scholarly journals NEW RATIONAL MODEL FOR THE CURRENT-INDUCED THREE DIMENSIONAL SCOUR BENEATH SUBMERGED PIPELINES

2020 ◽  
pp. 11
Author(s):  
Titi Sui ◽  
Leon Heine Staunstrup ◽  
Stefan Carstensen ◽  
David R. Fuhrman
Keyword(s):  
Three Dimensional ◽  
Subsequent Development ◽  
Migration Velocity ◽  
Rational Approach ◽  
Rational Model ◽  
Clear Water ◽  
Governing Parameter ◽  
Scour Hole ◽  
Bed Scour ◽  
Horizontal Cylinders

New experiments involving the three-dimensional current-induced live-bed scour beneath submerged horizontal cylinders are presented, spanning larger Shields parameter and cylinder-to-sediment diameter ratio than previous studies. Specific emphasis is on gaining a better understanding of, and ability to predict, the span migration velocity during the initial and subsequent development of such a scour hole. Consistent with previous experimental observations, both a primary (faster) and secondary (slower) span migration are observed. Process visualization of suspended sediment patterns are in line with prior speculation that this transition coincides with reduced local bed shear stress amplifications as the scour hole both deepens and widens. Dimensional analysis and physical insight are combined, leading to a new rational model for predicting the span migration velocity in both live-bed and clear-water regimes, with predictions naturally coinciding at the limit of far field incipient motion conditions. In both regimes the data cluster as predicted, and fitted closed-form expressions are provided for predicting the span migration velocity. The rational approach likewise includes a new and simple criterion for the transition from primary to secondary migration in the live-bed regime. In the clear-water regime the model incorporates primary dependence on the ratio of the Shields parameter to its critical value, resolving apparent contradictions with a previous study which suggests that the depth-based Froude number is the most important governing parameter. The developed rational model can be used to quantitatively predict all known major features of the span migration velocity in the early stages of the three dimensional (live-bed and clear-water) scour beneath submerged horizontal cylinders induced by perpendicular flow, and can hence be regarded as the first complete model for this evolution.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/7BCXoqafbH4

scholarly journals Velocity and Turbulent flow field at around the cylindrical Pier

2020 ◽  
Vol 9 (4) ◽  
pp. 534-548
Keyword(s):  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Flow Behaviour ◽  
Acoustic Doppler Velocimeter ◽  
Wake Region ◽  
Velocity Data ◽  
Clear Water ◽  
Control Structures ◽  
Upstream Side ◽  
Scour Hole

This experimental study shows the velocity and turbulence field at vicinity of cylindrical pier with scour hole under clear water condition. The three dimensional velocity data were obtained at 5 cm, 10 cm, 20 cm and 30 cm from the pier with use of Acoustic Doppler Velocimeter at 360 degrees around the pier with 30-degree interval. The flow behaviour were extensively analyzed with the help of time averaged normalized velocity, Turbulent intensity, Turbulent kinetic energy and Reynolds shear stress plots. The study shows the flow behaviour at inside the scour hole, at scour hole ring and outside the scour hole which gives the elusive view of flow at vicinity of pier. An upstream side pier, the flow behaviour almost follows the similar trend but behind a cylinder the flow is asymmetry due to wake vortex and vortex shedding found at the wake region. This study offers an ample cognizance of flow structure at vicinity of circular pier, which is essential in order to design an effective scour control structures like rip-rap, W weir, vanes, slot and etc.,

Shape and energies of a dynamically propagating crack under bending

2003 ◽  
Vol 18 (10) ◽  
pp. 2379-2386 ◽  
Author(s):  
Dov Sherman ◽  
Ilan Be'ery
Keyword(s):  
Crack Propagation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Crack Front ◽  
Three Dimensional ◽  
Strain Energy Release ◽  
Governing Parameter ◽  
Propagating Crack ◽  
Front Shape

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

The Anatomy of Uncertainty

2021 ◽  
pp. 31-58
Author(s):  
Paul K.J. Han
Keyword(s):  
Conceptual Framework ◽  
Three Dimensional ◽  
Rational Approach ◽  
Subjective Reality ◽  
Medical Uncertainty

Chapter 3 describes the anatomy of medical uncertainty, identifying key attributes that give it a three-dimensional conceptual shape, form, and structure. It characterizes uncertainty in terms of its (1) fundamental sources (root causes), (2) issues (substantive problems), and (3) loci (persons in whose minds uncertainty resides) and presents a conceptual framework that allows the variety of uncertainties in medicine to be classified and better understood. The chapter makes the case that in all of these ways, a three-dimensional conceptual framework can facilitate a more intentional, targeted, and rational approach to evaluating medical uncertainty. By providing a way of visualizing, ordering, and objectifying an otherwise invisible, disordered, subjective reality, the framework can ultimately enable clinicians and patients to better manage medical uncertainty.

