【文章內(nèi)容簡(jiǎn)介】 ps are needed. Empiricism es into the picture during attempts to model the variety of constitutive relationships that show up in conservation equations. For instance, Ayala et have presented a unified twofluid model for the analysis of natural gas flow in pipeline in multiphase flow regimes. Their formulation assumes that both gas and its condensate are a continuum and invokes the basic laws of continuum mechanics in one dimension coupled with a thermodynamic phase behavior model. In their work, the required semiempirical relationships needed to give mathematical closure to the model are discussed in detail. Smallscale Interest and Computational Physics The study of smallscale multiphase flow has proved to be extremely difficult for researchers due to the elusive nature of the phenomena and the inherent limitations of experimental setups. A great deal of progress has been made on the development of useful smallscale experimental studies, but numerical experiments or models still remain the most effective way of studying 本科畢業(yè)設(shè)計(jì)（論文）外文翻譯 7 such detailed flow behaviour. The challenge of modelling smallscale multiphase flow resides in the finite nature of the puter power typically available to the modeller and the difficulty of tracking separated phases (and interfaces between them) with sharply different properties. The interplay of these two factors has historically limited the plexity of the systems that can be studied using smallscale simulation. However, during the last decade, major progress has been achieved by implementing a variety of numerical techniques, which typically depend upon the flow pattern type that prevails under the conditions of the study. The study of smallscale phenomena started when a group of scientists at the Los Alamos National Laboratory began to develop the basis of Computational Fluid Dynamics (CFD) in the early and mid1960s. In multiphase flow modelling within smallscale interest, the NavierStokes equations – with the appropriate boundary conditions – are solved through a suitable numerical method – . finite volumes, finite differences, finite elements or spectral methods. The main problem arises when considering that some boundary conditions are timedependent, since they are located at phase boundaries, which are free to move, deform, break up or coalesce. Different methods have been proposed。 here we mention a few of them. The most mon smallscale modelling approach discretises the flow domain using a regular and stationary grid – . the wellknown Eulerian frame of reference for fluid motion. The first smallscale Eulerian method proposed was the markerandcell (MAC) method, where marker particles distributed uniformly in each fluid were used to identify each fluid. Using this method, in the late 1960s Harlow and Shanon studied the splash when a drop hits a liquid surface. The MAC method has bee obsolete since then and has largely been replaced by others that use marker functions instead – . the socalled 本科畢業(yè)設(shè)計(jì)（論文）外文翻譯 8 volumeoffluid (VOF) method. In the VOF method, the transition between two fluids takes place within the context of one grid cell. The main problem associated with this is the difficulty of maintaining a sharply defined boundary between two flowing fluids. In order to address this difficulty, levelset (LT) methods use continuous – rather than discontinuous – marker functions in order to identify the fluids. The use of continuous marker functions creates smooth transition zones between the two fluids of interest and avoids the difficulty of maintaining a sharply defined boundary. Some other smallscale modelling approaches use the Lagrangian frame of reference for fluid motion. In Lagrangian methods, the numerical grid follows the fluid and deforms with it. In this approach, the motion of the fluid interface needs to be modelled in order to accurately capture the new fluid positions at each timestep. At every timestep, the grid is refitted and adjusted to match the location of the new, displaced boundaries. In the 1980s, Ryskin and Leal used this method to study the steady rise of buoyant, deformable, axisymmetric bubbles, while Oran and Boris studied the breakup of a twodimensional drop. A similar approach, called front tracking, is also used, where a separate front marks the interface but a fixed grid is used for the fluid within each phase。 however, the fixed grid is modified near the front so a single grid line follows the interface. Smallscale modelling typically takes advantage of certain multiphase flow conditions that can greatly simplify the modelling process. For example, it is possible to simplify the NavierStokes equations by ignoring inertia pletely (Stokes flow) or by ignoring viscous effect (inviscid flows) in the limit of low and high Reynolds numbers, respectively. These two limiting cases are typically studied with boundary integral methods. The study of dispersed flows, for 本科畢業(yè)設(shè)計(jì)（論文）外文翻譯 9 example, can be made especially amenable to smallscale simulation since the study of one of the phases (. the dispersed phase) can be greatly simplified. Two main methods are used to simulate dispersed flows: the EulerianEulerian or the EulerianLagrangian approa