©
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10/24/2013
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Introduction to Computational Fluid
Dynamics
Lecture 2: CFD Introduction
©
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Numerical Simulations
System

level CFD problems
Includes all components in the product
Component or detail

level problems
Identifies the issues in a specific component or a sub

component
Different tools for the level of analysis
Coupled physics (fluid

structure interactions)
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CFD Codes
Available commercial codes
–
fluent, star

cd, Exa, cfd

ace, cfx etc.
Other structures codes with fluids capability
–
ansys, algor, cosmos
etc.
Supporting grid generation and post

processing codes
NASA and other government lab codes
Netlib, Linpack routines for new code development
Mathematica or Maple for difference equation generation
Use of spreadsheets (and vb

based macros) for simple solutions
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What is Computational Fluid Dynamics?
Computational Fluid Dynamics
(CFD) is the science of predicting
fluid flow, heat transfer, mass transfer, chemical reactions, and related
phenomena by solving the
mathematical equations
which govern these
processes using a
numerical process
(that is, on a computer).
The result of CFD analyses is relevant engineering data used in:
conceptual studies of new designs
detailed product development
troubleshooting
redesign
CFD analysis complements testing and experimentation.
Reduces the total effort required in the laboratory.
Courtesy: Fluent, Inc
.
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Applications
Applications of CFD are numerous!
flow and heat transfer in industrial processes (boilers, heat exchangers,
combustion equipment, pumps, blowers, piping, etc.)
aerodynamics of ground vehicles, aircraft, missiles
film coating, thermoforming in material processing applications
flow and heat transfer in propulsion and power generation systems
ventilation, heating, and cooling flows in buildings
chemical vapor deposition (CVD) for integrated circuit manufacturing
heat transfer for electronics packaging applications
and many, many more...
Courtesy: Fluent, Inc
.
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10/24/2013
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CFD

How It Works
Analysis begins with a
mathematical model
of a
physical problem.
Conservation of matter, momentum, and
energy must be satisfied throughout the
region of interest.
Fluid properties are modeled empirically.
Simplifying assumptions
are made in order
to make the problem tractable (e.g., steady

state, incompressible, inviscid, two

dimensional).
Provide appropriate initial and/or boundary
conditions for the problem.
Domain for bottle filling
problem.
Filling
Nozzle
Bottle
Courtesy: Fluent, Inc
.
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CFD

How It Works (2)
CFD applies numerical methods (called
discretization
) to develop approximations of the
governing equations of fluid mechanics and the fluid
region to be studied.
Governing differential equations
algebraic
The collection of cells is called the
grid
or
mesh
.
The set of approximating equations are solved
numerically (on a computer) for the flow field
variables at each node or cell.
System of equations are solved simultaneously to
provide solution.
The solution is
post

processed
to extract quantities of
interest (e.g. lift, drag, heat transfer, separation points,
pressure loss, etc.).
Mesh for bottle filling
problem.
Courtesy: Fluent, Inc
.
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Ram Ramanan
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An Example: Water flow over a tube bank
Goal
compute average pressure drop, heat
transfer per tube row
Assumptions
flow is two

dimensional, laminar,
incompressible
flow approaching tube bank is steady with
a known velocity
body forces due to gravity are negligible
flow is translationally periodic (i.e.
geometry repeats itself)
Physical System can be modeled
with repeating geometry.
Courtesy: Fluent, Inc
.
©
Ram Ramanan
10/24/2013
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Mesh Generation
Geometry created or imported into
preprocessor for meshing.
Mesh is generated for the fluid region
(and/or solid region for conduction).
A fine structured mesh is placed
around cylinders to help resolve
boundary layer flow.
Unstructured mesh is used for
remaining fluid areas.
Identify interfaces to which boundary
conditions will be applied.
cylindrical walls
inlet and outlets
symmetry and periodic faces
Section of mesh for tube bank problem
Courtesy: Fluent, Inc
.
©
Ram Ramanan
10/24/2013
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Using the Solver
Import mesh.
Select solver
methodology.
Define operating and
boundary conditions.
e.g., no

