Computational fluid dynamic, or CFD for short, is undergoing important expan-sion in terms of the number of courses offered at the universities. There are some software packages available which solve fluid flow problems. The equations gov-erning the flow of the gas in CFD, namely Navier-Stocks equations, are written in a finite difference form. The program has solved the equations with the aid of a computer on a grid of points that cover the body of the separator [2].
The CFD programs appeared in the 1950s, and since then, they have been developed continually. This is due to development of hardware and software. One needs a solid background in both fluid mechanics and numerical analysis to work in CFD. People have made significant errors due to a lack of knowledge in one way or another. Therefore, it is important to obtain a working knowledge of these subjects before using the program [20].
2.12.1 Numerical solution
Numerical solution is the study of methods of computing of numerical data and using a computer to calculate the answer. By using CFD, a program solves the Navier-Stocks equations for all the grid points. The grid is essentially a discrete representative of the geometric domain on which the problem is to be solved. The position of any grid point within the domain is identified by a set of two (in 2D) or three (in 3D) indices, e.g.(i,j,k). People who employ this method for solving the problems are worried about some issues, namely the rate of convergence, i.e.
how long does it take for the method to find an answer, the validity of the answer and, are there any other solutions in addition to the one found [20]?
2.12.2 Turbulence models
Most flows that we meet in practical engineering are turbulent. Turbulence there-fore requires special treatment. Hoffmann and Stein [2] stated that direct turbu-lence modeling such CFD simulations are carried out in small geometries. This field is advancing as the computational power increases. The number of grid points
and the time steps needed are to high. Consequently, turbulence models are re-quired. In this thesis, there will be a brief description of some of the different models.
Direct numerical simulation
In direct numerical simulation, the Navier-Stokes equations are solved without av-eraging or approximation other than numerical discretizations and the errors can be estimated and controlled. In the DNS model, all of the motions included in the flow are solved. The domain on which the computation is performed must be at least as large as the physical domain to be considered or the largest turbulent eddy. This is because to be sure that all of the significant structures of the turbu-lence have been captured. All of the kinetic energy must be captured in a valid simulation. This can happen on the smallest scales, the ones on which viscosity is active. Therefore the size of the grid should not be larger than a viscous determi-nation scale that is called the Kolmogoroff scale(η).
Ferzinger [20] announced that the number of grid points that can be used in a computation are limited by the processing speed and memory of the machine on which it is carried out. For this reason, DNS is possible only for flows at rel-atively low Reynolds numbers up to a few hundred. By using DNS, one can get detailed useful information about the flow. You obtain detailed information about the velocity, pressure and any other variable of interest at a large number of grid points. It is far more information than any engineer needs. Furthermore, DNS is to expensive to be employed and can not be used as a design tool.
Large eddy simulation (LED)
According to Ferziger [20], turbulent flows include a range of eddy sizes. The large scale eddies contain much more energy than the smaller scale ones. Their size and strength make them the most effective transporters of the conserved properties, but the smaller ones are much weaker and provide little transport of these properties. Even if DNS is generally more expensive in comparison to LES, but it is more accurate. By using large eddy simulation, the largest eddies in the flow can be solved and the smaller eddies will be modelled. Breuer [21]
said that Reynolds-averaged Navier-Stokes equations combined with the statistical turbulence models, and an appropriate description using it is difficult to achieve.
The large eddy simulation(LES) offers a suitable method for solving such flow problems. The large eddies in LES are depending strongly on the special flow configuration and are resolved numerically, whereas the fine scale turbulence has to be modeled by a subgrid scale model. It is important that before LES can be used for applications of practical relevance, the influence on the quality of LES solutions must be understood. This includes numerical aspects such as resolution requirements, and modelling aspects such as subgrid scale models.
K-Epsilon model
The K-epsilon model is a two equation model, i.e. it contains two transport equations to represent the turbulent properties of the flow. It is one of the most common turbulent models. The first transport variable is turbulent kinetic(K) and the second transport variable is the turbulent dissipation(). The first variable determines the energy in the turbulence, whereas the second variable determines the scale of the turbulence. This model has been useful for free shear layer flows with relatively small pressure gradients [22].
Reynolds Stress Transport Models(RSM)
Reynolds stress models which are based on dynamic equations stress tensors are the most complex models that are used today. These equations can be derived from Navier-Stokes equations. This is the most complex model. Reynolds stress models have greater potential to represent turbulent flow phenomena more ac-curately. The use of this model has provided excellent results for some flows, namely swirling flows, and flows with strong curvature and with separation from the curved surface [20]. Since they are anisotropic turbulence models, the tur-bulence properties depend on the direction of the flow which works with swirling flows, flows with strong curvature, etc.
2.12.3 Eulerian and Lagrangian models
There are two ways of simulating the particle flow. When both the particles and fluid are treated as a continuous phase , it corresponds to the Eulerian approach. In this case, the continuum equations are solved for both phases with an appropriate interaction [22]. In the Lagrangian approach, the fluid is still treated as continuum, but the particles phase is treated as single particles. This approach involves the tracking of a single particle through the fluid flow field . This method is good for mechanisms of disperse phase behaviour, such as particle-particle and particle-wall interactions. Eulerian is less computer intensive and is good to utilize on a large scale, but Lagrangian is very computer intensive, and can therefore be used on very small systems [23].