Low Re Turbulence model VS Low Re flow and Turbulence Modelling background
 

Dear All,

I am trying to establish my understanding regarding turbulence modelling. Could you please help clarify these question/correct me if I understand it wrongly.

1. the words "LOW REYNOLDS NUMBER" in Low Reynolds number turbulence models (Spalart-Allmaras, original k-omega) and low Reynolds number flow are different?

2. The flow can be divided into 3 distinct regions; laminar > transitional > turbulence

Is Reynolds Number the only one parameter that we use to differentiate these 3 flow regimes? Or is it one of many more parameters?

I understand that unattached flow, vortices, re-circulation, separation are the characteristics of turbulence. Can a laminar flow have such behaviours?

I have modelled an air flow through compressor blade cascade (7 blades in a single row) and found that the maximum local Reynolds number is only less than 2000 (what I learnt from School is that if the Re is to be turbulent then Re must be over 2300), however, due to the very high angle of attack of the blade (36 degrees) the flow over the pressure side of the blade becomes unatttached from the surface and recirculation zones are predicted. >>> to me, this is obviously behaviours of turbulent flow. But think about Re of 2000, should this be classify as laminar flow?

Could you please suggest and fix my logic/reasonings as I am very confused.



Thank you very much for all informative comments.

I try to give some insight....

laminar, transitional and turbulent regions are someway a schematic representation of the flow features over a standard model of the flow encountering a plate wall. Such regions develop along the streamwise direction.
Actually, in real flows, you can have these three regimes to coexist in the same flow problem.
The Reynolds number has to be considered with care. Its value depends on the choice of the characteristic velocity and lenght scale. If you use a characteristic domain lenght scale and velocity, for example the height of a channel and the centerline velocity you get a certain value. But in the same flow problem you could use different lenght and velocity. For example, if you consider the Kolmogorov scale and the BL velocity, you get a Re number of O(1). That simply says that the flow at that lenght scale is laminar, despite the global turbulent regime.
Furthermore, laminar flow can be unsteay and can have separation. For example the laminar flow behind a cylinder is unsteady and generate a vortex shedding at one specific frequency. When it becomes turbulent, at higher Reynolds number, the flow generates more vortical structures and several other frequencies appear in such a way that the energy spectra is much more extended.

Thank you so much FMDenaro,

Your comment is very informative. However, 2 questions arise from reading your comment;

1. You mentioned the UNSTEADY LAMINAR flow, is this different from TURBULENT flow? From some textbooks Ive read, they all mention about the fluctuation-portion of the velocity (deviation from the mean velocity) which occurs along the time axis when they explain turbulent flows to the readers. Does this not mean that any UNSTEADY flow (in terms of any variables, pressure, temperature, density, velocity) is automatically classified as being turbulent? What exactly the criteria which determine laminar/turbulent/transitional? I am sorry for this somewhat stupid question but the boundary between turbulent/laminar is not very clear to me.

2. So, no matter what behaviours (separation, vortices, recirculation) appear in the flow, they has nothing to do with whether or not the flow is laminar or turbulent? They must be judged solely by the Reynolds number? A laminar flow can have separation/recirculation and on the other hand the turbulent flow can be smoothly flow attached to a surface?

No, unsteady flows can be laminar. The difference with turbulent flows is that in laminar regime you have one or few characteristic frequency whiles in turbulent regime you see a wide range of frequency. That characterizes the turbulent spectra from a laminar one that shows one or few peaks.

Again, Re number must be taken with care. I suggest a reading to fundamental textbooks. For example, Kundu for general topics of fluid dynamics and Pope for specific aspect of turbulence

For example your blood flow is unsteady (because your heart beats 60-80 beats per min) & this is almost always laminar. A turbulent blood flow means you should go to the hospital and see a Doctor because you are probably about to have a heart attack. Changing in time and deviation from a mean value is not necessarily turbulent. Turbulent fluctuations are broad in the spectra sense and turbulent flows contain many active scales (+ lots of other things).

laminar vs transition vs turbulent can't really be divided up in a distinct way. Heck, there isn't even a precise definition of what is laminar and what is turbulence. It is very muddy. You really should pick up a book or watch some Youtube videos to learn what makes a turbulent flow turbulent. There is a very unsatisfying description on Wikipedia, but nonetheless there is still quite a huge body of text that still does not capture what is turbulence.

Unattached flow, flow vortices, recirculation, separation are basic flow scenarios not necessarily turbulent. Except for vortices, all of these are much more likely to occur in laminar flows than turbulent ones. None of these yet have the characteristics of turbulent flows (namely, broadband spectra).

A local Re number of (put any number here) means nothing until you say what is the velocity and length scale you are using. Also, flow through compressor cascades is mostly external flow, having characteristics of flow over flat plates rather than channel flow. In this case the Re you should be referencing is 500k and not the 2300 for pipe flows. Of course the 500k is based on a completely different length scale.

A low Re model refers to whether or not a particular implementation of a yet unspecified model produces the correct behavior asymptotic/limiting behavior as you approach walls. Some models like vanilla k-epsilon do not, and when they are implemented in a way such that they recover the right behavior they get dubbed low Re model. Some models like k-omega models always have correct behavior but depending on who you ask they make call it just k-omega.

A low Re number flow... Is some magical Reynolds number associated with some flow. But again this means nothing until you say what velocity you are talking about and what length scale.