Turbulence quantification and sediment resuspensionin an oscillating grid chamber

J.J. Orlins, J.S. Gulliver

Abstract An oscillating grid chamber has been developedto study sediment suspension, desorption of compoundsfrom the resuspended sediment, and air–water masstransfer. The chamber is designed to allow researchers tostudy desorption of contaminants from cohesive sedi-ments and the flux of those contaminants to the vaporphase. The chamber uses a single vertically oscillating griddriven by a DC motor and closed-loop controller. Sedi-ment to be studied is placed in the bottom of the chamberand entrained into the water column by the turbulencegenerated by the oscillating grid. A two-component laserDoppler velocimeter (LDV) was used to measure the tur-bulent velocity field inside the chamber. Detailed mappingof the turbulent kinetic energy (TKE) produced by thisgrid arrangement was compared with established grid-stirred systems. At distances closer to the grid than twogrid bar spacings, large lateral gradients exist in the TKE.The suspension of cohesive sediments was also studiedusing this chamber. Steady-state suspended sedimentconcentrations were achieved within 30 min for a varietyof turbulence levels. By adjusting the grid operatingparameters, the TKE can be set to simulate the turbulencefound either at the bed or free surface in open-channelflow systems. With some care, the oscillating grid chambercan be used as a simple laboratory analogue to studyvarious environmental processes within the flow or ateither the sediment–water or air–water interface.

List of symbolsC1; C2; C2 constantsf grid oscillation frequency (T)1)g gravitational constant (LT)2)h depth of open-channel flow (L)M spacing between bars in oscillating grid (L)S grid stroke length (L)SEGL slope of energy grade line in open-channel

flow (m/m)TKE total kinetic energy of turbulence (L2T)2)TSS total suspended solids concentration (ML)3)U* bed shear velocity (LT)1)U; V instantaneous horizontal velocities (LT)1)W instantaneous vertical velocities (LT)1)U;V;W mean velocities (LT-1)u; v; w instantaneous velocity fluctuations (LT)1)u¢; v¢; w¢ root mean square (rms) turbulent velocity

fluctuations (LT)1)uw Reynolds stress (L2T)2)y vertical distance from bed in open-channel

flow (L)z vertical distance from grid (L)a constantj Von Karman constantm kinematic viscosity (L2T)1)P Cole’s wake parameterR* Reynolds number based on shear velocity

and flow depth, U*h/m

1IntroductionContaminated sediments can pose a hazard to benthic andaquatic organisms. When such sediments are disturbed byeither natural causes (such as storms or floods in rivers) oranthropogenic ones (such as dredging operations), thepotential exists for contaminants to desorb from the sed-iments. Once the compounds are in the dissolved phase,they can be advected away from their original locale, andcan also volatilize to the atmosphere. Understanding thedesorption process and the means by which these com-pounds volatilize is of great importance in predicting theirfate and transport.

Until recently, there has been little experimental workdone on evaluating the release of contaminants fromsediments and their flux to the vapor phase. Someresearchers (Valsaraj et al. 1995) have proposedmodels describing the flux of semi-volatile organic com-pounds from sediments to water and atmosphere, butmeasurements of mass transfer rates have been lacking.

Experiments in Fluids 34 (2003) 662–677

DOI 10.1007/s00348-003-0595-z

662

Received: 3 March 2001 / Accepted: 27 December 2002Published online: 9 May 2003 Springer-Verlag 2003

J.J. Orlins (&)Department of Civil and Environmental Engineering,Rowan University, 201 Mullica Hill Road,Glassboro, NJ 08028, USAE-mail: orlins@rowan.eduTel.: +1-856-2565328Fax: +1-856-2565242

J.S. GulliverSt. Anthony Falls Laboratory, Department of Civil Engineering,University of Minnesota, Mississippi River at 3rd Avenue SE,Minneapolis, MN 55414, USA

This research was funded in part by support from the EPA’sHazardous Substance Research Center, South and Southwest,at Louisiana State University. The authors would like to thankK.T. Valsaraj and L.J. Thibodeaux for their support andcollaboration in this research

To help remedy this situation, laboratory equipmenthas been developed to resuspend contaminated sedimentsunder controlled conditions and measure the flux ofcontaminants to the water and vapor phases. The desiredcharacteristics were that the device should be smallenough to run simultaneous experiments on hazardouschemicals, should not have significant scale effects, andshould simulate the turbulence of a free-surface flow. Thislaboratory-scale apparatus could then be used to quantifymass transfer from contaminated sediments to the waterand vapor phases, and thus verify predictive models foruse in real-world applications.

The equipment developed includes a number ofsquare sediment resuspension chambers. Contaminatedsediment is placed in the bottom of each chamber, andthen entrained into the water column by turbulencegenerated by an oscillating grid. The flux of chemicalsfrom the sediments to the water and air phases is thenmeasured.

This paper describes the design of the chambers,quantification of the turbulence in the chambers, and testsof sediment resuspension under a variety of operatingconditions. The relationship between turbulence at the freesurface generated by the oscillating grid and air–water gastransfer will be examined in a forthcoming article. The useof these chambers for chemical flux measurements isdescribed in Valsaraj et al. (1997).

