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.

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.

MODELING THE ORGANIC REMOVAL AND OXYGEN CONSUMPTION BY BIOFILMS IN AN OPEN-CHANNEL FLOW

1994 ◽  
Vol 30 (2) ◽  
pp. 53-61 ◽  
Author(s):  
Shiyu Li ◽  
Guang Hao Chen
Keyword(s):  
Water Quality ◽  
Oxygen Consumption ◽  
River Water ◽  
Channel Flow ◽  
Diffusion Layer ◽  
Open Channel ◽  
Open Channel Flow ◽  
River Water Quality ◽  
Monod Kinetics ◽  
Organic Removal

A mathematical model is proposed to predict the removal of dissolved organic substances and the consumption of dissolved oxygen by attached biofilms in an open-channel flow. The model combines the biofilm equations with the conventional Streeter–Phelps type equations of river water quality by considering the mass transfer of organics and oxygen in the river water through the diffusion layer into the biofilm. It is assumed that the diffusion and reaction within the biofilm are of steady-state, and follow Monod kinetics. The model is solved numerically with a trial-and-error method. The simulation results of the model for an ideal case of river flow and biofilm show that the organic removal rate and oxygen consumption rate caused by the biofilm are greater than that by suspended biomass. The effects of diffusion layer thickness, flow velocity, and biofilm thickness on the change of river water quality are discussed.

Sign in / Sign up

Export Citation Format

Share Document