Stilling basin design for inlet sluice with vertical dropstructure: Scale model results vs. literature formulae
J. Vercruysse & K. VerelstFlanders Hydraulics Research, Antwerp, Belgium
T. De MulderHydraulics Laboratory, Department of Civil Engineering, Ghent University, Ghent, Belgium
ABSTRACT: Within the framework of the Updated Sigmaplan, Flood control Areas (FCA) with a ControlledReduced Tide (CRT) are set up in several polders along the tidal section of the river Scheldt and its tributaries.The reduced tide is introduced by means of simple inlet and outlet sluices located in the levee between the riverand the polder. In recent designs, the inlet sluice is placed on top of the outlet sluice. At water intake, the waterdrops from the brink of an inlet sluice apron into a stilling basin, integrated with the floor slab of the underlyingoutlet sluice. Flanders Hydraulics Research performed a scale model based review of several desktop designs ofthis type of combined inlet and outlet structures. This paper compares the scale model results and predictions ofliterature formulae for drop structures and stilling basins, upon which the desktop designs were based. Severaltypes of sluice geometries – with a straight stilling basin, a locally deepened stilling basin and a stilling basinwith baffle blocks – were studied. This comparison exercise concludes that suitable formulae are available fora stilling basin design when the tailwater depth at the polder side equals the conjugate water depth. For highertailwater depths, no suitable literature formulae seem to be available and physical (or numerical) modelling isrecommended.
1 INTRODUCTION
In 1976 a major flooding event occurred in the ScheldtEstuary (Belgium). After this event the so calledSigmaplan was elaborated in 1977. One of the mea-sures of the Sigmaplan to mitigate flood risks was tobuild a set of Flood Control Areas (FCA’s). To this end,well-chosen polders along the tidal river Scheldt andits tributaries were selected. The FCA’s are filled, dur-ing storm tide, through overflow over a lowered leveeand emptied, during low tide, through an outlet sluice.In this way, the top levels of the storm surge are loweredby storing a volume of water in the FCA’s.
Due to industrialization and urbanization many ofthe estuarine habitats have disappeared or degradedover the course of time. These changing physical cir-cumstances, together with new insights resulted intoan update of the original Sigmaplan in 2005. Besidessafety against flooding, the Updated Sigmaplan aimsto contribute to the restoration of estuarine habitats.One measure is to create a semi-diurnal, ControlledReduced Tide (CRT), in some of the FCA’s. To thisend, an FCA is equipped with a well-designed inletsluice, positioned high in the levee between the riverand the polder, and an outlet sluice at a lower positionin the levee.
The first two designed FCA-CRT’s are Lippenbroekand Kruibeke-Bazel-Rupelmonde.The inlet and outlet
Figure 1. Principle drawing of a combined inlet and outletstructure.
sluices in these FCA-CRT’s were separated in two dif-ferent structures (De Mulder et al., 2013). For the newFCA-CRT’s, the inlet and outlet sluices are combinedin one structure (Vercruysse et al., 2013) of whicha principle drawing is given in Figure 1. Note thatthe inlet sluice is put on top of the outlet sluice. Atwater intake, water from the river flows into the inletsluice and is subsequently subjected to a vertical dropat the brink of the inlet sluice’s floor slab. To dissi-pate the energy of the incoming water, a stilling basinis provided, integrated in the floor slab of the outletsluice. Downstream of the concrete section, a bottomprotection with gabions is foreseen.
Combining the in- and outlet sluice into one struc-ture has economic and ecological benefits (De Mulderet al., 2013).
The required sill levels and (total) cross-sectionalareas of the combined inlet and outlet structures have
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Figure 2. Test section of scale model. Arrow indicates theflow direction at water intake.
been determined at Flanders Hydraulics Research bymeans of a numerical model study.The goal is to obtaina suitable reduced tide, i.e. aiming at a distinct springtide/neap tide cycle, in the FCA-CRT. The detailedstructural design of the FCA-CRT’s, and the combinedinlet and outlet structure, was outsourced by the Water-way Administration to distinct consulting engineeringfirms. They made a desktop design based on literatureformulae. Flanders Hydraulics Research performed ascale model based review of several desktop designsof this type of combined inlet and outlet structures.
