Friction Velocity from Law of the Wall

In summary, the conversation involved studying data from a Hot Wire Anemometry lab to investigate turbulent flow of air near a flat wall. The participants were trying to find the friction velocity from the laminar near wall region using a method mentioned in a paper by Kline et al. They discussed the process of finding the frictional velocity through direct measurement of wall shear stress and how it involves plotting a graph of velocity versus distance from the wall. One participant expressed confusion about the exact steps and asked for clarification. Another participant provided a formula for determining the wall shear stress but did not give specific instructions.
  • #1
pobatso
17
0
Hi all,

Am currently studying a set of data from a Hot Wire Anemeotry lab that was done a few days ago. The experiment was investigating a turbulent flow of air in a wind tunnel near a flat wall.

As part of the write up, we're ment to find the friction velocity from the laminar near wall region of the data, specifically Y+<10, on a method based on the one used in a paper by Kline et al.

Now it appears that they are finding the frictional velocity from a direct measurement of wall shear stress (t), as u*=(t.rho)^0.5. This is done by plotting a graph of U (velocity) Vs. Y for the laminar near wall region and somehow getting a value for t from the slope of the near wall region.

I'm a bit confused as to the exact steps of how they went about this and was wondering if anyone could help shed some light. Hope I've explained it adequately.

Cheers,
pobatso
 
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  • #2
Very near to the wall (typically y+ < 5-10) in a turbulent boundary u+ = y+

If you understand what u+ and y+ are then you can use the above equation and your measurments to determine the wall shear stress.

Since this is probably for school I won't tell you exactly what to do. But it's relatively straight forward.
 

What is the law of the wall?

The law of the wall is a principle in fluid mechanics that describes the relationship between the velocity of a fluid and the distance from a solid boundary. It states that as the distance from the boundary increases, the velocity of the fluid will approach a constant value known as the "friction velocity."

How is friction velocity calculated using the law of the wall?

The friction velocity is calculated using the law of the wall by taking the square root of the product of the kinematic viscosity and the shear stress at the boundary. This can be expressed as u* = √(ντ).

What is the significance of friction velocity?

Friction velocity is an important parameter in fluid mechanics as it is used to calculate a number of other variables, such as shear stress, which is essential in understanding the behavior of fluids near boundaries. It is also used in various atmospheric and oceanic models to study turbulent flow.

Is the law of the wall applicable to all fluids?

The law of the wall is primarily used for turbulent flows in air or water. It is not applicable to all fluids, as it relies on the assumption of a constant shear stress at the boundary and a logarithmic velocity profile. Other fluids, such as non-Newtonian fluids, may require different approaches.

How accurate is the law of the wall?

The law of the wall is a widely accepted and extensively studied principle in fluid mechanics, and its predictions are generally accurate for turbulent flows near boundaries. However, its accuracy may be affected by factors such as the roughness of the boundary or the presence of strong pressure gradients.

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