Revised Clear-Water and Live-Bed Contraction Scour Analysis (2021)

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7-1   Computational Applications 7.1 Overview The design of the laboratory experiments and diagnostic interpretation of results from the experiments was aided and extended using computational modeling. As noted in Section 3.5, the 1D numerical model HEC-RAS was used to confirm the hydraulics of flow through the test setup (i.e., to check on adequacy of lengths of the two channel sections that constitute the setup, and to develop a discharge versus flow depth rating curve for the approach channel upstream of, and at, the contraction). A 2D, depth-averaged numerical modeling was also used to provide insight as to several important aspects of flow through an open-channel contraction. Detailed diagnostic insight from 3D numerical modeling was also obtained for regions of complex flow (e.g., at the contraction entrance). Thus, computational modeling provided insights regarding the com- plexity of the scour flow field and, thereby, the influence of channel geometry and alignment on scour depth. The study used SRH-2D, a model originally developed by the U.S. Department of the Interior, Bureau of Reclamation (Lai 2008) and adopted by FHWA (Robinson et al. 2019). The model implements a flexible-mesh, finite-volume numerical algorithm to solve depth-averaged St. Venant equations. The Surface-water Modeling System (SMS) interface was used to imple- ment and manage the SRH model. The study used the 3D numerical model called FLOW-3D, a privately developed and supported numerical model created by Flow Science, Inc. The primary FLOW-3D model implements the Navier-Stokes equations using the Volume of Fluid (VOF) method and an explicit variable time step solver within a structured grid computational mesh. Additionally, terrain and obstructions to flow are represented using the proprietary Fractional Area-Volume Obstacle Representation (FAVOR™) method. For the initial 2D model analysis, the contraction configuration was essentially the same as shown in Figure 2-4. This model was used to produce information such as indicated in Figure 7-1, which shows a contraction of flow through a rectangular channel. The following information of primary interest in understanding the flow field through a contraction was obtained from the 2D numerical model: (a) Velocity maxima and their locations (b) The length of the short contraction leading to the long contraction (c) The approximate magnitude of vorticity of large-scale turbulence structures in the contraction entrance, notably the flow separation eddy formed at the contraction entrance (d) The influence of contraction entrance geometry on items (a) through (c) (e) The influence of contraction ratio, W2/W1, on items (a) through (c) C H A P T E R 7

7-2 Revised Clear-Water and Live-Bed Contraction Scour Analysis Figure 7-1 identifies items (a) through (c), and illustrates their location and extent. Vorticity associated with flow separation at the contraction is important because its magnitude relates to locations of deepest scour in the short contraction. Trends in maximum depth of scour are related to vorticity and maximum values of velocity. 7.2 Applications In analyzing the hydraulics of contraction scour, it is important to understand how a practi- tioner would model the pre-scour condition. Accordingly, two flume experiments from previ- ous chapters were modeled numerically. One clear-water test at the Severe contraction ratio from Chapter 4 (CW_0.25-0.75) and one live-bed test at the Moderate contraction ratio from Chapter 5 (LB_0.50-2.0) were selected for this effort. Calibration of the numerical models to the observed test data provides valuable insight (from the practitioner’s perspective) as to how these flume experiments would appear to the practitioner without a prior understanding of the laboratory scour results. Secondly, numerical modeling of these flume experiments provides valuable information regarding pre-scour hydraulic conditions. These conditions are rapidly altered by scour in the laboratory flume during the initial stages of a test, and thus, are difficult to document experimentally. Current guidance in HEC-18 estimates scour for both clear-water and live-bed conditions as the difference between two flow depths: y y y (7.1)s 2 0= − where ys is the estimated depth of scour; y2 is the predicted flow depth in the contracted section after scour occurs; and y0 is the flow depth in the contracted section prior to scour. In addition, for live-bed scour, the flow depth y2 is a function of the flow depth y1 in the upstream approach section prior to scour. As noted in Chapter 2, y1 changes during the course of a test as contraction scour occurs. 7.2.1 Laboratory Data CSU provided experimental parameters, post-scour water surface profiles, and a LiDAR bed elevation dataset for Tests CW_0.25-0.75 and LB_0.50-2.0. The post-scour bed LiDAR Figure 7-1. A plan view of an initial 2D numerical simulation (using SRH-2D) of flow through a contraction. The locations of items (a) through (c) are tentatively indicated.

