Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.     

Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

A widespread belief in the study of granular flow is the existence of “homogeneous cooling states”, i.e., self-similar solutions which would attract all solutions, faster than the equilibrium solution does. In most cases, the existence of these self-similar solutions is an open problem. Here we consider a one-dimensional model, which has been used for some years, and for which simple self-similar solutions do exist. However, we prove that the approximation is quite poor. Our proof makes use of the powerful and simple tools of mass transportation, and exploits the structure of the evolution equation, seen as a nonlinear transport equation.     

WAVE PROPAGATION IN A SYSTEM OF COAXIAL TUBES FILLED WITH INCOMPRESSIBLE MEDIA: A MODEL OF PULSE TRANSMISSION IN THE INTRACRANIAL ARTERIES

The propagation of harmonic waves through a system formed of coaxial tubes filled with incompressible continua is considered as a model of arterial pulse propagation in the craniospinal cavity. The inner tube represents a blood vessel and is modelled as a thin-walled membrane shell. The outer tube is assumed to be rigid to account for the constraint imposed on the vessels by the skull and the vertebrae. We consider two models: in the first model the annulus between the tubes is filled with fluid; in the second model the annulus is filled with a viscoelastic solid separated from the tubes by thin layers of fluid. In both models, the elastic tube is filled with fluid. The motion of the fluid is described by the linearized form of the Navier–Stokes equations, and the motion of the solid by classical elasticity theory. The results show that the wave speed in the system is lower than that for a fluid-filled elastic tube free of any constraint. This is due to the stresses generated to satisfy the condition that the volume in the system has to be conserved. However, the effect of the constraint weakens as the radius of the outer tube is increased, and it should be insignificant for the typical physiological parameter range.     

Time studies of ionization processes

Summary Measurements of the temporal growth of ionization between parallel plane electrodes in hydrogen have been made. The results show that for low values ( 40 V/cm mm Hg) of the ratio of electric fieldE to gas pressurep the growth times can be short ( 1s for over-voltages V 1 %) while at values ofE/p 300 V/cm mm Hg the times are of the order of milli seconds withV 5%. Comparison of the experimental data with Davidson's mathematical analysis of current growth based upon the action of primary and secondary ionization processes shows that the relative significance of the possible secondary processes changes asE/p is altered. For the low values ofE/p, the predominant secondary process contributing to the growth was found to be photoelectric emission from the cathode, but with increasing values ofE/p the role of positive ion interaction with the cathode becomes increasingly important. No single secondary process was exclusively operating in any of the conditions examined.     

Aeroacoustical coupling in a ducted shallow cavity and fluid/structure effects on a steam line

A pure tone phenomenon has been observed at 460 Hz in a piping steam line. The acoustical energy has been identified to be generated in an open gate valve and to be of cavity noise type. This energy is then transmitted to the main pipe by fluid/structure coupling. The objectives here are to display the mechanism of the flow acoustic coupling in the cavity and in the duct through an aeroacoustical analysis and to understand the way of energy transfer from the fluid to the main pipe through a vibroacoustical analysis. Concerning the first objective, an experimental study by means of 2/7 scale models in air is analysed by means of numerical flow simulation. The flow acoustic phenomena are modelled by computing the Euler equations. Two different computations are carried out: in the first one, a pure Euler modelling is used, in the second one, a boundary layer obtained from experimental data is introduced in the computation in order to have a realistic flow profile upstream the cavity. The boundary layer flow profile appears to be essential to recover the experimentally observed coupling between the shear-layer instability and the acoustical transverse mode of the pipe. The numerical results confirm that the second aerodynamic mode is responsible for the oscillation. While the predicted frequency agrees about 1% with the scale model experiments, the predicted amplitude is approximately 15 dB too low. For the second objective, fluid/structure coupling in the main pipe is studied using two fully coupled methods. The first method consists in a modal analysis of the line using a fluid–structure finite element model. The second one is based on the analysis of dispersion diagrams derived from the local equations of cylindrical shells filled with fluid. The way of energy transfer in transverse acoustical waves coupled with flexion-ovalization deformations of the pipe is highlighted using both methods. The dispersion diagrams allow a fast and accurate analysis. The modal analysis using a finite-element model may complete the first one with quantitative data. The link between the fluid/acoustic and the fluid/structure analysis is then the excitation of the transverse acoustical mode of the duct.     

