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November 28, 2020, 07:43 
High Mach number flow

#1 
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Thibaut
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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 NavierStokes 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 ? 

November 28, 2020, 13:37 

#2 
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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 NavierStokes and Euler equations is not only viscosity.


November 28, 2020, 13:37 

#3  
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Filippo Maria Denaro
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Quote:
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 45 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. 

November 29, 2020, 03:07 

#4 
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Thibaut
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ok I see.
For me the Euler equations was the NavierStokes 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 NavierSokes model. The question I had also, is more about the voc : if we consider the NavierStokes 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... 

November 29, 2020, 03:41 

#5 
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Filippo Maria Denaro
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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 inviscidlike. 

November 29, 2020, 04:03 

#6  
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Thibaut
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Quote:
This gradient appear in shocks areas right ? 

November 29, 2020, 04:19 

#7  
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Filippo Maria Denaro
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Quote:
I strongly suggest to study the topics on a good textbook. 

November 29, 2020, 07:04 

#8  
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Thibaut
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Ok thank you !
Quote:


November 29, 2020, 07:15 

#9  
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Filippo Maria Denaro
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Quote:
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. 

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mach number, viscous flow 
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