scholarly journals The Logarithmic Law of the Wall in Flows over Mobile Lattice-Arranged Granular Beds

Water ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1166 ◽  
Author(s):  
Federica Antico ◽  
Ana Ricardo ◽  
Rui Ferreira
Keyword(s):  
Open Channel ◽  
Channel Flows ◽  
Roughness Height ◽  
Spherical Particles ◽  
Open Channel Flows ◽  
Von Karman ◽  
Log Law ◽  
Definition Of ◽  
Von Kármán ◽  
Best Fit

The purpose of the present paper is to provide further insights on the definition of the parameters of the log-law in open-channel flows with rough mobile granular beds. Emphasis is placed in the study of flows over cohesionless granular beds composed of monosized spherical particles in simple lattice arrangements. Potentially influencing factors such as grain size distribution, grain shape and density or cohesion are not addressed in this study. This allows for a preliminary discussion of the amount of complexity needed to obtain the log-law features observed in more realistic open-channel flows. Data collection included instantaneous streamwise and bed-normal flow velocities, acquired with a two-dimensional and two-component (2D2C) Particle Image Velocimetry (PIV) system. The issue of the non uniqueness of the definition of the parameters of the log-law is addressed by testing several hypotheses. In what concerns the von Kármán parameter, κ , it is considered as flow-independent or flow-dependent (a fitting parameter). As for the geometric roughness scale, k s , it results from a best fit procedure or is computed from a roughness function. In the latter case, the parameter B is imposed as 8.5 or is calculated from the best fit estimate. The analysis of the results reveals that a flow dependent von Kármán parameter, lower than the constant κ = 0.40 , should be preferred. Forcing κ = 0.40 leads to non-physical values of k s and would imply extending the inner layer up about 50% of the flow depth which is physically difficult to explain. Considering a flow dependent von Kármán parameter allows for coherent explanations for the values of the remaining parameters (the geometric roughness scale k s , the displacement height Δ , the roughness height z 0 ). In particular, for the same transport rate, the roughness height obtained in a natural sediment bed is much greater than in the case of bed made of monosized glass spheres, underlining the influence of the bed surface complexity (texture and self-organized bed forms, in the water-worked cases) on the definition of the log-law parameters.

On the definition of the shear velocity in rough bed open channel flows

2006 ◽  
Author(s):  
C Manes ◽  
D Pokrajac ◽  
I McEwan ◽  
J Finnigan ◽  
V Nikora
Keyword(s):  
Open Channel ◽  
Shear Velocity ◽  
Channel Flows ◽  
Open Channel Flows ◽  
Rough Bed ◽  
Definition Of

scholarly journals Reconsideration of the overlap region in smooth shallow open channel flows

2017 ◽  
Vol 44 (3) ◽  
pp. 161-173 ◽  
Author(s):  
Mehdi Heidari ◽  
Ram Balachandar ◽  
Vesselina Roussinova ◽  
Ronald M. Barron
Keyword(s):  
Least Squares ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Data Sets ◽  
Mixing Length ◽  
Von Karman ◽  
Log Law ◽  
Von Kármán ◽  
Overlap Region

In this paper, data sets for mean velocity distributions in smooth shallow open channel flow are reconsidered to evaluate the characteristics of the overlap region and estimate the friction velocity (u∗). Both new and existing velocity measurements are used in the analysis. The velocity profiles are obtained using laser Doppler velocimetry and particle image velocimetry at typical Reynolds numbers (20 000–60 000) achieved in laboratory flumes. Validation of the estimated u∗ values using different forms of power law is established by comparing these values with the ones available in literature. Also, the Reynolds shear stress distribution based on two-dimensional measurements validate the estimated u∗. The availability of new data sets allows one to verify the usefulness of the log-law and evaluate the log-law constants. Different fitting methods; least squares, derivative, and scattered methods are used to evaluate the value of von Kármán coefficient. It is found that the value of κ obtained from the least squares method varies between 0.35 and 0.51 and depends on the Reynolds number. This refutes the conventional constant value assumption for the von Kármán coefficient (κ = 0.41). By considering the Prandtl’s mixing-length theory, the present values of the von Kármán coefficient are used to evaluate the mixing length distributions. The mixing length distributions in smooth open channel flow are found to depend on Reθ.

