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1. Introduction to Computational
Fluid Dynamics

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…

17. 17
Physics
Fluid Mechanics
Inviscid Viscous
Laminar Turbulence
Internal
(pipe,valve)
External
(airfoil, ship)
Compressible
(air, acoustic)
Incompressible
(water)
Components of Fluid Mechanics

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






24. Turbulent Boundary Layer
24
Wall
y
x
d
U0
Bulk Stream
Outer layer
Fully turbulent layer
Sublayer + buffer layer
Edge of boundary layer

25. 25

d

d









y
u
y
y
u
u
dy
U
d w
y
w















Scale
Length
Viscous
Velocity
Friction
Stress
Shear
Wall
0
y+ is similar to a local Reynolds number.
Small y+ - Viscous effects dominate
Large y+ - Turbulence dominates

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)

37. 37
Grid Resolution

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)

43. 43
Post-processing (Parallel Plates)

44. 44
Post-Processing (example)
 Pressure contour and
velocity vectors .
 Note the locations of
the highest and lowest
pressure regions.

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

46. CFD Example
46
Sulzer Chemtech
250 Y Plastic
Structured Packing

47. Geometry
47
• CT > STL > CFD
• CT = 0.322 mm
Min Resolution
• Copy/Pasted 2x
• Surface Wrapping
• Adaptive Meshing
• Tetrahedral Mesh
• Polyhedral Mesh

48. 48
Mess Dimensions

49. 49
Experiment vs. Simulation
y = 23.462x1.8022
R² = 0.9998 y = 21.97910x1.76234
R² = 0.99996
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Pressure
Loss
(Pa)
F-factor (ft/s*[lb/ft3]1/2)
Simulation
N2 - July 27
N2 - July 28

50. 50
Velocity Map

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/