As I mentioned above, in principle such a LES simulation with CHT is possible, but only on the expense of massive Linux Cluster computation time. If I say "massive ressources" then I mean something like several hundreds of CPU cores.

What are the reasons:

1) LES by itself is already a rather expensive simulation method. Usually a good quality LES takes a couple of days on - let's say - 100-200 CPU cores. Mesh resolution depends on the simulated Re number and resolved flow/geometry features, but it is absolutely clear, that you cannot do a good LES on 1 million mesh elements. LES is in any case full 3d and even for a backward facing step you need a certain minimum resolution in the 3rd coordinate direction. And it is forbidden (physically invalid !!) to apply symmetry boundary conditions in a scale-resolving simulation like LES. Even periodicity is a wrong assumption, sine real turbulence is chaotic but not periodic or symmetric.

2) Second, combining LES with conjugate heat transfer is extremely expensive. The reason is, that the time-scales of the LES and the thermal conduction processes in solids are orders of magnitude different in terms of applicable and required time-scales. In the LES you need very small time-scales in order to resolve the motion of large and medium size turbulent eddies and their turbulent fluctuations for pressure, velocity, temperature. In the solid you need to run from your thermal initialization (which is usually not a thermal equilibrium state) to the fully developed temperature distribution in both the solid and fluid domain. Since it is a transient simulation, you cannot apply different timescales in the different domains, like this is usually done in steady-state simulations in order to speed-up this process of finding the new thermal equilibrium, after temperature distributions have fully developed. So you need to run the LES for a substantially linger time for combined LES/CHT in comparison with doing "only" a full LES simulation without CHT. This usually makes LES/CHT so expensive, that with "normal" computational resources it is not possible to do it. But at the peak of science with supercomputers it can be done.

3) In order to quicker arrive at the seeked thermal equilibrium state in fully developed LES conditions one can apply a "trick". In order to let the temperature distribution develop itself more quickly - in particular in the solid domain - one can artificially increase the thermal conductivity value of the solid material by 1-2 orders of magnitude over a certain simulation time period. By that the solid material can quicker heat up to the desired thermal state from the applied boundary conditions and one can save simulation time. But afterwards, if the thermal conductivity value has been set back to normal, one need to run still a larger number of LES through-flow times for the geometry in order to get rid of the influence of this artificially increased physical parameter in the obtained solution.

Finally - I have tried with colleages in an industrial project with VOITH Hydro a similar CFD analyses. And we finished this project with a bit mixed success. The computational resources (~350 CPU cores at that time several years ago in 2014) were not yet really sufficient to obtai a 100% good result of SAS_SST/CHT simulation. But maybe you like to study our publication:

http://www.drthfrank.de/publications/2014/140515_ACUM_2014_CKasprzyk_et_al.pdf

Best regards,

Dr. Th. Frank.

Yes, LES can be performed at moderately high Re number. But your problem must be modelled as a 3D geometry and the grid must be enough fine to resolve the dynamic and thermal BLs. Nowdays, LES is performed commonly over grids of several millions of computational nodes. Only 1 million of nodes could be hardly sufficient for Re=10^3.

Thank You very much sir

You are not mentioning your computational resources, which are available to you. Without that information a good answer cannot be given. And I have a bit doubt, that 1 Million mesh cells are sufficient.

In general doing such a LES is for sure possible, e.g. if computational resources are plenty available like on the SuperMUC-NG supercomputer of Leibniz Supercomputing Center, Garching, germany with its approx. 310.000 CPU cores.

On such a resource an LES for such a comparible simple geometry should be done within a couple of days.

Best regards,

Dr. Th. Frank.

Thank you Very much sir for your kind help, your answer is very helpful for us .But sir, we don't have enough amount of computer resources. We only have a machine with 32 cores.

Mohan Krishna

cosider that, depending on the grid resolution, your computational resource could run an LES. However, the number of days for the solution depends on the specific hardware more than on the number of core. Are you able to manage at least 107 nodes ?

Thank you sir

Yes It is possible but it depends on the grid resolution

As I mentioned above, in principle such a LES simulation with CHT is possible, but only on the expense of massive Linux Cluster computation time. If I say "massive ressources" then I mean something like several hundreds of CPU cores.

What are the reasons:

1) LES by itself is already a rather expensive simulation method. Usually a good quality LES takes a couple of days on - let's say - 100-200 CPU cores. Mesh resolution depends on the simulated Re number and resolved flow/geometry features, but it is absolutely clear, that you cannot do a good LES on 1 million mesh elements. LES is in any case full 3d and even for a backward facing step you need a certain minimum resolution in the 3rd coordinate direction. And it is forbidden (physically invalid !!) to apply symmetry boundary conditions in a scale-resolving simulation like LES. Even periodicity is a wrong assumption, sine real turbulence is chaotic but not periodic or symmetric.

