scholarly journals A Moment-Based Chezy Formula for Bed Shear Stress in Varied Flow

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1254
Author(s):  
Mohamed Elgamal

Despite its limitations, the Chezy bed shear stress formula is commonly used in depth-averaged flow numerical models as closure for estimating mutual tractive stresses with underneath boundaries. This paper proposes a novel moment-based formula that could be considered a revised version of the Chezy formula and can be used to estimate local variations of the bed shear stress under more complex and varied flow conditions with accelerating–decelerating flow fields. The formula depends on two velocity scales: the depth-averaged velocity, Uo, and a new moment-based velocity scale, u1. The new formula is calibrated using 10 experiments for flow over fixed bedforms, and the calibration coefficient is found to linearly correlate with h/Δ and h/zo ratios. The formula is also applied for the case of air flow across a negative step, jet water flow downstream a gate, and 2D water flow downstream an oblique negative step, and reasonably satisfactory agreement with the measured data is found. The new formula could be used in vertically averaged and moment models to disclose part of the information already lost by the vertical integration procedure.

2016 ◽  
Vol 30 (6) ◽  
pp. 916-925 ◽  
Author(s):  
Hai-long Huang ◽  
Qi-hua Zuo ◽  
Yi-ren Zhou ◽  
Yu-sheng Shen ◽  
Lan-xi Li

Author(s):  
Dipankar Biswas ◽  
Steven A. Lottes ◽  
Pradip Majumdar ◽  
Milivoje Kostic

Bridges are a significant component of the ground transportation infrastructure in the United States. With about sixty percent of bridge failures due to hydraulic causes, primarily scour, application of computational fluid dynamics (CFD) analysis techniques to the assessment of risk of bridge failure under flood conditions can provide increased accuracy in scour risk assessment at a relatively low cost. The analysis can be used to make optimum use of limited federal and state funds available to maintain and replace bridges and ensure public safety while traveling on the nation’s roads and highways during and after floods. Scour is the erosion of riverbed material during high flow conditions, such as floods. When scouring of the supporting soil around the piers and abutments of bridges takes place, risk of bridge failure increases. A simulation methodology to conservatively predict equilibrium shape and size of the scour hole under pressure flow conditions for flooded bridge decks using commercial CFD software was developed. The computational methodology has been developed using C++ to compute changes in the bed contour outside of the CFD software and generate a re-meshing script to change the bed boundary contour. STAR-CD was used to run the hydrodynamic analysis to obtain bed shear stress, and a BASH script was developed to automate cycling between computing bed shear stress with the CFD software and computing changes in the bed contour due to scour predicted using the computed shear stress for the current bed contour. A single-phase moving boundary formulation has been developed to compute the equilibrium scour hole contour that proceeds through a series of quasi-steady CFD computations. It is based on CFD analysis of the flow fields around the flooded bridge deck and shear stress computed at the bed modeled as a rough wall. A high Reynolds number k-ε turbulence model with standard wall functions, based on a Reynolds-Averaged Navier-Stokes (RANS) turbulence model, was used to compute bed shear stress. The scour sites on the bed were identified as those sites where the computed shear stress exceeded the critical shear stress computed from a published correlation for flat bed conditions. Comparison with experimental data obtained from the Turner-Fairbank Highway Research Center (TFHRC), McLean, VA, USA, revealed larger discrepancies than anticipated between the bridge inundation ratio and the scour hole depth. Although scour hole slopes were small for the cases tested, a correction to critical shear stress to account for bed slope was also tested. It did not significantly improve the correlation between CFD prediction and experimental observations. These results may be a consequence of using only excess shear stress above critical as a criteria for scour when other physical mechanisms also contribute to the initiation of scour. Prediction of scour depth using federal guidelines over predicts scour depth by as much as an order of magnitude in some cases. Over prediction is acceptable for purposes of ensuring bridge safety. CFD methods for scour prediction can be a significant improvement of current methods as long as under prediction of scour depth is avoided. Conservative scour prediction using CFD methods can be achieved by using conservative values of parameters such as critical shear stress and effective bed roughness.


