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.

On scaling pipe flows with sinusoidal transversely corrugated walls: analysis of data from the laminar to the low-Reynolds-number turbulent regime

2015 ◽  
Vol 779 ◽  
pp. 245-274 ◽  
Author(s):  
S. Saha ◽  
J. C. Klewicki ◽  
A. Ooi ◽  
H. M. Blackburn
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Separation ◽  
Rough Wall ◽  
Recent Analysis ◽  
Wall Structure ◽  
Turbulent Regime ◽  
Smooth Wall ◽  
Wall Flows ◽  
The Mean

Direct numerical simulation was used to study laminar and turbulent flows in circular pipes with smoothly corrugated walls. The corrugation wavelength was kept constant at $0.419D$, where $D$ is the mean diameter of the wavy-wall pipe and the corrugation height was varied from zero to $0.08D$. Flow rates were varied in steps between low values that generate laminar flow and higher values where the flow is in the post-transitional turbulent regime. Simulations in the turbulent regime were also carried out at a constant Reynolds number, $\mathit{Re}_{{\it\tau}}=314$, for all corrugation heights. It was found that even in the laminar regime, larger-amplitude corrugations produce flow separation. This leads to the proportion of pressure drop attributable to pressure drag being approximately 50 %, and rising to approximately 85 % in transitional rough-wall flow. The near-wall structure of turbulent flow is seen to be heavily influenced by the effects of flow separation and reattachment. Farther from the wall, the statistical profiles examined exhibit behaviours characteristic of smooth-wall flows or distributed roughness rough-wall flows. These observations support Townsend’s wall-similarity hypothesis. The organized nature of the present roughness allows the mean pressure drop to be written as a function of the corrugation height. When this is exploited in an analysis of the mean dynamical equation, the scaling problem is explicitly revealed to result from the combined influences of roughness and Reynolds number. The present results support the recent analysis and observations of Mehdi et al. (J. Fluid Mech., vol. 731, 2013, pp. 682–712), indicating that the length scale given by the distance from the wall at which the mean viscous force loses leading order is important to describing these combined influences, as well as providing a dynamically self-consistent connection to the scaling structure of smooth-wall pipe flow.

scholarly journals Reynolds-number-dependent turbulent inertia and onset of log region in pipe flows

2014 ◽  
Vol 757 ◽  
pp. 747-769 ◽  
Author(s):  
C. Chin ◽  
J. Philip ◽  
J. Klewicki ◽  
A. Ooi ◽  
I. Marusic
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Wall Turbulence ◽  
Viscous Force ◽  
Advective Transport ◽  
Leading Order ◽  
Pipe Flows ◽  
Change Of Scale ◽  
The Mean

AbstractA detailed analysis of the ‘turbulent inertia’ (TI) term (the wall-normal gradient of the Reynolds shear stress,$\mathrm{d} \langle -uv\rangle /\mathrm{d} y $), in the axial mean momentum equation is presented for turbulent pipe flows at friction Reynolds numbers$\delta ^{+} \approx 500$, 1000 and 2000 using direct numerical simulation. Two different decompositions for TI are employed to further understand the mean structure of wall turbulence. In the first, the TI term is decomposed into the sum of two velocity–vorticity correlations ($\langle v \omega _z \rangle + \langle - w \omega _y \rangle $) and their co-spectra, which we interpret as an advective transport (vorticity dispersion) contribution and a change-of-scale effect (associated with the mechanism of vorticity stretching and reorientation). In the second decomposition, TI is equivalently represented as the wall-normal gradient of the Reynolds shear stress co-spectra, which serves to clarify the accelerative or decelerative effects associated with turbulent motions at different scales. The results show that the inner-normalised position,$y_m^{+}$, where the TI profile crosses zero, as well as the beginning of the logarithmic region of the wall turbulent flows (where the viscous force is leading order) move outwards in unison with increasing Reynolds number as$y_m^{+} \sim \sqrt{\delta ^{+}}$because the eddies located close to$y_m^{+}$are influenced by large-scale accelerating motions of the type$\langle - w \omega _y \rangle $related to the change-of-scale effect (due to vorticity stretching). These large-scale motions of$O(\delta ^{+})$gain a spectrum of larger length scales with increasing$\delta ^{+}$and are related to the emergence of a secondary peak in the$-uv$co-spectra. With increasing Reynolds number, the influence of the$O(\delta ^{+})$motions promotes viscosity to act over increasingly longer times, thereby increasing the$y^{+}$extent over which the mean viscous force retains leading order. Furthermore, the TI decompositions show that the$\langle v \omega _z \rangle $motions (advective transport and/or dispersion of vorticity) are the dominant mechanism in and above the log region, whereas$\langle - w \omega _y \rangle $motions (vorticity stretching and/or reorientation) are most significant below the log region. The motions associated with$\langle - w \omega _y \rangle $predominantly underlie accelerations, whereas$\langle v \omega _z \rangle $primarily contribute to decelerations. Finally, a description of the structure of wall turbulence deduced from the present analysis and our physical interpretation is presented, and is shown to be consistent with previous flow visualisation studies.

