Stilling basin design for inlet sluice with vertical drop structure: Scale model results vs. literature formulae

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1 Sustainable Hydraulics in the Era of Global Change Erpicum et al. (Eds.) 2016 Taylor & Francis Group, London, ISBN Stilling basin design for inlet sluice with vertical drop structure: Scale model results vs. literature formulae J. Vercruysse & K. Verelst Flanders Hydraulics Research, Antwerp, Belgium T. De Mulder Hydraulics Laboratory, Department of Civil Engineering, Ghent University, Ghent, Belgium ABSTRACT: Within the framework of the Updated Sigmaplan, Flood control Areas (FCA) with a Controlled Reduced 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 river and the polder. In recent designs, the inlet sluice is placed on top of the outlet sluice. At water intake, the water drops from the brink of an inlet sluice apron into a stilling basin, integrated with the floor slab of the underlying outlet sluice. Flanders Hydraulics Research performed a scale model based review of several desktop designs of this type of combined inlet and outlet structures. This paper compares the scale model results and predictions of literature formulae for drop structures and stilling basins, upon which the desktop designs were based. Several types of sluice geometries with a straight stilling basin, a locally deepened stilling basin and a stilling basin with baffle blocks were studied. This comparison exercise concludes that suitable formulae are available for a stilling basin design when the tailwater depth at the polder side equals the conjugate water depth. For higher tailwater depths, no suitable literature formulae seem to be available and physical (or numerical) modelling is recommended. 1 INTRODUCTION In 1976 a major flooding event occurred in the Scheldt Estuary (Belgium). After this event the so called Sigmaplan was elaborated in One of the measures of the Sigmaplan to mitigate flood risks was to build a set of Flood Control Areas (FCA s). To this end, well-chosen polders along the tidal river Scheldt and its tributaries were selected. The FCA s are filled, during storm tide, through overflow over a lowered levee and emptied, during low tide, through an outlet sluice. In this way, the top levels of the storm surge are lowered by storing a volume of water in the FCA s. Due to industrialization and urbanization many of the estuarine habitats have disappeared or degraded over the course of time. These changing physical circumstances, together with new insights resulted into an update of the original Sigmaplan in Besides safety against flooding, the Updated Sigmaplan aims to contribute to the restoration of estuarine habitats. One measure is to create a semi-diurnal, Controlled Reduced Tide (CRT), in some of the FCA s. To this end, an FCA is equipped with a well-designed inlet sluice, positioned high in the levee between the river and the polder, and an outlet sluice at a lower position in the levee. The first two designed FCA-CRT s are Lippenbroek and Kruibeke-Bazel-Rupelmonde. The inlet and outlet Figure 1. Principle drawing of a combined inlet and outlet structure. sluices in these FCA-CRT s were separated in two different structures (De Mulder et al., 2013). For the new FCA-CRT s, the inlet and outlet sluices are combined in one structure (Vercruysse et al., 2013) of which a principle drawing is given in Figure 1. Note that the inlet sluice is put on top of the outlet sluice. At water intake, water from the river flows into the inlet sluice and is subsequently subjected to a vertical drop at the brink of the inlet sluice s floor slab. To dissipate the energy of the incoming water, a stilling basin is provided, integrated in the floor slab of the outlet sluice. Downstream of the concrete section, a bottom protection with gabions is foreseen. Combining the in- and outlet sluice into one structure has economic and ecological benefits (De Mulder et al., 2013). The required sill levels and (total) cross-sectional areas of the combined inlet and outlet structures have 579