Thermal analysis of the roll in the strip casting process

Coiled strip can be directly produced through the twin-roll strip casting process from the melt by incorporating casting and hot rolling together into a single step. In this unique process, the strip formation from the molten metal critically relies upon the casting rolls. Thus, the design of the rolls is extremely essential. The coupled heat transfer and deformation analysis of the casting roll is carried out in a two-dimensional numerical model, using a finite element program (MARC) to examine the thermal stress and displacement. The effects of several factors such as the nickel overlay thickness on the roll surface, the casting speed, and the roll diameter on thermal characteristics are investigated.     

Modeling micro-inertia in heterogeneous materials under dynamic loading

A continuum model including micro-inertia for heterogeneous materials under dynamic loading is proposed using a micro-mechanics method. The macro strain and stress are defined as the volume averages of the strain and stress fields in the representative volume element (RVE). The macro equations of motion are derived by using Hamilton’s principle together with the strain energy density and kinetic energy density involving the micro-inertia terms. The new macro equations of motion are used to study harmonic and transient wave propagation in layered media. Using a simple linear displacement field for the RVE, the dispersion curves obtained from the present model agree with the exact solutions very well for a range of wavelengths. The present model is also applied to analyze the transient response of layered media subjected to a triangular pulse loading. Comparison is made between the results of the present model and a finite element analysis.     

Generation of the Third Harmonics by Plane Waves in Murnaghan Materials

We demonstrate that it is expedient to use the complete expansion of the potential in terms of strain gradients for materials whose deformation is described by Murnaghan's potential. The cubic terms are retained in the constitutive equations, in addition to the classical quadratic terms. An analysis of the nonlinear system of wave equations reveals that the third harmonics can be generated. As an example, the nonlinear interaction of plane waves is analyzed for the following three cases of waves entering a medium: (i) a longitudinal wave, (ii) a vertically polarized transverse wave, and (iii) vertically and horizontally polarized transverse waves     

Dislocation behaviours ahead of crack tip

In this paper, a unified mechanics model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations within the plastic zone in the form of an inverse pile up are treated as discrete elastic edge dislocations. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear governing equations are obtained which take into account for the interaction between the emitted dislocations and cohesive zone and the nonlinear interaction between sliding displacement and the opening displacement. After discretization, the governing equations are transformed into a set nonlinear algebraic equations which are solved with Newton-Raphson Method. The results of calculation for pure shearing and combined tension and shear loading after dislocation emission are given in detail. Finally, the process of dislocation nucleation and emission on a pair of symmetric slip planes of angle α with respect to the crack plane under pure mode I load is analysed. The equilibrium positions and the number of emitted dislocation are determined. Several possible competition behaviors of dislocation emission vs cleavage are revealed.     

Shear-induced aggregation and break up of fibril clusters close to the percolation concentration

To probe the behaviour of fibrillar assemblies of ovalbumin under oscillatory shear, close to the percolation concentration, c_p (7.5%), rheo-optical measurements and Fourier transform rheology were performed. Different results were found close to c_p (7.3%), compared to slightly further away from c_p (6.9 and 7.1%). For 6.9 and 7.1%, a decrease in complex viscosity, and a linear increase in birefringence, n, with increasing strain was observed, indicating deformation and orientation of the fibril clusters. For 7.3%, a decrease in complex viscosity was followed by an increase in complex viscosity with increasing strain, which coincided with a strong increase in n, dichroism, n, and the intensity of the normalized third harmonic (I₃/I₁). This regime was followed by a second decrease in complex viscosity, where n,n and I₃/I₁ decreased. In the first regime where the viscosity was decreasing with increasing strain, deformation and orientation of existing clusters takes place. At higher oscillatory shear, a larger deformation occurs and larger structures are formed, which is most likely aggregation of the clusters. Finally, at even higher strains, the clusters break up again. An increase in complex viscosity, n, n and I₃/I₁ was observed when a second strain sweep was performed 30 min after the first. This indicates that the shear-induced cluster formation and break up are not completely reversible, and the initial cluster size distribution is not recovered after cessation of flow.