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54 CHAPTER 3. Research Methodology 3.1 Introduction The research was organized into three integrated components including both experimental and computational studies. At Georgia Tech, clear-water scour (CWS) experiments were conducted for a compound channel and bridge geometry similar to that found in middle Georgia at a physical scale of 1:45. Parallel experiments were undertaken at the University of Auckland for CWS at a scale of 1:30 in one compound-channel flume and for live-bed scour (LBS) in another compound-channel flume at a scale of 1:45. These experiments were conducted to confirm that the CWS results were not influenced by scale effects and to include LBS as well as CWS results in the study. All experiments incorporated an erodible floodplain and main channel with an embankment and spill-through abutment protected by rock riprap including a riprap blanket around the toe. Some limited experiments were also done for solid wingwall abutments with riprap blanket protection. The embankment lengths included long setback abutments (LSA), short setback abutments (SSA), and bankline abutments (BLA). Two-column rectangular piers were included in experiments at Georgia Tech to capture interactions of pier scour with other types. In addition to experiments with free flow (F) through the model bridges at Georgia Tech and Auckland, higher flow rates and tailwater levels were introduced to simulate submerged orifice flow (SO) and overtopping (OT) flow thereby reproducing the interplay of lateral contraction and vertical contraction scour processes. Experiments were organized so as to isolate each type of scour and then combine them one by one to gauge the degree of interaction in producing the maximum total scour depth for comparison with the simple addition of each type of scour depth as though the processes were independent. Computational studies were performed at Cardiff University. An array of different numerical techniques was involved to expand the range of variation of the experimental variables, achieve a fuller understanding of the role of turbulence in combined scour processes, and to compare more complex models with simpler ones. To this end, the study implemented large-eddy simulation (LES), 3D Reynolds-Averaged Navier-Stokes (RANS) simulations, and 2D depth-averaged computations. The numerical simulations were carried out for the Georgia Tech flume setup with a fixed bed prior to scour and for one case of the equilibrium scour hole after scour. Two different abutment lengths were included and both F and OT flows were modeled. Numerical results were compared with each other for different levels of computational modeling and with the laboratory measurements of the flow field, including turbulence measurements, obtained in the Georgia Tech flume.
55 3.2 Experiments at Georgia Tech 3.2.1 Experimental Setup Hong (2013) completed a comprehensive set of experiments on a modified laboratory cross- section based on the Towaliga River model described previously and shown in Figure 2-16. The same modified cross-section and bridge design were utilized in this research. For these experiments, the cross section was simplified to find more general features of the flow field and to obtain more widely applicable abutment/contraction scour results for free flow (F), submerged orifice flow (SO), and overtopping flow (OT) with an erodible embankment protected by riprap, including a riprap blanket designed according to the guidelines in HEC-23 (Lagasse 2009). The shape of the floodplain was altered to be horizontal on both sides of the main channel cross- section while preserving the original parabolic shape of the main channel as shown in Figure 3-1. The channel was constructed to have a straight alignment rather than the prototype mild meandering planform. Figure 3-1. Modified Towaliga River model The physical model was installed in a 14-ft (4.3 m) wide flume with a length of 80 ft (24.4 m) and a depth of 2.5 ft (0.76 m). Sand with d50 = 1.1 mm and Ïg = 1.3 was placed in the test section of the flume to a depth of 1.0 ft (0.31 m) to form a movable bed having a length of 22 ft (6.1 m). The upstream flow reach was 15 ft (4.6 m) long and filled with 3.3 mm gravel followed by a 20- ft reach of the 1.1 mm sand to provide fully-rough turbulent flow and a fully-developed boundary layer upstream of the test section. The main channel and floodplain were formed with the aid of plywood templates. As shown in Figure 3-2(a), length of the erodible abutment La was varied such that La/Bf had values of 0.41, 0.53, and 0.77 in the left floodplain, while La/Bf = 1.0 on the right floodplain for all experiments. Embankment dimensions are shown in Figure 3-2(b). The embankment was
56 constructed of hand-compacted 1.1 mm sand with a 2:1 side slope and a spill-through abutment shape. A few experiments were conducted with a solid 45º wingwall abutment. Rounded rock having d50 = 9 mm protected the embankment and formed the riprap apron designed according to the guidelines in HEC-23 (Lagasse et al. 2009) and embedded at the toe of the embankment and abutment for both spill-through and wingwall shapes. The apron was 0.4 ft (12 cm) wide with a thickness of approximately 1.5d50. A plan view of the test section is shown in Figure 3-2(c). Sections 1, 4, and 5 identify locations where velocity and turbulence measurements were made. A standard bridge deck design in the state of Georgia for a roadway width of 40 ft (12.2 m) was constructed at a 1:45 scale to include bridge girders and parapet as shown in Figure 3-3. 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 12 14 B ed E le va tio n z ( ft) Lateral distance (ft) La = 3.5 ft 4.5 ft 6.5 ft BLf = 8.5 ft BRf = 2.75 ftBmc = 2.75 ft 0.288 ft 0.387 ft 1.0 1.5 2.0 -0.5 0.5 1.5 2.5 El ev at io n (ft ) Longitudinal distance (ft) 0.956 ft 0.075 ft 0.288 ft 2 1 (a) (b) Section 1 Approach Section Section 2 U/S Abutment toe Section 3 U/S Bridge Section Section 4 D/S Bridge Section Section 5 D/S Abutment toe 1 -6 -4 -2 0 2 4 X (ft) 14 12 10 8 6 4 2 0 Y (ft ) 4 5Sections Flow Direction 0.3 0.5 0.7 0.9 1.1 1.3 1.5 Elevation Z (ft) 2 3 (c) Figure 3-2. (a) Model bridge cross-section including embankment and bridge deck; (b) Model cross-section of embankment and bridge deck; (c) Plan view of flume test section with LSA on left floodplain and BLA on right floodplain. All 1:45 scale model dimensions in ft.
57 0.375 10.725 0.90 0.375 2.40 0.40 0.75 0.375 Flow Flow Figure 3-3. Top and side views of model bridge deck (dimensions in inches at 1:45 model scale). The critical shear stress for the sand in the test section with d50 = 0.0036 ft (1.1 mm) was determined from Shieldsâ diagram to be 0.012 lb/ft2 (0.57 Pa). Critical velocities were calculated from Keuleganâs equation (Sturm 2009), and they varied from 1.10 to 1.22 ft/s (0.34 to 0.37 m/s) in the floodplain and 1.20 to 1.25 ft/s (0.37 to 0.38 m/s) in the main channel due to variations in flow depth. Water supply to the flume is provided by a constant head tank which continuously overflows as a result of pumping from the laboratory sump into the tank. Outflow from the head tank is introduced into the upstream end of the flume and the flume discharges back into the sump. Maximum capacity of the water supply system is 10 cfs (0.283 m3/s), and discharge is measured with a magnetic flow meter having an uncertainty of ±0.005 cfs (1.4Ã10Ë4 m3/s). The entrance to the flume contains a flow-stilling device that includes two offset rows of vertical slats between which a horsehair filter is placed followed by an expanded metal screen. Tailwater elevation is controlled by an adjustable, inclined overflow plate hinged at the bottom and lifted by a steel cable winch.
