VISCOUS DISSIPATION
 

What is viscous dissipation and where is it important? Is it effected by Mach No.? By how much magnitude this effects temperature distribution for supersonic flow?

Re: VISCOUS DISSIPATION
 

Viscous dissipation occurs only in turbulence flows.

For example in the turbulent energy equation First order k-e model, it is described as the rate in which turbulent kinetic energy is converted into thermal Kinetic Energy. A more precise definition would be as follows, the Viscous Dissipation term is the destruction of fluctuating velocity gradients by the action of viscous stresses.

Smaller and Smaller Eddies are dissipated by the molecular viscosity near the wall. So it would be very important in the near solid boundaries.

Hope this is in some way helpful.

Re: VISCOUS DISSIPATION
 

I would define viscous dissipation as the transformation of kinetic energy to internal energy (heating up the fluid) due to viscosity. This includes both turbulent kinetic energy and mean flow kinetic energy.

Re: VISCOUS DISSIPATION
 

Thank you for your responses, but these two responses are brief and also there is no difference b/w dissipation and viscous dissipation. Would anyone please explain these in more detail? Thanks, Robert

Re: VISCOUS DISSIPATION
 

Dissipation means the same as viscous dissipation.

Usually when you talk about dissipation in fluid dynamics you mean dissipation of energy, although you can also talk about dissipation of vorticity etc. sometimes.

In a viscous fluid flow the viscosity of the fluid will take energy from the motion of the fluid (kinetic energy) and transform it into internal energy of the fluid. That means heating up the fluid. This process is partially irreversible and is referred to as dissipation, or viscous dissipation.

For a turbulent flow dissipation includes both dissipation of turbulent motions (energy) and mean flow motion. However, the turbulent dissipation is usually completely dominating.

Dissipation is high in regions with large gradients (boundary layers, shear layers etc.) and also in regions with very high turbulence levels (wakes etc.).

Hope that helps.

Re: VISCOUS DISSIPATION
 

"Dissipation" on its own is a slightly imprecise term and needs placing in context in order to hone its meaning (even then it can still be a bit wooly). One usually refers to dissipation of something. "Viscous dissipation" usually refers to the work done by the velocity against the viscous stresses - ie an irreversible process where mechanical energy (useful) is turned into thermal engery (not so useful). But some mild confusion can arise concerning mean/fluctuating/instantaneous components in time-averaged equations of turbulent motion and sometimes the term labelled "viscous dissipation" contains a transportive component. At high Mach numbers (in air - the Reynolds number is also a significant parameter) there is a substantial temperature rise in the boundary layer due to "viscous dissipation".

Re: VISCOUS DISSIPATION
 

Is there any difference b/w aerodynamic heating and viscous heat dissipation? waiting for reply , Julia

Re: VISCOUS DISSIPATION
 

The terms are slightly imprecise when out of context. You would have to state in terms of physical processes what was precisely meant by the two expressions (which would of course answer your own question). It is certainly possible that the terms differ in the context that they were used since the change in state of the fluid can give rise to temperature gradients and heat flow (as can other things). I would suggest looking in a text book or asking the people using the expressions exactly which physical processes they wish to embrace with the expressions. Sorry to duck the question but a definitve answer could be misleading.

Re: VISCOUS DISSIPATION
 

How viscous dissipation and kinetic energy of turbulence are related? Also its effect on static temperature and density? Thanks, Daniel

Re: VISCOUS DISSIPATION
 

I would suggest looking in a good text book to answer this sort of question.

Generally, viscous dissipation is taken to be the irreversible transfer of mechanical energy to heat by the flow working against the viscous stresses. This occurs at all lengths scales but is dominanted by the contribution from the Kolmogorov scales which are the smallest and most intense.

If one takes a Reynolds averaged view, the flow does work against the Reynolds stresses and the viscous stresses (but because the work done term now involves mean rather fluctuating velocity gradients the second term is now very small at high Reynolds numbers).

The work done against the Reynolds stresses is the transfer of energy from the mean flow into the turbulence. It is the source term in the kinetic energy of turbulence transport equation. The viscous dissipation is the sink term in the transport equation (plus the small direct contribution from the mean flow). The physical linkage between the two is the energy cascade where vortex stretching progressively reduces the length scale and increases the velocity scale of the turbulent motion. However, in a typical RANS turbulence model (eg k-e) both the source and sink terms are linked directly to the work done against the Reynolds stesses.

The energy transferred to heat will raise the temperature of the fluid. The effect on density will depend on Mach No and what the flow is doing.

I suspect I have not adequately answered the question by introducing concepts with which you are unfamiliar. I would, again, suggest looking in a text book and filling in your own gaps.

viscous dissipation
 

viscous dissipation is also important in the flow of fluids having high viscosities. temperature of the fluid increases because of it.

Viscous dissipation
 

Can some one tell me the favorable conditions for viscous dissipation to occur in case of flow past cylinder??

