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Michael June 16, 1999 11:00

Natural convection at a cube
Hi there,

calculating the natural convection at a heated cube in a room with cold inflow from the ceiling downwards i observed that above a certain temperature difference between cube and inflow the the 4 bouyant jets caused by the 4 side walls of the cube start to oscillate while below that temperature difference the flow is steady. At the moment I am not quite sure, whether these oscillation have a real physical reason or caused by numerics. Could someone give me a hint on that problem.



John C. Chien June 16, 1999 13:22

Re: Natural convection at a cube
(1). If you are solving the transient equations, normally it is not a problem. You can't force it to become steady state. Unless it diverges eventually. The first step is usually the mesh refinement, especially pay attention to the upper edge of the cube where a new shear layer is formed. (2). If you are solving the steady state equations, the solution oscillation simply says that you are unable to obtain a solution. ( the steady state equations do not accept oscillating solutions. ) There could be many things wrong, such as mesh size and density, treatment of boundary conditions, numerical algorithm used, turbulence models, solution controls(under-relaxation parameters), etc... In addition to the mesh refinement, you can try the first-order upwind method to find out whether you still have the same problem or not. (3). Welcome to the facinating world of CFD.

Patrick Godon June 16, 1999 13:29

Re: Natural convection at a cube
Hi There,

There might be a Kelvin-Helmholtz (shearing) intability developing in the region between the flow going upwards (convective currents due to the Raylegi-Taylors instability) and the ambient medium. When the temperature difference is increased the Rayleigh-Taylor instability is stronger and therefore the flow is more convective (going upwards faster -say) and therefore the shear between the convective flow and the medium is increased, leading to a stronger Kelvin-Helmholtz shearing instability. The situation is similar to that of a jet. The jet propagates fast in a medium at rest, and therefore there is a shear between them. If the velocity of the Jet is v and that of the medium is zero, the change of the velocity (in the outer envelope of the jet) occurs over a distance (say) d: the veolicty across the jet changes from v to 0 over d. The wave length of the instability (in the vertical direction) is of the order of 2*pi*d . The oscillations are wavy-like. The instability can lead to the formation of nice spiral like patterns and eventually turbulence. A good similar example is the smoke of a cigarette (even if you don't smoke).

If the instability is numerical it will probably be a two points oscillation rather than a wavy pattern.

Cheers, Patrick.

Tim June 17, 1999 09:52

Re: Natural convection at a cube
Hi Patrick,

is this instability similar to that mechanism which causes the formation of a Karman vortex street above a critical Reynoldsnumber in a flow over a bluff body ?


Patrick Godon June 17, 1999 13:55

Re: Natural convection at a cube
In both cases the formation of spiral patterns is due to the roll over of the flow induced by the differential velocity (shear) when the flow passes an obstacle (a rigid body or a perturbed interface between two flows with different velocities).

Michael June 25, 1999 03:34

Re: Natural convection at a cube
Hi Patrick,

could you give me an advise, where I can find more about the phenomenon of Kelvin-Helmholtz instability ?


Patrick Godon June 25, 1999 10:39

Re: Natural convection at a cube
There are a few good books that you could try, some are very analytical, others are more technical.

Chandrasekhar, Hydrodynamic and Hydromagnetic instability (much of it is theory, more for advanced studies).

Drazin and Reid, I don't remember the title, but something on hydrodynamic of course. It is more technical, given some examples of the everyday-life (clouds pattern etc..).

I think the book of Lin too.

And any other book on Fluid Dynamics should have a section or a chapter on that. Sometimes it is also refered to as the shearing instability. Textbooks on terrestrial atmosphere might have a different terminology and I think they use the KH instability for a particular case in the stability of a stratified atmosphere.

In any case any good book on Hydro should be fine.



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