comparing hec-ras v5.0 2-d results with verification...

Comparing HEC-RAS v5.0 2-D Results with

Verification Datasets

1. David Ford Consulting Engineers, Inc., Sacramento, CA

2. USACE Hydrologic Engineering Center, Davis, CA

September 8, 2016

Sacramento FMA conference

Tom Molls1, Gary Brunner2, & Alejandro Sanchez2

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

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Review HEC-RAS 5.0 Verification and Validation Research Study

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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

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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)

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Field Test Cases:

1. Malpasset Dam Break

2. New Madrid Floodway, May 2001 Flood

3. Sacramento River

4. Hopefully more???

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What We are Presenting Today:





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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.

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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].

Model Setup

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Parameter Value

Manning’s roughness coefficient

0.01 s/m1/3

Current velocity 1 m/s

Grid resolution 25 m

Initial water surface elevation

0 m

Governing equationsShallow Water EquationsDiffusion Wave Equations

Time step 10 s

Implicit weighting factor 1 (default)

Water surface tolerance 0.001 m (default)

Volume tolerance 0.001 m (default)

Results and Discussion

Comparison of analytical and computed water depth profiles at different times using the HEC-RAS Diffusion Wave Equation solver

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0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Wat

er d

epth

(m

)

Distance (m)

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


Comparison of analytical and computed water depth profiles at different times using the HEC-RAS Shallow Water Equation solver

12

0

0.2

0.4

0.6

0.8

1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Wat

er d

epth

(m

)

Distance (m)

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


Comparison of analytical and computed current velocity profiles at different times using the HEC-RAS Diffusion Wave Equation solver

13

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Cu

rren

t V

elo

city

(m

/s)

Distance (m)

Computed, 5 minAnalytical, 5 minComputed, 20 minAnalytical, 20 minComputed, 35 minAnalytical, 35 minComputed, 50 minAnalytical, 50 minComputed, 65 minAnalytical, 65 min


Comparison of analytical and computed current velocity profiles at different times using the HEC-RAS Shallow Wave Equation solver

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0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Cu

rre

nt

Ve

loci

ty (

m/s

)

Distance (m)

Computed, 5 minAnalytical, 5 minComputed, 20 minAnalytical, 20 minComputed, 35 minAnalytical, 35 minComputed, 50 minAnalytical, 50 minComputed, 65 minAnalytical, 65 min


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 (1x106) percent.

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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 two-dimensional geometry. Model results are compared with measured discharge data for three different unsteady precipitation events.

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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.

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

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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

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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.

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20


Case C1

21

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 20 40 60 80 100 120

Dis

char

ge (

m3/s

)

Time (s)

Computed, SWEComputed, DWEMeasuredRain


Case 2B

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0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 20 40 60 80 100 120

Dis

char

ge (

m3/s

)

Time (s)

Computed, SWE

Computed, DWE

Measured

Rain


Case 2C

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0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 20 40 60 80 100 120

Dis

char

ge (

m3/s

)

Time (s)

Computed, SWE

Computed, DWE

Measured

Rain


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.

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Computing the “correct” eddy zone requires modeling turbulence. In HEC-RAS, the turbulence terms are controlled with the eddy viscosity mixing coefficient (DT).

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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.

“Full” 2D Depth-averaged (Saint Venant or Shallow Water) Equations

To make pretty 2D pictures you need to solve these equations.

