Comparing HEC-RAS v5.0 2-D Results with Verification Datasets Tom Molls 1, Gary Brunner 2, & Alejandro Sanchez 2 1. David Ford Consulting Engineers, Inc., Sacramento, CA 2. USACE Hydrologic Engineering Center, Davis, CA September 8, 2016 Sacramento FMA conference
Outline Review current HEC-RAS verification and validation research study. Present four test cases: Flood Wave Propagation over a Flat Surface Surface Runoff in a 2D Geometry Channel with a Sudden Expansion Creating an Eddy Zone Subcritical Flow in a Converging Channel 2
Review HEC-RAS 5.0 Verification and Validation Research Study 3
HEC-RAS 5.0 Verification and Validation Research Study HEC is performing a comprehensive verification and validation study for HEC-RAS 5.0. This will cover: 1D Steady Flow 1D Unsteady Flow 2D Unsteady Flow The following types of data sets are being used for this research work: Analytical and textbook data sets Laboratory experiments Field data (real-world flood events with observed observations) 4
Current Analyses Performed Analytical and textbook data sets: 1. Chow Steady Flow Backwater Profiles 2. Flood Propagation over a Flat and Frictionless Plane 3. Sloshing in a Rectangular Basin 4. Long-wave Run-up on a Planar Slope 5. Flow Transitions over a Bump 6. Dam Break on a Flat and Frictionless Bed 7. Surface Runoff on a Plane 5
Current Analyses Performed Laboratory test cases: 1. Surface Runoff in a 2D Geometry 2. 180 Degree Bend 3. Compound Channel 4. Sudden Expansion 5. Flow around a Spur Dike 6. Sudden Dam Break in a Sloping Flume 7. Flow Transitions over a Trapezoidal Weir 8. Converging Channel (Sub to Supercritical Flow) 6
Current Analyses Performed Field Test Cases: 1. Malpasset Dam Break 2. New Madrid Floodway, May 2001 Flood 3. Sacramento River 4. Hopefully more??? 7
What We are Presenting Today: Flood Wave Propagation over a Flat Surface Surface Runoff in a 2D Geometry Channel with a Sudden Expansion Creating an Eddy Zone Subcritical Flow in a Converging Channel 8
Flood Wave Propagation over a Flat Surface The test case is useful for evaluating the model wetting capability and the correct implementation of the non-linear Shallow Water Equations (SWE) and Diffusion Wave Equations (DWE). The test case is based on a simplified 1D geometry with a flat bed slope. A clever analytical solution was provided by Hunter et al. (2005) in which the wetting front moves forward while preserving its shape. The model features that are verified include the upstream flow hydrograph boundary condition and water volume conservation and stability during wetting of cells. Leandro, J., Chen, A.S., and Schumann, A. 2014. A 2D Parallel Diffusive Wave Model for Floodplain Inundation with Variable Time Step (P-DWave). Journal of Hydrology, [In Press]. 9
Model Setup Parameter Manning s roughness coefficient Current velocity Grid resolution Initial water surface elevation Governing equations 0.01 s/m 1/3 1 m/s 25 m 0 m Value Shallow Water Equations Diffusion Wave Equations Time step Implicit weighting factor Water surface tolerance Volume tolerance 10 s 1 (default) 0.001 m (default) 0.001 m (default) 10
