comparing hec-ras v5.0 2-d results with verification datasets€¦ · the hec-ras results computed...

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

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


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


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: 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.

9

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 equations Shallow Water Equations Diffusion 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

11

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 minAnalytical, 5 minComputed, 20 minAnalytical, 20 minComputed, 35 minAnalytical, 35 minComputed, 50 minAnalytical, 50 minComputed, 65 minAnalytical, 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)



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

Curr

ent V

eloc

ity (m

/s)

Distance (m)



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

14

0

0.2

0.4

0.6

0.8

1

0 1000 2000 3000 4000 5000

Curr

ent V

eloc

ity (m

/s)

Distance (m)



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.

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

16

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

Disc

harg

e (m

3 /s)

Time (s)

Computed, SWEComputed, DWEMeasuredRain


Case 2B

22

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 20 40 60 80 100 120

Disc

harg

e (m

3 /s)

Time (s)

Computed, SWE

Computed, DWE

Measured

Rain


Case 2C

23

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0 20 40 60 80 100 120

Disc

harg

e (m

3 /s)

Time (s)

Computed, SWEComputed, DWEMeasuredRain


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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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 (DT).

25

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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𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑡𝑡

+𝜕𝜕𝜕𝜕𝑥𝑥

ℎ𝑈𝑈2 +𝑔𝑔ℎ2

2+𝜕𝜕𝜕𝜕𝑦𝑦

ℎ𝑈𝑈𝑈𝑈 = −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑜𝑜 + 𝑆𝑆𝑓𝑓𝑜𝑜 +𝜕𝜕 𝑇𝑇𝑜𝑜𝑜𝑜𝜕𝜕𝑥𝑥

+𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑦𝑦

𝜕𝜕ℎ𝜕𝜕𝑡𝑡

+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥

+𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦

= 0


+𝜕𝜕𝜕𝜕𝑥𝑥

ℎ𝑈𝑈𝑈𝑈 +𝜕𝜕𝜕𝜕𝑦𝑦


2= −𝑔𝑔ℎ 𝑆𝑆𝑜𝑜𝑥𝑥 + 𝑆𝑆𝑓𝑓𝑥𝑥 +

𝜕𝜕 𝑇𝑇𝑜𝑜𝑥𝑥𝜕𝜕𝑥𝑥

+𝜕𝜕 𝑇𝑇𝑥𝑥𝑥𝑥𝜕𝜕𝑦𝑦

𝑆𝑆𝑓𝑓𝑜𝑜 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2

𝐶𝐶02ℎ4 3⁄ 𝑆𝑆𝑓𝑓𝑥𝑥 =𝑛𝑛𝑈𝑈 𝑈𝑈2 + 𝑈𝑈2

𝐶𝐶02ℎ4 3⁄

𝑇𝑇𝑜𝑜𝑜𝑜 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥

𝑇𝑇𝑜𝑜𝑥𝑥 = 𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑥𝑥


𝑇𝑇𝑥𝑥𝑥𝑥 = 2𝜈𝜈𝑡𝑡𝜕𝜕 ℎ𝑈𝑈𝜕𝜕𝑦𝑦

where,

𝑆𝑆𝑜𝑜𝑜𝑜 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑥𝑥

𝑆𝑆𝑜𝑜𝑥𝑥 =𝜕𝜕𝑧𝑧𝑏𝑏𝜕𝜕𝑦𝑦

and,

𝜈𝜈𝑡𝑡 = 𝐷𝐷𝑇𝑇 ∙ 𝑓𝑓 ℎ,𝑈𝑈,𝑈𝑈

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

27

18 m

Flow

1.2

m

0.6

m

Experimental Data (Velocity Transects)

28

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

29

Qu = 0.018 cms

h d =

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)

0.35 0.0

Results (Baseline Velocity Profiles)

31

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

32

LRAS≈4.6 m

Vmag (m/s)

0.35 0.0

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.

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.

34

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

35

Experimental Data (Depth Contours and Flow)

36

Inlet conditions:

F ≈ 0.32 V ≈ 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

37 1 ft 4.75 ft 1 ft

h u=

0.55

ft

h d=

0.36

ft

Results (Baseline WSP and Flow) WSPRAS slightly below measured profile QRAS = 1.34 cfs < Qexp=1.45 cfs (≈ 7% difference)

38

Depth (ft)

0.56 0.36

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

40

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.

41

Questions?

Tom Molls: [email protected]

Gary Brunner: [email protected]

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

47

Water “pooling” in 1-D SA

Overland flow in 2-D flow area

“Full” 2D Depth-averaged (Saint Venant or Shallow Water) Equations To make pretty 2D pictures you need to solve these equations.

48


+𝜕𝜕𝜕𝜕𝑥𝑥


2+𝜕𝜕𝜕𝜕𝑦𝑦






= 0


+𝜕𝜕𝜕𝜕𝑥𝑥








𝐶𝐶02ℎ4 3⁄





where,



and,

𝜈𝜈𝑡𝑡 = 𝐷𝐷𝑇𝑇 ∙ 𝑓𝑓 ℎ,𝑈𝑈,𝑈𝑈

“Approximate” 2-D Depth-averaged (Diffusive Wave) Equations

Neglect convective acceleration terms.

49


+𝜕𝜕𝜕𝜕𝑥𝑥


2+𝜕𝜕𝜕𝜕𝑦𝑦






= 0


+𝜕𝜕𝜕𝜕𝑥𝑥








𝐶𝐶2ℎ4 3⁄





where,



0

0 0

0

comparing hec-ras v5.0 2-d results with verification datasets€¦ · the hec-ras results computed...

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