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?
 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…)
 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
What next, 2…
 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