The Effect of Froude Number on Flow Field of U-Shaped Channel Along a Side Weir in Supercritical Flow Regime

AbstractSide weirs with triangular channel are used as flow controlling devices in draining and irrigation networks. By installing a side weir on the main conduits side walls, the runoff overflows from the weir and are conducted toward the diversion channel. In this study, changing of the flow free surface and the turbulence of the flow field in triangular channels with side weir are numerically simulated using volume of fluid (VOF) scheme and RNG k–ε turbulence model. In the present paper, the pattern of the spatially varied flow with decreasing discharge in both subcritical and supercritical flow regimes for triangular channels with side weirs was simulated. The present numerical model has precisely predicted the changes of the water surface and the specific energy. In subcritical regime, the flow depth is from the beginning of the weir toward its end is followed by an increase and in supercritical conditions is followed by a reduction in depth. For both subcritical and supercritical regimes, a drop in the surface in the first third of the weir’s opening and a surface jump in the final third of its length has occurred. Along the mentioned surface jump the amount of the kinetic energy increases and the potential energy reduces. According to results of the simulation, the maximum longitudinal velocity for subcritical flow regime occurs in the first third of the length of the side weir and for supercritical flow regime, almost in the middle of the weir opening happens. In both subcritical and supercritical regimes, the maximum transverse velocity has occurred in the final third of the length of the side weir.

Download Full-text

Discharge Coefficient of Rectangular Side Weirs on Circular Channels

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2016-0033 ◽

2016 ◽

Vol 17 (7-8) ◽

pp. 391-399 ◽

Cited By ~ 6

Author(s):

Hamed Azimi ◽

Saeid Shabanlou ◽

Isa Ebtehaj ◽

Hossein Bonakdari

Keyword(s):

Free Surface ◽

Numerical Model ◽

Flow Regime ◽

Discharge Coefficient ◽

Three Dimensional ◽

Free Surface Flow ◽

Energy Difference ◽

Surface Flow ◽

Side Weir ◽

Supercritical Flow

AbstractIn this study, the flow turbulence and variations of the supercritical free surface flow in a circular channel along a side weir are simulated as three dimensional using the RNG k-ε turbulence model and volume of fluid (VOF) scheme. Comparison between the numerical model and experimental measurements shows that the numerical model simulates the free surface flow with good accuracy. According to the numerical model results, the specific energy variations along the side weir for the supercritical flow regime are almost constant and the energy drop is not significant but by increasing the side weir length the energy difference between the side weir upstream and downstream increases. Next, using the nonlinear regression (NLR) and analysis of the simulation results, some relationships for calculating the discharge coefficient of side weir on circular channels in supercritical flow regime are provided.

Download Full-text

The conditions for occurrence of critical flow regime of water in the open stream

E3S Web of Conferences ◽

10.1051/e3sconf/20199705006 ◽

2019 ◽

Vol 97 ◽

pp. 05006

Author(s):

Yuliya Bryanskaya ◽

Aleksandra Ostiakova

Keyword(s):

Froude Number ◽

Flow Regime ◽

Water Flow ◽

Practical Interest ◽

Open Water ◽

Critical Regime ◽

Critical Flow ◽

Channel Processes ◽

Channel Deformations ◽

Critical Flow Regime

For the solution of engineering problems require increasingly accurate estimates of the hydraulic characteristics of the water streams. To date, it is impossible to consider sufficiently complete theoretical and experimental justification of the main provisions of the theory of turbulence, hydraulic resistance, channel processes. The composition of tasks related to flows in wide channels, turbulence problems are of scientific and practical interest. Various interpretations of the determination of the critical Froude number in wide open water flows based on observations and theoretical transformations are considered. The conditions for the emergence of a critical regime of water flow in an open wide channel are analyzed in order to estimate the critical Froude number and critical depth. Estimates of the critical Froude number for laboratory and field conditions are given. The estimations allow us to consider the proposed approach acceptable for determining the conditions of occurrence of the critical flow regime. The General, physical interpretation of conditions of occurrence of the critical regime of water flow on the basis of phenomenological approach is specified. The results take into account the values of the components of the total specific energy of the section. This shows the estimated calculation. The results obtained theoretically make it possible to compare the above interpretations and determine their applicability, and the results of the analysis can be useful for the estimated calculations of flows in channels and river flows in rigid, undeformable boundaries and with minor channel deformations.

