INTERFACE FORCES CALCULATION FOR MULTIPHASE FLOW SIMULATION

Multiphase flows are important in most industrial applications including energy conversion, paper manufacturing, medical and nuclear applications. Many combustion and energy systems involve dilute multiphase flow, ranging from droplet sprays in high-speed gas turbine combustor flow to bubbly pipe flows of chemical reactors. A better understanding of the multiphase interactions can lead to increases in performance, reduction in cost and improved safety in several important engineering areas [1]. Up to very recently, the design of equipments involving multiphase flows relied strongly on correlations obtained experimentally. This narrows the range of the design variables. Experimental studies present a number of difficulties because the probes can interfere with the flow and because multiphase systems can be optically opaque. Considerable amount of research has been done in developing measuring systems based on new optical and laser technologies. Moreover, multiphase flows are well known for the difficulties in setting up fully controlled physical experiments. Fine measurements, like the flow inside bubbles, or flows near the bubble surface to investigate the existence of local slip flow are not easy to realize. But the only way for improving the interface models is to set up fine measurements close to the interface. Computer simulations, in the other hand, permit to include or neglect gravity, account for the effects of the geometrical configuration, process modifications and to perform many others variations in the physical problem. But, the great complexity of scales of the phenomena of practical multiphase flows, with different length and time scales interacting in a broad range is very difficult to model mathematically. One example is the coalescence of drops or bubbles where the interfaces are free to deform and break up. The forces in such systems are very complex, of different types and in the spatial-temporal domain, therefore observed over a large range of length scales [2]. Only recently it has become possible to experimentally observe the rapid motions during the coalescence of two water drops [3]. Generally, the averaged description is used to model multiphase flow in an industrial level, the so-called Eulerian model, where the dispersed phase, like the continuous one, is described as a continuous fluid with appropriate closures (interfacial momentum transfer between the phases, which includes a number of force contributions like viscous drag, added mass and lift, among others ). In these models, only the averaged local properties are calculated. The properties of each individual dispersed particle or bubble, can be modeled by the Lagrangian formulation, but unfortunately the amount of particles or bubbles that can be tracked is, even today and in the near future, very limited, [4]. Other method to describe multiphase flow is the interface tracking methods. These methods describe both fluids with one set of equations and solve another equation for the evolution of the interfaces between the fluids. The closures required in the Eulerian model have to be modeled or provided by empirical data. The problem can be to find closures that are as simple as possible, while incorporating just enough physics to accomplish this, for a given range or phenomena and a specified accuracy. It could be provided by direct numerical experiments. This approach requires transient numerical experiments at the scale of the closure model. One could simulate the motion of one bubble, resolving all scales of the flow and then calculate the forces acting on the bubble. The same procedure can be used for two or three bubbles or for an array of bubbles. The forces are then calculated and the relative importance of them could be determined and compared with empirical data. This procedure is easily controlled, in principle, better than the same experiment, providing better results. However, the difficulty in realizing fine experiments and also to solve numerically the complex multiphase flows, even for few bubbles, hinders the development of general closure models to be used with the two-fluid approach. In this paper we present a brief review of the important forces entering the interface models for multiphase flow simulation. We also present some numerical results for the buoyancy bubble flow in a straight channel as well as a ABSTRACT Despite the tremendous growth in computational resources, multiphase flows are far from being simulated with generality and accuracy. Keeping track of all interfaces and applying the proper boundary conditions, for example in an industrial gas-liquid flow, is not yet foreseeing possible in a near future, if it will, with the numerical background now available. The growth of the use of simulation tools for multiphase flows rely, therefore, in creating interface models which tries to represent with more fidelity the complex physics happening at the interfaces. This is a research topic which has a very large body of literature available, both on the fundamental physics as well as in theoretical analysis of the forces acting at the interfaces. This paper follows this trend, and an interfacial tracking method (VOF) is used to simulate the behavior of a rising bubble immersed in a quiescent liquid, as well as the buoyancy-driven motion of a viscous drop in a constricted channel. A brief review of the important interfacial forces used in CFD simulations of multiphase flows are discussed. Numerical results are compared with the available experimental data and the interfacial forces calculated from the numerical data are compared with numerical and experimental results. Attention given to the transient behavior of the coefficients normally used in CFD simulations. INTERFACE FORCES CALCULATION FOR MULTIPHASE FLOW SIMULATION