#### 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??