I have posted a question titled as " Turbulence model in flow driven by surface tension" before. Still I wish you can help me on this subject. My questions are (1) How can I give a reasonable initial condition for a unsteady turbulence flow? For steady problems, the finial result does not depend on Initial Conditions(I.C). But for unsteady flow, different results can come from different I.C. (2)Could you please suggest me any paper about Turbulent Model involving free surface.

Thank you in Advance.

The choice of a suitable turbulence model for a free-surface flow is a very difficult task. I think it would be usefull to you to have a look at a paper published by V. Armenio where he uses an SGS model to deal with the turbulence in a sloshing water problem. The full reference is: Armenio, V. 'AN IMPROVED MAC METHOD (SIMAC) FOR UNSTEADY HIGH-REYNOLDS FREE SURFACE FLOWS', Int. journal for Num. Methods in Fluids, vol. 24, 185-214, 1997.

Cheers

N.C. Reis

(1). What do you mean by "Turbulence model in flow driven by surface tension"? you must be dealing with a very special kind of flow. (2). Could you tell us exactly what you are trying to solve? Is this internal flow or external flow? How is the flow driven by the surface tension? Is this a transient flow or a steady state flow? Is the surface tension creating the turbulence ? (3). No one can give you answers you need, unless you can explain clearly the problem your are trying to solve. I think most people would associate the free surface problem to the liquid motion in a tank, or wave motion in the ocean. It is like a matching game where the answer is matched to the question.

The flow model had be describled before, although Dr. Andy had gave me some suggestions, but I has no experience on dealing with Turbulent flow before, and I need more of your suggestings. The model is that a cylindrical liquid bridge of length L held by surface tension forces between two parallel, coaxial solid rods of equal radii R. A temperature difference DT is imposed over the liquid bridge at the disks.

L=100 mm, R=20 mm, DT=100 k, Prandtl number Pr=74 ...

According to experiment and numerical results in literatures and also our recent numerical results, we can sure this flow with above given condition is under turbulent regime. The free surface is taken as non-deformable. For small temperature diffence DT, the flow is 2D axis symmetry roll structure, and it becomes 3D periodic flow and finial tubulence flow with increasing of DT.

This specified flow is driven by surface tension and has strong curvature of free surface. This simulation is time consuming according to our experience on simulation under periodic oscillory regime. It seems that we should take this as 3D transient turbulent flow prblem, because this flow is come from the transition of 3D periodic oscillatory flow with larger DT.

Hi there.

I am not completely sure what I am going to suggest is possible, but I was thinking that if mainly the flow near the deformable surface is important, then you could try to approximate your 3D incompressible flow with a deformable surface by a 2D shallow-water equations (the same the real 3D atmosphere of our planet is approximated with a 2D shallow water equation - analog to a 2D compressible flow). As pointed out by John these are also free-surface flows.

Namely, if your cylindrical coordinates are (r, phi, z), then I would work only in the plane (phi, z) and integrate in r (or do some other assumption in this direction). Then the radius of the liquid in the radial direction r would be (say) h, and the tension force would be derive from a potential that would depend on h (or some power of it). The force would just be the derivatives of it. The exact form of the potential as a function of h has to be derived analytically from the relation for the tension as a function of r or the change of r (over the plane phi z). THen there would be of course only a motion of the flow in the (phi,z) plane that would propagates actually on the surface of the 'cylindrical bridge' of fluid. The shallow water equations are used to represent free surface flow (ocean, atmosphere..). In addition you would have this temperature difference in the z direction, and periodic boundary conditions in the phi one. You would have waves propagating in (phi, z) like surface waves.

Concerning unsteady flows and initial conditions, some flows are unstable when the amplitude of the perturbation exceeds some critical value (these are called non-linearly unstable flows). If the flow transit to turbulence because of the instability, the the transition is called sub-critical. So basically there are two regimes of the flow: stable when the amplitude of the perturbation is less than the critical value, and unstable when the amplitude is larger. The value of the critical value of the amplitude depends on the Reynodls number of the flow. If there are other processes in the flow then the instability depends on other numbers (Rayleigh, etc..). Some other flows are linearly unstable, in that no matter how small is the initial perturbation, the flow is always unstable.

Cheers, Patrick.

(1). It took me a while to see the problem you are trying to solve. It looks like that you have a slender liquid column,cylindrical in shape with the length to diameter ratio of 5, which is suspended in the vertical direction at the top and the bottom by two solid cylinders of equal diameters. As you claimed that it is the surface tension forces between the liquid and the solid cylinders which keeps the liquid in the position. It is amazing that one is able to do such a trick. (2). Assuming that my picture is correct, then, your problem seems to be finding out the flow behavior when the bottom of the liquid is heated to a temperature 100K higher than the temperature at the top of the liquid. (3). I think, the temperature difference will change the picture in two ways:a) it will create convection, that is the hot fluid at the center will move upward, and the cold fluid near the surface will move downward. But, because of the viscous effect and the slenderness ratio of the liquid column, it will form several cells. It's just my guess. b). it will affect the surface tension force locally because of the non-uniform temperature. I know that temperature can affect the surface tension between liquid and solid surface in different ways. In addition, the viscosity also will be affected. Now the boundary condition in the vertical direction is no longer constant. (4). If you have the governing equations and boundary conditions derived(which I can't help you. ), then, you can run the program to solve the flow field with zero temperature difference initially. By gradually changing the temperature boundary condition, you can eventually reach the 100k difference. This should not be a problem because I think you would like to heat the bottom gradually. Naturally, this is a laminar flow case. (5). Some low Reynolds number turbulence models have been shown capable of calculating flow with transition, that is if you plug it in the code, the flow field solution in the laminar, transitional and turbulent regions will come out naturally. In other words, you don't have to set the location or divide the region into laminar or turbulent sub-regions. You need to do some journal paper search in this area (numerical heat transfer journals will be the ideal place to start the search). (6). With such a low Reynolds number turbulence model included in the program, you can simulate the flow in the same way, that is, starting with zero temperature difference and gradually incresing the bottom surface temperature untill the 100K difference is reached. (7). If you can keep the surface shape of the liquid relatively fixed, then, the calculation should be fairly straightforward, I think. (8). 2-D calculation could be the starting point,although 3-D should be all right. If the flow field developed into a spiral motion, then the 3-D would be able to capture it.