58 The point gage and a calibrated capacitance wave gage (RBR Ltd. Model WG-50) were mounted on the flume carriage which rode on parallel rails to measure water surface elevations throughout the test section. Elevations of the deformed bed at the end of the scour process were measured by pinging the bed with sound waves using this feature of an acoustic Doppler velocimeter (ADV). A point gage measured the flume bed near the abutment and piers. Point velocities and turbulence quantities in the bridge test section were measured with three different types of SonTek (2001) 16 MHz microADV probes: 3D down-looking, 3D side-looking and 2D side-looking. When measurements were needed at points close to the free surface and at shallow water depths, the 2D and the 3D side-looking ADV were used. The operating principle of the ADV is based on the Doppler frequency shift of emitted acoustic signals after reflection by small sound-scattering particles assumed to be moving at the same velocity as the fluid. Accuracy of the ADV measurements of velocity and turbulence quantities was evaluated by Voulgaris and Trowbridge (1998) in flume experiments. Their analysis showed that the ADV sensor can accurately measure both mean velocity and Reynolds stress. However, Doppler noise from the ADV often exists, especially when the flow velocity exceeds the pre-set velocity range or when there is contamination from the previous acoustic pulses reflected from boundaries of complex geometries. Noise also occurs when a high level of turbulence exists at the measuring location. Hence, filtering of the signal is needed before analyzing the mean point velocity and turbulent quantities. The signal was filtered by requiring a minimum value of the correlation coefficient, which is a measure of the consistency of the reflected signal, of 70% and a minimum signal-to-noise ratio (SNR) of 15 (SonTek 2001). In addition, the phase-space despiking algorithm of Goring and Nikora (2002) was applied to remove any spikes in the time record caused by aliasing of the Doppler signal which sometimes occurs near a boundary. The percentage of remaining data samples after filtering was maintained to be larger than 50% for further quality control. Kaolin clay particles were used as seeding materials to improve the signal strength and correlation values. Typical correlation values in these experiments were greater than 90% and SNR>15. Garcia et al. (2007) pointed out that the ADV sampling duration is case-specific which can be determined by long-term sampling at a single point. They also recommended operating at the maximum feasible sampling frequency while also cautioning that higher frequencies increase the Doppler noise. In the experiments in this study, the required sampling duration was a minimum of 2 min and sometimes as much as 5 min near the bed, and the sampling frequency was selected to be 25 to 50 Hz based on previous experiments at Georgia Tech (Lee, et al. 2004, Ge et al. 2005, and Hong, S. 2005). Turbulence spectra were checked to identify any cases with excessive noise. 3.2.2 Experimental Procedure The experiments for two primary relative embankment/abutment lengths of La/Bf = 0.41 and 0.77 on the left floodplain were conducted for a series of increasing discharges accompanied by corresponding rises in the tail water so that F, SO, and OT flows could be investigated. One
59 series of runs for La/Bf =0.53 was added for further study of vertical contraction and pier scour interactions. The embankment on the right floodplain was maintained at a constant length with the abutment toe terminating at the upper edge of the main channel bank (La/Bf = 1.0). The abutment lengths were defined as long setback abutments (LSA), short setback abutments (SSA), and bankline abutments (BLA) depending on the location of the primary scour hole. The LSA was defined for the scour hole occurring on the floodplain, while for SSA and BLA the scour hole was located in the main channel. Specific values of La/Bf that correspond to this classification are developed in Chapter 4. In addition to water surface profiles, comprehensive velocity and turbulence profiles were measured for a fixed bed prior to scour at several cross sections (C.S.) including the approach- flow cross section (C.S. 1 in Figure 3-2(c) and at two cross sections, one located at the downstream face of the bridge (C.S. 4) and the other at the downstream toe of the embankment (C.S. 5). At the approach-flow section, point velocities were measured along multiple vertical profiles which were separated by 1 ft (0.30 m) laterally in the floodplain and 0.5 ft (0.15 m) in the main channel. Ten point velocities were taken at each vertical profile in the floodplain while measuring 15 point velocities in each vertical section in the main channel. In the bridge cross section, velocities were taken every 0.5 ft (0.15 m) laterally in both the floodplain and main channel. A minimum of eight measuring points in each vertical profile and as many as 15 points were measured at C.S. 4. Point velocity profiles were integrated over the depth and either floodplain or main channel width to obtain the width-averaged values of discharge per unit width between C.S. 4 and C.S. 1 (q2/q1) for the floodplain and main channel. In addition, near-bottom velocities and turbulence values at a distance of 0.016 ft (5 mm) above the bed and at relative heights above the bed of 0.2 and 0.4 times the depth were measured at C.S. 5. In two experiments, detailed velocity and turbulence measurements were made inside an equilibrium scour hole on the floodplain. When equilibrium scour conditions were reached at the end of approximately five days, comprehensive measurements of the entire bathymetry of the bed including the scour hole were made. Bed elevation measurements were taken with the ADV and a point gage at a lateral spacing of 0.2 ft (0.061 m) over ten cross sections in the scoured region under and downstream of the bridge. A total of 41 flume experiments were completed in which the independent variables of discharge (Q), tailwater elevation (T.W.), and relative abutment length (La/Bf) were controlled for various configurations of bridge elements to capture scour interactions as shown in Table 3-1. In some runs, piers were introduced at varying distances from the abutment toe, Lp, relative to the abutment setback distance from the edge of the main channel, W =(Bf â La). Most of the piers were a pair of square columns, 1.0 in. by 1.0 in. (2.5 cm by 2.5 cm), with a spacing of 5.5 in. (14.0 cm) from center to center in the streamwise direction. Four experimental runs were conducted with solid rectangular-wall piers having dimensions of 1.0 in. by 6.5 in. (2.5 cm by 16.5 cm) identified by the symbol âwâ following the value of Lp/W in the table. Values of Lp/W varied from 0.18 (pier in the abutment scour hole in the left floodplain) to 1.0 (pier at the top of the left bank of the main channel). One series of runs (32-38) focused on vertical contraction