2 Figure 2. Test section of scale model. Arrow indicates the flow direction at water intake. been determined at Flanders Hydraulics Research by means of a numerical model study.the goal is to obtain a suitable reduced tide, i.e. aiming at a distinct spring tide/neap tide cycle, in the FCA-CRT. The detailed structural design of the FCA-CRT s, and the combined inlet and outlet structure, was outsourced by the Waterway Administration to distinct consulting engineering firms. They made a desktop design based on literature formulae. Flanders Hydraulics Research performed a scale model based review of several desktop designs of this type of combined inlet and outlet structures. An overview of the scale model and the tested geometries are presented in section 2. To facilitate the comparison between scale model results and literature formula the results of the scale model tests are presented dimensionless, based upon the length and velocity scales described in section 3. The following sections present a comparison between literature formulae and scale model results for the conjugate water depth (section 4), the drop length (section 5) and the end of the hydraulic jump (section 6). Most literature formulae are valid for a tailwater depth equal to the conjugate water depth. Section 7 discusses some examples of flow patterns and velocities for higher tailwater depths then the conjugate water depth. A conclusion is formulated in section 8. 2 SCALE MODEL TESTS 2.1 Model scale The hydraulic review was carried out by means of scale model experiments, adopting a so-called 2DV modeling approach. The flow pattern was only studied in the vertical symmetry plane of one combined inlet and outlet structure. The scale model of the combined inlet and outlet structure (geometrical scale 1:8 using Froude scaling), was built into a section of the current flume with a length of 15.0 m, a width of 0.56 m and a height of 1.0 m. Figure 2 shows the scale model s test section. By using exchangeable plates fixed on movable mechanical lifts, it was possible to test the different structures and easily adopt geometrical changes. Aeration of the falling nappe is provided by a tube mounted under the ceiling of the outlet culvert. The following measurements were carried out: water level upstream and downstream with 2 electronic water level gauges (BTL5-E17, from Balluff, accuracy 1 mm). discharge by electromagnetic discharge meters on the supply conduits (Aquaflux K from Khrone, accuracy better than 1% of measured discharge), near bottom velocity with 2 electromagnetic point velocimeters (EMS from Deltares, accuracy 1% of the measured velocity). Besides these measurements, also visual registrations 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 till December 2013, the combined inlet and outlet structures of following FCA-CRT s were tested: Bergenmeersen (BGM), Dijlemonding (DLM), Vlassenbroek (VLB), De Bunt (BNT). These combined inlet and outlet structures differ in the drop height and in design choices made by the respective consulting firms. First the initial desktop designed geometry was tested in the scale model. Based on the test results, alternative geometries were defined in agreement with the Waterway Administration and tested. Due to the long roof above the stilling basin of DLM the scale model tests for this structure were mainly focused on the flow pattern downstream of the structure rather than on the flow pattern in the stilling basin. For this reason, the results of DLM are not comparable with the results of the other tested geometries The locally deepened stilling basin for BNT is identical to a tested geometry for VLB, although the roofs of these geometries differ. Due to the identical stilling basin only a limited number of experiments were carried out for BNT. Consequently this paper only presents results of BGM and VLB. The tested geometries of BGM and VLB are named with the abovementioned abbreviation of the FCA- CRT (BGM, VLB), followed by G and a follow-up number starting with 1, being the desktop designed geometry. For the analysis in this paper the tested geometries are divided into 3 categories: Geometries with a straight stilling basin, see Figure 3. Geometries with a locally deepened stilling basin with end sill, see Figure 4. Geometries with a straight or locally deepened stilling basin with baffle blocks, see Figure 5. Note that the dimensions in these figures are expressed relative to the drop height z, defined as the vertical distance between the upper face of the inlet sluice apron and the upper face of the stilling basin apron. For BGM, only geometries with a straight stilling basin (without end sill) and a straight stilling basin with 580

3 Figure 3. Tested geometries with a straight stilling basin. Arrow indicates the flow direction at water intake. Figure 6. Schematic illustration hydraulic jump. The structures of BGM and VLB are relatively limited in length; the (concrete) stilling basin apron ends between 4.00 z and 5.61 z downstream of the drop (not indicated in Figures 3, 4 and 5). 3 DIMENSIONLESS PRESENTATION OF RESULTS Figure 4. Tested geometries with a locally deepened stilling basin and end sill. Arrow indicates the flow direction at water intake. At water intake, water from the river flows into the inlet sluice and is subjected to a vertical drop at the brink of the inlet sluice s floor slab. Consequently a hydraulic jump is formed. This is schematically presented in Figure 6, also indicating the symbols that are used in this paper. To facilitate the comparison of the tested geometries, the results in this paper will be presented in dimensionless form. Therefore the drop height z is used as length scale for the lengths and levels. The critical water depth, scaled with the drop height z, is used to quantify the discharge per unit width. The critical water depth is namely only a function of the discharge per unit width q [m 3 /(ms)]: Figure 5. Tested geometries with baffle blocks. Arrow indicates the flow direction at water intake. baffle blocks were tested. To investigate the influence of the outlet sluice for BGM also a geometry with a vertical wall below the brink of the inlet culvert apron, was tested (BGM G3). For VLB geometries belonging to the 3 categories were tested. The baffle blocks were designed according to the design rules for a USBR type III stilling basin (Peterka, 1984; Thompson & Kilgore, 2006). Note that this implies an application of the design rules outside their validity range (which corresponds to a stilling basin at the toe of a downward sloping chute, contrary to the vertical drop pertaining to the present structures). For the design of the baffle blocks, the start of the basin is defined as the drop length determined by the formula from Chanson (section 5, eq. 6). where d c = critical water depth [m], z = drop height [m], q = discharge per unit width [m 3 /(ms)], g = gravity acceleration [m/s 2 ]. For the dimensionless presentation of the velocity, the theoretical maximum velocity in the stilling basin V 1 will be applied as velocity scale, which is defined as the ratio of the discharge per unit width q and the water depth before the hydraulic jumpy 1 (V 1 = q/y 1 ). The latter quantity will be computed with the formula from Rand (1955): wherey 1 = water depth before jump [m], d c = critical water depth = (q 2 /g) 1/3 [m], z = drop height [m]; q = discharge per unit width [m 3 /(ms)], g = gravity acceleration [m/s 2 ]. 581