2) Second, combining LES with conjugate heat transfer is extremely expensive. The reason is, that the time-scales of the LES and the thermal conduction processes in solids are orders of magnitude different in terms of applicable and required time-scales. In the LES you need very small time-scales in order to resolve the motion of large and medium size turbulent eddies and their turbulent fluctuations for pressure, velocity, temperature. In the solid you need to run from your thermal initialization (which is usually not a thermal equilibrium state) to the fully developed temperature distribution in both the solid and fluid domain. Since it is a transient simulation, you cannot apply different timescales in the different domains, like this is usually done in steady-state simulations in order to speed-up this process of finding the new thermal equilibrium, after temperature distributions have fully developed. So you need to run the LES for a substantially linger time for combined LES/CHT in comparison with doing "only" a full LES simulation without CHT. This usually makes LES/CHT so expensive, that with "normal" computational resources it is not possible to do it. But at the peak of science with supercomputers it can be done.

3) In order to quicker arrive at the seeked thermal equilibrium state in fully developed LES conditions one can apply a "trick". In order to let the temperature distribution develop itself more quickly - in particular in the solid domain - one can artificially increase the thermal conductivity value of the solid material by 1-2 orders of magnitude over a certain simulation time period. By that the solid material can quicker heat up to the desired thermal state from the applied boundary conditions and one can save simulation time. But afterwards, if the thermal conductivity value has been set back to normal, one need to run still a larger number of LES through-flow times for the geometry in order to get rid of the influence of this artificially increased physical parameter in the obtained solution.

Finally - I have tried with colleages in an industrial project with VOITH Hydro a similar CFD analyses. And we finished this project with a bit mixed success. The computational resources (~350 CPU cores at that time several years ago in 2014) were not yet really sufficient to obtai a 100% good result of SAS_SST/CHT simulation. But maybe you like to study our publication:

http://www.drthfrank.de/publications/2014/140515_ACUM_2014_CKasprzyk_et_al.pdf

Best regards,

Dr. Th. Frank.

I totally agree Thomas Frank I would just address that the suitability of the periodicity condition (not only in LES but also in DNS, DES, URANS) can be physically assessed by the analysis of the spatial correlations. If the zero separation point is within the periodicity lenght, this assumption is suitable.

Filippo Maria Denaro in regards to periodicity length, would it not be the integral of the correlation (rather than it's zero crossing) a more relevant length scale in determining the domain width?

The integral length in spanwise direction can be estimated somehow in a “try and see” procedure. What is making you suppose that the integral is more relevant?

Professor @Denaro, this discussion reminds me a presentation from professor Moin where he demonstrated that a poor periodic resolution lead to a solution that “seemed” good but it was bad. Juding by the large Re number, I’d second your point of view and @Thomas opinion about cluster. Even with that, the amount of data will be huge. So, they will need not only computing power but also, a parallel file system capable of handeling such intese I/O.

Julio, yes it is quite intuitive that a periodicity induces on the flow a somehow non-physical condition and that the chosen lenght must be enough bigger than the biggest vortical structures you could expect. This analsys can be found in literature since 30 years ago, by Jimenez and Moin for example.

Article Numerical investigation of transitional and turbulent backwa...

Filippo Maria Denaro physically this would be a sort of "integral length scale", taking the integral of the correlation rather than the zero crossing takes into account the "correlatedness" of the flow at all locations those two points. (I agree trial and error is usually the best approach, but sometimes one may be able to get a head start using available data, hence my suggestion).

From a more practical standpoint, one can picture cases where the correlation function does not cross zero or where the location of the zero crossing is affected by long-range correlations. For example, in HIT the correlation function of u_x along x would approach zero monotonically but would not cross it. Conversely, quasi-2D structures can introduce long range correlations giving the impression the domain should be much larger than necessary in practice.

Felipe Alves Portela

yes, you can define the transversal integral lenght scale according to the (6.48) in the Pope's textbook. It is defined as an integral extending up to infinity, thus the autocorrelation must be and integrable function. In practice that means you assume the autocorrelation is described on the computational domain up to the point the separation vanishes.

Historically, the experiment of Comte-Bellot (1963) used the two point-correlation and then the well-known simulations of Kim & Moin (1982) followed such approach.

In my opinion, I would ensure that the correlation tends to vanish.

Filippo Maria Denaro I also agree, but Felipe Alves Portela made a right point....even for wide domains the spanwise correlation not always decays to zero for all flow quantities (and I am not sure if it is sufficient if some do, while others don't)......I guess, in the end, you probably won't get around a study of the domain size, if there is no reference literature for the test case available