[Geysers] Geyser vent velocities

[Bill Johnson]

I ran this question past my son, who is a Ph.D. student in volcanology with
a specific interest in phreatomagmatic eruptions, some of it getting fairly
close to this problem.  I'll spare the list some of the details of what he
had to say, but one important point he raises is that in the analogous
situation of lava fountaining, the ballistic approximation is *not* good
for correlating exit velocity and fountain height.  The main problem,
although there are many, is drag.  Treating lava fountaining as ballistic
tends to overestimate the fountain height given exit velocity (or,
equivalently, underestimate the exit velocity given a known height) by very
large factors.  This problem is obviously going to be worse when the ejecta
are significantly less dense than lava.  There are lots of other things in
play -- buoyancy of the eruption column is another important one -- but
just the one is enough to cause one to be highly cautious about treating
the column as ballistic/Newtonian.

He says some of the modeling codes he uses might be a starting point for
doing better computationally, but probably none are directly applicable.
He's checking to see whether his fellow grad students have anything more
immediately useful, but his recommendation is direct measurements, and he
has some ideas of how to do that.  If the original poster (I've lost the
attribution) can drop me some e-mail, I'll try to connect the dots, or the
people, offline.  Best address for me is canbelto(at)gmail(dot)com.

Interesting problem.  Let me know if I can help.
-- Bill Johnson (aka M. W. Johnson, Ph.D., dad of P. J. Johnson, who will
also be Ph.D. one of these days...)


On Thu, Dec 4, 2014 at 4:49 PM, Davis, Brian L. <brdavis at iusb.edu> wrote:

> > Is there hard data on exit velocities for various geysers?
> > Educated guesses an one?
>
> I don't know of any hard data on the nozzle velocities of natural geysers…
> even with modern video, trying to find something identifiable to "track" in
> the plume is a tough call. You can do the simple physics approximation (but
> see below): based on conservation of energy, the peak height is related to
> the initial velocity by v = sqrt( 2 g h). For a bunch of selected geysers…
> Steamboat, up to 380'… exit velocity up to156 ft/sec
> Beehive, up tp 200'… exit velocity around 113 ft/sec
> Giant (Mastiff function) up to 300'… exit velocity 139 ft/sec
> OF at around 180'… exit velocity 107 ft/sec
> Waimangu jets up to 1,500'… hey, why not… exit velocity about 310 ft/sec
>
> The problem here is this assumes all motion above the visible vent of the
> geyser is "ballistic": moving under the influence of gravity alone. And
> that is almost *certainly* not the case. Entraining of air into the
> eruption column ('air friction' if you will) will reduce the plume height,
> so ignoring it means we've underestimated the exit velocities… but by how
> much will depend on the plume profile (does it spread? Tall and narrow, or
> wide?) and height (taller implies more time to incorporate more air). There
> is also in some cases the possible contribution of phase changes and
> expansion after the plume leaves the vent, although looking at most plumes
> these are going to be minor, and would mean that the above analysis is an
> underestimate.
>
> Susan Kieffer mentions a better way with respect to Old Faithful in one of
> her review papers, using a jet approximation, but I've not run the numbers
> yet… if people are interested, just ask, I'll be happy to. But she notes
> that a ballistic approximation estimates an exit velocity for OF of 102
> ft/sec, while a more proper negatively buoyant plume model estimates an
> exit velocity of 256 ft/sec, about 2.5 times faster… so take the above
> "ballistic" approximation with a very huge grain of sinter-impregnanted
> salt ;)
>
> There's a further really interesting complication on geyser jets… the
> speed of sound in a two-phase fluid can be extremely low (because the mass
> is still high, but the gas means the average fluid is still highly
> compressible). As a result water/steam mixes can have very low sonic
> velocities, around 60-70 feet/sec. Note that this is *lower* than most of
> these estimated exit velocities, meaning that condition in the throat of a
> geyser are likely only a little bit subsonic (and may hit, within the
> throat, Mach 1, exhibiting choked flow and a host of odd supersonic
> behaviors).
>
> --
> Brian "please let me do this in meters next time" Davis
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> Geysers at lists.wallawalla.edu
> 
>
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