Question about momentum transfer from fluids to discrete particles

[dand5]

Hi, I am having trouble find information on the following topic, I think mostly in part because I don't know the correct terminology.

Basically, I have a number of particles that are falling at their terminal velocities within a gaseous fluid, and turbulent velocity fluctuations in the fluid itselfs occur which transfer momentum to these particles. I was wondering if there is some theory that might describe how much momentum these particles would extract from the fluid. (The turbulent theory used is based on continuity assumptions of variables such as velocity, though the particles are discrete -- I think that is what is confusing me.)


Thanks in advance for any help.

 

[Clausius2]

Hi, I am having trouble find information on the following topic, I think mostly in part because I don't know the correct terminology.

Basically, I have a number of particles that are falling at their terminal velocities within a gaseous fluid, and turbulent velocity fluctuations in the fluid itselfs occur which transfer momentum to these particles. I was wondering if there is some theory that might describe how much momentum these particles would extract from the fluid. (The turbulent theory used is based on continuity assumptions of variables such as velocity, though the particles are discrete -- I think that is what is confusing me.)


Thanks in advance for any help.

There is A LOT of work done in those things man. You only have to go to a search engine and look for papers about that matter. From aerosols to long range dispersion people have researched a lot on the motion of particles in turbulent flows. Basically one couples the equation of motion of the particle with the bulk flow equations. The latter ones can have a reaction from the particle onto the fluid depending on the mass of the particle, or what is the same, depending on the Stokes Number. The Stokes Number measures the amount of slip that a particle suffers when carried by a flow. The issue here is that the forces acting on the particle may depend on the small scales of your turbulent flow (again depending on your particle diameter and the Reynolds Number). If so the small scales of your turbulent flow may have a great importance on the motion of the particle. However, solving the small scales is the main issue of solving a turbulent flow, and as you know using a model for modelling those scales (such that LES) can collaborate to the innacuracy of the computed forces lying on the equation of motion of each particle.

There are some approximations that consider the particles as a passive scalar transported by the flow (like dust or mass fraction), this last assumption is only valid when your Knudsen number of the cloud is small enough for considering continuous the derivatives of the scalar field.

 

[dand5]

Basically one couples the equation of motion of the particle with the bulk flow equations. The latter ones can have a reaction from the particle onto the fluid depending on the mass of the particle, or what is the same, depending on the Stokes Number.

I have looked at a lot of this research. The problem it poses for me is precisely the fact that in most cases a diffussion equation for the heavy particles is coupled together with the fluid equations, and the diffusion coefficient is said to depend on velocity correlations. To solve this kind of flow problem, I think, you either solve the closure problem for this new set of equations or you do some sort of LES up to the scale of the particles you are try to simulate. I really can't do either at this point.

On the other hand, I do have a closure method that predicts to reasonable accuracy the turbulent statistics for a flow over a particular boundary. I am assuming the the energy absorbed by the embedded particles in the fluid is negligable as to have no discernable impact on the evolution of the turbulent flow. Using this, I have a way of computing the PDF for the particle distribution at some later time, kind of like with brownian motion, except the random movements are not statistically independent. The thing is so far, I have simply assumed that once the particles achieve their terminal fall speed, they will be instantaneously lifted/pushed down by turbulent updraft/downdraft and will accelerate to
the vector sum of the turbulent fluctuation and it's terminal fall speed. But, I am suspecting that if the inertial effects are included this may change the resulting velocity of the particle by orders of magnitude?

So I guess this is more a classical physics question than a fluid mechanics one.

I suspect there is a ton of research on this, I just need the keywords so I can google, library search, or whatever.

Thankyou.