On Wed, 1 Oct 2003, David Masten wrote:
>> there's a book in the local
>> library on rocket propellant tanking. IIRC it has a chapter on
>> calculating slosh effects, etc. If
>> you would like, I could probably sink a half hour or so into mining
>> some equations from it...
>
>That would be great. Giving us a title and author would be a good thing
>as well.
That's probably Elliot Ring, "Rocket propellant and pressurization systems",
which does indeed have a "Slosh" chapter.
Knowing this won't help you. :-) Unless you've got a good library handy,
that is. It's yet another early-60s book, and this one is *seriously*
scarce. A knowledgeable used-book dealer will want $200+ for it.
(After years of looking, I saw a copy at a mere $80. I ordered it
instantly. Mine, mine, all mine! :-))
NASA SP-8009 ("Propellant slosh loads") and SP-8031 ("Slosh suppression")
may be less thorough, but *them* you should be able to find online. (If
not, let me know, I've got PDFs.) In case it's of interest, I attach
copies of the notes I made on them first time I read them. Don't remember
whether the ERPS list passes attachments; if it doesn't I'll re-send
separately.
(For that matter, if you need a photocopy of Ring's slosh chapter badly,
let me know.)
Henry Spencer
[EMAIL PROTECTED]
SP-8009, Propellant slosh loads, 1968. MIT A&A.
Damping by wiping action on tank walls is weak.
Dynamic couplng betwee slosh and elastic structures needs watching,
especially since it can couple to other components, e.g. in Pogo.
arsj d61, Abramson, mech model for cylindrical-tank slosh, a61
bottom shape effects. jsr j66 Dodge baffled tanks.
Second-mode slosh mass is only about 3% of first, and so second
and higher mode sloshing is usually negligible... for cylindrical
tanks! In subdivided tanks, this is not always true, e.g. in a
quarter-cylinder the second-mode mass is 43% of first.
Slosh frequencies of many tank shapes can be predicted by treating
them as cylindrical tanks with radius same as that at liquid surface
and depth selected to match fluid volume.
For flat-bottom rigid cylindrical tank, lateral slosh freqs are
(in rad/s) sqrt(en * g/a * tanh(en*h/a)) where a is radius in ft,
h is fluid depth in ft, g is longitudinal acceleration, and en is
1.841 for first mode, 5.331 for second, 8.536 third, 11.706 fourth.
For deep liquids, this is roughly sqrt(en * g/a).
Wiping damping found to correlate with B = 1/nu * sqrt(g*a^3),
where nu is coeff of kinematc viscosity, g is longitudinal
acceleration, a is tank radius. Logarithmic damping in circular
cylindrical tank is about 4.98/sqrt(B).
Lateral slosh adds pressure loading on walls and thus forces and
moments affecting control.
Elastic deformation of walls seems to have little effect on slosh
frequencies and location of sloshing mass, but beware that vice-versa
is more problematic, with slosh definitely affecting coupled bending
frequencies.
SP-8031, Slosh suppression, 1969. MIT A&A.
An early Jupiter was lost because a stepped pitch program had a
step frequency close to the fundamental slosh frequency, causing
loss of control. A Blue Streak was lost because early assessments
of slosh had not been updated after design changes, and the result
was structural failure. The first Saturn I cut off engines slightly
too early, because a coupling with roll control induced rotating
slosh which uncovered the feed line momentarily.
jsr j67 Schwind on flexible baffles contains a detailed discussion
of baffle design which is not specific to flexible baffles.
The S-IVB used rigid nonstructural baffles built with nylon fabric
in its LH2 tank. Radial tension cords sewn into the baffle run
from inboard eyelets to outboard studs. Segments are joined along
radial lines by lacing, and inboard and outboard edges are hemmed
around circumferential tension cords. This design appears to be
as rigid as metal baffles and is lighter and easier to assemble
inside a tank. Attention must be given to tearing stresses.
There is almost always a gap between ring baffles and the wall,
for drainage, although there are indications that baffle effectiveness
drops if the gap gets large.
S-IVB cutoff was done in two stages, separated by 3/4 of a slosh
cycle. There was a conical baffle just below the expected liquid
level at cutoff, and a deflector high in the tank to keep liquid
away from the vent.
Recommended design goals: fundamental bending frequency above
slosh frequency above control frequency.
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