Results and Discussion Comparison of analytical and computed water depth profiles at different times using the HEC-RAS Diffusion Wave Equation solver Water depth (m) 1 0.8 0.6 0.4 Computed, 5 min Analytical, 5 min Computed, 20 min Analytical, 20 min Computed, 35 min Analytical, 35 min Computed, 50 min Analytical, 50 min Computed, 65 min Analytical, 65 min 0.2 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Distance (m) 11
Results and Discussion Comparison of analytical and computed water depth profiles at different times using the HEC-RAS Shallow Water Equation solver Water depth (m) 1 0.8 0.6 0.4 Computed, 5 min Analytical, 5 min Computed, 20 min Analytical, 20 min Computed, 35 min Analytical, 35 min Computed, 50 min Analytical, 50 min Computed, 65 min Analytical, 65 min 0.2 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Distance (m) 12
Results and Discussion Comparison of analytical and computed current velocity profiles at different times using the HEC-RAS Diffusion Wave Equation solver Current Velocity (m/s) 1 0.8 0.6 0.4 0.2 0 Computed, 5 min Analytical, 5 min Computed, 20 min Analytical, 20 min Computed, 35 min Analytical, 35 min Computed, 50 min Analytical, 50 min Computed, 65 min Analytical, 65 min 0 1000 2000 3000 4000 5000 Distance (m) 13
Results and Discussion Comparison of analytical and computed current velocity profiles at different times using the HEC-RAS Shallow Wave Equation solver Current Velocity (m/s) 1 0.8 0.6 0.4 0.2 0 Computed, 5 min Analytical, 5 min Computed, 20 min Analytical, 20 min Computed, 35 min Analytical, 35 min Computed, 50 min Analytical, 50 min Computed, 65 min Analytical, 65 min 0 1000 2000 3000 4000 5000 Distance (m) 14
Results and Discussion The HEC-RAS results computed with both the SWE and DWE solvers agree well with the analytical solution. There are small discrepancies near the edge of the moving front. Both solvers produce leading edges that advance slightly faster than the analytical solution s. The face of the wetting front is very steep and is difficult for models to resolve. The DWE solver produces an overshoot of the current velocity slightly behind the leading flood wave, while the SWE undershoots in the same region. The water volume conservation computed for both runs less than.000001 (1x10 6 ) percent. 15
Surface Runoff in a 2D Geometry The purpose of the test case is to validate HEC-RAS for simulating surface runoff. The test case has spatially uniform but unsteady rainfall and a twodimensional geometry. Model results are compared with measured discharge data for three different unsteady precipitation events. Cea et. al. (2008). Hydrologic Forecasting of Fast Flood Events in Small Catchments with a 2D-SWE Model. Numerical model and experimental validation. In: World Water Congress 2008, 1 4 September 2008, Montpellier, France. 16
Test Facility 2m X 2.5m rectangular basin 3 stainless steel planes with 5% slopes 2 walls located to block flow and increase the time of concentration Rainfall is simulated with 100 nozzles in a grid over basin 17
Experimental Data Three rainfall events with different intensities and durations were run: 1. Case C1: 317 mm/hr for 45s 2. Case 2B: 320 mm/hr for 25s 4s stop 320 mm/hr for 25s 3. Case 2C: 328 mm/hr for 25s 7s stop 328 mm/hr for 25s 18
Model Setup 2 x 2 cm grid cells Manning s n = 0.009 Initial Depth = Dry Time Step = 0.025 s Theta = 0.60 Eddy Viscosity Coef. = 0.2 Shallow Water Equations (SWE) and Diffusion Wave Equations (DWE) were run. 19
Results and Discussion 20
