scholarly journals The Similarity of the Velocity Defect Profile for the Outer Layer in Smooth Wall and Rough Wall Turbulent Boundary Layers.

2001 ◽  
Vol 67 (660) ◽  
pp. 1975-1982
Author(s):  
Takatsugu KAMEDA ◽  
Hideo OSAKA ◽  
Shinsuke MOCHIZUKI
Keyword(s):  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers ◽  
Rough Wall ◽  
Smooth Wall ◽  
Velocity Defect ◽  
Defect Profile

Mean force structure and its scaling in rough-wall turbulent boundary layers

2013 ◽  
Vol 731 ◽  
pp. 682-712 ◽  
Author(s):  
Faraz Mehdi ◽  
J. C. Klewicki ◽  
C. M. White
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Characteristic Length ◽  
Turbulent Boundary Layers ◽  
Rough Wall ◽  
Viscous Force ◽  
Leading Order ◽  
Smooth Wall ◽  
Wall Flows ◽  
The Mean

AbstractThe combined roughness/Reynolds number problem is explored. Existing and newly acquired data from zero pressure gradient rough-wall turbulent boundary layers are used to clarify the leading order balances of terms in the mean dynamical equation. For the variety of roughnesses examined, it is revealed that the mean viscous force retains dominant order above (and often well above) the roughness crests. Mean force balance data are shown to be usefully organized relative to the characteristic length scale, which is equal or proportional to the width of the region from the wall to where the leading order mean dynamics become described by a balance between the mean and turbulent inertia. This is equivalently the width of the region from the wall to where the mean viscous force loses leading order. For both smooth-wall and rough-wall flows, the wall-normal extent of this region consistently ends just beyond the zero-crossing of the turbulent inertia term. In smooth-wall flow this characteristic length is a known function of Reynolds number. The present analyses indicate that for rough-wall flows the wall-normal position where the mean dynamics become inertial is an irreducible function of roughness and Reynolds number, as it is an inherent function of the relative scale separations between the inner, roughness, and outer lengths. These findings indicate that, for any given roughness, new dynamical regimes will typically emerge as the Reynolds number increases. For the present range of parameters, there appear to be three identifiable regimes. These correspond to the ratio of the equivalent sand grain roughness to the characteristic length being less than, equal to, or greater than$O(1)$. The relative influences of the inner, outer, and roughness length scales on the characteristic length are explored empirically. A prediction for the decay rate of the mean vorticity is developed via extension of the smooth-wall theory. Existing data are shown to exhibit good agreement with this extension. Overall, the present results appear to expose unifying connections between the structure of smooth- and rough-wall flows. Among other findings, the present analyses show promise toward providing a self-consistent and dynamically meaningful way of identifying the domain where the wall similarity hypothesis, if operative, should hold.

Applicability of Taylor’s hypothesis in rough- and smooth-wall boundary layers

2016 ◽  
Vol 812 ◽  
pp. 398-417 ◽  
Author(s):  
D. T. Squire ◽  
N. Hutchins ◽  
C. Morrill-Winter ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Boundary Layers ◽  
Outer Region ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Normal Velocity ◽  
Turbulent Shear Flow ◽  
Smooth Wall ◽  
Wall Boundary ◽  
Taylor’S Hypothesis ◽  
Velocity Spectra

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number ($\unicode[STIX]{x1D6FF}^{+}\approx 12\,000$). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956).

Experimental and Computational Study of 2D Smooth Wall Turbulent Boundary Layers in Pressure Gradient

2022 ◽  
Author(s):  
Danny Fritsch ◽  
Vidya Vishwanathan ◽  
Christopher J. Roy ◽  
Todd Lowe ◽  
William J. Devenport ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Computational Study ◽  
Turbulent Boundary Layers ◽  
Smooth Wall

Modelling smooth- and transitionally rough-wall turbulent channel flow by leveraging inner–outer interactions and principal component analysis

2019 ◽  
Vol 863 ◽  
pp. 407-453 ◽  
Author(s):  
Sicong Wu ◽  
Kenneth T. Christensen ◽  
Carlos Pantano
Keyword(s):  
Principal Component Analysis ◽  
Outer Layer ◽  
Principal Component ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Wall Turbulence ◽  
Rough Wall ◽  
Smooth Wall ◽  
Wall Flow ◽  
Near Wall

