[Taendyr]

Hello,



I was wondering if we can consider a high Mach number flow as viscous ?


The first thing is: if we try to solve the Navier-Stokes equation for high Mach number, do we consider the flow as viscous since we consider the viscosity non 0 ?



The second is: If we want to solve high Mach number, do we just need to solve the Euler equations ?

[Eifoehn4]

As always, it depends on the problem you are interested in. It's true that for higher Mach number diffusive effects might become smaller. However, you can not generalize this to all high Mach applications. Also note that the difference between Navier-Stokes and Euler equations is not only viscosity.

[FMDenaro]

Originally Posted by Taendyr

Hello,



I was wondering if we can consider a high Mach number flow as viscous ?


The first thing is: if we try to solve the Navier-Stokes equation for high Mach number, do we consider the flow as viscous since we consider the viscosity non 0 ?



The second is: If we want to solve high Mach number, do we just need to solve the Euler equations ?

The choice of a viscous or inviscid model does not depend on the Mach number. You decide to consider or not the viscosity of the fluid and that enters into the Reynolds number.
Usually, the Euler equations are used for shock problems since the shock layer for a viscous flow is smaller than a common grid size.

But remember that for Mach number greater than 4-5 you reach high temperatures after the shock wave and the model of the perfect gas is not valid, ioniziation and chemical reaction being in effects. That happens also for viscous models.

[Taendyr]

ok I see.

For me the Euler equations was the Navier-Stokes equations without the diffusive terms i.e. no viscosity and no heat transfert. And also a different boundary condition for the velocity.


So it is totally my choice to consider one model or another.
For example if I want to model the turbulence, I should use the Navier-Sokes model.



The question I had also, is more about the voc : if we consider the Navier-Stokes equations with a high Mach number and a low viscosity, we consider a viscous model. But do we still call the flow a viscous flow ? What I'm trying to mean is that even if we consider a viscous model, the behaviour of the flow might seem more inviscid than viscous. I don't know if I'm really clear...

[FMDenaro]

It is exactly the same concept that introduce the BL theory. Small viscosity acts when high velocity gradients make the diffusive flux having magnitude comparabile to the convective flux.
In regions of smooth gradients the flow is inviscid-like.

[Taendyr]

It is exactly the same concept that introduce the BL theory. Small viscosity acts when high velocity gradients make the diffusive flux having magnitude comparabile to the convective flux.
In regions of smooth gradients the flow is inviscid-like

I don't know this theory (I'm actually a math student getting into cfd). So you are saying taht since the velocity gradient appears in the diffusive flux, the viscosity has a role when this gradient is important.

This gradient appear in shocks areas right ?

[FMDenaro]

Originally Posted by Taendyr

I don't know this theory (I'm actually a math student getting into cfd). So you are saying taht since the velocity gradient appears in the diffusive flux, the viscosity has a role when this gradient is important.

This gradient appear in shocks areas right ?

Yes, in nature the shock is not a mathematical singularity as described in the inviscid flow theory. The variables are continuous in the shock thickness but such a layer is very small O(10^-6) m. Thus, you have very very high gradients, on a computational standard grid this thickness is often not resolved and the shock appears like a discontinuity between two cells.
I strongly suggest to study the topics on a good textbook.

[Taendyr]

Ok thank you !

I strongly suggest to study the topics on a good textbook.

I actually had 2 months to find some papers about compressible solvers (better if high Mach number) read them and do a small report. What made me ask this question is when I sent the title "Some different solvers for compressible viscous flows" one answered me "is it really viscous at high Mach number ?" which made me doubt on my work

[FMDenaro]

Originally Posted by Taendyr

Ok thank you !

I actually had 2 months to find some papers about compressible solvers (better if high Mach number) read them and do a small report. What made me ask this question is when I sent the title "Some different solvers for compressible viscous flows" one answered me "is it really viscous at high Mach number ?" which made me doubt on my work

There is not only the numerics in compressible flow topics but also many relevant physical topics.

The question "is it really viscous at high Mach number ?" makes no sense. In nature a real flow is always viscous, the Mach number say nothing about that (it is a ratio between the kinetic and enthalpy energies). High Mach number flows are generally associated to high velocity (and kinetic energy) so that you can suppose to have also high Reynolds number flow. This latter would drive to the choice of using an "inviscid model" (that is an approximation of the real flow) but you must be aware that the inviscid model can fail in regions of high velocity gradients (like in the boundary layer). Furthermore, inviscid model should be carefully apporached in terms of the weak form. But a weak solution can be not unique and you have to describe a physically admissible solution.

Again, you need to study fundamental textbooks before to approach the study of the papers published on journals.