We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)

We review recent advances in laser cell surgery, and investigate the working mechanisms of femtosecond laser nanoprocessing in biomaterials with oscillator pulses of 80-MHz repetition rate and with amplified pulses of 1-kHz repetition rate. Plasma formation in water, the evolution of the temperature distribution, thermoelastic stress generation, and stress-induced bubble formation are numerically simulated for NA=1.3, and the outcome is compared to experimental results. Mechanisms and the spatial resolution of femtosecond laser surgery are then compared to the features of continuous-wave (cw) microbeams. We find that free electrons are produced in a fairly large irradiance range below the optical breakdown threshold, with a deterministic relationship between free-electron density and irradiance. This provides a large ‘tuning range’ for the creation of spatially extremely confined chemical, thermal, and mechanical effects via free-electron generation. Dissection at 80-MHz repetition rate is performed in the low-density plasma regime at pulse energies well below the optical breakdown threshold and only slightly higher than used for nonlinear imaging. It is mediated by free-electron-induced chemical decomposition (bond breaking) in conjunction with multiphoton-induced chemistry, and hardly related to heating or thermoelastic stresses. When the energy is raised, accumulative heating occurs and long-lasting bubbles are produced by tissue dissociation into volatile fragments, which is usually unwanted. By contrast, dissection at 1-kHz repetition rate is performed using more than 10-fold larger pulse energies and relies on thermoelastically induced formation of minute transient cavities with lifetimes <100 ns. Both modes of femtosecond laser nanoprocessing can achieve a 2–3 fold better precision than cell surgery using cw irradiation, and enable manipulation at arbitrary locations.

Mechanisms of femtosecond laser nanosurgery of cells and tissues

The application of strong electric fields in water and organic liquids has been studied for several years, because of its importance in electrical transmission processes and its practical applications in biology, chemistry, and electrochemistry. More recently, liquid-phase electrical discharge reactors have been investigated, and are being developed, for many environmental applications, including drinking water and wastewater treatment, as well as, potentially, for environmentally benign chemical processes. This paper reviews the current status of research on the application of high-voltage electrical discharges for promoting chemical reactions in the aqueous phase, with particular emphasis on applications to water cleaning.

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Electrohydraulic Discharge and Nonthermal Plasma for Water Treatment

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations.

/pdf/interaction-of-weak-shock-waves-with-cylindrical-and-3vq64ewnw3.pdf

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

Results of flow visualization experiments of an impulsively accelerated plane interface between air and SF6 are reported. The shock tube used for the experiments has a larger test section than in previous experiments. The larger extent of uniform test flow relative to nonuniform boundary-layer flow permits unambiguous interpretation of flow-visualization photographs, and the influence of shock-wave/boundary-layer interactions is no longer dominant. The strong wall vortex observed in previous studies is not observed in these experiments. It is found that the thin membrane, which forms the initially plane interface, has a significant influence on the initial growth rate of the interface thickness. However, the measured growth rates after the first reflected shock are independent of membrane configuration and are in good agreement with analytical predictions.

Experiments on the Richtmyer-Meshkov instability of an air/SF 6 interface

In an experimental investigation of the transient processes that occur when a single
droplet of butane at the superheat limit vaporizes explosively, short-exposure photographs
and fast-response pressure measurements have been used to construct a
description of the complete explosion process. It is observed that only a single bubble
forms within the drop during each explosion, and that the growth proceeds on a microsecond
time scale. An interfacial instability driven by rapid evaporation has been
observed on the surface of the bubbles. It is suggested that the Landau mechanism of
instability, originally described in connection with the instability of laminar flames,
also applies to rapid evaporation at the superheat limit.
The photographic evidence and the pressure data are used to estimate the evaporative
mass flux across the liquid-vapour interface after the onset of instability. The
;ate of evaporation is shown to be two orders of magnitude greater than would be
predicted by conventional bubble-growth theories that do not account for the effects
of instability. An estimate of the mean density within the bubbles during the evaporative
stage indicates that it is more than one half of the critical density of butane.
Additional interesting dynamical effects that are observed include a series of toroidal
waves that form on the interface between the butane vapour and the external host
liquid in the bubble column apparatus after the bubble has grown large enough to
contact the outer edge of the drop, and violent oscillations of the bubble that occur on
a millisecond time scale, after evaporation of the liquid butane is complete, that cause
the disintegration of the bubble into a cloud of tiny bubbles by Rayleigh-Taylor
instability.

