From: Subject: Introduction to CFD Date: Sat, 30 Oct 2004 10:24:08 -0500 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C4BE6A.97256E40" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C4BE6A.97256E40 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.kostic.niu.edu/fluenthelp/FlowLAB-help/intro.htm Introduction to CFD

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Appendix A: Introduction to Computational Fluid=20 Dynamics

Note:  A"grid" is the same thing as = a "mesh";=20 the two words are used interchangeably here and throughout this = manual.=20

A.1 What is = Computational=20 Fluid Dynamics (CFD)

Computational Fluid Dynamics (CFD) is a computer-based analysis = technique=20 used for predicting various physical and chemical phenomena (fluid flow, = heat=20 transfer, mass transfer, chemical reactions, phase change, combustion, = flow=20 acoustics, to name a few). It works by numerically solving the = mathematical=20 equations governing these phenomena. CFD is fast becoming a powerful = tool, used=20 in conjunction with conventional design techniques, to analyze = engineering=20 problems.

Dynamics of fluids are governed by coupled non-linear partial = differential=20 equations, which are derived from the basic physical laws of = conservation of=20 mass, momentum, and energy. Analytical solutions of such equations are = possible=20 only for very simple flow domains with certain assumptions made about = the=20 properties of the fluids involved. For conventional design of equipment, = devices, and structures used for controlling fluid flow patterns, = designers have=20 to rely upon empirical formulae, rules of thumb, and experimentation. = However,=20 there are many inherent problems with these conventional design = processes.=20 Empirical formulae and rules of thumb are extremely specific to the = problem at=20 hand and are not globally usable because of the non-linearity of the = governing=20 equations. For example, a rule of thumb for designing an aircraft wing = may not=20 be applicable for designing a wing mounted on a racing car, as the = upstream flow=20 conditions are completely different for the two configurations.

The above reasons make experimentation the leading conventional = design=20 technique. However, there are many limitations of experimentation = techniques as=20 well:

All these limitations are overcome by CFD, since it is a numerical = simulation=20 technique which does not require a prototype to be built, is not = thwarted by=20 measurement capabilities, and can provide extremely detailed data as and = when=20 required. Using CFD, you can build a computational model that represents = a=20 system or device that you want to study. Then you apply the fluid flow = physics=20 to this virtual prototype, and the software provides a prediction of the = fluid=20 flow pattern and other physical phenomena. CFD analysis not only = complements=20 testing and experimentation, but leads to a substantial saving of time = as a=20 large number of options can be tested much before the prototyping = stage.

CFD is, thus, a tool for compressing the design and development = cycle. The=20 major reasons why using CFD analysis is relevant for engineering = applications=20 are summarized below:

  • Visualizing designs - There are many devices = and=20 systems that are very difficult to prototype. Often, CFD analysis = shows you=20 parts of the system or phenomena happening within the system that = would not=20 otherwise be visible through any other means. CFD gives you a means of = visualizing and enhanced understanding of your designs.

  • Comprehensive Information - Experiments only = permit=20 data to be extracted at a limited number of locations in the system. = CFD=20 allows the analyst to examine a large number of locations in the = region of=20 interest, and yields a comprehensive set of flow parameters for = examination.=20

  • Making predictions using comprehensive = results - As CFD=20 is a tool for predicting what will happen under a given set of = circumstances,=20 it can analyze numerous hypothetical options very quickly. You give it = variables and it gives you related outcomes. Thus, in a short time, = you can=20 predict how your design will perform, and test many variations until = you=20 arrive at an optimal result. All of this is done before physical = prototyping=20 and testing. The foresight you gain from CFD helps you to design = better and=20 faster.

  • Improved design ability - Better and faster design or = analysis leads=20 to shorter design cycles. This leads to huge savings in terms of cost = and time=20 and the product gets to the market faster. Equipment improvements are = built=20 and installed with minimal downtime.=20 =

=

  • Speed - CFD simulations can be executed in a short period of = time.=20 Quick turnaround means engineering data can be introduced early in the = design=20 process.

  • Ability to Simulate Real Conditions - Many = flow and=20 heat transfer processes cannot be (easily) tested - for example, = hypersonic=20 flow at Mach 20. CFD provides the ability to theoretically simulate = any=20 physical = condition.
  • Ability to Simulate Ideal Conditions - CFD = allows great=20 control over the physical process, and provides the ability to isolate = specific phenomena for study. For example, a heat transfer process can = be=20 idealized with adiabatic, constant heat flux, or constant temperature=20 = boundaries.

