CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

Gallalian Invariance

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   June 8, 2005, 05:31
Default Gallalian Invariance
  #1
Wayne
Guest
 
Posts: n/a
hi, can someone expalin to me what Gallalian Invariance is.

i am a beginer so need a fairly simple answer, as i keep seeing it written when i read about properties of equations.

  Reply With Quote

Old   June 8, 2005, 05:45
Default Re: Gallalian Invariance
  #2
Tom
Guest
 
Posts: n/a
It's nothing more than (a special case of) Newtons first law; i.e. the equivalence of inertial frames. Mathematically this means that the equations of motion are the same in any two (inertial) frames of reference; e.g. make the transformation x -> x + ct, u -> u + c for any constant c then the equations remain unchanged.

  Reply With Quote

Old   June 8, 2005, 07:30
Default Re: Gallalian Invariance
  #3
Wayne
Guest
 
Posts: n/a
sorry for my lack of understanding - but what is an 'inertial' frame?

do u just mean that where ever i look at it from or how ever i am travelling it looks the same???

is stress gallalian invariant? and if so why?

thanks for your help.

  Reply With Quote

Old   June 8, 2005, 07:44
Default Re: Gallalian Invariance
  #4
Tom
Guest
 
Posts: n/a
An inertial frame is one moving at constant velocity with respect to another frame (the fixed stars in Newtonian mechanics - see any basic school book on physics or applied mathematics).

The stress tensor is invariant under a Gallalean transformation because in a fluid the stresses depend upon the velocity gradient and not the actual velocity (for a Newtonian fluid stress is proportinal to strain).

If the stress tensor was not invariant then the Navier-Stokes equations would no be invariant.

  Reply With Quote

Old   June 8, 2005, 08:13
Default Re: Gallalian Invariance
  #5
Jonas Larsson
Guest
 
Posts: n/a
Check out:

http://en.wikipedia.org/wiki/Galilean_invariance

All laws of classical Newtonian physics should be Galilean invariant. This of course applies to most fluid dynamics laws, including the Navier-Stokes equations. Galelian invariance is often used as a criteria in developing sound physical models for things like turbulence.

For very high speeds, and applications like astrophysics, where clasical mechanics need to be replaced by relativity the laws of physics need no longer be Galilean invariant. Galilean invarance is then replaced by Lorentz invariance... but that is another interesting story. Wikipedia will give you more info if you are interested.
  Reply With Quote

Old   June 8, 2005, 09:17
Default Re: Gallalian Invariance
  #6
multi
Guest
 
Posts: n/a
That is fine Tom I do believe in that.

Say we have a mixture two-phase flow, can we treat the two fluid media in a way to reduce the stress tensor to pressure????
  Reply With Quote

Old   June 9, 2005, 05:44
Default Re: Gallalian Invariance
  #7
Tom
Guest
 
Posts: n/a
I haven't done much work on mixture theory (I'm assuming you are talking about a mixture rather than two fluids separated by a material surface*) - however since in a 1 phase fluid the answer to your question is no in general (the exception being the inviscid limit) then I think it's safe to say the answer is no. In some cases (e.g. inviscid type limit) then it may be possible in special cases to reduce the stress to a (modified) pressure type term.

(*) In this case, in the inviscid limit, the stress is simply the pressure in each phase which you can treat as a single function. this function will be either continuous (no surface tension) or jumps (with surface tension) across the material surface(s).
  Reply With Quote

Old   June 9, 2005, 10:44
Default Re: Gallalian Invariance
  #8
multi
Guest
 
Posts: n/a
This is interesting staff ! Yes about mixture two-phase flow say gas-liquid. So the relative velocity is taken in account i.e. there is an extra equation. In fact I come across thermodynamically compatible systems where the stress tensor reduced to the pressure. During the analysis I find P = P_1 + P_2 using typical EOS for the mixture and for the gas & liquid phases. The interesting side is that the system not biased on the Navier-Stock equations and written in a hyperbolic conservative form. Do believe in this thermodynamically compatible systems……what do you think???
  Reply With Quote

Old   June 10, 2005, 04:51
Default Re: Gallalian Invariance
  #9
Tom
Guest
 
Posts: n/a
If it's not based upon the generalized Navier-Stokes (i.e. the reacting continua equations) then I'm not too sure what you are doing - although I suspect you're using statistical mechanics (which I know very little about). If your approach is a statistical mechanics approach then the ''extra'' stresses are usual hidden leaving only the explicit treatment of the pressure.

In the case of the reacting continua equations you should be able to see which terms in the equations you are approximating and which you are negecting. From what you say about the relative velocities I would assume that you have retained what Truesdell called (if I recall correctly) the "apparrent" stresses. This leaves the two pressure contributions to the stress tensor, which you have, plus the internal/viscous stresses. These internal stresses comprise the normal viscosity of each fluid and the stress of one fluid upon the other. I suspect that your thermodynamically consistent model does not have these terms? (This is probably a reasonable approximation provided you are not interested in boundary effects such as flow separation.

Hope the above ramblings help,

Tom.

P.S. Maybe you should post your question, in more detail, in a new thread - somebody who knows more about what you're doing may reply?
  Reply With Quote

Old   June 17, 2005, 04:28
Default Re: Gallalian Invariance
  #10
David Liu
Guest
 
Posts: n/a
Navier-Stokes equations is of Galilean invariance? The answer is No! You can try that. For example, we assume that one conical pipe flow in the ground accords with NS equation. Then we move this pipe to another inertia frame which moves in a constant speed.

We will found that it will no longer obey NS equation.

  Reply With Quote

Old   June 17, 2005, 06:02
Default Re: Gallalian Invariance
  #11
Tom
Guest
 
Posts: n/a
The Navier-Stokes equations ARE Galilean invariant - it's the boundary conditions that aren't (by changing to a different inertial frame the boundary will appear to move).
  Reply With Quote

Old   June 20, 2005, 00:58
Default Re: Gallalian Invariance
  #12
David Liu
Guest
 
Posts: n/a
For steady flow, NS equation in Vector form:

V . Grad V = Grad p + Div. T

After changing to another inertia system, V changed, but Grad V, Grad p, Div.T do not change their value in the new system.

So that the above equation is not correct any more. That is, left side is not equal to right side.

Is it right?

Thanks, David
  Reply With Quote

Old   June 20, 2005, 04:23
Default Re: Gallalian Invariance
  #13
Tom
Guest
 
Posts: n/a
No it's incorrect. A steady state solution in one inertial frame will be unsteady in another (the Galilean transform involves time).
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
Invariance of relative total temperature jpo FLUENT 0 June 9, 2011 15:39
Gallalian Invariance -------Again David Liu Main CFD Forum 2 June 20, 2005 01:01
Asymptotic (invariance) assumption in turbulence vasanth Main CFD Forum 0 October 24, 2004 11:14
Riemann Invariance Javier Main CFD Forum 2 March 25, 1999 09:02
Gausian Invariance Tom Main CFD Forum 1 August 12, 1998 15:04


All times are GMT -4. The time now is 03:15.