60 scour with no abutments so that La/Bf = 0. Runs 23-27 were conducted for forty-five degree wingwall (WW) abutments while all others were spill-through abutments with 2:1 side slopes. Relative flow intensity in the approach flow section (V1/Vc) varied from 0.54 to 0.90 in the floodplain and from 0.65 to 1.0 in the main channel which covered a wide range of CWS conditions. The relative degree of overtopping as measured by the ratio of overtopping discharge to total discharge (Qot/Q) varied from 0.3 to 0.4. The ratio of floodplain width to main channel width, Bf/Bm, was 3.15 for the left floodplain and 1.04 for the right floodplain. Table 3-1. List of CWS experimental runs at Georgia Tech. (F = free flow, SO = submerged orifice flow, OT =overtopping flow, Qot = overtopping discharge, Q =total discharge, T.W. = tailwater, Vfc1 = critical approach flow velocity on the floodplain, Vmc1 = critical approach velocity in the main channel, A = local abutment scour; P = pier scour; L = lateral contraction scour and V = vertical contraction scour). See Figure 2-1 for definition of all other variables. Run La/ Bf Flow type 1 1 fc f V V 1 1 mc m V V 1 1 m f Y Y W L p Q Qot Q, cfs T.W. elev., ft Scour components A P L V 1 0.41 F 0.542 0.723 0.487 - - 3.0 1.480 * * 2 SO 0.589 0.725 0.556 - - 4.0 1.547 * * * 3 OT 0.561 0.653 0.651 - 0.303 5.5 1.714 * * * 4 F 0.655 0.841 0.493 - - 3.7 1.477 * * 5 OT 0.683 0.823 0.657 - 0.340 7.0 1.717 * * * 6 F 0.648 0.820 0.495 0.18 - 3.7 1.477 * * * 28 SO 0.589 0.725 0.557 - 4.0 1.547 * * * * 7 OT 0.683 0.822 0.658 0.340 7.0 1.717 * * * * 8 F 0.648 0.820 0.494 0.35 - 3.7 1.477 * * * 29 SO 0.589 0.725 0.557 - 4.0 1.547 * * * * 9 OT 0.683 0.822 0.658 0.340 7.0 1.717 * * * * 18 F 0.586 0.712 0.554 - - 4.0 1.547 * * 10 0.77 F 0.659 0.879 0.509 - - 3.8 1.470 * * 11 SO 0.579 0.711 0.585 - - 4.4 1.522 * * * 12 OT 0.623 0.784 0.662 - 0.406 6.5 1.714 * * * 14 F 0.660 0.879 0.509 0.40 - 3.8 1.470 * * * 30 SO 0.579 0.711 0.585 - 4.4 1.522 * * * * 15 OT 0.622 0.784 0.663 0.407 6.5 1.714 * * * * 16 F 0.659 0.878 0.509 1.0 - 3.8 1.470 * * * 31 SO 0.579 0.711 0.585 - 4.4 1.522 * * * *
61 Run La/ Bf Flow type 1 1 fc f V V 1 1 mc m V V 1 1 m f Y Y W L p Q Qot Q, cfs T.W. elev., ft Scour components A P L V 17 OT 0.622 0.784 0.664 0.407 6.5 1.714 * * * * 19 F 0.590 0.791 0.557 - - 4.4 1.522 * * 32 0 SO 0.831 0.974 0.522 - - 5.0 1.522 * 33 SO 0.902 1.041 0.529 - - 5.5 1.522 * 35 OT 0.740 0.802 0.648 - 0.385 7.0 1.714 * 36 SO 0.832 0.974 0.522 0.4 & 1.0 - 5 1.522 * * 37 SO 0.902 1.041 0.527 - 5.5 1.522 * * 38 OT 0.731 0.801 0.649 0.385 7.0 1.714 * * 22 0.41 WW F 0.542 0.723 0.486 - - 3.0 1.480 * * 23 SO 0.589 0.725 0.556 - - 4.0 1.547 * * * 24 OT 0.561 0.653 0.651 - 0.307 5.5 1.714 * * * 25 0.77 WW F 0.659 0.879 0.507 - - 3.8 1.470 * * 26 SO 0.579 0.711 0.585 - - 4.4 1.522 * * * 27 OT 0.623 0.784 0.662 - 0.406 6.5 1.714 * * * 39 0.41 F 0.648 0.820 0.495 0.18w - 3.7 1.477 * * * 40 SO 0.589 0.725 0.557 0.18w - 4.0 1.547 * * * * 41 F 0.648 0.820 0.494 0.35w - 3.7 1.477 * * * 42 SO 0.589 0.725 0.556 0.35w - 4.0 1.547 * * * * 43 0.53 F 0.613 0.831 0.487 0.23, 0.65 - 3.3 1.475 * * * * 44 SO 0.590 0.726 0.575 0.48, 0.78 - 4.1 1.572 * * * * 45 SO 0.569 0.682 0.581 0.43, 0.85 - 3.9 1.582 * * * * 3.2.3 Scour Interaction Categories In the last four columns of Table 3-1, the combination of scour components present in each experimental run are shown; however, a better picture of the methodology of the experiments can be seen by organizing the experiments into the types of scour interactions that were studied as shown in Table 3-2. Across the top rows of the table the experiment numbers, abutment lengths, pier position, and type of flow are presented. The run numbers coincide with those in Table 3-1 and in the final work plan, but four of the originally planned experiments were not performed because of redundancy while others were added. Some special cases of wingwall abutments and wall piers are noted as well as the case of no embankment for study of vertical
62 contraction scour alone. The first column of the table shows how the various components of scour were combined in different collections of experiments to study total scour with interactions. For this purpose, four main categories of interaction are color coded and identified as Categories I, II, III, and IV to coincide with the specific scour prediction procedures developed for each category. In addition, two groups of experiments were devoted to studying pier scour and vertical contraction scour alone for comparison with existing scour prediction, thereby providing validation and quality control of all experiments. The symbol âYâ appears in the table for each experiment in which a particular scour category could be isolated, and the âYâ symbols given in color denote 45-degree solid wingwall abutments (with riprap blanket), bankline piers and wall piers. All other abutments were spill-through, and all other piers were dual-column rectangular piers on the floodplain as described previously. In the last column of Table 3-2, the total numbers of experiments that applied to each scour category are summarized. The proposed categories of scour interaction in Table 3-2 are defined by: I. Abutment/Lateral Contraction Scour with or without Vertical Contraction Scour for LSA: combination of local scour around the abutment induced by the turbulent structure of the flow and acceleration of the flow resulting from the width constriction offered by the bridge opening for free flow around LSA with or without the addition of vertical contraction scour in SO and OT flows; II. Abutment/Lateral Contraction Scour with or without Vertical Contraction Scour for SS/BLA: same combination as Category I, but for SSA and BLA; III. Abutment/Lateral Contraction Scour for LSA with pier scour in F, SO, and OT flow; IV. Vertical Contraction Scour and Pier Scour in the floodplain outside the zone of influence of the abutment.
