Realization of the Turbulent Boundary Layer over the Rough Wall Satisfied the Conditions of Complete Similarity and Its Mean Flow Quantities

Abstract

Mean flow quantities have been investigated for the equilibrium boundary layer evolving over the rough wall with a roughness height that is proportional to streamwise distance. The wall shear stress measured by drag balance with a floating element device of a zero displacement mechanism. The local skin friction coefficient is independent of both streamwise distance and momentum thickness Reynolds number and has a value of 0.00826. The boundary layer thickness is proportional to the streamwise distance. The relative roughness height then maintains a constant value. The log-law profile has the same slope of that of the smooth wall turbulent boundary layer in the logarithmic liner part. The value of the roughness function increases in the streamwise direction. The wake parameter approaches to a constant value of approximately 0.70. In addition, the value is consistent with the result determined from the analytical method using the momentum integral equation and Coles's wake law. For the analytical result, the wake parameter decreases with increasing friction parameter.

Drag of a turbulent boundary layer with transverse 2D circular rods on the wall

“…The values of C p (C p = 0.0084, 0.0086 and 0.0085 at x = 2.54, 2.84 and 3.14 m, respectively), obtained by integrating these profiles, showed only a small variation (about 2.5 %) in x and is within the experimental error. The results of θ from the smoothwall data of Kulandaivelu (2012) and the rough-wall data of Kameda et al (2008) (linearly increasing roughness height) over a comparable streamwise fetch are plotted in Fig. 4.…”

“…6, we report the distributions of mean velocity, velocity defect, and turbulence intensity profiles in (Kulandaivelu 2012) and rough wall with linearly increasing roughness height (red symbols) (Kameda et al 2008). The dashed lines represent linear fits obtained by least-squares regressions for the three data sets smooth-and rough-wall boundary layer flows using δ and U τ as scaling parameters.…”

“…The dashed lines represent linear fits obtained by least-squares regressions for the three data sets smooth-and rough-wall boundary layer flows using δ and U τ as scaling parameters. The smooth-wall data from a developing boundary layer (U ∞ = 20.1 m/s, 7300 ≤ Re θ ≤ 10,850 (Kulandaivelu 2012) and the rough-wall data of Kameda et al (2008) with linearly increasing roughness height are used for the purpose of comparison. Symbols represent the data at different streamwise locations.…”

“…3, and the error in the origin (d 0 ) is determined by calculating the centroid of the moments of the pressure forces acting on the roughness element (see Jackson 1981;Leonardi et al 2003, for a full description of the method). In the measurements of Kameda et al (2008), U τ has been obtained independently using a drag balance. However, they obtained d 0 by assuming that the slope (i.e., κ −1 ) of the log region in the mean velocity profile is same in both smooth and rough walls.…”

“…Further, it is observed that the slope of the log region in the mean velocity profile over the rough wall ( = 8k) appears to be lower than the slope of the log region over smooth wall and rough wall (k ∝ x). Note that the slope over the rough wall (k ∝ x; Kameda et al 2008) was forced to match the slope over smooth wall. This difference in the slopes of the log region requires further investigation and is outside the purview of the paper.…”