An overview of the scale model and the testedgeometries are presented in section 2. To facilitate thecomparison between scale model results and litera-ture formula the results of the scale model tests arepresented dimensionless, based upon the length andvelocity scales described in section 3. The followingsections present a comparison between literature for-mulae and scale model results for the conjugate waterdepth (section 4), the drop length (section 5) and theend of the hydraulic jump (section 6). Most litera-ture formulae are valid for a tailwater depth equal tothe conjugate water depth. Section 7 discusses someexamples of flow patterns and velocities for highertailwater depths then the conjugate water depth. Aconclusion is formulated in section 8.
2 SCALE MODEL TESTS
2.1 Model scale
The hydraulic review was carried out by means of scalemodel experiments, adopting a so-called 2DV model-ing approach. The flow pattern was only studied in thevertical symmetry plane of one combined inlet andoutlet structure.
The scale model of the combined inlet and outletstructure (geometrical scale 1:8 using Froude scaling),was built into a section of the current flume with alength of 15.0 m, a width of 0.56 m and a height of1.0 m. Figure 2 shows the scale model’s test section. Byusing exchangeable plates fixed on movable mechan-ical lifts, it was possible to test the different structuresand easily adopt geometrical changes. Aeration of thefalling nappe is provided by a tube mounted under theceiling of the outlet culvert.
The following measurements were carried out:
• water level upstream and downstream with 2 elec-tronic water level gauges (BTL5-E17, from Balluff,accuracy 1 mm).
• discharge by electromagnetic discharge meters onthe supply conduits (Aquaflux K from Khrone,accuracy better than 1% of measured discharge),
• near bottom velocity with 2 electromagnetic pointvelocimeters (EMS from Deltares, accuracy 1% ofthe measured velocity).
Besides these measurements, also visual registra-tions were carried out of:
• the drop length,• the end of the hydraulic jump,• the water level in the outlet culvert.
2.2 Tested geometries
In the timeframe of the research, January 2012 tillDecember 2013, the combined inlet and outlet struc-tures of following FCA-CRT’s were tested:
• Bergenmeersen (BGM),• Dijlemonding (DLM),• Vlassenbroek (VLB),• De Bunt (BNT).
These combined inlet and outlet structures differin the drop height and in design choices made by therespective consulting firms.
First the initial desktop designed geometry wastested in the scale model. Based on the test results,alternative geometries were defined in agreement withthe Waterway Administration and tested.
Due to the long roof above the stilling basin of DLMthe scale model tests for this structure were mainlyfocused on the flow pattern downstream of the struc-ture rather than on the flow pattern in the stilling basin.For this reason, the results of DLM are not compara-ble with the results of the other tested geometries Thelocally deepened stilling basin for BNT is identical toa tested geometry for VLB, although the roofs of thesegeometries differ. Due to the identical stilling basinonly a limited number of experiments were carried outfor BNT. Consequently this paper only presents resultsof BGM and VLB.
The tested geometries of BGM and VLB are namedwith the abovementioned abbreviation of the FCA-CRT (BGM, VLB), followed by “G” and a follow-upnumber starting with 1, being the desktop designedgeometry. For the analysis in this paper the testedgeometries are divided into 3 categories:
• Geometries with a straight stilling basin, seeFigure 3.
• Geometries with a locally deepened stilling basinwith end sill, see Figure 4.
• Geometries with a straight or locally deepenedstilling basin with baffle blocks, see Figure 5.
Note that the dimensions in these figures areexpressed relative to the drop height �z, defined asthe vertical distance between the upper face of theinlet sluice apron and the upper face of the stillingbasin apron.
