Influence de la géométrie des premiers corps sur les instabilités de contact - cas du crissement

International audienceThe squeal is often studied because it is uncomfortable for the user and the environment of the vehicle although not harming the operation of the brake mechanism. A preceding study showed experimentally that, for a convenient value of the coefficient of friction and an adequate third body, the appearance of the squeal can be directly related to the geometry of the first bodies. The results presented here deal with the evolution of the tendencies (amplitude, frequency...) of the vibrations induced by friction according to the relative angle between the surfaces of the first bodies. This is a first stage to propose modifications of the first bodies to solve the problems of squeal

Rayleigh–Bénard instability of an Ellis fluid saturated porous channel with an isoflux boundary

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation show-ing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid

Unstable Convection in a Vertical Double–Layer Porous Slab

A convective stability analysis of the flow in a vertical fluid-saturated porous slab made of two layers with different thermophysical properties is presented. The external boundaries are isothermal with one of them impermeable while the other is open to an external fluid reservoir. This study is a development of previous investigations on the onset of thermal instability in a vertical heterogeneous porous slab where the heterogeneity may be either continuous or piecewise as determined by a multilayer structure. The aim of this paper is investigating whether a two-layer structure of the porous slab may lead to the onset of cellular convection patterns. The linear stability analysis is carried out under the assumption that one porous layer has a thermal conductivity much higher than the other layer. This assumption may be justified for the model of a heat transfer enhancement system involving a saturated metal foam. A flow model for the natural convection based on Darcy’s momentum transfer in a porous medium is adopted. The buoyancy-induced basic flow state is evaluated analytically. Small-amplitude two-dimensional perturbations of the basic state are introduced, thus leading to a linear set of governing equations for the disturbances. A normal mode analysis allows one to formulate the stability eigenvalue problem. The numerical solution of the stability eigenvalue problem provides the onset conditions for the thermal instability. Moreover, the results evidence that the permeability ratio of the two layers is a key parameter for the critical conditions of the instability

Dissipation instability of Couette-like adiabatic flows in a plane channel

The mixed convection flow in a plane channel with adiabatic boundaries is examined. The boundaries have an externally prescribed relative velocity defining a Couette-like setup for the flow. A stationary flow regime is maintained with a constant velocity difference between the boundaries, considered as thermally insulated. The effect of viscous dissipation induces a heat source in the flow domain and, hence, a temperature gradient. The nonuniform temperature distribution causes, in turn, a buoyancy force and a combined forced and free flow regime. Dual mixed convection flows occur for a given velocity difference. Their structure is analysed where, in general, only one branch of the dual flows is compatible with the Oberbeck-Boussinesq approximation, for realistic values of the Gebhart number. A linear stability analysis of the basic stationary flows with viscous dissipation is carried out. The stability eigenvalue problem is solved numerically, leading to the determination of the neutral stability curves and the critical values of the Peclet number, for different Gebhart numbers. An analytical asymptotic solution in the special case of perturbations with infinite wavelength is also developed

Buoyancy-Induced Instability of a Power-Law Fluid Saturating a Vertical Porous Slab

Many engineering applications involve porous media and rely on non-Newtonian working fluids. In this paper, the seepage flow of a non-Newtonian fluid saturating a vertical porous layer is studied. The buoyant flow is thermally driven by the boundaries of the porous layer, which are permeable surfaces kept at different temperatures. In order to model the seepage flow of both shear-Thinning (pseudoplastic) and shear-Thickening (dilatant) fluids, reference is made to the Ostwald-de Waele rheological model implemented via the power-law extended form of Darcy's law. The basic stationary flow is parallel to the vertical axis and shows a single-cell pattern, where the cell has infinite height and can display a core-region of enhanced/inhibited flow according to the fluid's rheological behavior. By applying small perturbations, a linear stability analysis of the basic flow is performed to determine the onset conditions for a multicellular pattern. This analysis is carried out numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are computed for different pseudoplastic and dilatant fluids. The behavior of a Newtonian fluid is also obtained as a limiting case

