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Numerical Simulations of the Flow and Sediment Transport Regimes Surrounding a Short Cylinder

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Numerical Simulations of the Flow and Sediment Transport Regimes Surrounding a Short Cylinder
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  IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 1, JANUARY 2007 249 Numerical Simulations of the Flow and SedimentTransport Regimes Surrounding a Short Cylinder Kimberly A. Hatton, Diane L. Foster, Peter Traykovski, and Heather D. Smith  Abstract— The 3-D flow field and bed stress surrounding a shortcylinder in response to combined wave and mean-flow forcingevents is examined. Model simulations are performed with a 3-Dnonhydrostatic computational fluid dynamics model, FLOW-3D.The model is forced with a range of characteristic tidal andwave velocities as observed in 12–15 m of water at the Martha’sVineyard Coastal Observatory (MVCO, Edgartown, MA). The2.4-m-long and 0.5-m diameter cylinder is buried 10% of thediameter on a flat, fixed bed. Regions of incipient motion are iden-tified through local estimates of the Shields parameter exceedingthe critical value. Potential areas of sediment deposition areidentified with local estimates of the Rouse parameter exceedingten. The model predictions of sediment response are in general inagreement with field observations of seabed morphology obtainedover a one-week period during the 2003–2004 MVCO mine burialexperiment. Both observations and simulations show potentialtransport occurring at the ends of the mine in wave-dominatedevents. Mean flows greater than 10 cm/s lead to the formation of largerscourpitsupstreamofthecylinder.Depositioninbothcasestends to occur along the sides, near the center of mass of the mine.However, the fixed-bed assumption prohibits the prediction of full perimeter scour as is observed in nature. Predicted scour andburial regimes for a range of wave and mean-flow combinationsare established.  Index Terms— Mine, scour, sediment transport. I. I NTRODUCTION T HE scouring of an erodible bed surrounding a submarineobject requires an understanding of the deformation of theflow field around the object as well as the response of the un-derlying sediment. Historical scour investigations of objects inaquaticenvironmentshavelargelybeenfocusedonverticalpilesor horizontal pipelines subjected to steady flow [1]. In the caseof vertical piles [2], sediment is eroded around the pile circum-ference, while in the case of horizontal pipelines [3], [4], sed-iment is eroded from under the pipeline. The eroded sedimentthat often deposits in the far wake as the flow reattaches can Manuscript received June 30, 2005; revisedSeptember 8, 2005; accepted Oc-tober 13, 2005. This work was supported in part by the U.S. Office of NavalResearch under the mine burial project N00014-00-1-0570. The work of K. A.Hatton was supported by the National Science Foundation Graduate ResearchFellowship. Guest Editor: R. H. Wilkens .K. A. Hatton was with the Environmental Engineering and Geodetic Science,Ohio State University, Columbus, OH 43210-1275 USA. She is now with theMalcolm Pirnie Inc., Columbus, OH 43240-2020 USA.D. L. Foster and H. D. Smith are with the Environmental Engineering andGeodetic Science, Ohio State University, Columbus, OH 43210-1275 USA(e-mail: foster.316@osu.edu).P. Traykovski is with the Applied Ocean Physics and Engineering Depart-ment, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 USA(e-mail: ptraykovski@whoi.edu).Digital Object Identifier 10.1109/JOE.2007.890986 eventually compromise the structure support. The evolution of the bed surrounding these objects is dependent on the object ge-ometry,thewaveandmean-flowforcing,andthesedimentchar-acteristics.Smallvariationsineachoftheseparameterscanleadto vastly different scour and burial regimes.Our ability to model scour and burial around submerged ob-stacles depends on how well the flow around the obstacle andthe individual sediment transport mechanisms can be resolved.Evenin steadyforcing environments, the flowfieldsaround 3-Dobjects are complex with temporally varying 3-D flow oftencharacterized by an upstream horseshoe vortex, streamline con-traction around the object, and vortex shedding in the wake. Forverticalpiles,theinitiationofscourisgenerallygovernedbythehorseshoevortexandthecontractionofstreamlines[1].Pipelinescour is initiated by a horizontal pressure gradient across thepipeline which induces a groundwater flow that ejects the sup-porting sediment from beneath the object [5]. In wave environ-ments, thescour surrounding 2-D objects (i.e., verticalpiles andpipelines) scales with the orbital excursion of the waves relativeto the object diameter. It is commonly parameterized with theKeulegan–Carpenter number (KC) given by(1)where is the amplitude of the maximum value of theundisturbed wave velocity outside the wave boundary layer,is the wave period, and is the object diameter [6], [1], [7]. For small bodies , the scour is dependent on vortexshedding