For BGM, only geometries with a straight stillingbasin (without end sill) and a straight stilling basin with
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Figure 3. Tested geometries with a straight stilling basin.Arrow indicates the flow direction at water intake.
Figure 4. Tested geometries with a locally deepened stillingbasin and end sill. Arrow indicates the flow direction at waterintake.
Figure 5. Tested geometries with baffle blocks. Arrowindicates the flow direction at water intake.
baffle blocks were tested. To investigate the influenceof the outlet sluice for BGM also a geometry with avertical wall below the brink of the inlet culvert apron,was tested (BGM G3). For VLB geometries belongingto the 3 categories were tested.
The baffle blocks were designed according to thedesign rules for a USBR type III stilling basin (Peterka,1984; Thompson & Kilgore, 2006). Note that thisimplies an application of the design rules outside theirvalidity range (which corresponds to a stilling basin atthe toe of a downward sloping chute, contrary to thevertical drop pertaining to the present structures). Forthe design of the baffle blocks, the start of the basin isdefined as the drop length determined by the formulafrom Chanson (section 5, eq. 6).
Figure 6. Schematic illustration hydraulic jump.
The structures of BGM and VLB are relatively lim-ited in length; the (concrete) stilling basin apron endsbetween 4.00 �z and 5.61 �z downstream of the drop(not indicated in Figures 3, 4 and 5).
3 DIMENSIONLESS PRESENTATIONOF RESULTS
At water intake, water from the river flows into theinlet sluice and is subjected to a vertical drop at thebrink of the inlet sluice’s floor slab. Consequently ahydraulic jump is formed. This is schematically pre-sented in Figure 6, also indicating the symbols that areused in this paper.
To facilitate the comparison of the tested geome-tries, the results in this paper will be presented indimensionless form. Therefore the drop height �z isused as length scale for the lengths and levels. Thecritical water depth, scaled with the drop height �z,is used to quantify the discharge per unit width. Thecritical water depth is namely only a function of thedischarge per unit width q [m3/(ms)]:
where dc = critical water depth [m], �z = dropheight [m], q = discharge per unit width [m3/(ms)],g = gravity acceleration [m/s2].
For the dimensionless presentation of the velocity,the theoretical maximum velocity in the stilling basinV1 will be applied as velocity scale, which is definedas the ratio of the discharge per unit width q and thewater depth before the hydraulic jumpY1 (V1 = q/Y1).The latter quantity will be computed with the formulafrom Rand (1955):
whereY1 = water depth before jump [m], dc = criticalwater depth = (q2/g)1/3 [m], �z = drop height [m];q = discharge per unit width [m3/(ms)], g = gravityacceleration [m/s2].
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Figure 7. Variation of conjugate water depth in function ofcritical water depth. Geometries with a straight stilling basin.
4 CONJUGATE WATER DEPTH
To transform the supercritical flow after the drop tosubcritical flow, a minimal tailwater depth, the conju-gate water depth, is necessary. This section comparesthe measured (in the scale model) and the computed(with literature formulae) conjugate water depth.
4.1 Formulae
For calculating the conjugate water depth downstreamof a vertical drop,Y2, formulae from Rand (1955) andChanson (2002) are available.Formula Rand (1955):
Formula Chanson (2002):
where Y2 = conjugate water depth [m], dc = criticalwater depth = (q2/g)1/3 [m], �z = drop height [m],q = discharge per unit width [m3/(ms)], g = gravityacceleration [m/s2].
4.2 Results
4.2.1 Straight stilling basinThe measured conjugate water depths for the geome-tries with a straight stilling basin (Figure 3) arepresented in Figure 7 as a function of the critical waterdepth.
Note in Figure 7 that there is no noticeable dif-ference between an aerated and a non-aerated fallingnappe and between an outlet sluice (BGM G1 andVLBG2) and a vertical wall (BGM G3). In Figure 8 the fore-going results are compared with the conjugate waterdepths according to equations (3) and (4).
