> Steady flow experiments, including with the original design, however, show smaller ratios of the two resistances in the range of 2 to 4.
So the simulations are off by a factor of 10? How is this possible?
"I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids." -- Miller
According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence?"
The Tesla Valve design is turbulence harnessed. When it comes to simulations of such, expect ... discrepancies.
As to the smoothness problem, that may get you to claim a $1,000,000 Millenium prize in mathematics, but plays no role whatsoever in practical simulations.
The simple truth is that computational fluid dynamics codes are nowhere near a calculator-like fire-and-forget reliability, even though the UI of commercial solvers implies as much when you just have to click a button to get 'an answer'. It's still much more of a black art and you really have to know (1) the physics, and (2) the numerics to reliably generate physically meaningful results.
The reality is that all the equations and formulas we use are approximation, even simple things like the actual direction of flow in a pipe aren’t as simple as you think take any pipe and flow fluid through it in one direction, now introduce a dye in the middle and without a recirculating system the dye will eventually creep up against the flow.
None of the equations you can nominally apply to fluid flows would enable you to predict nor explain this. There are now diffusion calculations that you can apply to calculate how much and how fast things could diffuse upstream, but these are essentially statistical models that we derived from experiments.
So back to the Tesla valve question, the simulation likely work on ideal flows and geometries which are nearly impossible to actually produce through engineering so the slightest of variations in the surface, fluid density etc. can have drastic impacts on the outcome.
It's hard to say since there is zero information about how the simulation they mentioned was done in the footnoted article. Most likely they either screwed up the mesh or the, more likely, the turbulence modelling. It's hard to say why the Wikipedia author chose that particular article/simulation results, since the article presenting the results is very superficial. If you look at results from other simulations you can find numbers between 1.5-7 depending on the exact simulation setup.
If you read the paper linked to in the footnote to the steady flow experiment you'll see that the results are very dependent on the turbulence and Reynolds number of the liquid so how you feed the liquid into the valve (how fast and how steady) can greatly impact your results. So if the simulation and the experiment used different pressures for the water entering the system, just that could explain some of the discrepancy.
Is water simulated like gas, sand, or spaghetti? Are internal grid configuration and electromagnetic properties considered usually? Water's chemistry and physics makes it such a special thing, no? What's the scale when things commonly fall apart? Is quantum computation a possible answer to scalability? Can you "divide and conquer" a fluid system? Do real life model measurements tell you much about upscaled applications?
I only know people hate fluid dynamics studying physics and that it's a hard problem.
The big 'problem' with fluid dynamics is that from the equations it looks like a really simple problem. The Navier-Stokes equation is a couple of lines and you can explain it to a reasonably smart high school student who has taken calculus.
And in the 'easy' case where you assume laminar flow and no turbulence it is pretty easy. The problem is when you introduce turbulence into the system then it becomes basically unsolvable and you are forced to rely on 'tricks' and approximations to make the problem computable. Most of the 'art' of CFD is picking the right tricks and approximations to solve the particular problem you have (the second 'art' is creating and a good mesh to run the solver on).