HEC-RAS v5.0: 2-D applications Tom Molls, Will Sicke, Holly Canada, Mike Konieczki, Ric McCallan David Ford Consulting Engineers, Inc. Sacramento, CA September 10, 2015: Palm Springs FMA conference
What did we do? Applied HEC-RAS v5.0 to several 2-D flow cases and analyzed the results. 1 project study (spillway + floodplain) 1 laboratory study (180 bend) 2
Short introduction 1-D and 2-D
HEC-RAS v4.1 (SAs are bathtubs and channels are 1-D) 4
HEC-RAS v5.0 (gridded SAs are smart bathtubs and channels can be 2-D as well) 5
Results in RAS mapper Water pooling in 1-D SA Overland flow in 2-D flow area 6
Full 2-D depth-averaged (Saint Venant or shallow water) equations To make pretty 2-D pictures you need to solve these equations. huu hvv + + = 0 huu tt hvv tt where, + xx huu2 + ggh2 2 + xx huuuu + yy hvv2 + ggh2 2 + yy huuuu = ggg SS oooo + SS ffff + TT xxxx = 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 xxxx = 2νν tt hvv yy 7
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 xxxx = 2νν tt hvv yy 8
Flow in a spillway chute Supercritical flow with a hydraulic jump
Project background PMF study Spillway capacity study Original study used HEC-RAS 1-D Inundation and erosion potential study Used HEC-RAS 2-D Extended 2-D model into spillway chute to provide proper inflow conditions to the floodplain Updated original 1-D spillway study with 2-D spillway results near the hydraulic jump 2-D analysis includes supercritical flow in spillway chute, and hydraulic jump in stilling basin 10
Terrain Stilling basin Spillway 11
Model domain Updated 2-D mesh 1-D SAs 2-D flow area jump Inflow hydrograph 12
Manual spillway mesh refinement Original Updated 2-D mesh 2-D mesh HEC-RAS geometry file Storage Area Is2D=-1 Storage Area Point Generation Data=0,0,10,10 Storage Area 2D Points= 18960 X-coord Y-coord X-coord Y-coord X-coord Y-coord X-coord Y-coord X-coord Y-coord X-coord Y-coord X-coord Y-coord X-coord Y-coord...... 13
Inundation results (maximum depth) jump deeper Inflow hydrograph 14
Inundation results (maximum velocity) jump faster Inflow hydrograph 15
Spillway characteristics Width: B 20 ft Slope: S o 0.27, θ 15 Q 7,247 cfs (V max 60 fps) F max 4.5 S o θ 1 16
Spillway WSP results HEC-RAS: Jump height: d 2 /d 1 3.4 Jump length: 125ft < L < 150ft L d 1 5.5ft V 1 60fps F 1 4.5 d 2 18.6ft V 2 9.3fps F 2 0.38 HEC-RAS 2-D HEC-RAS 1-D 17
Spillway hydraulic jump (comparison with USBR measurements) Jump height: HEC-RAS: d 2 /d 1 3.4 USBR: d 2 /d 1 5.7 Jump length: HEC-RAS: L 135ft USBR: L 190ft from USBR EM 25 (1984) Hydraulic design of stilling basins and energy dissipators USBR results represent upper limit because some flow leaks over our spillway walls and the spillway becomes slightly wider 18
Spillway 2-D model summary 2-D mesh was manually refined in the spillway Modeled supercritical flow in the spillway Hydraulic jump was modeled internally (without boundary condition influence) Flow entering the floodplain was modeled internally (with proper model computed velocity and depth) High speed spillway flow: Required using full momentum equations Required a small time step for stability purposes Resulted in longer model run times 19
Flow around a 180 channel bend Subcritical flow with superelevation and velocity redistribution
Molls (1992, 1995) Developed a 2-D model and applied it to several verification test cases (including a 180 bend). 21
Bend characteristics 180 bend with rectangular (B=0.8 m) cross section and straight upstream and downstream reaches Horizontal bottom (S 0 =0) Tight bend, mean radius-to-width ratio of 1.0 Smooth channel, n = 0.01 Subcritical flow, Q = 0.0123 m 3 /s and F = 0.11 No flow separation at bend exit Experimental data collected by Rozovskii (1957) and reported in Leschziner and Rodi (1978) and Molls and Chaudhry (1995) 22
Bend data 23
Bend data h=0.058 m dh 7-8 mm 0.4 m/s Flow Flow Velocity Depth 24
