Fluid mechanics navier stokes flow around geometry

AI Thread Summary
The discussion focuses on modeling fluid flow around geometries, specifically 2-D flow around a circle, using the Navier-Stokes equations. It highlights the challenge of finding analytical solutions for external flows, noting that solutions like the Blasius solution exist mainly for laminar flow over flat surfaces. The conversation emphasizes that 2-D flow around a cylinder typically does not yield analytical solutions due to complexities like flow separation and unsteady wake patterns. The participants clarify that "very low Reynolds number" is context-dependent, particularly in relation to Stokes flow, which is valid when Re is much less than 1. Overall, the thread underscores the difficulties in modeling viscous flows and the need for specific conditions to apply certain fluid dynamics principles effectively.
member 428835
hey pf!

i am studying fluid mechanics and was wondering if any of you are familiar with a flow around some geometry? for example, perhaps a 2-D fluid flowing around a circle?

if so please reply, as i am wondering how to model the navier-stokes equations. i'll be happy to post the equations and my thoughts if you would like me to?

for the record, i am using white's book, and while it is great, i have not seen any examples dealing with 2-D flow around geometry. so far it's been flow in between plates and against a wall.

thanks so much for your support and interset!

josh
 
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The problem is that in general you can't find a solution to the Navier-Stokes equations analytically, especially external flows. There are some that are possible, like laminar flow over a flat plate (the Blasius solution), but these are relatively few and far between.

Except at very low Reynolds number, the 2-D flow around a circle (or cylinder, for example) is one such flow where an analytical solution is not possible for a viscous flow. You have to deal with flow separation and an unsteady wake (for example, try Googling von Kármán vortex street).
 
thanks you guys! hey bonehead, what do we consider "very low Re number"? would it be possible to model, say, syrup sliding over a plate with a slight angle as a low reynolds number, or is this too fast?
 
That depends on the context. With a cylinder in a viscous flow, very low Reynolds number in regards to whether Stokes flow is valid is typically considered to be Re \ll 1. It doesn't really make sense to just ask what constitutes very low Reynolds number in a random situation since you aren't really specifying in that case what physical phenomenon you are hoping to capture or avoid. For example, in Stokes flow, very low Reynolds number represents the region where the assumptions used in deriving it are valid.
 

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