2. 2
Outline
What is CFD?
Why use CFD?
Where is CFD used?
Physics
Modeling
Numerics
CFD process
Resources
3. 3
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.
4. 4
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
5. 5
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
6. 6
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.
7. 7
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
8. 8
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
9. 9
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
10. 10
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
11. 11
Where is CFD used? (Hydraulics)
• Where is CFD used?
– Aerospace
– Appliances
– Automotive
– Biomedical
– Chemical Processing
– HVAC&R
– Hydraulics
– Marine
– Oil & Gas
– Power Generation
– Sports
12. 12
Where is CFD used? (Marine)
• Where is CFD used?
– Aerospace
– Appliances
– Automotive
– Biomedical
– Chemical Processing
– HVAC&R
– Hydraulics
– Marine
– Oil & Gas
– Power Generation
– Sports
13. 13
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
14. 14
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
15. 15
Where is CFD used? (Sports)
• Where is CFD used?
– Aerospace
– Appliances
– Automotive
– Biomedical
– Chemical Processing
– HVAC&R
– Hydraulics
– Marine
– Oil & Gas
– Power Generation
– Sports
16. 16
Physics
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, g, Gr,
Ec)
– Free-surface flow and surface tension (Fr, We)
– Chemical reactions, mass transfer
– etc…
18. 18
Governing Equations
Continuity
Equation of motion
(Equations based on “average” velocity)
x
zx
yx
xx
x
z
x
y
x
x
x
g
z
y
x
x
p
z
u
u
y
u
u
x
u
u
t
u
0
z
y
x u
z
u
y
u
x
t
19. Claude-Louis Navier George Gabriel Stokes
Navier-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)
20. 20
Navier-Stokes Equations
(constant and m)
g
v
p
v
Dt
D
m
2
x
x
x
x
x
z
x
y
x
x
x
g
z
u
y
u
x
u
x
p
z
u
u
y
u
u
x
u
u
t
u
m
2
2
2
2
2
2
y
y
y
y
y
z
y
y
y
x
y
g
z
u
y
u
x
u
y
p
z
u
u
y
u
u
x
u
u
t
u
m
2
2
2
2
2
2
z
z
z
z
z
z
z
y
z
x
z
g
z
u
y
u
x
u
z
p
z
u
u
y
u
u
x
u
u
t
u
m
2
2
2
2
2
2
21. Navier–Stokes Example
21
Fluid
L
x
y
)
x
-
Lx
(
2
1
Expression
Final
0
2
L
L
at x
0
0,
at x
0
B.C.
2
x
Integrate
x
Integrate
0
2
y
2
1
2
1
2
y
1
2
2
g
dy
p
d
u
C
g
dy
p
d
C
u
u
C
x
C
g
dy
p
d
u
C
g
dy
p
d
dx
u
d
g
dx
u
d
dy
p
d
y
y
y
y
m
m
m
m
m
Laminar Flow
Static Parallel Plates
y
y
y
y
y
z
y
y
y
x
y
g
z
u
y
u
x
u
y
p
z
u
u
y
u
u
x
u
u
t
u
m
2
2
2
2
2
2
22. 22
Modeling
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-e,
K-w, 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)
23. 23
Turbulent Flow Representation
(K-e as an example)
velocity
ous
instantane
u
and
flow,
of
direction
in the
ty
net veloci
constant
u
velocity,
deviating
u'
:
Where
u'
u
u
i
i
26. 26
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 efficient
In COMSOL, a minimum y+ of 11.06 is enforced. To
maintain accuracy, ensure cells meet this requirement
y+ and Turbulence Models
27. 27
Numerics / Discretization
Computational solution of the IBVP
Method dependent upon the model equations and
physics
Several components to formulation
– Discretization and linearization
– Assembly of system of algebraic equations
– Solve the system and get approximate solutions
28. 28
Finite Differences
Methods of Solution
Direct methods Iterative methods
Cramer’s Rule, Gauss elimination
LU decomposition
Jacobi method, Gauss-Seidel
Method, SOR method
6
2
2
,
3
3
,
2
2
,
,
1
,
x
x
u
x
x
u
x
u
u
x
u
j
i
j
i
j
i
j
i
j
i
Finite difference
representation
Truncation error
29. 29
Numeric Solution
(Finite Differences)
o x
i i+1
i-1
j+1
j
j-1
imax
jmax
x
y
6
2
3
,
3
3
2
,
2
2
,
,
,
1
x
x
u
x
x
u
x
x
u
u
u
j
i
j
i
j
i
j
i
j
i
Taylor’s Series Expansion
u i,j = velocity of fluid
Discrete Grid Points
30. 30
Finite Difference Truncation Error
percent
Error
f
for
solution
Exact
f
f
x
x
f
x
f
x
x
f
x
f
x
f
x
at
x
x
f
n
x
x
f
x
x
f
x
x
f
x
f
x
x
f
n
j
i
n
n
j
i
775
.
0
9823
.
0
)
22
.
0
(
9899
.
0
)
02
.
0
(
)]
2
.
0
(
2
cos[
2
)
2
.
0
(
)
22
.
0
(
)
(
02
.
0
????
)
22
.
0
(
9511
.
0
)
(
2
.
0
:
2
sin
)
(
!
2
)
(
,
2
,
2
2
31. 31
CFD process
Geometry description
Specification of flow conditions and properties
Selection of models
Specification of initial and boundary conditions
Grid generation and transformation
Specification of numerical parameters
Flow solution
Post processing: Analysis, and visualization
Uncertainty assessment
32. 32
Geometry 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)
33. 33
Flow 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.
34. 34
Selection 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.
35. 35
Initial and boundary conditions
For 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. 36
Grid 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)
38. 38
Grid 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. 39
Grid transformation
y
x
o 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)
40. 40
Numerical parameters & flow
solution
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)
41. 41
Numerical parameters & flow
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
42. 42
Post-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)
45. 45
Uncertainty 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
51. 51
Software 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/