in the wake of the object.Recent laboratory and numerical investigations have consid-ered the effects of introducing surface-mounted, 3-D objects toflow fields. Several geometries have been examined including[8] pyramids [9], cubes [10], [11], [8], spheres [12], hemi- spheres [13], and short cylinders [14]. The deformations of the flow field around and over the object ends reduces the hori-zontal pressure gradient applied across the object diameter andmay reduce or eliminate the piping present on 2-D pipelines.The flow deformation over the object also reduces the strengthof the horseshoe vortex as is present with 2-D vertical piles. Alimited number of laboratory investigations [15], [13] have con- sidered the flow field and scour around 3-D objects in wave andmean-flow environments. The scour around surface-mountedspheres in wave environments has been shown to have smallervolumes than in comparable mean-flow environments [12].Truelsen  et al.  [12] also showed that the scour in wave environ-ments is a function of both the bed stress and the KC number.However, in the mean-flow environment, the scour is purely afunction of the bed stress.The geometry of short, horizontal cylinders (i.e., mines) cre-ates a new set of hydrodynamic conditions resulting from the 0364-9059/$25.00 © 2007 IEEE  250 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 1, JANUARY 2007 Fig. 1. Acoustic images obtained during the MVCO experiment show the seabed geometry surrounding a single cylinder (a) before, (b) during, (c) near the peak,and (d) following the storm. The cone shape seen in the upper left side of (a)–(d) is the instrument mount. A time series of the 3-h mean    and root-mean-squared (rms) horizontal velocities        are given in the lower panel. The vertical lines correspond to morphology images (a)–(d) above. Peak mean andrms velocities in the 6 h before each of the morphology images (a)–(d) are identified with    and 3   , respectively. 3-Dflowfieldandtheabilityofthecylindertoroll,shift,andro-tate on the bed. Lab investigations exposing a submerged shortcylinder to waves showed that the 3-D scour pattern is corre-lated to both the Shields parameter and vortex shedding [15].Field observations of cylindrical mines in coastal environments,where wave and tidal velocities are often perpendicular, haveshown that the cylinder generally rotates until the longitudinalaxis is parallel to mean flows and perpendicular to the direc-tion of wave propagation [16]. Previous studies have indicatedthat cylindrical mines scour by a repeated sequence of the minescouring, rolling into the scour pit, and scouring again untilburied.Overasinglestormevent,thebedshowssignificantvari-ationinscourandburialregimes.Completeperimeterscoursur-rounding the mine occurs in high forcing conditions and partialburial occurs in low forcing conditions [16].The objective of this investigation is to examine the initi-ation of scour and deposition surrounding a short cylindricalobject resting on a bed using a 3-D computational fluid dy-namics model. Predictions of the initiation of scour and deposi-tion surrounding the object are made for a variety of wave andmean-flow climates consistent with two full-scale field experi-ments. Consistent with available field observations, the cylinderis oriented parallel to the mean flows and perpendicular to wavepropagation.Thesesimulationsareevaluatedwithfieldobserva-tions obtained before, during, and following an observed stormevent. Finally, regimes of scour and deposition initiation areidentified over a range of wave and mean-flow conditions.II. O BSERVATIONS The objective of the 2003–2004 collaborative Martha’sVineyard Coastal Observatory (MVCO, Edgartown, MA) mineburial experiment was to observe the near- and far-field waveand sediment climatology surrounding inert cylindrical minesplaced on a sediment bed. The cylindrical objects were placedin intermediate water depths of 12–15 m [17]. In the near-field,the free-stream velocity field, cylinder orientation, and seabedgeometry surrounding a short, cylindrical, mine-like objectwere observed. Vertical profiles of velocity were measured at50-cm range bins with an upward looking acoustic Dopplerprofiler (ADP) located 20 m from the object. Observationsof seabed geometry and backscatter intensity were obtainedwith a two-axis rotary sonar with a set frequency of 975 kHz.The instrument resolved the bed morphology and backscatterintensity over a 4-m radius surrounding the object, with aspatial resolution of approximately 10 cm in the horizontal and  HATTON  et al. : NUMERICAL SIMULATIONS OF THE FLOW AND SEDIMENT TRANSPORT REGIMES 251 approximately 5 cm in the vertical. The longitudinal axis of thecylinder was oriented 88 relative to the north.During the two-month experiment, a single storm event withsignificantwaveheightsofupto3m,waveperiodsrangingfrom4 to 8 s, and orbital wave velocities up to 50 cm/s in thenorth–south direction, occurred(Fig. 1). Theorientation of tidalflows relative to the north during the observations of in-terest was generally 100 , while was 210 . This two-daystorm event resulted in large evolutions of the local seabed ge-ometry surrounding the cylinder.III. M ODEL The 3-D flow simulations are performed with a commercialnonhydrostatic finite-difference model, FLOW-3D. This modelhas previously been used to resolve the flow and scour aroundbridge piers [18] and the flow around a submarine pipeline [19]. The model resolves fluid–fluid and fluid–air interfaces with anonboundaryfittedrectangulargridandavolumeoffluid(VOF)approach which resolves the grid cells into separate fractional-fluidcomponentscontainingthefractionofwaterandfractionof solidinthecell.Similarly,afractionalarea-volumeobstaclerep-resentation (FAVOR) approach is used to parametrize the flowwithin cells which contain fluid-obstacle boundaries.The model solves the 3-D Reynolds averaged Navier–Stokes(RANS) equations for incompressible flow simultaneously withthe continuity equation given by(2)The RANS equations are given as(3)where(4)where is the mean velocity, is the pressure, is the frac-tional open area open to flow in the direction, is the frac-tional volume open to flow, represents the body accelera-tions, represents the viscous accelerations, is the strainrate tensor, is the wall shear stress, is the density of water,is the kinematic viscosity, and is the kinematic eddy vis-cosity.In these simulations, the equations of motion are closed withthe standard closure scheme given by(5)where is the turbulent kinetic energy, is a closure coef-ficient, and is the dissipation rate as given in [20]. Compar-isons of , renormalization group (RNG), and large eddysimulation (LES) closure schemes with laboratory observationsof a 2-D cylinder lying on a flat bed and over a scoured bedfound that the mean-velocity predictions for each of the closure Fig.2. Gridusedtoresolvetheflowaroundthecylinder.Allunitsareinmeters.The cylinder is buried by 10% of its diameter (i.e., 5 cm), which results in a0.3 m 2   2.4-m bed surface area occupied by the cylinder. schemes were within 4% of the data [19]. The closure ac-curately predicted the wake reattachment point of the cylinderplaced on a flat bed. Predictions of the Strouhal number withthe closure scheme were consistent with the observations;however, the amplitude of the vortex shedding was smaller thanthe LES predictions and dependent on the grid resolution.In these calculations, a fixed horizontal cylinder, 2.4 m inlength with a diameter of 0.5 m, is lying on a flat, fixed bed. Tobe consistent with the initial sonar observations of the cylinderposition, the burial depth of the cylinder in the simulations waschosen as 10% of the diameter. This resulted in a 0.3-m-wideand 2.4-m-long section of bed surface area occupied by thecylinder. The domain is resolved with a rectangular grid with0.035 m 0.035 m 0.035-m cells in the region immedi-ately surrounding the cylinder which is linearly stretched to0.1 m 0.1 m 0.1 m at the boundaries (Fig. 2). A domain sizeof 6 m 9 m 2 m allowed for the upstream development of the bottom boundary layer and the downstream evolution of thewake. This resulted in 157, 215, and 38 grid cells in the do-main in the -, -, and -directions, respectively. The equilib-rium time for each simulation was determined as the time re-quired for the fluid at the beginning of the domain to reach thedownstream boundary (i.e., model simulation time was 112 and49 s for mean-flow velocities of 10 and 25 cm/s, respectively).Theequilibriumtimeforsimulationswith0cm/smean-flowve-locity was three complete wave periods. Time step sizes for thesimulationsarecalculatedbythemodeltoensurenumericalsta-bility. For the simulations, the direction of wave propagationand mean flow is assumed to be 0 and 90 relative to north, re-spectively. Consequently, the north and south boundaries wereforced with time-dependent free-stream wave velocities. Con-sistent with the MVCO observations (see Table I for a summaryof the observations), these velocities vary from 0 to 50 cm/s,with a wave period of 7 s. The west boundary was forced withthe mean-flow velocities varying from 0 to 25 cm/s, and theeast boundary was defined with a continuative outflow condi-tion (see Table II for a summary of the simulations). A no-slipconditionwasassumedatthebottomboundary,andaNikuradsebedroughness equivalenttothefinegrain(  252 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 32, NO. 1, JANUARY 2007 TABLE IO BSERVED  F REE -S TREAM  F LOW  C ONDITIONS  D URING THE  S TORM TABLE IIF ORCING  C ONDITIONS FOR  M ODEL  S IMULATIONS 0.15 mm) sands typicalof theMVCOsite was assumed. Asym-metry condition was assumed at the top of the domain.IV. R ESULTS Model simulations are performed for the range of wave andmean forcing conditions specified in Table II. Locations of incipient motion are assumed when the maximum value of the magnitude of the Shields parameter overa wave period exceeds the critical value . Themagnitude of the Shields parameter is given by(6)The instantaneous components of the Shields parameter are de-fined with(7)where is the specific gravity and is the grain size( 0.15 mm). The shear