[kevinpwp]

Hello,
I'm simulating non-Newtonian fluid past a cylinder. (Power Law)

One weird thing is if I set the Reynolds number to a constant number for example ReD=10,000 and change the velocity and density in a way that the Reynolds number remains 10,000, the maximum pressure on the surface of the cylinder changes!

The Reynolds number for the non-Newtonian fluid past a cylinder is

Re=(rho*U^(2-n)*D^n)/K

What is that for?

[LuckyTran]

The velocity and density changed, so why is it weird that pressure changes?

The Reynolds number quoted is the Metzner Reed Reynolds number in pipe flows, used to make force the friction factor of pipes with non-newtonian fluids to collapse onto the one for newtonian fluids. Note that for the same Reynolds number and friction factor, if you change the density and velocity, you'll also get a different pressure drop! Is it still weird?

[kevinpwp]

Thanks for your reply.

But, what is the purpose of the Reynolds number? To make the flow non-dimensional so you can use the obtained results for another flow with the same Reynolds number (not the same conditions). No matter what is the density or upstream velocity or diameter of the cylinder. The only important thing is Reynolds number. Am I wrong?

[LuckyTran]

Pressure should very clearly not be constant because we use it as a state variable...

Changing any one of the dimensional parameters will almost certainly make all other dimensional parameters change. If you change a parameter that has units on it (i.e. velocity has units of m/s, density has units of kg/m^3) then (almost all) other dimensional parameters will change as well. See the Buckingham pi theorem. There are only a very few limited number of very special parameters (certain functional groups) that will not change, the rest can be scaled. But dynamic similitude does not mean dynamically static.

What is not changed when you fix a Reynolds number is the other functional groups. You don't get to cherry pick and decide what these are arbitrarily.


In the case of flow around a cylinder, what is nominally constant with Reynolds number is the lift and drag coefficients, not the pressure.

[kevinpwp]

Thank you very much.

You said other parameters can be scaled. For example, suppose that the pressure drop is equal to X when the inlet velocity is U1. If we change the inlet velocity to U2 and also change the density in a way that Reynolds remains constant, then how can we scale the results to predict the pressure drop?

[LuckyTran]

The drag coefficient will be the same since the Reynolds number is the same. So from your first case at a given velocity V1 and density rho1, you determine the Reynolds number and Drag coefficient. Now you choose (i.e. scale) your case to a different velocity V2 and density rho2. You scale also the force F2 and from there determine the new pressure (don't forget you need to calculate the new dynamic head 0.5*rho2*V2^2) but keeping Reynolds number and the drag coefficient fixed. At least, this is how you do it for Newtonian fluids. For non-Newtonian fluids, the idea is the modified Reynolds number takes care of the non-Newtonian stuff. And it does, nominally.