63 Table 3-2. Experimental runs organized by combinations of scour components 0.41 0.77 0.53 1 2 3 4 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 41 42 43 44 45 Type of Flow F SO OT F OT F OT F OT F SO OT F OT F OT F SO OT F SO OT SO SO SO SO SO SO OT SO SO OT F SO F SO F SO SO Pier Location (L p/W ) 0.18 0.18 0.35 0.35 0.4 0.4 1 1 0.18 0.35 0.4 1 0.18 0.18 0.35 0.35 0.23 0.48 0.45 Vertical Contraction Scour Y Y Y Y Y Y Y Y Y Y 3Y Y Y 3Y Y Y Y 21 Pier Scour Y Y+Y Y+Y Y Y 4+2+1 IâAbutment/Contraction Scour LSA (Free Flow) Y Y Y Y Y Y Y Y Y Y 8+2 IâAbutment/Contraction Scour  LSA + Vertical Contraction Scour (SO/OT Flow) Y Y Y Y Y Y Y Y Y Y Y 7+4 IIâAbutment/Contraction Scour BLA/ SSA ( Free Flow) Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y 13+2 IIâAbutment/Contraction Scour  BLA/SSA + Vertical Contraction Scour (SO/OT Flow) Y Y Y Y Y 2Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y 18+4 IIIâAbutment/Contraction Scour + Pier Scour (Free Flow) Y Y Y Y Y 4+1 IIIâAll Components Together (SO/OT Flow) Y Y Y Y Y Y Y Y Y Y Y 10+1 IVâVertical Contraction + Pier Scour Y+Y Y Y Y 3+1+1 W/O Abutment 0.41 Walled Pier (La /B f ) = 0.53 No Br 0.4&1.0 Scour Component/s Experiment Number Total  Observations(L a /B f ) = 0.41 (L a /B f ) = 0.77 0.41/WWA 0.77/WWA 0.41 0.77 Y Y Y BANK LINE PIER READINGS WING WALL ABUTMENT READINGS WALL PIER READINGS LEGEND
64 The prediction of combined abutment scour and lateral contraction scour in free flow with a formula of the same type has been suggested previously by Sturm (2006) and Ettema et al. (2011) for Category I and Category II scour. Hong et al. (2015) suggested that the formulas for free flow could be extended to SO and OT flows in Category I and Category II scour. Type III interactions were two-way such that the influence of pier location on the depth of maximum abutment/lateral contraction scour was studied as well as the effect of abutment/lateral contraction scour on the maximum depth of pier scour. The two-way interaction occurred because of different locations of maximum scour depth caused by the two different scour components. Type IV interactions were studied for cases of no embankment in place but with a pier in the floodplain and the bridge deck installed across the full width of the flume. In addition, it was possible to obtain Type IV interactions for a LSA with the pier in the floodplain far removed from the toe of the embankment where no lateral contraction scour occurred. 3.3 Experiments at University of Auckland 3.3.1 Experimental Setup Two sets of experiments were performed at the University of Auckland in two separate flumes. Live-bed scour experiments were conducted in a 5-ft (1.5-m) wide LBS flume, while clear-water scour was studied in an 8-ft (2.4-m) wide CWS flume. A compound channel was constructed in each of the flumes with a single floodplain adjacent to a trapezoidal main channel. In order to verify the absence of scale effects, the bridge scale in the CWS experiments was 1:30 for comparison with the Georgia Tech CWS experiments that utilized a 1:45 scale. The purpose of the LBS experiments was to expand the scope of the study to include the common field case of LBS in the main channel, and the bridge was constructed at a 1:45 scale in the LBS flume to match the bridge model at Georgia Tech. Approach-flow conditions in the floodplain of the LBS flume were clear-water scour, while live-bed scour occurred in the main channel. In the CWS flume, both floodplain and main channel experienced CWS. Experimental conditions were selected to achieve F, SO, and OT flows in both the LBS and CWS flumes. Figure 3-4 depicts the LBS flume and its compound channel cross-section. The flume is 5 ft (1.5 m) wide, 3.9 ft (1.2-m) deep and 148 ft (45 m) long. The flume has a rectangular cross-section and is supported on two castellated beams that are centrally pivoted to allow for adjustment of the flume slope. The test section is 15 ft (4.6 m) long and located 85 ft (26 m) downstream of the inlet section. Two separate pumps with variable-speed controllers deliver the sand slurry and clear-water flows at the upstream end of the flume. The inlet section is divided into three sub- inlets, and the slurry enters into the flume from the top sub-inlet. Sand is collected in a trap at the downstream end of the flume. The compound channel cross-section shown in Figure 3-4(b) consists of a trapezoidal main channel with a 2:1 side slope and a width of 1.5 ft (0.46 m) that adjoins a floodplain having a width of 3.5 ft or 1.07 m (Bf/Bm = 2.33). Three relative abutment lengths of La/Bf = 0.50, 0.65, and 0.80 were installed in the flume. Clear-water scour experiments were conducted in an 8-ft (2.4-m) wide flume which has a depth of 2.0 ft (0.6 m) and a length of 54 ft (16.5 m). The flume is supported by two universal beams
65 which pivot about a central support as controlled by screw jacks to adjust the flume slope. Flow straighteners are located at the inlet of the flume, and a weir downstream of the flume controls tailwater elevations. Water supply is provided from an upper reservoir which serves as a constant head tank. The flow rate in the flume was calculated using ADV measurements across the approach flow section. The test section has a length of 9.2 ft (2.8 m) with an upstream approach flow length of 23.0 ft (7.0 m). The compound channel cross-section is shown in Figure 3-5. The trapezoidal main channel has a width of 2.62 ft (0.80 m) and a side slope of 2:1 beside a floodplain width of 5.25 ft (1.60 m) such that Bf/Bm = 2.0. Spill-through and 45-degree wingwall abutments were installed in the compound channel cross-section with abutment lengths of La/Bf = 0.80 and 0.50. The bridge deck design was identical to that shown previously in the Georgia Tech flume (Figure 3-3) except it was constructed at a scale of 1:30 instead of 1:45. (a) (b) Figure 3-4. Schematic of 5-ft wide Auckland LBS flume: (a) profile and dimensions; and (b) compound channel cross section
66 Figure 3-5. Schematic of compound channel cross section in 8-ft wide Auckland CWS flume. Four preliminary experiments in the LBS flume were necessary in order to establish a floodplain roughness that produced a typical compound-channel velocity distribution across the approach- flow cross section while also providing bank stability under the circumstances of higher flow velocities for the LBS case. As shown in Figure 3-6(a), uniform rocks (d50â 16 mm) were used to simulate the floodplain roughness. The distribution density of the rocks was determined by trial and error. In the CWS flume, rocks of uniform size (d50 â 22-mm) were placed on the floodplain as well. The selected alternative for protecting the approach-flow channel bank was mats of small cable-tied tiles as shown on the left side of Figure 3-6(b). In addition, the embankment and spill-through slope were protected by two layers of riprap along with a riprap apron designed according to HEC-23 (Lagasse et al. 2009) as shown in Figure 3-6(b). The riprap was divided into five size groups with increasing sizes as the discharge and flow depth increased. The smallest group varied in size from 8-13 mm while the largest group size was 25-31 mm. (a) (b) Figure 3-6. (a) Roughening of floodplain in 5-ft wide LBS flume; (b) overhead view of upstream bank protection, embankment riprap layer and riprap apron (flow from left to right).