Spiral flow in a bend (not captured by 2-D equations) v θ v r z r θ v z from Blanckaert and de Vriend (2004) 25
180 bend vs natural meander 180 laboratory bend Single tight bend with rectangular cross section Fixed bed Faster velocity along inner wall, at bend entrance Faster velocity along outer wall, at bend exit Natural meander Series of gentler bends with irregular cross section Moveable bed Main flow path along outer wall Deposition inside, erosion outside 26
180 bend vs natural meander (diagram) Photo by Eric Jones adapted from California rivers and streams (1995) by Jeffrey Mount Faster velocity inside Main flow path toward outside 27
Bend HEC-RAS initial setup HEC-RAS results show proper trends Vmag (m/s) h 0.057 m R c =0.8 m Q=0.0123 m 3 /s B=0.8 m dx=dy=0.04 m 28
2 grids with similar grid cell size but different orientation HEC-RAS generated grid (initial setup) Curvilinear grid (manually created) 29
Vmag (m/s) Effect of grid orientation V 0.12 m/s V 0.19 m/s V 0.33 m/s V 0.34 m/s HEC-RAS generated grid (initial setup) Curvilinear grid (manually created) More closely matches experimental data, but bend inner wall velocity is too low 30
Bend HEC-RAS final setup (yields best results) Full momentum equations Curvilinear grid with dx = 0.02 m (reduced from 0.04) dt = 0.05 s (Cr 1) Other default parameters (no eddy viscosity) h 0.057 m Vmag (m/s) Q=0.0123 m 3 /s 31
Bend HEC-RAS final velocity results C E F F D E A C D Vmag (m/s) Q=0.0123 m 3 /s U 0 =0.265 m/s B A HEC-RAS 2-D B Note: U t /U 0 =1.5 U t =0.4m/s 32
Bend HEC-RAS final depth results F C B E D A E F A C B D Depth (cm) 6.2 HEC-RAS 2-D (inner) HEC-RAS 2-D (outer) 5.0 33
Courant Number (Cr) Numerical stability criterion that imposes a constraint on the time step (dt), the grid cell size (dx), and the flow velocity (V) Cr = V (dt/dx) Rearranging provides a way to estimate the computational time step: dt = Cr (dx/v) Typical Cr range: 0.5 < Cr < 5 A rule of thumb is to start with Cr 1 For final setup: dt 1 (0.02/0.4) = 0.05 s 34
Effect of Courant Number (same grid, different time step) Vmag (m/s) V 0.22 m/s V 0.19 m/s V 0.33 m/s V 0.39 m/s Cr 0.2 ; dt=0.01 s Cr 1 ; dt=0.05 s More closely matches experimental data 35
Bend HEC-RAS Courant sensitivity velocity results C E F F D E A C D Vmag (m/s) Q=0.0123 m 3 /s U 0 =0.265 m/s B A HEC-RAS 2-D Cr 1.0 ; dt=0.05s Cr 0.2 ; dt=0.01s B Note: U t /U 0 =1.5 U t =0.4m/s 36
Bend HEC-RAS Courant sensitivity depth results F C B E D A E F A C B D Depth (cm) 6.2 5.0 HEC-RAS 2-D Inner (Cr 1.0 ; dt=0.05s) Inner (Cr 0.2 ; dt=0.01s) Outer (Cr 1.0 ; dt=0.05s) Outer (Cr 0.2 ; dt=0.01s) 37
180 bend 2-D model summary Use full momentum equations HEC-RAS results: Reproduce properly the bend flow characteristics (superelevation and velocity redistribution) Are consistent with previous 2-D results and match well with the experimental data Are influenced by grid cell size and orientation Are influenced by the computational time step 2-D studies should include grid cell size and time step sensitivity test 38
2-D modeling is a new feature in HEC-RAS v5.0 but it s been around for quite a while
Kuipers and Vreugdenhil (1973) 40
Questions? Tom Molls: tmolls@ford-consulting.com Presentation and data available at: www.ford-consulting.com\highlights HydroCalc: www.hydrocalc2000.com 41
Backup slides 42
Superelevation (design manual equation) Approximate bend flow as irrotational vortex Assume: v r =0 ; v z =0 ; dv θ /dz=0 ; dp/dθ=0 ; d/dt=0 (1/ρ) p/ r = v 2 θ/r Assume: p=ρgh ; v θ =V=Q/A ; r = R c (ρ/ρ)g h/ r = V 2 /R c v θ h o V 2 r odr h= hi grc r i ho h i = V2 grc r o r i r θ z dh v r =0 dh= V2 B gr c v z =0 43
Superelevation (design calculation estimate) B=0.8 m R c =0.8 m Q = 0.0123 m 3 /s h in 5.8 cm V in = Q/A in = 0.265 m/s dh= V2 B gr c = 0.2652 0.8 9.81 0.8 =0.0072 m Corps EM1110-2-1601 Hydraulic Design of Flood Control Channels dh 7-8 mm 44