What is the "characteristic length scale" when calculation Reynolds- and Peclet-Numbe

RobertHB · April 5, 2018, 03:53

Hello,
the definition of the caracteristic lenth scale for both, Re as well as Pe, seems to be used interchangeably from publication to publication. Is there a general rule on how to choose the characteristic length scale?

In particular, I want to simulate the flow across a wavey surface and the a complex geometry (see attachments).
I think that for the surface flow, the length of my domain would be a good choice for L when calculating Re. In the complex topography i'd choose the average width of the channels, as they seem to be the limiting factor.

I have no clue about the definition of the lengthscale for Pe, for neither of the problems.

Can someone provide we with some insight?
With best regards,
Robert

piu58 · April 5, 2018, 04:59

Osborne Reynolds worked with tubes. It was logical for him to use the inner diameter. If you use the Reynolds number for circulation you have to chose an appropriate measure.
Of course, this changes form publication to publication. But it is very easy to convert the given Re number to another measure.

FMDenaro · April 5, 2018, 07:07

Any lenght you use will produce a Reynolds number, nothing is wrong in this fact. The key is that we want that the non-dimensional numbers give us an idea of the magnitude of each term in the non-dimensional equations. To make this correct, the process of non-dimensionalization is not sufficient, we need to normalize the non-dimensional terms using the lenght, time and velocity scales that characterize the flow problem.
For example, in your first figure you could use the wavelenght of the geometry or the height of the hill.

Then, Peclet number is nothing but Re*Pr.

RobertHB · April 6, 2018, 03:27

Quote:

Originally Posted by FMDenaro

[...] using the lenght, time and velocity scales that characterize the flow problem.
For example, in your first figure you could use the wavelenght of the geometry or the height of the hill.

Thanks for your answer Denaro. If i understand you correctly the question to find the right length to use in the calculation of Re is to find the lenght of the feature that has the most influence on the fluid flow, right?

FMDenaro · April 6, 2018, 04:04

Quote:

Originally Posted by RobertHB

Thanks for your answer Denaro. If i understand you correctly the question to find the right length to uns in the calculation of Re is to finde the lenght of the feature that has the most influence on the fluid flow, right?

yes, correct.

April 5, 2018, 04:59		#2
piu58 Senior Member Uwe Pilz Join Date: Feb 2017 Location: Leipzig, Germany Posts: 744 Rep Power: 15	Osborne Reynolds worked with tubes. It was logical for him to use the inner diameter. If you use the Reynolds number for circulation you have to chose an appropriate measure. Of course, this changes form publication to publication. But it is very easy to convert the given Re number to another measure. __________________ Uwe Pilz -- Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)

April 5, 2018, 07:07		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,775 Rep Power: 71	Any lenght you use will produce a Reynolds number, nothing is wrong in this fact. The key is that we want that the non-dimensional numbers give us an idea of the magnitude of each term in the non-dimensional equations. To make this correct, the process of non-dimensionalization is not sufficient, we need to normalize the non-dimensional terms using the lenght, time and velocity scales that characterize the flow problem. For example, in your first figure you could use the wavelenght of the geometry or the height of the hill. Then, Peclet number is nothing but Re*Pr.