67 Two batches of sediment were used for the movable bed sections in both the CWS and LBS flumes. Their gradation curves were nearly identical. The median size was d50 = 0.84 mm, and the size distribution had a geometric standard deviation of Ïg =1.35 which qualifies the sand to be classified as âuniformâ. Critical velocities varied from approximately 1.1 ft/s (0.34 m/s) in the floodplain to 1.4 ft/s (0.43 m/s) in the main channel. Velocity and turbulence measurements were made in the LBS and CWS flumes using two ADVs, a side-looking Vectrino+ and a down-looking Vectrino+. Both ADVs are non-intrusive, high-resolution and three-dimensional (four acoustic receivers) Doppler current meters. The side-looking Vectrino+ was mainly used for velocity measurements in shallow water, the top layer of water and the overtopping flow. Because the sampling volume is located 50-mm away from the transmitter, the down-looking Vectrino+ was mainly used for velocity and near-bottom turbulence measurements in relatively deep water. Quality control procedures for the ADV data were similar to those established at Georgia Tech (Lee and Sturm 2009) and described in Section 3.2.1. The experimental protocol included sampling durations of two to five minutes, filtering and despiking of the signal, repeated measurements, flow seeding when necessary, and checking of the spectrum for excess noise. An ultrasonic depth sounder was used to measure the time history of scour at a fixed location and to measure the movement of dunes through the test section. The depth sounder was also employed to measure the bed bathymetry after scour. Transverse bed profiles were measured every 0.16 to 0.32 ft (0.05 to 0.10 m) along the length of the test section. The depth sounder was mounted on a trolley. The transverse position was tracked with a digital potentiometer attached to a wheel. Measurements were made every 0.0064 ft (2.0 mm) along each transverse profile. 3.3.2 Experimental Procedure For each experiment, the sediment bed was levelled using a channel-shaped plywood form mounted on the carriage over the flume. Then the abutment, the bridge deck, rock riprap layers and the main channel bank protection were installed. The flume was slowly filled with water, without disturbing the levelled bed. When the water level reached the desired elevation, the wave skimmer was adjusted for the flow depth and the channel slope was set for the desired flow rate. Then the pump controller was activated and the discharge was slowly increased to the target value over about a minute. The duration of the scour experiments was typically 20-192 hours. Some experiments were run with a few more hours of post-equilibrium time to better observe the propagation of sand dunes. During the experiment, five ultrasonic depth sounders were positioned in the vicinity of the bridge section to record the scour history at different sub- sections of the channel. At the end of each scour experiment, the bed bathymetry was measured using one ultrasonic depth sounder. Velocity and turbulence measurements were taken over an immobilized channel bed. In order to avoid uneven settlement, the movable bed section was replaced by concrete blocks supporting galvanized steel sheets coated with the experimental sand and containing grooves for placement of the riprap for different abutment lengths. Flow measurements were carried out in the LBS
68 flume at the approach flow section designated as Cross Section 1 (C.S. 1), at the bridge section (C.S.4 and C.S.5 located as in the Georgia Tech experiments and shown in Figure 3-2(c)), and along the flume immediately downstream of the abutment. For the first six experiments at C.S.1, velocity measurements were taken for multiple vertical profiles, which were laterally spaced by 0.16 to 0.32 ft (50-100 mm) in the main channel, and 0.32 to 0.64 ft (100 to 200 mm) on the floodplain. For each vertical profile in the main channel, typically 15 to 20 measurements were taken over the water depth, while 5 to 15 measurements were taken in the floodplain profiles. Each measurement took two minutes based on a time sensitivity analysis. From the first six experiments, it was determined that the velocity profiles in the approach flow section were logarithmic so that for the remaining experiments, depth-averaged velocity was measured at the relative vertical position of 0.4 times the depth. At C.S. 4, the velocity distribution was not logarithmic so full velocity and turbulence profiles were measured. For near-bottom measurements, the duration of each measurement was 5 minutes at distances of 0.016 and 0.032 ft (5 and 10 mm) above the bed. Only near-bottom measurements were taken at C.S. 5 and downstream of the abutment. Similar measurements at C.S. 1 and C.S. 4 were taken in the CWS flume for long setback abutments. Experimental conditions for 18 Auckland LBS experiments are given in Table 3-3. Three abutment lengths were tested. Flow intensity in terms of V1/Vc varied from 0.50 to 1.08 in the floodplain and from 1.0 to 1.53 in the main channel; in other words, the bed in each experiment experienced CWS in the floodplain and LBS in the main channel. Discharge overtopping ratios fell in the range 0.38 to 0.48 which were somewhat larger than for the Georgia Tech CWS experiments which varied from 0.31 to 0.41. Only abutment/lateral contraction and vertical contraction scour were studied at Auckland, and so all scour interactions were either Category I or Category II. Table 3-4 summarizes experimental conditions for the 25 CWS experiments at Auckland for which Bf/Bm = 2.0. These experiments included both spill-through and wingwall abutments having relative abutment lengths of La/Bf = 0.8 and 0.5. Clear-water scour conditions occurred in both the floodplain (V1/Vc = 0.45 to 0.89) and main channel (V1/Vc = 0.5 to 1.0). Discharge overtopping ratios varied from 0.06 to 0.46. As in the LBS experiments, scour interactions were either Category I or II.
69 Table 3-3. Experimental conditions for LBS experiments in the UoA 5-ft wide flume (Bf/Bm = 2.3) Run La/ Bf Flow type 1 1 fc f V V 1 1 mc m V V 1 1 m f Y Y Q Qot Q, cfs T.W. elev., ft Scour components A L V 1 0.8 F 0.49 1.00 0.41 - 1.3 1.50 * * 2 SO 0.67 1.02 0.52 - 2.0 1.58 * * * 3 OT 0.75 0.99 0.62 0.38 3.0 1.74 * * * 4 F 0.67 1.39 0.43 - 2.0 1.49 * * 5 SO 0.91 1.35 0.52 - 2.7 1.50 * * * 6 OT 1.00 1.34 0.63 0.42 4.3 1.72 * * * 7 0.5 F 0.58 1.08 0.42 - 1.4 1.53 * * 8 SO 0.63 1.04 0.52 - 2.1 1.61 * * * 9 OT 0.78 1.05 0.61 0.48 3.3 1.77 * * * 10 F 0.81 1.53 0.42 - 2.1 1.52 * * 11 SO 0.89 1.47 0.51 - 2.9 1.54 * * * 12 OT 1.08 1.42 0.62 0.45 4.6 1.75 * * * 13 0.65 F 0.49 1.01 0.42 - 1.3 1.52 * * 14 SO 0.63 1.03 0.52 - 2.0 1.59 * * * 15 OT 0.78 1.04 0.61 0.44 3.2 1.76 * * * 16 F 0.71 1.45 0.43 - 2.0 1.51 * * 17 SO 0.87 1.43 0.51 - 2.8 1.51 * * * 18 OT 1.07 1.38 0.62 0.47 4.6 1.74 * * *
