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LECTURE 1
Computational Fluid Dynamics (CFD) wb1428
Mathieu [email protected]://www.ahd.tudelft.nl/∼mathieu/CFD.html
http://www.ahd.tudelft.nlinfo for studentswb1428 Computational Fluid Dynamics
Fluid dynamics groupStromingsleerbuilding part 5Broom 1-32015-2782997
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• relevance CFD
• preview of CFD
• subject of lectures
• examination
• material
• questionnaire
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What is CFD about?
• Fluid dynamics
• Theoretical
• Experimental
• CFD: Computational
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Why (Computational) Fluid Dynamics?
• flows in nature and technology
• flows combined with heat transfer
• flows combined with particle transfer
• flows with free surfaces (water waves)
• flows with free surfaces (oil-water droplet)
• flows with chemistry
• flows with moving boundaries
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Near the surface: boundary layer flow.
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Contours of X Velocity (m/s) Feb 07, 2007FLUENT 6.2 (2d, dp, segregated, ske)
1.97e+00
-1.13e+00
-9.21e-01
-7.14e-01
-5.07e-01
-3.01e-01
-9.42e-02
1.12e-01
3.19e-01
5.26e-01
7.32e-01
9.39e-01
1.15e+00
1.35e+00
1.56e+00
1.77e+00
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Path Lines Colored by Particle ID (Time=1.0739e+02) Feb 08, 2005FLUENT 6.1 (2d, dp, segregated, lam, unsteady)
2.90e+01
0.00e+00
1.45e+00
2.90e+00
4.35e+00
5.80e+00
7.25e+00
8.70e+00
1.01e+01
1.16e+01
1.31e+01
1.45e+01
1.59e+01
1.74e+01
1.89e+01
2.03e+01
2.18e+01
2.32e+01
2.46e+01
2.61e+01
2.75e+01
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Contours of Vorticity Magnitude (1/s) (Time=1.0739e+02) Feb 08, 2005FLUENT 6.1 (2d, dp, segregated, lam, unsteady)
4.37e+00
1.07e-04
2.18e-01
4.37e-01
6.55e-01
8.73e-01
1.09e+00
1.31e+00
1.53e+00
1.75e+00
1.96e+00
2.18e+00
2.40e+00
2.62e+00
2.84e+00
3.06e+00
3.27e+00
3.49e+00
3.71e+00
3.93e+00
4.15e+00
Contours of X Velocity (m/s) (Time=1.0739e+02) Feb 08, 2005FLUENT 6.1 (2d, dp, segregated, lam, unsteady)
1.74e+00
-3.63e-01
-2.58e-01
-1.53e-01
-4.75e-02
5.76e-02
1.63e-01
2.68e-01
3.73e-01
4.78e-01
5.83e-01
6.88e-01
7.93e-01
8.98e-01
1.00e+00
1.11e+00
1.21e+00
1.32e+00
1.42e+00
1.53e+00
1.63e+00
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A sphere
Contours of Axial Velocity (m/s)FLUENT 6.1 (axi, dp, segregated, RSM)
Apr 20, 2004
1.35e+00
1.28e+00
1.21e+00
1.13e+00
1.06e+00
9.88e-01
9.15e-01
8.42e-01
7.70e-01
6.97e-01
6.25e-01
5.52e-01
4.79e-01
4.07e-01
3.34e-01
2.62e-01
1.89e-01
1.16e-01
4.37e-02
-2.89e-02
-1.01e-01
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Grid Apr 20, 2004FLUENT 6.1 (axi, dp, segregated, RSM)
Grid Apr 20, 200FLUENT 6.1 (axi, dp, segregated, RSM)
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Contours of Static Pressure (pascal) Apr 20, 2004FLUENT 6.1 (axi, dp, segregated, RSM)
1.08e+03
7.00e+00
6.05e+01
1.14e+02
1.67e+02
2.21e+02
2.74e+02
3.28e+02
3.81e+02
4.35e+02
4.88e+02
5.42e+02
5.95e+02
6.49e+02
7.02e+02
7.56e+02
8.09e+02
8.63e+02
9.16e+02
9.70e+02
1.02e+03
Pressure Coefficient vs. Curve Length Apr 20, 2004FLUENT 6.1 (axi, dp, segregated, RSM)
Curve Length (m)
-1.25e+00
-1.00e+00
-7.50e-01
-5.00e-01
-2.50e-01
0.00e+00
2.50e-01
5.00e-01
7.50e-01
1.00e+00
0 0.5 1 1.5 2 2.5 3 3.5
PressureCoefficient
expsphere
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Contours of X Velocity (m/s) (Time=1.5000e+01)FLUENT 6.1 (3d, dp, segregated, ske, unsteady)
Feb 09, 2005
6.26e-025.63e-025.01e-024.38e-023.75e-023.13e-022.50e-021.88e-021.25e-026.26e-03-3.47e-18-6.26e-03-1.25e-02-1.88e-02-2.50e-02-3.13e-02-3.75e-02-4.38e-02-5.01e-02-5.63e-02-6.26e-02
Z
YX
Contours of X Velocity (m/s) (Time=1.5000e+01)FLUENT 6.1 (3d, dp, segregated, ske, unsteady
Feb 09, 20
6.26e-02
5.63e-02
5.01e-02
4.38e-02
3.75e-02
3.13e-02
2.50e-02
1.88e-02
1.25e-02
6.26e-03
-3.47e-18
-6.26e-03
-1.25e-02
-1.88e-02
-2.50e-02
-3.13e-02
-3.75e-02
-4.38e-02
-5.01e-02
-5.63e-02
-6.26e-02
Z
YX
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Contours of Volume fraction (water) (Time=1.8750e+00) Jan 06, 2005FLUENT 6.1 (2d, dp, segregated, vof, rngke, unsteady)
1.00e+00
0.00e+00
5.00e-01
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Why Computational Fluid Dynamics?
