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Introduction to Computational Introduction to Computational Fluid DynamicsFluid Dynamics
Adapted from notes by:
Tao Xing and Fred Stern
The University of Iowa
2
OutlineOutline
What is CFD?Why use CFD?Where is CFD used? PhysicsModelingNumericsCFD processResources
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What is CFD?What is CFD?
What is CFD and its objective?
– Computational Fluid Dynamics– Historically Analytical Fluid Dynamics (AFD) and EFD
(Experimental Fluid Dynamics) was used. CFD has become feasible due to the advent of high speed digital computers.
– Computer simulation for prediction of fluid-flow phenomena. – The objective of CFD is to model the continuous fluids with
Partial Differential Equations (PDEs) and discretize PDEs into an algebra problem (Taylor series), solve it, validate it and achieve simulation based design.
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Why use CFD?Why use CFD?
Why use CFD?– Analysis and Design
Simulation-based design instead of “build & test”– More cost effectively and more rapidly than with experiments– CFD solution provides high-fidelity database for interrogation of
flow field Simulation of physical fluid phenomena that are difficult to be
measured by experiments– Scale simulations (e.g., full-scale ships, airplanes)– Hazards (e.g., explosions, radiation, pollution)– Physics (e.g., weather prediction, planetary boundary layer,
stellar evolution)
– Knowledge and exploration of flow physics
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Where is CFD used? (Aerospace)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
F18 Store Separation
Wing-Body Interaction Hypersonic Launch Vehicle
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Where is CFD used? (Appliances)
• Where is CFD used?– Aerospace
– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
Surface-heat-flux plots of the No-Frost refrigerator and freezer compartments helped BOSCH-SIEMENS engineers to optimize the location of air inlets.
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Where is CFD used? (Automotive)
• Where is CFD used?– Aerospace– Appliances
– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
External Aerodynamics Undercarriage Aerodynamics
Interior Ventilation Engine Cooling
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Where is CFD used? (Biomedical)
• Where is CFD used?– Aerospace– Appliances– Automotive
– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
Temperature and natural convection currents in the eye following laser heating.
Spinal Catheter
Medtronic Blood Pump
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Where is CFD used? (Chemical Processing)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical
– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
Polymerization reactor vessel - prediction of flow separation and residence time effects.
Shear rate distribution in twin-screw extruder simulation
Twin-screw extruder modeling
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Where is CFD used? (HVAC&R)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing
– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
Particle traces of copier VOC emissions colored by concentration level fall behind the copier and then circulate through the room before exiting the exhaust.
Mean age of air contours indicate location of fresh supply air
Streamlines for workstation ventilation
Flow pathlines colored by pressure quantify head loss in ductwork
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Where is CFD used? (Hydraulics)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R
– Hydraulics– Marine– Oil & Gas– Power Generation– Sports
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Where is CFD used? (Marine)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics
– Marine– Oil & Gas– Power Generation– Sports
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Where is CFD used? (Oil & Gas)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine
– Oil & Gas– Power Generation– Sports
Flow vectors and pressure distribution on an offshore oil rig
Flow of lubricating mud over drill bit
Volume fraction of water
Volume fraction of oil
Volume fraction of gas
Analysis of multiphase separator
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Where is CFD used? (Power Generation)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas
– Power Generation– Sports
Flow pattern through a water turbine.
