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INTRODUCTION TO CFD
ARVIND DESHPANDE
3/7/2012 Arvind Deshpande (VJTI) 2
Introduction
Computational Fluid Dynamics or CFD is theanalysis of systems involving fluid flow, heattransfer and associated phenomena such aschemical reactions by means of computer basedsimulation.
A tool for solving PDE’s
3 fundamental principles:
Mass is conserved (Continuity equation);
Newton’s second law (Navier-Stokes Eqn);
Energy is conserved (Bernoulli’s Equation)
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Introduction
Governing equations - PDE’s or integral
equations
Analytical and experimental approach (Old)
“A theory is something nobody believes except the person proposing the theory and an experiment is something everybody believes except the person doing the experiment”
--Albert Einstein
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Numerical Solutions (New)
Computers can only do the following:
Add, Subtract, Multiply and Divide
Perform simple logical operations
Display colours on the screen
What is Discretization?
Analytical Solution : Continuous
Numerical Solution : Discrete
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Introduction
CFD - Science of determining a numerical solution to the
governing equations of fluid flow whilst advancing the
solution through space or time to obtain a numerical
description of the complete flow field of interest.
It is very important to know velocity, pressure and
temperature fields in a large no. of applications
involving fluids i.e liquids and gases. The
performance of devices such as turbo machinery
and heat exchangers is determined entirely by the
pattern of fluid motion within them.
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Why CFD?
Growth in complexity of unsolved engineering problems
Need for quick solutions of moderate accuracy
Absence of analytical solutions
The prohibitive costs involved in performing even scaled
laboratory experiments
Efficient solution algorithms
Developments in computers in terms of speed and
storage
Serial/parallel/web computing
Sophisticated pre and post processing facilities
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Procedure
1. Virtual model
2. The flow region or calculation domain is divided into alarge number of finite volumes or cells
3. Partial differential equations are discretized using awide range of techniques: finite difference, finitevolume or finite element
4. Algebraic equations gathered into matrices which aresolved by an iterative procedure
5. Numerical solution gives the values of the dependentvariables at discrete locations
6. Chemical reaction, Multiphase flow, mixing, phasechange, mechanical movement
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CFD - Third approach in fluid dynamics
CFD today is equal partner with pure theory andpure experiment in the analysis and solution of fluiddynamic problems.
It nicely and synergistically complements the othertwo approaches of pure theory and pure experiment,but it will never replace either of these approaches.
CFD carry out numerical experiments.
Numerical experiments carried out in parallel withphysical experiments in the laboratory cansometimes be used to help interpret physicalexperiment.
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Advantages of CFD
It complements experimental and theoretical fluid dynamicsby providing an alternative cost effective means of simulatingreal flows.
Insight
Better visualization and enhanced understanding of designs.
Foresight
Testing many variations until you arrive at an optimal resultbefore physical prototyping and testing. Practically unlimitedlevel of detail of results at virtually no added expense.
Efficiency
Compression of design and development cycle.
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Advantages of CFD
The simulation results in prediction of the flow fields and
engineering parameters, which are very useful in the Design
and Optimization of processes and equipments.
Substantial reduction of lead times and costs of new designs
Ability to study systems where controlled experiments are
difficult or impossible to perform (e.g. very large systems)
Ability to study systems under hazardous conditions at and
beyond their normal performance limits (e.g. safety studies
and accident scenarios)
CFD is slowly becoming part and parcel of Computer Aided
Engineering (CAE)
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Why do we use CFD ?
Complements actual
engineering testing
Reduces engineering testing
costs
Provides comprehensive data
not easily obtainable from
experimental tests.