• speed of computers
• price of computers
• speed of numerical algorithms
• data accessible
• change geometry at little cost
• try out ideal circumstances
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Activities of a CFD modelerWriting a big code
• write code (10 %)
– paper work 8%
∗ writing out an integral balance
∗ interpolation
– implementation 2%
• find bugs (80 %)
• validate (10%)
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Activities of a CFD modelerCalculating realistic cases
• Clean the geometry (80 %)
• Make a grid (15 %)
• Validate the code (3%)
• Run the problem (2%)
VALIDATION????
• codes contain bugs
• user chooses a method
• user determines flow regime (turbulent, laminar)
• grid quality
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What is this lecture about?
• Fluid Dynamics on computer
• Solve fluid flow equations on computer
• Write your own code or
• Use a commercial package: Fluent
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Writing your own code:
• takes time
• takes experience
• spend time on non-essential subjects
BUT:
• you see the code
• you understand what the code does
• you can repair bugs
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Using a commercial package:
• preprocessor
• postprocessor
• programming done for you
• manual
• help desk
• takes less time
• takes less experience
BUT:
• you do not see the code
• you do not always understand what the code does
• no bug repair
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IN PRACTICE:
• you will use a commercial code
• continuity, manual, helpdesk
Do commercial codes always work?NO.
• commercial codes have bugs
• numerical algorithms do not always work
• commercial code is collection of tools
• you still need to understand the tools
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Commercial packages
• fluent http://www.fluent.com
• CFX http://www-waterloo.ansys.com/cfx/
• ansys http://www-waterloo.ansys.com/
• starcd http://www.cd-adapco.com note same as comet!
• comet http://www.cd-adapco.com note same as starcd!
• femlab http://www.comsol.com/
• flow3D http://www.flow3d.com
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Objectives of lectures (in principle)
• background of the package
• simulate model problems
• some model problems in matlab
• simulate fluid flow using commercial CFD package
• use/choose numerical method
• make numerical grid
• use/choose physical model
• discuss and validate results
• why validation?
– rounding errors
– approximation errors
– modeling errors
– CFD package errors
( )
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Objective: learn about flow solverWhat does a flow solver doDiscretization
T(x)
T1 T2 T3 T4 T5
T4 T5 T6
T6
T3T2T1 T7
Discretization → equationsSolution of equationsVisualization of solution
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Why discretize?
• more equations
• profile assumption
• when profile: ”easy” equation/solution (computer is dumm!)
• x (space) or t (time)
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• linear profile assumption in t between points
• derivative dydt ∼ Δy
Δt
• derivative can be calculated (approximated) IF y known in points
• how about a profile assumption in a differential equation?
2
1
t1
y1
y2
t2
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dy
dt= −Ky
dC
dt= −KC
• radioactive decay
• chemical reaction species C with abundant other species
• solve with finite difference method
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2
1
t1
y1
y2
t2
dy
dt= −Ky
dy
dt∼ Δy
Δt= −Ky
y2 − y1
Δt= −Ky
y2 − y1
Δt= −Ky1
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y2 − y1
Δt= −Ky1
y2 = y1 − ΔtKy1
• if you know y1, you get y2
• we have assumed constant derivative, linear profile between points!
