module 1 PPT.pptx

INTRODUCTION TO CFD
Uddhav Nimbalkar
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Introduction
2
 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.
 3 fundamental principles:
Mass is conserved (Continuity Equation)
Newton’s second law (Navier-Stokes Equation)
Energy is conserved (Energy Equation)
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Introduction
3
 Governing equations - PDE’s or integral
equations
 Analytical and experimental approach (Old)
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Numerical Approach (New)
4
 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
5
 CFD - Science of determining a numerical solution
to the governing equations of fluid flow while
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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Introduction
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 Scientific information such as boundary-
layer, flow separation, wake formation,
vortex shedding etc. is important in fluid
dynamics.
 Determination of quantities of engineering
interest: different types of forces (lift/drag),
heat transfer coefficient, wall shear stress,
pressure drop etc.
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disciplines
within
fluid
The different
contained
computational
dynamics
The three basic
to solve
in fluid
and heat
approaches
problems
dynamics
transfer
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Why CFD?
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 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
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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
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Analytical (theoretical) approach
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 Governing equations/mathematical models
(Conservation of mass, momentum and energy).
 Sometimes additional equations are needed:
equation of state, turbulence closure, chemical
reactions, etc.
 Analytical approach => “Closed-form” solutions.
 Often times requires use of advanced mathematical
techniques.
 Limited to simple geometrical and physical situations
– restricted use.
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Experimental approach
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 Dimensional analysis/model studies.
 Measurement of relevant quantities (velocity,
pressure, temperature, etc.).
 Analysis of measurement data – flow field
information.
 Capable of being most realistic.
 Equipment issues, scaling issues, measurement
issues.
 Time consuming, and can be very expensive.
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Computational (numerical) approach
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 Use of a computer to solve the governing equations.
 “Number crunching”, i.e., solution obtained in terms
of numbers.
 Analysis of solution (plotting, etc.).
 Can handle complicated geometries and physics.
numerical schemes, computational cost (still
 Truncation errors, model limitations, issues with
an
issue in some cases).
 Very affordable and hence highly popular, in recent
times.
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CFD - Third approach in fluid dynamics
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 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.
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Advantages of CFD
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 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.
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Advantages of CFD
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 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)
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Advantages of CFD
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 CFD is extensively employed as a design
and analysis tool in the industry.
 CFD enables compact and efficient
designs.
 CFD helps to locate optimum conditions
for the operation of engineering systems.
 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
testing costs
 Provides
engineering
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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1/19/2019 Arvind Deshpande (VJTI) 18
Benefits of CFD
Reduce System Cost
Improve Performance
Understand
Problems
Reduce Design Time
& Cost 18
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HOW IT DIFFERS FROM STRESS
ANALYSIS?
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 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
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 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: Design of hydraulic, steam, gas, wind
Turbines, pumps , compressors, blowers, fans etc.
 Flow and heat transfer in thermal power plants and
nuclear power reactors
 HVAC
 Manufacturing – Casting simulation, injection molding of
plastics
 Marine engineering: loads on off-shore structures
 Hydrodynamics of ships, submarines, torpedo etc.
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Applications of CFD
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 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
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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
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Flow through the turbine
draft tube
distributor
runner
rotating blades
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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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Fluid flows around thespinnaker
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
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on an F1 car
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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
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 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
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2. Solver
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• 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.
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Finite Difference Method (FDM)
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 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.
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Finite Element Method (FEM)
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 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
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Finite Volume Method (FVM)
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 Almost all well established and thoroughly validated general-
purpose commercial codes adopt the finite volume method as
their standard numerical solution technique. e.g. 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.
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3.Post-processor
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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 (temperature,
pressure) 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
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 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
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 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.
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CFD – A Big Picture
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 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.
 Without proper guidance, the use of commercial software
packages poses risks likened to placing potent weaponry in
the hands of poorly trained soldiers.
 There is every possibility of users with inadequate training
causing more harm than good through flawed interpretation of
results produced through such packages.
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CFD – A Big Picture
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 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.
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Identification and formulation of flow
problem
51
 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
52
 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
 Numerical techniques for verification involves finding out sources of
error in spatial & temporal discretization, iterative convergence, and
rounding off errors
 Checking out if time steps adequate for all situations
 Validation
 Is the simulation matching with experimental data
 Experimental data helps validation of similar simulations
 Scientific literature
 Verification is a mathematics and validation is a physics issue.
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What basics do you need to do develop a
successful student of CFD ?
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 Develop a thorough understanding of the
fundamentals of Fluid Mechanics, Heat Transfer
and CFD
 Get exposure to the physics
algorithms
 Develop good programming skills
and solution
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WHAT IS IMPORTANT?
54
CFD
Numerical
Methods
Mathematics
Fluid Mechanics, Heat Transfer
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WHAT IS IMPORTANT?
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 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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Conclusions
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• 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
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Governing equations of fluid flow
(Navier Stokes equations)
57
(Zmomentum)
(Y momentum)
(X momentum)
t
  div(V)  0(Mass)
i
t
P  RT &i  CvT(Equations of state)
(i)
 div(Vi)  pdivV  div(kgradT)    S (Internal Energy)
Mz
(w)
 div(Vw)  
p
 div(gradw)  S
t z
My
(v)
 div(Vv)  
p
 div(gradv)  S
t y
Mx
(u)
 div(Vu)  
p
 div(gradu) S
t x
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General Transport equation in
Differential form
58