2BackgroundIn natural systems, sediment resuspension is driven byturbulent shear stresses at the sediment–water interface.One way to simulate this process is with an oscillating-gridturbulence generator. Oscillating grids have been usedsince the 1950s to develop nearly isotropic, laterallyhomogeneous turbulence on a small scale, without themean shear associated with water flowing over a surface.Numerous investigators have used these grids to studytopics such as mixing across density interfaces (e.g.,Thompson and Turner 1975; Hopfinger and Toly 1976),turbulence near an air–water interface (e.g., Brumley andJirka 1987); sediment resuspension (e.g., Tsai and Lick1986; Huppert et al. 1995); and desorption of contaminantsfrom sediments (e.g., Connolly et al. 1983; Valsaraj et al.1997). In this paper the turbulent kinetic energy will bemapped across a greater portion of the chamber, and theresuspension of cohesive sediments will be quantified.Both of these are important parameters for sediment–water chemical flux characterization.

2.1Previous researchInitially, researchers used turbulence generated by oscil-lating grids as a one-dimensional analogue for studyingmixing across stratified density interfaces. Such densityinterfaces are common in the natural environment,occurring as thermoclines and pycnoclines in reservoirs,lakes, and oceans. Functional relationships between theturbulence generated and the operational parameters ofoscillating grids were developed by Thompson and Turner(1975) and Hopfinger and Toly (1976), among others.

These studies were aimed primarily at determining fluidentrainment rates across the interfaces. These researchersused square mixing tanks and single-plane grids made ofsquare bars; turbulent velocities were measured withhot-film anemometers.

Mass transfer across a shear-free water–air interfacehas also been studied using grid-stirred tanks. Brumleyand Jirka (1987) and Chu and Jirka (1992) examined thestructure of turbulence close to the free surface, andrelated this to gas transfer by measuring dissolved oxygenprofiles in the concentration boundary layer. The aim ofthese studies was to determine how the turbulence belowthe free surface affects mass transfer rates. These studiesalso used a square tank geometry and hot-film probes, andmeasured dissolved oxygen concentrations near the freesurface with an oxygen microprobe.

Oscillating grids have been used to study resuspensionof sediments. Tsai and Lick (1986) used a small, portabledevice to estimate the resuspension potential (i.e., thecritical shear stress) for cohesive sediments in the field.Their device was a small (12.7 cm diameter) cylinder usinga vertically oscillating perforated plate (instead of a grid ofsquare bars) for the turbulence generator. They found thatthe mass of material eroded from the sediment–waterinterface was proportional to the oscillation frequency ofthe plate, but did not correlate this to the actual turbulencein their device. Rather, they related operational parametersto bed shear by means of an indirect calibration: theycompared suspended sediment concentrations from theirfield device with those obtained in an annular flume. Thebed shear in the flume was calculated based on velocityprofile measurements; the assumption was made that theshear in their oscillating grid device must be equal to thatin the flume for identical suspended sediment concentra-tions.

Huppert et al. (1995) also used an oscillating grid tostudy entrainment of non-cohesive sediments. For thesestudies, they used very dense solutions of silt-sized siliconcarbide particles, and measured the entrainment of sedi-ment to the overlying (sediment-free) water column. Theycompared these results with those obtained from experi-ments with non-particulate density interfaces; the funda-mental difference is that the sediment particles responsiblefor the density gradient can settle out of solution. Sincethey utilized the same oscillating grid and tank asThompson and Turner, the turbulence parameters derivedfrom earlier studies were directly applicable. However,their results are not directly comparable with those of Tsaiand Lick, because Huppert et al. did not use natural sed-iments, had a different tank geometry, and placed theiroscillating grid at the bottom of their tank, in the densesuspension layer.

Brunk et al. (1996) used an array of horizontallyoscillating grids to simulate open-channel flow turbulenceas a function of depth. These researchers used their‘‘differential turbulence column’’ to suspend sedimentusing both vertically homogeneous and vertically decayingturbulence fields. With a vertically decaying turbulenceprofile set up to model that found in open-channel flow,they found that the total suspended sediment concentra-tion profiles followed conventional theories, and

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concluded that their apparatus can be used to study manyenvironmental processes. However, in the oscillating gridarrangement used in their work, there is a lateral variationin turbulence, which results in non-uniform turbulenceconditions across the sediment–water interface.

Finally, Connolly et al. (1983) used an oscillating gridreactor to study the desorption of Kepone (a hydrophobic,organic compound) from natural sediments. For theirexperiments, they used a tall circular tank with a numberof stacked oscillating grids, but they made use ofHopfinger and Toly’s relationships between grid opera-tional parameters and turbulence (which were developedfor a square tank with a single grid). They found thatequilibrium partitioning between the dissolved and sorbedphases of chemical is a linear function of dissolved phasedconcentration and an inversely non-linear function ofsuspended sediment concentration. In addition, theyfound that the partition coefficient is not only highlydependent on the chemical of concern, but also on thesediment type, indicating the complexity of sedimentsorption equilibria.

