scholarly journals Information Entropy Theory Applied to the Dip-Phenomenon Analysis in Open Channel Flows

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 554 ◽  
Author(s):  
Domenica Mirauda ◽  
Maria Grazia Russo
Keyword(s):  
Free Surface ◽  
Cross Section ◽  
Information Entropy ◽  
Maximum Velocity ◽  
Free Surface Flows ◽  
Secondary Flows ◽  
Open Channels ◽  
Accurate Estimation ◽  
Entropy Theory ◽  
Mean Velocity

The knowledge of the fluid discharge in free surface flows requires a great number of velocity measurements along the whole cross-section, taking up a large amount of time, using expensive equipment, and employing specialized labor. To overcome these obstacles, various models have been developed thus far that show how to estimate the mean velocity through the maximum velocity. In three-dimensional open channels, the maximum velocity can be located below the free surface because of the presence of secondary flows mainly originating by the sidewalls, an occurrence known as dip-phenomenon. In this condition, predicting the maximum velocity position is quite difficult and has always represented a challenge to most hydraulic engineers and researchers. In the present study, a mathematical model derived from the information entropy theory is proposed to evaluate the velocity-dip-position over the entire cross-section of both wide and narrow open channels, thus overcoming the limitations of the existing methods. Large literature measurement sets, collected in uniform and non-uniform flows, were used to test the validity of the model, showing good agreement with the experimental data and providing an accurate estimation of the dip-position.

Discussion on Venkat & Spaulding: “Numerical Simulation of Nonlinear Free-Surface Flows Generated by a Heaving Body of Arbitrary Cross Section”

1991 ◽  
Vol 35 (03) ◽  
pp. 250-253
Author(s):  
Apostolos Papanikolaou
Keyword(s):  
Free Surface ◽  
Cross Section ◽  
Euler Method ◽  
Free Surface Flows ◽  
Arbitrary Cross Section ◽  
Circular Cylinders ◽  
Published Data ◽  
The Time Domain ◽  
Heave Motion ◽  
Nonlinear Free Surface

A method has been presented recently by Venkat and Spaulding to solve the nonlinear boundary-value problem of oscillating two-dimensional cylinders of arbitrary cross section on the free surface of a fluid. The method relies on a second-order finite-difference technique with a modified Euler method for the time domain and a successive over-relaxation procedure for the spatial domain. The authors compare their numerical results with those of other authors (theoretical and experimental), as they have published data for specialized forms like a wedge, circular cylinders, and ship-like sections in forced heave motion (references [4] to [7] and [22], [23] of the paper).

Vertical Velocity Profile on the Noncircular Flow Cross-Section of Water Intake Pipeline with Deposition on Bottom

2013 ◽  
Vol 864-867 ◽  
pp. 2050-2055
Author(s):  
Xiao Xiao Li ◽  
Xiao Dong Zhao ◽  
Xiao Feng Luo
Keyword(s):  
Cross Section ◽  
Water Intake ◽  
Cross Sections ◽  
Vertical Velocity ◽  
Maximum Velocity ◽  
Mean Velocity ◽  
Flow Cross Section ◽  
Fine Sediments ◽  
Deposition Thickness ◽  
Flow Cross

Under small water-intake flow or overhaul periods, sediments deposit in the water intake pipeline with noncircular flow cross-section formed. According to the hydrostatic settling test results of fine sediments in circular pipeline, the sectional features of the deposition on pipe bottom is provided. And the vertical velocity profiles on perpendicular bisectors of noncircular flow cross-sections are measured under three kinds of typical deposition thickness. The relative positions of the maximum velocity point and the center of flow cross-section should be determined with an overall consideration to the two factors of wall roughness and wall restraint which is controlled by the transverse width of flow cross-section. When the mean velocity of flow cross-section keeps a constant value, the larger the deposition thickness is, the larger the velocity near the deposition surface, which is more favorable for sediment incipient motion.

