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.

Three-dimensional numerical model for open-channels with free-surface variations

2003 ◽  
Vol 41 (1) ◽  
pp. 110-112
Author(s):  
ZhixiaN. Cao ◽  
Rodney Day ◽  
Sarah Liriano
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Three Dimensional ◽  
Open Channels

scholarly journals The Theory and Observational Evidence for Streamlets: A New Velocity-Based Feature Model of Jet Streams and Eddies in the Oceans

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Alexander V. Kazansky ◽  
Antonina A. Shupikova
Keyword(s):  
Cross Sections ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Feature Model ◽  
Optimal Interpolation ◽  
Jet Streams ◽  
Synoptic Features ◽  
Parametric Functions ◽  
Oblique Cone

The aim of this study is the verification of a new velocity-based feature model, called streamlets, proposed recently for objective analysis of the three-dimensional velocity structure of jet streams and eddies in the oceans. Streamlets are continuously imbedded shearing vortex solenoids having two forms: cylindrical (for jets) or toroidal (for eddies, considered as self-closed jets). Both these forms comprise stream coordinates based on streamlines of maximum velocity as an axis and vertical velocity cross-sections defined as an oblique cone with elliptical base. Assimilation of velocity measurements is accomplished by fitting this cone to available data using the well-known Nelder-Mead simplex downhill algorithm for finding the minimum of nonlinear parametric functions. Advantages of the streamlet model are discussed emphasizing its functional integrity. The focus is on velocity data assimilation based on coherency of synoptic scale features as opposed to usual pointwise assimilation methods such as averaging or optimal interpolation. Case studies present synoptic features of a different origin and scale including surface-intensified and subsurface baroclinic examples as well as deep barotropic ones demonstrating universality of the model. The theory of streamlets is also addressed in this paper, since it further sustain the streamlet model.

scholarly journals EXPERIMENTAL STUDY OF SOLITARY WAVE EVOLUTION OVER A 3D SHALLOW SHELF

2011 ◽  
Vol 1 (32) ◽  
pp. 1 ◽  
Author(s):  
Patrick J. Lynett ◽  
David Swigler ◽  
Sangyoung Son ◽  
Duncan Bryant ◽  
Scott Socolofsky
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Turbulent Energy ◽  
Shelf Break ◽  
Plan View ◽  
Fluid Velocities ◽  
Water Region ◽  
Side Walls

A laboratory experiment was performed to investigate the three-dimensional turbulence and kinematic properties that develop due to a breaking solitary propagating over an irregular shallow water bathymetry. The bathymetry consisted of a deep water region connected to a shallow shelf via a relatively steep slope. The offshore boundary of the shelf break varied in the longshore direction, such that the shelf had a triangular shape in plan view, with the widest part of the shelf along the basin centerline. Free surface elevations and fluid velocities were measured using wave gauges and three-dimensional acoustic-Doppler velocimeters (ADVs), respectively. From the free surface elevations the evolution and runup of the wave was revealed; while from the ADVs, the velocity and turbulent energy was determined and specific turbulent events and coherent structures were identified. It was found that significant shoaling was confined to areas with gentler sloping bathymetry near the basin side walls and the runup varied weakly in the alongshore direction. The runup was characterized by a refraction-generated jetting mechanism caused by the convergence of water mass near the basin centerline. The jetting mechanism caused the greatest cross-shore velocities to be located near the basin centerline. The greatest turbulent events were well correlated to borefronts, of which there were four, caused by the leading wave, beach reflections, and shelf-trapped oscillations. Along the shelf break, a large, shallow-water eddy developed which was found to have a peculiar three-dimensional flow field, where maximum velocity components were found at mid-depth.

An Experimental Study of Three Dimensional Flow Structures for Effect of Crossflow on Central Discharge of Wastewater

2014 ◽  
Vol 955-959 ◽  
pp. 3361-3364
Author(s):  
Zhi Yong Dong ◽  
Guo Liang Yu ◽  
Yu Ying Zhao
Keyword(s):  
Transverse Velocity ◽  
Near Field ◽  
Longitudinal Velocity ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Flow Structures ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Jet Trajectory ◽  
Crossflow Velocity

Effects of crossflow on flow field structures of central discharge were experimentally investigated in the flume. For the sake of comparing and analyzing, longitudinal velocity u, vertical velocity w and transverse velocity v in the near field of central discharge were measured by Micro ADV in stagnant and crossflow waters, respectively. Velocity vectors and velocity profiles on the planes of xoy, yoz and xoz were given. Effects of crossflow on three-dimensional flow structures of central discharge jet were analyzed. The experimental results showed that a phenomena of flow around object occurred when crossflow encountered central discharge jet, which bended jet trajectory downward. The maximum velocity of jet deviated the original location, the deviation depends on initial velocity at the discharge outlet and crossflow velocity.

scholarly journals Roughness Effect on Velocity Distribution in Selected Reach of Shatt al-Arab River

2020 ◽  
Vol 26 (8) ◽  
pp. 46-58
Author(s):  
Amjed M. Abbas ◽  
Abdul-Ilah Y. Mohammed
Keyword(s):  
Velocity Distribution ◽  
Cross Sections ◽  
Longitudinal Velocity ◽  
Arabian Gulf ◽  
Maximum Velocity ◽  
Appreciable Effect ◽  
River Bed ◽  
Bed Roughness ◽  
Depth Ranges ◽  
The City

