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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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