We model the problem of path instability of a rising bubble by considering the bubble as a spheroidal body of fixed shape, and we solve numerically the coupled fluid-body problem. Numerical results show that this model exhibits path instability for large enough values of the control parameters. The corresponding characteristics of the zigzag and spiral paths are in good agreement with experimental observations. Analysis of the vorticity field behind the bubble reveals that a wake instability leading to a double threaded wake is the primary cause of the path instability.

The three-dimensional flow past two identical spherical bubbles moving side by side in a viscous fluid is studied numerically by solving the full Navier–Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition. The present study describes the interaction between the two bubbles over a wide range of Reynolds number ($0.02\,{\le}\,Re\,{\le}\,500$, $Re$ being based on the bubble diameter and rise velocity), and separation $S$ ($2.25\,{\le}\,S\,{\le}\,20$, S being the distance between the bubble centres normalized by the bubble radius). The flow structure, the vorticity field, the sign of the interaction force and the magnitude of the drag and lift forces are analysed; in particular the latter are compared with analytical expressions available in the potential flow limit and in the limit of low-but-finite Reynolds number. This study sheds light on the role of the vorticity generated at the bubble surface in the interaction process. When vorticity remains confined in a boundary layer whose thickness is small compared to the distance between the two bubbles, the interaction is dominated by the irrotational mechanism that results in an attractive transverse force. In contrast, when viscous effects are sufficiently large, the vorticity field about each bubble interacts with that existing about the other bubble, resulting in a repulsive transverse force. Computational results combined with available high-Reynolds-number theory provide empirical expressions for the drag and lift forces in the moderate-to-large Reynolds number regime. They show that the transverse force changes sign for a critical Reynolds number whose value depends on the separation. Using these computational results it is shown that, depending on their initial separation, freely moving bubbles may either reach a stable equilibrium separation or move apart from each other up to infinity.

Direct numerical simulations of the flow past a fixed oblate spheroidal bubble are carried out to determine the range of parameters within which the flow may be unstable, and to gain some insight into the instability mechanism. The bubble aspect ratio χ (i.e. the ratio of the major axis length over the minor axis length) is varied from 2.0 to 2.5 while the Reynolds number (based on the upstream velocity and equivalent bubble diameter) is varied in the range 102 ≤ Re ≤ 3 × 103. As vorticity generation at the bubble surface is at the root of the instability, theoretical estimates for the maximum of the surface vorticity and the surface vorticity flux are first derived. It is shown that, for large aspect ratios and high Reynolds numbers, the former evolves as χ8/3 while the latter is proportional to χ7/2Re−1/2. Then it is found numerically that the flow first becomes unstable for χ = χc ≈ 2.21. As the surface vorticity becomes independent of Re for large enough Reynolds number, the flow is unstable only within a finite range of Re, this range being an increasing function of χ − χc. An empirical criterion based on the maximum of the vorticity generated at the body surface is built to determine whether the flow is stable or not. It is shown that this criterion also predicts the correct threshold for the wake instability past a rigid sphere, suggesting that the nature of the body surface does not really matter in the instability mechanism. Also the first two bifurcations of the flow are similar in nature to those found in flows past rigid axisymmetric bluff bodies, such as a sphere or a disk. Wake dynamics become more complex at higher Reynolds number, until the Re−1/2-dependency of the surface vorticity flux makes the flow recover its steadiness and eventually its axisymmetry. A qualitative analysis of the azimuthal vorticity field in the base flow at the rear of the bubble is finally carried out to make some progress in the understanding of the primary instability. It is suggested that the instability originates in a thin region of the flow where the vorticity gradients have to turn almost at right angle to satisfy two different constraints, one at the bubble surface, the other within the standing eddy.

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The numerical results obtained by Mougin & Magnaudet (Phys. Rev. Lett. vol. 88, 2002a, 14502) for the flow past a freely moving spheroidal bubble with a prescribed spheroidal shape are processed to analyse the evolution of the forces and torques experienced by the bubble when it rises along a planar zigzag and a circular helix. It is found that, as soon as the wake becomes three-dimensional, a lateral force with a strength comparable with that of the buoyancy force occurs. This force, together with the corresponding torque, drives the horizontal movements of the bubble. The force and torque balances reveal how these wake-induced effects are balanced by added-mass effects to make possible the existence of zigzag and helical motions along which the angle between the velocity and the symmetry axis of the bubble remains small. The evolution of the wake during the zigzag indicates that the sign of the trailing vortices, and thus that of the wake-induced force and torque, is governed by the rotation of the bubble and reveals the sensitivity of the wake dynamics to the changes in the bubble velocity and rotation rate.

Several studies based on in vivo or in vitro models have found promising results for the noble gas argon in neuroprotection against ischaemic pathologies. The development of argon as a medicinal product includes the requirement for toxicity testing through non-clinical studies. The long exposure period of animals (rats) during several days results in technical and logistic challenges related to the gas administration. In particular, a minimum of 10 air changes per hour (ACH) to maintain animal welfare results in extremely large volumes of experimental gas required if the gas is not recirculated. The difficulty with handling the many cylinders prompted the development of such a recirculation-based design. To distribute the recirculating gas to individually ventilated cages and monitor them properly was deemed more difficult than constructing a single large enclosure that will hold several open cages. To address these concerns, a computational fluid dynamics (CFD) analysis of the preliminary design was performed. A purpose-made exposure chamber was designed based on the CFD simulations. Comparisons of the simulation results to measurements of gas concentration at two cage positions while filling show that the CFD results compare well to these limited experiments. Thus, we believe that the CFD results are representative of the gas distribution throughout the enclosure. The CFD shows that the design provides better gas distribution (i.e. a higher effective air change rate) than predicted by 10 ACH.

Air Liquide has been involved in the design of industrial furnaces (glass melting, reheating, aluminum, …) for several years. Thanks to that experience, known-how and expertise in modeling such applications have been developed. Dedicated simulation tools — 0D for global heat and mass balance, 1D for the prediction of longitudinal temperature profiles and 3D for detailed analysis — have been built. Each of them is very helpful when used relevantly and offers numerous opportunities at each step of the design of a furnace. In such kind of applications, the temperature levels are very high (up to 2500 K). As a consequence it is very crucial to simulate the radiative heat transfer as accurately as possible. This requires the use of a radiation model that can take into account complex geometries, non-isothermal media and various gas mixture compositions. Very often, three-dimensional simulations are necessary and reduction to smaller dimension problems is difficult or inadequate. The present paper introduces a new radiation model for computing two-dimensionally radiative heat transfer in an industrial furnace with a piecewise distributed load. To reduce the three-dimensional problem to two dimensions, the method consists in coupling the 2D radiation transport equation to a boundary condition based on view factors through an imaginary plane to homogenize the radiative behavior of the load surface. A solution procedure using the discrete transfer method associated to a weighted-sum-of-gray-gases database to deal with absorption and emission of a CO2-H2O mixture is proposed. Simulation results are finally compared to an analytical formula and then to a full-3D approach taking into account participating media, non-isothermal and gray walls. All tests show that this model can be used to simulate industrial configurations with a good accuracy.

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