Introduction to cfd

INTRODUCTION TO CFD

ARVIND DESHPANDE

Introduction

 Computational Fluid Dynamics or CFD is the
analysis of systems involving fluid flow, heat
transfer and associated phenomena such as
chemical reactions by means of computer based
simulation.
 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)

3/7/2012 Arvind Deshpande (VJTI) 2

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


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


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.


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


Procedure
1. Virtual model
2. The flow region or calculation domain is divided into a
large number of finite volumes or cells
3. Partial differential equations are discretized using a
wide range of techniques: finite difference, finite
volume or finite element
4. Algebraic equations gathered into matrices which are
solved by an iterative procedure
5. Numerical solution gives the values of the dependent
variables at discrete locations
6. Chemical reaction, Multiphase flow, mixing, phase
change, mechanical movement


CFD - Third approach in fluid dynamics

 CFD today is equal partner with pure theory and
pure experiment in the analysis and solution of fluid
dynamic problems.
 It nicely and synergistically complements the other
two 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 with
physical experiments in the laboratory can
sometimes be used to help interpret physical
experiment.


Advantages of CFD

 It complements experimental and theoretical fluid dynamics
by providing an alternative cost effective means of simulating
real flows.
 Insight
Better visualization and enhanced understanding of designs.
 Foresight
Testing many variations until you arrive at an optimal result
before physical prototyping and testing. Practically unlimited
level of detail of results at virtually no added expense.
 Efficiency
Compression of design and development cycle.


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)


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


Benefits of CFD

Understand
Reduce System Cost Problems

Improve Performance
Reduce Design Time
3/7/2012 Arvind Deshpande (VJTI) & Cost 13

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.


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 and
nuclear power reactors
 HVAC
 Manufacturing – Casting simulation, injection moulding
of plastics
 Marine engineering: loads on off-shore structures
 Hydrodynamics of ships, submarines, torpedo etc.


Applications of CFD
 Electrical and electronic engineering: cooling of equipment like
transformers, 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 of
buildings, 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 water
movement
 Biomedical engineering: Flow in arteries, blood vessels,
heart, nasal cavity, Inhalers


Pressure distribution on a pickup van with
pathlines


Streamlines on a Submarine with the
surface colored with Pressure


Aerospace applications


Automotive applications

Evaporating diesel fuel inside an
autothermal reformer mixing chamber


Temperature
distribution in
IC Engine


Surface pressure distribution in an
automotive engine cooling jacket.


Cooling of transformers


Flow pathlines and temperature distribution in a
fan-cooled computer cabinet.


FLOW IN LUNGS-Inhaling and exhaling of air


Applications in Chemical Engg.


Biomedical applications


Flow through the turbine
distributor

runner

draft tube

rotating blades

29

Computed flow in the runner

30

Computed flow in the draft tube


Some more applications



Vortical structures generated by an
Fluid flows around the spinnaker and
aircraft landing gear
main sail of a racing yacht design

Temperatures on flame surface
Pressure distribution
modeled using LES and state-of the-
on an F1 car
art combustion models


CFD USAGE & GROWTH
60 %

40 %
Worldwide:
1 Billion USD 18 %
17 %
15 % 15 %

India:
Rs 50 Cr
Projected Growth Rate
Estimated annual
expenditure on CFD analysis
Extrapolation of Published estimates

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


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


Methodology in CFD

Pre Processor
 Pre processor
 Geometry generation
 Geometry cleanup
 Meshing
 Solver
Solver  Problem specification
 Additional models
 Numerical computation
 Post Processor
 Line and Contour data
Post Processor
 Average Values
 Report Generation


1. Pre-processor

 Definition of the geometry of the region of interest: the computational
domain
 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 volumes
or elements)
 Accuracy of a solution, calculation time and cost in terms of necessary
computer hardware are dependent on the fineness of the grid.
 Over 50% of time spent in industry on a CFD project is devoted to the
definition of domain geometry and grid generation.
 Selection of the physical and chemical phenomena that need to be
modeled.
 Definition of fluid properties.
 Specification of appropriate boundary conditions at cells which coincide with
or touch the domain boundary


2. Solver

• CFD is the art of replacing the differential
equation governing the Fluid Flow, with a set
of algebraic equations (the process is called
discretization), which in turn can be solved
with the aid of a digital computer to get an
approximate solution.


Finite difference method

 Domain including the boundary of the physical
problem is covered by a grid or mesh
 At each of the interior grid point the original
Differential Equations are replaced by equivalent
finite difference approximations
 Truncated Taylor series expansions are often used
to generate finite difference approximations of
derivatives of  in terms of point samples of  at
each 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.