The overall aim of the current project was to develop adevice for resuspending cohesive sediments in a controlledmanner that would allow measurement of the flux ofchemical compounds from the sediments to the water andvapor phases. The well-established body of literaturebriefly described above provided the basis for selecting anoscillating grid mechanism to generate shear-free turbu-lence to resuspend the sediments. However, no previouswork has been done on linking all of the aspects men-tioned above (sediment resuspension M turbulence M

air–water mass transfer) together in one experimentalsetup. In addition, detailed measurements of the turbu-lence within the mixing chamber were needed to charac-terize the relationship between turbulence, sedimententrainment, and mass transfer. Finally, it was desired todevelop similitude relationships between turbulence gen-erated by an oscillating grid and turbulence in a boundarylayer flow.

2.2Theory of turbulence in grid-stirred reactorsIn a typical arrangement, a grid of square bars or mesh isoscillated vertically in a tank by an electric motor with aneccentric drive. The stroke (distance the grid travels upand down) and frequency of oscillation can be varied. Therms turbulent velocity fluctuations decay with the distanceaway from the grid. For a grid with square bars, it has beenshown (Hopfinger and Toly 1976; DeSilva and Fernando1992) that the horizontal (u¢, v¢) and vertical (w¢) rmsfluctuations can be described by

u0 ¼ v0 ¼ffiffiffiffiffi

u2p

¼ C1M0:5S1:5fz�1

w0 ¼ffiffiffiffiffiffi

w2p

¼ C2M0:5S1:5fz�1 ð1Þwhere S is the stroke length, f is the oscillation frequency, zis the distance away from a virtual origin, M is the meshspacing of the grid, and C1 and C2 are constants that maydepend on the geometric parameters of the grid. Here, uand w are the instantaneous velocity fluctuations (u=U)U; w=W)W ), where U and W are the instantaneous

velocities and the overbars denote the mean values).Hopfinger and Toly report values of C1 and C2 ofapproximately 0.25 and 0.27, while DeSilva and Fernando(1992) measured values of approximately 0.22 and 0.26,respectively.

The empirical relationships for the turbulent velocityfluctuations do not hold until one reaches a significantdistance from the grid. The turbulence near the grid is nothomogeneous. Various relationships have been proposedfor the limiting distance beyond which Eq. (1) areapplicable. Atkinson et al. (1987) concluded that therelationships held for z>2M, while DeSilva and Fernando(1992) found that for ‘‘small’’ strokes, the relationshipsheld for z>4S.

One of the advantages for using oscillating grids forstudying turbulence and mixing phenomena is that there isno mean shear. Unlike a boundary-layer flow, where uni-directional shear is generated at the fixed boundaries, theoscillating grid produces no net flow direction, and thusno mean shear. This is not to say that there is no shearpresent at all; rather, the average shear over space and timeis zero. The convenience of using a mean shear stress tocharacterize the turbulence is not possible in an oscillatinggrid chamber.

Since there is no mean shear in the oscillating gridchamber, the TKE of the turbulence can provide a basis forcomparing sediment resuspension and mass transferunder differing operating conditions. The TKE can bedefined from the rms velocity fluctuations:

TKE ¼ 12ðu02þ v0

2þw02Þ ð2Þ

Substituting in our physical parameters S, f, z, and M,and making the assumption that v¢=u¢, the TKE can beestimated as

TKE ¼ 12ð2C2

1 þ C22ÞðM0:5S1:5fz�1 Þ2 ¼ aðMS3f 2z�2Þ ð3Þ

where a would be 0.082 using DeSilva and Fernando’svalues of C1 and C2.

3Experimental aspects

3.1Experimental setupThe design of the sediment resuspension/chemical fluxchambers was derived from other oscillating gridarrangements reported in the literature. A square chamberwas chosen for construction and LDV access consider-ations. A large plan-form area was desired to reduce theimportance of wall effects in sediment entrainment andmeasurement of chemical fluxes across the air–waterinterface.

The sediment resuspension chamber was manufacturedout of clear acrylic plastic, as shown in Fig. 1. Thechamber is a cube 0.5 m on each side, with a tight fittinglid. The grid consists of an 8·8 mesh made out of 1.27 cmsquare aluminum bars, with a center-to-center spacing of6.25 cm, and a bar length of 49 cm. The grid is connectedto a 1/3 HP variable-speed DC motor by a stainless steelshaft and eccentric drive. A steel frame supports the drivemotor and is permanently fastened to the lid.

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Two different methods were used to fasten the grid tothe central drive shaft. In the initial grid configuration, astainless steel plate was clamped across the central open-ing in the grid, and the drive shaft fastened through a holein this plate. This design was chosen initially due to itsrelatively simple construction. In the second configurationtested, four smaller connecting shafts were fastened to thegrid at the bar intersections closest to the grid center, andthen drawn together to connect to the central shaft. Thisconfiguration resulted in a somewhat more cumbersomeand fragile attachment, but the turbulence characteristicsof the chamber were more uniform in the horizontal plane.