t
()
 div(V)  div(grad)  S
Rate of
increase of φ
of fluid
element
Net rate of flow
of φ out of the
fluid element
Rate of increase of φ
due to diffusion
Rate of increase
of φ due to
sources
Basis for FDM
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General Transport equation in Integral
form
CV CV
59

CV  CV
 
 dv div(V)dv  div(grad)dv Sdv
t
Rate of increase Net rate of
of φ fluid element decrease of φ
due to convection
across the
boundaries
Net rate of increase
of φ due to diffusion
across the
boundaries
Net Rate of
creation of φ
Basis for FVM
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Gauss divergence theorem
 ^ 
div.Bdv  n.Bda
V A
) 60
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form
A A CV
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CV 
  
 dv n.(V)da  n.(grad)da Sdv
t
^ ^
Rate of increase Net rate of
of φ fluid element decrease of φ
due to convection
across the
boundaries
Net rate of increase
of φ due to diffusion
across the
boundaries
Net Rate of
creation of φ
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form
^ ^
n.(V)da  n.(grad)da Sdv(steady)
A A CV
I 62
^ ^
t A t A tCV
t CV 
  
t
 dvdt  n.(V)dadt  n.(grad)dadt  Sdvdt(unsteady)
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Boundary conditions
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 Real driver for any particular solution
 Dirichlet boundary condition - Specification of
dependent variables along the boundary
e.g. For Viscous flow, Wall boundary condition
V = Vw at the surface (No slip)
For a stationary wall, V = 0
Known wall temperature, T= Tw
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Newmann boundary condition
 Specification of
derivatives of dependent
variables along the
boundary
e.g. 1) if wall temperature
is changing due to heat
to the
transfer from or
surface
2) Adiabatic wall
 n

n

 T   0
K
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T
 n

n

 T   
q.
. 

 n

n

q   K
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Robbins Condition
The Derivative of the dependent variable is given as a
function of the dependent variable on the boundary.
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Inlet and outlet
 Inlet – Density, velocity and temperature at inlet
 Outlet – location where flow is approximately
unidirectional and where surface stresses take
known values.
 For external flows away from solid objects and
for internal flow, at a location where no change
in any of the velocity components in direction
across the boundary and Fn = -P & Ft = 0
 Specified pressure,
n
Arvind Deshpande (VJTI) 1/19/2019
66
 0,
T
 0
un
n
66
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Specifying Well Posed Boundary Conditions
for external flow
69
 In general, if the object has height H and width W, domain should be
at least more than : 5H high, 10W wide, with at least 2H
upstream of the object and 10 H downstream of the object
 Verify that there are no significant pressure gradients normal to any
of the boundaries of the computational domain. If there are, then it
would be wise to enlarge the size of the domain
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ANSYS FLUENT CFD Solver is based on
the Finite Volume method
***Domain is discretized into
a finite number of control
volumes.
***General conservation (transport)
equations for mass, momentum,
energy, species, etc. are solved on this set of control
volumes