Computational Applications 7-3   dataset was adjusted downwards by 110.1426 ft for Test CW_0.25-0.75 and by 110.1160 ft for Test LB_0.50-2.0, such that the pre-scour bed elevation equaled zero elevation. These adjusted post-scour datasets were then used to define the elevations of the numerically modeled terrain. 7.2.2 General Methodology Recognizing that the technology used to numerically model the experiments may alter the nature of the calculated results, three commonly used modeling platforms were selected. These consisted of HEC-RAS 1D Version 5.0.3 published by the U.S. Army Corps of Engi- neers; SRH-2D published by the U.S. Bureau of Reclamation (Lai 2008) and implemented using the SMS Version 13.0.8 published by Aquaveo; and FLOW-3D published by Flow Science, Inc. (2019). While most of the hydraulic parameters of the experiments were known from the laboratory conditions, the precise roughness values for the system needed to be calibrated for each model. Because the water surface profiles provided by CSU were collected in the post-scour condition, a roughness value for each numerical model was calibrated by running numerous simulations with varying roughness values. RMS error, see Eq. (7.2), was used to compare the predicted water surface profile with the measured values and identify the optimal roughness value (see Section 3.5). RMS Observed Predicted (7.2)2∑( )= − Both HEC-RAS 1D and SRH-2D use a Manning’s n value as a lumped parameter to model energy or momentum losses due to boundary roughness and some portion of the turbulent losses. However, FLOW-3D applies a von Karman based roughness height to determine the logarithmic velocity profile and effective shear stress at the boundary. While the implementa- tion of roughness height differs significantly from Manning’s n, with the application of several assumptions and approximations, roughness height can be converted to Manning’s n with the use of the following equation, in which roughness height is k and hydraulic radius is Rh (Souders and Hirt 2002). log R k 0.046 n R 1.088 (7.3)h h 1 6    = − This conversion equation from roughness height to Manning’s n was used to compare the 3D calibration values with those of the 1D and 2D models. Table 7-1 provides a summary of the roughness calibration results. Once the roughness value for the post-scour condition of each experiment was calibrated, the pre-scour conditions were simulated using that calibrated roughness value. Model Description CW_0.25-0.75 LB_0.50-2.0 HEC-RAS 1D (coarse resolution) n = 0.028 n = 0.020 HEC-RAS 1D (fine resolution) n = 0.026 n = 0.038 SRH-2D n = 0.019 n = 0.035 FLOW-3D k = 0.20 ft (n ≈ 0.026) k = 1.65 ft (n ≈ 0.058) Table 7-1. Results of roughness calibrations.

7-4 Revised Clear-Water and Live-Bed Contraction Scour Analysis 7.3 Calibration to Clear-Water Contraction Scour Test CW_0.25-0.75 Conditions for Test CW_0.25-0.75 are summarized in Table 7-2. 7.3.1 1D Model: Coarse Resolution The 1D HEC-RAS was used with a cross section spacing corresponding to the predetermined data collection stations used to define the water surface as measured from the data collection carriage. Cross section spacing ranged from 1.3 ft in the vicinity of the contraction throat to 10.0 ft further downstream in the long contracted section. At each cross section, the bed was modeled as a horizontal surface extending from the left flume wall to the right. Figure 7-2 shows the initial and final water surface and bed profiles as determined from the HEC-RAS model with the coarse cross section spacing. 7.3.2 1D Model: Fine Resolution The 1D HEC-RAS was also used with a cross section spacing of 1.0 ft for the entire flume length. To capture the ripple-dune bedforms more accurately, the LiDAR scan of the final bed surface was used to define the bathymetry at each HEC-RAS cross section to a typical resolution of 0.1 ft, as illustrated in Figure 7-3. The initial and final water surface and bed profiles as deter- mined from the HEC-RAS model with the fine cross section spacing are shown in Figure 7-4. 7.3.3 2D Model: Fine Resolution The 2D model SRH-2D was used to simulate the hydraulic conditions of clear-water Test CW_0.25-0.75. SRH-2D was used to create a 2D hydraulic model of the post-scour laboratory conditions. Model elements were primarily perpendicular quadrilaterals at a uniform 0.1 ft spacing. However, in the area of width transition in the contraction throat, triangular elements were used, also with a 0.1 ft spacing. Figure 7-5 shows the mesh configu- ration and is shaded to represent the topographic elevations. The elevation of each node was defined using the post-scour LiDAR data, while a plane bed at elevation zero was used to represent the pre-scour bed conditions. Test number Duration(hours) Contraction ratio B2/B1 Velocity ratio Vn1/Vc Discharge Q (ft3/s) y2 tailgate (ft) CW_0.25-0.75 30.5 0.25 0.75 3.05 0.58 Table 7-2. Summary of test conditions, Test CW_0.25-0.75. Figure 7-2. HEC-RAS calibration, Test CW_0.25-0.75 using coarse resolution model.

