![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
brooksmoses) wrote2007-07-26 11:58 am
Ph.D Defense Announcement
Simulation of Multiphase Fluid Flows using a Spatial Filtering Process
Advisor: Chris Edwards
Department of Mechanical Engineering
Stanford University
Location: MERL Conference Room (Rm. 203)
Refreshments served at 9:15am
A fundamental problem in the computation of spray atomization, breaking waves, and many other multiphase flows is the treatment of multiscale surface phenomena. Existing methods typically assume that the flow structures are either fully resolved on the computational grid, or are entirely unresolved (i.e., point particles). However, real droplet- producing flows often involve a continuous cascade of scales from large initial structures that break up into smaller and smaller structures and eventually into droplets, and neither method is applicable for the intermediate scales. This work proposes an alternate formulation which is applicable for flows over the entire range of scales from resolved to unresolved.
We formulate the mass and momentum equations for each fluid in the system in a manner which is well-defined over the entire computational domain, including outside the region where the fluid is located. This can then be spatially averaged (in a manner akin to filtering in large- eddy simulations of turbulent computations) in a manner that is independent of the locations of the fluid interfaces. The result is a flowfield in which both the flow velocities and the surface structures have been separated into resolved and unresolved components, and a set of equations for the evolution of the resolved components.
This formulation can then be combined with models for the specific flow under consideration. These models include models for the viscous stress tensor, for the interactions between fluids at the phase boundaries, and for the effects of the unresolved-scale flow on the spatially-averaged momentum advection. With particular choices of models, many existing methods such as immersed boundary methods, continuuum-surface-force representations of surface tension, and point-particle methods can be recovered as special cases of this formulation. As a result, the formulation can be used to evaluate the range of applicability of these methods, and to suggest enhancements to them.
Computations of flow around circular and spherical particles are used to demonstrate the behavior of the method for partly-resolved and unresolved flows. These calculations illustrate how the formulation can be used to evaluate existing methods for momentum exchange---in this case, point-particle methods---and to suggest enhancements for them. In particular, we find that the applicability of the point-particle assumption is strongly dependent on Reynolds number, and that for cases where a significant wake is present, point-force models can result in inaccurate veclocity fields even when the particle is nearly two orders of magnitude smaller than the filter. Further, we find that point- particle models can be enhanced significantly by including an axial dipole term to represent the unresolved-scale momentum advection effects in the near-particle flow.
no subject
no subject
go you!
no subject
no subject
no subject
no subject
In any case, though, consider that a typical fuel injector in a jet engine produces tens or hundreds of millions of micron-sized droplets per second -- and those droplets (and their distribution) is important if this is part of a model of the combustion that's going on. These obviously can't be fully resolved; in general, they can't even be tracked as point-particles, and instead the computations track "parcels" that represent hundreds or thousands of individual droplets.
On the other hand, these droplets come from the breakup of larger droplets, and those come from the breakup of larger things, and so on up to the initial stream of fuel going through the injector. And that stream and the initial breakup there is a sufficiently complicated process that there's no way to compute it accurately without fully resolving it.
So, if you're trying to compute the full behavior of the spray in that combustor, there are bits of liquid that need to be entirely resolved, and liquid drops that need to be entirely unresolved. And -- and this is where the problems come in -- there are liquid bits at all sizes between those two extremes. No matter what size of grid you pick, somewhere in that range, there are going to be some liquid bits that are about the same size as the grid spacing, and for those some subfilter-scale modeling is definitely going to be required.
The formulation that I derived is something that's intended to span that entire range from the fully-resolved to the unresolved. The particular particle computations that I did are a simple example of using that formulation for something in the smaller end, working up from particles that should be essentially unresolved up to larger particles that are only a factor of 2 or 4 smaller than the grid spacing.
(Now, you may wonder about how I'm freely interchanging "droplet" and "particle" there. Outside the immediate breakup region of a fuel-injector spray, the droplets very quickly relax to quasi-steady states, and most of them are small enough that that means a nearly spherical shape. And very tiny amounts of surface contamination -- which are always present in reality -- are sufficient to keep the surface from moving, so there's no internal circulation. Thus, a solid spherical particle is a quite good approximation for most of the drops in such a spray.)
no subject
no subject
no subject
no subject
no subject
no subject
no subject
MAO
no subject
no subject
no subject
no subject
Can't come, the commute would be a bit much, but I'll think of you.
no subject
no subject
MKK
no subject
no subject
I won't make it, since I'll be teachering, but I'll be on the same campus, and thinking of you!