scholarly journals Entropy Wake Law for Streamwise Velocity Profiles in Smooth Rectangular Open Channels

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 654
Author(s):  
Domenica Mirauda ◽  
Maria Grazia Russo
Keyword(s):  
Free Surface ◽  
Cross Sections ◽  
Water Discharge ◽  
Longitudinal Velocity ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Streamwise Velocity ◽  
Open Channels ◽  
Entropy Model ◽  
Modified Entropy

In narrow open channels, the three-dimensional nature of the flow and the transport momentum from the sidewalls to the central region cause the maximum longitudinal velocity to occur below the water surface. The entropy model is unable to accurately describe the velocities near the free surface when the dip phenomenon exists. The present paper proposes a new dip-modified entropy law for steady open channel flows, which consists of three additional terms: the first one similar to Coles’ function; the second one linearly proportional to the logarithmic distance from the free surface; and the third one depending on the cubic correction near the maximum velocity. The validity of the new model was tested on a set of laboratory measurements carried out in a straight rectangular flume with smooth boundaries and for different values of water discharge, bottom slope, and aspect ratio. A detailed error analysis showed good agreement with the data measured through the present research and a more accurate prediction of the velocity-dip-position compared with the one evaluated through the original entropy model. In addition, the modified entropy wake law matched very well with other literature data collected in rectangular cross-sections with different flow conditions.

Reynolds Number Effects on the Characteristics of Twin Jets Interacting With a Free Surface

2016 ◽  
Author(s):  
M. S. Rahman ◽  
E. M. Nabess ◽  
M. F. Tachie
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Maximum Velocity ◽  
Mean Velocity ◽  
Free Jet ◽  
Turbulent Characteristics ◽  
Reynolds Number Effects ◽  
Velocity Decay ◽  
Twin Jets ◽  
Velocity Measuring

The effects of Reynolds number on the turbulent characteristics of surface attaching twin jet were investigated experimentally. Particle image velocimetry was used as the velocity measuring technique. Twin jets were produced using square orifice nozzle pair. The Reynolds numbers based on the jet exit velocity and the nozzle width were varied from 2620 to 7900. The offset height ratio was fixed at 2 during the experiments. The jet reattached to the free surface and the reattachment length decreased with increase of Reynolds number. Free surface showed significant effect on the maximum velocity decay, jet spread, streamwise mean velocity distribution, Reynolds shear and normal stresses in the upper jet. The decay and spread rate of the lower jet was comparable to free jet due to less confinement effect. The mean and turbulent quantities reported herein were nearly independent of Reynolds number. Proper orthogonal decomposition was performed to reveal the dynamic role of the energetic structures embedded within the flow.

Free-surface Taylor vortices

1994 ◽  
Vol 261 ◽  
pp. 169-198 ◽  
Author(s):  
F. J. Wang ◽  
G. A. Domoto
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Numerical Method ◽  
Secondary Flow ◽  
Stokes Equations ◽  
Hydrodynamic Instability ◽  
Three Dimensional ◽  
Free Surface Flows ◽  
Secondary Flows ◽  
Two Dimensional

The hydrodynamic instability of a viscous incompressible flow with a free surface is studied both numerically and experimentally. While the free-surface flow is basically two-dimensional at low Reynolds numbers, a three-dimensional secondary flow pattern similar to the Taylor vorticies between two concentric cylinders appears at higher rotational speeds. The secondary flow has periodic velocity components in the axial direction and is characterized by a distinct spatially periodic variation in surface height similar to a standing wave. A numerical method, using boundary-fitted coordinates and multigrid methods to solve the Navier–Stokes equations in primitive variables, is developed to treat two-dimensional free-surface flows. A similar numerical technique is applied to the linearized three-dimensional perturbation equations to treat the onset of secondary flows. Experimental measurements have been obtained using light sheet techniques to visualize the secondary flow near the free surface. Photographs of streak lines were taken and compared to the numerical calculations. It has been shown that the solution of the linearized equations contains most of the important features of the nonlinear secondary flows at Reynolds number higher than the critical value. The experimental results also show that the numerical method predicts well the onset of instability in terms of the critical wavenumber and Reynolds number.