Figure 8. Comparison of conjugate water depth formulaewith measurements. Geometries with a straight stilling basin.
Table 1. Comparing trend line coefficients with formulaRand and Chanson.
Rand Chanson Experiments(1955) (2002)
factor 1.66 1.565 1.835exponent 0.81 0.809 0.930
Figure 9. Conjugate water depth in function of critical waterdepth. Geometries with a locally deepened stilling basin.
Figure 8 also contains a trend line of the measure-ments. This trend line is of the same power law type asequations (3) and (4). The computed parameters (fac-tor and exponent) are presented in Table 1. Note inFigure 8 and Table 1 that the experimental trend lineis somewhat steeper than the curves corresponding tothe Rand and Chanson formulae.
4.2.2 Locally deepened stilling basinFor the geometries with a locally deepened stillingbasin, Figure 9 presents the variation of the conjugatewater depths as a function of the critical water depth.Note that the conjugate water depth is referenced tothe bottom of the locally deepened stilling basin. ForVLB G5, a suitable hydraulic jump was formed inde-pendent of the tailwater depth for all tested criticalwater depths. Therefore, no results for VLB G5 arepresented in Figure 9.
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Figure 10. Conjugate water depth in function of criticalwater depth. Geometries with baffle blocks.
For VLB G4 and G6, a rather good agreement isfound between the measurements and the formulaefrom Rand and Chanson. For VLB G3, however, theconjugate water depth is underestimated for highercritical water depths. During the tests it was noticedthat for VLB G3 the falling nappe reached the aprondownstream of the locally deepened stilling basin athigher critical water depths.
4.2.3 Baffle blocksThe measured conjugate water depths for the experi-ments with baffle blocks (Figure 5) are presented inFigure 10. Only results for BGM G8 and G9 are pre-sented. For VLB G7, a suitable hydraulic jump wasformed independent of the tailwater depth for all testedcritical water depths. The baffle blocks for BGM weredesigned for a critical water depth of dc/�z = 0.62.Thompson & Kilgore (2006) mentioned, although notrecommended, that the conjugate water depth can bereduced with a factor 0.85 when using a USBR typeIII stilling basin. For this reason, the conjugate waterdepths computed according to formulae (3) and (4) andreduced with a factor 0.85, are presented in Figure 9.
Figure 10 shows that the baffle blocks only reducethe conjugate water depth with a factor 0.85 for thedesign critical water depth (dc/�z = 0.62). For higher(respectively lower) critical water depths the computedconjugate water depth underestimates (respectivelyoverestimates) the measured value.
Figure 10 shows also that the measurements do notfollow the same power type law as both the literatureformulae.
5 DROP LENGTH
This section presents a comparison between the mea-sured and the computed drop length.
5.1 Formulae
For calculating the drop length downstream of a ver-tical drop, formulae from Rand (1955) and Chanson(2002) are available.
Figure 11. Visually determination of the drop length.
Figure 12. Variation of drop length in function of criticalwater depth.
Formula Rand (1955):
Formula Chanson (2002):
where LD = drop length [m], dc = critical waterdepth = (q2/g)1/3 [m], �z = drop height [m], q = dis-charge per unit width [m3/(ms)], g = gravity accelera-tion [m/s2].
Note that the formulae above are representative foran aerated nappe. When the nappe is not aerated thedrop length is smaller.
5.2 Results
In the scale model the drop length was visually deter-mined for a flow pattern with downstream supercriticalflow, as illustrated in Figure 11.
The measured and computed drop lengths for BGMG1, VLB G2 and VLB G6 are compared in Figure 12.The drop length was not determined for VLB G3 andG4 (respectively VLB G5) because the drop height ofthese geometries are equal to VLB G2 (respectivelyVLB G6).
The drop length computed with the formula fromChanson is a good estimation of the measured drop
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length for VLB G2 aerated, VLB G6 aerated and (forcritical water depths exceeding dc/�z = 0.48) BGMG1 aerated. The drop length tends to reduce when thenappe is not aerated.