Steps solving problem by ANSYS
FLUENT
To solve Engineering problems using ANSYS
FLUENT the necessary steps are-
(1)Pre-analysis
(2)Geometry
(3)Mesh
(4)Physical Setup
(5)Numerical Solution
(6)Verification & Validation

Steps for your Simulation
• Geometry: You have to make the geometry. You can
use ANSYS design modeler software, which you can use
from ANSYS WORKBENCH. You can also use any other
CAD Software you like, such as AutoCAD, Solidworks,
CATIA, Autocad Inventor etc.
• Meshing: Meshing is one of the most important step
for your simulation. Simulation results depend on
Mesh quality. Low quality Mesh can produce poor
simulation result, even divergence.
These steps are pre-possessing. In this
course, you don’t have to deal with Geometry & Mesh
now. These will be provided, so that you can start from
the next steps.

Steps for your Simulation
• Physical Setup: It is done in the solver ANSYS.
Your concentration will be to understand and
perform physical setup, numerical result, and
Verification & Validation.
In physical setup step, you give inputs
for solution accuracy, boundary condition,
physics involved, material involved, properties
of involved etc. In a nutshell, here you
numerically depict the real situation you want
to simulate.

FLUENT tabs
These tabs allow you to describe your
problem’s physics and control your
simulation. For this course, our
current objective is to be familiar with
these tabs, know some details about
them and use them for a successful
simulation. These will be discussed
briefly.

FLUENT tabs: General
First you have to deal with this
tab. Here you will define general
type of your case, for example
time is steady/transient.

FLUENT tabs: General
• Two types of solvers are available-Pressure based &
Density based. Details about these tabs are beyond the
scope of this course.
• You can remember a rule of thumb, if density is not
changing then you will use Pressure based solver.
• Pressure based solver is the default, and should used
for most cases, handles the Mach number in the range
0~2-3.
• For solving higher Mach number problems, Density
based solver are used. Or they are used for special
cases, for example, to capture interacting shock waves.

FLUENT tabs: Models
***Here you actually define
the governing equation
(or Model) you want
to use to solve your problem.
***If you select
viscous-Laminar, continuity &
N-S equations suitable for
Laminar flows are on. If you
on Energy, Energy equation
will on in your solver. For
Viscous- Turbulent models
equations would be solved
for turbulent flow, and solver
will include relevant turbulent
models to solve your problem.

FLUENT tabs: Models
• Most of the time we will use viscous-laminar & viscous-
turbulence models.
• Viscous-laminar model is straight forward, it is very
simple to use.
• Viscous-turbulent models have different varieties.
There are 1, 2, 3 equations turbulent models. 2
equations models, especially k-epsilon & k-omega
models are very popular. We will use k-epsilon
standard model immediately. After selecting K-epsilon
Standard model you have to choose wall functions- we
will use enhanced wall function in our immediate
analysis.

FLUENT tabs: Materials
This tab is like a inventory. You can use the
edit/create button to copy any material
from ANSYS database, or edit properties of
the selected material. Here you will keep all
the material you are working with, or you
want to work in future.

FLUENT tabs: Cell Zone condition
Here you will select material form the material zone,
to your cell zone. First, you have to select the zone for
modification, then select the material type from the
option tab called type , then press edit to select the
material.

FLUENT tabs: Boundary condition
You have to use the
type, edit options to
assign the boundary
conditions.

