Help request: Insulating effects in turbulent plumes

[El Moose Monstero]

Hi everyone,

Just on the offchance that there might be some help available, I have a request for help from those in the know about such things. Basically I'm doing some work with volcanic ash within the core of the eruption plume, of which the greatest inhibition is that there is absolutely no data about the temperature gradients likely to exist within the plume as it goes from leaving the vent at 800°C to traversing the atmosphere, rising and entraining atmospheric air etc.

We've contemplated basic estimates knowing initial plume speed, time taken to reach maximum heights etc and top-of-cloud temperature estimates, but these give us extremely rough estimates and very short contact times which we've been told aren't really worth considering. We were hoping that there might exist a central core relatively well protected from entraining cold air which might let an ash particle remain at high temperatures for longer time frames than particles on the outer edge.

I was hoping that people might be able to point me in the direction of the right subject areas to read into (as I don't want to spend time reading into papers about one subject, only to have someone say 'oh, that doesn't apply in this case because of x'. Ideally, there might be a reference from another field of research which might give us a ballpark estimate or some justification for giving an estimate, there isn't time for an indepth piece of work on this, but this is a hole in my project which needs plugging.

Any help would be greatly appreciated - this is well outside my normal field of research.

Thanks for your time,

[Darth Wong]

Sorry, but we only did a little bit of aerodynamic studies when I was in school; it wasn't really my area of specialty. Erik_t does more work with airflows so you might try asking him, but his work is still going to be more in the area of aerofoils and other aircraft-related things, which is in turn not well-related to what you're asking about.

[Surlethe]

So you're looking for models of the temperature gradients inside an eruption plume? Off the top of my head, you could try looking for models of heat transport in fluids.

I'm tempted to say you ought to model this as a fluid with certain boundary conditions, but I don't know what sort of properties you'd have to assume to model ash and the mixture of various gases I assume are being emitted.

[raptor3x]

What kind of mach number are you seeing at the exit of the volcano? Are you looking for a general analytical relationship or something more specific?

[El Moose Monstero]

What kind of mach number are you seeing at the exit of the volcano? Are you looking for a general analytical relationship or something more specific?

Mach 1 I think. Ideally I'd be looking for an estimate of the cooling rate at the centre line of the plume, I can probably dig out some generic figures / parameters for a 'typical eruption', but I'd need to know what parameters would be needed. As a simple assumption, it could probably be just considered as a steam plume, as water vapour is the major component, as any possible estimate for this is better than the currently available estimate (which is nothing!).

Thanks to everyone who has responded - this was always a long shot but I thought I'd ask on the off chance.

[raptor3x]

I'm not sure how much time you're looking to put into this or how much computational resources you have on hand, but if you could probably get a pretty good estimate via a CFD simulation if you can safely assume uniform non-interacting dust particles. I think most CFD solvers should be able to track particle temperature. That said, like with all atmospheric simulations, you'd need gobs of computational resources.

[erik_t]

I'm in the eighth level of airport hell right now, but I'll give this a more serious look later.

[Darth Wong]

So you're looking for models of the temperature gradients inside an eruption plume? Off the top of my head, you could try looking for models of heat transport in fluids.

I'm tempted to say you ought to model this as a fluid with certain boundary conditions, but I don't know what sort of properties you'd have to assume to model ash and the mixture of various gases I assume are being emitted.

The problem is that most models of heat transfer in fluids tend to rely on empirically derived coefficients.