Shatt al-Arab is the only navigational artery in Iraq, extending from the city of Qurna to its mouth in the Arabian Gulf at the city of Al-Fao within the governorate of Basrah for a length of approximately 204 km. Its width ranges from 400 m to 2000 m, and its depth ranges from 8 m to 20 m. The southern part of it, 93 km long from Umm al-Rassas Island to Ras al-Bisha, represents the international border between Iraq and Iran, where the Thalweg line represents the border between the two countries, which is the deepest point in the riverbed (according to the 1975 Algiers Agreement). The western bank (the Iraqi side) within the common border of Shatt al-Arab is subject to continuous erosion, which leads to the shifting of the Thalweg line towards Iraqi territory and thus leads to loss of Iraqi land to Iran. Reducing flow velocity along the Iraqi side can lead to reducing or preventing erosion in the river. Increasing the riverbed roughness will reduce the velocity of flow and then reducing the erosion. This principle was adopted in this study to investigate the effect of increasing roughness in a strip along a reach of the riverbed on the distribution of longitudinal velocity in cross-sections at the rest of the selected reach. A reach of Shatt al-Arab with a length of 2500 m, located 34 km north of Fao City, was selected to represent the study area. This reach was simulated by using numerical modeling CFD solver (fluent) with three different roughnesses for an upstream part of the river bed and the velocities compared with the natural (original) roughness of Shatt al-Arab. The results showed an appreciable effect of the increased bed roughness on the velocity distribution and the maximum velocity location by shifting it to the other side.

scholarly journals 3D Primary Geochemical Halo Modeling and Its Application to the Ore Prediction of the Jiama Polymetallic Deposit, Tibet, China

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zhongping Tao ◽  
Bingli Liu ◽  
Ke Guo ◽  
Na Guo ◽  
Cheng Li ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Mineral Resources ◽  
Principal Component ◽  
Kernel Principal Component Analysis ◽  
Geochemical Data ◽  
Entropy Model ◽  
Uncertainty Prediction ◽  
Polymetallic Deposit ◽  
Metallogenic Belt

The identification of primary geochemical haloes can be used to predict mineral resources in deep-seated orebodies through the delineation of element distributions. The Jiama deposits a typical skarn–porphyry Cu–polymetallic deposit in the Gangdese metallogenic belt of Tibet. The Cu–polymetallic skarn, Cu–Mo hornfels, and Mo ± Cu porphyry mineralization there exhibit superimposed geochemical haloes at depth. Three-dimensional (3D) primary geochemical halo modeling was undertaken for the deposit with the aim of providing geochemical data to describe element distributions in 3D space. An overall geochemical zonation of Zn(Pb) → Au → Cu(Ag) → Mo gained from geochemical cross-sections, together with dip-direction skarn zonation Pb–Zn(Cu) → Cu(Au–Ag–Mo) → Mo(Cu) → Cu–Mo(Au–Ag) and vertical zonation Cu–(Pb–Zn) → Mo–(Cu) → Mo–Cu–(Ag–Au–Pb–Zn) → Mo in the #24 exploration profile, indicates potential mineralization at depth. Integrated geochemical anomalies were extracted by kernel principal component analysis, which has the advantage of accommodating nonlinear data. A maximum-entropy model was constructed for deep mineral resources of uncertainty prediction. Three potential deep mineral targets are proposed on the basis of the obtained geochemical information and background.

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.

Experimental and Theoretical Study of the Swirling Flow in Centrifugal Compressor Volutes

1990 ◽  
Vol 112 (1) ◽  
pp. 38-43 ◽  
Author(s):  
R. A. Van den Braembussche ◽  
B. M. Ha¨nde
Keyword(s):  
Centrifugal Compressor ◽  
Cross Sections ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Three Dimensional Flow ◽  
Static Pressure Distribution ◽  
Swirl Velocity ◽  
Isentropic Flows ◽  
Operating Points

Measurements of the three-dimensional flow in a simplified model of a centrifugal compressor volute at design and off-design operation are presented. A nearly constant swirl velocity is observed near the walls and a forced vortex type of flow is observed in the center. This velocity distribution is almost identical at all cross sections and all operating points. An explanation is given on how this swirl distribution results from the specific way a volute is filled with fluid. The throughflow velocity component shows a large crosswise variation. A minimum or maximum velocity is observed at the volute center depending on the operating point. A simple analytic model, based on the radial equilibrium of forces, is described. Calculations for isentropic flows reveal the relation between the swirl distribution and the large increase of throughflow velocity toward the center. This explains why volutes should be designed with negative blockage. Nonisentropic calculations, using the experimental loss distribution, correctly reproduce the measured throughflow velocity and static pressure distribution.

scholarly journals A Study of the Formation of Velocity Counter Lines and Secondary (Spiral) Flows in Different Cross Sections of Divergent, Convergent and Uniform Arcs

2017 ◽  
Vol 7 (1) ◽  
pp. 1391-1397
Author(s):  
A. Liaghat ◽  
N. Tavanpour
Keyword(s):  
Mechanical Properties ◽  
Numerical Model ◽  
Flow Field ◽  
Cross Sections ◽  
Numerical Models ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Measured Data ◽  
Spiral Flow ◽  
Water Level Variations

The mechanical properties of flow are very complex in channel arcs. Therefore, dynamic numerical models of fluids are considered effective tools in predicting such flow fields. In this study, the numerical model was validated by the measures of a uniform U-shaped arc with a width of 0.6 meter. Then two similar U shaped arcs, divergent and convergent, were simulated by a three-dimensional numerical model with variable widths from 0.6 to 0.75 meters and 0.6 to 0.45 meters. Validating the numerical model by measured data in the uniform 180-degree arc showed that the model can simulate the flow field in the uniform arc very well. Results regarding several parameters such as rout of maximum velocity, maximum velocity line, water level variations, power of spiral flow, existence of a rotating cell are stated and discussed.

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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