scholarly journals Bluff bodies in deep turbulent boundary layers: Reynolds-number issues

2007 ◽  
Vol 571 ◽  
pp. 97-118 ◽  
Author(s):  
HEE CHANG LIM ◽  
IAN P. CASTRO ◽  
ROGER P. HOXEY
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Delta Wing ◽  
Body Height ◽  
Turbulent Boundary Layers ◽  
The Body ◽  
Bluff Bodies ◽  
Mean Flow ◽  
Order Of Magnitude ◽  
The Mean

It is generally assumed that flows around wall-mounted sharp-edged bluff bodies submerged in thick turbulent boundary layers are essentially independent of the Reynolds number Re, provided that this exceeds some (2–3) × 104. (Re is based on the body height and upstream velocity at that height.) This is a particularization of the general principle of Reynolds-number similarity and it has important implications, most notably that it allows model scale testing in wind tunnels of, for example, atmospheric flows around buildings. A significant part of the literature on wind engineering thus describes work which implicitly rests on the validity of this assumption. This paper presents new wind-tunnel data obtained in the ‘classical’ case of thick fully turbulent boundary-layer flow over a surface-mounted cube, covering an Re range of well over an order of magnitude (that is, a factor of 22). The results are also compared with new field data, providing a further order of magnitude increase in Re. It is demonstrated that if on the one hand the flow around the obstacle does not contain strong concentrated-vortex motions (like the delta-wing-type motions present for a cube oriented at 45° to the oncoming flow), Re effects only appear on fluctuating quantities such as the r.m.s. fluctuating surface pressures. If, on the other hand, the flow is characterized by the presence of such vortex motions, Re effects are significant even on mean-flow quantities such as the mean surface pressures or the mean velocities near the surfaces. It is thus concluded that although, in certain circumstances and for some quantities, the Reynolds-number-independency assumption is valid, there are other important quantities and circumstances for which it is not.

Turbulence structure in rough- and smooth-wall boundary layers

2007 ◽  
Vol 592 ◽  
pp. 263-293 ◽  
Author(s):  
R. J. VOLINO ◽  
M. P. SCHULTZ ◽  
K. A. FLACK
Keyword(s):  
Boundary Layers ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Rough Wall ◽  
Turbulence Structure ◽  
Smooth Wall ◽  
Hairpin Vortices ◽  
Wall Flows ◽  
Wall Boundary ◽  
Cross Correlations

Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a woven mesh surface at Reynolds numbers approximately equal to those for the smooth wall. Fully rough conditions were achieved. The present work focuses on turbulence structure, as documented through spectra of the fluctuating velocity components, swirl strength, and two-point auto- and cross-correlations of the fluctuating velocity and swirl. The present results are in good agreement, both qualitatively and quantitatively, with the turbulence structure for smooth-wall boundary layers documented in the literature. The boundary layer is characterized by packets of hairpin vortices which induce low-speed regions with regular spanwise spacing. The same types of structure are observed for the rough- and smooth-wall flows. When the measured quantities are normalized using outer variables, some differences are observed, but quantitative similarity, in large part, holds. The present results support and help to explain the previously documented outer-region similarity in turbulence statistics between smooth- and rough-wall boundary layers.

scholarly journals An invariant representation of mean inertia: theoretical basis for a log law in turbulent boundary layers

2017 ◽  
Vol 813 ◽  
pp. 594-617 ◽  
Author(s):  
Caleb Morrill-Winter ◽  
Jimmy Philip ◽  
Joseph Klewicki
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Large Reynolds Number ◽  
Gradient Force ◽  
Scaling Analysis ◽  
Pressure Gradient Force ◽  
The Mean

A refined scaling analysis of the two-dimensional mean momentum balance (MMB) for the zero-pressure-gradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds numbers, $\unicode[STIX]{x1D6FF}^{+}$. For canonical boundary layers, the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds number scaling for the log layer onset and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The physical reasoning is that the mean inertia is primarily a large-scale outer layer contribution, the ‘shape’ of which becomes invariant of $\unicode[STIX]{x1D6FF}^{+}$ with increasing $\unicode[STIX]{x1D6FF}^{+}$, and with a ‘magnitude’ that is inversely proportional to $\unicode[STIX]{x1D6FF}^{+}$. The present analyses are enabled and corroborated using recent high resolution, large Reynolds number hot-wire measurements of all the terms in the TBL MMB.

The Pressure Signature of High Reynolds Number Smooth Wall Turbulent Boundary Layers in Pressure Gradient Family

2020 ◽  
Author(s):  
Danny Fritsch ◽  
Vidya Vishwanathan ◽  
Julie Duetsch-Patel ◽  
Aldo Gargiulo ◽  
Kevin T. Lowe ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
High Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Smooth Wall ◽  
High Reynolds
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