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Computational fluid dynamics (CFD) codes that are able to describe in detail the dynamic evolution of the deformable interface in gas-liquid or liquid-liquid flows may be a valuable tool to explore the potential of multi-fluid flow in narrow channels for process intensification. In the present paper, a computational exercise for co-current bubble-train flow in a square vertical mini-channel is performed to investigate the performance of well-known CFD codes for this type of flows. The computations are based on the volume-of-fluid method (VOF) where the transport equation for the liquid volumetric fraction is solved either by the methods involving a geometrical reconstruction of the interface or by the methods that use higher-order difference schemes instead. The codes contributing to the present code-to-code comparison are an in-house code and the commercial CFD packages CFX, FLUENT and STAR-CD. Results are presented for two basic cases. In the first one, the flow is driven by buoyancy only, while in the second case the flow is additionally forced by an external pressure gradient. The results of the code-to-code comparison show that only the VOF method with interface reconstruction leads to physically sound and consistent results, whereas the use of difference schemes for the volume fraction equation shows some deficiencies.

The stability of a train of equally sized and variably spaced gas bubbles that move within a continuous wetting liquid phase through a straight square minichannel is investigated numerically by a volume-of-fluid method. The flow is laminar and cocurrent upward and driven by a pressure gradient and buoyancy. The simulations start from fluid at rest with two identical bubbles placed on the axis of the computational domain, the size of the bubbles being comparable to that of the channel. In vertical direction, periodic boundary conditions are used. These result in two liquid slugs of variable length, depending on the initial bubble-to-bubble distance. The time evolution of the length of both liquid slugs during the simulation indicates if the bubble train flow is "stable" ͑equal terminal length of both liquid slugs͒ or "unstable" ͑contact of both bubbles͒. Several cases are considered, which differ with respect to bubble size, domain size, initial bubble shape, and separation. All cases lead to axisymmetric bubbles with the capillary number in the range of 0.11-0.23. The results show that a recirculation pattern develops in the liquid slug when its length exceeds a critical value that is about 10%-20% of the channel width. If a recirculation pattern exists in both liquid slugs, then the bubble train flow is stable. When there is a recirculation pattern in one liquid slug and a bypass flow in the other, the bubble train flow may be stable or not depending on the local flow field in the liquid slugs close to the channel centerline. These results suggest that a general criterion for the stability of bubble train flow cannot be formulated in terms of the capillary and Reynolds number only, but must take into account the length of the liquid slug.

a b s t r a c tIn this study, a thermodynamic analysis of a gamma type Stirling engine is performed by using a quasi steady flow model based on Urieli and Berchowitz's works. The Stirling engine analysis is performed for five principal fields: compression room, expansion room, cooler, heater and regenerator. The conservation law of the mass and the energy equations are derived for the related sections. A FORTRAN code is developed to solve the derived equations for all process parameters like pressure, temperature, mass flow, dissipation and convection losses for the different spaces (compression space, cooler, regenerator, heater and expansion space) as a function of the crank angle. The developed model gave more precise results for the pressure profile than the models available in the literature.

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