70 Table 3-4. Experimental conditions for CWS experiments in the UoA 8-ft wide flume (Bf/Bm = 2.0) Run La/ Bf Flow type 1 1 fc f V V 1 1 mc m V V 1 1 m f Y Y Q Qot Q, cfs T.W. elev., ft Scour components A L V 1 0.8 F 0.45 0.75 0.47 1.9 1.54 * * 2 SO 0.55 0.80 0.57 2.8 1.64 * * * 3 OT 0.57 0.71 0.67 0.36 4.2 1.87 * * * 4 F 0.58 0.98 0.49 2.6 1.55 * * 5 SO 0.77 0.91 0.61 4.3 1.70 * * * 6 OT 0.76 0.86 0.66 0.25 5.3 1.82 * * * 7 OT 0.89 0.89 0.69 0.40 6.7 1.91 * * * 8 OT 0.56 0.60 0.69 0.42 4.2 1.90 * * * 9 F 0.56 0.75 0.50 2.3 1.59 * * 10# OT 0.59 0.67 0.62 0.06 3.3 1.77 * * * 11 0.5 F 0.48 0.81 0.48 2.1 1.57 * * 12# OT 0.55 0.70 0.60 0.06 3.1 1.69 * * * 13 OT 0.49 0.56 0.65 0.31 3.1 1.84 * * * 14 F 0.66 1.03 0.54 3.1 1.62 * * 15# OT 0.81 0.91 0.64 0.23 4.9 1.76 * * * 16 OT 0.79 0.79 0.68 0.46 5.5 1.90 * * * 17 SO 0.57 0.87 0.57 3.0 1.64 * * * 18 0.5WW SO 0.55 0.87 0.57 3.0 1.64 * * * 19 OT 0.49 0.56 0.65 0.31 3.1 1.84 * * * 20 OT 0.81 0.91 0.64 0.23 4.9 1.76 * * * 21 OT 0.79 0.79 0.68 0.46 5.5 1.90 * * * 22 0.8WW OT 0.60 0.72 0.61 0.06 3.2 1.75 * * * 23 F 0.55 0.79 0.49 2.3 1.57 * * 24 OT 0.48 0.50 0.66 0.31 3.1 1.85 * * * 25 OT 0.80 0.76 0.69 0.46 5.5 1.90 * * * #Outliers not included in regression analysis
71 3.4 Computer Modeling at Cardiff University In this project, the in-house code HYDRO3D (Stoesser and Nikora 2008, Stoesser 2010, Bomminayuni and Stoesser 2011) was employed to achieve the project objectives related to the role of turbulence in combined scour processes. The code features two turbulence modes, a large-eddy simulation mode (described in 3.4.1) and a RANS mode (described in 3.4.2). In addition, SRH-2D, Sedimentation and River Hydraulics â Two-Dimensional, a two-dimensional (2D) RANS-based CFD model under development at the Bureau of Reclamation, was assessed in terms of its ability to predict accurately the relevant hydraulic quantities needed to compute maximum scour depth during a bridge design process. SRH-2D is described briefly in section 3.4.3. HYDRO3D solves the Navier-Stokes equations using explicit finite difference discretization on uniform Cartesian grids with a staggered arrangement of the variables. The code is parallelized with Message Passing Interface (MPI) based on domain decomposition. 3.4.1 Large-Eddy Simulations In Cartesian coordinates, the governing equations for an unsteady, incompressible, viscous flow of a Newtonian fluid can be written as follows: 0= x u i i ï¶ ï¶ (3-1) i jj i ij jii f+ xx u + x p= x )u(u + t u ï²ï² ï ï² 11 2 ï¶ï¶ ï¶ ï¶ ï¶ïï¶ ï¶ ï¶ ï¶ (3-2) where ui and uj (i,j = 1,2,3) are the velocity vector components in the corresponding spatial directions x, y and z, t is the time, p is the pressure, Ï is the density and μ is the dynamic viscosity of the fluid and fi represents a body force. In the method of LES spatial filtering of equations (3-1) and (3-2) is performed with the goal to separate the large, energy carrying eddies that are directly resolved from the smaller eddies that are modeled. The present finite difference approach uses a top-hat filter by discrete operators. The turbulent scales that are smaller than the grid size are accounted for through the subgrid- scale (SGS) tensor given by jiiij uuuu=Ï ï ijtijkkij S=Ï ïï¤ï´ 23 1 ïï (3-3) where tï is the subgrid-scale turbulent viscosity, ijï¤ is the Kronecker symbol and ijS is the rate of strain tensor for the resolved scale and it is defined by ï·ï·ï¸ ï¶ ï§ï§ï¨ ï¦ ï¶ ï¶ï«ï¶ ï¶ï½ i j j i ij x u x uS 2 1 (3-4)
72 The resulting governing equations for simulation of the large scales become: 0ï½ï¶ ï¶ i i x u (3-5) i j ij jj i ij jii f+ x Ï xx u + x p= x )uu( + t u ï²ï² ï ï² 11 2 ï¶ ï¶ï«ï¶ï¶ ï¶ ï¶ ï¶ïï¶ ï¶ ï¶ ï¶ (3-6) where the overbar denotes filtered quantity. In this study, the WALE model (Nicoud and Ducros 1999) is employed to compute SGS stresses and to close the filtered Navier-Stokes equations. In the WALE model, the eddy viscosity is modeled by ï¨ ï© ï¨ ï© ï¨ ï© ijdijdijijij d ij d ij st S SSSS SS L 4/52/5 2/3 2 ï«ï½ï (3-7) where sL is the mixing length for the subgrid scales and dijS is defined as ï¨ ï© 222 3 1 2 1 kkijjiij d ij gggS ï¤ïï«ï½ and j i ij x ug ï¶ ï¶ï½ (3-8) The WALE model is designed to return the correct wall asymptotic (y+3) behavior for wall bounded flows, where y+3 is the distance to the wall expressed in wall units. A fifth order WENO scheme (Croce et al. 2004) is used for the convective term in the momentum equation (3-6). The WENO scheme offers a stable, high-order approximation of the derivative using a weighted combination of multiple stencils. It takes into account all stencils and assigns the largest weight to the smoothest stencil. Second order central differencing schemes are used to approximate the diffusive term in the momentum equation and the pressure gradient terms. The code uses a fractal step method for time advancement together with a Poisson equation type pressure correction method to satisfy the fluid incompressibility condition. The convective and diffusive terms are first explicitly advanced in time using a low-storage third- order explicit three-step Runge-Kutta (RK3) that is second-order accurate and for which a numerical stability criterion based on the Courant-Friedrichs-Levy (CFL) number, here CFL = 0.2, is applied which provided the variable time step. The so projected intermediate velocities are then corrected using the solution of the pressure correction equation. A multi-grid method is employed to solve the Poisson equation and the code is parallelized via domain decomposition. The standard MPI accomplishes communication between sub-domains. In this project, the water surface is varying to a great extent, in particular for the overtopping flows, but also for the submerged orifice cases and the free flow cases. Therefore the numerical model requires an adequate and accurate treatment. In HYDRO3D the level set method (LSM) developed by Osher and Sethian (1988), which is an interface-capturing method for a two-phase (water and air) flow performed on a fixed grid, is employed. The LSM employs a level set signed distance function,ï¦ , which has zero value at the phase interface and is positive in air and negative in water. This method is formulated as:
73 ï¯ï¯ ï¯ ï® ï¯ï¯ ï¯ ï ï¬ ïïï¾ ïïï½ ïïï¼ liquid gas xif xif xif tx 0 0 0 ),(ï¦ (3-9) where gasï and liquidï represent the fluid domains for gas and liquid, respectively, and ï is the interface. The interface moves with the fluid particles, expressed through a pure advection equation of the form (Sethian and Smereka 2003): 0ï½ï¶ ï¶ï«ï¶ ï¶ i i x u t ï¦ï¦ (3-10) Since density and viscosity are constant along the particle paths for immiscible fluids, discontinuities in these properties at the interface will cause numerical instabilities. This is avoided by the introduction of a transition zone that smooths density and viscosity values at the interface. The transition zone is defined as ï¥ï¦ ï£ where ï¥ is half the thickness of the interface, which in this study is two grid spaces. Both density and viscosity values are smoothed by employing a Heaviside function, )(ï¦H , as follows (Zhao et al. 1996, Osher and Fedkiw 2002); )()()( ï¦ï²ï²ï²ï¦ï² Hglg ïï«ï½ and )()()( ï¦ïïïï¦ï Hglg ïï«ï½ (3-11) where ï¯ï¯ ï¯ ï® ï¯ï¯ ï¯ ï ï¬ ï¾ ï£ïºï» ï¹ïªï« ï© ï·ï¸ ï¶ï§ï¨ ï¦ï«ï« ïï¼ ï½ ï¥ï¦ ï¥ï¦ï¥ ï°ï¦ ï°ï¥ ï¦ ï¥ï¦ ï¦ if if if H 1 sin11 2 1 0 )( (3-12) The LSM has proven successful in the description of complex multi-phase boundaries and it gives continuous approximations (e.g. Yue et al. 2003, Croce et al. 2004). On the other hand, the LSM is known to have difficulties in conserving mass for strongly distorted interfaces due to numerical dissipation introduced in the discretization of Eq. 3-10 when using upwind biased schemes. Because this is a pure advection problem, central differencing schemes are unstable (e.g. Rodi et al. 2013). To minimize numerical dissipation, a fifth order WENO scheme (Croce et al. 2004) is used. Another difficulty with LSM is that ï¦ does not maintain its property of 1ï½ïï¦ as time proceeds. To overcome this problem, a re-initialization technique introduced by Sussman et al. (1994) is employed, which also helps in improving mass conservation issues. The re-initialized signed distance function d is obtained by solving the partial differential equation given by (Sussman et al. 1994):
74 0)1)(( 0 ï½ïïï«ï¶ ï¶ ddsdï´ (3-13) where ),()0,(0 txxd ï¦ï½ , ï´ is the artificial time and )( 0ds is the smoothed signed function given as: 2 0 2 0 0 0 )( )( ï¥dd d ds ïï« ï½ (3-14) This re-initialization is applied throughout the transition zone within several iteration steps, ï´ ï¥ ï where ï¥ represents one grid space. Those adjustments to the level set function are employed only for computational cells lying on the interface, so that there is no need to solve this partial differential equation for the whole domain. The LSM implementation in HYDRO3D was validated successfully for a number of complex flow cases including bridge overtopping and bridge abutment flows (see Kara et al., 2015a and 2015b) HYDRO3D is based on Cartesian coordinates and for the flows to be simulated here, the code requires special treatment due to the complex geometries (abutments, submerged bridge) and the parabolic main channel. HYDRO3D is equipped with the immersed boundaries (IB) method. The IB method allows the definition of arbitrarily shaped bodies inside a fluid domain and the method maintains the no-slip condition of the fluid on boundaries that do not conform to the Cartesian grid. In HYDRO3D the direct forcing IB method of Uhlmann (2005) is used. The immersed or submerged bodies are built as a set of solid points or Lagrangian markers that a r e representing the desired body shape. The method is based on the argument that the solid markers exert a force (fi in Eq. 3-6) over the fluid cells to correct the Eulerian velocity and to enforce the desired velocity at their location. More details of the implementation of the IB method in HYDRO3D and its validation can be found in Ouro et al. (2015). 3.4.2 Three-Dimensional Reynolds-Averaged Navier-Stokes Equations The Reynolds-Averaged Navier-Stokes (RANS) equations read: 0ï½ï¶ ï¶ i i x u (3-15) j ij jj i ij jii x Ï xx u+ x p= x )uu( + t u ï¶ ï¶ï«ï¶ï¶ ï¶ ï¶ ï¶ïï¶ ï¶ ï¶ ï¶ 21 ï² ï ï² (3-16) where in the context of RANS the overbar denotes time averaging over a given period of time. The tensor ijÏ is the Reynolds stress term and similar to LES requires a closure model. In this work the most popular turbulence closure model, i.e. the standard k-ï¥ model, is employed and details of this model can be found in Rodi (1993). For the sake of brevity they are not repeated
75 here. Temporal and spatial derivatives in the RANS mode are calculated in exactly the same manner as in the LES mode. The 3D RANS version of HYDRO3D features both the level set method and the immersed boundary method. 3.4.3. Two-Dimensional Reynolds-Averaged Navier-Stokes Equations SRH-2D is an unstructured hybrid mesh-based numerical method to simulate open channel flows and is based on the three-dimensional work of Lai et al. (2003). In SRH-2D the numerical formulation is applicable to arbitrarily shaped cells for the 2D depth-averaged flow equations. These are obtained by vertical integration of the three-dimensional Navier-Stokes equations leading to the standard St. Venant equations. The depth-averaged eddy viscosity is calculated using the parabolic model or the two-equation k- ε model. Bed roughness is approximated using Manningâs equation and the hydrostatic assumption allows replacing the pressure with the local water depth. The water-depth gradient acts as the driving force for the flow. In SRH-2D the governing equations are discretized using the segregated finite-volume approach of Lai et al. (2003). The solution domain is covered with an unstructured mesh and cells may assume the shapes of arbitrary polygons. All dependent variables are stored at the geometric centers of the polygonal cells. The governing equations are integrated over polygonal cells using the Gauss integral. Convective and diffusive terms are approximated with central differencing schemes; however for stability purposes (for high Peclet numbers) a damping term is added to the central difference expression for the convective fluxes similar to the concept of artificial viscosity. A SIMPLEC pressure correction algorithm together with the Rhie and Chow (1983) procedure are adopted to couple the momentum equation with the continuity equation to obtain an oscillation-free pressure field and to fulfill the incompressibility condition. SRH-2D features a robust wetting-drying algorithm to handle complex bathymetries with varying discharge and water surface extents. This algorithm eliminates the need to generate multiple meshes. The wetting-drying algorithm identifies mesh cells as wet, here if the water depth is above 1.0 mm. The numerical solution is computed only in wet cells. The wetting and drying algorithm ensures that both mass and momentum are conserved by the procedure as there is no artificial water redistribution. 3.4.4 Numerical Setups and Boundary Conditions The computational domain for the simulations is depicted in Figure 3-7. The compound channel geometry matches the one from the experiment and is of width W=14ft and length L=45ft. The water depth H varies from experiment to experiment, i.e. lowest for the free flow cases and greatest for the overtopping cases. The downstream water depth H is set to be the same as in the experiment and the free surface solver provides the water surface profile during the simulation. Water surface profiles are then validated using the experimental data. The computational domains are discretized with uniform grids. Several test simulations were performed a priori to determine the most suitable grid spacing, a compromise between numerical accuracy and speed