Observations:
• t1 and t2 closer → y1 and y2 closer and approximation derivative moreaccurate
• and vice versa
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 5 10 15 20 25 30 35 40
y
t
grafiek
numericalexact
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 5 10 15 20 25 30 35 40
y
t
grafiek
numericalexact
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 5 10 15 20 25 30 35 40
y
t
grafiek
numericalexact
-1
-0.5
0
0.5
1
1.5
2
0 5 10 15 20 25 30 35 40
y
t
grafiek
numericalexact
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-80
-60
-40
-20
0
20
40
60
80
100
120
0 50 100 150 200 250
y
t
grafiek
numericalexact
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Observations:
• the smaller the timestep the more accurate
• the bigger the timestep the less accurate
• the interpolated exact solution also becomes less accurate
• the calculated solution becomes even less accurate and also becomesnon-physical
– errors accumulate
– errors can grow: instability
too big timestep, NO programming errors, still:
• non-physical values
• instability
y2 = y1 − ΔtKy1
y2 = (1 − ΔtK)y1
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y2 = y1 − ΔtKy1
y2 = (1 − ΔtK)y1
y2 = My1
For the physical solution
• y2 < y1
Solution decays.
• y > 0
Solution stays positive.
• y → 0
Solution goes to 0 for long times.
•M < 1
• Δt < 1/K
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THIS FORMULA WILL BE ENCOUNTERED MANY TIMESy2 = My1M < 1
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• problems in a simple model calculation
• commercial codes can suffer from similar problems
• this can happen in a (much) more complicated situation
• study numerical effects (errors) in simplified situations
• study numerical effects (errors) in building-block flows
• where does the error come from?
– physical model
– numerical error
– programming error
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The finite volume method, an integral balance
SOURCE
FLUX 1 FLUX 2
• volume ΔV
• side surface A
• length Δx
• Fouriers law: net flux q = −k∂T∂x
• Midpoint rule: source = ∫ sdV = Smp ∗ ΔV
Result: k ∗ T1−2∗T2+T3Δx2 = S2
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Working with a package. Flow around buildings.
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OUTLINE
• Fluid flow: Navier-Stokes
• Model equations: diffusion, advection, advection-diffusion, wave equa-tion
• finite difference, finite volume (finite element)
• model eqns: Poisson, diffusion, advection, wave
• discretisation, numerical error, stability, explicit, implicit
• matrix equation solvers
• mass conservation (pressure correction)
• Navier-Stokes (incompressible, compressible), heat transfer
• fluent solver structure, boundary conditions, setting up a problem influent
• grid generation
• turbulence
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• building block flows
– boundary layer
– square cylinder
– round cylinder
– airfoil
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Lecture form
• lectures
• exercises: matlab
• exercises: fluent
LOOK on the www for announcements!computer exercise PC room Pallas on Thu 21 Feb!
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Examination
• assignment: fluid flow calculation with matlab/Fluent
• suggest your own flow
– (in practice) 2D, axi-symmetric
– you should have some qualitative and quantitative info
• suggest your own assignment
• assignment: exercise by hand and with matlab (optional)
• discussion of report (2 page, pointwise, plus figures/results)
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Examination
• assignment plus disscussion 60%
• some exercises 40%
– determine order of method by taylor series
– write out a discretisation/interpolation (equation, BC)
– evaluate grids
– make a stability analysis
– interpret numerical errors in a simulation
• three credit points
• you want more? Come up with a more realistic (matlab/Fluent) prob-lem (1 point)
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Material
• sheets on www
• background material:
– Ferziger & Peric, Computational methods for fluid dynamics, Springer
– J. van Kan, Numerieke wiskunde voor technici, DUP
– Delft Fluent User Grouphttp://www.ahd.tudelft.nl/∼mathieu/fluent group/index.html
– Pre-requisites:
∗ Heat transfer: Winterton, ”Heat transfer”, OUP (90 pages)
∗ Advanced Fluid dynamics
· Lecture notes FREE notes,http://www.ahd.tudelft.nl, education
· Batchelor ”Fluid Dynamics”
· Kundu and Cohen, ”Fluid Dynamics”
· Tritton, ”Physical fluid dynamics”.
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limitations of lectures (in principle)
• incompressible (density = constant)
• low Ma compressible (density NOT constant), perhaps some compress-ible
• Flow, plus possibly
– physical models for turbulence
– heat transfer, mass transfer
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• CFD
• Fluid Dynamics
• Computer
• you
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questionnaire
• did you do advanced fluid dynamics?
• did you do anything numerical before (v Kan, numerical analysis)
• what programming languages do you know (Fortran, C, C++, Pascal,matlab)