A.2 CFD=20 Applications

CFD modeling is a powerful tool used by almost every application that = involves advanced engineering, replacing slow experimentation = techniques. CFD=20 modeling becomes useful for process analysis due to either one or more = of the=20 following reasons:

  1. Scale-up laws are not available =
  2. Detailed information on equipment behavior is needed =
  3. Unit operations involve complex physics (multiphase = flows,=20 reactions. viscoelastic effects, etc.)
  4. Empirical correlations or bulk models are not = available=20
  5. Comparison of design alternatives=20

Some of the industrial and non-industrial fields where CFD is used = are given=20 below, along with some examples:

Figure 2 - (a) Centrifugal Pump (b) Contours of = velocity=20 magnitude

A.3 CFD Analysis - = How it=20 Works

The equations governing fluid flow and other physical phenomena are = highly=20 nonlinear and coupled, with no analytical solutions possible for = non-trivial=20 flow regimes; hence, it is not possible to find one solution for the = entire flow=20 domain. CFD analysis works by decomposing the domain into a number of = subdomains=20 (domain discretization) and reducing them to a set of algebraic = equations=20 (discretization of governing equations), which are then solved for each=20 subdomain. While solving these equations within a subdomain, continuity = of=20 solution variables across boundaries contiguous with other subdomains = has to be=20 maintained. This reduces the system of governing partial differential = equations=20 for the original domain to a set of linear algebraic equations.

In CFD terminology, the task of decomposing the domain into = subdomains is=20 known as grid, or mesh, generation (see = Mesh=20 Generation). The term "mesh generation" is derived from the fact = that=20 earlier CFD analyses were performed for two-dimensional domains, and the = geometric representation of such discretized domains resembles a mesh or = grid.=20 Figures 4 (a) and 4 (b) illustrate a simple two-dimensional domain for a = flow=20 around an airfoil, and the mesh created in the domain for CFD analysis. = Each=20 subdomain is called a mesh element.

Figure 4 (a) - Two-dimensional domain for an=20 airfoil


Figure 4 (b) - Mesh for flow around the airfoil

There are many widely accepted methods for discretization of = equations, and=20 for solving the resulting set of algebraic equations (see = Discretization=20 Schemes). There are certain constraints on the solution variables at = the=20 boundaries of the domain (like no-slip conditions between fluids and = solids for=20 viscous flows), which make this system of equations a boundary value = problem.=20 These constraints are known as boundary conditions (see = Implementation=20 of Boundary Conditions) for the fluid flow.

As mentioned earlier, CFD analysis begins with a mathematical model = of a=20 physical problem. Analysis is done in three main stages - preprocessing, = solving, and postprocessing. Fluent provides a suite of state-of-the-art = CFD=20 tools, with easy-to-use designs, to help you solve your CFD problems. =

A.3.1 Preprocessing

Preprocessing allows the users to define the problem and make it = amenable to=20 numerical solution. The first step in this stage is defining the problem = to be=20 solved, the determination of the extent of the computational domain, = that is,=20 the part of the physical system that you are interested in analyzing and = the=20 type of model which is suitable - either a two dimensional or a=20 three-dimensional model. Once the computational domain has been = identified, a=20 geometric representation is created for it by using any standard mesh = generation=20 utility, for example, GAMBIT. The domain is then discretized into a = suitable=20 number of mesh elements (see = Mesh=20 Generation). The number of mesh elements, or mesh size, is chosen = based upon=20 the computing power available, the complexity of the geometry, and the = detail=20 required from the solution.

Finally, the boundary zones of the model are specified. Boundary = zones define=20 the physical and operational characteristics of the computational domain = at its=20 boundaries and within specific regions. It is important to identify the = various=20 boundaries of the flow domain and to mark them as separate zones in this = step,=20 as this allows appropriate boundary conditions to be specified for = obtaining the=20 correct solutions.

A.3.2=20 Solving

The solving stage involves specifying the fluid and flow properties, = choosing=20 the discretization scheme, and collectively solving the discretized = algebraic=20 equations. Determination of a solution procedure means taking into = consideration=20 the following issues - Can the problem be solved simply, using the = default=20 solver formulation and solution parameters? Can convergence be = accelerated with=20 a more judicious solution procedure? Will the problem fit within the = memory=20 constraints of your computer? How long will the problem take to converge = on your=20 computer?

There are various algorithms available (see = Discretization=20 Schemes) for discretizing and solving the equations. The first step = in the=20 solution process is defining the physics of the flow. The appropriate = equations=20 are selected, depending on the flow properties - is the flow inviscid, = laminar,=20 or turbulent, is it unsteady or steady, is heat transfer important, will = the=20 fluid be treated as incompressible or compressible. Next, the type of = material=20 and the relevant material properties (for example, molecular viscosity, = specific=20 heat) are selected. Lastly, the appropriate boundary conditions (for = example,=20 specification of velocity of the fluid coming into the domain, pressure = of the=20 fluid at the outlet of the domain) for the analysis are specified. The = solution=20 is then calculated after adjusting the solution parameters such as the=20 under-relaxation factors, discretization schemes, multigrid parameters, = and=20 other flow solver parameters. Before solving, you must initialize the = flow field=20 to provide a starting point for the solution.

