[Nek5000-users] Question about method & error

[nek5000-users at lists.mcs.anl.gov]

On Wed, 2010-04-07 at 09:54 -0500, nek5000-users at lists.mcs.anl.gov
wrote:
> Hi Frank,
> 
> Actually, the only thing that would be specified at the interface
> is the surface tension sigma, which would generate a jump in the 
> stress across the interface.  The fluid and surface would dynamically
> accommodate to these stresses - and would come to a steady state
> geometry if that's the what the dynamics dictates.   The temperature
> would still satisfy the heat equation, and of course you could have
> different rho-Cp and k in each region.
> 
> The code will generate the correct jump in pressure according to the
> surface tension.   (We can check this with the case of a spherical
> drop.)
> 
> Of course, w/o Lee around we'll have to sort all this out to make
> certain it does what we expect... but I'm fairly confident that it
> will.
> 
> Paul

Hi Paul,

OK, I think I understand it.  Taking the surface tension coefficient as:
sigma = sigma0 - sigma1*T
The size of the jump in the pressure between the liquid and the gas
would be determined by the size of sigma0 and the surface curvature.
This would mean then that, assuming an incompressible fluid, the only
effect of sigma0 would be to define the mean pressure difference between
the gas and the liquid.  Do this view seem correct?

Cheers,
Frank


> 
> > Paul,
> > 
> > Great to hear that.  Question; an internal interface has the meaning of
> > an internal boundary condition at which velocity and temperature, but
> > not pressure, boundary conditions can be set? 
> > 
> > Since the normal velocity at the interface is set to zero and the
> > interface completely separates the two fluids, the absolute value of the
> > pressure in the two fluids is independent in the model I have in mind.
> > To put in other words, no pressure gradients across the interface exist
> > in the model.  But I guess that will always be the case in the spectral
> > element method, as long as the interface is not inside an element.
> > 
> > Cheers,
> > Frank
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-- 
Frank Herbert Muldoon, Ph.D. Mechanical Engineering
Technische Universität Wien (Technical University of Vienna)
Inst. f. Strömungsmechanik und Wärmeübertragung (Institute of Fluid
Mechanics and Heat Transfer)
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1040 Wien
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fmuldoo (skype)
http://tetra.fluid.tuwien.ac.at/fmuldoo/public_html/webpage/frank-muldoon.html