Development of a Three-Dimensional Iterative Methodology Using a Commercial CFD Code for Flow Scouring Around Bridge Piers

2012 ◽  
Author(s):  
Phani Ganesh Elapolu ◽  
Pradip Majumdar ◽  
Steven A. Lottes ◽  
Milivoje Kostic
Keyword(s):  
Shear Stress ◽  
Three Dimensional ◽  
Critical Shear Stress ◽  
Shear Stresses ◽  
Computational Domain ◽  
Time Step ◽  
Mesh Morphing ◽  
River Bed ◽  
Scour Hole ◽  
The Stability

One of the major concerns affecting the safety of bridges with foundation supports in river-beds is the scouring of river-bed material from bridge supports during floods. Scour is the engineering term for the erosion caused by water around bridge elements such as piers, monopiles, or abutments. Scour holes around a monopile can jeopardize the stability of the whole structure and will require deeper piling or local armoring of the river-bed. About 500,000 bridges in the National Bridge Registry are over waterways. Many of these are considered as vulnerable to scour, about five percent are classified as scour critical, and over the last 30 years bridge failures caused by foundation scour have averaged about one every two weeks. Therefore it is of great importance to predict the correct scour development for a given bridge and flood conditions. Apart from saving time and money, integrity of bridges are important in ensuring public safety. Recent advances in computing boundary motion in combination with mesh morphing to maintain mesh quality in computational fluid dynamic analysis can be applied to predict the scour hole development, analyze the local scour phenomenon, and predict the scour hole shape and size around a pier. The main objective of the present study was to develop and implement a three dimensional iterative procedure to predict the scour hole formation around a cylindrical pier using the mesh morphing capabilities in the STARCCM+ commercial CFD code. A computational methodology has been developed using Python and Java Macros and implemented using a Bash script on a LINUX high performance computer cluster. An implicit unsteady approach was used to obtain the bed shear stresses. The mesh was iteratively deformed towards the equilibrium scour position based on the excess shear stress above the critical shear stress (supercritical shear stress). The model solves the flow field using Reynolds Averaged Navier-Stokes (RANS) equations, and the standard k–ε turbulence model. The iterative process involves stretching (morphing) a meshed domain after every time step, away from the bottom where scouring flow parameters are supercritical, and remeshing the relevant computational domain after a certain number of time steps when the morphed mesh compromises the stability of further simulation. The simulation model was validated by comparing results with limited experimental data available in the literature.

The piecewise constant symmetric potential vorticity vortex in geophysical flows

2008 ◽  
Vol 614 ◽  
pp. 145-172 ◽  
Author(s):  
ÁLVARO VIÚDEZ
Keyword(s):  
Potential Vorticity ◽  
Three Dimensional ◽  
Static Stability ◽  
Geophysical Flows ◽  
Radial Dependence ◽  
Radial Solutions ◽  
Finite Radius ◽  
Piecewise Constant ◽  
Order Of Magnitude ◽  
Horizontal Cylinders

The concept of piecewise constant symmetric vortex in the context of three-dimensional baroclinic balanced geophysical flows is explored. The pressure gradients generated by horizontal cylinders and spherical balls of uniform potential vorticity (PV), or uniform material invariants, are obtained either analytically or numerically, in the general case of Boussinesq and f-plane dynamics as well as under the quasi-geostrophic and semigeostrophic dynamical approximations. Based on the order of magnitude of the different terms in the PV inversion equation, approximated PV equations are deduced. In some of these cases, radial solutions are possible and the interior and exterior solutions are found analytically. In the case of non-radial dependence, exterior solutions can be found numerically. Linear, and upper and lower bound approximations to the full PV inversion equations, and their respective solutions, are also included. However, the general solution for the pressure gradient in the vortex exterior does not have spherical symmetry and remains as an important theoretical challenge. It is suggested that, in order to maintain everywhere the inertial and static stability of the balanced geophysical flows, small balls of finite radius, rather than PV singularities, could become, specially in numerical applications, useful mathematical objects.