6 END OF HYDRAULIC JUMP
During the experiments, the end of the hydraulic jumpwas visually registrated as the location where no moreturbulent bursts were visible at the free surface. Thedistance between this location and the vertical drop isthen compared with predictions (from literature for-mulae) of the cumulative value of the drop length andthe length of the subsequent hydraulic jump.
6.1 Formulae
The drop length, LD, is computed according to theformula from Chanson (eq. 6), see section 5.
The length of the hydraulic jump, Lj, is computedusing the following formulae:Rand (1955):
The end of the hydraulic jump, i.e. the cumulativelength of the drop and the hydraulic jump, LD + Lj,is presented as a function of the critical water depth inFigures 13 and 14 for the geometries with a straightstilling basin (Figure 3) and for those with a locallydeepened stilling basin (Figure 4), respectively.
For a geometry with baffle blocks no results will bepresented in this section, due to the increased uncer-tainty of the visually determined end of the hydraulicjump.
Taking into account the visual registration of the endof the hydraulic jump, there is a rather good agreementbetween the measured cumulative length and the rangeof cumulative lengths computed with formulae of Sil-vester and Rand. For some combinations of geometry
Figure 13. Cumulative length of drop and hydraulic jumpin function of critical water depth. Geometries with a straightstilling basin.
Figure 14. Variation of cumulative length of drop andhydraulic jump in function of critical water depth. Geometrieswith a locally deepened stilling basin.
and critical water depths, there is a significant increasein the cumulative length when the nappe is aerated,whereas for other combinations, there is no noticeableeffect.
For VLB G3, G4 and G6, a rather good agreementis found between the measured cumulative length andthe range of cumulative lengths computed with for-mulae of Silvester and Rand. For VLB G5 a hydraulicjump is formed in the stilling basin, independent of thetailwater depth. As a consequence, the measurementsof the end of the hydraulic jump pertain to a lowertailwater depth, in comparison to the conjugate waterdepth for the other geometries.
7 HIGHER TAILWATER DEPTHS
The formulae and results discussed in sections 4,5 and 6 are valid for a tailwater depth correspond-ing to the conjugate water depth. In this section,results belonging to higher tailwater depths will beconsidered.
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Figure 15. Variation of near bottom velocity in functionof tailwater depth – Geometry BGM G1, aerated, withdc/�z = 0.645 – for 3 distances x/�z downstream of the drop.
7.1 Formulae
Stilling basin design formulae in literature are basedon a design discharge. The conjugate water depthis then computed based on this discharge value andthe structure geometry. When following this designstrategy, a stilling basin is designed with downstream(polder) water depths more or less equal to the conju-gate water depth. For higher tailwater depths than theconjugate water depth, no suitable literature formu-lae were found by the authors. However, the combinedinlet and outlet structures for the FCA-CRT’s will haveto deal with a broad combination of upstream (river)and downstream (polder) water levels. Consequently,the formulae discussed in sections 4, 5 and 6 are notwell suited and no comparison with literature formulaewill be made in this section.
7.2 Results
For each of the three types of stilling basin geometries(a straight stilling basin, a locally deepened stillingbasin and a stilling basin using baffle blocks), as anexample, only a selection of scale model results willbe presented. This selection will be limited to the vari-ation of the near bottom velocity and the variation ofthe flow pattern in function of the tail water depth.
7.2.1 Straight stilling basinFor BGM G1, the variation of the near bottom veloc-ities at three distances downstream of the drop arepresented in Figure 15 as a function of the tailwaterdepth.
Figure 15 shows a rapid transition between super-critical and subcritical flow speeds in the rangeHTWL/�z = 1.10 to 1.15. After this sudden drop, thenear bottom velocity recovers somewhat. However,for tailwater depths exceeding 1.4, the near bottomvelocity gradually decreases.