Figure 7-3. Typical HEC-RAS cross section, Test CW_0.25-0.75 using the fine resolution model.

7-6 Revised Clear-Water and Live-Bed Contraction Scour Analysis -1.5 -1.0 -0.5 0.0 0.5 1.0 10 20 30 40 50 60 70 80 El ev ati on (ft ) Station (ft) Initial WS (HEC-RAS) Final WS (HEC-RAS) Final WS (observed) Initial Bed Final Bed Initial bed Final bed Figure 7-4. HEC-RAS calibration, Test CW_0.25-0.75 using the fine resolution model. Figure 7-5. SRH-2D model mesh for clear-water Test CW_0.25-0.75 showing post-scour bed elevations. (Note: entire flume length is not shown.)

Computational Applications 7-7   Figure 7-6 shows the calibration results from SRH-2D for clear-water Test CW_0.25-0.75. Comparing Figure 7-6 with Figure 7-2 (1D coarse resolution model) and Figure 7-4 (1D fine resolution model) shows remarkably consistent results. 7.3.4 3D Model: Fine Resolution FLOW-3D was used to create a 3D hydraulic model of the post-scour laboratory conditions for Test CW_0.25-0.75. The structured grid of cubic elements was uniformly spaced at 0.1 ft. The numerical model uses Flow Science, Inc.’s, FAVOR method to represent the bed and flume geometry. Figure 7-7 shows the CW_0.25-0.75 post-scour experiment geometry as input into FLOW-3D as defined by the post-scour LiDAR data. Figure 7-8 illustrates the calibration results from FLOW-3D for clear-water Test CW_0.25-0.75. Initial bed Final bed (centerline) Figure 7-6. SRH-2D Model calibration results for clear-water Test CW_0.25-0.75. Figure 7-7. FLOW-3D post-scour bed elevation for clear-water Test CW_0.25-0.75. (Note: entire flume length is not shown.)

7-8 Revised Clear-Water and Live-Bed Contraction Scour Analysis Calibration to observed water surface elevations using FLOW-3D produces nearly identical results compared with the 1D and 2D models discussed previously. In addition, the difference between pre-scour and post-scour water surface elevations are very similar for all the models. 7.4 Calibration to Live-Bed Contraction Scour Test LB_0.50-2.0 Conditions for Test LB_0.50-2.0 are summarized in Table 7-3. 7.4.1 1D Model: Coarse Resolution The 1D HEC-RAS was used with a cross section spacing corresponding to the predetermined data collection stations used to define the water surface as measured from the data collection carriage. Cross section spacing ranged from 1.3 ft in the vicinity of the contraction throat to 10.0 ft further downstream in the contracted section. At each cross section, the bed was modeled as a horizontal surface extending from the left flume wall to the right. Figure 7-9 shows the initial and final water surface and bed profiles as determined from the HEC-RAS model with the coarse cross section spacing. 7.4.2 1D Model: Fine Resolution The 1D HEC-RAS was used with a cross section spacing of 1.0 ft for the entire flume length. To capture the ripple-dune bedforms more accurately, the LiDAR scan of the final bed surface Initial bed Final bed (centerline) Figure 7-8. FLOW-3D model calibration results for clear-water Test CW_0.25-0.75. Test number Duration(hours) Contraction ratio B2/B1 Velocity ratio Vn1/Vc Discharge Q (ft3/s) y2 tailgate (ft) LB_0.50-2.0 7 0.50 2.0 8.14 0.58 Table 7-3. Summary of test conditions, Test LB_0.50-2.0.

