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

How to get pressure tensor?

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

Reply
 
LinkBack Thread Tools Display Modes
Old   March 21, 2003, 08:33
Default How to get pressure tensor?
  #1
Quain_tchew
Guest
 
Posts: n/a
Pressure can be derived from free energy. P=- \frac{\partial F}{\partial V}

For nonhomogeneous fluid, the pressure is not a scalar, but a tensor. Then how to get this tensor?

Who can give me some advices or tell me some paper about it?

Thanks.
  Reply With Quote

Old   March 21, 2003, 09:41
Default Re: How to get pressure tensor?
  #2
Tom
Guest
 
Posts: n/a
Actually the pressure is ALWAYS a scalar by definition. (In a nonhomogenous fluid it's the rest of the stress tensor that's changed; i.e the extrenous stress).
  Reply With Quote

Old   March 21, 2003, 09:56
Default Re: How to get pressure tensor?
  #3
Quain_tchew
Guest
 
Posts: n/a
Sorry, maybe I didn't state it clearly.

I'm working on the problem about gas-liquid interface, in which there is suface tension. Some papers pointed out that there were nondiagonal componants in the pressure tensor.
  Reply With Quote

Old   March 21, 2003, 11:55
Default Re: How to get pressure tensor?
  #4
Tom
Guest
 
Posts: n/a
In the case of a gas-liquid interface with surface tension you simply have

jump in pressure [P] across the interface = T( 1/R_1 + 1/R_2)

where T is the surface tension and R_1,2 are the principal radii of curvature.

You then have the usual equations for the flow velocity and pressure in the liquid and gas separately.

(The pressure Tensor is p times the kronnecker delta where p is a scalar in all cases - even in reacting mixtures/combustion theory)
  Reply With Quote

Old   March 21, 2003, 22:11
Default Re: How to get pressure tensor?
  #5
Quain_tchew
Guest
 
Posts: n/a
If I use the Laplace equation, I have to compute the two curvature of the interface which means I have to trace the interface.

Now I use diffuse interface model, in which the interface is not sharp and I can only get the derivative of the density.

In fact, in nonhomogeneous fluid, the free energy has some another terms about the derivative of the density and which the free energy fuction of homogeneous fluid hasn't. I wish to derive the pressure tensor from this free energy with the derivative of the density.

In fact, some papers did this work. But there is no detail.
  Reply With Quote

Old   March 22, 2003, 18:02
Default Re: How to get pressure tensor?
  #6
cfdeye
Guest
 
Posts: n/a
why the pressure is ALWAYS a scalar by definition. where is the EOS in that case, could you please expalin the reason.
  Reply With Quote

Old   March 23, 2003, 02:24
Default Re: How to get pressure tensor?
  #7
Dean
Guest
 
Posts: n/a
If you derive the Navier-Stokes equation by taking moments of the Boltzmann equation, you find that you have to evaluate a second-rank stress tensor. In the limit of a collision-dominated fluid (mean free path << length scale of the flow), this tensor reduces to the scalar pressure times the unit tensor, plus the viscous stresses. This is the limit in which we normally do thermodynamics. The surface tension at an interface is an additional physical effect, and it is also a continuum concept.
  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
Calculation of the Governing Equations Mihail CFX 7 September 7, 2014 06:27
Setup/monitor points of pressure and force coefficients siw CFX 3 October 22, 2010 06:07
Operating condition in Fluent MASOUD FLUENT 3 September 16, 2010 17:50
Pressure Condition sidd CD-adapco 0 April 2, 2007 09:31
Setting pressure and velocity in inlet Asghari FLUENT 5 September 22, 2006 13:23


All times are GMT -4. The time now is 08:40.