scale difference in spillway modeling
 

Hello.

I want to simulate a ogee spillway and compare the software data with laboratory results.
My results of laboratory data are for prototype(real) like pressure, velocity and etc.
Is there a difference between simulating the spillway with laboratory geometry and prototype geometry? Or i should decrease the dimensions of 3d model of prototype according to model scale?
Please help me immediately.

Free surface scaling is related to the Froude number Fr. Flow rate Q, velocity U, force F, and pressure P all scale between physical models (lab) and prototype (field) by assuming constant gravity at both lab and field locations, and using a constant Froude number Fr at both. The Reynolds number will not be constant at both, unless two different fluids are used (which is expensive). Turbulent effects scale approximately by Reynolds number and roughness height, so they will be distorted, especially if the model is much smaller than the prototype. Air entrainment does not scale solely by Re or Fr, so entrainment effects will be distorted. Surface tension effects in the lab model may distort scaling as well, since the Weber number is not the same.

When modeling in CFD, you have to be aware of the scaling (or lack of scaling) of different processes: if you model the prototype with CFD, the results should be similar to the prototype test results, but may not match the lab experiment. If you model the lab test with CFD, the results should look like the lab results but maybe not like the prototype. If you try to compare a CFD model of the prototype to results from the scaled (small) lab model, you may or may not get matching, depending on how much the viscous, surface tension, and air entrainment effects contributed to the lab model results. See Chanson, H. "The Hydraulics of Open Channel Flow" for a good description of scaling in free-surface and confined flow models.

Thank you for your reply.
I just want to compare the results in CFD with laboratory data but my laboratory data have become in field data with froud similarity.i want to know, Is there a difference between time of calculation the spillway with laboratory geometry and prototype geometry in CFD since the height of spillway in lab is 3m and in field is 100m.

You can scale the time by velocity and length.

Uproto/Umodel = sqrt(Lproto/Lmodel) = sqrt(33.3) = 5.77.

t_transit = Ltravelled/U

you can find that a packet of water crosses the scale model in about 17% of the time it takes a packet of water to cross the prototype, so it should come to steady state more quickly than the prototype does. You would need to find out if the paper results were time-scaled to give flow conditions at different times, though: some authors don't scale time by velocity.

my geometry dimensions in prototype is about 40 times larger than the geometry dimensions in model. i mean that, if i simulate the prototype in software, the time of calculations is equal to simulate the model in software? and i should use more mesh in prototype?
since the prototype dimensions larger than the model dimensions.

If you choose the same relative discretisation of your geometry modell, the simulation in prototype scale should be slightly faster than in modell scale because of the different relative velocities.