Components

CFD uses a computer to solve the mathematical equations for the problem at hand. The main components of a CFD design cycle are as follows:

? The human being (analyst) who states the problem to be solved

? Scientific knowledge (models, methods) expressed mathematically

? The computer code (software) which embodies this knowledge and provides detailed instructions (algorithms) for

? The computer hardware which performs the actual calculations

? The human being who inspects and interprets the simulation results

CFD is a highly interdisciplinary research area which lies at the interface of physics, applied mathematics, and computer science.

CFD Analysis Process

1. Problem statement

2. Mathematical model

3. Mesh generation

4. Space discretization

5. Time discretization

6. Iterative solver

7. CFD software

8. Simulation

9. Post processing

10. Verification

Mathematical Model

1. Choose a suitable flow model (viewpoint) and reference frame.

2. Identify the forces which cause and influence the fluid motion.

3. Define the computational domain in which to solve the problem.

4. Formulate conservation laws for the mass, momentum, and energy.

5. Simplify the governing equations to reduce the computational effort:

? use available information about the prevailing flow regime

? check for symmetries and predominant flow directions (1D/2D)

? neglect the terms which have little or no influence on the results

? model the effect of small-scale fluctuations that cannot be captured

? incorporate a prior knowledge (measurement data, CFD results)

? Add constitutive relations and specify initial/boundary conditions.

Discretization Process

The PDE system is transformed into a set of algebraic equations

? Mesh generation (decomposition into cells/elements) structured or unstructured, triangular or quadrilateral?

? CAD tools + grid generators (Delaunay, advancing front)

? mesh size, adaptive refinement in ‘interesting’ flow regions

2. Space discretization (approximation of spatial derivatives)

? finite differences/volumes/elements

? high- vs. low-order approximations

3. Time discretization (approximation of temporal derivatives)

? explicit vs. implicit schemes, stability constraints

? local time-stepping, adaptive time step control

Turbulence Models

The standard k-? model

The standard k-? model is a semi-empirical model based on model transport equations for the turbulence kinetic energy (k) and its dissipation rate (?). The model transport equation for k is derived from the exact equation, while the model transport equation for ? was obtained using physical reasoning and bears little resemblance to its mathematically exact counterpart.

These default values have been determined from experiments with air and water for fundamental turbulent shear flows including homogeneous shear flows and decaying isotropic grid turbulence. They have been found to work fairly well for a wide range of wall-bounded and free shear flows.

CFD Simulations

The computing times for a flow simulation depend on

? the choice of numerical algorithms and data structures

? linear algebra tools, stopping criteria for iterative solvers

? discretization parameters (mesh quality, mesh size, time step)

? cost per time step and convergence rates for outer iterations

? programming language (most CFD codes are written in Fortran)

? Many other things (hardware, vectorization, parallelization etc.)

? The quality of simulation results depends on

? the mathematical model and underlying assumptions

? approximation type, stability of the numerical scheme

? mesh, time step, error indicators, stopping criteria

Post-processing and Analysis

Post processing of the simulation results is performed in order to extract the desired information from the computed flow field

? calculation of derived quantities (stream function, vortices)

? calculation of integral parameters (lift, drag, total mass)

? visualization (representation of numbers as images)

? 1D data: function values connected by straight lines

? 2D data: streamlines, contour levels, color diagrams

? 3D data: cutline, cut planes, iso surfaces, iso volumes

? Arrow plots, particle tracing, animations.

? Systematic data analysis by means of statistical tools

? Debugging, verification, and validation of the CFD model

Advantages

? Design and analysis, and optimization of body shapes.

? A few simulations at one design can reveal merits of one variant over the other.

? Quicker and less expensive changes to configuration and their numerical simulation.

? Smoothing of the configuration to reduce pressure drag levels.

? Detailed flow field information.

SOFTWARE USED

? Created geometry and domain in ANSYS workbench.

? Numerical Investigation of the flatplate model was carried out using solver FLUENT module of ANSYS.

PROCEDURE FOR FLOW ANALYSIS

1. Creating geometry in ANSYS workbench.

2. Create domain.

3. Add material and define boundaries.

4. Mesh the region between domain and geometry (structured Meshing).

5. Refine the mesh near the flat plate, at the top of the surface and at the bottom to ensure appropriate flow capturing.

6. Check the mesh quality and smooth mesh if required.

7. Define boundary conditions, initialize the flow and set up solver parameters using FLUENT-Pre.

9. Run Solver.

10. Calculate pressure, velocity and drag variations using FLUENT – Post.