What on earth is the criteria for the compressible fluid flow , Ma>0.3 or Ma>1 ?

When Ma>0.3, the fluid flow is considered as compressible. However, for the flow over a two-dimensional flat plate at Ma=0.5, the calculation of boundary layer thickness is about the same as the theory value for uncompressible case. Why?

After looking through some books ,such as F.M. White's Viscous Fluid Flow, H.Sclichting's Boundary-Layer Theory , what they mentioned the compressible fluid flow seems refer to the cases of Ma>1.

So, it comes to the conclusion that when Ma>1, we ,in practice, use the theory for the compressible case . Is this right, Sir?

Another rule of thumb of the measure of incompressibility is the change of density.If it lies within a certain range then flow can be assumed incompressible.Further as long as the incompressible code is able to capture the physics even if it slightly into the compressible regime it would be fine.

>Another rule of thumb of the measure of incompressibility is the change of density.

Not to increase the present confusion: Let's be more precise.

a) Compressibility is the ability of density to change due to pressure changes. Mathematically, the derivative of density with respect to pressure is a measure for compressibility. (Density can also change because of temperature changes, which has nothing to do with compressibility.)

b) The above not a "rule of thumb", it's the definition of compressibility.

Here's the rule of thumb. The density on the surface of an airfoil (or any other object) will vary between the absolute minimum (the density at the point of highest local Mach number) and the absolute maxmimum (stagnation density). The ratio of stagnation density to local static density is a function of local Mach number, for ideal gases. For air as an ideal gas (ratio of specific heats = 1.4), the stagnation density is about 5% higher than the static density at a Mach number of 0.3. Hence, if the maximum Mach number on the surface of an airfoil is 0.3, the density in the entire flow field will vary by no more than 5%, which is relatively small. This is the reason why Mach 0.3 is generally considered as upper limit for "incompressible" flow. For any Mach number above that, you will expect larger variations of density.

You'll notice that this rule of thumb is based on the variation of density within a flow field. This isn't exactly the definition of compressibility as stated above (hence, "rule of thumb"). Notice also, that it is the *local* maximum Mach number that matters, not the free-stream value! At the same free-stream Mach number, compressibility will be much more apparent on a thick airfoil than on a flat plate. With a flat plate in subsonic flow, the highest Mach number occurs very locally at the leading edge and that is a singular point, anyway!

I guess you'll see the complications of "rules of thumb". You may use them as you wish, but understand and keep in mind where they come from.

1- Incompressibility hypothesis is not a physical one, IT IS an engineering design hypothesis 2- As posted before, Engineers in their designs neglect changes in density as a result of pressure changes when they are less than 3% (Which corresponds to Mach =0.3 for air flows)(Check The derivation in Anderson Book) 3- It is up to you to decide whether this hypothesis is valid in your design/research or not

To introduce more confusion - sometimes (e.g. high lift multielement airfoils) you can have a significant change of density even at Ma<0.3. And for some applications like aeroacustics even very small density changes have to be accounted for, which can be observed even at nearly zero Mach numbers.

Thanks Harish for---

"as long as the incompressible code is able to capture the physics "

Thanks Mani for "I guess you'll see the complications of "rules of thumb". You may use them as you wish, but understand and keep in mind where they come from. "