Instability of adiabatic shear flows in a channel

The combined forced and free convection flow of a Newtonian fluid in a horizontal planeparallel channel is examined. The boundary walls are considered as adiabatic, so that the only thermal effect acting in the fluid is the viscous dissipation due to the nonzero shear flow. As the shear flow may be caused by either an imposed horizontal pressure gradient or an imposed velocity difference between the bounding walls, one may envisage two scenarios where the stationary basic flow is Poiseuille-like or Couette-like, respectively. Both cases are surveyed with a special focus on practically significant cases where the Gebhart number is considered as very small, though nonzero. Furthermore, the Prandtl number is assumed as extremely large, thus pinpointing a scenario of creeping buoyant flow with a fluid having a very large viscosity. Within such a framework, the instability of the basic flow is analysed versus small amplitude perturbations

Thermal Convection of an Ellis Fluid Saturating a Porous Layer with Constant Heat Flux Boundary Conditions

The present work analyzes the thermal instability of mixed convection in a horizontal porous channel that is saturated by a shear-thinning fluid following Ellis’ rheology. The fluid layer is heated from below by a constant heat flux and cooled from above by the same heat flux. The instability of such a system is investigated by means of a small-disturbances analysis and the resulting eigenvalue problem is solved numerically by means of a shooting method. It is demonstrated that the most unstable modes on the instability threshold are those with infinite wavelength and an analytical expression for such conditions is derived from an asymptotic analysis. Results show that the non-Newtonian character of the fluid has a destabilizing role

Wavepacket instability in a rectangular porous channel uniformly heated from below

This paper is aimed to investigate the transition to absolute instability in a porous layer with horizontal throughflow. The importance of this analysis is due to the possible experimental failure to detect growing perturbations which are localised in space and which may be convected away by the throughflow. The instability of the uniform flow in a horizontal rectangular channel subject to uniform heating from below and cooled from above is studied. While the lower wall is modelled as an impermeable isoflux plane, the upper wall is assumed to be impermeable and imperfectly conducting, so that a Robin temperature condition with a given Biot number is prescribed. The sidewalls are assumed to be adiabatic and impermeable. The basic state considered here is a stationary parallel flow with a vertical uniform temperature gradient, namely the typical configuration describing the Darcy–Bénard instability with throughflow. The linear instability of localised wavepackets is analysed, thus detecting the parametric conditions for the transition to absolute instability. The absolute instability is formulated through an eigenvalue problem based on an eighth–order system of ordinary differential equations. The solution is sought numerically by utilising the shooting method. The threshold to absolute instability is detected versus the Péclet number associated with the basic flow rate along the channel

Stability analysis of dual viscous flows saturating a vertical porous pipe

The linear stability analysis of a mixed convection viscous flow in a vertical porous pipe is here investigated. The contribution of viscous heating is assumed to be non negligible. A fully developed flow regime is assumed for the basic state. The local balance equations for this state display dual stationary solutions. The dual branches of stationary solutions are determined numerically. Since the pipe is characterised by an isothermal lateral surface, the viscous heating is the sole cause of the buoyancy force. In order to investigate the stability of the basic dual solutions, small amplitude disturbances with the form of normal modes are superposed to the basic state. The solution of the eigenvalue problem obtained allows one to determine the growth rate associated to both the basic solution branches. The sign of the growth rate determines whether the particular basic solution is stable or unstable

Sieve-in-the-Middle: Improved MITM Attacks (Full Version)

This paper presents a new generic technique, named sieve-in-the-middle, which improves meet-in-the-middle attacks in the sense that it provides an attack on a higher number of rounds. Instead of selecting the key candidates by searching for a collision in an intermediate state which can be computed forwards and backwards, we here look for the existence of valid transitions through some middle sbox. Combining this technique with short bicliques allows to freely add one or two more rounds with the same time complexity. Moreover, when the key size of the cipher is larger than its block size, we show how to build the bicliques by an improved technique which does not require any additional data (on the contrary to previous biclique attacks). These techniques apply to PRESENT, DES, PRINCE and AES, improving the previously known results on these four ciphers. In particular, our attack on PRINCE applies to 8 rounds (out of 12), instead of 6 in the previous cryptanalyses. Some results are also given for theoretically estimating the sieving probability provided by some subsets of the input and output bits of a given sbox