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Introduction to Computational
Fluid Dynamics (CFD)
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Computational fluid dynamicsFluid dynamics is the science of fluid motion.
Fluid flow is commonly studied in one of three ways:Experimental fluid dynamics.
Theoretical fluid dynamics.
Numerically: computational fluid dynamics (CFD).
Computational fluid dynamics (CFD) is the science of predicting
fluid flow, heat transfer, mass transfer, chemical reactions, andrelated phenomena by solving the mathematical equationswhich govern these processes using a numerical process.
The result of CFD analyses is relevant engineering data used in:
Conceptual studies of new designs.
Detailed product development.
Troubleshooting.
Redesign.
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CFD analysis complements testing and experimentation.
Reduces the total effort required in the laboratoryHistorically only Analytical Fluid Dynamics (AFD) and Experimental FluidDynamics (EFD).
CFD made possible by the advent of digital computer and advancingwith improvements of computer resources
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Why use CFD?
Analysis and Design1. Simulation-based design instead of build & testMore cost effective and more rapid than EFD
CFD provides high-fidelity database for diagnosing flowfield
2. Simulation of physical fluid phenomena that aredifficult for experimentsFull scale simulations (e.g., ships and airplanes)
Environmental effects (wind, weather, etc.)
Hazards (e.g., explosions, radiation, pollution)
Physics (e.g., planetary boundary layer, stellar
evolution)
Knowledge and exploration of flow physics
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Where is CFD used?
Where is CFD used?
Aerospace
Automotive
Biomedical
ChemicalProcessing
HVAC
Hydraulics
Marine
Oil & Gas Power Generation
Sports
F18 Store Separation
Temperature and naturalconvection currents in the eyefollowing laser heating.
Aerospace
Automotive
Biomedical
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Where is CFD used?
Polymerization reactor vessel - predictionof flow separation and residence timeeffects.
Streamlines for workstationventilation
Where is CFD used? Aerospacee
Automotive
Biomedical
ChemicalProcessing
HVAC
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
HVAC
Chemical Processing
Hydraulics
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Where is CFD used?
Where is CFD used? Aerospace
Automotive
Biomedical
Chemical Processing HVAC
Hydraulics
Marine
Oil & Gas
Power Generation Sports
Flow of lubricating
mud over drill bit Flow around coolingtowers
Marine (movie)
Oil & Gas
Sports
Power Generation
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Domain for bottle filling
problem.
Filling
Nozzle
Bottle
CFD - how it works
Analysis begins with a mathematicalmodel of a physical problem.
Conservation of matter, momentum, andenergy must be satisfied throughout theregion of interest.
Fluid properties are modeled empirically.
Simplifying assumptions are made inorder to make the problem tractable(e.g., steady-state, incompressible,inviscid, two-dimensional).
Provide appropriate initial and boundaryconditions for the problem.
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Mesh for bottle filling
problem.
CFD - how it works (2)CFD applies numerical methods (calleddiscretization) to develop approximations
of the governing equations of fluidmechanics in the fluid region of interest.
Governing differential equations: algebraic.
The collection of cells is called the grid.
The set of algebraic equations are solvednumerically (on a computer) for the flow fieldvariables at each node or cell.
System of equations are solved simultaneouslyto provide solution.
The solution is post-processed to extractquantities of interest (e.g. lift, drag,torque, heat transfer, separation,pressure loss, etc.).
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CFD process
Purposesof CFD codes will be different for different
applications: investigation of bubble-fluid interactions for bubblyflows, study of wave induced massively separated flows forfree-surface, etc.
Depend on the specific purpose and flow conditions of theproblem, different CFD codescan be chosen for differentapplications (aerospace, marines, combustion, multi-phaseflows, etc.)
Once purposes and CFD codes chosen, CFD process is thesteps to set up the IBVP problem and run the code:
1. Geometry
2. Physics3. Mesh
4. Solve
5. Reports
6. Post processing
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CFD Process
Viscous
Model
Boundary
Conditions
Initial
Conditions
Convergent
Limit
Contours
Precisions
(single/
double)
Numerical
Scheme
Vectors
StreamlinesVerification
Geometry
Select
Geometry
Geometry
Parameters
Physics Mesh Solve Post-
Processing
Compressible
ON/OFF
Flow
properties
Unstructured
(automatic/
manual)
Steady/
Unsteady
Forces Report(lift/drag, shear
stress, etc)
XY Plot
Domain
Shape and
Size
Heat Transfer
ON/OFF
Structured
(automatic/
manual)
Iterations/
Steps
Validation
Reports
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Geometry
Selection of an appropriate coordinate
Determine the domain size and shape
Any simplifications needed?
What kinds of shapes needed to be used to best
resolve the geometry? (lines, circular, ovals, etc.) For commercial code, geometry is usually createdusing commercial software (either separated from thecommercial code itself, like Gambit, or combinedtogether, like FlowLab)
For research code, commercial software (e.g.Gridgen) is used.