4 Figure 7. Variation of conjugate water depth in function of critical water depth. Geometries with a straight stilling basin. 4 CONJUGATE WATER DEPTH To transform the supercritical flow after the drop to subcritical flow, a minimal tailwater depth, the conjugate water depth, is necessary. This section compares the measured (in the scale model) and the computed (with literature formulae) conjugate water depth. Figure 8. Comparison of conjugate water depth formulae with measurements. Geometries with a straight stilling basin. Table 1. Comparing trend line coefficients with formula Rand and Chanson. Rand Chanson Experiments (1955) (2002) factor exponent Formulae For calculating the conjugate water depth downstream of a vertical drop,y 2, formulae from Rand (1955) and Chanson (2002) are available. Formula Rand (1955): Formula Chanson (2002): Figure 9. Conjugate water depth in function of critical water depth. Geometries with a locally deepened stilling basin. where Y 2 = conjugate water depth [m], d c = critical water depth = (q 2 /g) 1/3 [m], z = drop height [m], q = discharge per unit width [m 3 /(ms)], g = gravity acceleration [m/s 2 ]. 4.2 Results Straight stilling basin The measured conjugate water depths for the geometries with a straight stilling basin (Figure 3) are presented in Figure 7 as a function of the critical water depth. Note in Figure 7 that there is no noticeable difference between an aerated and a non-aerated falling nappe and between an outlet sluice (BGM G1 andvlb G2) and a vertical wall (BGM G3). In Figure 8 the foregoing results are compared with the conjugate water depths according to equations (3) and (4). Figure 8 also contains a trend line of the measurements. This trend line is of the same power law type as equations (3) and (4). The computed parameters (factor and exponent) are presented in Table 1. Note in Figure 8 and Table 1 that the experimental trend line is somewhat steeper than the curves corresponding to the Rand and Chanson formulae Locally deepened stilling basin For the geometries with a locally deepened stilling basin, Figure 9 presents the variation of the conjugate water depths as a function of the critical water depth. Note that the conjugate water depth is referenced to the bottom of the locally deepened stilling basin. For VLB G5, a suitable hydraulic jump was formed independent of the tailwater depth for all tested critical water depths. Therefore, no results for VLB G5 are presented in Figure

5 Figure 11. Visually determination of the drop length. Figure 10. Conjugate water depth in function of critical water depth. Geometries with baffle blocks. For VLB G4 and G6, a rather good agreement is found between the measurements and the formulae from Rand and Chanson. For VLB G3, however, the conjugate water depth is underestimated for higher critical water depths. During the tests it was noticed that for VLB G3 the falling nappe reached the apron downstream of the locally deepened stilling basin at higher critical water depths Baffle blocks The measured conjugate water depths for the experiments with baffle blocks (Figure 5) are presented in Figure 10. Only results for BGM G8 and G9 are presented. For VLB G7, a suitable hydraulic jump was formed independent of the tailwater depth for all tested critical water depths. The baffle blocks for BGM were designed for a critical water depth of d c / z = Thompson & Kilgore (2006) mentioned, although not recommended, that the conjugate water depth can be reduced with a factor 0.85 when using a USBR type III stilling basin. For this reason, the conjugate water depths computed according to formulae (3) and (4) and reduced with a factor 0.85, are presented in Figure 9. Figure 10 shows that the baffle blocks only reduce the conjugate water depth with a factor 0.85 for the design critical water depth (d c / z = 0.62). For higher (respectively lower) critical water depths the computed conjugate water depth underestimates (respectively overestimates) the measured value. Figure 10 shows also that the measurements do not follow the same power type law as both the literature formulae. 5 DROP LENGTH This section presents a comparison between the measured and the computed drop length. 5.1 Formulae For calculating the drop length downstream of a vertical drop, formulae from Rand (1955) and Chanson (2002) are available. Figure 12. Variation of drop length in function of critical water depth. Formula Rand (1955): Formula Chanson (2002): where L D = drop length [m], d c = critical water depth = (q 2 /g) 1/3 [m], z = drop height [m], q = discharge per unit width [m 3 /(ms)], g = gravity acceleration [m/s 2 ]. Note that the formulae above are representative for an aerated nappe. When the nappe is not aerated the drop length is smaller. 5.2 Results In the scale model the drop length was visually determined for a flow pattern with downstream supercritical flow, as illustrated in Figure 11. The measured and computed drop lengths for BGM G1, VLB G2 and VLB G6 are compared in Figure 12. The drop length was not determined for VLB G3 and G4 (respectively VLB G5) because the drop height of these geometries are equal to VLB G2 (respectively VLB G6). The drop length computed with the formula from Chanson is a good estimation of the measured drop 583

