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Viscous Heating



 
 
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  #1  
Old May 2nd 07, 06:01 AM posted to sci.physics,sci.astro
John Schutkeker
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Has the theory of viscous heating of an ordinary fluid been developed?
  #2  
Old May 2nd 07, 11:55 AM posted to sci.physics,sci.astro
Greg Neill[_5_]
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"John Schutkeker" wrote in message
. 102...

Has the theory of viscous heating of an ordinary fluid been developed?


What's "an ordinary fluid"? What's not?

Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.


  #3  
Old May 2nd 07, 07:56 PM posted to sci.physics,sci.astro
John Schutkeker
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Bruce Scott TOK ] wrote in
:

John Schutkeker wrote:

Has the theory of viscous heating of an ordinary fluid been developed?


Are you interested in Navier Stokes fluids (i.e., gasdynamics) or
actual liquids where the quantum physics determines the
microproperties?


AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making me
ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you mentioned?
There should be only one equation, and it's NS, although the viscosity
may be a complicted function, rather than a constant. But it should
still be NS, shouldn't it?

I'm interested in a fluid whose properties are hardly even known:
planetary mantles and cores, like Earth and Enceladus. Nobody
knows exactly what are those fluid properties, raising a whole 'nother
theory question that I plan to gloss over.

I'm thinking that under such high pressures, Enceladus' "mantle" may be
a highly viscous liquid, which might be something like a solution of
liquids like N2, NH3, and CH4, etc. Unfortunately, it may also be the
mixture of solid/liquid phases that we colloquially know as "slush."

Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.

Yes in both cases though I'm only familiar with the details of the
first. Have a look at _Physical Kinetics_ in the Landau/Lif****z
series.


I'm planning to get stared by taking the momentum equation and
applying P = F dot v. A viscous force of F = mu Del^2 v, gives P = v mu
del^2 v, and (ha ha) all that's needed is the velocity profile. Again,
I'm sure I can make some primitive assumptions from known tidal
geometries, to get started, but the next correction would involve
self-consistent flows, which is a whole 'nother physics problem to
solve.

I might try my hand at that one, once I've got the zero order model down
on paper. For that, I'll need the tidal force field of a body under
tidal distortion. Where would you look for that, if you had to?

If you're interested in non-equilibrium thermodynamics then there are
several texts on that as well. Look up a book called _Process
Thermodynamics_ for a decent example. I've got it loaned out long
enough to have forgotten the author's name.


Thanks, that sounds very useful.
  #4  
Old May 2nd 07, 07:58 PM posted to sci.physics,sci.astro
John Schutkeker
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Default Viscous Heating

"Greg Neill" wrote in news:46386dd3$0$30274
:

"John Schutkeker" wrote in message
. 102...

Has the theory of viscous heating of an ordinary fluid been developed?


What's "an ordinary fluid"? What's not?


The stuff we're familiar with in ordinary life, with no extreme states of
condensed matter or plasmas. I guess I should have said "incompressible
liquid."

Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.


Theory, not measurement.
  #5  
Old May 2nd 07, 08:22 PM posted to sci.physics,sci.astro
Greg Neill[_5_]
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Default Viscous Heating

"John Schutkeker" wrote in message
. 17.102...
"Greg Neill" wrote in news:46386dd3$0$30274
:

"John Schutkeker" wrote in message
. 102...

Has the theory of viscous heating of an ordinary fluid been developed?


What's "an ordinary fluid"? What's not?


The stuff we're familiar with in ordinary life, with no extreme states of
condensed matter or plasmas. I guess I should have said "incompressible
liquid."

Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.


Theory, not measurement.


"Viscous damping", "Hysteretic damping"


  #6  
Old May 2nd 07, 09:23 PM posted to sci.physics,sci.astro
dlzc
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Posts: 1,426
Default Viscous Heating

Dear John Schutkeker:

On May 2, 11:56 am, John Schutkeker
wrote:
Bruce Scott TOK ] wrote :

....
Are you interested in Navier Stokes fluids (i.e.,
gasdynamics) or actual liquids where the quantum
physics determines the microproperties?


AFAIK, Navier-Stokes (NS) is just a momentum
balance equation, making me ask, since when don't
liquids obey the same force balances on a
differential fluid element as gasses?


Navier Stokes works with viscosity, which is an energy loss term.

If that's true, what momentum equation replaces
NS, in the incompressible liquid case you mentioned?


It depends you your simplifications from NS.

There should be only one equation, and it's NS,
although the viscosity may be a complicted function,
rather than a constant.


Having viscosity a function of the flow field only makes it more
complex. But you are already talking about an insoluble PDE without
simplifying assumptions. So it just adds to computation time for a
numerical solution.

But it should still be NS, shouldn't it?


I believe so, yes.

I'm interested in a fluid whose properties are hardly
even known: planetary mantles and cores, like Earth
and Enceladus. Nobody knows exactly what are
those fluid properties, raising a whole 'nother theory
question that I plan to gloss over.

I'm thinking that under such high pressures,
Enceladus' "mantle" may be a highly viscous liquid,
which might be something like a solution of liquids
like N2, NH3, and CH4, etc. Unfortunately, it may
also be the mixture of solid/liquid phases that we
colloquially know as "slush."


Any permanent features on the surface? Something like the "Great Red
Spot" of Jupiter notwithstanding...

