Introduction to Computational Fluid Dynamics (CFD)

Computational fluid dynamics (CFD) is the use of computers and numerical methods to solve problems involving fluid flow.  The ultimate goal of the field of Computational Fluid Dynamics (CFD) is to understand the physical events that occur in the flow of fluids around and within designated object.  CFD is predicting what will happen, quantitatively, when fluids flow. The governing equations  the fluid motion are based on fundamental physiscs principles :

–  change of mass = 0

–  change of momentum = force × time

–  change of energy = work + heat

Navier-Stokes Equations are the governing equations of Computational Fluid Dynamics. It is based on the conservation law of physical properties of fluid. The principle of conservational law is the change of properties, for example mass, energy, and momentum, in an object is decided by the input and output. For example, the change of mass in the object is as follows :

Which means : M = const

Applying the mass, momentum and energy conservation, we can derive the continuity equation, momentum equation and energy equation as follows :

If the fluid is compressible, we can simplify the continuity equation and momentum equation as follows :

How old is CFD? CFD is one of the areas that are being dramatically developed for the last several decades.  Its early beginnings were in the 1960’s. Its first successes came to prominence in the 1970’s.  The creation of the CFD-service industry started in the 1980’s. The industry expanded significantly in the 1990’s.  

Expansion continued in the Second Millennium as CFD packages developed easier connections with those for CAD and solid-stress analysis.  A significant change of the near future is likely to involve the use of pay-as-you go remote computing, via Internet.

How does CFD make predictions? This is the process of CFD  : Firstly, we have a fluid problem. To solve this problem, we should know the physical properties of fluid by using Fluid Mechanics. Then we can use mathematical equations to describe these physical properties. 

This is Navier-Stokes Equation and it is the governing equation of CFD. As the Navier-Stokes Equation is analytical, human can understand it and solve them on a piece of paper. But if we want to solve this equation by computer, we have to translate it to the discretized form. The translators are numerical discretization methods, such as Finite Difference, Finite Element, Finite Volume methods.

Consequently, we also need to divide our whole problem domain into many small parts because our discretization is based on them. Then, we can write programs to solve them. The typical languages are Fortran, C, Phyton, etc. Normally the programs are run on workstations or supercomputers.

At the end, we can get our simulation results. We can compare and analyze the simulation results with experiments and the real problem. If the results are not sufficient to solve the problem, we have to repeat the process until find satisfied solution.

Why use CFD?

CFD simulations of fluid flow will enable :architects to design comfortable and safe living environments, designers of vehicles to improve the aerodynamic characteristics, chemical engineers to maximize the yield from their equipment, petroleum engineers to devise optimal oil recovery strategies, surgeons to cure arterial diseases, meteorologists to forecast the weather and warn of natural  disasters, safety experts to reduce health risks from radiation and other hazards, military organizations to develop weapons and estimate the damage, CFD practitioners to make big bucks by selling colorful pictures.

Experiments Vs Simulations. CFD analysis complements testing and experimentation by reducing total effort and cost required for experimentation and data acquisition.

 

Can CFD be trusted? The results of a CFD simulation are never 100% reliable because :

–  the input data may involve too much guessing or imprecision

–  the mathematical model of the problem at hand may be inadequate

–  the accuracy of the results is limited by the available computing power

–  for laminar flows rather than turbulent ones

–  for single-phase flows rather than multi-phase flows;

–  for chemically-inert rather than chemically-reactive materials;

–  for single chemical reactions rather than multiple ones;

–  for simple fluids rather than those of complex composition.

Main Stages in a CFD Simulation. All CFD codes contain three main stages: (1) A pre-processor, which is used to input the problem geometry, generate the grid, define the flow parameter and the boundary conditions to the code. (2) A flow solver, which is used to solve the governing equations of the flow subject to the conditions provided. (3) A post-processor, which is used to massage the data and show the results in graphical and easy to read format.

Validation of CFD models. Validations amounts to checking if the model itself is adequate for practical purposes. Are we solving the right equations or not ? The goal of verification and validation is to ensure that the CFD code produces reasonable results for a certain range of flow problems. Beneath are very simple steps to checking your CFD simulation results :

Verify the code to make sure that the numerical solutions are correct ; Compare the results with available experimental data (making a  provision for measurement to check if   the reality is represented accurately enough ; Perform sensitivity analysis and a parametric study to assess the inherent uncertainty due to the insufficient understanding of physical processes ; Try using different models, geometry, and initial/boundary conditions ; Report the findings, document model limitations and parameter settings.

Literature :

CFD-Wiki http://www.cfd-online.com/Wiki/Main Page

Kuzmin, Dmitri. ” Introduction to Computational Fluid Dynamics” . University of Dortmund

Zuo,Wangda.  ” Introduction of Computational Fluid Dynamics”.  JASS 05, St. Petersburg

Thank You.....Everyone is Number One