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-   -   Why do we treat incompressible flow for Mach (http://www.cfd-online.com/Forums/main/15376-why-do-we-treat-incompressible-flow-mach.html)

 key July 2, 2008 08:22

Why do we treat incompressible flow for Mach

Hi, I have one query. Why do we treat incompressible flow for Mach less than 0.3 Is there any reason??

 Ramesh. K July 2, 2008 08:28

Re: Why do we treat incompressible flow for Mach

for mach 0.3 the variation in density is so less that it is essentially constant so that u can treat it as nearly incompressible flow

 otd July 2, 2008 08:46

Re: Why do we treat incompressible flow for Mach

It was explained to me years ago that

"compressibility goes like Mach Number squared. 0.3^2 = 0.09, or about 10%. Since most engineering calculations have 10% error anyway, M < 0.03 can be treated as incompressible."

You have to decide for yourself if this statement is in fact true. Then you decide if you can accept a 10% error in your calculations.

The payoff for accepting the error is of course that the energy conservation equation uncouples from the NS equations.

 saravanan July 2, 2008 09:34

Re: Why do we treat incompressible flow for Mach

hi the density change associated with increase in mach number gets underestimated largely above m=0.3.typically if u take the isentropic eqn for density and plot it wrt mach no,u will get an increase in density ratio ( i.e total/static)of 4.5% for m=0.3 which is 1 for incompressible flows(contant density).also the rate of decrease in static density wrt to mach number follows a parabolic curve such that at higher mach numbers the variations becomes much larger.as otd said this error on density is not very significant for practical purposes till m=0.3 and the flow can be assumed incompressible provoided this is the max mach number encountered in your flow domain.

 Charles July 2, 2008 14:52

Re: Why do we treat incompressible flow for Mach

Simple rule for subsonic compressible flows says that you can scale forces according to the factor ((1/(1-M^2))^0.5. At M=0.3, this compressibility factor = 1.048, i.e. just about 105%. 5% change in force is an arbitrary, but convenient, threshold value of "significant" compressible effects. M=0.3 is also close to 100 m/s, or close to 200 knots (at sealevel), which also makes it a convenient cut-off point for low-speed aerodynamics.

 key July 3, 2008 02:57

Re: Why do we treat incompressible flow for Mach

Thanks all

 Rami July 3, 2008 03:56

Re: Why do we treat incompressible flow for Mach

... And there is another point. Most compressible solvers will have convergence difficulties as M approaches 0, unless special techniques are used. This gives the motivation (besides what was also said before) to assume incompressibility for M<0.3.

 Jinwon park July 7, 2008 13:58

Re: Why do we treat incompressible flow for Mach

I wonder that Mach number is the value at certain point or averaged or the lowest or the highest value within a domain. Could you advice me how to determine the stage that compressible solvers may be troublesome? I am really curious about the moment when we can consider a stage as to be incompressible. Thanks in advance!

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