Longitudinal Viscous Flow in Granular Gases

The flow characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$, a uniform density $n(t)\propto a(t)$, and a uniform temperature $T(t)$ is analyzed for dilute granular gases by means of a BGK-like model kinetic equation in $d$ dimensions. For a given value of the coefficient of normal restitution $\alpha$, the relevant control parameter of the problem is the reduced deformation rate $a^*(t)=a(t)/\nu(t)$ (which plays the role of the Knudsen number), where $\nu(t)\propto n(t)\sqrt{T(t)}$ is an effective collision frequency. The relevant response parameter is a nonlinear viscosity function $\eta^*(a^*)$ defined from the difference between the normal stress $P_{xx}(t)$ and the hydrostatic pressure $p(t)=n(t)T(t)$. The main results of the paper are: (a) an exact first-order ordinary differential equation for $\eta^*(a^*)$ is derived from the kinetic model; (b) a recursion relation for the coefficients of the Chapman--Enskog expansion of $\eta^*(a^*)$ in powers of $a^*$ is obtained; (c) the Chapman--Enskog expansion is shown to diverge for elastic collisions ($\alpha=1$) and converge for inelastic collisions ($\alpha<1$), in the latter case with a radius of convergence that increases with inelasticity; (d) a simple approximate analytical solution for $\eta^*(a^*)$, hardly distinguishable from the numerical solution of the differential equation, is constructed.Comment: 6 pages; 3 figures; presented in the 26th International Symposium on Rarefied Gas Dynamics (Kyoto, Japan, July 21-25, 2008

The effect of die half angle in tube nosing with relieved die

This research concentrates on rotary nosing using cone shape dies, in particular using “relieved dies”. “Relieved die” is a cone-shape die with contact surfaces and grounddown relieved surfaces. The objective of this research is to improve the forming limit by reducing the necessary force during the process. The present research focuses attention on the effect of die half angle. Die half angle is important parameter because the angle of nosing depends on the angle of the die in press and rotary nosing. According to the previous research, the forming limit is highest when the number of contact areas is three [1]. Therefore, this paper researched on the effect of die half angle by experiment and calculation, FEM, under the condition that the number of contact areas is three. It is revealed that the optimum contact angle changes depending on the die half angle

Observation of Microscopic Deformation Behavior of Cork

Cork is a material that has many characteristics, for instance, light weight, elasticity, insulation against heat, impermeability for liquid, and so forth. There are two types of cork, the natural and the agglomerated corks. In the present paper, compression tests of the natural and the agglomerated cork specimens were carried out. The compression test were done in various directions. Compressive stress was measured by a original compression apparatus, and stress-strain curves were obtained in various directions of the cork specimens. In the natural cork, there are differences between the radial and the non-radial direction. The recovery of dimensions after compression was also studied in respective directions. The structure of the deformed surface was observed by a scanning electron microscope

Modelling of anthropogenic pollutant diffusion in the atmosphere and applications to civil protection monitoring

A basic feature of fluid mechanics concerns the frictionless phase-space dynamics of particles in an incompressible fluid. The issue, besides its theoretical interest in turbulence theory, is important in many applications, such as the pollutant dynamics in the atmosphere, a problem relevant for civil protection monitoring of air quality. Actually, both the numerical simulation of the ABL (atmospheric boundary layer) portion of the atmosphere and that of pollutant dynamics may generally require the correct definition of the Lagrangian dynamics which characterizes arbitrary fluid elements of incompressible thermofluids. We claim that particularly important for applications would be to consider these trajectories as phase-space trajectories. This involves, however, the unfolding of a fundamental theoretical problem up to now substantially unsolved: {\it namely the determination of the exact frictionless dynamics of tracer particles in an incompressible fluid, treated either as a deterministic or a turbulent (i.e., stochastic) continuum.} In this paper we intend to formulate the necessary theoretical framework to construct such a type of description. This is based on a phase-space inverse kinetic theory (IKT) approach recently developed for incompressible fluids (Ellero \textit{et al.}, 2004-2008). {\it Our claim is that the conditional frictionless dynamics of a tracer particles - which corresponds to a prescribed velocity probability density and an arbitrary choice of the relevant fluid fields - can be exactly specified}.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Inverse kinetic theory for incompressible thermofluids

An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed fluid. From the mathematical viewpoint this involves the formal description of a fluid by means of a classical dynamical system which advances in time the relevant fluid fields. The possibility of defining an IKT for the 3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero \textit{et al}, 2004-2007) raises the interesting question whether the theory can be applied also to thermofluids, in such a way to satisfy also the second principle of thermodynamics. The goal of this paper is to prove that such a generalization is actually possible, by means of a suitable \textit{extended phase-space formulation}. We consider, as a reference test, the case of non-isentropic incompressible thermofluids, whose dynamics is described by the Fourier and the incompressible Navier-Stokes equations, the latter subject to the conditions of validity of the Boussinesq approximation.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008