Turbulent open-channel flows over mobile granular low-tortuosity beds: velocity distribution and friction factor

2020 ◽  
Author(s):  
Rui M L Ferreira ◽  
Rigden Y Tenzin ◽  
Ana M Ricardo
Keyword(s):  
Hydraulic Conductivity ◽  
Friction Factor ◽  
Open Channel ◽  
High Conductivity ◽  
Channel Flows ◽  
Rough Boundary ◽  
Roughness Parameters ◽  
Mean Flow ◽  
Open Channel Flows ◽  
Log Law

<p>Open channel flows over granular mobile beds are affected by the nature and intensity of hyporheic/surface mass and momentum exchanges. Near-bed surface mean flow and turbulence find an equilibrium with the flow in the hyporheic region and with the type and amount of granular material transported in equilibrium conditions. The processes involved in these adaptive process are not well known. This work addresses this knowledge gap and it is aimed at describing the effect of the hydraulic conductivity on the friction factor and on the parameters of the log-law that is thought to constitute a valid model for the turbulent flow in the overlapping region of fully developed hydraulically rough boundary layers over mobile cohesionless beds. To fulfil the objectives, experimental tests performed in high conductivity beds (mono-sized glass sphere beads) are compared with the existing database of low conductivity beds of Ferreira et al. (2012), keeping constant the range of values of porosity, Shields parameters and roughness Reynolds numbers. The hydraulic conductivity is varied by changing the tortuosity (and the dimensions of the pore paths) and not the porosity.</p><p>A new database of instantaneous velocities was acquired with Particle Image Velocimetry (PIV) and processed to gather time-averaged velocities and space-time (double-averaged) quantities, namely velocities, Reynolds stresses and form-induced stresses. The hydraulic conductivity was measured for both types of bed.</p><p>The parameters of log-law obtained from high conductivity are compared with low conductivity of existing database, for mobile and immobile bed conditions. The main finding can be summarized as follows.</p><p>i. Hydraulic conductivity does not affect the location of the zero plane of the log-law, the thickness of the region above the crests where the flow is determined by roughness.</p><p>ii. Increasing the hydraulic conductivity does not appear to decrease the value of bed roughness parameters such as the roughness heigh.</p><p>iii. Higher hydraulic conductivity is associated to a structural change: the same near-bed velocity can be achieved with lower shear stress in the inner region. A lower friction factor, (<em>u</em><sub>*</sub>/<em>U</em>)<sup>2</sup>, is thus registered.</p><p>iv. Flows over high conductivity beds appear drag-reducing even if roughness parameters do not change appreciably.</p><p> </p><p>This research was partially supported by Portuguese and European funds, within the COMPETE 2020 and PORL-FEDER programs, through project PTDC/CTA-OHR/29360/2017 RiverCure</p>

Friction velocity and power law velocity profile in smooth and rough shallow open channel flows

2002 ◽  
Vol 29 (2) ◽  
pp. 256-266 ◽  
Author(s):  
R Balachandar ◽  
D Blakely ◽  
J Bugg
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Froude Number ◽  
Power Law ◽  
Friction Velocity ◽  
Open Channel ◽  
Rough Surfaces ◽  
Channel Flows ◽  
Open Channel Flows ◽  
Log Law

This paper examines the mean velocity profiles in shallow, turbulent open channel flows. Velocity measurements were carried out in flows over smooth and rough beds using a laser-Doppler anemometer. One set of profiles, composed of 29 velocity distributions, was obtained in flows over a polished smooth aluminum plate. Three sets of profiles were obtained in flows over rough surfaces. The rough surfaces were formed by two sizes of sand grains and a wire mesh. The flow conditions over the rough surface are in the transitional roughness state. The measurements were obtained along the centerline of the flume at three different Froude numbers (Fr ~ 0.3, 0.8, 1.0). The lowest Froude number was selected to obtain data in the range of most other open channel testing programs and to represent a low subcritical Froude number. For each surface, the Reynolds number based on the boundary layer momentum thickness was varied from about 600 to 3000. In view of the recent questions concerning the applicability of the log-law and the debate regarding log-law versus power law, the turbulent inner region of the boundary layer is inspected. The fit of one type of power law for shallow flows over a smooth surface is considered. The appropriateness of extending this law to flows over rough surfaces is also examined. Alternate methods for determining the friction velocity of flows over smooth and rough surfaces are considered and compared with standard methods currently in use.Key words: power law, open channel flow, velocity profile, surface roughness.

scholarly journals Re-examining log law velocity profile in smooth open channel flows

2020 ◽  
Vol 20 (4) ◽  
pp. 953-986 ◽  
Author(s):  
Nadeeka S. Miguntanna ◽  
Hamish Moses ◽  
Muttucumaru Sivakumar ◽  
Shu-Qing Yang ◽  
Keith James Enever ◽  
...  
Keyword(s):  
Velocity Profile ◽  
Open Channel ◽  
Channel Flows ◽  
Open Channel Flows ◽  
Log Law
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