7.2.2 Locally deepened stilling basinFigure 16 presents an example of the influence of theroof on the flow pattern for a geometry with a locallydeepened stilling basin.
Figure 16. Influence of roof on flow pattern (GeometryVLB G5 with dc/�z = 0.373).
From Figure 16 follows that the falling nappe tra-jectory overtops the end sill for a tailwater depthHTWL/�z = 1.14. At this condition, the variation ofthe near bottom velocity in function of the tailwa-ter depth shows an increasing velocity, as shown inFigure 17. These increased near bottom velocities arepresent in a rather narrow range of tailwater depths,from HTWL/�z = 1.11 to HTWL/�z = 1.16. Beyonda tailwater depth HTWL/�z = 1.16, the falling nappemakes contact with the roof of the combined inletand outlet structure. The near bottom velocity thendecreases again and resumes similar values as prior tothe increase.
7.2.3 Baffle blocksFigure 18 presents an example of the variation of theflow pattern in presence of baffle blocks for 3 tailwaterdepths.
From Figure 18 follows that an increase of the tail-water depth results in a decrease of the angle of thenappe (with the horizontal). Consequently, at a certaintailwater depth the location where the falling nappetouches the bottom is situated downstream of the loca-tion of the baffle blocks. The further increasing ofthe tailwater depth results into a contact of the fallingnappe with the roof of the culvert and a redirectionof the flow towards the bottom of the stilling basin,(Figure 18 bottom panel). This effect is also visible inthe variation of the near bottom velocity in functionof the tailwater depth, which is shown in Figure 19.
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Figure 17. Variation of the near bottom velocity in func-tion of tailwater depth (Geometry VLB G5, non-aerated, withdc/�z = 0.373) for x/�z = 3.3 and x/�z = 5.3 downstreamof the drop.
Figure 18. Influence of baffle blocks on flow pattern(Geometry BGM G8 with dc/�z = 0.645).
The near bottom velocity first increases with anincreasing tailwater depth and then decreases whenthe falling nappe makes contact with the roof.
8 CONCLUSIONS
In the framework of the design of Flood control Areas(FCA) with a Controlled Reduced Tide (CRT) for theUpdated Sigmaplan, Flanders Hydraulics Researchperformed a scale model based review of differentdesktop designs of combined inlet and outlet struc-tures. This paper compares scale model measurementsand the predictions of literature formulae for dropstructures and stilling basins. Three types of geome-tries are discussed: a straight stilling basin, a locallydeepened stilling basin and a stilling basin with baffleblocks.
Figure 19. Near bottom velocity in function of tailwaterdepth (Geometry BGM G8 with dc/�z = 0.645) for differentdistances x/�z downstream of the drop.
For a straight stilling basin and a tailwater depthequal to the conjugate water depth, the comparisonwith literature formula shows that the conjugate waterdepth, the drop length and the hydraulic jump lengthcan be predicted rather well using the available liter-ature formulae. These formulae are also valid for awell-designed locally deepened stilling basin with anend sill of a limited height. For a stilling basin withbaffle blocks designed according the design rules fora USBR type III stilling basin, the conjugate waterdepth can be reduced with a factor 0.85.
The combined inlet and outlet structures for theFCA-CRT’s will have to deal with a broad combi-nation of upstream and downstream water levels. Forhigher tailwater depths than the conjugate water depth,no suitable literature formulae were found by theauthors and physical (or numerical) modelling is rec-ommended for designing the combined inlet and outletstructure.
The increase of the tailwater depth results into adecrease of the angle of the falling nappe and a flowpattern varying from a free hydraulic jump, over adrowned hydraulic jump, a free surface jet, to cul-vert flow. Especially for the geometry with a locallydeepened stilling basin or baffle blocks, care should betaken that the falling nappe touches the bottom withinthe locally deepened stilling basin or upstream of thebaffle blocks, in case of higher tailwater depths. Other-wise, these situations could lead to an increase in nearbottom velocity downstream of the construction anddegradation of the downstream bottom protection.
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