1. Transient Mixed Flow Modeling Capability in SRH-2D for Culverts and Bridges
Yong G. Lai

2. Outline Background Equations/Numerical Methods
Verification/Demonstration
Concluding Remarks

3. What is Mixed Flow?
Transition between free surface open channel flows and pressurized conduit flows
Examples: Culvert; Bridge; Sewer/Storm Water System & other closed conduit system

4. Numerical Methods Large body of literature Challenges
A recent review: Bousso et al. (2013), J. Hydraulic Eng 139(4)
Challenges
Two sets of equations with fast transient flows
Discontinuous interface between free and pressurized flows
Complex wave propagation

5. Existing Numerical Methods
Two Major Approaches
One-Equation (Preissmann Slot)
Two-Equation (Multi-Phase)
Primarily 1D Models
Suitable for most applications
But 2D needed for, e.g., flooding with culverts/bridges, curved conduit etc.

6. Present Objective A 2D Mixed Flow Model Preissmann Slot Method
Few 2D Models: Maranzoni et al. (2015) (Advances in Water Resources)
Built on SRH-2D (1D used at present)
Capable of fast transient modeling?
Preissmann Slot Method
Extension to unstructured mesh

7. Preissmann Slot Concept

8. Key Advantages & Limitations
Pressurized zones reduce to open-channel equations
“Slot” simulates fluid compressibility & conduit deformation
Limitations:
“False Volumes” added in the slot introduce solution errors!
Slot width needs be minimized for accuracy
But increased slot width reduces oscillations around shock waves

9. 2D Preissmann Slot Method

10. Our Extension to Polygons

11. Governing Equations

12. Discretization: Continuity Eqn

13. Numerical Algorithm Finite-Volume Collocated Method
Pressure Head as Primary Variables (vs Density-Based)
Implicit Time Integration
SIMPLE-C Algorithm
Sub-, Super-, and Trans-Critical Flows
Arbitrary Shaped Mesh Cells
Wetting-Drying Algorithm

14. Model Verification: Fast Transient Cases

15. Test 1: Colliding Flows Left: Head=0.8 m Velocity= 2.0 m/s
Right: Head=0.8 m Velocity=-2.0 m/s
Ceiling: 1.0 m
Slot_Ratio = 0.005

16. Test 1: Comparison
Exact Solution: From Rankine-Hugoniot Relation and Exact Riemann Solver (Solid)
Slower wave speed (due to slot introduced)
Head Oscillation near shock is visible (symbols)

17. Test 2: Dam-Break Left: Head=3.0 m Velocity= 0.0 m/s
Right: Head=0.5 m Velocity= 0.0 m/s
Ceiling: 1.0 m
What to expect? Right-traveling shock; Left-traveling rarefaction wave for depressurization

18. Test 2: Comparison Solid: Exact Solution at time=0.3 s Symbol: SRH-2D
Slot_Ratio:

19. Test 3: 2D Circular Dam-Break
Left: Head=10 m Velocity= 0.0 m/s
Right: Head= 1 m Velocity= 0.0 m/s
Ceiling: 5.0 m Pressure Zone Radius: 11 m
What to expect? Right-traveling shock; Left-traveling rarefaction wave for depressurization
Model: Triangular Mesh

20. Test 3: Dam-Break Animation

21. Test 3: Comparison Solid: SRH-2D Solution from 2D Triangular Mesh
Dash: Reference “Exact” Solution from 1D Radial Solution

22. Demonstration: Dam-Break Flood through a Bridge
Dam Water Depth: 15 m; Channel Water Depth: 1.5m

23. Results at Time = 10 s
Dam Water Depth: 15 m; Channel Water Depth: 1.5m

24. Concluding Remarks
Preissmann Slot Concept is extended to 2D models with arbitrary mesh cells
Equations are derived
2D transient mixed flow capability is successfully developed into SRH-2D
Test cases demonstrate the accuracy of the model implementation

25. THANK YOU
QUESTIONS ?