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

Fri Apr 2 07:17:42 CDT 2010

On Fri, 2010-04-02 at 14:02 +0200, nek5000-users at lists.mcs.anl.gov
wrote:
> Ok I see. It's hard to say if NEK can handle a problem like this.
> Do you know what's needed on a solver level to tackle such a problem?

Hi Stefan,

My idea of the coupling would be to (at each time step):

1)  solve the liquid using some guess for the velocity and temperature
at the interface

2)  define the tangential stress at and heat flux across the interface
from using the values of the velocity and temperature in the liquid

3)  using the tangential stress and heat flux from 2 as boundary
conditions, solve for the gas (including at the interface).

4) using the velocity and temperature at the interface found in 3, goto
1 and repeat till convergence.

> 
> I think you want to run two NEK instances which are coupled through an interface boundary condition, right?

Yes, that would be the goal. Each instance would have different fluid
properties, and be connected to the other through the mentioned BCs at
the interface.

Are you aware of any uses of Nek5000 to solve surface tension (Marangoni
effect) driven flows?

Cheers,
Frank

> 
> Stefan
> 
> 
> On Apr 2, 2010, at 1:49 PM, nek5000-users at lists.mcs.anl.gov wrote:
> 
> > 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
> >>> 
> >>> _______________________________________________
> >>> Nek5000-users mailing list
> >>> Nek5000-users at lists.mcs.anl.gov
> >>> https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
> >> 
> >> _______________________________________________
> >> Nek5000-users mailing list
> >> Nek5000-users at lists.mcs.anl.gov
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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
> > 
> > _______________________________________________
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> > Nek5000-users at lists.mcs.anl.gov
> > https://lists.mcs.anl.gov/mailman/listinfo/nek5000-users
> 
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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