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The two terms are equal due to the product rule and continuity equation. The use of the continuity equation might not be obvious, however. In their notation, the Reynolds decomposition is $u_i = \overline{u}_i + u^\prime_i$. Taking the continuity equation and averaging leads to: $$\frac{\partial \overline{u}_j}{\partial x_j} = 0$$ Subtract the equation ...

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The problem you have is more complicated than you think. Any industry that deals with the storage and movement of granulated/powdered materials has to deal with this and most have unique solutions. You need to look at the principles of hopper design. Some of the things that affect any design will be: The angle of repose of the material you intend to use. ...

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It is just saying that since there is no turbulence or dissipation being computed; your solution will be less accurate for lower and lower permeability. As I read it; eddy currents in this model will cross the medium. For a thin wire fence this would match reality; for a furnace filter it would not because the air is laminar as it exits the filter. The ...

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Dolphin skin seems to have properties that limit drag, also by reducing turbulence: In the late 1950s the aerodynamicist Max Kramer claimed that a dolphin ensured a low level of friction drag by maintaining the laminar flow over most parts of its body. The dolphin’s skin having an unusually ordered inner structure was considered to be a natural compliant ...

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I think you have a pretty comprehensive list. Some things could be more general such as flow straighteners could also include airfoils for correcting flow around obtuse geometry. Other geometry which may fall under your scope can isolate turbulent areas of flow from laminar areas of flow. Like in a spinning ball flow indicator for example. Here are the ...

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Disclaimer: As you requested general guidelines here they are. After having a converged solution, you need to investigate it thoroughly and look for clues that the choice of the turbulence model altered the flow in an un-physical way. My Rules of Thumb for Turbulence Models The more additional transport equations you solve: the more possibilities exists ...

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For the equilibrium boundary layer, the local skin friction coefficient is independent of two parameters, both the streamwise distance and the Reynolds number, based on the momentum thickness, and the boundary layer thickness is proportional to the streamwise distance. On the other hand, for the non-equilibrium boundary layer, the local skin friction ...

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No, inviscid flows are not necessarily turbulent. If there is nothing to "trip" the turbulence, then the flow will remain laminar. Features which could trip the turbulence include vibration, small temperature fluctuations, any geometric imperfections, velocity field imperfections, and other similar things. For example, potential flow is a type of inviscid ...

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Assuming you are wanting to minimize turbulence in the region of the pump, you would probably need to use flow straighteners somewhere upstream of the pump. You would have to study the optimal diameter and length of the straighteners. MIT simply used drinking straws to do this in a wind tunnel. Here are a couple of the more well known papers on the ...

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In wind tunnels usually meshes and/or honeycombs are used to reduce turbulence. However, to really achieve low turbulence it's probably not enough to add a single component to your facility. I rather suspect you need to evaluate the overall design. Some kind of diffusors at the pipe end(s) might be helpful. If you look at the flow behind bridge pillars, you ...

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One method is to use a hot wire anemometer. This (about 50 pages, ignoring the product-specific stuff at the end) is a good read. In principle, a hot wire anemometer is simply a metal wire (often platinum-coated tungsten wire with a diameter of a few micrometers) with an electrical current passed through it. The rate of heat loss from the wire depends on ...

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There are two ways of "wall treatment" both feature two layers but at different $y^+$. The general idea is that the velocity gradients in the boundary layer are so high that one would need a very high number of grid cells in order to resolve those gradients. In order to overcome that the flow close to the wall is modeled by one of the following algebraic ...

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I am not entirely sure I follow your derivations, specifically I'm not sure where you get the equation for the Von Karman mixing length, and why the equivalence of tau and $\tau_0$ give you the Prandtl turbulence model that you write afterwards (apologies since I can't get the equations to format properly, but I am referring to the equations you write ...

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Wavelength is with reference to Kolmogorov's theory of turbulence. Kolmogorov postulated a theory for how turbulence is conveyed from large to small scale eddies, as you described. The wavelength and frequency origins are buried deep in the mathematics of the theory. Basically, the theory postulates an energy spectrum for turbulence, which divides the energy ...

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I'm not sure if there is any further context to this meme, but I would have chosen B) Unsteady Uniform Flow. Since almost all real flows are unsteady and non-uniform, it is really an application of assumptions to characterize the flow as something simpler to analyze. I would assume a flood is highly transient, therefore, unsteady. There is probably not a ...

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I solved my problem. I refined the mesh. Part of the problem was the high aspect ratio of my cells, because my tube is very thin in comparison to the length. I have solved the problem laminar and then take this as a starting value for my turbulence model. My results are physical now and the flow is fully developed some time after the expansion. Thanks to ...

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Non-laminar flow is often hard to characterize with much mathematical rigor (though in certain special cases and geometries may be done with a little limitation). The phenomena depends heavily on channel geometry. For example, A backflow eddy can develop from a sudden stepwise increase in channel height/width. The Reynolds number of the fluid flow under ...

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Adding to these above ideas&techniques, In flexible pipes, along with the flexibility we can have filaments(flagellum ) on the walls. These could dissipate the turbulence kenetic energy for the same $Re$. But we have to pay interms of pressure loss.

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Short answer: The FLUENT approach is trivial. Many information are lost due to the space-averaging process - over a representative elementary volume - of the governing equations (which is the essence of every porous model that tries to avoid the complexity of the real geometry of the porous media), So any turbulence model is not to "reproduce the fine ...

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The simple answer Reynolds number can be more simply defined as the ratio of Inertial forces to Viscous forces. viscous >> inertial = Laminar viscous << inertial = Turbulent This is why when speed/flow rate increases fluids go towards/become turbulent as you're increasing the inertia of the fluid. Based on this logic if you had inviscid (no ...

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