• Here you have to select boundary type for each
boundary(surface/edge/point) of your case geometry.
• Available Boundary conditions type: Here various
boundary types are given for your reference. Later
description of the important boundary types will be given.
• External Boundaries:
General:
-Pressure Inlet
-Pressure outlet
Incompressible:
-Velocity inlet
-Outflow

Compressible
-Mass flow inlet
-Pressure far field
Other
-Wall
-Symmetry
-Axis
-Periodic
Special
-Inlet/Outlet vent
-Intake/Exhaust Fan
Internal Boundaries
-Fan
-Interior
-Porous Jump
-Radiator
-Wall

• Above mentions boundary types is only for reference. You will
encounter will all of them in Future if you work in CFD. Presently
you can concentrate to understand only the most commonly used
boundary types. These will be discussed now in brief.
• Velocity Inlet:
-These are suitable for incompressible flow, and not recommended for
compressible flow.
-It applies a uniform velocity profile at the boundary unless UDF (user
defined function) is used.
-Velocity specification method s:
(1)Magnitude normal to boundary
(2)Components
(3)Magnitude and direction
(4)Turbulent quantities (if you are using turbulent models)
(5)Thermal conditions(if Energy equation is on)

• Pressure Outlet: It is suitable for both
incompressible and compressible flow. Here the
input is the static gauge pressure of the
environment into which the flow exists.
• Wall Boundaries: It works like physical wall. In
viscous flow, no slip conditions are applied at
walls. For Turbulent flows, wall roughness can be
defined.
• Axis boundaries: These are only used for 2D
axisymmetric flows. Here no user inputs are
required. It defines the axis of symmetry.

FLUENT tabs: Dynamic Mesh
• You can ship this step now. It is used only for
simulating moving objects, such as for
simulation a moving turbine blade.

FLUENT tabs: Reference Values
***In the compute from option, you will choose from
where computation will start, in most cases it is the inlet.
***In the reference zone, you will select the zone that
represent your whole computational domain.
***You have to select other reference values for your
problem. These values are uses only for calculation some
additional quantity, such as to calculate Drag coefficient,
or skin friction coefficient. General solution of the
simulation is not affected by the reference values.
For example, the solution of continuity & N-S equations
are not affected by the reference values.

FLUENT tabs: Solution Methods
***Here you will select the
solution method you want to use.
Each method has it’s own benefit &
weaknesses. You can also choose
the discretization method for
pressure & momentum.
***Try to use Second order upwind
for discretization. Second order
schemes give more accurate result,
and first order scheme helps in
convergence.

FLUENT tabs: Solution Methods
• SIMPLE method is very popular & widely used.
We will use SIMPLE method in our first
examples in classes.
• Coupled method is also popular, and helps in
convergence. If you get divergence in SIMPLE
method for any simulation, you can try to use
Coupled method, sometimes this technique
solves the problem of divergence.

FLUENT tabs: Solution Control
***We will use default values in this
tab. But if you get divergence under
SIMPLE method, you can lower the
under-factor for the variable that
causing the error.

FLUENT tabs: Solution Monitors

FLUENT tabs: Solution Control
• Here you can monitor your simulation. In the
residual monitor you can select the level of
floating point accuracy you want. You can add
additional monitors for additional properties.
For example, you can add additional monitors
to plot drag coefficient, lift coefficient,
momentum coefficient. We will demonstrate
these in classes.

FLUENT tabs: Solution Initialization
***Before run your simulation, you have
to initialize the simulation. You can
both standard & Hybrid initialization.
***In Standard initialization, all cells
have the same value at initial.
***Hybrid initialization makes
non-uniform initial guess, which is
sometimes helpful, specially for
complex geometry hybrid initialization
sometimes results convergence in less
iteration.

FLUENT tabs: Calculation activity
***You can Autosave your
simulation result
(case & data files) after a fixed
iteration.

FLUENT tabs: Run Calculation
***Here you simply command that
how many iterations you want to
perform.
***Here Solver setting ends.