Results and Discussion Case C1 Discharge (m 3 /s) 0.0005 0.0004 0.0003 0.0002 0.0001 Computed, SWE Computed, DWE Measured Rain 0.0000 0 20 40 60 80 100 120 Time (s) 21
Results and Discussion Case 2B 0.0005 Discharge (m 3 /s) 0.0004 0.0003 0.0002 0.0001 Computed, SWE Computed, DWE Measured Rain 0.0000 0 20 40 60 80 100 120 Time (s) 22
Results and Discussion Case 2C Discharge (m 3 /s) 0.0005 0.0004 0.0003 0.0002 0.0001 Computed, SWE Computed, DWE Measured Rain 0.0000 0 20 40 60 80 100 120 Time (s) 23
Results and Discussion The Shallow Water Equations (SWE) performed very well on all three tests. The SWE model captures the rise, peak flow and time, as well as the fall compared to the observed hydrograph. The Diffusion Wave Equations (DWE) had too early of a rise, slightly higher peak flows, and too quick of a fall compared to the observed hydrograph. The experiment is very dynamic with sharp changes in fluid directions and velocities around the walls. 24
Channel with a Sudden Expansion Creating an Eddy Zone Computing the correct eddy zone requires modeling turbulence. In HEC-RAS, the turbulence terms are controlled with the eddy viscosity mixing coefficient (D T ). Xie, B.L. (1996). Experiment on Flow in a Sudden-expanded Channel. Technical report, Wuhan Univ., China. Reported in: Wu et. al. (2004). Comparison of Five Depth-averaged 2-D Turbulence Models for River Flows. Archives of Hydro-Engineering and Env. Mech., 51(2), 183-200. 25
Full 2D Depth-averaged (Saint Venant or Shallow Water) Equations To make pretty 2D pictures you need to solve these equations. huu tt hvv tt where, + xx huu2 + ggh2 2 + huu + xx huuuu + yy hvv2 + ggh2 2 SS ffff = nnuu UU2 + VV 2 CC 2 0 h 4 3 SS ffff = nnvv UU2 + VV 2 CC 2 0 h 4 3 hvv + = 0 + yy huuuu = ggg SS oooo + SS ffff + TT xxxx = ggg SS oooo + SS ffff + TT xxxx SS oooo = zz bb + TT xxxx + TT yyyy SS oooo = zz bb huu TT xxxx = 2νν tt xx and, νν tt = DD TT ff h, UU, VV TT xxxx = νν tt huu hvv + yy TT yyyy = 2νν tt hvv yy 26
Test Facility Rect. channel (B u = 0.6 m ; B d = 1.2 m) n = 0.013 (cement) S 0 = 0.0001 0 Q = 0.01815 cms = 0.641 cfs 0.6 m Flow 1.2 m 18 m 27
Experimental Data (Velocity Transects) X=0 m X=2 m X=4 m L exp 4.6 m X=1 m X=3 m X=5 m 28
Model Setup Mesh cell size: dx = 0.05 m Computation time step: dt = 0.015 s, Cr = Vdt/dx 1 n = 0.013 (concrete) D T = 0.55, eddy viscosity coefficient (0.1 < D T < 5, from RAS 2D User s Manual) S 0 = 0 BC: Q u = 0.018 cms ; h d = 0.1 m Full shallow water equations Q u = 0.018 cms h d = 0.1 m 29
Results (Baseline Eddy Zone) D T = 0.55, eddy viscosity coefficient L RAS matches experimental reattachment length L RAS = L exp 4.6 m L RAS 4.6 m Vmag (m/s) 0.0 0.35 30
Results (Baseline Velocity Profiles) X=0 m X=2 m X=4 m L exp 4.6 m X=1 m X=3 m X=5 m 31
Sensitivity Test (Vary D T, Eddy Viscosity Coefficient) Reattachment length is dependent on D T Increasing D T reduces L RAS D T =0.0 L RAS 5.3 m D T =0.55 L RAS 4.6 m Vmag (m/s) D T =1.0 0.0 0.35 L RAS 4.0 m 32
Results Summary Computed eddy zone reattachment length matches experimental length (with D T = 0.55). Computed transverse velocity profiles closely match experimental profiles. This is an interesting test case because it requires modeling turbulence. 33
