scholarly journals Reinvestigating the Parabolic-Shaped Eddy Viscosity Profile for Free Surface Flows

Hydrology ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 126
Author(s):  
Rafik Absi
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Velocity Profile ◽  
Eddy Viscosity ◽  
Velocity Profiles ◽  
Free Surface Flows ◽  
Analytical Models ◽  
Surface Flows ◽  
Viscosity Models ◽  
Viscosity Profile

The flow in rivers is turbulent. The main parameter related to turbulence in rivers is the eddy viscosity, which is used to model a turbulent flow and is involved in the determination of both velocities and sediment concentrations. A well-known and largely used vertical distribution of eddy viscosity in free surface flows (open channels and rivers) is given by the parabolic profile that is based on the logarithmic velocity profile assumption and is valid therefore only in the log-law layer. It was improved thanks to the log-wake law velocity profile. These two eddy viscosities are obtained from velocity profiles, and the main shortcoming of the log-wake profile is the empirical Coles’ parameter. A more rigorous and reliable analytical eddy viscosity model is needed. In this study, we present two analytical eddy viscosity models based on the concepts of velocity and length scales, which are related to the exponentially decreasing turbulent kinetic energy (TKE) function and mixing length, namely, (1) the exponential-type profile of eddy viscosity and (2) an eddy viscosity based on an extension of von Karman’s similarity hypothesis. The eddy viscosity from the second model is -independent, while the eddy viscosity from the first model is -dependent (where is the friction Reynolds number). The proposed analytical models were validated through computation of velocity profiles, obtained from the resolution of the momentum equation and comparisons to experimental data. With an additional correction function related to the damping effect of turbulence near the free surface, both models are similar to the log-wake-modified eddy viscosity profile but with different values of the Coles’ parameter, i.e., for the first model and for the second model. These values are similar to those found in open-channel flow experiments. This provides an explanation about the accuracy of these two analytical models in the outer part of free surface flows. For large values of ( > 2000), the first model becomes independent, and the two coefficients reach asymptotic values. Finally, the two proposed eddy viscosity models are validated by experimental data of eddy viscosity.

A theoretical analysis of free-surface flows of saturated granular–liquid mixtures

2008 ◽  
Vol 608 ◽  
pp. 393-410 ◽  
Author(s):  
D. BERZI ◽  
J. T. JENKINS
Keyword(s):  
Free Surface ◽  
Theoretical Analysis ◽  
Eddy Viscosity ◽  
Numerical Solutions ◽  
Liquid Mixtures ◽  
Free Surface Flows ◽  
Two Phase ◽  
Surface Flows ◽  
Physical Experiments ◽  
Analytical Expressions

A simple two-phase model for steady fully developed flows of particles and water over erodible inclined beds is developed for situations in which the water and particles have the same depth. The rheology of the particles is based on recent numerical simulations and physical experiments, the rheology of the fluid is based on an eddy viscosity, and the interaction between the particles and the fluid is through drag and buoyancy. Numerical solutions of the resulting differential equations and boundary conditions provide velocity profiles of the fluid and particles, the concentration profile of the particles, and the depth of the flow at a given angle of inclination of the bed. Simple approximations permit analytical expressions for the flow velocities and the depth of flow to be obtained that agree with the numerical solutions and those measured in experiments.

Experimental investigation of viscoplastic free-surface flows in a steady uniform regime

2014 ◽  
Vol 754 ◽  
pp. 332-364 ◽  
Author(s):  
Guillaume Chambon ◽  
A. Ghemmour ◽  
M. Naaim
Keyword(s):  
Free Surface ◽  
Slope Angle ◽  
Velocity Profiles ◽  
Free Surface Flows ◽  
Experimental Results ◽  
Constitutive Law ◽  
Height Velocity ◽  
Rheological Parameters ◽  
Surface Flows ◽  
Theoretical Predictions

AbstractWe present experimental results focused on the hydraulic properties of free-surface flows of viscoplastic fluids. The objective is to investigate the possibility of predicting macroscopic flow properties on the base of conventional rheometrical characterization of the fluids. The experiments are performed in an inclined conveyor-belt channel allowing us to generate gravity-driven surges which remain stationary in the laboratory frame. Two different types of materials are studied: Kaolin slurries and Carbopol microgels. Global height–velocity relationships and local velocity profiles are measured in the uniform zone for different experimental conditions (slope angle, rheological parameters). These data are then compared to theoretical predictions based on the Herschel–Bulkley constitutive law and independent measurements of the rheological parameters. Great care has been devoted to the determination of experimental uncertainties, including those associated with the rheometrical characterization. For Kaolin, the experimental results show excellent agreement with theoretical predictions. With Carbopol, on the contrary, a systematic discrepancy between measured and theoretical flow heights is observed. The velocity profiles do nevertheless remain consistent with a Herschel–Bulkley rheology, and we show that all experimental data can be explained by increasing the rheological parameters (yield stress and consistency) by 10–20 % compared to the values measured in the rheometer. Potential interpretations for this discrepancy are discussed.

scholarly journals Viscous free-surface flows past cylinders

2020 ◽  
Vol 5 (8) ◽  
Author(s):  
Edward M. Hinton ◽  
Andrew J. Hogg ◽  
Herbert E. Huppert
Keyword(s):  
Free Surface ◽  
Free Surface Flows ◽  
Surface Flows
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