2007 ◽  
Vol 34 (10) ◽  
pp. 1312-1323 ◽  
Author(s):  
Bahram Gharabaghi ◽  
Chris Inkratas ◽  
Spyros Beltaos ◽  
Bommanna Krishnappan

The Mackenzie River has several anomalous deep scour holes in a number of river channels in its delta. Proposed gas pipeline crossings have renewed interest in studying the stability of these scour holes. The main goal of this research project was to study flow velocity and bed shear stress distributions for a 30 m deep hole in the East Channel of the Mackenzie Delta as a first step toward assessing the stability of the scour hole and the risk of its migration during various flow conditions. In this study, a three-dimensional (3D) finite element flow model, FLUENT, using the renormalization group (RNG) k-ε turbulence model (where k is the turbulent kinetic energy and ε is the turbulence dissipation rate) was set up for the scour hole and calibrated using detailed measurements of 3D flow velocities, obtained with an acoustic doppler current profiler. The numerical model was then applied to predict flow velocity and bed shear stress distributions in and around the scour hole for three flow conditions (720, 1000, and 1400 m3/s). Results indicate that two vortices are formed in the river elbow above the scour hole. As the flow rate changed, the sizes of the vortices varied. The region upstream of the hole experienced the greatest magnitudes of bed shear stress.Key words: computational fluid dynamics, finite element, bed shear stress, deep hole, flow reversal.


2021 ◽  
Author(s):  
Stephan Niewerth ◽  
Francisco Núñez-González ◽  
Toni Llull

<p>The entrainment and transport of sediment by hydrodynamic mechanisms is strongly related to bed shear stress exerted by flow. Therefore, to quantify sediment transport and to determine sediment incipient motion conditions, accurate estimations of bed shear stress are required. Most of the existing methods used in hydraulics and river engineering to determine bed shear stress are indirect, and are mostly restricted to limited flow conditions or contain a large degree of uncertainty. Although devices to perform direct measurements of boundary shear stress exist, they are normally based on expensive technology. We developed a shear plate for direct shear stress measurements, using relatively low cost components. In this work we present preliminary results of measurements performed with the new shear plate, to characterize the bottom shear stress generated by a ship propeller. The data result in the expected quadratic relation between bed shear stress and jet velocities, and also give evidence of a good reproducibility. We show that the new shear plate appears to be a promising device for reliable measurements of submerged boundary shear stress under a wide range of environments and flow conditions.</p>


2011 ◽  
Vol 684 ◽  
pp. 251-283 ◽  
Author(s):  
Dominic A. van der A ◽  
Tom O’Donoghue ◽  
Alan G. Davies ◽  
Jan S. Ribberink

AbstractExperiments have been conducted in a large oscillatory flow tunnel to investigate the effects of acceleration skewness on oscillatory boundary layer flow over fixed beds. As well as enabling experimental investigation of the effects of acceleration skewness, the new experiments add substantially to the relatively few existing detailed experimental datasets for oscillatory boundary layer flow conditions that correspond to full-scale sea wave conditions. Two types of bed roughness and a range of high-Reynolds-number, $\mathit{Re}\ensuremath{\sim} O(1{0}^{6} )$, oscillatory flow conditions, varying from sinusoidal to highly acceleration-skewed, are considered. Results show the structure of the intra-wave velocity profile, the time-averaged residual flow and boundary layer thickness for varying degrees of acceleration skewness, $\ensuremath{\beta} $. Turbulence intensity measurements from particle image velocimetry (PIV) and laser Doppler anemometry (LDA) show very good agreement. Turbulence intensity and Reynolds stress increase as the flow accelerates after flow reversal, are maximum at around maximum free-stream velocity and decay as the flow decelerates. The intra-wave turbulence depends strongly on $\ensuremath{\beta} $ but period-averaged turbulent quantities are largely independent of $\ensuremath{\beta} $. There is generally good agreement between bed shear stress estimates obtained using the log-law and using the momentum integral equation, and flow acceleration skewness leads to high bed shear stress asymmetry between flow half-cycles. Turbulent Reynolds stress is much less than the shear stress obtained from the momentum integral; analysis of the stress contributors shows that significant phase-averaged vertical velocities exist near the bed throughout the flow cycle, which lead to an additional shear stress, $\ensuremath{-} \rho \tilde {u} \tilde {w} $; near the bed this stress is at least as large as the turbulent Reynolds stress.


