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-   -   Inviscid Turbulent flow (http://www.cfd-online.com/Forums/main/122782-inviscid-turbulent-flow.html)

Vino August 28, 2013 02:12

Inviscid Turbulent flow
 
I have a strange question. Is there any possibility that an inviscid flow can be a turbulent flow and do we use any inviscid turbulent model for our practical application?

arizwan August 28, 2013 03:15

Inviscid Turbulent flow
 
Yes, If the fluid has no viscosity, the viscous force will be small compared to inertial force. So the value of the Reynold’s number will be high. So we will have turbulent flow. But one thing practically, there is no invisid fluid, as every fluid has some viscosity. But for our calculation purpose if the fluid has low viscosity, we assume the viscosity is zero.

FMDenaro August 28, 2013 03:51

inviscid turbulence is a theoretical situation: for zero viscosity (infinite Reynolds number) the turbulence features an energy cascade extending up to an infinite wavenumbers since the Kolomogorov scale is zero. No dissipative part of the energy spectrum exists.
In such case, no DNS is realizable and LES can be performed with some care.
See this LES:
http://www-personal.engin.umd.umich....nn_Dhanak2.pdf

duri August 28, 2013 11:19

Quote:

Originally Posted by Vino (Post 448440)
Is there any possibility that an inviscid flow can be a turbulent flow and do we use any inviscid turbulent model for our practical application?

Euler equation can only convect rotation and can't generate it without viscosity. Viscosity is necessary for turbulence. Perfect slip condtion at wall and at shear will not develop turbulence unless it is convected from inlet condition.
There is no such inviscid tubulent model, what ever dissipation a cfd solver gives is purely numerical. Since high reynolds number flow can be approximated to inviscid flow except near boundary layer, it cannot be used for many cases except were viscous effects dominates.

cfdnewbie August 28, 2013 11:54

Quote:

Originally Posted by duri (Post 448556)
Euler equation can only convect rotation and can't generate it without viscosity. Viscosity is necessary for turbulence. Perfect slip condtion at wall and at shear will not develop turbulence unless it is convected from inlet condition.
There is no such inviscid tubulent model, what ever dissipation a cfd solver gives is purely numerical. Since high reynolds number flow can be approximated to inviscid flow except near boundary layer, it cannot be used for many cases except were viscous effects dominates.


Turbulence is generated through a vortex stretching mechanism, which only required three-dimensionality. Viscosity is NOT needed to produce a scale cascade, only to limit the cascade to a finite bandwidth.

FMDenaro August 28, 2013 11:58

Quote:

Originally Posted by duri (Post 448556)
Euler equation can only convect rotation and can't generate it without viscosity. Viscosity is necessary for turbulence. Perfect slip condtion at wall and at shear will not develop turbulence unless it is convected from inlet condition.
There is no such inviscid tubulent model, what ever dissipation a cfd solver gives is purely numerical. Since high reynolds number flow can be approximated to inviscid flow except near boundary layer, it cannot be used for many cases except were viscous effects dominates.

This is not exactly true... inertial energy cascade is determinated by the non-linear term that produces higher and higher wavenumbers components of the flow.
Vorticity equation exists too for inviscid flows and stretching term does not vanish for Euler equation.
The contribution of the viscosity is in the appearance of the end of the inertiale energy cascade due to the dissipation.

agd August 28, 2013 12:44

While it is true that turbulence is generated by vortex stretching, which is present even in inviscid flows, the question still presents itself: where does the vorticity arise. Since the original poster stated that his interest is in practical applications, this question is not a trivial one. In any application with solid walls, the absence of viscosity not only eliminates a source of vorticity production, but also removes a strong local damping function of turbulence. Substituting numerical dissipation for physical viscosity has always seemed a little off to me, and I'm still skeptical of results from such simulations. Of course, I had a colleague once who said that all turbulence models are just rough approximations, and maybe an inviscid approach is just a little rougher than most.

FMDenaro August 28, 2013 12:57

Quote:

Originally Posted by agd (Post 448572)
While it is true that turbulence is generated by vortex stretching, which is present even in inviscid flows, the question still presents itself: where does the vorticity arise. Since the original poster stated that his interest is in practical applications, this question is not a trivial one. In any application with solid walls, the absence of viscosity not only eliminates a source of vorticity production, but also removes a strong local damping function of turbulence. Substituting numerical dissipation for physical viscosity has always seemed a little off to me, and I'm still skeptical of results from such simulations. Of course, I had a colleague once who said that all turbulence models are just rough approximations, and maybe an inviscid approach is just a little rougher than most.

Your comment is wellcome, further to the vorticity equation for inviscid flows, the problem must be closed by BC.s and initial condition for vorticity. If no initial vorticity exists and no vorticity flows into the domain then you are right. At least excluding the case of internal production of vorticity that can be modelled by some device producing circulation (I was thinking something like MVG).

Vino August 29, 2013 08:14

Quote:

Originally Posted by cfdnewbie (Post 448563)
Turbulence is generated through a vortex stretching mechanism, which only required three-dimensionality. Viscosity is NOT needed to produce a scale cascade, only to limit the cascade to a finite bandwidth.


My doubt again is, as our friend said above, is there any possibility that an inviscid flow can generate turbulence? even when we stir inviscid flow with spoon for example, we can not generate vorticity, because of slip condition.( i agree that the situation is different for practical idealization which was my original question )

FMDenaro August 29, 2013 08:48

Ok, let's stop for a moment thinking about vorticity.
Consider the 1D inviscid Burgers equation

du/dt + d/dx (u^2/2) =0

This model produces what is called "Burgulence", see http://arxiv.org/pdf/nlin/0012033.pdf

Now consider a very smooth initial condition, for example u(x,0) = u0*sin(x), you will simply see that the Fourier component exp(ikx) when inserted into the non linear term will produce exp(2ikx) and so on for time passing...
This is the generation of a scale cascade adn is a model to understand the born of turbulence.
The issue is that even a very smooth initial field can produce an infinite number of wavelenghts.
Of course, if the initial is exactly zero you can not generate nothing but if you have some "small fluctuations" superimposed this generates a cascade.

in 2 and 3D cases, the scenario is the same, the non linearity in the momentum equation generates the scale cascade that can be seen by the vorticity in the stretching action. Viscosity will only dissipate vortices at the Kolmogorov scale (well, the dissipation starts at the Taylor microscale and continues up to the Kolmogorov scale)

In conclusion, any practical application in which velocity gradients are present and interact by means of the non linear convection, produce scale cascade despite of the absence of viscosity.

Vino August 29, 2013 15:07

Thank you very much. Now i got some better clarity regarding this.


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