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Fluid dynamics is one of the most challenging areas of physics. Even with powerful computers and the use of simplifying assumptions, accurate simulations of fluid flow can be notoriously difficult to obtain. Researchers often need to predict the behavior of fluids in real-world applications, such as oil flowing through a pipeline. To make the problem easier, it has been common practice to assume that at the interface between the fluid and the solid boundary -- in this case, the pipe wall -- the fluid flows without slipping. However, the evidence to support this shortcut has been lacking. More recent research has shown the slippage can occur under certain circumstances, but the physical mechanism has remained mysterious.
Now, to more rigorously understand the origin of flow slippage, researchers at The University of Tokyo created an advanced mathematical model that includes the possibility of dissolved gas turning into bubbles on the pipe's inner surface.
"The no-slip boundary condition of liquid flow is one of the most fundamental assumptions in fluid dynamics," explains first author Yuji Kurotani. "However, there is no rigorous physical foundation for this condition, which ignores the effects of gas bubbles."
Journal Reference
Yuji Kurotani, Hajime Tanaka, Yuji Kurotani et al. A novel physical mechanism of liquid flow slippage on a solid surface [open], Science Advances (DOI: 10.1126/sciadv.aaz0504)
(Score: 0) by Anonymous Coward on Thursday April 02 2020, @03:55AM (3 children)
I have some experience running fluid dynamics simulations, including a lot using a model called CM1 [ucar.edu]. In this case, the fluid is a gas rather than a liquid, but it's still a fluid dynamics simulation, and the same principles apply.
For many idealized simulations of atmospheric processes, the lower boundary is actually free slip rather than no slip. Neither is entirely realistic, but a free slip lower boundary is actually quite common. With a no slip boundary condition, the flow at the boundary is zero. With a free slip boundary condition, the flow at the boundary retains the full component of motion parallel to the boundary. In reality, a partial slip boundary is probably best for atmospheric simulations, in which the component of the velocity parallel to the boundary is decreased somewhat, but isn't zero.
While the idea of a free slip or a partial slip boundary may be somewhat novel in simulating the flow of a fluid through a pipe, these assumptions are commonly used in atmospheric fluid dynamics models. There is definitely shear within the boundary layer, so a free slip boundary condition is unrealistic. But even that is commonly used for idealized simulations of many atmospheric processes. In the atmosphere, there isn't the equivalent of tiny bubbles. In fairness, the velocity a molecule above the surface is probably extremely close to zero, but the vertical levels are spaced tens or hundreds of meters apart, and the lowest model level isn't right at the surface. Because we observe tiny bubbles forming in the atmosphere, and yet a partial slip lower boundary tends to work well, I'm wondering if there's more to the partial slippage at the boundary in the simulations beyond just the formation of bubbles from dissolved gas.
(Score: 2) by MostCynical on Thursday April 02 2020, @05:35AM (2 children)
doesn't the 'roughness' of the surface (compared to both the molecular size and the effective 'surface' of the fluid) change the behaviour, or do the models also assume perfect 'smoothness'?
"I guess once you start doubting, there's no end to it." -Batou, Ghost in the Shell: Stand Alone Complex
(Score: 1, Informative) by Anonymous Coward on Thursday April 02 2020, @05:57AM (1 child)
The free slip and no slip boundary conditions are the endpoints of a range of possible lower boundary conditions. For those, there's no need to otherwise specify surface roughness because it's implicit by the free slip or no slip boundary conditions. A partial slip boundary condition is in between the free slip and no slip endpoints. For a partial slip boundary, it is necessary to specify information like the surface roughness. In the real world, there's no such thing as a free slip boundary. Everything has some roughness, however small it may be in some instances. We use a free slip boundary condition when we want to understand a particular process in isolation, so we remove anything that might complicate modeling that process, which includes things like surface roughness. A free slip lower boundary isn't realistic, but it can be helpful in simplifying some experiments. But for something more realistic, factors like surface roughness are important and need to be specified in the model.
As for the effective length of the surface, the model is numerically integrating a set of equations on a three-dimensional grid. You can specify terrain, which causes the vertical coordinates to follow the terrain. The model would have to take into account, and it would have the effect of accounting for the effective surface length on the scale of the model grid. As for whether that's accounted for on a subgrid scale, I'm less certain about that, and I'd need to look at the model code to find out. I suspect it's only accounted for on the scale of the model grid, so variations in the surface area on smaller scales probably aren't accounted for.
(Score: 0) by Anonymous Coward on Thursday April 02 2020, @05:08PM
Couple of comments/questions--have done wind tunnel testing, but no CFD.
I can see where "free slip" boundary conditions would be really useful for simulating the walls of a wind tunnel -- it would avoid the boundary layer buildup along the length of the tunnel, avoiding the need to simulate boundary layer reduction used in some real-life tunnels. Would still need to have no/low slip for the model in the tunnel.
In terms of atmospheric boundary layer, no-slip must be pretty close to reality since it's possible to light a match and start a camp fire in a gale...if you get right down to ground level.