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Numerical Simulations
ystem- eve pro ems
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
va a e commerc a co es uent, sta -c , xa, c -ace, c x etc.
Other structures codes with fluids capability ansys, algor, cosmosetc.
Supporting grid generation and post-processing codes
NASA and other government lab codes
Netlib, Lin ack routines for new code develo ment
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?
omputat ona u ynamcs s t e sc ence o pre ct ng
fluid flow, heat transfer, mass transfer, chemical reactions, and relatedphenomena by solving the mathematical equationswhich govern these
, .
The result of CFD analyses is relevant engineering data used in:
conceptual studies of new designs eta e pro uct eveopment
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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CFD - How It Works
Fillin nayss egns w t a mat ematca mo e
of a physical problem. Conservation of matter, momentum, and
Nozzle
Bottle
region of interest.
Fluid properties are modeled empirically.
to make the problem tractable (e.g., steady-state, incompressible, inviscid, two-dimensional).
Provide appropriate initial and/or boundaryconditions for the problem.
Domain for bottle fillingpro em.
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CFD - How It Works (2)
CFD applies numerical methods (calledscret zat on to eveop approx mat ons o t e
governing equations of fluid mechanics and the fluidregion to be studied.
overnng eren a equa ons age rac
The collection of cells is called thegrid or mesh.
The set of approximating equations are solvednumer ca y on a compuer or e ow evariables at each node or cell.
System of equations are solved simultaneously to.
The solution is post-processedto extract quantities ofinterest (e.g. lift, drag, heat transfer, separation points, Mesh for bottle filling
, . . .
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An Example: Water flow over a tube bank
Goal
compute average pressure drop, heattransfer 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 negligiblePhysical System can be modeled
ow s transatona y per o c .e.geometry repeats itself)
with repeating geometry.
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Mesh Generation
preprocessor for meshing. Mesh is generated for the fluid region
(and/or solid re ion for conduction).
A fine structured mesh is placedaround cylinders to help resolve
boundary layer flow.
remaining fluid areas.
Identify interfaces to which boundaryconditions will be applied.
cylindrical walls inlet and outlets
symmetry and periodic facesSection of mesh for tube bank problem
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Post-processing
xtract reevant engneer ng
data from solution in theform of:
x-y po s
contour plots
vector plots sur acevo ume negra on
forces
fluxes
partc e traector es
Temperature contours within the fluid region.
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Advantages of CFD
ow ost
Using physical experiments and tests to get essential engineering data fordesign can be expensive.
ompua ona smua ons are rea vey nexpensve, an coss are eyto decrease as computers become more powerful.
Speed smua ons can e execue n a s or per o o me.
Quick turnaround means engineering data can be introduced early in thedesign process
Many flow and heat transfer processes can not be (easily) tested - e.g.
hypersonic flow at Mach 20
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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 toisolate specific phenomena for study.
Example: a heat transfer process can be idealized with adiabatic, constant heatflux, or constant temperature boundaries.
Comprehensive Information
Experiments only permit data to beextracted at a limited number oflocations in the system (e.g. pressureand temperature probes, heat flux
, , .
CFD allows the analyst to examine alarge number of locations in the regionof interest, and yields a comprehensiveset of flow parameters forexamination.
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Limitations of CFD (2)
oun ary on t ons
As with physical models, the accuracy of the CFD solution is only as goodas the initial/boundary conditions provided to the numerical model.
xampe: ow n a uc w su en expanson
If flow is supplied to domain by a pipe, you should use a fully-developedprofile for velocity rather than assume uniform conditions.
ComputationalDomain
ComputationalDomain
Fully DevelopedInlet Profile
Uniform InletProfile
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Summary
omputatona u ynamcs s a power u way o mo e ng u
flow, heat transfer, and related processes for a wide range of importantscientific and engineering problems.
e cost o o ng as ecrease ramat ca y n recent years, anwill continue to do so as computers become more and more powerful.
Courtesy: Fluent, Inc.
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Numerical solution methods
onssency an runca on errors
As h-> 0, error -> 0 (hn, tn) Stability
Convergence
Gets close to exact solution
Physical quantities are conserved
Boundedness (Lies within physical bounds)
Realizability (Be able to model the physics)
Accuracy (Modeling, Discretization and Iterative solver errors)
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CFD Methodologies
nte erence met o
Simple grids (rectangular)
Complex geometries -> Transform to simple geometry (coordinaterans orma on
Finite volume method
Complex geometries (conserve across faces) Finite element metho
Complex geometries (element level transformation)
Spectral element method
Higher order interpolations in elements Lattice-gas methods
Basic momentum rinci le-base