Prediction of Solid/Free-Surface Juncture Boundary Layer and Wake of a Surface-Piercing Flat Plate at Low Froude Number

1998 ◽  
Vol 120 (2) ◽  
pp. 354-362 ◽  
Author(s):  
Madhu Sreedhar ◽  
Fred Stern
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Froude Number ◽  
Secondary Flows ◽  
Wall Region ◽  
Normal Stresses ◽  
Streamwise Vorticity ◽  
Reynolds Stresses ◽  
Mean Velocity

Results are reported of a RANS simulation investigation on the prediction of turbulence-driven secondary flows at the free-surface juncture of a surface-piercing flat plate at low Froude numbers. The turbulence model combines a nonlinear eddy viscosity model and a modified version of a free-surface correction formula. The different elements of the model are combined and the model constants calibrated based on the premises that the anisotropy of the normal stresses is mainly responsible for the dynamics of the flow in the juncture region, and an accurate modeling of the normal-stress anisotropy as obtained from the data is a primary requirement for the successful prediction of the overall flow field. The predicted mean velocity, streamwise vorticity, turbulent kinetic energy, and other quantities at the juncture are then compared with data and analyzed with regard to findings of related studies. In agreement with the experimental observations, the simulated flow at large depths was essentially two-dimensional and displayed all the major features of zero pressure gradient boundary layer and wake, including the anisotropy of normal stresses in the near-wall region. In the boundary-layer free-surface juncture region, the major features of interest that were predicted include the generation of secondary flows and the thickening of the boundary layer near the free surface. In the wake free-surface juncture region, even though secondary flows and a thickening of the wake width near the free surface were predicted in accordance with the experimental observations, the overall comparison with the experiment was not as satisfactory as the boundary-layer juncture. This is partly due to the lack of a strong coherent flow structure in the wake juncture and the presence of possible wave effects in the wake in the experiments. An examination of the terms in the Reynolds-averaged streamwise vorticity equation reconfirmed the importance of the anisotropy of the normal Reynolds stresses in the production of streamwise vorticity. The free-surface wave elevations were negligible for the present model problem for the nonzero Froude number studied. Finally, concluding remarks are presented with regards to extensions for practical geometries such as surface ship flows.

scholarly journals Assessment of velocity fields through open-channel flows with an empiric law

2008 ◽  
Vol 57 (11) ◽  
pp. 1763-1768 ◽  
Author(s):  
J. B. Bardiaux ◽  
J. Vazquez ◽  
R. Mosé
Keyword(s):  
Free Surface ◽  
Velocity Distribution ◽  
Solid Mechanics ◽  
Water Discharge ◽  
Maximum Velocity ◽  
Free Surface Flows ◽  
Velocity Fields ◽  
Profile Measurement ◽  
Discharge System ◽  
Practical Applications

Most sewer managers are currently confronted with the evaluation of the water discharges, that flow through their networks or go to the discharge system, i.e. rivers in the majority of cases. In this context, the Urban Hydraulic Systems laboratory of the ENGEES is working on the relation between velocity fields and metrology assessment through a partnership with the Fluid and Solid Mechanics Institute of Strasbourg (IMFS). The responsibility is clearly to transform a velocity profile measurement, given by a Doppler sensor developed by the IMFS team, into a water discharge evaluation. The velocity distribution in a cross section of the flow in a channel has attracted the interests of many researchers over the years, due to its practical applications. In the case of free surface flows in narrow open channels the maximum velocity is below the free surface. This phenomenon, usually called “dip-phenomenon”, amongst other things, raises the problem of the area explored in the section of measurements. The work presented here tries to create a simple relation making possible to associate the flow with the velocity distribution. This step allows to insert the sensor position into the flow calculation

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