HEC-RAS v5.0: 2-D applicationsc.ymcdn.com/.../Thursday/HEC-RAS-v5.0-2-D-Application.pdf · HEC-RAS...
Transcript of HEC-RAS v5.0: 2-D applicationsc.ymcdn.com/.../Thursday/HEC-RAS-v5.0-2-D-Application.pdf · HEC-RAS...
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
“Full” 2-D depth-averaged (Saint Venant or shallow water) equations
• To make pretty 2-D pictures you need to solve these equations.
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𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑡𝑡
+𝜕𝜕𝜕𝜕𝑥𝑥
ℎ𝑈𝑈2 +𝑔𝑔ℎ2
2+𝜕𝜕𝜕𝜕𝑦𝑦
ℎ𝑈𝑈𝑈𝑈 = −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑜𝑜 + 𝑆𝑆𝑓𝑓𝑜𝑜 +𝜕𝜕 𝑇𝑇𝑜𝑜𝑜𝑜𝜕𝜕𝑥𝑥
+𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑦𝑦
𝜕𝜕ℎ𝜕𝜕𝑡𝑡
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
= 0
𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑡𝑡
+𝜕𝜕𝜕𝜕𝑥𝑥
ℎ𝑈𝑈𝑈𝑈 +𝜕𝜕𝜕𝜕𝑦𝑦
ℎ𝑈𝑈2 +𝑔𝑔ℎ2
2= −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑥𝑥 + 𝑆𝑆𝑓𝑓𝑥𝑥 +
𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑥𝑥
+𝜕𝜕 𝑇𝑇𝑥𝑥𝑥𝑥𝜕𝜕𝑦𝑦
𝑆𝑆𝑓𝑓𝑜𝑜 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2
𝐶𝐶2 ℎ ⁄4 3 𝑆𝑆𝑓𝑓𝑥𝑥 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2
𝐶𝐶2 ℎ ⁄4 3
𝑇𝑇𝑜𝑜𝑜𝑜 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥 𝑇𝑇𝑜𝑜𝑥𝑥 = 𝜈𝜈𝑡𝑡
𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
𝑇𝑇𝑜𝑜𝑜𝑜 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
where,
𝑆𝑆𝑜𝑜𝑜𝑜 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑥𝑥
𝑆𝑆𝑜𝑜𝑥𝑥 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑦𝑦
“Approximate” 2-D depth-averaged (diffusive wave) equations
• Neglect convective acceleration terms.
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𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑡𝑡
+𝜕𝜕𝜕𝜕𝑥𝑥
ℎ𝑈𝑈2 +𝑔𝑔ℎ2
2+𝜕𝜕𝜕𝜕𝑦𝑦
ℎ𝑈𝑈𝑈𝑈 = −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑜𝑜 + 𝑆𝑆𝑓𝑓𝑜𝑜 +𝜕𝜕 𝑇𝑇𝑜𝑜𝑜𝑜𝜕𝜕𝑥𝑥
+𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑦𝑦
𝜕𝜕ℎ𝜕𝜕𝑡𝑡
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
= 0
𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑡𝑡
+𝜕𝜕𝜕𝜕𝑥𝑥
ℎ𝑈𝑈𝑈𝑈 +𝜕𝜕𝜕𝜕𝑦𝑦
ℎ𝑈𝑈2 +𝑔𝑔ℎ2
2= −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑥𝑥 + 𝑆𝑆𝑓𝑓𝑥𝑥 +
𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑥𝑥
+𝜕𝜕 𝑇𝑇𝑥𝑥𝑥𝑥𝜕𝜕𝑦𝑦
𝑆𝑆𝑓𝑓𝑜𝑜 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2
𝐶𝐶2 ℎ ⁄4 3 𝑆𝑆𝑓𝑓𝑥𝑥 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2
𝐶𝐶2 ℎ ⁄4 3
𝑇𝑇𝑜𝑜𝑜𝑜 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥 𝑇𝑇𝑜𝑜𝑥𝑥 = 𝜈𝜈𝑡𝑡
𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥
+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
𝑇𝑇𝑜𝑜𝑜𝑜 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦
where,
𝑆𝑆𝑜𝑜𝑜𝑜 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑥𝑥
𝑆𝑆𝑜𝑜𝑥𝑥 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑦𝑦
0
00
0
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
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Updated2-D mesh
Manual spillway mesh refinement
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Original2-D mesh HEC-RAS geometry file
Storage Area Is2D=-1Storage Area Point Generation Data=0,0,10,10Storage Area 2D Points= 18960X-coord Y-coord X-coord Y-coordX-coord Y-coord X-coord Y-coordX-coord Y-coord X-coord Y-coordX-coord Y-coord X-coord Y-coord......................