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Rapid evaporation at the superheat limit

This paper reports an experimental investigation, using shadowgraphs and pressure measurements, of the detailed behaviour of converging weak shock waves near three different kinds of focus. Shocks are brought to a focus by reflecting initially plane fronts from concave end walls in a large shock tube. The reflectors are shaped to generate perfect foci, aretes and caustics. It is found that, near the focus of a shock discontinuity, a complex wave field develops, which always has the same basic character, and which is always essentially nonlinear. A diffracted wave field forms behind the non-uniform converging shock; its compressive portions steepen to form diffraction shocks, while diffracted expansion waves overtake and weaken the diffraction shocks. The diffraction shocks participate in a Mach reflexion process near the focus, whose development is determined by competition between the convergence of the sides of the focusing front and acceleration of its central portion. In fact, depending on the aperture of the convergence and the strength of the initial wave, the three-shock intersections of the Mach reflexions either cross on a surface of symmetry or remain uncrossed. In the former case, which is observed if the shock wave is relatively weak, the wavefronts emerge from focus crossed and folded, in accordance with the predictions of geometrical acoustics theory. In the latter, the strong-shock case, the fronts beyond focus are uncrossed, as predicted by the theory of shock dynamics. It is emphasized that in both cases the behaviour at the focus is nonlinear. The overtaking of the diffraction shocks by the diffracted expansions limits the amplitude of the converging wave near focus, and is the mechanism by which the maximum amplification factor observed at focus is determined. In all cases, maximum pressures are limited to rather low values.

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The focusing of weak shock waves

The study of the fluid dynamics of violent volcanic eruptions by laboratory experiment is described, and the important fluid-dynamic processes that can be examined in laboratory models are discussed in detail. In preliminary experiments, pure gases are erupted from small reservoirs. The gases used are Freon 12 and Freon 22, two gases of high molecular weight and high density that are good analogs of heavy and particulate-laden volcanic gases; nitrogen, a moderate molecular weight, moderate density gas for which the thermodynamic properties are well known; and helium, a low molecular weight, lowdensity gas that is used as a basis for comparison with the behavior of the heavier gases and as an analog of steam, the gas that dominates many volcanic eruptions. Transient jets erupt from the reservoir into the laboratory upon rupture of a thin diaphragm at the exit of a convergent nozzle. The gas accelerates from rest in the reservoir to high velocity in the jet. Reservoir pressures and geometries are such that the fluid velocity in the jets is initially supersonic and later decays to subsonic. The measured reservoir pressure decreases as the fluid expands through repetitively reflecting rarefaction waves, but for the conditions of these experiments, a simple steady-discharge model is sufficient to explain the pressure decay and to predict the duration of the flow. Density variations in the flow field have been visualized with schlieren and shadowgraph photography. The observed structure of the jet is correlated with the measured pressure history. The starting vortex generated when the diaphragm ruptures becomes the head of the jet. Though the exit velocity is sonic, the flow head in the helium jet decelerates to about one-third of sonic velocity in the first few nozzle diameters, the nitrogen head decelerates to about three-fourths of sonic velocity, while Freon maintains nearly sonic velocity. The impulsive acceleration of reservoir fluid into the surrounding atmosphere produces a compression wave. The strength of this wave depends primarily on the sound speed of the fluid in the reservoir but also, secondarily with opposite effect, on the density: helium produces a relatively strong atmospheric shock while the Freons do not produce any optically observable wave front. Well-formed N waves are detected with a microphone far from the reservoir. Barrel shocks, Mach disks, and other familiar features of steady underexpanded supersonic jets form inside the jet almost immediately after passage of the flow head. These features are maintained until the pressure in the reservoir decays to sonic conditions. At low pressures the jets are relatively structureless. Gas-particle jets from volcanic eruptions may behave as pseudogases if particle concentrations and mass and momentum exchange between the components are sufficiently small. The sound speed of volcanic pseudogases can be as large as 1000 m s^(−1) or as small as a few tens of meters per second depending on the mass loading and initial temperature. Fluids of high sound speed produce stronger atmospheric shock waves than do those of low sound speed. Therefore eruption of a hot gas lightly laden with particulates should produce a stronger shock than eruption of a cooler or heavily laden fluid. An empirical expression suggests that the initial velocity of the head of supersonic volcanic jets is controlled by the sound speed and the ratio of the density of the erupting fluid to that of the atmosphere. The duration of gas or pseudogas eruptions is controlled by the sound speed of the fluid and the ratio of reservoir volume to vent area.

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Bradford Sturtevant

Papers

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

Experiments on the Richtmyer-Meshkov instability of an air/SF 6 interface

Rapid evaporation at the superheat limit

The focusing of weak shock waves

Laboratory studies of volcanic jets