Finite Element Method
 The solution domain is discretized into number of small sub
regions (i.e. Finite Elements).
 Select an approximating function known as interpolation
polynomial to represent the variation of the dependent variable
over the elements.
 The piecewise approximating functions for  are substituted into
the equation it will not hold exactly and a residual is defined to
measure the errors.
 The integration of the governing differential equation (often
PDEs) with suitable weighting Function, over each elements to
produce a set of algebraic equations-one equation for each
element.
 The set of algebraic equations are then solved to get the
approximate solution of the problem.
 Structural Design, Vibration Analysis, Fluid Dynamics, Heat
Transfer and Magnetohydrodynamics


Finite volume method

 FLUENT, PHOENICS, and STAR-CD
 Integration of the governing equations of fluid flow over
all 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 of
finite – difference – type approximations for the terms in
the integrated equation representing flow process such
as convection, diffusion and sources. This converts the
integral equations into a system of algebraic equations.
 Solution of the algebraic equations by an iterative
method.


Rate of change of  in the Net flux of  due to
control volume with respect to = convection into the +
time control volume

Net flux of  due to
diffusion into the +
control volume

Net rate of creation
of  inside the
control volume


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 which
have only magnitude, not direction, such as temperature, pressure
and 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


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.



 Conservativeness – Local conservation of fluid
property for each control volume. It also ensures
global conservation of fluid property for the entire
domain.
 Boundedness – In a linear problem, without sources
the solution is bounded by the maximum and
minimum boundary values of the flow variables.
Similar to stability.
 Transportiveness – Numerical schemes must
account for the directionality of influencing in terms
of the relative strength of diffusion to convection.



 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.


 CFD is no substitute for experimental work, but a very powerful problem
solving tool.
 Comparison with experimental test work
High end – Velocity measurements by hot wire or laser Doppler
anemometer
Static pressure or temperature measurements with static pitot tube
traverse 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.g
ASME
 Main outcome of any CFD exercise is improved understanding of the
behaviour of the system.
 Main ingredients for success in CFD are experience and a thorough
understanding of the physics of the fluid flows and fundamentals of the
numerical algorithms.


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 solve
the fluid mechanics problem numerically on a computer.
 Commercial CFD codes may be extremely powerful, but their operation still
requires a high level of skill and understanding from the operator to obtain
meaningful results in complex situations.
 Users of CFD must know fundamentals of fluid dynamics, heat transfer,
turbulence, chemical reactions and numerical solution algorithms. They
must have adequate knowledge of the physics of the problem.
 In CFD, the user is responsible for correctly choosing the tools. He must
note that that CFD solution for a problem gets generated due the sequential
usage of chosen tools from the collection of tools available in the software.
 The user of CFD must get familiarized with all possible tools before he
starts using them. Best solutions are possible if correct tools are chosen in
the correct sequence.
 The quality of the results depends on the background of the user, quality of
the tools and the capability of the computer.


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.


Verification and Validation
 Verification and validation increase our confidence in the
simulation
 No computer software can be proved to have no errors.
 We can state that software is wrong if evidence to this effect can be
collected
 Verification is solving the chosen equations right
 Numerical techniques for verification involves finding out sources of
error in spatial & temporal discretisation, iterative convergence, and
rounding 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


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


WHAT IS IMPORTANT?

CFD
Numerical
Methods

Mathematics

Fluid Mechanics, Heat Transfer


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

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


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

Syllabus
1 Introduction: Definition and overview of CFD, need, Advantages of CFD, 2
Applications of CFD, CFD methodology, Convergence, consistency, stability,
iterative convergence, grid independence, Verification and validation
2 Governing equations of mass, momentum and energy : Derivation, 6
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
3 Discretisation methods – Introduction to Finite Difference Method, Finite Volume 6
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
4 Grid Generation: Structured and Unstructured Grids, General transformations of 4
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

Syllabus
5 Finite volume method for diffusion problems (Conduction): Steady state one 6
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 Finite volume method for advection-diffusion problems (Convection- 6
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
7 Solution algorithms for pressure velocity coupling in steady flows: 6
Staggered grids, SIMPLE, SIMPLER, SIMPLEC, PISO algorithms, unsteady flows
8 Turbulence modeling : Turbulence, its effect on governing equations, turbulence 4
models – k-ε , RSM, ASM, LES etc.
9 Post processing – xy plots, contour plots, vector plots, streamline plots etc. 2

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


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Introduction to cfd

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