Reduces the product-to-market
time and costs
Helps understand defects,
problems and issues in
product/process
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Benefits of CFD
Reduce System Cost
Improve Performance
Understand
Problems
Reduce Design Time
& Cost
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HOW IT DIFFERS FROM STRESS
ANALYSIS? Stress analysis is generally check for safe working of the design,
Very rarely the performance of the system depends on the stress levels
The governing equations are linear Ease of solution
Not much dependencies on the grid or mesh
Need of auxiliary physics and models for CFD Turbulence
Reactions
Multiple phases their transformations
Confined domains
Conservation of only energy, against conservation of mass, forces and energy
CFD problems are, in general, more difficult to solve. Hence CFD was lagging behind structural mechanics.
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Applications of CFD
Aerodynamics of aircraft : lift and drag
Automotive : External flow over the body of a vehicle or internal flow through the engine, combustion, Engine cooling
Turbo machinery: Turbines, pumps , compressors etc.
Flow and heat transfer in thermal power plants andnuclear power reactors
HVAC
Manufacturing – Casting simulation, injection mouldingof plastics
Marine engineering: loads on off-shore structures
Hydrodynamics of ships, submarines, torpedo etc.
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Applications of CFD
Electrical and electronic engineering: cooling of equipment liketransformers, Computers, microcircuits, Semiconductor processing,Optical fibre manufacturing
Chemical process engineering: mixing and separation, chemical reactors, polymer molding
Transport of slurries in process industries
Environmental engineering: External and internal environment ofbuildings, wind loading, Investigating the effects of fire and smoke,distribution of pollutants and effluents in air or water,
Hydrology and oceanography: flows in rivers, oceans
Meteorology: weather prediction
Enhanced oil recovery from rock formations
Geophysical flows: atmospheric convection and ground watermovement
Biomedical engineering: Flow in arteries, blood vessels,heart, nasal cavity, Inhalers
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Pressure distribution on a pickup van with
pathlines
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Streamlines on a Submarine with the
surface colored with Pressure
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Aerospace applications
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Aerospace applications
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Automotive applications
Evaporating diesel fuel inside an
autothermal reformer mixing chamber
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Temperature
distribution in
IC Engine
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Surface pressure distribution in an
automotive engine cooling jacket.
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Cooling of transformers
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Flow pathlines and temperature distribution in a
fan-cooled computer cabinet.
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FLOW IN LUNGS-Inhaling and exhaling of air
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Applications in Chemical Engg.
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Biomedical applications
29
Flow through the turbine
draft tube
runner
distributor
rotating blades
30
Computed flow in the runner
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Computed flow in the draft tube
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Some more applications
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Some more applications
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Some more applications
Fluid flows around the spinnaker and
main sail of a racing yacht design
Vortical structures generated by an
aircraft landing gear
Temperatures on flame surface
modeled using LES and state-of the-
art combustion models
Pressure distribution
on an F1 car
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CFD USAGE & GROWTH
Extrapolation of Published estimates
Estimated annual
expenditure on CFD analysis
Worldwide:
1 Billion USD
India:
Rs 50 Cr
15 %
40 %
17 %15 %
Projected Growth Rate
60 %
18 %
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National Scenario in CFD
Educational / Research Institutes – IIT’s, IISc, BARC
Industry –
NAL, BHEL, SAIL, GTRE, Cummins, Mahindra, Birla
group
GE, TCS
The number of companies adopting CFD is increasing in
a major way in India each year
CFD is the fastest growing sector of the CAD/CAM/CAE
market with a projected 40-50% growth each year in
CFD in India
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National Scenario in CFD
The demand for CFD is spurred by:
Indian companies wanting to improve quality and compete globally
CFD is predominantly used in Automotive Industry, Power Generation Industry and Chemical & Petrochemical Industry
MNC Engineering centers located in India and bringing their design/analysis work here and serving overseas clients
Working on all aspects of design, analysis and performance improvement using CFD
Indian Science and Defence Labs enhancing their CFD research
Defense labs like DRDO, NAL - Application of CFD to high-speed propulsion systems etc.
