[Nek5000-users] surface tension (Marangoni effect) driven flows

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

On Fri, 2010-04-02 at 13:30 +0200, nek5000-users at lists.mcs.anl.gov
wrote:
> Hi Frank,
> 
> I guess you have to deal with a sharp interface in your two-phase flow problem.
> The question is how do you resolve this interface having in mind (a) accuracy and (b) boundness (stability).
> 
> High-order methods are typically less robust to under-resolution and you need to play some tricks to get a bounded solution (e.g. using flux-limiters).
> 
> How do you plan to tackle this problem?

Hello Stefan,

The interface does not need to be resolved, it is known.  The situation
is the following.  There is a liquid drop surrounded by gas.  The
surface tension of the liquid is high enough that the shape of the
liquid (i.e., the interface) is not affected by the flow in the liquid
or in the gas.  Therefore the shape of the interface is determined
entirely by the contact angle and gravity.  However, the gas "sees" the
liquid and vice versa, thanks to the continuity of velocity,
temperature, tangential stress and heat flux across the interface.  It
is worth noting that, taking an incompressible gas and liquid, the
pressure level of the gas is not coupled to that of the liquid.  So the
problem can be thought of as two separate simulations which have a
boundary across which they share the above boundary conditions.  So not
a true two-phase flow.

Cheers,
Frank

> 
> 
> -Stefan
> 
>  
> On Apr 2, 2010, at 1:14 PM, nek5000-users at lists.mcs.anl.gov wrote:
> 
> > Hello all,
> > 
> > I am interested in the opinion of users and developers as to whether it
> > is practical to use Nek5000 for a "two-phase" flow problem.  I write
> > "two-phase" since the interface between the two fluids is fixed, with
> > only the shear stress and tangential velocity matched there (normal
> > velocity being zero) and temperature and normal heat flux.  In addition,
> > on the liquid side of the interface there is a shear stress proportional
> > to the temperature gradient along the interface (Marangoni effect).  
> > 
> > Also, am I correct in understanding that all components of velocity are
> > stored at the same location (the Gauss–Lobatto–Legendre points), while
> > the pressure is located at the Gauss–Legendre points?  This being in
> > contrast to a MAC type staggered grid, where each velocity component
> > resides at different spatial locations.
> > 
> > Cheers,
> > Frank
> > 
> > -- 
> > 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)
> > Resselgasse 3
> > 1040 Wien
> > Tel: +4315880132232
> > Fax: +4315880132299 
> > Cell:+436765203470
> > fmuldoo (skype)
> > http://tetra.fluid.tuwien.ac.at/fmuldoo/public_html/webpage/frank-muldoon.html
> > 
> > _______________________________________________
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> > Nek5000-users at lists.mcs.anl.gov
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> 
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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)
Resselgasse 3
1040 Wien
Tel: +4315880132232
Fax: +4315880132299 
Cell:+436765203470
fmuldoo (skype)
http://tetra.fluid.tuwien.ac.at/fmuldoo/public_html/webpage/frank-muldoon.html