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

Dimensionless Parameter and Navier Stokes

Register Blogs Community New Posts Updated Threads Search

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   February 28, 2006, 12:26
Default Dimensionless Parameter and Navier Stokes
  #1
John
Guest
 
Posts: n/a
Ok heres the problem I face, there is a question I have been given but I am damned if I can make ends meat of it.

Basically the questions asks, by using dimensionless parameter try to normalize the Navier Stokes equation.

Now my Uni friends though you differentiate the equation I have been on cfd-online but to no avail, I think it may be a little advance, the rest I can do like the closure problem etc I just do not get what he is trying to ask?
  Reply With Quote

Old   February 28, 2006, 16:14
Default Re: Dimensionless Parameter and Navier Stokes
  #2
CFD_ACE
Guest
 
Posts: n/a
Try relpacing terms with non-dimensionless quantities:

e.g.

Starting with,

d(rho*u)dt + ud(rho*u)dx + mu*d2udx2 = 0

Let U = u/Uo

T = tUo/L

X = x/L

MU = mu/MUo

RHO=rho/RHOo

where Uo,RHOo,MUo and L are all suitable reference scales (for example freestream values).

Making substitutions we have:

(Uo*Uo*RHOo/L)*d(RHO*U)dT + (Uo*Uo*RHOo/L)*Ud(RHO*U)dX + (MUo*Uo/L/L)*MU*d2UdX2 = 0

Dividing throught by the constant in front of the time derivative we obtain:

d(RHO*U)dT + Ud(RHO*U)dx + (MUo/Uo/L/RHOo)*MU*d2UdX2 = 0

  Reply With Quote

Old   February 28, 2006, 22:52
Default Re: Dimensionless Parameter and Navier Stokes
  #3
Peter
Guest
 
Posts: n/a
So I take it your Uni has no library with books in it?
  Reply With Quote

Old   March 1, 2006, 04:10
Default Re: Dimensionless Parameter and Navier Stokes
  #4
John
Guest
 
Posts: n/a
nope just comics :~)
  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



All times are GMT -4. The time now is 23:34.