A.3.3=20 Postprocessing

Once the discretized equations have been solved, a discrete solution = for the=20 flow variables is available for the domain at each mesh element. This = solution=20 can be processed to obtain the values of the flow variables at any = location=20 within the flow domain by standard interpolation techniques. It is = customary for=20 CFD packages to provide powerful graphics capabilities for visually = analyzing=20 the solution, as well as to report values of various flow quantities. = These=20 features are collectively referred to as postprocessing capabilities. = Based on=20 the computation results, you can refine the grid, or consider making=20 modifications to the numerical or physical model.

Some of the postprocessing capabilities offered by Fluent software = packages=20 are - viewing the domain geometry and grid, viewing the contour and = vector=20 plots, viewing path lines and particle tracks, displaying animation = sequences,=20 manipulating views, reporting the computed results (like fluxes, surface = and=20 volume integrals), and plotting data. For example, Figures 5 (a) and (b) = display=20 the contour and vector plots for a simulation of a two-dimensional = turbulent=20 fluid flow in a partially filled spinning bowl.

Figure 5 (a) - Contours of stream function in a = partially filled=20 spinning bowl

Figure 5 (b) - Velocity vectors for air and water in a = partially=20 filled spinning bowl

To summarize, once you have determined the important features of the = problem=20 you want to solve, you will follow the basic procedural steps shown = below.=20

A.4 Mesh=20 Generation

Mesh generation is one of the most critical and time-consuming tasks = in CFD=20 analysis. A mesh needs to be tailored well so that results obtained are=20 optimally accurate. Since the governing equations are highly nonlinear = it is=20 important to discretize the domain into sufficiently small elements to = capture=20 the flow details, and still keep the mesh size small enough to suit the=20 available computing power.

A geometric representation of the flow domain is required for = creating a=20 mesh. Any standard CAD package can be used for creating the geometry. = Most=20 preprocessors also provide limited CAD functionalities for creating = geometries=20 before meshing. User input is required to decide the number of mesh = elements to=20 be created in the domain, and their sizes. This can be done by changing = the=20 various parameters available while creating the mesh, like the type of = elements=20 used, and whether a structured or unstructured mesh is created.

Meshes can be qualified as either structured or unstructured based on = whether=20 a regular pattern can be created for the connectivity of mesh elements = with=20 their neighbors. A structured mesh is a mesh that has a regular = arrangement of=20 its cells, and can be defined by specifying the parameters of the = arrangement.=20 Each cell is not defined separately. Figure 6 shows an example of a = structured=20 mesh.

Figure 6 - Structured mesh

An unstructured mesh is a mesh that has a irregular = arrangement of=20 its cells. Each cell and its connections to adjacent cells is defined=20 separately. Figure 7 shows an example of an unstructured mesh.

Figure 7 - Unstructured mesh

Various geometric shapes can be used as mesh elements. In = two-dimensions,=20 mesh elements can be triangles, quadrilaterals, and even higher order = polygons,=20 though the first two are the most predominantly used. In = three-dimensions, mesh=20 elements can be tetrahedra, hexahedra, pyramids, and triangular prisms. = Meshes=20 are often referred to by the type of the elements they contain. Hence, = "tri"=20 meshes are made up entirely of triangles, and "hex" meshes are made up = entirely=20 of hexahedra. Meshes which contain more than one type of mesh elements = are known=20 as hybrid meshes. An example of a hybrid mesh is shown in Figure 8.. =

Figure 8 - Hybrid mesh

Sometimes it is not possible to mesh the entire geometry together. = Such cases=20 can also arise if an existing mesh for a domain is used for CFD analysis = inside=20 a larger flow domain. In such cases, it is sometimes possible to create = the mesh=20 on the larger domain (with a void in place of the smaller domain) and = the=20 smaller domain separately, and then juxtapose the two meshes together. = The mesh=20 elements at the common interface of the two meshed domains may not = match. Such=20 interfaces are known as non-conformal interfaces, and the solvers need = to=20 calculate interpolated values of flow variables across the interface to = maintain=20 the conservation laws. An example of a non-conformal mesh is given in = Figure 9.=20

Figure 9 - Non-conformal mesh

A.5=20 Discretization Schemes

Numerical solutions of the governing equations for fluid dynamics = work by=20 converting the partial differential equations to algebraic equations. = Such=20 conversions are achieved by means of approximating the flow variables by = suitable functions and discretizing the governing equations by = substituting such=20 approximations for flow variables. Based upon the type of approximation=20 functions, and the discretization schemes used, solving techniques can = be=20 broadly classified in four major categories.=20