Non defence labs - Focusing on materials and chemicals areas
Students knowledgeable in CFD are being produced by only a handful of Institutes in India today
The mismatch between the demand and availability of students is growing each year at a large rate
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Methodology in CFD
Pre processor Geometry generation
Geometry cleanup
Meshing
Solver Problem specification
Additional models
Numerical computation
Post Processor Line and Contour data
Average Values
Report Generation
Pre Processor
Solver
Post Processor
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1. Pre-processor
Definition of the geometry of the region of interest: the computationaldomain
Creating regions of fluid flow, solid regions and surface boundary names
Grid generation – the sub-division of the domain into a number of smaller,non-overlapping sub-domains: a grid (or mesh) of cells (or control volumesor elements)
Accuracy of a solution, calculation time and cost in terms of necessarycomputer hardware are dependent on the fineness of the grid.
Over 50% of time spent in industry on a CFD project is devoted to thedefinition of domain geometry and grid generation.
Selection of the physical and chemical phenomena that need to bemodeled.
Definition of fluid properties.
Specification of appropriate boundary conditions at cells which coincide withor touch the domain boundary
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2. Solver
• CFD is the art of replacing the differentialequation governing the Fluid Flow, with a setof algebraic equations (the process is calleddiscretization), which in turn can be solvedwith the aid of a digital computer to get an
approximate solution.
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Finite difference method
Domain including the boundary of the physicalproblem is covered by a grid or mesh
At each of the interior grid point the originalDifferential Equations are replaced by equivalentfinite difference approximations
Truncated Taylor series expansions are often usedto generate finite difference approximations ofderivatives of in terms of point samples of ateach grid point and its immediate neighbours
Most popular during the early days of CFD
FDM has the most formal foundation because, its inherent straightforwardness and simplicity.
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Finite Element Method
The solution domain is discretized into number of small subregions (i.e. Finite Elements).
Select an approximating function known as interpolationpolynomial to represent the variation of the dependent variableover the elements.
The piecewise approximating functions for are substituted intothe equation it will not hold exactly and a residual is defined tomeasure the errors.
The integration of the governing differential equation (oftenPDEs) with suitable weighting Function, over each elements toproduce a set of algebraic equations-one equation for eachelement.
The set of algebraic equations are then solved to get theapproximate solution of the problem.
Structural Design, Vibration Analysis, Fluid Dynamics, HeatTransfer and Magnetohydrodynamics
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Finite volume method
FLUENT, PHOENICS, and STAR-CD
Integration of the governing equations of fluid flow overall the (finite) control volumes of the solution domain.This is equivalent to applying a basic conservation law(e.g. for mass or momentum) to each control volume.
Discretisation involves the substitution of a variety offinite – difference – type approximations for the terms inthe integrated equation representing flow process suchas convection, diffusion and sources. This converts theintegral equations into a system of algebraic equations.
Solution of the algebraic equations by an iterativemethod.
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Rate of change of in the
control volume with respect to
time
=Net flux of due to
convection into the
control volume
+
Net flux of due to
diffusion into the
control volume
+
Net rate of creation
of inside the
control volume
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3.Post-processor
Versatile data visualization tools.
Domain geometry and grid display
Vector plots showing the direction and magnitude of the flow.
Line and shaded contour plots
2D and 3D surface plots
Particle tracking
View manipulation (translation, rotation, scaling etc.)
Visualization of the variation of scalar variables (variables whichhave only magnitude, not direction, such as temperature, pressureand speed) through the domain.
Quantitative numerical calculations.
Charts showing graphical plots of variables
Hardcopy output
Animation for dynamic result display
Data export facilities for further manipulation external to the code
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Problem solving with CFD
Convergence – The property of a numerical method to produce a solution which approaches the exact solution as the grid spacing, is reduced to zero.
Consistency - The property of a numerical method to produce system of algebraic equations solution which are equivalent to original governing equations as the grid spacing, is reduced to zero.
Stability - associated with damping of errors as the numerical method proceeds. If a technique is not stable, even round off errors in the initial data can cause wild oscillations or divergence.
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Problem solving with CFD
Conservativeness – Local conservation of fluidproperty for each control volume. It also ensuresglobal conservation of fluid property for the entiredomain.
