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Measurement of Wall Shear Stress
Published in Richard J. Goldstein, Fluid Mechanics Measurements, 2017
Thomas J. Hanratty, Jay A. Campbell
The application of the Preston tube and this calibration to turbulent boundary layer flows depends on the accuracy of the law of the wall. For turbulent flow in pipes or turbulent boundary layers with small pressure gradients, the law of the wall is usually assumed to hold, provided 2dt/d or dt/δ is less than 0.1, where 8 is the boundary layer thickness. For turbulent boundary layers with large positive or negative pressure gradients, the law of the wall holds over a smaller distance, so that dt/δ must be an even smaller quantity in order to use the universal calibration. For many situations, an example of which would be a separated region, the law of the wall is not correct, and the Preston tube cannot be used if it extends beyond the region where U¯=(τ¯w/μ)y.
Measurement of Wall Shear Stress
Published in Ethirajan Rathakrishnan, Instrumentation, Measurements, and Experiments in Fluids, 2016
The wall shear stress in a turbulent boundary layer can also be estimated using the law of the wall. Even though in principle the wall shear stress can be obtained from the velocity distribution in the wall region, that is, τw = μ,(∂U/∂y)y=0, in practice it is difficult to measure the velocity near the surface on account of the pitot tube size and its displacement effect. To circumvent this difficulty, the law of the wall may be used to determine the velocity U. It is sufficient if the velocity distribution is known in the logarithmic region, say between yU*/v = 10 and 100, where U* is the characteristic velocity τw/ρ. To evaluate the coefficient of skin friction Cf, plot the mean velocity profile in the form U/U* = A ln (yU*/v) + B, using various values for U*, where A and B are constants. When the correct U* is used, the slope of the straight line will be equal to 5.6 and the intercept will be equal to 5.4. This process is somewhat tedious. Alternately, a plot of the mean velocity profile in the form U/U∞ vs yU∞/v can be used. For each value of Cf there will be a different curve. Compare the present plotting with a standard chart where the curves are already drawn for different values of Cf. This method is known as Clauser’s technique (White, 1991).
Convection Analysis
Published in Anthony F. Mills, Heat and Mass Transfer, 2018
The straight line seen in Fig. 5.28 has a slope of 2.43, and thus k = 0.41. The most appropriate value of the von Kármán constant κ has been in some dispute for many years, and values from 0.40 to 0.44 have been widely used. Equation (5.131) is often called the law of the wall.
Hybrid CFD-experimental investigation into the effect of sparger orifice size on the metallurgical response of coal in a pilot-scale flotation column
Published in International Journal of Coal Preparation and Utilization, 2022
Arefeh Zahab Nazouri, Vahideh Shojaei, Hamid Khoshdast, Ahmad Hassanzadeh
In fluid dynamics, the law of the wall (a.k.a logarithmic law of the wall) states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of distance from that point to the wall, or the boundary of the fluid region. Therefore, when using turbulence modeling the wall functions play a vital role. When wall function is used, the center of the first cell adjacent to the wall should be in the logarithmic layer region. To ensure this, Y+ was selected to make the size of the first cell of the boundary layer large enough, resulting in smaller number of geometry meshes and lower computational costs. Generally, the Y+ takes the following values depending on the type of wall functions (Golshahifar 2009) as i) standard wall functions (30 < Y+ <300), ii) scalable wall functions (Y+ ≥11.225), iii) non-equilibrium wall functions (30 < Y+ < 300) and iv) enhanced wall treatment (Y+ < 5).
Numerical modeling of converging compound channel flow
Published in ISH Journal of Hydraulic Engineering, 2018
B. Naik, K. K. Khatua, Nigel Wright, A. Sleigh, P. Singh
Thus, standard wall function which uses log-law of the wall to compute the wall shear stress is used (Spalding 1980). Fluid flows over rough surfaces are encountered in diverse situations. If the modeling is a turbulent wall-bounded flow in which the wall roughness effects are considered significant, it can include the wall roughness effects through the law-of-the-wall modified for roughness.Free Surface