How do we decide that a particular fluid flow problem (say a real life flow problem !) needs turbulence modeling while trying to simulate the same. It's known that Reynold's number alone cannot (atleast for some cases) determine whether the flow is turbulent.

In short, what will we loose if laminar model is applied for a high Reynold's number flow ?

Well, you get a 3-D unsteady flow problem (in the instantenous properties), with the spectrum of important scales depending on the Reynolds number (see eg. Tennekes and Lumley: A first course ...). In order to get the right answer you need to resolve ALL scales of the flow (both in space and time). This gives you the history of instantenous data, which then needs to be averaged to get the engineering result you really want (nobody is bothered with, for example, the "turbulent" fluctuation history of the drag coefficient for a car, only with the mean value!). If you mess things up (not enough resolution, inaccurate numerical model, inappropriate averaging), you're likely to get poor results. So, the answer is: "If you've got computer power coming out of your ears, you don't need any turbulence modelling (that's called Direct Numerical Simulation, DNS)." For the rest of us, there's still Reynolds averaging (which gives you the mean properties) and turbulence modelling of some sort.

Why at all do we need Navier-Stokes equation? We can simulate flow problems by using Molecular Dynamics or Boltzmann equation.

Andrzej

Can Molecular Dynamics be applied to all the large-scale fluid dynamical problems now?

No, it can't. Neither now, nor in the future. The same is true for "exact" NS equations. It is not because we will not have enough computer power. Simply, we are not able to control boundary and initial conditions to do exact large scale simulation. At large distances such as in atmospheric, ocean, or 10 000 km pipeline network flow fields are uncorrelated to a great degree. It does not mean that DNS is useless. It can be an excellent tool helping us to define turbulence models, in the same way as molecular dynamics or Boltzmann equation can give us values for viscosity, thermal conductivity, or diffusion coefficient.

Andrzej

Oh, come on!! I agree that Navier-Stokes equations contain a certain amuont of modelling (diffusion terms), which, as you say, can actually be derived from molecular dynamics. But by going back to molecules, you have thrown away the mathematical model of a continuum, whereas simple scale analysis shows this to be unnecessary! Let me give you a different suggestion: why bother with the molecules at all - we can always go for electrons, protons and neutrons (or maybe even go for something more exotic).

I think you did not understand my message. May be, because I tried to be little sarcastic. Anyway, I would be the last one to suggest using molecular approach to model macroscopic flows. On the contrary, I think that each length scale has its own the most appropriate model. Models from the lower length scale can deliver missing constants or closure lows for the higher length scale. Navier-Stoks equations are not exception. They are averaged Boltzmann equations and they need constants from molecular level. Moving to the still greater length scales, the Navier-Stoks equations need to be averaged to get any meaningful results for say Re > 10,000. Missing constants and closure laws in averaged NS equations can be obtained from the previous level, i.e., from the local instantaneous NS equations. I think that RNG turbulence model was derived in this way. I used this approach to derived some closures for the averaged two-phase flow equations from the local instantaneous NS equations written for two phases and for interface. I do not know if someone used DNS to do that, but I think it is feasible.

Andrzej

Yeah, I completely agree with you (I might have got carried away as well, sorry): DNS (and molecular dynamics, if you like) most definitely have a place in numerical simulations - all I was saying is that their "price-preformance" should be kept in mind. Of course, when you need to understand the underlying physics in order to do modelling, price-performance is not an issue; DNS and lattice Bolzman become an ireplacable source of information.