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Physics Flow conditions and fluid properties
1. Flow conditions: inviscid, viscous, laminar, orturbulent, etc.
2. Fluid properties: density, viscosity, and
thermal conductivity, etc.
3. Flow conditions and properties usually presented indimensional form in industrial commercial CFDsoftware, whereas in non-dimensional variables forresearch codes.
Selection of models: different models usually fixed bycodes, options for user to choose
Initial and Boundary Conditions: not fixed by codes,user needs specify them for different applications.
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Mesh
Meshes should be well designed to resolveimportant flow features which are dependent uponflow condition parameters (e.g., Re), such as thegrid refinement inside the wall boundary layer
Mesh can be generated by either commercial codes(Gridgen, Gambit, etc.) or research code (usingalgebraic vs. PDE based, conformal mapping, etc.)
The mesh, together with the boundary conditionsneed to be exported from commercial software in a
certain format that can be recognized by theresearch CFD code or other commercial CFDsoftware.
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Reports Reports saved the time history of the residuals of
the velocity, pressure and temperature, etc.
Report the integral quantities, such as total pressuredrop, friction factor (pipe flow), lift and dragcoefficients (airfoil flow), etc.
XY plots could present the centerlinevelocity/pressure distribution, friction factordistribution (pipe flow), pressure coefficientdistribution (airfoil flow).
AFD or EFD data can be imported and put on top ofthe XY plots for validation
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Post-processing Analysis and visualization
Calculation of derived variablesVorticity
Wall shear stress
Calculation of integral parameters: forces,moments
Visualization (usually with commercialsoftware) Simple 2D contours
3D contour isosurface plots
Vector plots and streamlines(streamlines are the lines whose
tangent direction is the same as thevelocity vectors)
Animations
Post-processing usually through usingcommercial software
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DiscretizationDomain is discretized into a finite set of control volumesor cells. The discretized domain is called the grid or the
mesh.
General conservation (transport) equations for mass,momentum, energy, etc., are discretized into algebraicequations.
All equations are solved to render flow field.
VAAV
dVSdddVt
AAV
unsteady convection diffusion generation
Eqn.
continuity 1
x-mom. u
y-mom. v
energy h
Fluid region of
pipe flow
discretized intofinite set of
control volumes
(mesh).
control
volume
D i d h id
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Design and create the gridShould you use a quad/hex grid, a tri/tet grid, a hybridgrid, or a non-conformal grid?
What degree of grid resolution is required in eachregion of the domain?
How many cells are required for the problem?
Will you use adaption to add resolution?Do you have sufficient computer memory?
triangle
quadrilateral
tetrahedron pyramid
prism or wedgehexahedronarbitrary polyhedron
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Tri/tet vs. quad/hex meshes
For simple geometries, quad/hex
meshes can provide high-qualitysolutions with fewer cells than acomparable tri/tet mesh.
For complex geometries,quad/hex meshes show nonumerical advantage, and youcan save meshing effort by usinga tri/tet mesh.
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Hybrid mesh example
Valve port grid.
Specific regions can be meshedwith different cell types.
Both efficiency and accuracy areenhanced relative to ahexahedral or tetrahedral meshalone.
Hybrid mesh for an
IC engine valve port
tet mesh
hex mesh
wedge mesh
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Grids can either be structured(hexahedral) or unstructured(tetrahedral). Depends upon type ofdiscretization scheme and application
Scheme Finite differences: structured
Finite volume or finite element:
structured or unstructured Application
Thin boundary layers bestresolved with highly-stretchedstructured grids
Unstructured grids useful forcomplex geometries
Unstructured grids permitautomatic adaptive refinementbased on the pressure gradient,or regions interested (FLUENT)
structured
unstructured
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Example of CFD Process (Mesh)
Grid need to be refined near the
foil surface to resolve the boundary
layer
N i l th d ( id
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Numerical methods (gridtransformation)
y
xo o
Physical domain Computational domain
x x
f f f f f
x x x
y y
f f f f f
y y y
Transformation between physical (x,y,z)
and computational (,,z) domains,important for body-fitted grids. The partial
derivatives at these two domains have the
relationship (2D as an example)
Transform
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Solvers and numerical parameters Solversinclude: tridiagonal, pentadiagonal solvers,,
solution-adaptive solver, multi-grid solvers, etc. Solvers can be either direct (Cramers rule, Gauss
elimination, LU decomposition) or iterative (Jacobimethod, Gauss-Seidel method, SOR method)
Numerical parameters need to be specified to control
the calculation. Under relaxation factor, convergence limit, etc. Different numerical schemes Monitor residuals (change of results between
iterations)
Number of iterations for steady flow or number oftime steps for unsteady flow
Single/double precisions
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Example of CFD Process (Solve)
Residuals vs. iteration
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Example of CFD Process (Reports)
E l f CFD P (P t i )
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Example of CFD Process (Post-processing)
Di h l
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Dinosaur mesh example
S t th i l d l
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Set up the numerical modelFor a given problem, you will need to:
Select appropriate physical models.Turbulence, combustion, multiphase, etc.