David A. Smith

  #7  
Old May 2nd 07, 09:36 PM posted to sci.physics,sci.astro
Timo A. Nieminen
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Default Viscous Heating

On Wed, 2 May 2007, John Schutkeker wrote:

Has the theory of viscous heating of an ordinary fluid been developed?


I was recently reading about free convection driven by isothermal spheres.
Heating due to viscosity was mentioned in passed, and in the case being
considered, dismissed as negligible. There's probably some number that can
sit alongside the Reynolds number, the Grashoff number, and the Nusselt
number that tells you whether you can ignore it.

It's important in high-speed flows (where there's a lot of kinetic energy
available to convert to heat). From attending the occasional talk on
scramjets, I get the impression that this kind of heating is what gets the
flow to ignition temperatures. The local shock tunnels start off at room
temperature and the flow gets hot enough to ionise stuff. If my copy of
Anderson was not sitting in a box downstairs, I'd look in it to see if
viscous heating is covered.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/...,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

  #8  
Old May 3rd 07, 12:50 AM posted to sci.physics,sci.astro
John Schutkeker
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Posts: 142
Default Viscous Heating

dlzc wrote in
ups.com:

On May 2, 11:56 am, John Schutkeker
Bruce Scott TOK ] wrote


There should be only one equation, and it's NS,
although the viscosity may be a complicted function,
rather than a constant.


Having viscosity a function of the flow field only makes it more
complex. But you are already talking about an insoluble PDE without
simplifying assumptions. So it just adds to computation time for a
numerical solution.


Of course there will be simplifying assumptions, probably based on
Reynolds number. Right mow, my intiution says laminar flow, but of
course that will have to be checked. If it's turbulent or transitional,
I'm not sure what to do, but I think that there are some empirical
models for the spectrum, right?

I'm not sure what to do abut the dissipation in that case, but wouldn't
it be something if tidal flows in the mantle (Earth or Enceladus) turned
out to be turbulent. I don't think it'll happen, because I'm predicting
that fluid in there to be extremely thick.

A turulent flow would be much more efficient at heating, and we observe
that there's healthy quantity of heat being generated in there. Less
for Enceladus, of course, but possibly still enough to make a lot of
liquid water under the crust of a frozen moon.

I need the pressure profiles.

Any permanent features on the surface? Something like the "Great Red
Spot" of Jupiter notwithstanding.


Nope, idealized case, for now, including just fluid layers, and not the
crust. The idea is to see whether crustal or interior losses dominate.
I'd have to assume a boundary condition at the crust.

But thanks for the red spot insight. These planets aren't gas giants,
but I don't know if that makes the issue go away. I wonder if the
presence of a surface crust would be enough to suppress that.
  #9  
Old May 3rd 07, 12:59 AM posted to sci.physics,sci.astro
John Schutkeker
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Posts: 142
Default Viscous Heating

"Timo A. Nieminen" wrote in
:

On Wed, 2 May 2007, John Schutkeker wrote:

Has the theory of viscous heating of an ordinary fluid been
developed?


I was recently reading about free convection driven by isothermal
spheres. Heating due to viscosity was mentioned in passed, and in the
case being considered, dismissed as negligible.


I'm wondering if they used the right viscosities. If the core and
mantle are so extremely thick, I'm wondering if they might not be
negligible. Something tells me that nobody's ever measured viscosities
of liquids under the extreme pressures of a planetary interior.

Of course, I could be wrong, in which case I'm wasting time. But I'm
more interested in the math and the model as much as the answers, so
this is as much for my own edification as it is for a result.

There's probably some
number that can sit alongside the Reynolds number, the Grashoff
number, and the Nusselt number that tells you whether you can ignore
it.


Thank you. That's a really good point.

It's important in high-speed flows (where there's a lot of kinetic
energy available to convert to heat). From attending the occasional
talk on scramjets, I get the impression that this kind of heating is
what gets the flow to ignition temperatures. The local shock tunnels
start off at room temperature and the flow gets hot enough to ionise
stuff. If my copy of Anderson was not sitting in a box downstairs, I'd
look in it to see if viscous heating is covered.


I forgot about that, but sonic flows do generate a lot of friction.
What's the title of Anderson?
  #10  
Old May 3rd 07, 01:43 AM posted to sci.physics,sci.astro
N:dlzc D:aol T:com \(dlzc\)
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Posts: 155
Default Viscous Heating

Dear John Schutkeker:

"John Schutkeker" wrote in
message
. 33.102...
....
Of course there will be simplifying assumptions, probably based
on
Reynolds number. Right mow, my intiution says laminar flow,
but of
course that will have to be checked. If it's turbulent or
transitional,
I'm not sure what to do, but I think that there are some
empirical
models for the spectrum, right?


I would look to heating models of aircraft wings. The leading
edge impact would be non-similar, but shear drag over the surface
woudl be what you are looking for.

Any permanent features on the surface? Something like the
"Great Red Spot" of Jupiter notwithstanding.


Nope, idealized case, for now, including just fluid layers, and
not the
crust. The idea is to see whether crustal or interior losses
dominate.
I'd have to assume a boundary condition at the crust.

But thanks for the red spot insight. These planets aren't gas
giants,
but I don't know if that makes the issue go away. I wonder if
the
presence of a surface crust would be enough to suppress that.


If you are requiring an entirely fluid surface (???), then you
must have some vortex... if not two. One would expect them at /
near the poles. Unlike Jupiter.

David A. Smith


 




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