Boundedness – In a linear problem, without sourcesthe solution is bounded by the maximum andminimum boundary values of the flow variables.Similar to stability.
Transportiveness – Numerical schemes mustaccount for the directionality of influencing in termsof the relative strength of diffusion to convection.
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Problem solving with CFD
Convergence of iterative process – Residuals
(measure of overall conservation of the flow
properties) are very small.
Good initial grid design relies largely on an insight
into the expected properties of the flow.
Background in the fluid dynamics of the problem
and experience of meshing similar problems helps.
Grid independence study - A procedure of
successive refinement of initially coarse grid until
certain key results do not change.
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Problem solving with CFD
CFD is no substitute for experimental work, but a very powerful problemsolving tool.
Comparison with experimental test work
High end – Velocity measurements by hot wire or laser Doppleranemometer
Static pressure or temperature measurements with static pitot tubetraverse can also be useful.
Comparison with previous experience
Comparison with analytical solutions of similar but simpler flows.
Comparison with closely related problems reported in the literature e.gASME
Main outcome of any CFD exercise is improved understanding of thebehaviour of the system.
Main ingredients for success in CFD are experience and a thoroughunderstanding of the physics of the fluid flows and fundamentals of thenumerical algorithms.
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CFD – A Big Picture
CFD (computational fluid dynamics) is not a CFD software.
Commercial software are purely a set of tools which can be used to solvethe fluid mechanics problem numerically on a computer.
Commercial CFD codes may be extremely powerful, but their operation stillrequires a high level of skill and understanding from the operator to obtainmeaningful results in complex situations.
Users of CFD must know fundamentals of fluid dynamics, heat transfer,turbulence, chemical reactions and numerical solution algorithms. Theymust have adequate knowledge of the physics of the problem.
In CFD, the user is responsible for correctly choosing the tools. He mustnote that that CFD solution for a problem gets generated due the sequentialusage of chosen tools from the collection of tools available in the software.
The user of CFD must get familiarized with all possible tools before hestarts using them. Best solutions are possible if correct tools are chosen inthe correct sequence.
The quality of the results depends on the background of the user, quality of
the tools and the capability of the computer.
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Identification and formulation of flow
problem User must decide the physical and chemical phenomenon that needed
to be considered
e.g. 2-D or 3-D
Incompressible or compressible
Laminar or turbulent
Single phase or 2 phase
Steady or unsteady
To make right choices require good modeling skills
Assumptions are required to reduce the complexity to a manageable level while preserving the important features of the problem.
Appropriateness of the simplifications introduced partly governs quality of information generated by CFD
Engineers need CFD codes that produce physically realistic results with good accuracy in simulations with finite grid.
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Verification and Validation
Verification and validation increase our confidence in thesimulation
No computer software can be proved to have no errors.
We can state that software is wrong if evidence to this effect can becollected
Verification is solving the chosen equations right
Numerical techniques for verification involves finding out sources oferror in spatial & temporal discretisation, iterative convergence, androunding off errors
Checking out if time steps adequate for all situations
Validation is Solving the right equation
Is the simulation matching with experimental data
Experimental data helps validation of similar simulations
Scientific literature
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What basics do you need to do develop a
successful student of CFD ?
Develop a thorough understanding of the
fundamentals of Fluid Mechanics, Heat Transfer
and CFD
Get exposure to the physics and solution
algorithms
Develop good programming skills
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WHAT IS IMPORTANT?
CFD
Numerical
Methods
Mathematics
Fluid Mechanics, Heat Transfer
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WHAT IS IMPORTANT?