1987 ◽  
Vol 14 (2) ◽  
pp. 216-220 ◽  
Author(s):  
Sunil K. Agrawal ◽  
Jatinder K. Bewtra

A modified approach to the design of grit chambers has been suggested in this paper. This approach is based on the concept of critical shear stress at the bed rather than mean velocity as used by T. R. Camp. It is recognized that the relationship between critical bed shear stress and mean velocity in a channel is not constant, as assumed by Camp, but varies according to the flow conditions. Critical bed shear stress values, obtained in the laboratory for different particle characteristics, are given in this paper. The proposed method should provide a more rational and a better design procedure for grit chambers. Key words: grit chambers, scouring, bed shear stress, initiation of motion.


2016 ◽  
Vol 64 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Oscar Herrera-Granados ◽  
Stanisław W. Kostecki

Abstract In this paper, two- and three-dimensional numerical modeling is applied in order to simulate water flow behavior over the new Niedów barrage in South Poland. The draining capacity of one of the flood alleviation structures (ogee weir) for exploitation and catastrophic conditions was estimated. In addition, the output of the numerical models is compared with experimental data. The experiments demonstrated that the draining capacity of the barrage alleviation scheme is sufficiently designed for catastrophic scenarios if water is flowing under steady flow conditions. Nevertheless, the new cofferdam, which is part of the temporal reconstruction works, is affecting the draining capacity of the whole low-head barrage project.


2018 ◽  
Vol 40 ◽  
pp. 05071 ◽  
Author(s):  
Jnana Ranjan Khuntia ◽  
Kamalini Devi ◽  
Sebastien Proust ◽  
Kishanjit Kumar Khatua

Very few studies have been carried out in the past in estimating depth-averaged velocity and bed shear stress in unsteady flow over rough beds. An experiment is thus conducted to investigate the vertical and lateral velocity profiles under unsteady flow conditions in a rough open channel for various flow depths. One hydrogram is repeatedly passed through the rectangular flume with a fixed rigid grass bed. Using micro Pitot tube and Acoustic Doppler Velocimeter (ADV), the flow patterns are investigated at both lateral and longitudinal positions over different cross-sections. For two typical flow depths, the velocities in both the rising limb and falling limb are observed. Hysteresis effect between stage-discharge (h ~ Q) rating curve between rising and falling limbs is illustrated. Lateral distribution of depth-averaged velocity and bed shear stress are plotted at three different cross sections and compared with the steady flow conditions. In falling limb of an unsteady flow case, both depth-averaged velocity and bed shear stress distribution in the central region is higher than that of steady flow case. However, in the rising limb, the bed shear stress of unsteady flow is less than that of steady flow case. Further, in an unsteady flow, the magnitude of depth-averaged velocity is found to increase towards the downstream sections. Along the downstream positions, bed shear stress values increase for lower flow depths and decrease for higher flow depth cases.


2011 ◽  
Vol 71-78 ◽  
pp. 1478-1483
Author(s):  
Chun Xin Zhong

Flexible vegetations supply great effect on river bank protection. It is important to study the critical flow conditions, including bed shear stress, scour duration and frictional velocity etc, causing damage of grass-covered revetment. Laboratory experiments prove that, destruction of turf can be estimated by observing the variation of water head. The experimental shear stress above vegetation zone has nonlinear relation with velocity square, which agrees with theoretic derivation. Before the turf destruction occurring, shear stress above vegetation zone increases with the scour duration and then goes to stabilization. This mentioned Shear stress will change suddenly when local scour damage happens, or keep stabilization while affine damage is on-going. Under the same flow conditions, the critical bed shear stress of reinforced turf is larger than that of natural turf. As far as the same-form revetments are concerned, the bed shear stress at breaking point increases with the flow velocity.


2012 ◽  
Vol 1 (33) ◽  
pp. 4
Author(s):  
Pierre-Yves Henry ◽  
Alf Tørum ◽  
Øivind Artsen ◽  
Dag Myrhaug ◽  
Muk Chen Ong

This study is focusing on the threshold of sand motion under random waves combined with a following current. The analysis is based on some flume experiments realized over a natural sand bed for different flow conditions (waves and currents). The main result comes as a map of the probability to exceed the threshold of sand motion, as a function of a wave and a current mobility parameter. These observations are compared to methods predicting the bed shear stress using an equivalent monochromatic wave, and links between the probability of exceeding the critical shear stress for initiation of sand motion and the calculated maximum bed shear stress are found.


Sign in / Sign up

Export Citation Format

Share Document