Next Steps
• The steps are post processing, i.e., analyzing your
simulation results and data, and verification.
• We will use CFD-post for post processing. We can
also use FLUENT solver for post-processing, but
CFD-post is easier & convenient.
• We want to verify whether or not our simulation
is correct? For verification, we can check whether
basic physical laws are maintained or not, using
FLUENT. For example, we can check that, does
our solution satisfy continuity equation? We will
see details about it in class.

Opening CFD Post
***If you open Solution tab from
FLUENT tree in WORKBENCH, CFD
post will open.
***We will work in CFD-post in
classes.

Other boundary conditions
 Open boundary
condition
 Symmetry boundary
condition
 Cyclic boundary
condition 1 2
99
 0
 0
 

n
n
un
TCET

Problem
Figure shows a large plate of
thickness L = 2 cm with constant
thermal conductivity of 0.5 W/m-K
and uniform heat generation of 1000
kW/M3. The faces A and B are at
1000C and 2000C respectively.
Assuming that the dimensions in the
y- and z-direction are so large that
temperature gradients are significant
in x-direction only, calculate the
steady state temperature
distribution. Compare the numerical
result with the analytical solution.
10
0
TCET

state heat
One dimensional steady
conduction with heat generation
𝑑 𝑑
𝑇
𝑑
𝑥 𝑑
𝑥
𝑘 + 𝑞= 0
𝑑2𝑇 𝑞
𝑑𝑥2+
𝑘
= 0
10
1
TCET

Finite Difference Method
𝑑2𝑇 𝑇𝑖−1− 2𝑇𝑖
+ 𝑇𝑖+1
𝑑𝑥2 =
∆𝑥2
𝑇𝑖−1− 2𝑇𝑖
+ 𝑇𝑖+1
+
𝑞
= 0
∆𝑥 2 𝑘
𝑖
− 1 𝑖
𝑇 − 2𝑇 + 𝑇𝑖
+1
𝑘
𝑞
= − ∆𝑥2
10
2
TCET

Finite Difference Method
10
3
𝑇1= 100
𝑇1 − 2𝑇2 + 𝑇3 = −32
𝑇2 − 2𝑇3 + 𝑇4 = −32
𝑇3 − 2𝑇4 + 𝑇5 = −32
𝑇4 − 2𝑇5 + 𝑇6 = −32
𝑇6= 200
TCET

Matrix form
10
4

100 



   

  
   
200
32
32
32
32

0
0


0
0
1
1 0 0 0 0
2 1 0 0
1  2 1 0
0 1 2 1
0 0 1 2
0 0 0 0
3
2 
1T6
1T5

0T4 
0 T
0T 
0T1 
TCET

Analytical solution
A
10
5


 TA 
q
L xx
TB
T  T
L 2k
Node Distance
(cm)
FDM
Solution
Analytical
Solution
1 0 100 100
2 0.4 184 184
3 0.8 236 236
4 1.2 256 256
5 1.6 244 244
6 2 200 200
TCET

Finite Volume Method
T=100 T=200
x=0 X=L
A
1
B
7
2 3 5 6
P
W w e E
Δx
4
(δx)w (δx)e
78 Arvind Deshpande(VJTI)
1/19/2019 10
6
TCET

𝑒
𝑤 𝑑𝑥
𝑑 𝑑
𝑇
𝑑
𝑥
𝑒
𝑘 𝑑𝑥+ 𝑞
𝑑
𝑥= 0
𝑤
𝑘
𝑑
𝑇
𝑑
𝑥
𝑑
𝑇
𝑑
𝑥
− 𝑘 + 𝑞∆𝑥= 0
𝑒 𝑤
𝑇𝐸− 𝑇𝑃
𝑘𝑒
𝛿𝑥 𝑒
𝑇𝑃− 𝑇𝑊
𝑤
− 𝑘𝑤
𝛿𝑥
+ 𝑞∆𝑥= 0
𝑘𝑤
𝛿𝑥𝑤
+
𝑘𝑒
𝛿𝑥𝑒
𝑇𝑃
=
𝑘𝑤
𝑊
𝑇 +
𝛿𝑥 𝑤 𝛿𝑥𝑒
𝑘𝑒
𝐸
10
7
𝑇 + 𝑞∆𝑥
𝑎𝑃𝑇𝑃= 𝑎𝑊 𝑇𝑊+ 𝑎𝐸𝑇𝐸
+ 𝑞∆𝑥
TCET