An acrylic guide is fastened to the back wall of the tankand prevents the grid from rotating in the tank. The gridstroke length can be adjusted from 2 to 12 cm by changingthe attachment location of a connecting rod between thevertical shaft and eccentric drive. The oscillation frequencyis set and maintained by a closed-loop programmablecontroller. Frequencies from 60 to 600 rev/min (1 to10 Hz) can be maintained, depending on the stroke length.

Sediment is placed in the bottom of the chamber byremoving the grid/lid/frame assembly. Water samples canbe removed from the tank via a sampling port in the lid of

the tank and a siphon tube immersed in the water abovethe grid or via sampling ports at various elevations on theside of the tank.

3.2Turbulence measurementsThe turbulent velocity field inside the mixing chamber wasmeasured using a two-component LDV, manufactured byTSI (St. Paul, Minn.). The system used a 5 W argon-ionlaser, Colorburst beam splitter, 350 mm focal distancefiber-optic probe, Color Link receiving optics, and anIFA 755 signal processor. The system was controlled by apersonal computer using TSI’s FIND for Windows dataacquisition and processing software.

For the velocity measurements, a false floor was in-stalled at an elevation of 10.2 cm to simulate the sediment–water interface for three of the tests. The side walls of thetank were cleaned and polished using a cleaningcompound made for acrylic plastic. Clean tap water wasused for the tests; generally, there was enough naturalparticulate matter in the water that seeding was notrequired. For some tests, seed particles were added,but had little effect on data acquisition rates.

The fiber optic probe was mounted on a 3-axis traversethat was controlled by the pc-based data acquisition sys-tem. The probe was positioned to look through one of theside walls of the chamber and measure the vertical and onehorizontal velocity component, also shown in Fig. 1. Theprobe could be positioned using the traverse for mea-surements at any location on one half of the chamber.

The LDV system was configured to measure velocitiesin the coincidence mode. This allowed direct computationof the Reynolds stress uw. Data were collected at a mea-surement location for 100 s or until 10,000 measurementshad been made. A frequency shift of 20 kHz was used forboth the horizontal and vertical measurement channels.With the laser set to provide between 1 and 2 W outputpower, data collection rates were typically between 50 and100 Hz.

In the initial series of tests with the original grid-mounting configuration, data were collected for threefrequencies (3.0, 5.0, and 7.0 Hz) and a 3 cm stroke lengthand a total water depth of approximately 25 cm. Two

Fig. 1. Experimental setup

Table 1. Summary of turbulence measurement test conditions in oscillating grid tank

Test No. Gridmountinga

Frequency(Hz)

Stroke(cm)

Water surfaceelevation

Bedelevation

Grid centerlineelevation

Net waterdepth

Fig. No.

(cm) (cm) (cm) (cm)

Detailed profile measurements3301 plate 3.0 3.0 35.0 10.2 23.2 24.8 33501 plate 5.0 3.0 35.0 10.2 23.2 24.8 43701 plate 7.0 3.0 35.0 10.2 23.2 24.8 53503 plate 5.0 3.0 35.0 0.0 23.2 35.0 63505 open 5.0 3.0 35.0 0.0 10.1 35.0 7

Detailed plane measurements3302 plate 3.0 3.0 35.0 10.2 23.2 24.8 83502 plate 5.0 3.0 35.0 10.2 23.2 24.8 93702 plate 7.0 3.0 35.0 10.2 23.2 24.8 103504 plate 5.0 3.0 35.0 0.0 23.2 35.0 113505 open 5.0 3.0 35.0 0.0 10.1 35.0 12

a‘‘Plate’’ indicates the original grid mounting method; ‘‘open’’ indicates the revised method

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additional tests were run with the original and revised gridmounting, and a total water depth of 35 cm. The testoperating conditions are summarized in Table 1.

For each condition, measurements were first madealong four profiles at roughly 1 cm vertical increments.The profiles were intended to characterize the decay ofturbulent velocity fluctuations and energy as a function ofdistance from the grid. In addition, data were collectedalong a number of planes above and below the grid. Thesemeasurements were intended to characterize the lateralvariability of the turbulence parameters.

Measurement parameters included the horizontal andvertical average velocities U, W, the rms velocityfluctuations u¢ and w¢, the relative turbulence intensities(e.g., u¢/U ), the Reynolds stress uw, and the u–w crosscorrelation coefficient. Raw data were stored in binaryform for each measurement location. Summary filescontaining all of the parameters for each measurementlocation were created for each test in an ASCII (text)format using the FIND software. These data files werethen used as input for further post-processing operationssuch as coordinate transformations, datum adjustments,and calculation of the TKE of the turbulence. Thesesecondary processing operations were conducted usingcustom programs written in the Microsoft QuickBasicprogramming language.

3.2.1Vertical profilesMeasurements of the turbulent velocities were made alongfour vertical profiles. Data were collected in both theregion from the bottom of the tank to the grid and fromthe grid to the free surface. The first profile was located atthe quarter point of the tank, at the center of an opening inthe grid; the second profile was located at the intersectionof two grid bars. The third and fourth profiles were locatedat symmetric positions on the other half of the tank. Theprofile locations are shown in Fig. 2a.