Viscous dissipation can be important in flows of polymers or oils. Non-dimensionalize the energy equation and calculate the dimensionless parameter in the viscous dissipation term.

viscous dissipation
 

viscous dissipation or viscous heating is a phenomenon that usually is neglected in macro-scale geometries. but in micro scale the v.d. effect has significant impress on results.

(e.g. in MACRO tube, by increasing mass flow inlet,the heat transfer coefficient{h} increases.But in MICRO tube increasing mass flow will result in reduction of heat transfer coef.{h} ...that's because of v.d effect)

h=q/(Tw - Tbulk) . in micro tubes v.d effect makes the fluid warmer(Tbulk increases)[consider a constant heat flux on tube...so Tw is independent to fluid] so the tempreture difference reduces and by reduction of DELTA T, h increases.

What does the dissipation of PDMS mean? Thank you.
 

What does the dissipation of PDMS mean? Thank you.

Viscous dissipation
 

How should i give dissipation term in buoyant jet problem?
I am comparing Fluent results with Experimental results but i am not getting dissipation of heat in near jet exit for fluent result.
Suggest me?

What do you mean by "how should i..."
Applying the v.d effect is as easy as ticking the term of viscous heating in energy equation in the solver.
Refards

Viscous dissipation
 

Please see the attachement

Here a i am sure about experimental results but the reduction in temperature for fluent result it is less from maximum of 110 degrees to only 108 degrees.

But for experimental which is from 110 degrees to 98 degrees which is realistic at distance of x/d=2.5

How much is the error?
How are you sure about the experimental results, since experimental investigations have some error.
The fact that your numerical results do not exactly fit with the expwrimental results can be due to poor mesh quality or bad boundary condition or use of inappropriate models in the solver.

Hi all,

I have read many papers in which use two different formulas for Viscous Dissipation:

tau : grad(U)
tau : D

where D = 0.5* ( grad(U) + transpose(grad(U)) )

Which one is correct?
Basically, Is there any difference between Stress Work & Viscous Dissipation?

Thanks

the correct definition is mu*S:S wherein S is the simmetric velocity gradient

Thanks, but this formula is just for Newtonian fluid. I want to use the general form of viscous dissipation to calculate for viscoelastic fluid in which tau is a independent tensor.

In non-Newtonian fluids the viscosity is a function of the strain

Not for all of them!
for viscoelastic fluids, we have a complex relation between tau and strain

I apologize for mixing two notation styles but expressing the dissipation term is a little difficult (for me) in a general sense using vector notation. I haven't mastered the two notations yet. =(

The stress work in the energy equation is:


and this can be expanded to:

The dissipation function is only the last part

The other term corresponds to a reversible transfer of kinetic/potential energy of the flow following the work-energy theorem (you can think of it as u times the momentum equation).


An example of this effect is in a developing pipe flow with uniform velocity inlet, and this is most easily seen in the laminar case. The effect of viscous forces accelerates the flow in the center of the pipe to higher than the inlet (into a parabolic profile). If stress work was purely dissipative, the flow wouldn't accelerate.


Only the last term corresponds to the irreversible conversion into thermal energy. Here it is not shown how the last term is irreversible. To do this proof, you have to show that it is positive semi-definite (and maybe invoke some thermodynamic arguments). Physics aside, that leads back to your actual question...

It looks like tau : grad(U) is more correct, unless I made some mathematical mistakes. At least, you know where it comes from.

However, D is computationally efficient because it is a symmetric tensor (less memory and faster to operate on). In numerical codes, it would make sense to use always compute instead of . Tau can be arbitrary without loss of generality so it works for newtonian and non-newtonian fluids.

Thanks for your complex answer, Licky.
It seems that is what I want. However, I have 2 other questions:
1. why do some papers use
viscous diss = tau : D
instead of what you mentioned (tau:gradU)?

2. what is exactly the first term? when is it important ? why didn't usually we see it in fluid mechanics papers?

regards,
Ali

The relation you are referring to is tau = mu(strain)*S. The relation is similar to that of Newtonian fluid but is non linear in the viscosity. The definition of the viscous dissipation (a term you will find in the balance of kinetic energy and, with changed sign, in the balance of internal energy) is straightforward.

1. There are a lot of vector/tensor identities that might be hiding that I don't recognize, so I hesitate to say that tau : D is wrong. However, as I mentioned, D is a symmetric matrix, and numerically this is much more efficient to handle than the full grad(U) tensor.

2. First, you find it in the energy equation. Fluid mechanics papers which only write down the continuity and momentum equations (i.e. the Navier-Stokes equations) will never show you this dissipation term (since dissipation is energy and not momentum). Second, the first term exactly balances the kinetic energy and potential energy so you can easily do some manipulations on your energy equation and it cancels some other terms. Depending on which form of energy equation you write down (and there are dozens of equally valid forms all in popular usage), you may or may not see the term.

Dear Kuck,
That was really helpful.
Thanks for participation in this discussion.