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𝜕 ℎ𝑈

𝜕𝑡+

𝜕

𝜕𝑥ℎ𝑈2 +

𝑔ℎ2

2+

𝜕

𝜕𝑦ℎ𝑈𝑉 = −𝑔ℎ 𝑆𝑜𝑥 + 𝑆𝑓𝑥 +

𝜕 𝑇𝑥𝑥𝜕𝑥

+𝜕 𝑇𝑥𝑦

𝜕𝑦

𝜕ℎ

𝜕𝑡+𝜕 ℎ𝑈

𝜕𝑥+𝜕 ℎ𝑉

𝜕𝑦= 0

𝜕 ℎ𝑉

𝜕𝑡+

𝜕

𝜕𝑥ℎ𝑈𝑉 +

𝜕

𝜕𝑦ℎ𝑉2 +

𝑔ℎ2

2= −𝑔ℎ 𝑆𝑜𝑦 + 𝑆𝑓𝑦 +

𝜕 𝑇𝑥𝑦

𝜕𝑥+𝜕 𝑇𝑦𝑦

𝜕𝑦

𝑆𝑓𝑥 =𝑛𝑈 𝑈2 + 𝑉2

𝐶02ℎ Τ4 3

𝑆𝑓𝑦 =𝑛𝑉 𝑈2 + 𝑉2

𝐶02ℎ Τ4 3

𝑇𝑥𝑥 = 2𝜈𝑡𝜕 ℎ𝑈

𝜕𝑥𝑇𝑥𝑦 = 𝜈𝑡

𝜕 ℎ𝑈

𝜕𝑥+𝜕 ℎ𝑉

𝜕𝑦𝑇𝑦𝑦 = 2𝜈𝑡

𝜕 ℎ𝑉

𝜕𝑦

where,

𝑆𝑜𝑥 =𝜕𝑧𝑏𝜕𝑥

𝑆𝑜𝑦 =𝜕𝑧𝑏𝜕𝑦

and,

𝜈𝑡 = 𝐷𝑇 ∙ 𝑓 ℎ, 𝑈, 𝑉

Test Facility

Rect. channel (Bu = 0.6 m ; Bd = 1.2 m)

n = 0.013 (cement)

S0 = 0.0001≈0

Q = 0.01815 cms = 0.641 cfs

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18 m

Flow

1.2

m

0.6

m

Experimental Data (Velocity Transects)

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Lexp≈4.6 m

X=0 m

X=1 m

X=2 m X=4 m

X=3 m X=5 m

Model Setup

Mesh cell size: dx = 0.05 m

Computation time step: dt = 0.015 s, Cr = Vdt/dx ≈ 1

n = 0.013 (concrete)

DT = 0.55, eddy viscosity coefficient(0.1 < DT < 5, from RAS 2D User’s Manual)

S0 = 0

BC: Qu = 0.018 cms ; hd = 0.1 m

“Full” shallow water equations

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Qu = 0.018 cms

hd =

0.1

m

Results (Baseline Eddy Zone)

DT = 0.55, eddy viscosity coefficient

LRAS matches experimental reattachment length

LRAS = Lexp ≈ 4.6 m

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LRAS ≈ 4.6 m

Vmag (m/s)

0.350.0

Results (Baseline Velocity Profiles)

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Lexp≈4.6 m

X=0 m

X=1 m

X=2 m X=4 m

X=3 m X=5 m

Sensitivity Test (Vary DT, Eddy Viscosity Coefficient)

Reattachment length is dependent on DT

Increasing DT reduces LRAS

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LRAS≈4.6 m

Vmag (m/s)

0.350.0

DT=0.55

DT=0.0

DT=1.0

LRAS≈4.0 m

LRAS≈5.3 m

Results Summary

Computed eddy zone reattachment length matches experimental length (with DT = 0.55).

Computed transverse velocity profiles closely match experimental profiles.

This is an “interesting” test case because it requires modeling turbulence.

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Based on specified stage boundary conditions (BCs), HEC-RAS computes the flow and water surface profile (WSP) through the channel contraction.

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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.

Test Facility

Rect. channel (Bu = 2 ft ; Bd = 1 ft)

Straight-walled contraction (L = 4.75 ft ; θ = 6°)

n ≈ 0.01 (cement and plaster)

S0 ≈ 0

Q = 1.45 cfs

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Experimental Data (Depth Contours and Flow)

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Inlet conditions:

F ≈ 0.32V ≈ 1.3 fps

F ≈ 1

Subcritical upstream flow accelerates though the contraction (velocity increases and depth decreases).

Model Setup

Mesh cell size: dx = 0.1 ft

Computation time step: dt = 0.025 s, Cr = Vdt/dx ≈ 1

n = 0.01

S0 = 0

BC: hu = 0.55 ft ; hd = 0.36 ft

“Full” shallow water equations

HEC-RAS computes flow, based on specified stage BCs

371 ft 4.75 ft 1 ft

hu=

0.5

5 ft

hd=

0.3

6 ft

Results (Baseline WSP and Flow)

WSPRAS slightly below measured profile

QRAS = 1.34 cfs < Qexp=1.45 cfs (≈ 7% difference)

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Depth (ft)

0.560.36

Results (Baseline Velocity)

Computed velocity increases through contraction

Vu = 1.2 ft/s ; Vd = 3.7 ft/s

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Velocity (fps)

1.2 3.8

Sensitivity Test (Slightly Increase Upstream Depth BC)

Increase hu from 0.55 ft to 0.58 ft, by 0.03 ft (0.36 in)

Now, QRAS = Qexp= 1.45 cfs

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hu=0.58 QRAS=1.45 cfs

QRAS=1.34 cfs

hu=0.55

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.

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Questions?

Tom Molls:

[email protected]

Gary Brunner:

[email protected]

Presentation available at:

www.ford-consulting.com/highlights

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