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Tom P December 13, 2007 06:01

log law for wind velocity profile
Can someone help please, I'm confused...

I'm trying to create a simple spreadsheet to give wind speeds at a range of heights, from one input wind speed at a reference height.

I want to do it using the log law, where u is a function of friction velocity. Friction velocity is fucntion of the wall shear stress. And the wall shear stress is a function of du/dy. I don't understand how to use this du/dy? I have 1 value for flow velocity (u) at height (y). I know du/dy is not simply u/y, but don't understand what else I can do!

Would greatly appreciate any help. Thank you.

pankaj saha December 13, 2007 07:11

Re: log law for wind velocity profile
how many u velocity you have?

ag December 13, 2007 10:04

Re: log law for wind velocity profile
Since u = 0 at the wall (where y = 0) then to a first approximation du/dy ~ u/y, where these values are taken very close to the wall. Depending on how far you are away from the wall this approximation will either be a good representation of du/dy, or a really bad approximation of du/dy. If you are assuming turbulent flow, and your reference velocity is in what would be the free-stream, then you would be better off using a power-law profile (see Schlichting or some other basic fluid mechanics reference). Is there a reason why you want to use the log-law profile?

Hendrik December 14, 2007 06:00

Re: log law for wind velocity profile
You need something extra: the rougness on the floor/bottom. In the atmosferic boundary layer world it's often called 'z0' and it corresponds to a kind of aerodynamic rougness length (it can be converted to Schlichtings sand rougness: z0=ks*exp(-kappa*B)). For a meteo mast on a plain grass field the 'z0' is 3 cm (standard WMO).

Take the log-law equation:

u+ = 1/kappa ln( (z+zd)/z0 )

with u+ = u/u* (u* the friction velocity) zd = displacement thickness, in case of a meteo mast set it to zero (it doesnot matter much in that case; contrary to the influence of kappa +- 0.42)

your measurement is at z = 10 m, you have a velocity u, assume a value for z0 (3cm) => u* follows => whole profile is known. there is no reason to use a power-law profile.

Tom P December 14, 2007 08:15

Re: log law for wind velocity profile
Thanks ag. Ok, good explanation. The reason I want to use the log law is because I have read in a few sources that it is more accurate than the power law, for example from wikipedia, the "alpha component of the power law is an empirically derived value which depends on the stability of the places where trees or structures impede the near-surface wind, the use of a constant 1/7 value for alpha may yield quite erronous estimates, and the log wind profile is preferred...even under neutral stability conditions, an exponent of 0.11 is more appropriate"

It is for a feasibility study for a wind turbine project, where I have a figures for the wind speed at 10m, 25m, and 45m AGL, from the BWEA. I would just use these to create a curve, but I'm pretty sure that they are just using the power law to give values for 2 out of the 3.

Greatly looking forward to your replies!

Tom P December 14, 2007 08:20

Re: log law for wind velocity profile
Hi Hendrik

ah, but u* = sqrt(wall shear stress / density), where the wall shear stress is a function of du/dy, hence du/dy is my problem?

Thank you for the time so far...please see my reply to Ag as the reason for doing this...Cheers

JWilliams December 14, 2007 10:31

Re: log law for wind velocity profile
Are you able to use something like this?

You will need to know the roughness height (zo) as was mentioned earlier.

I believe the reference to Stull, 2000 is titled meteorology for scientists and engineers

Hendrik December 14, 2007 15:16

Re: log law for wind velocity profile
Yes and no... you need to start the curve/profile somehow, call it 'z0', du/dy or wall shear stress; they are linked together. A rough(er) wall has a higher shear stress, lower du/dy and a higher 'z0'. In the z0-form of the log-law you use the friction velocity u*, that's all. (ignoring the displacement thickness).

So you have data on 10, 25 and 45 m; a large empty field (grass, water) in front. Start curve fitting and find the best 'z0'. You're done.

(if you cannot estimate the surrounding of a mast, then the only option you have is to work out the rms of the fluctuating velocities; it's a measure of the roughness (in front!) of the mast. then you assume that the shear is constant in the lower part of the boundary layer etc... estimating 'z0' is easier)

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