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

steady state creeping flow

Register Blogs Community New Posts Updated Threads Search

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   March 28, 2004, 19:07
Default steady state creeping flow
  #1
dominik
Guest
 
Posts: n/a
Hi,

x-momentum equation for steady-state creeping flow in FV formulation is:

\eta \int_A grad(u) \cdot \hat{n} dA - \int_A p \hat{x} \cdot \hat{n} dA = 0

where u is x-component of velocity, \int_A is surface integral, \cdot is dot product, \hat{x} and \hat{n} denote cartesian unit x vector and normalized outward normal to the surface, respectively. In steady state creeping flow in a tube the two integrals have both to be zero or both be equal. Now, the problem is that the first one is zero then, as expected (no gradients in fully developed duct flow, forget viscosity on walls), but the second one is not - for square grid example:

\int_A p \hat{x} \cdot \hat{n} dA = (p_e-p_w)\delta y

where p_e, p_w denote pressures on east/west faces and \delta y is grid spacing. THIS IS NOT ZERO in steady state (otherwise fluid doesnt flow) but the sum of diffusive fluxes IS zero (no gradients). That way I cant reach steady state. Please help me find the error.

regards, Dominik
  Reply With Quote

Old   March 29, 2004, 05:37
Default Re: steady state creeping flow
  #2
Tom
Guest
 
Posts: n/a
The nonzero (constant) pressure gradient is balanced by the shear u_y which is nonzero.

(If you're working with the depth averaged equations then you need to incorporate the viscous stress at the walls.)
  Reply With Quote

Old   March 29, 2004, 08:36
Default Re: steady state creeping flow
  #3
dominik
Guest
 
Posts: n/a
Thank you for an answer. but I have shear stress term close to walls: I replace diffusive flux by -eta*du/dy do you mean I should have it too in ANY control volume? or do you mean that the flaaaaat parabolic profile extending to tube center is able to balance pressure gradient even there? thank you dominik
  Reply With Quote

Old   March 29, 2004, 10:26
Default Re: steady state creeping flow
  #4
Tom
Guest
 
Posts: n/a
I mean the 2nd; i.e. the shear stress u_y exactly balances the pressure gradient in the flat case so that your first term in your equation is not exactly zero (d/dx is zero for u as you say but d/dy is not)
  Reply With Quote

Old   March 29, 2004, 10:29
Default Re: steady state creeping flow
  #5
dominik
Guest
 
Posts: n/a
I see your point. I was underestimating the parabolic profile in the domain due to noslip walls (I thought it was effectively flat). Thank you. Dominik
  Reply With Quote

Reply


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 Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
mass flow in is not equal to mass flow out saii CFX 12 March 19, 2018 06:21
plz help,urgent, vof model steady state Garima Chaudhary FLUENT 4 March 15, 2018 13:22
Steady state Ruben Main CFD Forum 43 May 7, 2011 04:32
Appropriate model for turbulent, steady state pipe elbow flow milos OpenFOAM Running, Solving & CFD 4 July 9, 2009 03:24
Free Surface Model for Steady State Flow Fred Main CFD Forum 2 February 3, 2006 00:08


All times are GMT -4. The time now is 14:16.