Non-Dimensional Numbers in CFD
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Transcript Non-Dimensional Numbers in CFD
ND Numbers in CFD and Setting up a
Problem
HARP REU Program 2012
Susan T. Brown, Ph.D.
Non-Dimensional Numbers in CFD
Ratio of forces or effects
Have no dimensions
If properly conceived, will scale
WHY IS THIS IMPORTANT?
Use to model experiments
Find constants
Determine validity of equation usage
Most-used numbers in CFD
Reynolds’ number = Re = inertia/viscosity = ρvL/μ
Froude number = Fr = inertia/gravity = v2/Lg
Peclet Number = Pe = convection/diffusion = vL/к
Prandtl number = Pr = viscosity/conduction = μ/ρк
Strouhal number =So =
characteristic length
distance travelled during period t
= fL/u
Considerations in CFD, or “Where do I
start?”
The actual scenario (it happens all the time):
“Um, okay, you are the CFD expert… We have this physical
problem. Model it and give us the answer.”
And, more often than not, we go away thinking, “Yeah, I can do
that!” And we go off and create a gorgeous and expensive 2or 3-D CFD model of whatever it was, and show them
streaklines or velocity vectors that are beautiful to behold in a
20-minute presentation in full technicolor. Are they happy?
NO! Why not? Because that’s not what they really wanted. They
don’t care a whit about the flow field. (Practical people
rarely do!)
A Better Place to Start
So… When you hear, “Model this,” the first question should be:
1. What do you want to know? Pressure, Force, Velocity,
what exactly?
And the second question should be:
2. How accurate does it have to be?
Answers to these two questions will determine if you should do
a “Back-of-the-envelope” calculation, rough parameter
model, or a full 3-D geometrical model.
What Physics are Involved?
What is the “fluid?” Gas, liquid?
Is it non-compressible?
Is it Newtonian?
What flow regime are we dealing with? Re?
What other non-dimensional numbers are important?
Do we need the energy equation? Heat transfer?
What is the Geometry like?
Simple, or Complex?
2D or 3D?
Does it matter for our problem?
Look in the Literature
Has this problem or anything similar been done before?
Similar solution available, at least for comparison?
What software did they use?
What software recommended for these type of problems?
What software/hardware do you have
available?
Where will you run your problem?
What is available for this type of problem?
Is it freeware, or do you have to buy a license?
Is it easy to learn, do you already know how, or will you have
to attend training?
Is there a “resident expert?”
Which software fits best?
Now that you have chosen your
software, what next?
Build your geometry
Does the “software” have its own tool for that, or do you have to use
something else. (Oops, maybe I want to use that other software that
does…)
Build your computational grid
NOT the same as geometry!
Can I use a uniform grid?
May need to refine in places where there are smaller scale phenomena
occurring.
Follow the rules wrt gridding!
NO sharp corners
NO hi aspect ratios between neighboring grids
Square with gradual change leads to stable computation
What next, 2…
Determine your domain boundaries.
Solution will be inaccurate a priori at the boundary unless
known, so set any boundary that is not a wall far away from the
“action.”
Want it large for solution accuracy, but small for computation
time.
Determine boundary conditions.
Must be known.
If you don’t know them, choose boundaries where you do.
Choose initial conditions.
The closer to the final solution you choose your ICs, the shorter
your simulation will have to run.
What next, 3..
Choose computational models.
Do you need a turbulence model?
What is available in your code?
What works best for your type of problem?
Don’t get too fancy to start, use the default.
Do you have a choice of computational solvers?
Use the default to start unless your type of problem requires the “special”
option.
Do you have multi-phase flow?
Put in physical properties.
The code does not magically know you have ocean water
instead of koolaid!
What next, 4
Remember numerical parameters.
Do you need to set the time step?
Are you running just a few time steps to start, to see what
happens, before you start a big batch job?
How are you outputting the results?
Where are results being stored for viewing?
Are you ready to submit your job?
Have I thought of everything??