Table of contents

The problem of the one-dimensional evaporation of a binary mixture is investigated by numerically solving a system of two coupled Boltzmann equations. The numerical method is based on the direct discretization of the Boltzmann equation and the Monte Carlo evaluation of the collision integrals. It is assumed that the fluid flows between an evaporating plate and a totally absorbing plate. The spatial profiles of macroscopic quantities as well as evaporation rates have been calculated for values of the Knudsen number between 1/2 and 1/20.

An experimental study of a natural convection loop placed in a nearly uniform negative vertical temperature gradient is reported. Distilled water and ethyl alcohol were tested as the working fluid, and two kinds of tori with different tube diameter were used, in order to cover a wide range of Rayleigh numbers as well as to check the one-dimensionality of the flow. The whole flow field was visualized by several standard methods, and was directly measured by means of a laser Doppler anemometer. The critical Rayleigh number, the Rayleigh number dependence of the Reynolds number, and the velocity profile of the quasi-one-dimensional flow along the loop were determined. The three-dimensional cellular structure appears at higher Rayleigh number and shows periodic and nonperiodic change both in space and in time with increase of the Rayleigh number.

A theoretical study of thermal convection in a vertically oriented thin toroidal loop which is placed in a uniform negative vertical temperature gradient is reported. The Boussinesq approximation is employed, and the first-order perturbed fields from a steady conduction state are obtained in the form of a double Fourier series. The critical Rayleigh number for the onset of convection is determined and various types of steady convective patterns, including cellular structure, are examined. Four typical modes are superposed to express the time-dependent velocity and temperature fields, whose mode-amplitudes constitute an extended version of the Lorenz model. Numerical simulation shows a sequence of transitions from steady to periodic, quasi-periodic, and chaotic states as the Rayleigh number is increased. The present model successfully explains our experimental results.

A high-resolution, three-dimensional finite-difference numerical study of natural convection flows of a viscous fluid in a differentially heated cubical box is reported. The vertical sidewalls of the enclosure are maintained at constant temperatures of different values. The other vertical walls (the end walls) are thermally insulated. For the horizontal walls, two kinds of thermal boundary conditions are specified: adiabatic and perfectly conducting. Computations have been performed for an air-filled cavity for Rayleigh numbers of 10⁵ and 10⁶. The specific effects of the horizontal thermal boundary conditions on the flow structure are examined in detail. In the case of conducting walls, heat transfer through the horizontal walls enhances the convective flow activities. The numerically predicted velocity and temperature profiles in the symmetry planes are consistent with previous experimental measurements and computations.

A numerical wave-absorption filter has been developed for an open boundary condition in the analysis of nonlinear and irregular wave evolution. The filter is composed of a simulated sponge layer and Sommerfeld's radiation condition at the outer edge of the layer. The wave-absorption characteristics of the filter have been investigated by applying the linear potential theory and a two-dimensional nonlinear boundary element model. In both cases, the filter is found to he applicable for a wide range of wave parameters. In order to realize an idealized "numerical wave tank", the present model also incorporates a nonreflective wave generator in the computational domain composed of a series of vertically aligned point sources. Numerous numerical experiments demonstrate that the present approach is effective in generating an arbitrary wave profile without reflection not only at the open boundaries but also at the wave generator.

The stable posture of a pair of parallel circular cylinders in a uniform flow was experimentally studied when it was free to rotate about an axis at the middle of the two cylinders. The cylinder pair comes to rest facing the oncoming flow side by side, the line connecting the centers of the two cylinders being perpendicular to the flow, when s/d = 0.5, where s is the distance between the center of rotation and the central axis of each cylinder and d is the diameter of the cylinder. When s/d = 1.0 or 1.5, the cylinder pair is stable both in tandem, with one cylinder behind the other, and in side-by-side arrangements to the oncoming flow. When s/d ⩾ 2.0, the cylinder pair is stable only in tandem arrangements.

The point explosion problem with internal heat transfer effects taken into account is analysed. The classical inviscid solutions to this problem yield a non-physical phenomenon of infinite temperature and zero density at the center of explosion for all times. With heat transfer fluxes considered, the solution near the center of symmetry is improved and finite values for temperature are obtained. The non-self-similar solution of the problem is based on the quasi-similar approximate technique which reduces the non-linear partial differential equations governing the problem to ordinary differential ones. However, this formulation yields a two-point boundary-value problem. To facilitate the integration, the flow field is first divided into two regions: an outer inviscid region and an inner region where dissipation effects are manifested. This results in two sets of ordinary differential equations expressing the conservation equations in the inner and outer regions which are then solved and matched together to yield the composite solution. Secondly, the problem is then transformed into an initial-value one. Using the results of the composite solution, the governing equations can be integrated directly from the center until the shock front. The structure of the non-self-similar flow fields with internal heat transfer effects is then fully determined for specified values of the heat transfer parameters.

The thermohaline circulation in a three-layer ventilated ocean is shown to have 81 steady states, 16 of them stable and the others unstable. One unstable steady state in a phase space corresponds to a repeller, the other states correspond to saddle points. There are neither cycles nor other closed phase trajectories. The possibility of oscillations is excluded both by the analytical investigation of the spectrum and by the numerical results.