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April 16, 2020, 03:53 
When can I use Euler equations?

#1 
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Hello,
I am wondering when I can simplify the NavierStokes Equations and just use the Euler Equations in CFD? Euler: NavierStokes for inviscid flow Reynolds number= ratio of inertial forces / viscous forces So to my understanding, for really high reynolds numbers, the viscous forces decrease, so we can use the euler equations. On the other hand: when we have high reynolds numbers, the flow is turbulent, where friction/viscous forces play an important role (I assume). I read that Euler can be used for high Mach Numbers, where the shock wave influence plays a more important role than the viscous forces. So for high Mach numbers also the reynolds numbers increase. Could someone bring light into my darkness? To which limits would you use Euler for calculations? Thanks! CellZone 

April 16, 2020, 04:40 

#2  
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Filippo Maria Denaro
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Euler equations are a mathematical model that does not allow to set a physical condition about the tangential velocity. Furthermore, the physical energy dissipation is not present and the captare of a real shock wave requires care. High Re number flows are still governed by the NSE, you can see that as the perturbed form of the Euler equations. If you need details about the dynamic and thermal BL you cannot use Euler. 

April 16, 2020, 08:05 

#3 
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Attached, high Re number, external aerodynamic flows is what comes first to my mind.
Everything where the inviscid pressure effects are orders of magnitude higher than viscous ones might be a good rule of thumb (maybe blasts, etc.) 

April 16, 2020, 10:37 

#4  
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Lucky
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The viscous forces don't decrease, they're still increasing. They're just increasing slower than the inertial force. Even if you take the limit as viscosity goes to zero, you have nonzero viscous dissipation because the velocity gradients can increase without bound. 

April 16, 2020, 14:58 

#5 
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First of all you should be aware that the difference between Euler and NavierStokes equations is not only viscosity.
In most cases it is useful to define the terms you want to talk about, e.g., what exactly do you mean when your are talking about Euler and NavierStokes equations. The classical NavierStokes equations consists of at least two different parabolic effects, heat conduction according to Fouriers law and viscous effects according to Stokes law. If you play with more general physics you have to consider more parabolic effects, e.g. Fickian law for multispecies or combustion. 

April 21, 2020, 15:09 

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Thanks to the rest! 

April 21, 2020, 21:54 

#7  
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No matter how much you talk about Reynolds or Mach number number, if you don't mention your application a advice is meaningless. Consider fuel injection or multiphase flows. Here, i would not recommend to run a simulations only with the Euler equations, even if viscous effects are small enough. Other physical effects, e.g. heat conduction, are here far more important. Your question is too general for a simple answer. Last edited by Eifoehn4; April 22, 2020 at 00:50. 

April 22, 2020, 08:27 

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What I learned in school (maybe I did not pay enough attention) is that Euler=Navier Stokes + zero viscosity... Never heard from conductivity ... makes me confused 

April 22, 2020, 08:51 

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Filippo Maria Denaro
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dE/dt= W  Q In order to have a reversible transfer of energy you need zero heat flux and the only reversibile part of the mechanical work. That is no viscosity and no conducibility 

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