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Introduction to Computational Fluid
Dynamics
Lecture 2: CFD Introduction
© Ram Ramanan
3/22/2016
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Numerical Simulations
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System-level CFD problems
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Component or detail-level problems
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Includes all components in the product
Identifies the issues in a specific component or a sub-component
Different tools for the level of analysis
Coupled physics (fluid-structure interactions)
© Ram Ramanan
3/22/2016
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CFD Codes
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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
© Ram Ramanan
3/22/2016
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What is Computational Fluid Dynamics?
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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:
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conceptual studies of new designs
detailed product development
troubleshooting
redesign
CFD analysis complements testing and experimentation.
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Reduces the total effort required in the laboratory.
Courtesy: Fluent, Inc
© Ram Ramanan
3/22/2016
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Applications
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Applications of CFD are numerous!
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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
© Ram Ramanan
3/22/2016
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CFD - How It Works
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Analysis begins with a mathematical model
of a physical problem.
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Bottle
Conservation of matter, momentum, and
energy must be satisfied throughout the
region of interest.
Fluid properties are modeled empirically.
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Filling
Nozzle
Simplifying assumptions are made in order
to make the problem tractable (e.g., steadystate, incompressible, inviscid, twodimensional).
Provide appropriate initial and/or boundary
conditions for the problem.
Domain for bottle filling
problem.
Courtesy: Fluent, Inc
© Ram Ramanan
3/22/2016
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CFD - How It Works (2)
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CFD applies numerical methods (called
discretization) to develop approximations of the
governing equations of fluid mechanics and the fluid
region to be studied.
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The set of approximating equations are solved
numerically (on a computer) for the flow field
variables at each node or cell.
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Governing differential equations  algebraic
The collection of cells is called the grid or mesh.
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.).
Courtesy: Fluent, Inc
Mesh for bottle filling
problem.
© Ram Ramanan
3/22/2016
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An Example: Water flow over a tube bank
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Goal
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compute average pressure drop, heat
transfer per tube row
Assumptions
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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)
Courtesy: Fluent, Inc
Physical System can be modeled
with repeating geometry.
© Ram Ramanan
3/22/2016
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Mesh Generation
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Geometry created or imported into
preprocessor for meshing.
Mesh is generated for the fluid region
(and/or solid region for conduction).
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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.
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cylindrical walls
inlet and outlets
symmetry and periodic faces
Courtesy: Fluent, Inc
Section of mesh for tube bank problem
© Ram Ramanan
3/22/2016
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Using the Solver
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Import mesh.
Select solver
methodology.
Define operating and
boundary conditions.
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e.g., no-slip, qw or
Tw at walls.
Initialize field and
iterate for solution.
Adjust solver
parameters and/or
mesh for convergence
problems.
Courtesy: Fluent, Inc
© Ram Ramanan
3/22/2016
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Post-processing
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Extract relevant engineering
data from solution in the
form of:
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x-y plots
contour plots
vector plots
surface/volume integration
forces
fluxes
particle trajectories
Temperature contours within the fluid region.
Courtesy: Fluent, Inc
© Ram Ramanan
3/22/2016
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Advantages of CFD
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Low Cost
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Speed
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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.
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
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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
3/22/2016
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Advantages of CFD (2)
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Ability to Simulate Ideal Conditions
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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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© Ram Ramanan
3/22/2016
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Limitations of CFD
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Physical Models
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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
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Solving equations on a computer invariably introduces numerical errors
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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
3/22/2016
.
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Limitations of CFD (2)
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Boundary Conditions
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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
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If flow is supplied to domain by a pipe, you should use a fully-developed
profile for velocity rather than assume uniform conditions.
Computational
Domain
Computational
Domain
Fully Developed
Inlet Profile
Uniform Inlet
Profile
poor
Courtesy: Fluent, Inc
better
© Ram Ramanan
3/22/2016
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Summary
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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
3/22/2016
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Numerical solution methods
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Consistency and truncation errors
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Stability
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Physical quantities are conserved
Boundedness (Lies within physical bounds)
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Gets close to exact solution
Conservation
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Converging methodology
Convergence
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As h-> 0, error -> 0 (hn, tn)
Higher order schemes can have overshoots and undershoots
Realizability (Be able to model the physics)
Accuracy (Modeling, Discretization and Iterative solver errors)
© Ram Ramanan
3/22/2016
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CFD Methodologies
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Finite difference method
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Finite volume method
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Complex geometries (element level transformation)
Spectral element method
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Complex geometries (conserve across faces)
Finite element method
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Simple grids (rectangular)
Complex geometries -> Transform to simple geometry (coordinate
transformation)
Higher order interpolations in elements
Lattice-gas methods
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Basic momentum principle-based
© Ram Ramanan
3/22/2016
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