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7/29/2019 PRESENTATION Computational Fluid Dynamics (CFD) Introduction
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Computational Fluid Dynamics (CFD)
IntroductionProfessor Salvador Vargas Daz
Universidad LibreUniversidad San Buenaventura
[email protected]@usb.bog.edu.co
mailto:[email protected]:[email protected]:[email protected]:[email protected]7/29/2019 PRESENTATION Computational Fluid Dynamics (CFD) Introduction
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Recommended texts
Anderson, JD: Computational Fluid Dynamicswell written text excellent introduction
uses finite difference approach
Versteeg, HK and Malalasekera, W: An Introductionto CFD
good finite volume intro
Content a little out-of-date
Ferziger, JH and Peric, MExcellent treatise on finite volume method for the
mathematics and fluids expert
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What is CFD?
CFD is the simulation of fluidsengineering systems using modeling(mathematical physical problemformulation) and numerical methods(discretization methods, solvers,numerical parameters, and gridgenerations, etc.)
Historically only Analytical Fluid Dynamics(AFD) and Experimental Fluid Dynamics
(EFD). CFD made possible by the advent of
digital computer and advancing withimprovements of computer resources
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Industrial problems (Analysis and Design)
1. Simulation-based design instead of build & test
More cost effective and more rapid than EFD
CFD provides high-fidelity database for diagnosing flow field
2. Simulation of physical fluid phenomena that are difficult for EFD Full 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)
Academic problems The goal is to understand the physical aspect of the process
Why use CFD?
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Where is used?
Aerospace
Automotive
Biomedical
Chemical
Processing HVAC
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
Aerospace
Automotive
Biomedical
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Where is used?
Aerospace
Automotive
Biomedical
Chemical
Processing HVAC
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
6
HVAC
Chemical Processing
Hydraulics
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Marine
Oil & Gas
Sports
Power Generation
Where is used?
Aerospace
Automotive
Biomedical
Chemical
Processing HVAC
Hydraulics
Marine
Oil & Gas
Power Generation
Sports
7
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How does a CFD code work?
Preprocessor create geometry
mesh volume
Processor solve a system of equations
approximation to subset or superset of Navier-Stokesequations
Post-processor Vector plots, contour plots, integrated values (eg total
pressure)
Colour For Directors
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Using CFD to solve a problem
1. Divide the fluid volume (surface) up intomanageable chunks (gridding)
2. Simplify the equations to be solved3. Set boundary conditions
4. Initialise the other grid values
5. Step through the grid ensuring that thesesimplified equations are satisfied at thegrid points and nearest neighbours
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Discretising equations
What are we solving?
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Components of the N-S equations
Need to know
values of each variable (eg u) at each point
values of the first derivative
values of cross-derivatives
values of second derivatives
..and more
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Forward approximation to value ofthe 1st derivative of u in space
u
xi-1 i+1i
dx
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Rearward approximation to value ofthe 1st derivative of u in space
u
xi-1 i+1i
dx
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Central approximation to value ofthe 1st derivative of u in space
u
xi-1 i+1i
dx
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Approximations to values of the 1stderivative of u in space
u
xi-1 i+1i
dx
rearward
forward
central
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1st & 2nd Order Finite Difference
x
uu
x
uii
id
1
x
uu
x
uii
id2
11
1st order forward difference
2nd
order central difference
x
uu
x
uii
id
1
1st order rearward difference
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Discretising equations
(Anderson)
.......62
3
,
3
32
,
2
2
,
,,1
x
x
ux
x
ux
x
uuu
jijiji
jiji
ddd
i,j i+1,ji-1,j
i+1,j+1i,j+1i-1,j+1
i-1,j-1i,j-1 i+1,j-1
The value of the variable, u, at the grid point i+1,j can beapproximated by a Taylor expansion:
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1st & 2nd Order Finite Difference
)(,,1
,
xO
x
uu
x
u jiji
ji
d
d
2,1,1
,
)(2
xOx
uu
x
u jiji
ji
dd
From the previous equation, we can find expressions
for the derivatives:
1st order forward
difference
2nd order central
difference
2,1,,1
,
2
2
)(22 xO
xuuu
xu jijiji
ji
dd
2nd order central
difference
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Practical consequences of
discretisationErrors arise from spacing of grid needs to be
small enough to represent the key aspects of
the flowErrors arise from the order of the equations
1st order should generally not be used
Only 2nd order solutions are acceptable forjournal publication
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Testing solution
Flow over a backward-facing step
Flow expands and leaves a
recirculating vortex behind the step
Solve to 2nd order and maintainlaminar flow
How long does the domain have
to be to ensure that the solution
is validUpstream?
Downstream?
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Testing solution
Start with a coarse grid
Solve the problem
Double the grid density Compare with the first solution
If the values have not changed significantly, it
is likely that the solution is grid-independent If the values have changed significantly,
continue until they stop changing
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