Potential and viscous flow methods
 

Hi all,
please help me in under standing the difference between potential and viscous flow methods.

see simplified flow models in

http://www.cfd-online.com/Wiki/Fluid_dynamics

if the flow is irrotational, then it's a potential flow. Vorticity is 0 in a potential flow. You actually need the viscous effects (note :not viscosity itself) to generate vorticity. 

> You actually need the viscous effects (note :not viscosity itself) to generate vorticity

Vorticity is generated at the wall to satisfy the velocity boundary condition. It's a kinematic process that involves only continuity and the definition of vorticity as the curl of velocity. So, even inviscid flow will induce wall vorticity. Viscosity acts to diffuse that wall vorticity into the main flow.

This discussion of whether vorticity generation is an inviscid or viscous process has been around for quite some time, and I don't think it's fully resolved. My view is to look at the math for the answer (as explained above)

adrin

from a mathematical point of view:

If:
Div v = 0
Curl v = 0

you can introduce both the real and the imaginary part of the complex potential function (v = Grad phior v = - curl psi ).

If:
Div v = 0
Curl v = z

you can still introduce the potential v = - curl psi .

If the vorticit z is generated by viscous effects or it exists in an inviscid flow it does not matter.

yes; viscosity does _not_ enter into the picture until it is diffused from the wall. Even for the potential flow case, which is the flow model at t = 0, there will be vorticity generation at the wall (as you seem to imply above). The wall-tangential gradient of the potential field is proportional to the wall vorticity.

adrin

Note that for inviscid flow, the tangential component of the velocity can generate a discontinuity (tangential velocity is not zero at the wall even for a not-moving wall).

However, classical potential flows are typical in aerodynamics where the distribution of singularities (sink, source, vortex) is introduced

That discontinuity yields the vorticity that is to be generated!

adrin

Bernoulli's equation which happens to be a potential flow (and hence no vorticity) is derived by neglecting the molecular diffusion term (viscous effects term) in the Navier-Stokes equation. I think this is the simplest explanation.