
[Sponsors] 
December 28, 2010, 21:52 
Some questions about incompressible flow,thx!

#1 
New Member
Aladdin
Join Date: Jan 2010
Posts: 26
Rep Power: 9 
Hi guys,
i got some words on a book, but i cannot understood them very well, it said "In the low speed fluid and gas,they are treated as imcompressible flow.There was no change in the density,so there is no relationship between momentum equations and mass conservation equations". Well ,my question is ,why? THX! 

December 29, 2010, 03:59 

#2  
New Member
Alexey
Join Date: May 2009
Location: St.Petersburg, Russia
Posts: 23
Rep Power: 9 
Quote:
It is known from compressible gasdynamic theory that density depends on Mach number M as where is the specific heat ratio, is the stagnation density, where u is the velocity and c is the speed of sound. Thus, when the maximum M (and maximum u) tends to zero, density becomes independent of u and M and may be treated as constant. In practice when maximum M < 0.1 flow may be considered as incompressible. 

December 29, 2010, 22:21 

#3 
New Member
Aladdin
Join Date: Jan 2010
Posts: 26
Rep Power: 9 
Quote:
WHY? 

December 30, 2010, 07:01 

#4 
Member
private
Join Date: Mar 2009
Posts: 74
Rep Power: 10 
With density constant, momentum and conservation depend only on velocities and pressure. In 3d flow, that's (for example) u, v, w, and p. With 3 momentum eqs. and continuity, that's 4 equations and 4 unknowns. They can (and are) solved without reference to Temperature, internal energy, etc.
Knowing u, v, w, p, etc, the energy equation is one equation in one unknown (temperature, internal energy, enthalpy, etc depending on the form you select for the equation). It might be better to say "the momentum equations are independent of the temperature" but temperature depends on the momentum and pressure. Some other folks might say the coupling between momentumcontinuity and energy is oneway only. That thing about 'no relationship' is sort of confusing. Hope this helps, OTD 

December 30, 2010, 07:46 

#5  
New Member
Alexey
Join Date: May 2009
Location: St.Petersburg, Russia
Posts: 23
Rep Power: 9 
Quote:
Let nondimensional pressure be: where is the constant background pressure, is the reference density and is the reference velocity. then the energy equation in nondimensional form can be written as Here is the reference Mach number. If tends to zero then the energy equation coincides with continuity equation div(u)=0! Thus energy equation in itself "disappears" for incompressible flows (M>0)! Therefore "momentum equations & mass conservation equations are no relationship with energy equations" Details see for example in Wesseling's papers 1. van der Heul DR, Vuik C, Wesseling P. A conservative pressure correction method for compressible flow at all speeds.// Int. J. Numer. Meth. Fluids, 2002, v. 40, pp. 521529. 2. I. Wenneker, A. Segal and P. Wesseling. A Machuniform unstructured grid method. // Int. J. Numer. Meth. Fluids, 2002, v. 40, pp. 12091235. 

December 30, 2010, 23:34 

#6 
New Member
Aladdin
Join Date: Jan 2010
Posts: 26
Rep Power: 9 
thanks for your reply, i got the quetion`s answer, your answer is very clear.


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Incompressible Ideal gas law  Leverkin  FLUENT  5  March 5, 2009 17:41 
Abt: the speed of sound in incompressible flows  jinwon park  Main CFD Forum  3  August 21, 2008 20:44 
Unsteady incompressible flow in a duct  questions  Sam  Main CFD Forum  3  February 22, 2006 09:04 
What is the total energy for incompressible fluid?  Harry Dong  Main CFD Forum  12  February 4, 2006 01:55 
Compressible vs. Incompressible formulations  Fernando Velasco Hurtado  Main CFD Forum  3  January 7, 2000 17:51 