Free-surface flow

In most cases the only appropriate approach to model multi-phase flows in micro reactors is to compute explicitly the time evolution of the gas/liquid or liquid/ liquid interface. For the motion of, e.g., a gas bubble in a surrounding liquid, this means that the position of the interface has to be determined as a function of time, including such effects as oscillations of the bubble. The corresponding transport phenomena are known as free surface flow and various numerical techniques for the computation of such flows have been developed in the past decades. Free surface flow simulations are computationally challenging and require special solution techniques which go beyond the standard CFD approaches discussed in Section 2.3. For this reason, the most common of these techniques will be briefly introduced in 

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Modelling of steady-state free surface flow corresponds to the solution of a boundary value problem while moving boundary tracking is, in general, viewed as an initial value problem. Therefore, classification of existing methods on the basis of their suitability for boundary value or initial value problems has also been advocated. 

An example describing the application of this algorithm to the finite element modelling of free surface flow of a Maxwell fluid is given in Chapter 5. 

Figure 5.8 The finite element mesh used to model free surface flow in example 5.2.1...

Nassehi, V. and Ghoreishy, M. H. R., 1997. Simulation of free surface flow in partially filled internal mixers. Int. Poly. Process. XII, 346-353. 

Atomization = Eotvos numher, Eo Two-phase flows, free surface flows Compressible flow, hydraulic transients Cavitation... 

To address these challenges, chemical engineers will need state-of-the-art analytical instruments, particularly those that can provide information about microstmctures for sizes down to atomic dimensions, surface properties in the presence of bulk fluids, and dynamic processes with time constants of less than a nanosecond. It will also be essential that chemical engineers become familiar with modem theoretical concepts of surface physics and chemistry, colloid physical chemistry, and rheology, particrrlarly as it apphes to free surface flow and flow near solid bormdaries. The application of theoretical concepts to rmderstanding the factors controlling surface properties and the evaluation of complex process models will require access to supercomputers. 

In addition to the methods described above, there exist a number of other methods for the computation of free-surface flows which allow a sharp interface to be maintained. The approach which resembles computational methods for single-... 

Another numerical study of free-surface flow patterns in narrow channels was conducted by Yang et al. [185]. They considered the flow of bubbles of different size driven by body forces, for example the rising of bubbles in a narrow capillary due to buoyancy. The lattice Boltzmann method [186] was used as a numerical scheme... 

G. D., Prediction of incompressible free Surface flows with an element-based finite volume method, Comput. Fluid Dyn. J. 4 (1995) 353-371. 

CFX4 User Manual, Surface sharpening in free surface flows, Ansys CFX. 

Eggers, J., Nonlinear dynamics and breakup of free surface flows. Rev. Modern Phys. 69, 865-930 (1997). 

Froude number A/Fr /VFr = V2/gL L= characteristic length (Inertial/gravity) forces Free surface flows... 

What is turbulent flow We will use the simple illustration of a free-surface flow given in Figure 5.1 to describe the essential points of the turbulence phenomena. Turbulent open-channel flow can be described with a temporal mean velocity profile that reaches a steady value with turbulent eddies superimposed on it. These turbulent eddies are continually moving about in three dimensions, restricted only by the boundaries of the flow, such that they are eliminated from the temporal mean velocity profile, u in Figure 5.1. It is this temporal mean velocity profile that is normally sketched in turbulent flows. 

Free Surface Flows under Compensated Gravity Conditions By M. Dreyer 2007. 128 figs., X, 272 pages... 

Wardle, K. E., T. R. Allen, and M. H. Anderson. 2008. Free Surface Flow in the Mixing Zone of an Annular Centrifugal Contactor. AIChE J. 54, 74—84. 

Gray, J.M.N.T., Wieland, M. and Hutter, K. (1999) Gravity-driven free surface flow of granular avalanches over complex basal topography. A Proceedings of Royal Society London 455, 1841-1874... 

Free-surface flow with interfacial transport processes is a subject of great interest since its effects can be seen both in nature and practical devices, such as the air-sea interface, ship wakes, and chemical processes like gas-absorption equipment. In many cases, it is necessary to investigate the interaction of the flow and the free surface or correlate the free-surface deformation with the flow characteristics beneath the liquid surface. To this end, PIV technique can be applied to some free-surface flows as a powerful experimental tool. 

F. M. Orr and L. E. Scriven, Rimming Flow Numerical Simulation of Steady, Viscous, Free-surface Flow with Surface Tension, J. Fluid Meek, 84, 145-165 (1978). 

In free surface flows such as that shown in Fig. 1.18 the gravitational acceleration g has an effect on h and this will again mean that an extra dimensionless variable will be involved, this being the Froude number, Fr, defined by ... 

E. Finite Element Solutions of Free Surface Flows 91... 

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