Define material properties.Fluid.
Solid.
Mixture.
Prescribe operating conditions.
Prescribe boundary conditions at all boundaryzones.
Provide an initial solution.
Set up solver controls.
Set up convergence monitors.
Compute the solution
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Compute the solutionThe discretized conservation equations are solvediteratively. A number of iterations are usually
required to reach a converged solution.
Convergence is reached when:
Changes in solution variables from one iteration to the nextare negligible.
Residuals provide a mechanism to help monitor this trend.Overall property conservation is achieved.
The accuracy of a converged solution is dependentupon:
Appropriateness and accuracy of the physical models.Grid resolution and independence.
Problem setup.
Examine the results
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Examine the resultsVisualization can be used to answer suchquestions as:
What is the overall flow pattern?
Is there separation?
Where do shocks, shear layers, etc. form?
Are key flow features being resolved?Are physical models and boundary conditionsappropriate?
Numerical reporting tools can be used to calculate
quantitative results, e.g:Lift, drag, and torque.
Average heat transfer coefficients.
Surface-averaged quantities.
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Velocity vectors around a dinosaur
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Velocity magnitude (0-6 m/s) on adinosaur
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Pressure field on a dinosaur
Forces on the dinosaur
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Forces on the dinosaurDrag force: 17.4 N.
Lift force: 5.5 N.
Wind velocity: 5 m/s.
Air density: 1.225 kg/m3.
The dinosaur is 3.2 m tall.
It has a projected frontal area of A = 2.91 m2
.The drag coefficient is:
11.091.2*25*225.1*5.0
4.17
2
2
1
Av
FC D
D
Consider revisions to the model
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Consider revisions to the model
Are physical models appropriate?Is flow turbulent?
Is flow unsteady?Are there compressibility effects?
Are there 3D effects?
Are boundary conditions correct?
Is the computational domain large enough?Are boundary conditions appropriate?
Are boundary values reasonable?
Is grid adequate?Can grid be adapted to improve results?
Does solution change significantly with adaption, or is the solutiongrid independent?
Does boundary resolution need to be improved?
Advantages of CFD
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Advantages of CFDRelatively low cost.
Using physical experiments and tests to get essential
engineering data for design can be expensive.CFD simulations are relatively inexpensive, and costs are likelyto 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 introducedearly in the design process.
Ability to simulate real conditions.
Many flow and heat transfer processes can not be (easily)
tested, e.g. hypersonic flow.
CFD provides the ability to theoretically simulate any physicalcondition.
Advantages of CFD (2)
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Advantages of CFD (2)
Ability to simulate ideal conditions.
CFD allows great control over the physical process, andprovides the ability to isolate specific phenomena for study.
Example: a heat transfer process can be idealized withadiabatic, constant heat flux, or constant temperatureboundaries.
Comprehensive information.Experiments only permit data to be extracted at a limitednumber of locations in the system (e.g. pressure andtemperature probes, heat flux gauges, LDV, etc.).
CFD allows the analyst to examine a large number of locationsin the region of interest, and yields a comprehensive set offlow parameters for examination.
Limitations of CFD
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Limitations of CFDPhysical models.
CFD solutions rely upon physical models of real world
processes (e.g. turbulence, compressibility, chemistry,multiphase flow, etc.).
The CFD solutions can only be as accurate as the physicalmodels on which they are based.
Numerical errors.
Solving equations on a computer invariably introducesnumerical errors.
Round-off error: due to finite word size available on thecomputer. Round-off errors will always exist (though they can
be small in most cases).Truncation error: due to approximations in the numericalmodels. Truncation errors will go to zero as the grid is refined.Mesh refinement is one way to deal with truncation error.
Limitations of CFD (2)
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poor better
Fully Developed Inlet
Profile
Computational
Domain
Computational
Domain
Uniform Inlet
Profile
Limitations of CFD (2)
Boundary conditions.
As with physical models, the accuracy of the CFDsolution is only as good as the initial/boundaryconditions provided to the numerical model.
Example: flow in a duct with sudden expansion. If
flow is supplied to domain by a pipe, you shoulduse a fully-developed profile for velocity ratherthan assume uniform conditions.
Summary
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Summary
CFD is a method to numerically calculate heattransfer and fluid flow.
Currently, its main application is as an engineeringmethod, to provide data that is complementary totheoretical and experimental data. This is mainly thedomain of commercially available codes and in-house
codes at large companies.CFD can also be used for purely scientific studies,e.g. into the fundamentals of turbulence. This ismore common in academic institutions and
government research laboratories. Codes are usuallydeveloped to specifically study a certain problem.