Download Full-text

Slit Wall Effect on the Stability of Wavy Vortex Flow

Advances in Mechanical Engineering ◽

10.1155/2014/853069 ◽

2014 ◽

Vol 6 ◽

pp. 853069 ◽

Cited By ~ 2

Author(s):

Dong Liu ◽

Ying-ze Wang ◽

Hyoung-Bum Kim ◽

Fang-neng Zhu ◽

Chun-lin Wang

Keyword(s):

Numerical Simulation ◽

Flow Field ◽

Radial Velocity ◽

Flow Regime ◽

Experimental Measurement ◽

Vortex Flow ◽

Wall Effect ◽

Taylor Vortices ◽

Simulation Results ◽

The Stability

The wavy vortex flow in the plain model was studied by experimental measurement; the preliminary feature of wavy vortex flow was obtained. This flow field in the plain model was also studied by numerical simulation. The reliability of numerical simulation was verified by comparing with the experimental and numerical simulation results. To study the slit wall effect on the wavy vortex flow regime, another two models with different slit number were considered; the slit number was 6 and 12. By comparing the wavy vortex flow field in different models, the axial fluctuation of Taylor vortices was found to be different, which was increased with the increasing of slit number. The maximum radial velocity from the inner cylinder to the outer one in the 6-slit number was increased by 12.7% compared to that of plain model. From the results of different circumferential position in the same slit model, it can be found that the maximum radial velocity in slit plane is significantly greater than that in other planes. The size of Taylor vortices in different models was also calculated, which was found to be increased in the 6-slit model but was not changed as the slit number increased further.

Download Full-text

Prediction of flow around a sharp-nosed bridge pier: influence of the Froude number and free-surface variation on the flow field

Journal of Hydraulic Research ◽

10.1080/00221686.2019.1631223 ◽

2019 ◽

Vol 58 (4) ◽

pp. 582-593

Author(s):

Recep Kahraman ◽

Matthew Riella ◽

Gavin R. Tabor ◽

Mohsen Ebrahimi ◽

Slobodan Djordjević ◽

...

Keyword(s):

Free Surface ◽

Flow Field ◽

Froude Number ◽

Bridge Pier ◽

Surface Variation

Download Full-text

Flows generated by the periodic horizontal oscillations of a sphere in a linearly stratified fluid

Journal of Fluid Mechanics ◽

10.1017/s0022112094004106 ◽

1994 ◽

Vol 263 ◽

pp. 245-270 ◽

Cited By ~ 5

Author(s):

Qiang Lin ◽

D. L. Boyer ◽

H. J. S. Fernando

Keyword(s):

Flow Field ◽

Flow Regime ◽

Numerical Models ◽

Stokes Number ◽

Stratified Fluid ◽

Circular Cylinders ◽

Wave Flow ◽

Motion Field ◽

Attached Flow ◽

Internal Froude Number

The flow field induced by a sphere oscillating horizontally in a linearly stratified fluid is studied using a series of laboratory experiments. The resulting flows are shown to depend on the Stokes number β, the Keulegan–Carpenter number KC and the internal Froude number Fr. For Fr [clubs ] 0.2, it is shown that the nature of the resulting flow field is approximately independent of Fr and, based on this observation, a flow regime diagram is developed in the (β, KC)-plane. The flow regimes include: (i) fully-attached flow; (ii) attached vortices; (iii) local vortex shedding; and (iv) standing eddy pair. An internal-wave flow regime is also identified but, for such flows, the motion field is a function of Fr as well. Some quantitative measures are given to allow for future comparisons of the present results with analytical and/or numerical models. Wherever possible, the results are compared with the experiments of Tatsuno & Bearman (1990) on right circular cylinders oscillating in homogeneous fluids.

Download Full-text

Study on the Best Depth of Stilling Basin with Shallow-Water Cushion

Water ◽

10.3390/w10121801 ◽

2018 ◽

Vol 10 (12) ◽

pp. 1801

Author(s):

Qiulin Li ◽

Lianxia Li ◽

Huasheng Liao

Keyword(s):

Energy Dissipation ◽

Shallow Water ◽

Froude Number ◽

Flow Regime ◽

Dissipation Rate ◽

Hydraulic Jump ◽

Energy Dissipation Rate ◽

Main Stream ◽

Stilling Basin ◽

Key Factor

The depth of the stilling basin with shallow-water cushion (SBSWC) is a key factor that affects the flow regime of hydraulic jump in the basin. However, the specific depth at which the water cushion is considered as ‘shallow’ has not been stated clearly by far, and only conceptual description is provided. Therefore, in order to define the best depth of SBSWC and its relationship between the Froude number at the inlet of the stilling basin, a large number of experiments were carried out to investigate SBSWC. First of all, 30 cases including five different Froude numbers and six depths were selected for which large eddy simulation (LES) was firstly verified by the experiments and then adopted to calculate the hydraulic characteristics in the stilling basin. Finally, three standards, based on the flow regime of hydraulic jump, the location of the main stream and the energy dissipation rate, were proposed to define the best depth of SBSWC. The three criteria are as follows: (1) a complete hydraulic jump occurs in the basin (2) the water cushion is about 1/10–1/3 deep of the stilling basin, and (3) the energy dissipation rate is more than 70% and the unit volume energy dissipation rate is as high as possible. It showed that the best depth ratio of SBSWC (depth to length ratio) was between 0.1 and 0.3 and it also indicated the best depth increased with the increase in Froude number. The results of the work are of significance to the design and optimizing of SBSWC.

