolved different unsteady vortex motions of the jet shear layers are studied and shown to have an important influence on heat transfer at the wall. They are used to explain existence of the second peak in Nusselt number for the case corresponding to twice the slot nozzle width. The predicted average surface Nusselt number profiles exhibit good agreement with experiments.     

Assessment of left heart and pulmonary circulation flow dynamics by a new pulsed mock circulatory system

We developed a new mock circulatory system that is able to accurately simulate the human blood circulation from the pulmonary valve to the peripheral systemic capillaries. Two independent hydraulic activations are used to activate an anatomical-shaped left atrial and a left ventricular silicon molds. Using a lumped model, we deduced the optimal voltage signals to control the pumps. We used harmonic analysis to validate the experimental pulmonary and systemic circulation models. Because realistic volumes are generated for the cavities and the resulting pressures were also coherent, the left atrium and left ventricle pressure–volume loops were concordant with those obtained in vivo. Finally we explored left atrium flow pattern using 2C-3D+T PIV measurements. This gave a first overview of the complex 3D flow dynamics inside realistic left atrium geometry.     

[r,s, t]-Colorings of Graph Products

Let G =  (V, E) be a graph with vertex set V and edge set E. Given non negative integers r, s and t, an [r, s, t]-coloring of a graph G is a proper total coloring where the neighboring elements of G (vertices and edges) receive colors with a certain difference r between colors of adjacent vertices, a difference s between colors of adjacent edges and a difference t between colors of a vertex and an incident edge. Thus [r, s, t]-colorings generalize the classical colorings of graphs and can have applications in different fields like scheduling, channel assignment problem, etc. The [r, s, t]-chromatic number χ _r,s,t (G) of G is the minimum k such that G admits an [r, s, t]-coloring. In our paper we propose several bounds for the [r, s, t]-chromatic number of the cartesian and direct products of some graphs.     

Solitary ion-acoustic wave propagation in the presence of electron trapping and background nonextensivity

Solitary ion-acoustic wave propagation in the presence of electron trapping is investigated within the theoretical framework of the Tsallis statistical mechanics. A physically meaningful Schamel-like distribution is outlined. In the small amplitude limit, the nonlinear dispersion relation is derived to analyze the global dependency of the main solitary wave quantities. It is found that for a given amplitude and trapping state, the solitary potential structure speeds up and broadens as the electron nonextensivity strengthens. Our results may be of basic interest for experiments that involve particle trapping. The flexibility provided by the nonextensive q-parameter enables one to obtain a good agreement between theory and experiment.     

Natural convection in inclined two dimensional rectangular cavities

Steady two-dimensional natural convection in fluid filled cavities is numerically investigated. The channel is heated from below and cooled from the top with insulated side walls and the inclination angle is varied. The field equations for a Newtonian Boussinesq fluid are solved numerically for three cavity height based Rayleigh numbers, Ra = 10⁴, 10⁵ and 10⁶, and several aspect ratios. The calculations are in excellent agreement with previously published benchmark results. The effect of the inclination of the cavity to the horizontal with the angle varying from 0° to 180° and the effect of the startup conditions on the flow pattern, temperature distribution and the heat transfer rates have been investigated. Flow admits different configurations at different angles as the angle of inclination is increased depending on the initial conditions. Regardless of the initial conditions Nusselt number Nu exhibits discontinuities triggered by gradual transition from multiple cell to a single cell configuration. The critical angle of inclination at which the discontinuity occurs is strongly influenced by the assumed startup field. The hysteresis effect previously reported is not always present when the calculations are reversed from 90° to 0°. A comprehensive study of the flow structure, the Nu variation with varying angle of inclination, the effect of the initial conditions and the hysteresis effect are presented.     

Robust nonlinear control synthesis by using centre manifold-based reduced models for the mitigating of friction-induced vibration

Nonlinear Dynamics - This paper is concerned with the synthesis of reduced-order robust nonlinear controllers for more efficient robust mitigating of friction-induced vibration (FIV) issued from...     

Characterization of plunging liquid jets: A combined experimental and numerical investigation

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.     

Flow characteristics in a model of a left ventricle in the presence of a dysfunctional mitral mechanical heart valve

Journal of Visualization -