velocity is calculated witha two-point linear interpolation at the bed given by(8)where is the von Karman constant, is the ve-locity in the direction at ( 1.73 cm off the bed), and[21].Here, the maximum Shields parameter is assumed to occurat the peak wave velocity. The resolution of the near-bed do-main ( 1.1 cm) prohibits the characterization of theflow through the wave bottom boundary layer. In the followingsimulation, the wave bottom boundary layer thickness is alwaysless than 3.5 cm. This quasi-steady approach will result in thebed stress being in phase with the free-stream velocity. The ten-dency of sediment to deposit is characterized with values of thenondimensional Rouse parameter, which represents the balancebetweenthesettlingvelocityandameasureoftheturbulentfluc-tuations required to maintain sediment suspension and is givenby(9)where is the settling velocity as defined by(10)where is the relative density of the sediment, is gravity,is the grain sieve diameter, and is given by(11)where is the grain Reynolds number given as(12)where is the kinematic viscosity. Sediment is assumed to de-posit at a location when the minimum Rouse parameter over thewave cycle exceeds ten [21]. The minimum Rouse parameteroccurs at maximum shear stress over a wave period for eachcell and is, therefore, the most restrictive estimate for sedimentdeposition.The model is evaluated with the sonar observations shownin Fig. 1 and described in Table I. In each of the four cases,we compare the model simulations with the forcing conditionsmost consistent with the observations. Direct comparison withthe model is not possible because the model simulations all as-sumeaflat,immobilebedwithacylinderburialof10%.Instead,we evaluate the predicted scour and depositional susceptibilitywith the evolution of the observations in response to the hydro-dynamic forcing.Before the storm on October 21, 2003 at 02:00:00  A . M ., flowconditions ( 8 cm/s and 26 cm/s) are con-sistent with the forcing conditions of simulation 2c (10 cm/s and 25 cm/s). There exists two areas ex-ceeding the critical limit for incipient motion, each approxi-mately1.5cylinderdiametersinwidth,attheendofthecylinderupstream of the mean flow [Fig. 3(a)]. Within these areas, themaximum Shields parameter reaches 0.2. Smaller areas of in-cipient motion, approximately 0.5 cylinder diameters wide, de-velop at the opposite end of the cylinder. Deposition for thissimulation, as predicted by the Rouse parameter, is limited tothe area immediately next to the cylinder [Fig. 3(b)]. The obser-vations [Fig. 3(c)]  HATTON  et al. : NUMERICAL SIMULATIONS OF THE FLOW AND SEDIMENT TRANSPORT REGIMES 253 Fig. 3. (a), (d), (g), and (j) Predicted Shields parameter. Scour is predicted to occur in the hatched areas. Arrows in the upper right-hand corner show the directionof wave propagation and mean flow for the simulation. The bed surface area occupied by the cylinder is shown with the gray rectangle. (b), (e), (h), and (k)Predicted Rouse parameter. Deposition is predicted to occur in the hatched areas. (c), (f), (i), and (l) Observed seabed geometry surrounding the cylinder. Thecylinder (dashed white rectangle) is located at the center of the observed area, while the small circle above the cylinder represents the instrument pole. show a bed depression indicative of ongoing scour occurringat the west end of the cylinder to a depth of 23 cm below thefar-field bed elevation. A small area of scour also occurs at thenortheast end of the cylinder, approximately 0.5 cylinder diam-eters wide, and is consistent with the predictions for simulation2c.Theobservationsaregenerallynotinconsistentwiththesim-ulation. However, the predicted region of scour at the west endis larger than observed and the small scour area at the southeastendofthecylinderisnotpresent.Thisdeviationmayresultfromthe forced wave velocity being slightly larger than the observedvelocity and also the assumed 90 approach of the mean flow.At the initiation of the storm on October 21, 2003 at02:00:00  P . M ., the flow conditions ( 30 cm/s and23 cm/s) are consistent with the forcing conditions of simulation 3c ( 25 cm/s and 25 cm/s). Thecritical limit for incipient motion is exceeded at both ends of the cylinder and along the cylinder to approximately 15% of thelength [Fig. 3(d)]. Deposition is limited to areas immediatelyalongside the longitudinal axis of the cylinder [Fig. 3(e)]. Theobservations [Fig. 3(f)] show the onset of scour surroundingthe entire perimeter of the cylinder. The scour depressionsextend along the longitudinal axis, 30% of the length of thecylinder, which is not predicted by the model. Consistent withthe simulations, the observations show relatively small amountsof deposition during this section of the storm.Near thepeakofthestorm,onOctober21,2003at07:00:00 P . M ., theflowconditions( 39cm/sand 17cm/s)areconsistentwiththeforcingconditionsofsimulation4c(50 cm/s and 25 cm/s). The predicted Shields param-eter exceeds the critical limit for incipient motion over the en-
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