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- Newsgroups: sci.physics.fusion
- Path: sparky!uunet!seas.smu.edu!vivaldi!aslws01!aslss01!terry
- From: terry@asl.dl.nec.com
- Subject: Re: Responses to Dale Bass
- Message-ID: <1993Jan8.214902.837@asl.dl.nec.com>
- Originator: terry@aslss01
- Sender: news@asl.dl.nec.com
- Nntp-Posting-Host: aslss01
- Organization: (Speaking only for myself)
- References: <1993Jan7.182337.19186@murdoch.acc.Virginia.EDU> <1993Jan7.234826.23344@asl.dl.nec.com> <1993Jan8.021210.27077@murdoch.acc.Virginia.EDU>
- Date: Fri, 8 Jan 1993 21:49:02 GMT
- Lines: 217
-
-
- In article <1993Jan8.021210.27077@murdoch.acc.Virginia.EDU>
- crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
-
- > ...
- > Words are much more dangerous than equations. Equations are well-defined
- > and can be examined quantititively for correlations with experience.
- > Words are fluid and mutable and ill-defined.
- > ...
-
- Alright! Concur completely. Precisely why I _stuck my neck out and sent
- out the UC draft_ -- so others would whack me up the side of the head and
- (maybe even occassionally) help me develop specific quantifications for it.
-
- I rushed it because it has very specific experimental implications, some
- of which seemed to be pretty relevant (and maybe even accurate). This was
- a terrible thing for me to do? Maybe next time I should sit on it for, oh,
- six months to a year and patent the daylights out of every other sentence?
- Alas, I just don't have that high of an opinion of my own ideas!
-
-
- > [terry writes:] ... _Do_ you call this a "shock wave," or not? ...
- >
- > Not exactly, there would be a rarefaction wave within the fluid. Some
- > people call your surface a 'contact wave'. However, you are still limited
- > in driving force to the ambient pressure...
-
- Ah. Thanks -- that will help in the lookup process.
-
-
- > Shock tubes are run somewhat this way, but you don't obtain fusion.
-
- The shock tube is nice as a verbal analogy, but it needs quantification.
- E.g., how precisely does the spherical curvature and very small size of
- the "bubble" vacuum scenario impact the behavior of contact waves?
-
- I will try to do a literature search on this to find the relevant articles,
- if they exist. (Boy do I miss D.C. UTA, maybe? Do you guys let off-campus
- computer types into your physics library without a leash?)
-
-
- > One can do an analysis of this collapse (an empty bubble as per Rayleigh),
- > but it breaks down at the time compressibility effects start to become
- > important (and starts to impede the acceleration process).
-
- Reasonable enough. In UC I even mentioned compressibility slowdown in the
- context of large, hard-to-rearrange molecules, and only proposed the wedge-
- out as likely to apply to small, mobile molecules. Unquantified, of course.
-
-
- > An even better way, though, to get the fluid to higher thermal energy is
- > to assume a spherical piston of some sort in a gas. Give the 'piston' a
- > massive whang, and a strong shock is created. As the center is approched,
- > the shock itself gets stronger.
-
- Yes, I assume that this is the same Landau et al model you've mentioned
- before as your approach to quantifying and formalizing cavitation problems.
- ($50K? Wowzers!) But do Landau et al explicitly include an analysis of the
- contact wave case, or not? (Sigh. Sorry that I don't just look it up, but
- I'm still trying to get a copy of the book.)
-
-
- > One can solve this using similarity methods (c.f. Landau and Lifshitz,
- > Fluid Mechanics, section 107). As the center of the the region approches,
- > the energy within the shock goes as
- >
- > E ~ R^{5-2/a}
- >
- > Where $a$ is a similarity parameter (about 0.7 for polytropic gases with
- > with gamma = 5/3 (monatomic) or gamma = 7/5 (diatomic).
- >
- > So, you can see that though the shock itself gets stronger, the energy it
- > contains the decreases drastically as one approaches the center.
-
- I hope I can interpret that correctly. Please let me know if I messed up:
-
- E - energy
- R - Radius of shock front
- $a$ - Same as "a"?
- a ~ 0.7 (for a first approximation?)
- polytropic - Sorry, my physics dictionary is at home
- gamma - (??) 'aven't the foggiest
- R^{5-2/a} - R to the exponent ( 5 - 2/a ) => ( 5 - 2/0.7 ) => ~ 2.1
-
- I'll assume that to be the correct interpretation for the rest of the
- discussion, and will apologize later if it is not... :) I assume, by
- the way, that this Landau et al equation is for shock waves only? It
- would seem plausible that modifications would be needed for contant waves.)
-
- So I guess you are saying that total energy decreases something close to
- R^2 as R drops towards zero.
-
- Of course, since _volume_ decreases as R^3, this would mean that the energy
- density (I'll call it D for the moment) in this shrinking region of space
- is _increasing_ as:
-
- D ~ R^2 / R^3 = 1/R
-
- Now given that energy _density_ is what a lot of folks might call "heat,"
- could you _please_ tell my why you seem to think everything that I say
- is a violation of the second law, yet the equation (as I've been able to
- interpret it) that you just gave is _not_?