Flow in a burner
Flow around cooling towers
Pathlines from the inlet colored by temperature during standard operating conditions
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Where is CFD used? (Sports)
• Where is CFD used?– Aerospace– Appliances– Automotive– Biomedical– Chemical Processing– HVAC&R– Hydraulics– Marine– Oil & Gas– Power Generation
– Sports
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PhysicsPhysics
CFD codes typically designed for representation of specific flow phenomenon– Viscous vs. inviscid (no viscous forces) (Re)– Turbulent vs. laminar (Re)– Incompressible vs. compressible (Ma)– Single- vs. multi-phase (Ca)– Thermal/density effects and energy equation (Pr, , Gr, Ec)– Free-surface flow and surface tension (Fr, We)– Chemical reactions, mass transfer– etc…
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PhysicsPhysics
Fluid Mechanics
Inviscid Viscous
Laminar Turbulence
Internal(pipe,valve)
External(airfoil, ship)Compressibl
e(air, acoustic)
Incompressible(water)
Components of Fluid Mechanics
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Governing EquationsGoverning Equations
Continuity
Equation of motion
(Equations based on “average” velocity)(Equations based on “average” velocity)
xzxyxxxx
zx
yx
xx g
zyxx
p
z
uu
y
uu
x
uu
t
u
0
zyx uz
uy
uxt
Claude-Louis Navier George Gabriel Stokes
Navier-Stokes EquationsNavier-Stokes Equations
C.L. M. H. Navier, Memoire sur les Lois du Mouvements des Fluides, Mem. de l’Acad. d. Sci.,6, 398 (1822)C.G. Stokes, On the Theories of the Internal Friction of Fluids in Motion, Trans. Cambridge Phys. Soc., 8, (1845)
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Navier-Stokes EquationsNavier-Stokes Equations(constant (constant and and ))
gvpvD t
D 2
xxxxx
zx
yx
xx g
z
u
y
u
x
u
x
p
z
uu
y
uu
x
uu
t
u
2
2
2
2
2
2
yyyyy
zy
yy
xy g
z
u
y
u
x
u
y
p
z
uu
y
uu
x
uu
t
u
2
2
2
2
2
2
zzzzz
zz
yz
xz g
z
u
y
u
x
u
z
p
z
uu
y
uu
x
uu
t
u
2
2
2
2
2
2
Navier–Stokes ExampleNavier–Stokes Example
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Fluid
L
x
y
)x-Lx(2
1 Expression Final
0 2
L
Lat x 0 0,at x 0 B.C.
2
x Integrate
x Integrate
0
2y
21
21
2
y
1
2
2
gdy
pdu
Cgdy
pdC
uu
CxCgdy
pdu
Cgdy
pd
dx
ud
gdx
ud
dy
pd
yy
y
y
Laminar Flow Static Parallel Plates
yyyyy
zy
yy
xy g
z
u
y
u
x
u
y
p
z
uu
y
uu
x
uu
t
u
2
2
2
2
2
2
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ModelingModeling Mathematical representation of the physical problem
– Some problems are exact (e.g., laminar pipe flow)– Exact solutions only exist for some simple cases. In these cases nonlinear
terms can be dropped from the N-S equations which allow analytical solution.– Most cases require models for flow behavior [e.g., K-, K-, Reynolds
Averaged Navier Stokes equations (RANS) or Large Eddy Simulation (LES) for turbulent flow]
Initial —Boundary Value Problem (IBVP), include: governing Partial Differential Equations (PDEs), Initial Conditions (ICs) and Boundary Conditions (BCs)
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Turbulent Flow RepresentationTurbulent Flow Representation
(K- (K- as an example) as an example)
velocityousinstantaneu and flow, ofdirection in the
ty net velociconstant uvelocity,deviatingu': Whereu'uu
i
i
Turbulent Boundary LayerTurbulent Boundary Layer
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Wall
y
x
U0
Bulk Stream
Outer layer
Fully turbulent layer
Sublayer + buffer layer
Edge of boundary layer
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yuyy
uu
dy
Udw
y
w
ScaleLength Viscous Velocity Friction StressShear Wall
0
y+ is similar to a local Reynolds number. Small y+ - Viscous effects dominateLarge y+ - Turbulence dominates
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COMSOL has many turbulent models available
Low-Re models require a y+ resolution of < 1 to guarantee accuracy
Low-Re models are necessary to accurately estimate skin friction and flow separation
High-Re models use wall functions to approximate averaged turbulent flow properties