Spillway characteristics
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• Width: B≈20 ft• Slope: So≈0.27, θ≈15°• Q≈7,247 cfs (Vmax≈60 fps)• Fmax≈4.5
So
1θ
• HEC-RAS:• Jump height: d2/d1 ≈ 3.4 • Jump length: 125ft < L < 150ft
Spillway WSP results
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HEC-RAS 2-DHEC-RAS 1-D
d1≈5.5ftV1≈60fpsF1≈4.5
d2≈18.6ftV2≈9.3fpsF2≈0.38
L
• Jump height:• HEC-RAS: d2/d1 ≈ 3.4 • USBR: d2/d1 ≈ 5.7
• Jump length:• HEC-RAS: L ≈ 135ft• USBR: L ≈ 190ft
• USBR results represent upper limit because some flow “leaks” over our spillway walls and the spillway becomes slightly wider
Spillway hydraulic jump (comparison with USBR measurements)
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from USBR EM 25 (1984) “Hydraulic design of stilling basins and energy dissipators”
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
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• Developed a 2-D model and applied it to several verification test cases (including a 180° bend).
Molls (1992, 1995)
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Bend characteristics
• 180° bend with rectangular (B=0.8 m) cross section and straight upstream and downstream reaches
• Horizontal bottom (S0=0)• “Tight” bend, mean radius-to-width ratio of 1.0• Smooth channel, n = 0.01• Subcritical flow, Q = 0.0123 m3/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)
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Spiral flow in a bend (not captured by 2-D equations)
25from Blanckaert and de Vriend (2004)
r
z
θ
vr
vz
vθ
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
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180° bend vs natural meander (diagram)
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Faster velocity inside Main flow path toward outside
adapted from “California rivers and streams” (1995) by Jeffrey Mount
Photo by Eric Jones
Bend HEC-RAS initial setup
• HEC-RAS results show “proper” trends
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Vmag (m/s)
Q=0.0123 m3/s
h≈0.
057
m
B=0.8 m
Rc=0.8 m
dx=dy=0.04 m
2 grids with similar grid cell size but different orientation
29HEC-RAS generated grid(initial setup)
Curvilinear grid (manually created)
Effect of grid orientation
30HEC-RAS generated grid(initial setup)
Curvilinear grid (manually created)More closely matches experimental data,but bend inner wall velocity is too low
Vmag (m/s)
V≈0.34 m/s
V≈0.19 m/s
V≈0.33 m/s
V≈0.12 m/s
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)
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Vmag (m/s)
Q=0.0123 m3/s
h≈0.
057
m
Bend HEC-RAS final velocity results
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Vmag (m/s)
Q=0.0123 m3/sU0=0.265 m/s B
A
A
B
DC
C
D
E
F
E
F
Note: Ut/U0=1.5 Ut=0.4m/s
HEC-RAS 2-D
Bend HEC-RAS final depth results
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Depth (cm)
5.0
6.2
B
A
C
E
D
F
B
A
C
ED
F
HEC-RAS 2-D (inner)HEC-RAS 2-D (outer)
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
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Effect of Courant Number(same grid, different time step)
35Cr≈0.2 ; dt=0.01 s Cr≈1 ; dt=0.05 s
More closely matches experimental data
Vmag (m/s)
V≈0.39 m/s
V≈0.19 m/s
V≈0.33 m/s
V≈0.22 m/s
Bend HEC-RAS Courant sensitivity velocity results
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Vmag (m/s)
Q=0.0123 m3/sU0=0.265 m/s B
A
A
B
DC
C
D
E
F
E
F
Note: Ut/U0=1.5 Ut=0.4m/s
Cr≈1.0 ; dt=0.05sCr≈0.2 ; dt=0.01s
HEC-RAS 2-D
Bend HEC-RAS Courant sensitivity depth results
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Depth (cm)
5.0
6.2
B
A
C
E
D
F
B
A
C
ED
F
Inner (Cr≈1.0 ; dt=0.05s)Inner (Cr≈0.2 ; dt=0.01s)
HEC-RAS 2-D
Outer (Cr≈1.0 ; dt=0.05s)Outer (Cr≈0.2 ; dt=0.01s)
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
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Questions?
• Tom Molls:• [email protected]
• Presentation and data available at:• www.ford-consulting.com\highlights
• HydroCalc:• www.hydrocalc2000.com
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• Approximate bend flow as irrotational vortex• Assume: vr=0 ; vz=0 ; dvθ/dz=0 ; dp/dθ=0 ; d/dt=0• (1/ρ)∙∂p/∂r = v2
θ/r• Assume: p=ρgh ; vθ=V=Q/A ; r = Rc
• (ρ/ρ)g∙∂h/∂r = V2/Rc
�hi
ho∂h=
V2
gRc�ri
rodr
ho−hi =V2
gRcro−ri
dh=V2BgRc
Superelevation (design manual equation)
43
r
zθ
vr=0
vz=0
vθ
dh