Download Full-text

Prototype Reynolds Number Vortex-Induced Vibration Tests on a Full-Scale Rigid Riser

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.4037538 ◽

2017 ◽

Vol 140 (1) ◽

Cited By ~ 2

Author(s):

Decao Yin ◽

Halvor Lie ◽

Rolf J. Baarholm

Keyword(s):

Surface Roughness ◽

Reynolds Number ◽

Flow Regime ◽

Amplitude Ratio ◽

Flow Regimes ◽

Offshore Structures ◽

Full Scale ◽

Displacement Amplitude ◽

Small Scale ◽

Supercritical Flow

Slender offshore structures in deep water subjected to currents may experience vortex-induced vibrations (VIV), which can cause significant fatigue damage. Extensive experimental researches have been conducted to study the VIV in the past several decades. However, most of the experimental works have small-scale models and relatively low Reynolds number (Re)—“subcritical” or even lower Reynolds number regime. There is a lack of full understanding of the VIV in prototype Re flow regime. Applying the results with low Re to a full-scale riser with prototype Re might have uncertainties due to the scaling effects. In addition, the surface roughness of the riser is also an important parameter, especially in critical Re regime, which is the case for prototype risers. In the present study, two full-scale rigid riser models with different surface roughness ratios were tested in the towing tank of MARINTEK in 2014. Stationary tests, pure crossflow (CF) free oscillation tests, and forced/controlled motion tests were carried out. Several conclusions could be made: The drag coefficient is dependent on the Re number and surface roughness ratio. At critical and supercritical flow regimes, the displacement amplitude ratio is less sensitive to Re than that at lower Re. The displacement amplitude ratio in subcritical flow regime is significantly larger than that in critical and supercritical flow regimes. Two excitation regions for the ‘smooth riser’ and one excitation region for the “rough riser” are identified.

Download Full-text

Prototype Reynolds Number VIV Tests on a Full-Scale Rigid Riser

Volume 2: Prof. Carl Martin Larsen and Dr. Owen Oakley Honoring Symposia on CFD and VIV ◽

10.1115/omae2017-61415 ◽

2017 ◽

Cited By ~ 1

Author(s):

Decao Yin ◽

Halvor Lie ◽

Rolf J. Baarholm

Keyword(s):

Surface Roughness ◽

Reynolds Number ◽

Flow Regime ◽

Amplitude Ratio ◽

Flow Regimes ◽

Offshore Structures ◽

Full Scale ◽

Displacement Amplitude ◽

Small Scale ◽

Supercritical Flow

Slender offshore structures in deep water subjected to currents may experience vortex-induced vibrations (VIV), which can cause significant fatigue damage. Extensive experimental researches have been conducted to study the VIV in the past several decades. However, most of the experimental works have small-scale models and relatively low Reynolds number (Re) - ‘subcritical’ or even lower Reynolds number regime. There is a lack of full understanding the VIV in prototype Re flow regime. Applying the results with low Re to a full scale riser with prototype Re might have uncertainties due to the scaling effects. In addition, the surface roughness of the riser is also an important parameter, especially in prototype Re regime. In present study, two full-scale rigid riser models with different surface roughness ratios were tested in the towing tank of MARINTEK in 2014. Stationary tests, pure cross-flow (CF) free oscillation tests and forced/controlled motion tests were carried out. Several conclusions could be made: • The drag coefficient is dependent on the Re number and surface roughness ratio. • At critical and supercritical flow regimes, the displacement amplitude ratio is less sensitive to Re than that at lower Re. The displacement amplitude ratio in subcritical flow regime is significantly larger than that in critical and supercritical flow regimes. • Two excitation regions for the ‘smooth riser’ and one excitation region for the ‘rough riser’ are identified.

Download Full-text

The flow field downstream of a hydraulic jump

Journal of Fluid Mechanics ◽

10.1017/s0022112095000966 ◽

1995 ◽

Vol 287 ◽

pp. 299-316 ◽

Cited By ~ 90

Author(s):

Hans G. Hornung ◽

Christian Willert ◽

Stewart Turner

Keyword(s):

Flow Field ◽

Froude Number ◽

Hydraulic Jump ◽

Control Volume ◽

Field Measurements ◽

Number Range ◽

Strong Shear ◽

The Mean ◽

Generation Mechanisms ◽

Particle Imaging

A control-volume analysis of a hydraulic jump is used to obtain the mean vorticity downstream of the jump as a function of the Froude number. To do this it is necessary to include the conservation of angular momentum. The mean vorticity increases from zero as the cube of Froude number minus one, and, in dimensionless form, approaches a constant at large Froude number. Digital particle imaging velocimetry was applied to travelling hydraulic jumps giving centre-plane velocity field images at a frequency of 15 Hz over a Froude number range of 2–6. The mean vorticity determined from these images confirms the control-volume prediction to within the accuracy of the experiment. The flow field measurements show that a strong shear layer is formed at the toe of the wave, and extends almost horizontally downstream, separating from the free surface at the toe. Various vorticity generation mechanisms are discussed.

Download Full-text