Less accurate, but more computationally efficientIn COMSOL, a minimum y+ of 11.06 is enforced. To maintain accuracy, ensure cells meet this requirement
yy++ and Turbulence Models and Turbulence Models
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Numerics / DiscretizationNumerics / Discretization
Computational solution of the IBVPMethod dependent upon the model equations and
physicsSeveral components to formulation
– Discretization and linearization– Assembly of system of algebraic equations– Solve the system and get approximate solutions
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Finite DifferencesFinite Differences
Methods of Solution
Direct methods Iterative methods
Cramer’s Rule, Gauss eliminationLU decomposition
Jacobi method, Gauss-SeidelMethod, SOR method
62
2
,
3
3
,
2
2,,1
,
x
x
ux
x
u
x
uu
x
u
jiji
jiji
ji
Finite differencerepresentation
Truncation error
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Numeric SolutionNumeric Solution (Finite Differences) (Finite Differences)
o xi i+1i-1
j+1j
j-1
imax
jmaxx
y
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3
,
3
32
,
2
2
,,,1
x
x
ux
x
ux
x
uuu
jijijijiji
Taylor’s Series Expansion u i,j = velocity of fluid
Discrete Grid Points
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Finite Difference Truncation ErrorFinite Difference Truncation Error
percentErrorfforsolutionExact
ff
xx
fxfxxf
xf
xfxat
xxf
n
x
x
fx
x
fx
x
fxfxxf
n
ji
n
n
ji
775.09823.0)22.0(
9899.0)02.0()]2.0(2cos[2)2.0()22.0(
)(
02.0????)22.0(
9511.0)(2.0:
2sin)(
!2)(
,
2
,
2
2
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CFD processCFD process
Geometry descriptionSpecification of flow conditions and propertiesSelection of modelsSpecification of initial and boundary conditionsGrid generation and transformationSpecification of numerical parametersFlow solutionPost processing: Analysis, and visualizationUncertainty assessment
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Geometry descriptionGeometry description
Typical approaches
– Make assumptions and simplifications
– CAD/CAE integration– Engineering drawings– Coordinates include Cartesian
system (x,y,z), cylindrical system (r, θ, z), and spherical system(r, θ, Φ)
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Flow conditions and propertiesFlow conditions and properties
Flow conditions and properties required are unique for each flow code and application– FlowLab requires all variables in dimensional
form– Because of focused application, research codes
often use non-dimensional variables.
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Selection of models for flow fieldSelection of models for flow field Direct Numerical Simulations (DNS) is to solve the N-S equations
directly without any modeling. Grid must be fine enough to resolve all flow scales. Applied for laminar flow and rare be used in turbulent flow.
Reynolds Averaged Navier-Stokes (NS) equations (RANS) is to perform averaging of NS equations and establishing turbulent models for the eddy viscosity. Too many averaging might damping vortical structures in turbulent flows
Large Eddy Simulation (LES), Smagorinsky’ constant model and dynamic model. Provide more instantaneous information than RANS did. Instability in complex geometries
Detached Eddy Simulation (DES) is to use one single formulation to combine the advantages of RANS and LES.
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Initial and boundary conditionsInitial and boundary conditionsFor steady/unsteady flow
IC should not affect final solution, only convergence path, i.e. iteration numbers needed to get the converged solution.
Robust codes should start most problems from very crude IC, . But more reasonable guess can speed up the convergence.
Boundary conditions– No-slip or slip-free on the wall, periodic, inlet (velocity
inlet, mass flow rate, constant pressure, etc.), outlet (constant pressure, velocity convective, buffer zone, zero-gradient), and non-reflecting (compressible flows, such as acoustics), etc.