Focus of the technology
Fundamentals
Domain knowledge
Numerical modeling and its limitations
Long time investment
Software tools will follow
Learning the tool just acquiring the skills
Tools will facilitate the solution process
Keep on changing
Can be learnt is short span
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Career Opportunities in CFD – An
Overview CFD offers career opportunities in different areas based on the
specific interest and skill set of the students Code development
Development of various modules of CFD software
Can be for general purpose software or for codes for specific application
Application of CFD software For solving industrial problems in diverse areas
Testing & Validation of CFD codes Usually for QA of multipurpose commercial software
Documentation for CFD codes Writing technical documents like user guides for commercial CFD
codes
In industry, opportunities in CFD application are relatively more than those in development, testing and documentation
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Conclusions
• CFD is a powerful tool to solve complex flows in
engineering systems. However:
• Extreme care should be taken while:
Generating geometry and grids,
Choosing flow model,
Boundary conditions
Material properties
Convergence criteria (grid independence)
Unless proper inputs are given and solution is
checked, the solution we get may not be the real
solution!!-It will be GIGO
Syllabus1 Introduction: Definition and overview of CFD, need, Advantages of CFD,
Applications of CFD, CFD methodology, Convergence, consistency, stability,
iterative convergence, grid independence, Verification and validation
2
2 Governing equations of mass, momentum and energy : Derivation,
Discussion of physical meanings and Presentation of forms particularly suitable to
CFD, Boundary Conditions – Dirichlet, Neumann, Robbins, initial conditions,
mathematical behavior of partial differential equations – Elliptic, parabolic &
hyperbolic equations, impact on CFD
6
3 Discretisation methods – Introduction to Finite Difference Method, Finite Volume
Method, Finite Element Method
Finite Difference method – Introduction to finite differences, difference equation,
Solution of discretised equations, Tri Diagonal Matrix Algorithm, explicit and
implicit approach, Errors and analysis of stability, Von-Neumann stability method,
CFL condition
6
4 Grid Generation: Structured and Unstructured Grids, General transformations of
the equations, body fitted coordinate systems, Algebraic and Elliptic Methods, O-
type, C- type and H-type structured grid generation multi block structured grids,
adaptive grids
4
Syllabus
5 Finite volume method for diffusion problems (Conduction): Steady state one
dimensional and two dimensional heat conduction with or without heat generation,
dealing with Dirichlet, Neumann, and Robins type boundary conditions, Multi-solid
heat conduction, Non-linear Heat Conduction, Unsteady heat conduction- Explicit,
Crank-Nicolson , Implicit schemes
6
6 Finite volume method for advection-diffusion problems (Convection-
conduction): Steady One-dimensional and Two Dimensional Convection-
Diffusion, Advection schemes-Central, first order upwind, hybrid, power law,
Second order upwind, QUICK etc., Properties of advection schemes –
Conservativeness, boundedness, transportiveness, False diffusion, unsteady
advection - diffusion
6
7 Solution algorithms for pressure velocity coupling in steady flows:
Staggered grids, SIMPLE, SIMPLER, SIMPLEC, PISO algorithms, unsteady flows
6
8 Turbulence modeling : Turbulence, its effect on governing equations, turbulence
models – k-ε , RSM, ASM, LES etc.
4
9 Post processing – xy plots, contour plots, vector plots, streamline plots etc. 2
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Reference
1) An Introduction to Computational Fluid Dynamics, The Finite Volume Method
H K Versteeg and W Malalasekera, Pearson Education, 2008.
2) Numerical Heat Transfer and Fluid Flow –
S V Patankar, Taylor & Francis, 1980.
A standard text on the details of numerical method
3) Computational Fluid Dynamics, The basics with applications
John.D.Anderson, JR.,Mcgraw-Hill International edition, 1995
4) Computational Fluid Flow and Heat Transfer
K.Muralidhar and T.Sundararajan, Narosa, 2007
5) Computational methods for fluid dynamics
Ferziger and Peric, Springer, 2004
6) Introduction to Computational Fluid Dynamics
A.W. Date, Cambridge, 2005. Web Sites
www.cfd-online.com
3/7/2012 Arvind Deshpande (VJTI) 62
Thank You
Hope You Enjoyed the
Tour of
Colorful / Computational
Fluid Dynamics!