Computational Fluid Dynamics Mechanical Engineering Courses Subject Detail. Teaching Scheme in Hours. Examination Scheme in marks. Reference Books.
EGM 6342: Fundamentals of Computational Fluid Dynamics
Sengupta Universities Press. Subject List. Mohammed Farid. CFD has wide applications in the areas of fluid and heat transfer within the aerospace and nuclear industries backed by the availability of powerful supercomputers. It has expanded into other industries such as the chemical and petro- chemical industries. It is only in recent years that it has been applied to the food industry, with a limited variety of food-related problems being investigated Scott and Richardson, CFD offers a powerful design and investigative tool to the process engineer in many applica- tions.
However, at present little use of this technology has been reported in the food industry. Its application in such areas would be beneficial for the better understanding of the complex interac- tions occurring in food systems. The development of CFD packages came from a need to solve complex fluid flow problems of a general nature for a wide range of geometry and boundary con- ditions Hatton and Carpenter, CFD works by dividing the physical environment of interest into a two or three-dimensional 3-D grid or mesh.
It contains a number of discrete cells and can evaluate fluid velocities, temperature, and pressure inside every one of the cells where fluid flows. This is done by the simultaneous solution of the equations describing fluid flow, heat, and mass transfer. The use of CFD techniques to solve a fluid flow and heat transfer problem is split into three dis- crete parts: pre processing, processing, and post processing. In general, different computer programs that form the CFD code must undertake each of the three tasks. Defining geometry for a CFD simulation.
Definition of the physical geometry of the environment in which the fluid flows, which is normally done by building up a geometric representation of the environment. Declaration of the boundary conditions of the physical environment. These boundary con- ditions will include defining certain areas such as the inlets and outlets for the fluid flow and the boundary areas of solids where heat transfer from or to the fluid can occur.
Fundamentals of Computational Fluid Dynamics | H. Lomax | Springer
Construction of a mesh or grid as a geometric representation of the physical environment. This mesh or grid will form the computational grid that will be used in the solution of the problem by the powerful mathematical techniques around which CFD is based. A uniform spacing mesh has regular rectangular cells with second-order accuracy. A nonuniform mesh Figure 4. In general, at any top, bottom, inlets, or outlets, the flow domain needs to be defined to set the appropriate boundary conditions.
For example, in the case of heating a fluid in a can, the velocity of the fluid and its temperature are set at the top, bottom, and wall of the can. Other types of boundary conditions that may need to be set are those for walls and solids particularly if they act as heat transfer boundaries Scott and Richardson, After defining the computational mesh and boundary conditions, the user needs to define the assumptions need to be made—for example, whether the flow is laminar or turbulent and whether heat transfer takes place or not. There are two methods of generating the grid and the setup data for any problem.
The second and more elegant method is based on a graphical user interface. In this method, the data is entered via a menu-driven procedure, which guides the user through all the separate stages in setting up a CFD simulation.
The choice of the coordinate system, the resolution of the computational grid, and the method of its generation will be dependent on the complexity of the simulation. Solution of the Problem Processor The solution of the problem by the CFD code is where a host of mathematical techniques is used to approximate the differential equations into algebraic form, which can be solved directly or iteratively.
Different CFD codes employ different solution techniques, but the physics is the same if it can be well defined and understood. The solution of the transport equations for the geometry under study is not a trivial matter and cannot be solved readily, if at all, by analytical techniques. CFD uses numerical techniques to solve discretized representations of the transport equations.
Direct or explicit numerical methods, which can be both extremely accurate and rapid, may be used if sufficient computing power is available. Many codes use iterative methods to solve the equations because they tend to be more robust, although they can take longer to converge.
Standard texts are available that provide good background material on numerical simulation and CFD. Analysis of the Results Postprocessor The results can be analyzed both numerically and graphically.
The postprocessor takes the numerical results and displays them as a visual representation. It displays a visual image of the physical geometry through which the fluid flows, with the option of printing a hard copy of all the results as tables of numbers and other means. It is possible to superimpose the velocity, pressure, and temperature distributions within the fluid.