6 length for VLB G2 aerated, VLB G6 aerated and (for critical water depths exceeding d c / z = 0.48) BGM G1 aerated. The drop length tends to reduce when the nappe is not aerated. 6 END OF HYDRAULIC JUMP During the experiments, the end of the hydraulic jump was visually registrated as the location where no more turbulent bursts were visible at the free surface. The distance between this location and the vertical drop is then compared with predictions (from literature formulae) of the cumulative value of the drop length and the length of the subsequent hydraulic jump. 6.1 Formulae The drop length, L D, is computed according to the formula from Chanson (eq. 6), see section 5. The length of the hydraulic jump, L j, is computed using the following formulae: Rand (1955): Figure 13. Cumulative length of drop and hydraulic jump in function of critical water depth. Geometries with a straight stilling basin. Silvester (1964): Hager et al. (1990): Figure 14. Variation of cumulative length of drop and hydraulic jump in function of critical water depth. Geometries with a locally deepened stilling basin. where L j = length of hydraulic jump [m], Y 2 = conjugate water depth (eq. 3) [m], Y 1 = water depth before jump (eq. 2), Fr 1 = Froude number before jump = (q/y 1 )/(g Y 1 ) 1/2 [ ], q = discharge per unit width [m 3 /(ms)], α j = coefficient (=22, when 4 Fr 1 12). 6.2 Results The end of the hydraulic jump, i.e. the cumulative length of the drop and the hydraulic jump, L D + L j, is presented as a function of the critical water depth in Figures 13 and 14 for the geometries with a straight stilling basin (Figure 3) and for those with a locally deepened stilling basin (Figure 4), respectively. For a geometry with baffle blocks no results will be presented in this section, due to the increased uncertainty of the visually determined end of the hydraulic jump. Taking into account the visual registration of the end of the hydraulic jump, there is a rather good agreement between the measured cumulative length and the range of cumulative lengths computed with formulae of Silvester and Rand. For some combinations of geometry and critical water depths, there is a significant increase in the cumulative length when the nappe is aerated, whereas for other combinations, there is no noticeable effect. For VLB G3, G4 and G6, a rather good agreement is found between the measured cumulative length and the range of cumulative lengths computed with formulae of Silvester and Rand. For VLB G5 a hydraulic jump is formed in the stilling basin, independent of the tailwater depth. As a consequence, the measurements of the end of the hydraulic jump pertain to a lower tailwater depth, in comparison to the conjugate water depth 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 corresponding to the conjugate water depth. In this section, results belonging to higher tailwater depths will be considered. 584