Computational Applications 7-9   was used to define the bathymetry at each HEC-RAS cross section to a typical resolution of 0.1 ft. The initial and final water surface and bed profiles as determined from the HEC-RAS model with the fine cross section spacing are shown in Figure 7-10. 7.4.3 2D Model: Fine Resolution The 2D SRH-2D was used to simulate the post-scour hydraulic conditions of live-bed Test LB_0.50-20. Elements were primarily perpendicular quadrilaterals at a uniform 0.1-ft spacing. However, in the area of width transition in the contraction throat, triangular elements were used, also with a 0.1-ft spacing. Figure 7-11 shows the mesh configuration and is shaded to represent the topographic elevations. The elevation of each node was defined using the post-scour LiDAR data, while a plane bed at elevation zero was used to represent the pre- scour bed conditions. Figure 7-12 shows the calibration results from SRH-2D for live-bed Test LB_0.50-2.0. -1.0 -0.5 0.0 0.5 1.0 0 10 20 30 40 50 60 70 80 90 100 El ev ati on ( ft ) Station (ft) Test LB_0.50-2.0 Centerline Initial WS (HEC-RAS) Final WS (HEC-RAS) Final WS (observed) Initial bed Final bed Initial bed Final bed Figure 7-9. HEC-RAS calibration, Test LB_0.50-2.0 using coarse resolution model. Initial bed Final bed (centerline) Figure 7-10. HEC-RAS calibration, Test LB_0.50-2.0 using fine resolution model.

7-10 Revised Clear-Water and Live-Bed Contraction Scour Analysis 7.4.4 3D Model: Fine Resolution FLOW-3D was used to create a 3D hydraulic model of the post-scour laboratory conditions for Test LB_0.50-2.0. The structured grid of cubic elements was uniformly spaced at 0.1 ft. The numerical model uses Flow Science, Inc.’s, FAVOR method to represent the bed and flume geometry. Figure 7-13 shows the LB_0.50-2.0 post-scour experiment geometry as input into FLOW-3D as defined by the post-scour LiDAR data. Figure 7-14 illustrates the calibration results from FLOW-3D for live-bed Test LB_0.50-2.0. Figure 7-11. SRH-2D model mesh for live-bed Test LB_0.50-2.0 showing post-scour bed elevations. (Note: entire flume length is not shown.) Note the deep scour holes at the corners of the contraction throat. Initial bed Final bed (centerline) Figure 7-12. SRH-2D calibration, Test LB_0.50-2.0.

Computational Applications 7-11   Calibration to observed water surface elevations using FLOW-3D produces nearly identical results compared with the 1D and 2D models discussed previously. In addition, the difference between pre-scour and post-scour water surface elevations is similar for all the models. 7.5 Results Numerical modeling of the pre-scour and post-scour conditions for Tests CW_0.25-0.75 and LB_0.50-2.0 show that there are significant changes in the hydraulic conditions upstream of the contraction resulting from scour in the long contracted reach. Good agreement was found Figure 7-13. FLOW-3D post-scour bed elevation for live-bed Test LB_0.50-2.0. (Note: entire flume length is not shown.) Initial bed Final bed (centerline) Figure 7-14. FLOW-3D model calibration results for live-bed Test LB_0.50-2.0.