The format of this display is a graphical contour with the option of displaying scaled arrows for vector quantities.
javaplanetorganiccoffeeroasters.makh.org/small-business-taxes.php The output file can contain all sorts of information, including the spatial coordinates of all of the cells in the computational mesh and the solved transport variables for each cell. In the case of a large CFD problem, say greater than , cells, it is obvious that the user does not want to read through this file. Thus, the second method offers the user the ability to visualize the results. This method, often referred to as postprocessing, takes the results from the CFD solver and allows the user to display variables graphically on the computer screen, for all or part of the flow domain. The user has the option to rotate the image in 3-D space or to zoom into areas of interest to extract the most useful information from the image.
Combining both visual and numerical results allows the optimal solution to be achieved for the problem under investigation. It is a computer code, which simulates fluid flow, heat transfer, chemical reactions, and related phenomena. It uses the finite volume method FVM , which is one of several computational methods used for solving heat transfer and fluid flow problems.
For solving the equations governing natural convection, Nield and Bejan , after examining a range of numerical techniques, concluded that the FVM is more appropriate than other methods of solution. The principle behind this numerical method is based on the control volume idea used in many fluid texts. This idea is applied on a cell basis and used to derive the conservation equations of mass, momentum, and energy from basic laws into a mathematical form known as finite volume equations FVE. In order to specify a problem, it is necessary to identify the computational domain, which totally covers the region of flow to be studied.
The computational domain may contain some sections where there is no fluid flow since these may be blocked. The computational domain must then be subdivided into a number of divisions in the three dimensions i. In general, topologically Cartesian grids take three forms which are as follows: a. Strict Cartesian A Cartesian grid is composed of cells formed by the intersection of three sets of mutually perpendicular parallel planes, on any one of which either x, y, or z is constant, these quantities being the distances in the three coordinate directions.
Cylindrical polar grids A cylindrical polar grid consists of cells formed by the intersection of r planes of constant z perpendicular to the axis of rotation r planes of constant x, which all pass through and thus intersect on that axis so that x now represents an angle in radius and not distance r concentric cylindrical surfaces of constant radial coordinate y c.
Body-fitted coordinates BFC A BFC is best imagined by supposing that a regular Cartesian grid is first embedded in a jellylike medium, which is then squeezed, bent, and twisted in an arbitrary way. All the cells in contact with another remain so. The velocities are directed along lines joining cell nodes and are therefore perpendicular to the cell faces for strict Cartesian and cylindrical polar grids. In body-fitted grids, this is not necessarily true, and hence careful calculation of flows across faces is required. In body-fitted grids, some form of a grid generation technique is required in order to specify the grid corner positions.
In cylindrical polar and body-fitted grids, the ideas behind the FVM are the same as those for strict Cartesian grids, but the mathematics is harder. The FVM may treat time in a manner that is similar to that used for the other dimensions with a Cartesian grid. This means that the time dimension is subdivided into NT discrete time planes at which a solution is obtained. These may be spaced in any desired manner but should obviously be concentrated at times when the flow is changing rapidly, such as the fine mesh time steps used in our work at the beginning of heating.
Three-dimensional notation will be discussed here for the geometry of the can and pouch being investigated in this book. For the cell with its node at P, which adjoins cells with their nodes at E, W, N, S, H, and L east, west, north, south, high, and low , the centers of the adjoining faces are e, w, n, s, h, and l having face areas of A e , A w , A n , A s , A h , and A l , respectively. Most properties are stored as values at the cell nodes, while velocities are stored at the cell faces.
This has computational advantages both in terms of stability and computational ease since the velocity related to flow across a face is specified at its center. This is done by assuming a staggered grid passing through the cell nodes and having the velocity at the face centers e, w, n, s, h, and l , as shown in the dashed lines in Figure 4. In the course of defining the computational domain, the optimum meshing arrangement should be decided upon.
The geometrical and time mesh subdivides the computational domain into small cells at which values of the medium properties, and solved variables, are stored Mallinson, Cell nomenclature showing cell nodes and staggered grid. Cell nomenclature showing staggered grid. Several meshing arrangements will be considered throughout this work.