Experimental study of the instability of unequal-strength counter-rotating vortex pairs

2003 ◽  
Vol 474 ◽  
pp. 35-84 ◽  
Author(s):  
J. M. ORTEGA ◽  
R. L. BRISTOL ◽  
Ö. SAVAŞ
Keyword(s):  
Three Dimensional ◽  
Subsequent Development ◽  
Vortex Pair ◽  
Tip Vortex ◽  
Two Dimensional ◽  
Experimental Conditions ◽  
Vortex Pairs ◽  
Circulation Ratio ◽  
Counter Rotating Vortex Pair ◽  
Wing Tip

A rapidly growing instability is observed to develop between unequal-strength counter- rotating vortex pairs. The vortex pairs are generated in a towing tank in the wakes of wings with outboard triangular flaps. The vortices from the wing tip and the inboard tip of the flap form the counter-rotating vortex pair on each side of the wing. The flow fields are studied using flow visualization and particle image velocimetry. Both chord- based and circulation-based Reynolds numbers are of O(105). The circulation strength ratios of the flap- to tip-vortex pairs range from −0.4 to −0.7. The initial sinuous stage of the instability of the weaker flap vortex has a wavelength of order one wing span and becomes observable in about 15 wing spans downstream of the wing. The nearly straight vortex filaments first form loops around the stronger wing-tip vortices. The loops soon detach and form rings and move in the wake under self-induction. These vortex rings can move to the other side of the wake. The subsequent development of the instability makes the nearly quasi-steady and two-dimensional wakes unsteady and three-dimensional over a distance of 50 to 100 wing spans. A rectangular wing is also used to generate the classical wake vortex pair with the circulation ratio of −1.0, which serves as a reference flow. This counter-rotating vortex pair, under similar experimental conditions, takes over 200 spans to develop visible deformations. Velocity, vorticity and enstrophy measurements in a fixed plane, in conjuction with the flow observations, are used to quantify the behaviour of the vortex pairs. The vortices in a pair initially orbit around their vorticity centroid, which takes the pair out of the path of the wing. Once the three-dimensional interactions develop, two-dimensional kinetic energy and enstrophy drop, and enstrophy dispersion radius increases sharply. This rapid transformation of the wake into a highly three-dimensional one offers a possible way of alleviating the hazard posed by the vortex wake of transport aircraft.

Clear Water Local Scour by Submerged Three-Dimensional Wall Jets: Effect of Tailwater Depth

2006 ◽  
Vol 132 (6) ◽  
pp. 575-580 ◽  
Author(s):  
M. A. A. Faruque ◽  
Partha Sarathi ◽  
Ram Balachandar
Keyword(s):  
Three Dimensional ◽  
Local Scour ◽  
Clear Water ◽  
Wall Jets

scholarly journals Effect of L-shaped slots on scour around a bridge abutment

2021 ◽  
Author(s):  
Neveen Y. Saad ◽  
Ehab M. Fattouh ◽  
M. Mokhtar
Keyword(s):  
Laboratory Experiments ◽  
Vertical Wall ◽  
Clear Water ◽  
Flow Conditions ◽  
Bridge Abutment ◽  
Scour Hole ◽  
Bed Materials ◽  
Bridge Failure ◽  
Study Laboratory ◽  
Area And Volume

Abstract Local scour is the most significant cause of bridge failure. Providing a short abutment with a straight slot has proved to be an effective method for reducing scour at this abutment. In this study, laboratory experiments have been conducted to investigate the effectiveness of using L-shaped slots in comparison to the commonly used straight slot, on the scour reduction at short vertical-wall abutment under clear-water flow conditions and uniform bed materials. The slots were just above the bed and their diameters equal to half the abutment's length. The results illustrated that it is essential to have a straight slot in any combination of slots, as any configuration without one is inefficient. Also, a combination of a straight slot with one side slot in the middle of the abutment's width gives better performance than an individual straight slot, as it reduces the depth, area, and volume of the scour hole by about 32.6, 26.8, and 43.6% respectively, in comparison to 23.2, 20.7, and 35.3% for the straight slot alone.

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