7-12 Revised Clear-Water and Live-Bed Contraction Scour Analysis between the results of 1D, 2D, and 3D numerical models. This confirms that the prevailing hydraulics of the long-contraction problem can be reliably modeled with the assumptions of a 1D model if water surface profile and cross section averaged velocity are the variables of concern. Previous investigations (Zey 2017) reveal that the flow conditions upstream of a contraction are not independent from the scour process within the long contracted reach. Tables 7-4 and 7-5 summarize the depth and velocity changes observed at the upstream approach section (station 10) for Tests CW_0.25-0.75 and LB_0.50-2.0, respectively. These results demonstrate that the pre-scour hydraulics differ significantly from the post-scour conditions. It is important to consider that the practitioner will only have access to the pre-scour hydraulics from which to predict scour. Condition Pre-Scour Post-Scour Change 1D Model 1D WSE (ft), coarse resolution 0.93 0.79 -0.14 ft (-15%) 1D Vavg (ft/s), coarse resolution 0.41 0.43 0.02 ft/s (+5%) 1D WSE (ft), fine resolution 0.89 0.79 -0.10 ft (-11%) 1D Vavg (ft/s), fine resolution 0.43 0.49 0.06 ft/s (+13%) 2D Model 2D WSE (ft) 0.90 0.80 -0.10 ft (-11%) 2D Vavg (ft/s) 0.42 0.48 0.06 ft/s (+13%) 3D Model 3D WSE (ft) 0.92 0.79 -0.13 ft (-14%) 3D Vavg (ft/s) 0.42 0.49 0.07 ft/s (+17%) WSE: water surface elevation. Vavg: average velocity. Table 7-4. Clear-water Test CW_0.25-0.75: depth and velocity at the upstream approach section (station 10.0). Condition Pre-Scour Post-Scour Change 1D Model 1D WSE (ft), coarse resolution 0.97 0.85 -0.12 ft (-12%) 1D Vavg (ft/s), coarse resolution 1.05 1.19 0.14 ft/s (+13%) 1D WSE (ft), fine resolution 1.08 0.85 -0.23 ft (-21%) 1D Vavg (ft/s), fine resolution 0.94 1.20 0.26 ft/s (+28%) 2D Model 2D WSE (ft) 1.08 0.85 -0.23 ft (-21%) 2D Vavg (ft/s) 0.94 1.20 0.26 ft/s (+28%) 3D Model 3D WSE (ft) 1.09 0.85 -0.24 ft (-22%) 3D Vavg (ft/s) 0.93 1.20 0.27 ft/s (+29%) WSE: water surface elevation. Vavg: average velocity. Table 7-5. Live-bed Test LB_0.50-2.0: depth and velocity at the upstream approach section (station 10.0).

Computational Applications 7-13   7.6 3D Flow Visualization Figure 7-15 presents a streamline flow visualization of Test LB_0.50-2.0. The figure was created using FLOW-3D CFD software, the laboratory flow boundary conditions, and the post-scour LiDAR dataset. Each streamline follows the path of flow from the upper left of the image into the contraction and out through the lower right of the image. The streamlines are colored according to the velocity magnitude. For this post-scour bed condition, the CFD model reveals that flow near the surface undergoes minimal lateral deflection while flow near the bed is redirected in a region extending from the wall to the center of the channel as it enters the contraction. As this highly redirected flow moves through the contraction, it pushes downwards into the most severe region of scour (and reduced velocity). Then, as the flow moves toward the center of the channel, it begins to rise toward the surface and accelerate. Figures 7-16 and 7-17 were created using FLOW-3D CFD software with the laboratory flow boundary conditions, the pre-scour conditions, and the post-scour LiDAR dataset. Both figures plot velocity magnitude by color and offer a longitudinal centerline section, a plan view of the flume bed, and a plan view of the water surface. By comparing the two figures, it is apparent that the smooth and predictable vertical velocity profile under pre-scour conditions changes to a much more variable pattern in the post-scour condition, where bedforms and scour play a significant role. Likewise, the plan view of the bed of the contraction changes significantly from Figure 7-16 to Figure 7-17 and the bed changes shape. In both figures, the bed and water surface plan view velocities in the throat of the contraction change between pre- and post-scour conditions, with lower velocities after scour has occurred. It should be noted that numerical models commonly available to state departments of transportation and their consultants are limited in the ability to accurately portray complex flow situations involving large-scale turbulence structures, the convection of turbulence struc- tures within the flow, and the spatial variability of bedform roughness. The results produced by these models must be interpreted with due awareness of the inherent limitations. Figure 7-15. Test LB_0.50-2.0 CFD Model (FLOW-3D) output of post-scour streamlines colored by velocity magnitude.

7-14 Revised Clear-Water and Live-Bed Contraction Scour Analysis Figure 7-16. Test LB_0.50-2.0 CFD Model (FLOW-3D) output of pre-scour velocity maps (from top to bottom: vertical longitudinal section along centerline, plan view of flow conditions on bed, plan view of flow conditions on water surface). Figure 7-17. Test LB_0.50-2.0 CFD Model (FLOW-3D) output of post-scour velocity maps (from top to bottom: vertical longitudinal section along centerline, plan view of flow conditions on bed, plan view of flow conditions on water surface).