Data were collected at 1 cm intervals along the verticalprofiles. Because of the configuration of the LDV optics,the measurement volume was not placed within approxi-mately 1 cm of the bed or free surface. Likewise, mea-surements were not made within 1 cm of the bottom andtop planes of the grid’s motion.

3.2.2Horizontal planesIn addition to the profile measurements, turbulent veloc-ities were also measured along a number of horizontalplanes above and below the grid. Measurements were ta-ken at horizontal increments of one-half the grid spacing(3.125 cm), as shown in Fig. 2b. With this arrangement,data were collected coincident with the intersection of twogrid bars, at the center of the openings in the grid, and atthe midpoints of each bar segment. This resulted in a 15·8grid of measurement points located in one half of the tank,for a total of 120 measurements per plane.

The measurement planes were located both above andbelow the grid. Above the grid, data were collected on planesnear the free surface, midway from the free surface to thegrid, and just above the grid. A similar arrangement wasused below the grid (near grid, midway to bed, near bed).

3.3Sediment entrainment measurementsA series of tests was conducted to determine the rela-tionship between cohesive sediment resuspension andturbulence generated by the oscillating grid. The sedi-ments tested came from University Lake, in Baton Rouge,Louisiana. The sediment composition was 10% sand, 76%silt, and 14% clay, with a organic carbon fraction of 0.041and particle bulk density of 2.5 g/cm3.

The total mass of suspended solids was measured as afunction of oscillation frequency, stroke length, and con-solidation time. Eight tests were run, with frequencies of150–650 rpm (2.5–10.8 Hz), strokes of 2, 3, and 4 cm, andconsolidation times of 2 and 11 days.

Prior to each test, the sediments were removed from thechamber, completely mixed with a rotary mixer, pouredback into the chamber, and allowed to consolidate for astandard period of time (2 or 11 days). After the consoli-dation period, the tank was slowly filled with water in amanner that did not disturb any of the sediments. Theinitial elevation of the sediments in the tank was typically10–11 cm, and the water level 35 cm. The grid wasadjusted to the desired stroke length (2, 3, or 4 cm),and positioned so that the center of motion was at anapproximate elevation of 23 cm (i.e., 12–13 cm above thebed).

Fig. 2a, b. Velocity measurement locations

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For each test, the grid was oscillated at the lowestdesired frequency, and water samples were withdrawn atregular intervals for later analysis. When an apparentsteady-state suspended sediment concentration had beenachieved, the oscillation frequency was increased, andmaintained at the new level until a new steady-stateconcentration was reached. This procedure was repeatedfor a number of frequencies. Water analyses for the firstfew tests indicated that steady-state concentrations(within measurement uncertainty) were approachedwithin 10–30 min. For later tests, the oscillation fre-quencies were then maintained for at least 30 min beforebeing increased.

Water samples were withdrawn from the regionbetween the grid and the free surface using a siphon,and placed in glass or plastic sample bottles for lateranalysis. TSS concentrations were determined by

filtering, drying, and weighing a known volume ofsample water according to Standard Method 2540D(APHA 1992).

4Results and discussion

4.1Spatial quantification of turbulenceThe results from the profile tests at the three frequenciestested are presented in Figs. 3, 4, 5, 6, and 7. Inaddition to the four profiles of the turbulence parame-ters, the figures show the average velocity componentsand the standard deviation of each, based on thevelocity measurements taken along lateral planes in thetank, described above. Since the results from the threetests are qualitatively similar, the majority of the

Fig. 3a–f. Velocity profiles, 3.0 Hz, originalgrid mounting, with false floor

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comments will be restricted to the second case shown(Fig. 4), with the 3 cm stroke and oscillation frequencyof 5.0 Hz.

4.1.1Mean velocitiesAs can be seen from the profiles of the horizontalvelocities (Fig. 4a) there appears to be little net lateralmovement in the tank. Likewise, the mean verticalvelocity (diamonds in Fig. 4b) is close to zero. (Here, themean velocity is defined as the arithmetic average of thefour profile measurements taken at a particular eleva-tion.) However, the individual profiles in Fig. 4b indicatelarge-scale vertical mixing, which appears to be depen-dent on the location with respect to the grid. This is adirect result of the mounting plate holding the grid to thevertical drive shaft.

From the profiles, it appears that fluid is pushed awayfrom the grid where the grid bars intersect (triangles,profiles 2 and 4), while it is pulled towards the grid at theopen areas (squares, profiles 1 and 3).

The standard deviation of all horizontal and verticalvelocity measurements at a particular elevation forprofile 1 are shown as error bars in Fig. 4a and b,respectively.

