Characteristic Length Scale
 

Hello Everyone:

I have a question on the characteristic length scale. Is the characteristic length used for calculating Reynolds number same as the characteristic length scale used for calculating Rayleigh number?

I read somewhere that there is some confusion about determining characteristic length scale for estimating Rayleigh number.

Thanks for all your help, Thomas

Re: Characteristic Length Scale
 

The characteristic length scale used to calculate the Reynolds number is usually the size of the computational domain (say L). The characteristic length scale used to calculate the Rayleigh number is the depth of the layer of the fluid (say d). The depth of the layer of the fluid is defined in the direction of the gravitational pull, and in this direction a temperature difference is applied (so d is mesured in the z-vertical direction for example). In many experiements (e.g. the one by Bernard in 1900) and in simulations, the vertical extent of the flow is much smaller than the horizontal one. Therefore, in this case L is much bigger than d. I guess this might be the place for the confusion that you mentioned. PG.

Re: Characteristic Length Scale
 

(1). I think, depending on the need, the Reynolds number can be defined using the length scale appropriate to the problem. (2). So, in the same problem, you can have Reynolds numbers based on the size of the domain, the height of the inlet, the inlet boundary layer thickness, the momentum thickness, the distance from the leading edge, the chord length of the blade,etc..,you name it. (3). As long as they are clearly defined and labeled, it should be all right. So, you can have several Reynolds numbers defined using different length scales, real or integrated scales.