-
- Also, I note that the energy density increases to infinity as the shock
- wave reaches the center, hmm? And here I thought you disagreed with me!
-
- I'm just kidding, of course. The billiard-ball like behavior of gas molecules
- under high pressures -- fugacity, as Dale mentioned -- will dominate in the
- end stages and keep such silly predictions from having any meaning. The
- question instead is how _far_ you can go with such increases before other
- effects begin bleeding away too much of the energy to give intensification.
-
- More specifically, the exponent for the total inbound energy wave equation
- should itself be a monotonically decreasing function f(R), reflecting the
- increasing importance of new energy draining mechanisms as the density and
- temperature of the matter inside a sphere of radius R increases. Thus the
- maximum energy density will be reached when:
-
- E = R^(f(R)) and f(R) = 3
-
- ... where the first equation gives the total inbound energy of the wave
- front. My wedge-out postulate is that for contact waves and small (e.g.,
- monatomic gases), the equation f(R) will remain relatively flat and below
- 3 for several orders of magnitude of R closer as it approaches R=0 than
- for classic shock waves.
-
- I do not know (yet) how to quantify that postulate. Nor I am convinced
- (yet) that such a quantification has _every_ been fully studied for the
- case of contact waves in very small spherical implosions.
-
-
- > Look at this another way. The inbound surface increases its velocity.
- > The velocity is limited by a) real gas effects b) energy.
-
- I'm unsure what you mean by "real gas effects."
-
- If by that you mean some kind of contrast to "ideal gases," you might note
- that I _never_ assumed ideal gases for the wedge-out idea. I don't see how
- you could and still expect to get plausible results on the size scales we
- are talking about, especially during the last few nanoseconds. Indeed, that
- is precisely why I keep insisting on _specific_ quantification of what goes
- on at a near-molecular level, not just extrapolations from larger scales.
-
- As for energy, see my earlier disucussion about energy _densities_ being
- the key issue, not the total wave energy.
-
-
- > ... even if you figure out a way to simply extract some tail of the
- > standard energy distribution (without violating the laws of thermodynamics),
- > you have to go way way up the tail to get to fusion energies. One has to
- > go so far up the tail that there are probably no such molecules actually
- > present in the fluid, and you cannot get the fluid to give them to by
- > itself you without violating the second law.
-
- Phffft. I never proposed this. I mentioned a diffusion selection mechanism
- simply to point out that such things happen (e.g., in Hilsch tubes). I was
- very specific in saying that to be really interesting some sort of further
- _acceleration_ of the gas molecules would be needed -- i.e., wedge-out.
-
- What is the point of arguing against assertions I never made?
-
- Also, you seem to be returning to the theme that _any_ instance of one
- particle gaining energy from two or more other ones is a violation of the
- second law. It is not, and I really don't care to rehash the issue again.
-
- You are very welcome to argue that the _specific_ case of very small, very
- round contact waves cannot do it, but the issue is whether there is enough
- structure and "order" of some sort in such systems to allow amplification
- effects to occur in them. _That_ is the real issue, not the second law.
-
- My entire argument has been based on the presence of just that kind of
- order (via the combination of high symmetry and no void gases), so I'm
- not about to throw without a much more detailed analysis of this case.
-
-
- > There is a way to quantify this gain in velocity, but it is not in the
- > thermodynamically organized fashion presented. However, my specific
- > second law objection was to a specific scheme. I do have general second
- > law objections, but it seems silly to bring them up in the absence of
- > some quantification.
- > ...
- > It doesn't matter. There will certainly be acceleration, but pressure-
- > limited, and nothing truly exciting for ordinary fluids under ordinary
- > conditions.
-
- A strong assertion, but I've heard somewhere or the other that "words are
- much more dangerous than equations." :) Would you care to quantify _your_
- claim that while there will be acceleration, it will be "nothing truly
- exciting for ordinary fluids under ordinary conditions?" (BTW, since when
- is severe cavitation an "ordinary" condition?)
-
- As for "pressure limited," I would like to see (or develop) a very specific
- quantification of small, highly spherical contact waves before responding.
-
- I might note that my own analysis of that scenario is based heavily on
- information and entropy arguments, and from that analysis I say that such
- cases are very interesting, even for ordinary fluids. Your analysis appears
- to be based primarily on an extrapolation of large-scale shock wave models
- to very small scales and the contact wave situation.
-
- I think there is room for further analysis and (I suspect) quantification
- that goes beyond the standard texts you've mentioned.
-
- Cheers,
- Terry Bollinger
-
-
- P.S. -- Dale, I know you from the other group. You've made some great
- observations and suggestions, but I am worried that this could
- be turning into one of your infamous ping-pong matches. Could
- we maybe tone it down a bit after this exchange? Feel free to
- get your response to this one in, but my next one is liable to
- be a lot shorter (up to and including zero bytes!)
-
- I look forward to being blasted by you again in the near future.
-
-
-