4.1.2Root mean square velocitiesThe rms of the turbulent velocity fluctuations are shown inFig. 4d and e. In addition to the measured profiles and theaverages over the whole tank, the expected rms velocityfluctuations based on the Hopfinger–Toly relationship(Eq. 1) are shown by the dashed line. It is apparent thatthe predictions are approached more closely by the data

Fig. 4a–f. Velocity profiles, 5.0 Hz, originalgrid mounting, with false floor

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away from the grid (i.e., near the bed and free surface).This is understandable, as the predictive relations are valid(based upon both Atkinson et al.’s and DeSilva and Fer-nando’s criteria) for distances greater than 12.5 cm fromthe center of grid motion for these operating conditions;this is roughly the distance from the grid to the bed andwater surface used in these experiments. For distances lessthan the criteria (which encompass the majority of thetank), the magnitude of the rms velocities above and belowthe openings in the grid (i.e., profiles 1 and 3) are con-siderably less than those coincident with the bar inter-sections (i.e., profiles 2 and 4).

4.1.3Reynolds stress and total kinetic energyThe mean Reynolds stress, uw, is quite small, as shownin Fig. 4c, with an average of zero and absolute value of

individual measurements less than roughly 2·10-4 m2/s2.This makes sense, as this type of mixing chamber hasno overall mean shear. It is interesting, however, to notethat there is little variation of uw with distance from thegrid.

The total kinetic energy of the turbulence was calculatedfrom the rms velocities using Eq. (2). Since the LDV systemonly measured velocities in one horizontal and the verticaldirections (i.e., u and w), the other horizontal velocity (v)was estimated based on the symmetry of the tank. A similarestimate was made for the horizontal rms velocities.

The variation of TKE with depth is shown in Fig. 4f. Farfrom the grid, the measured values compare favorably withthe TKE predicted using Eq. (3), which is based on theHopfinger–Toly relationship for rms velocities. Again,magnitudes of the TKE are substantially less for profiles 1and 3 than for profiles 2 and 4 close to the grid. In this

Fig. 5a–f. Velocity profiles, 7.0 Hz, originalgrid mounting, with false floor

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region, it is likely that the TKE for profiles 1 and 3 is moregreatly influenced by the wake from the oscillating grid. Ifthis is true, the lesser of the two criteria, z‡4S or z‡2M, forapplying the Hopfinger–Toly relationship is probably mostapplicable.

Within the ‘‘near-grid’’region, the TKE at locationscoincident with grid bar intersections is approximatelytriple that at the ‘‘holes’’ between grid bars for anoscillation frequency of 3.0 Hz (Fig. 3), and approxi-mately double for an oscillation frequency of 5.0 Hz(Fig. 4). This local horizontal variation in TKE decreasesgradually with distance away from the grid, until thez=2M or z=4S criteria is reached. For the 7.0 Hz oscil-lation frequency test case (Fig. 5), this trend is reversedvery close to the grid, with TKE values at the barintersections slightly less than those above or below the‘‘holes.’’ It appears that the local horizontal and vertical

rms velocity fluctuations are damped at the bar inter-sections for the higher oscillation frequencies, resultingin the relative reduction in TKE at these locations.However, the average of the TKE at all four profilelocations does increase with increasing oscillation fre-quency, as expected.

The lateral variation in TKE is shown in Figs. 8, 9, 10,11, and 12. Close to the grid, there are steep energy gra-dients, while farther from the grid (near the sediment–water and air–water interfaces) the turbulence is moreuniform. This variation in TKE near the grid may also beseen in Fig. 4f, where the extremes in the variation arerepresented by the difference between the square and tri-angular symbols (i.e., profiles 1 and 3 versus profiles 2 and4). In addition, with the original grid mounting configu-ration, there exists a region of elevated TKE near thecenter of the tank (Figs. 8, 9, 10, and 11).

Fig. 6a–f. Velocity profiles, 5.0 Hz, originalgrid mounting, without false floor

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4.1.4Effect of false floorThe initial turbulence measurement tests were conductedwith a false floor in the bottom of the tank, to simulate thephysical boundary condition of the sediment–waterinterface. One test was conducted without the false floor,such that the oscillating grid was able to mix fluid in theentire tank volume. Profiles from these tests are shown inFigs. 4 and 6, and perspective views of the TKE in planesabove and below the grid are shown in Figs. 9 and 11.

Quantitatively, the results between the two differenttests are similar. The net horizontal velocities throughoutthe depth of the tank are close to zero (Figs. 4a and 6a).Likewise, the net average vertical velocities (diamonds inFigs. 4b and 6b) are close to zero, but as with the other testcases, there are large local variations, depending on whe-ther the measurement profile was located under a grid barintersection or hole.

Without the false floor, it appears that there are smallsecondary currents at the bottom of the tank (Fig. 6a,elevation 0–25 mm). These result in a slight increase in therms velocities near this fixed boundary, and a corre-sponding increase in TKE. Since the distance from the gridto the free surface was the same between these two tests,there appear to be no differences in the profiles above thegrid.

The overall spatial distribution of TKE (Figs. 9 and 11)appear quite similar with and without the false floor. Theapparent TKE (color) variations between the two casesresult from slight variations in the location of the visual-ization plane above and below the grid.

4.1.5Effect of grid mounting systemA region of elevated TKE exists near the center of the tankfor each of the test cases with the original mounting plate.