36
Grid generationGrid generation Grids can either be structured (hexahedral) or
unstructured (tetrahedral). Depends upon type of discretization scheme and application
– Scheme Finite differences: structured Finite volume or finite element:
structured or unstructured– Application
Thin boundary layers best resolved with highly-stretched structured grids
Unstructured grids useful for complex geometries
Unstructured grids permit automatic adaptive refinement based on the pressure gradient, or regions of interest (FLUENT)
37
Grid ResolutionGrid Resolution
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Grid generation and transformationGrid generation and transformation
Grids designed to resolve important flow features which are dependent upon flow parameters (e.g., Re)
Commercial codes such as Gridgen, Gambit
For research code, grid generated by one of several methods (algebraic vs. PDE based, conformal mapping)
For complex geometries, body-fitted coordinate system will have to be applied (next slide). Grid transformation from the physical domain to the computational domain will be necessary
Sample grid established by Gambit of FLUENT
39
Grid transformationGrid transformationy
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 () domains, important for body-fitted grids. The partial derivatives at these two domains have the relationship (2D as an example)
40
Numerical parameters & flow Numerical parameters & flow solutionsolution
Numerical parameters are used to control flow solution. – Under relaxation factor, tridiagonal or pentadiagonal solvers – CFD Labs using FlowLab
Monitor residuals (change of results between iterations) Number of iterations for steady flow or number of time steps for unsteady flow
Flow solution– Solve the momentum, pressure Poisson equations and get flow field quantities, such as velocity, turbulence intensity,
pressure and integral quantities (drag forces)
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Numerical parameters & flow Numerical parameters & flow solution solution
Typical time history of residuals
The closer the flow field to the converged solution, the smaller the speed of the residuals decreasing.
Solution converged, residuals do not change after more iterations
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Post-processingPost-processing Analysis, and visualization
– Calculation of derived variables Vorticity Wall shear stress
– Calculation of integral parameters: forces, moments– Visualization (usually with commercial software)
Simple X-Y plots Simple 2D contours 3D contour carpet plots Vector plots and streamlines (streamlines are the lines
whose tangent direction is the same as the velocity vectors)
Animations (dozens of sample pictures in a series of time were shown continuously)
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Post-processing (Parallel Plates)Post-processing (Parallel Plates)
44
Post-Processing (example)Post-Processing (example)
Pressure contour and velocity vectors .
Note the locations of the highest and lowest pressure regions.
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Uncertainty assessmentUncertainty assessment Rigorous methodology for uncertainty assessment using
statistical and engineering concepts– Verification: process for assessing simulation numerical uncertainty
Iterative convergence: monitoring point & integral quantities should change within the convergence criterions
Grid independent studies: 3-grids and Richardson Extrapolation– Validation: process for assessing simulation modeling uncertainty by
using benchmark experimental data Certification: full Verification and Validation done for a
certain range of geometries & parameters which are well known and then extrapolated, qualitatively as well as quantitative
– Simulating flows for which experiments are difficult (e.g., full-scale Reynolds numbers, hypersonic flows, off-design conditions)
– Objective: Simulation-based design
CFD ExampleCFD Example
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Sulzer Chemtech250 Y Plastic Structured Packing
GeometryGeometry
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• CT > STL > CFD
• CT = 0.322 mm Min Resolution
• Copy/Pasted 2x
• Surface Wrapping
• Adaptive Meshing
• Tetrahedral Mesh
• Polyhedral Mesh
48
Mess DimensionsMess Dimensions
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Experiment vs. SimulationExperiment vs. Simulation
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Velocity MapVelocity Map
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Software and resourcesSoftware and resources CFD software was built upon physics, modeling, numerics. Two types of available software
– Commercial (e.g., FLUENT, CFX, Star-CCM, COMSOL)– Research (e.g., CFDSHIP-IOWA, U2RANS)
More information on CFD can be got on the following website:– CFD Online: http://www.cfd-online.com/– CFD software
FLUENT: http://www.fluent.com/ COMSOL http://www.comsol.com/ CD-adapco: http://www.cd-adapco.com/
– Grid generation software Gridgen: http://www.pointwise.com GridPro: http://www.gridpro.com/
– Visualization software Tecplot: http://www.amtec.com/ Fieldview: http://www.ilight.com/
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