slip, q
w
or
T
w
at walls.
Initialize field and
iterate for solution.
Adjust solver
parameters and/or
mesh for convergence
problems.
Courtesy: Fluent, Inc
.
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Post

processing
Extract relevant engineering
data from solution in the
form of:
x

y plots
contour plots
vector plots
surface/volume integration
forces
fluxes
particle trajectories
Temperature contours within the fluid region.
Courtesy: Fluent, Inc
.
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Advantages of CFD
Low Cost
Using physical experiments and tests to get essential engineering data for
design can be expensive.
Computational simulations are relatively inexpensive, and costs are likely
to decrease as computers become more powerful.
Speed
CFD simulations can be executed in a short period of time.
Quick turnaround means engineering data can be introduced early in the
design process
Ability to Simulate Real Conditions
Many flow and heat transfer processes can not be (easily) tested

e.g.
hypersonic flow at Mach 20
CFD provides the ability to theoretically simulate any physical condition
Courtesy: Fluent, Inc
.
©
Ram Ramanan
10/24/2013
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Advantages of CFD (2)
Ability to Simulate Ideal Conditions
CFD allows great control over the physical process, and provides the ability to
isolate specific phenomena for study.
Example: a heat transfer process can be idealized with adiabatic, constant heat
flux, or constant temperature boundaries.
Comprehensive Information
Experiments only permit data to be
extracted at a limited number of
locations in the system (e.g. pressure
and temperature probes, heat flux
gauges, LDV, etc.)
CFD allows the analyst to examine a
large number of locations in the region
of interest, and yields a comprehensive
set of flow parameters for
examination.
Courtesy: Fluent, Inc
.
©
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10/24/2013
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Limitations of CFD
Physical Models
CFD solutions rely upon physical models of real world processes (e.g.
turbulence, compressibility, chemistry, multiphase flow, etc.).
The solutions that are obtained through CFD can only be as accurate as
the physical models on which they are based.
Numerical Errors
Solving equations on a computer invariably introduces numerical errors
Round

off error

errors due to finite word size available on the computer
Truncation error

error due to approximations in the numerical models
Round

off errors will always exist (though they should be small in most
cases)
Truncation errors will go to zero as the grid is refined

so
mesh
refinement
is one way to deal with truncation error.
Courtesy: Fluent, Inc
.
©
Ram Ramanan
10/24/2013
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Limitations of CFD (2)
Boundary Conditions
As with physical models, the accuracy of the CFD solution is only as good
as the initial/boundary conditions provided to the numerical model.
Example: Flow in a duct with sudden expansion
If flow is supplied to domain by a pipe, you should use a fully

developed
profile for velocity rather than assume uniform conditions.
poor
better
Fully Developed
Inlet Profile
Computational
Domain
Computational
Domain
Uniform Inlet
Profile
Courtesy: Fluent, Inc
.
©
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10/24/2013
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Summary
Computational Fluid Dynamics is a powerful way of modeling fluid
flow, heat transfer, and related processes for a wide range of important
scientific and engineering problems.
The cost of doing CFD has decreased dramatically in recent years, and
will continue to do so as computers become more and more powerful.
Courtesy: Fluent, Inc
.
©
Ram Ramanan
10/24/2013
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Numerical solution methods
Consistency and truncation errors
As h

> 0, error

> 0 (h
n
, t
n
)
Stability
Converging methodology
Convergence
Gets close to exact solution
Conservation
Physical quantities are conserved
Boundedness (Lies within physical bounds)
Higher order schemes can have overshoots and undershoots
Realizability (Be able to model the physics)
Accuracy (Modeling, Discretization and Iterative solver errors)
©
Ram Ramanan
10/24/2013
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CFD Methodologies
Finite difference method
Simple grids (rectangular)
Complex geometries

> Transform to simple geometry (coordinate
transformation)
Finite volume method
Complex geometries (conserve across faces)
Finite element method
Complex geometries (element level transformation)
Spectral element method
Higher order interpolations in elements
Lattice

gas methods
Basic momentum principle

based
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