Fig. 7a–f. Velocity profiles, 5.0 Hz, revised gridmounting, without false floor

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This can be seen as a ‘‘bulls-eye’’ in the TKE contoursshown in Figs. 8, 9, 10, and 11 at the (x, y) location (250,250). The support plate covered a large portion of thecenter-most grid open space, and set up localized sec-ondary currents with high rms velocities, as can be seen inFigs. 3b, 4b, 5b, and 6b.

To reduce these secondary currents and the associatedelevated turbulence levels, the rigid mounting plate wasreplaced with four small shafts, connected directly to thegrid at the bar intersections closest to the center of thegrid.

With this configuration, LDV measurements wereonly taken in the planar configuration, with threemeasurement elevations below the grid and four above.Measurements corresponding to the profile locationsshown in Fig. 2a were extracted from this data set, andare shown plotted as profiles in Fig. 7. The spatial dis-tribution of TKE for this configuration is shown inFig. 12.

With the revised mounting configuration, both thehorizontal and vertical velocities in each profilehave lesser magnitudes than with the original

Fig. 8. Spatial distribution ofTKE, 3.0 Hz, original gridmounting, with false floor

Fig. 9. Spatial distribution ofTKE, 5.0 Hz, original gridmounting, with false floor

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mounting, as can be seen by comparing Figs. 6 and 7.Especially notable are the vertical velocities close to thegrid (Figs. 6b and 7b). With the revised mountingconfiguration, the ‘‘push-pull’’ effect of the mountingplate is eliminated, resulting in more uniform velocityprofiles.

The overall spatial distribution of TKE is much moreuniform at any given elevation with the revised mounting,as can be seen by comparing Figs. 9, 11, and 12. With therevised mounting, there is no ‘‘bulls-eye’’ region of higherTKE at the center of the tank. However, the smaller-scalegradients in TKE still exist in the region close to the grid,

Fig. 10. Spatial distribution ofTKE, 7.0 Hz, original gridmounting, with false floor

Fig. 11. Spatial distribution ofTKE, 5.0 Hz, original gridmounting, without false floor

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with elevated values at the bar intersections and lowervalues at the grid openings.

4.2Sediment entrainmentThe time-history of suspended sediment concentrationfor a representative test is shown in Fig. 13. Initially, atlow turbulence levels (i.e., low oscillation frequencies),there was no sediment entrainment. During this periodof testing, the water samples withdrawn represent thenominally clean tap water introduced to the tank, andprovide an indication of the lower limit of quantitativeanalysis that was obtained. As the energy input to thesystem was increased by raising the grid oscillationfrequency, the instantaneous shear at the bed raisedabove the threshold critical shear. After this point,entrainment occurred rapidly. Steady state concentra-tions were achieved within 30 min, with a maximumobserved TSS load of about 3.0 g/l at the highest oscil-lation frequency.

To allow interpretation of the TSS data, the total kineticenergy (TKE) at the sediment–water interface was esti-mated for each operating condition using Eq. (3). Thesteady-state suspended sediment concentrations were thenplotted for each test as a function of the estimated TKE, asshown in Fig. 14.

There is a distinct difference in resuspension betweenthe sediments allowed to consolidate for 11 days and thosetested after only 2 days. This is expected, as cohesivesediments that have a greater consolidation will require agreater critical shear to initiate resuspension from the bed.

At a TKE of roughly 1.2·10-3 m2/s2, however, the totalsuspended solids concentration was similar for both con-solidation times.

4.3Use of the chamber as an analogue to natural systemsSince an oscillating grid chamber produces reproduciblelevels of uniform turbulence, it can be used as a one-dimensional analogue to a boundary layer flow in naturalsystems.

The uni-directional orientation of a boundary layerflow allows turbulence to be readily quantified through amean boundary shear. For the confined boundary layer ofopen channel flow, Nezu and Nakagawa (1993) note thatthe free-stream, transverse, and vertical rms velocityfluctuations (u¢, v¢, w¢) can be expressed as

u0=U� ¼ 2:30 expð�y=hÞv0=U� ¼ 1:27 expð�y=hÞw0=U� ¼ 1:63 expð�y=hÞ

ð4Þ

where U* is the bed shear velocity, y is the distance fromthe bed, and h is the flow depth. Of course, at y=0 all threefluctuating velocity components are equal to zero and aty=h the vertical fluctuating velocity component w¢generally approaches zero.

With an oscillating grid, however, the simplification ofturbulence represented by a mean boundary shear doesnot work. Although there is shear produced by an oscil-lating grid, the temporal mean shear is zero, as shown inFigs. 3c, 4c, and 5c. We must therefore use more robust

Fig. 12. Spatial distribution ofTKE, 5.0 Hz, revised gridmounting, without false floor

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terms such as the total kinetic energy of the turbulence toquantify the turbulence.

4.3.1Total kinetic energyThe rms expressions in Eq. (4) can be combined usingEq. (2) into the form:

TKE=U2� ¼ 4:78 exp �2y=hð Þ ð5Þ

These expressions can allow estimation of the TKE nearthe bed and free surface in open channel flows.

