Fluid mechanics navier stokes flow around geometry

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Discussion Overview

The discussion centers around modeling fluid flow, specifically the Navier-Stokes equations, in the context of two-dimensional flows around geometries such as a circle or cylinder. Participants explore the challenges of finding analytical solutions for these flows, particularly in relation to Reynolds numbers and flow characteristics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Josh, seeks guidance on modeling 2-D fluid flow around geometries using the Navier-Stokes equations, noting a lack of examples in their reference material.
  • Another participant provides a link to a resource that may contain relevant information.
  • A participant mentions that analytical solutions to the Navier-Stokes equations are generally difficult to obtain for external flows, with few exceptions like laminar flow over a flat plate.
  • It is noted that for 2-D flow around a circle or cylinder, analytical solutions are typically not possible at higher Reynolds numbers due to flow separation and unsteady wake phenomena.
  • Josh inquires about what constitutes "very low Reynolds number" and whether syrup sliding over a plate at a slight angle could be modeled as such.
  • Another participant clarifies that "very low Reynolds number" is context-dependent and typically refers to Re << 1 for Stokes flow, emphasizing the importance of specifying the physical phenomena being modeled.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding Reynolds numbers and the applicability of Stokes flow, indicating that there is no consensus on what constitutes "very low Reynolds number" in different contexts.

Contextual Notes

The discussion highlights the complexity of fluid dynamics modeling, particularly the dependence on Reynolds number and the specific physical scenarios being considered. There are unresolved questions about the applicability of certain flow models in different situations.

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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