Direct numerical simulations (DNS) of turbulent channel flow over rough surfaces, formed from hexagonally packed arrays of hemispheres on both walls, were performed at friction Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=200$, $400$ and $600$. The inner normalized roughness height $k^{+}=20$ was maintained for all Reynolds numbers, meaning all flows were classified as transitionally rough. The spacing between hemispheres was varied within $d/k=2$–$4$. The statistical properties of the rough-wall flows were contrasted against a complementary smooth-wall DNS at $Re_{\unicode[STIX]{x1D70F}}=400$ and literature data at $Re_{\unicode[STIX]{x1D70F}}=2003$ revealing strong modifications of the near-wall turbulence, although the outer-layer structure was found to be qualitatively consistent with smooth-wall flow. Amplitude modulation (AM) analysis was used to explore the degree of interaction between the flow in the roughness sublayer and that of the outer layer utilizing all velocity components. This analysis revealed stronger modulation effects, compared to smooth-wall flow, on the near-wall small-scale fluctuations by the larger-scale structures residing in the outer layer irrespective of roughness arrangement and Reynolds number. A predictive inner–outer model based on these interactions, and exploiting principal component analysis (PCA), was developed to predict the statistics of higher-order moments of all velocity fluctuations, thus addressing modelling of anisotropic effects introduced by roughness. The results show excellent agreement between the predicted near-wall statistics up to fourth-order moments compared to the original statistics from the DNS, which highlights the utility of the PCA-enhanced AM model in generating physics-based predictions in both smooth- and rough-wall turbulence.

Finite-difference outer-layer, analytic inner-layer method for turbulent boundary layers

AIAA Journal ◽  
1989 ◽  
Vol 27 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Richard A. Wahls ◽  
Richard W. Barnwell ◽  
Fred R. DeJarnette
Keyword(s):  
Finite Difference ◽  
Boundary Layers ◽  
Outer Layer ◽  
Turbulent Boundary Layers ◽  
Layer Method

scholarly journals On the decay of dispersive motions in the outer region of rough-wall boundary layers

2019 ◽  
Vol 862 ◽  
Author(s):  
Johan Meyers ◽  
Bharathram Ganapathisubramani ◽  
Raúl Bayoán Cal
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Outer Layer ◽  
Stokes Equations ◽  
Outer Region ◽  
Rough Wall ◽  
Rough Boundary ◽  
Mean Flow ◽  
Wall Boundary

In rough-wall boundary layers, wall-parallel non-homogeneous mean-flow solutions exist that lead to so-called dispersive velocity components and dispersive stresses. They play a significant role in the mean-flow momentum balance near the wall, but typically disappear in the outer layer. A theoretical framework is presented to study the decay of dispersive motions in the outer layer. To this end, the problem is formulated in Fourier space, and a set of governing ordinary differential equations per mode in wavenumber space is derived by linearizing the Reynolds-averaged Navier–Stokes equations around a constant background velocity. With further simplifications, analytically tractable solutions are found consisting of linear combinations of $\exp (-kz)$ and $\exp (-Kz)$, with $z$ the wall distance, $k$ the magnitude of the horizontal wavevector $\boldsymbol{k}$, and where $K(\boldsymbol{k},Re)$ is a function of $\boldsymbol{k}$ and the Reynolds number $Re$. Moreover, for $k\rightarrow \infty$ or $k_{1}\rightarrow 0$ (with $k_{1}$ the stream-wise wavenumber), $K\rightarrow k$ is found, in which case solutions consist of a linear combination of $\exp (-kz)$ and $z\exp (-kz)$, and are independent of the Reynolds number. These analytical relations are compared in the limit of $k_{1}=0$ to the rough boundary layer experiments by Vanderwel & Ganapathisubramani (J. Fluid Mech., vol. 774, 2015, R2) and are in reasonable agreement for $\ell _{k}/\unicode[STIX]{x1D6FF}\leqslant 0.5$, with $\unicode[STIX]{x1D6FF}$ the boundary-layer thickness and $\ell _{k}=2\unicode[STIX]{x03C0}/k$.

Sign in / Sign up

Export Citation Format

Share Document