L. M. de Socio

Gas flow in a permeable medium

The dynamics of gases in permeable media is approached both experimentally and by numerical simulations. The experiments were performed in matrices made of packed beds of spheres in rarefied conditions and a model for the direct simulation of the molecular kinetics is proposed. Comparisons between experimental data and numerical results show the influence of the main parameters of the gas–solid interaction and the range of validity of the model. Moreover it is shown that there is a flow condition for the minimum permeability of the medium to the gas flow. Such a minimum depends upon the Knudsen number, and can be explained by the molecular dynamics as in the well-known Knudsen’s experiment on capillaries.

Random heat equation: Solutions by the stochastic adaptive interpolation method

Abstract The one-dimensional nonlinear heat equation is considered with stochastic coefficients and initial/boundary values in a finite strip and in the half-space. Approximated solutions are obtained by the stochastic adaptive interpolation method which corresponds first to transforming the original partial differential equation into a system of ordinary differential equations via a generalization to the stochastic case of the Bellmans differential quadrature method. The system of ordinary differential equations is then solved by a continuous approximation following by Adomians decomposition method, and the solutions are compared with those obtained by more standard numerical techniques.

Effects of the Centrifugal Forces on a Gas Between Rotating Cylinders

The gas e ow between two concentric rotating cylinders is investigated over a wide range of governing dimensionless products. Analytic solutions are given for the free molecular e ow, for the Bhatnagar ‐Gross‐Krook model up to the e rst-order approximation, and for the hydrodynamic limit in the Chapman ‐Enskog expansion. The slip e ow boundary conditionsareextensively discussed, and a constructivesolution to the transitional e ow is proposed. Numerical direct simulation data are obtained and adopted as exact reference experimental results.

Impact of floats on water

The impact of a wedge-shaped body on the free surface of a weightless inviscid incompressible liquid is considered. Both symmetrical and unsymmetrical entries at constant velocity are dealt with. The differential problem corresponds to the physico-mathematical model of a distribution of potential singularities and, in particular, the flow singularities at the ends of the wetted regions are represented by sinks. A conformal transformation of the flow field is adopted and the unknown intensities of the discontinuities are found by an optimization procedure, together with the solution of the nonlinear free-surface problem. The flow separation at a sideslip is also considered.

Coupling of conduction and forced convection past an impulsively started infinite flat plate

Abstract In this paper the unsteady coupling of conduction and convection for a thin body in a high speed stream is considered. The body is modeled as a strip on one side of which the fluid is impulsively started in motion whereas on the other side two different thermal boundary conditions are given : constant temperature or vanishing heat flux. In the first part of the analysis an approximate solution of the energy equation in the solid enables us to obtain relations between the temperature and the heat flux at solidfluid interface which are more accurate than those currently used in the literature. In the second part the exact solution of the two problems that arise from the coupling of the thermofluid-dynamic equations and the relations between the temperature and its derivatives at the interface are presented.

Stability and admittance of a channel flow over a permeable interface

The stability and the admittance analysis are considered for a Poiseuille flow running over a permeable slab. The case where a suction, due to a cross flow, is present through both the channel and the porous slab is also dealt with. An analytic solution is found for the basic flow in the entire field whereas the stability analysis and the evaluation of the admittance at the interface are numerically carried out. The errors made in the usually simplified analyses are fully discussed.

Simulation and modelling of flows between rotating cylinders. Influence of Knudsen number

The equations which govern a number of models for flows between rotating cylinders at different Knudsen numbers are solved numerically by means of the direct simulation Monte Carlo method (DSMCM) to show their limitations. The DSMC code was firstly tested and validated against existing experimental data and then its results represented the reference data base for evaluating the characteristics of each model.

A model for the compressible flow through a porous medium

A model for a continuum gas flowing through a porous matrix is proposed where the gas kinetics is governed by the Boltzmann equation and the solid phase by the energy equation. In the Boltzmann equation the integral relative to the gas–solid collisions is evaluated as for the collisions of hard spheres molecules against much heavier and longer straight particles (Lebowitz model of a sticks gas), randomly distributed in space according to a Maxwellian function with zero mean velocity. The mean flow is one-dimensional but the molecules are free to move in all three space dimensions. In the continuum limit, the moments of the Boltzmann equation provide the mass continuity, energy and momentum equations, the last one expressing the Darcy law for a compressible gas. The transport coefficients are analytically evaluated and a few examples are dealt with.

Kinetic models for a gas filled porous matrix. WAVE PROPAGATION

The propagation of small perturbation in a gas filled porous matrix is investigated. The skeleton is supposed rigid and governed by the energy balance equation, where the heat exchanged between the two phases is taken into account. The Boltzmann equation is written for the gas where the integrals of the collisions between gas and solid particles are evaluated as those for the particles of a mixture. Different choices of the time and space scales lead to models equations which hold for different rarefaction regimes. The wave propagation characteristics are then dealt with in various situations.

A NONLINEAR INVERSE PHASE TRANSITION PROBLEM FOR THE HEAT EQUATION

This paper proposes a method for the solution of two inverse problems which are governed by the nonlinear heat equation in one space dimension. In the first case phase transition occurs at the moving interface which divides two media. In the second one a random heat source is placed at a moving point. In both cases the temperature is assigned, as a function of time and within a random error, at a given fixed point. The solution procedure leads to quantitative results and is based on the Stochastic Adaptative Interpolation method.