Considering the case of normal flow in an open channel,the shear velocity is related to the flow depth and channelslope: U*=(ghSEGL)1/2, where SEGL is the slope of the energygrade line and g is the gravitational constant. Thus,

TKE ¼ 4:78 expð�2y=hÞðghSEGLÞ ð6ÞThe limiting cases are at the fixed bed (y/h fi 0) andfree surface (y/h fi 1). In these cases, the total

kinetic energy is simply a function of the depth of flow andslope:

TKEbed ¼ 4:78 ghSEGLð ÞTKEFS ¼ 0:65 ghSEGLð Þ ð7Þ

To simulate the turbulence levels close to the bedassociated with a natural flow, the operational parametersof the oscillating grid (stroke, frequency, etc.) can beadjusted to achieve the desired level of turbulence. Forthe case of open-channel flow turbulence close to thebed, this can be done by substituting Eq. (3) into (7),and solving for either the stroke length, frequency, ordistance from the grid to the bed:

S3f 2

z2¼ 4:78

aMghSEGLð Þ ð8Þ

To simulate other conditions (e.g., estuarine environ-ments), the same approach can be used, provided a suit-

Fig. 13. Suspended sediment concentrationvs. time

Fig. 14. Suspended sediment concentrationvs. TKE

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able expression for the TKE present in that system can befound.

4.3.2Reynolds stressThe Reynolds stress of an open-channel flow has beeninvestigated in a manner similar to the rms velocity fluc-tuations shown in Eq. (4). Nezu and Nakagawa (1993)express the mean Reynolds stress as

�uw=U2� ¼ 1� y=hð Þ � Vt

Vt y=hð Þ � 1jR�

hy

� �

þ pP sin p yh

� �

h i

ð9Þwhere j is the Von Karman constant, P is Cole’s wakeparameter, and R* is the Reynolds number based on shearvelocity and flow depth.

As mentioned previously, the convenience of using themean shear stress to characterize turbulence in an oscil-lating grid chamber is not possible. This is borne out bythe fact that the measurements of the Reynolds stress inthe present study do not show any consistent trends withdistance from the oscillating grid. The maximum absolutevalue of the individual profile measurements was less than2·10-4 m2/s2 for all test conditions investigated. Forcomparison, the mean Reynolds stress (calculated usingEq. 9) for an open channel flow such as the MississippiRiver near Minneapolis ranges from about 6·10-8 m2/s2 atthe water surface to about 4·10-3 m2/s2 at the river bed.Although the Reynolds stress is not an appropriate scalingparameter (versus the TKE of the turbulence), we can seethat the oscillating grid thus produces Reynolds stresslevels comparable with those nearer the bottom of a largeopen channel flow.

5ConclusionsThe primary objectives of the current work were to de-velop a laboratory-scale device for studying the release ofchemical compounds from sediment entrained in the wa-ter column; characterize the relationship between turbu-lence and sediment entrainment in the device; and todevelop similitude relationships between the turbulence inthe device and that found in a boundary layer flow. Theresulting equipment is a square plastic flux chamber withturbulence generated by a vertically oscillating grid.Measurements were made of turbulence generated by thisdevice and sediment entrainment for a variety of operatingconditions, and relationships were developed betweenturbulence in open-channel flows and the operationalparameters of the oscillating grid. This device can be usedto quantify mass transfer from contaminated sediments tothe water and vapor phases, and thus be used to help verifypredictive models of contaminant transport in real-worldapplications.

The turbulent flow field in the oscillating gridchamber described here is fairly uniform at sufficientdistances away from the grid, regardless of the methodused to attach the grid to the drive shaft. When a solidplate is used to attach the grid to the drive shaft, aregion of higher turbulence exists in the center of the

tank, coincident with the plate. This ‘‘bulls-eye’’ area ofelevated turbulence levels is not present when the grid isfastened to the drive shaft in a less obtrusive manner. Inaddition, the rms velocity fluctuations and total kineticenergy are described well by the Hopfinger–Toly rela-tionship (Eqs. 1 and 3) at distances greater than abouttwice the grid bar spacing (i.e., 12.5 cm for the gridused in this work). However, at locations closer to thegrid, there exist large gradients in the rms velocities andTKE.

This type of mixing chamber is capable ofsuspending cohesive sediments under a variety of con-ditions. Steady-state suspended sediment concentrationsare reached fairly quickly (10–30 min). The maximumTSS concentrations achieved ranged from 0.01 to 3.0 g/lfor the sediments tested. The amount of sediment en-trained was a function of the energy input to the systemfrom the oscillating grid and the sediment consolidationtime.

The oscillating grid mixing chamber can be used as ananalogue to open-channel flow systems by setting oper-ational parameters of the grid (stroke, frequency, etc.)such that the total kinetic energy of the turbulencematches that expected either at the bed or free surface foran open channel flow. In this manner, the chamber canserve as a simple, self-contained test bed for evaluatingthe flux of chemical from sediments to water and fromwater to the atmosphere. Since the chamber can be sealedoff from the laboratory atmosphere, chemical flux testsusing hazardous or toxic compounds can be performedin relative safety. Due to the predictable and reproduciblenature of the turbulence generated by the oscillating grid,replicate tests of sediment resuspension and chemicalfluxes can be readily accomplished.

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