Finite Volume Method
10
8
𝑇1 = 100
−250𝑇1 + 3752𝑇2 − 125𝑇3 = 4000
−125𝑇2 + 250𝑇3 − 125𝑇4 = 4000
−125𝑇3 + 250𝑇4 − 125𝑇5 = 4000
−125𝑇4 + 250𝑇5 − 125𝑇6 = 4000
−125𝑇5 + 375𝑇6 − 250𝑇7 = 4000
𝑇7 = 200
TCET

Matrix form
10
9


 
 100 
  
   

4000
4000
4000
4000
4000
4000
2 
0T6 
T7

T5

T4
T3
T 
T1 










1 0 0 0 0 0 0
250 375 125 0 0 0 0
0 125 250 125 0 0 0
0 0 125 250 125 0 0
0 0 0 125 250 125 0
0 0 0 0 125 375 25
0 0 0 0 0 0 1
TCET

Analytical solution
A
11
0


 TA 
q
L xx
TB
T  T
L 2k
Node Distance
(cm)
FVM
Solution
Analytical
Solution
1 0 100 100
2 0.2 146 150
3 0.6 214 218
4 1.0 250 254
5 1.4 254 258
6 1.8 226 230
7 2 200 200
TCET

References
11
1
1. S V Patankar, Numerical Heat Transfer and Fluid Flow, ANE BOOKS-NEW DELHI,
Special Indian First Edition
2. H K Versteeg and W. Malalasekera, An Introduction to Computational Fluid
Dynamics-The Finite Volume Method, Pearson Education, Second Indian Edition,
2010
3. Atul Sharma, Introduction to Computational Fluid Dynamics: Development,
Application and Analysis, Ane books Pvt.Ltd., 2016
4. Jiyuan Tu, Guan Heng Yeoh, Chaoqun Liu, Computational Fluid Dynamics: A
Practical Approach, Elsevier, Second Edition, 2012
5. John. D. Anderson, Jr., Computational Fluid Dynamics - The basics with applications,
McGraw-Hill, Indian Edition , 2012
6. A.W. Date, Introduction to Computational Fluid Dynamics, Cambridge University
Press, 2005
7. Ferziger and Peric, Computational Methods for Fluid Dynamics, Springer, Third
Edition, 2008
TCET

References
11
2
 Web Sites
www.cfd-online.com
http://cfdmadeeasy.org/
TCET

NPTEL Courses (Web)
11
3
1. http://nptel.ac.in/courses/112107080/ - Computational
Fluid Dynamics by Dr. K. M. Singh, IIT Roorkee
2. http://nptel.ac.in/courses/112104030/ - Computational
Fluid Dynamics and Heat Transfer by Prof. Gautam
Biswas, IIT Kanpur
TCET

NPTEL Courses (Video)
1. http://nptel.ac.in/courses/112107079/ - Computational Fluid
Dynamics by Dr. K. M. Singh, IIT Roorkee
Dynamics by Prof. Sreenivas Jayanti , IIT Madras
Dynamics by Prof. Sreenivas Jayanti , IIT Madras
Dynamics by Prof. S. Chakraborty, IIT Kharagpur
Dynamics by Prof. S. Chakraborty, IIT Kharagpur
6. http://nptel.ac.in/courses/112106186/ - Foundation of
Computational Fluid Dynamics by Prof. S. Vengadeshan, IIT
Madras
11
4
TCET

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