7 Figure 15. Variation of near bottom velocity in function of tailwater depth Geometry BGM G1, aerated, with d c / z = for 3 distances x/ z downstream of the drop. 7.1 Formulae Stilling basin design formulae in literature are based on a design discharge. The conjugate water depth is then computed based on this discharge value and the structure geometry. When following this design strategy, a stilling basin is designed with downstream (polder) water depths more or less equal to the conjugate water depth. For higher tailwater depths than the conjugate water depth, no suitable literature formulae were found by the authors. However, the combined inlet and outlet structures for the FCA-CRT s will have to deal with a broad combination of upstream (river) and downstream (polder) water levels. Consequently, the formulae discussed in sections 4, 5 and 6 are not well suited and no comparison with literature formulae will 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 stilling basin and a stilling basin using baffle blocks), as an example, only a selection of scale model results will be presented. This selection will be limited to the variation of the near bottom velocity and the variation of the flow pattern in function of the tail water depth Straight stilling basin For BGM G1, the variation of the near bottom velocities at three distances downstream of the drop are presented in Figure 15 as a function of the tailwater depth. Figure 15 shows a rapid transition between supercritical and subcritical flow speeds in the range H TWL / z = 1.10 to After this sudden drop, the near bottom velocity recovers somewhat. However, for tailwater depths exceeding 1.4, the near bottom velocity gradually decreases Locally deepened stilling basin Figure 16 presents an example of the influence of the roof on the flow pattern for a geometry with a locally deepened stilling basin. Figure 16. Influence of roof on flow pattern (Geometry VLB G5 with d c / z = 0.373). From Figure 16 follows that the falling nappe trajectory overtops the end sill for a tailwater depth H TWL / z = At this condition, the variation of the near bottom velocity in function of the tailwater depth shows an increasing velocity, as shown in Figure 17. These increased near bottom velocities are present in a rather narrow range of tailwater depths, from H TWL / z = 1.11 to H TWL / z = Beyond a tailwater depth H TWL / z = 1.16, the falling nappe makes contact with the roof of the combined inlet and outlet structure. The near bottom velocity then decreases again and resumes similar values as prior to the increase Baffle blocks Figure 18 presents an example of the variation of the flow pattern in presence of baffle blocks for 3 tailwater depths. From Figure 18 follows that an increase of the tailwater depth results in a decrease of the angle of the nappe (with the horizontal). Consequently, at a certain tailwater depth the location where the falling nappe touches the bottom is situated downstream of the location of the baffle blocks. The further increasing of the tailwater depth results into a contact of the falling nappe with the roof of the culvert and a redirection of the flow towards the bottom of the stilling basin, (Figure 18 bottom panel). This effect is also visible in the variation of the near bottom velocity in function of the tailwater depth, which is shown in Figure

8 Figure 17. Variation of the near bottom velocity in function of tailwater depth (Geometry VLB G5, non-aerated, with d c / z = 0.373) for x/ z = 3.3 and x/ z = 5.3 downstream of the drop. Figure 18. Influence of baffle blocks on flow pattern (Geometry BGM G8 with d c / z = 0.645). The near bottom velocity first increases with an increasing tailwater depth and then decreases when the 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 the Updated Sigmaplan, Flanders Hydraulics Research performed a scale model based review of different desktop designs of combined inlet and outlet structures. This paper compares scale model measurements and the predictions of literature formulae for drop structures and stilling basins. Three types of geometries are discussed: a straight stilling basin, a locally deepened stilling basin and a stilling basin with baffle blocks. Figure 19. Near bottom velocity in function of tailwater depth (Geometry BGM G8 with d c / z = 0.645) for different distances x/ z downstream of the drop. For a straight stilling basin and a tailwater depth equal to the conjugate water depth, the comparison with literature formula shows that the conjugate water depth, the drop length and the hydraulic jump length can be predicted rather well using the available literature formulae. These formulae are also valid for a well-designed locally deepened stilling basin with an end sill of a limited height. For a stilling basin with baffle blocks designed according the design rules for a USBR type III stilling basin, the conjugate water depth can be reduced with a factor The combined inlet and outlet structures for the FCA-CRT s will have to deal with a broad combination of upstream and downstream water levels. For higher tailwater depths than the conjugate water depth, no suitable literature formulae were found by the authors and physical (or numerical) modelling is recommended for designing the combined inlet and outlet structure. The increase of the tailwater depth results into a decrease of the angle of the falling nappe and a flow pattern varying from a free hydraulic jump, over a drowned hydraulic jump, a free surface jet, to culvert flow. Especially for the geometry with a locally deepened stilling basin or baffle blocks, care should be taken that the falling nappe touches the bottom within the locally deepened stilling basin or upstream of the baffle blocks, in case of higher tailwater depths. Otherwise, these situations could lead to an increase in near bottom velocity downstream of the construction and degradation of the downstream bottom protection. REFERENCES Chanson, H. (2002). The hydraulics of stepped chutes and spillways. Swets & Zeitlinger: Lisse. ISBN De Mulder, T.; Vercruysse, J.; Verelst, K.; Peeters, P.; Maris, T.; Meire, P. (2013). Inlet sluices for flood control areas with controlled reduced tide in the Scheldt estuary: an overview. Proc. of Int. Workshop on Hydraulic Design of Low-Head-Structures (IWLHS 2013), Karlsruhe, Germany: Bundesanstalt für Wasserbau (BAW), p

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