Subcritical Flow in a Converging Channel Based on specified stage boundary conditions (BCs), HEC-RAS computes the flow and water surface profile (WSP) through the channel contraction. Coles, D. and Shintaku, T. (1943). Experimental Relation between Sudden Wall Angle Changes and Standing Waves in Supercritical Flow. B.S. Thesis Lehigh University, Bethlehem, PA. Reported in: Ippen, A. and Dawson, J. (1951). Design of Channel Contractions. Symposium on High-velocity Flow in Open Channels, Transactions ASCE, vol. 116, 326-346. 34
Test Facility Rect. channel (B u = 2 ft ; B d = 1 ft) Straight-walled contraction (L = 4.75 ft ; θ = 6 ) n 0.01 (cement and plaster) S 0 0 Q = 1.45 cfs 35
Experimental Data (Depth Contours and Flow) Subcritical upstream flow accelerates though the contraction (velocity increases and depth decreases). F 0.32 V 1.3 fps F 1 Inlet conditions: 36
Model Setup Mesh cell size: dx = 0.1 ft Computation time step: dt = 0.025 s, Cr = Vdt/dx 1 n = 0.01 S 0 = 0 BC: h u = 0.55 ft ; h d = 0.36 ft Full shallow water equations HEC-RAS computes flow, based on specified stage BCs h u =0.55 ft h d =0.36 ft 1 ft 4.75 ft 1 ft 37
Results (Baseline WSP and Flow) WSP RAS slightly below measured profile Q RAS = 1.34 cfs < Q exp =1.45 cfs ( 7% difference) Depth (ft) 0.36 0.56 38
Results (Baseline Velocity) Computed velocity increases through contraction V u = 1.2 ft/s ; V d = 3.7 ft/s Velocity (fps) 1.2 3.8 39
Sensitivity Test (Slightly Increase Upstream Depth BC) Increase h u from 0.55 ft to 0.58 ft, by 0.03 ft (0.36 in) Now, Q RAS = Q exp = 1.45 cfs h u =0.58 h u =0.55 Q RAS =1.45 cfs Q RAS =1.34 cfs 40
Results Summary Computed results show the proper trends (increasing velocity and decreasing depth). Computed WSP is slightly lower than the measured data (maximum difference 7%). The computed flow is slightly lower than the measured flow. This is an interesting test case because HEC-RAS must compute the flow based on specified stage BCs. 41
Questions? Tom Molls: tmolls@ford-consulting.com Gary Brunner: Gary.Brunner@usace.army.mil Presentation available at: www.ford-consulting.com/highlights 42
Backup slides 43
Short Introduction 1-D and 2-D 44
HEC-RAS v4.1 (SAs are Bathtubs and Channels are 1-D) 45
HEC-RAS v5.0 (Gridded SAs are Smart Bathtubs and Channels can be 2-D as well) 46
Results in RAS mapper Water pooling in 1-D SA Overland flow in 2-D flow area 47
Full 2D Depth-averaged (Saint Venant or Shallow Water) Equations To make pretty 2D pictures you need to solve these equations. huu tt hvv tt where, + xx huu2 + ggh2 2 + huu + xx huuuu + yy hvv2 + ggh2 2 SS ffff = nnuu UU2 + VV 2 CC 2 0 h 4 3 SS ffff = nnvv UU2 + VV 2 CC 2 0 h 4 3 hvv + = 0 + yy huuuu = ggg SS oooo + SS ffff + TT xxxx = ggg SS oooo + SS ffff + TT xxxx SS oooo = zz bb + TT xxxx + TT yyyy SS oooo = zz bb huu TT xxxx = 2νν tt xx and, νν tt = DD TT ff h, UU, VV TT xxxx = νν tt huu hvv + yy TT yyyy = 2νν tt hvv yy 48
Approximate 2-D Depth-averaged (Diffusive Wave) Equations Neglect convective acceleration terms. huu tt hvv tt where, 0 + xx huu2 + ggh2 2 0 huu + + xx huuuu + yy hvv2 + ggh2 2 hvv + = 0 + yy huuuu = ggg SS oooo + SS ffff + TT xxxx 0 0 = ggg SS oooo + SS ffff + TT xxxx + TT xxxx + TT yyyy SS ffff = nnuu UU2 + VV 2 CC 2 h 4 3 SS ffff = nnvv UU2 + VV 2 CC 2 h 4 3 SS oooo = zz bb SS oooo = zz bb TT xxxx = 2νν tt huu xx TT xxxx = νν tt huu hvv + yy TT yyyy = 2νν tt hvv yy 49