76 Figure 3-7 Computational domain of the numerical simulations of execution. The grid employed for all simulations uses approximately 50 million grid points, regardless of the case. Validation of the simulations (reported in the next Chapter) confirmed the accuracy. In addition to the selected grids two fine grid simulations (featuring approx. 290 Mio grid points) were carried out with the goal to demonstrate the effect of grid refinement and to demonstrate adequacy of the medium grid. The details of the chosen numerical grids are provided in Table 3-5. The code HYDRO3D is based on Cartesian coordinates so that some specific treatment is required to represent accurately and adequately parts of the domain that are non-Cartesian. This is accomplished using the immersed boundary method, a method that allows prescribing second-order accurate boundary conditions on non-body conforming grids. The basic principle is described in various papers, for instance Ouro et al (2015) for HYDRO3D. Briefly, a set of Lagrangian markers are used to form the immersed boundary inside the fluid domain and a special algorithm is employed that transfers information between the fluid and immersed boundary points with the goal to satisfy the no-slip boundary condition for the fluid near the immersed boundaries. Table 3-6 provides the resolution details of the immersed boundaries in terms of number of Lagrangian markers per non-body-conforming geometry. At the side walls and floodplain bed the no-slip boundary condition is applied. The Cartesian grid includes both water and air and the level set method determines the location of the interface during the simulation and at every time step. At the outflow boundary a convective boundary
77 condition is applied. At the inlet a fully-developed compound channel flow field is prescribed. The detailed velocity distributions at the inlet plane for each simulation are obtained from separate pre-cursor simulations. They are described in the following section. Table 3-5: Details of the numerical grids used for the various models No. Case Resolution Grid points HPC Procs. LES 1 F_LSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 51 x106 300 2 SO_LSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 51 x106 300 3 OT_LSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 53 x106 300 10 F_SSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 51 x106 300 11 SO_SSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 51 x106 300 12 OT_SSA 0.39 in.Ã0.39 in.Ã0.16 in. 1 cmÃ1 cmÃ0.4 cm 53 x106 300 1a F_LSA_fine 0.20 in.Ã0.20 in.Ã0.08 in. 0.5 cmÃ0.5 cmÃ0.2 cm 293 x106 1008 3a OT_LSA_fine 0.20 in.Ã0.20 in.Ã0.08 in. 0.5 cmÃ0.5 cmÃ0.2 cm 293 x106 1008 18 Scour_LSA 0.20 in.Ã0.20 in.Ã0.08 in. 0.5 cmÃ0.5 cmÃ0.2 cm 293 x106 1008 RANS 1b 2D_RANS_FF_LSA 2.0 in.Ã1.6 in. 5 cmÃ4 cm 32 x103 16 1c 3D_RANS_FF_LSA 1.6 in.Ã0.8 in.Ã0.3 in. 4 cmÃ2 cmÃ0.8 cm 4 x106 300 *FF â Free flow, SO â Submerged orifice, OT â Overtopping , LSB â Long set back, SSB â Short set back
78 Table 3-6: Resolution of the Immersed Boundaries Case Bridge deck Abutments MC Scour Total LES_LSA_Medium 52x103 175 x103 261 x103 - 488 x103 LES_SSA_Medium 52 x103 259 x103 261 x103 - 572 x103 LES_LSA_Fine 318 x103 2.1 x106 608 x10 - 3 x106 LES_Scour_Fine 318 x103 2.1 x106 608 x103 731 x103 3.7 x106 3D_RANS_LSA - 12 x103 43 x103 - 55 x103 3D_RANS_SSA - 18 x103 43 x103 - 61 x103 * MC â Main Channel, FP â Floodplain 1 varies between cases, depending on flow depth 3.4.5 Pre-Cursor Simulations Pre-cursor simulations were performed for both LES and 3D RANS with the objective to provide realistic inflow conditions for the main simulation. The computational setups of the pre-cursor simulations were chosen to match the experimental conditions in the Georgia Tech flume for the approach flow conditions. The first pre-cursor simulation was validated with measured data for one of the free flow cases. Upon successful validation, pre-cursor simulations were run for all other setups. The computational domain matches the corresponding width of 14 ft (4.3 m) of the compound channel including the fixed width and depth of the parabolic main channel and the floodplains on either side of the main channel. The depth of the floodplain was set to match each of the experimental setups. The domain in the streamwise direction was approximately 25 ft (7.6 m) and periodic boundary conditions in the inflow and outflow were used to mimic an infinitely long channel assuming the approach flow was fully developed at the measurement cross-section. The channel dimensions were approximately 38H x 21H x H, where H is the maximum depth in the main channel. The domain is sketched in Figure 3-8. The parabolic main channel and the bed of the floodplain were constructed using the immersed boundary method. For the approach flow the water surface variations were minimal so that the free surface was set as a frictionless rigid lid and was treated as a plane of symmetry. The side walls of the channel were treated as a no- slip boundary condition where no flow was allowed to pass through. Medium and fine grid simulations were carried out. The grid resolutions of the pre-cursor simulations are detailed in Table 3-7.
79 Figure 3-8: Domain of the compound channel of the pre-cursor simulations in plain view Fig. 3-9 presents both the instantaneous and time-averaged streamwise velocity contours in a cross-section. The top contour plot is annotated with letters (a)-(l) to show the locations where the experimental velocity profiles were taken. As expected, streamwise velocities are highest in the main channel and lower on the floodplains up to approximately 0.3m/s on the floodplain, despite the relatively shallow water depth. Figure 3-10 demonstrates the validation of the streamwise time-averaged velocity. Profiles of the LES are plotted against the experimental data at selected locations within the cross-section, the locations of which are annotated in Fig. 3-9. The agreement between the LES and experimental results is relatively good at most locations. Nearly all profiles match remarkably well the measurements. At profiles (b), (c) and (f) the velocity at the first grid point off the wall is slightly underpredicted due to the immersed boundary treatment on the slope of the parabolic main channel. The immersed boundary points are individual Langragian points approximating a local no-slip condition which requires very fine grids near the boundaries. However, the goal of providing physically realistic inflow conditions was achieved and the pre-cursor simulation was deemed sufficiently accurate. Table 3-7: Grid resolution details of the pre-cursor simulations Case Resolution Grid points Length Width (m) LES_Medium 0.39 in. Ã0.39 in. Ã0.16 in 10.2 x106 9.8 ft 14.0 ft (1 cmÃ1 cmÃ0.4 cm) (3 m) (4.26 m) LES_Fine 0.20 in.Ã0.20 in.Ã0.08 in 81.8 x106 9.8 ft 14.0 ft (0.5 cmÃ0.5 cmÃ0.2 cm) (3 m) (4.26 m)
80 Figure 3-9: Contours of the instantaneous (top) and time-averaged streamwise velocity in the cross-section of the compound channel Figure 3-10: Measured (dots) and simulated (lines) profiles of the streamwise velocity of the approach flow
