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

Transient Mixed Flow Modeling Capability in SRH-2D for Culverts and Bridges Yong G. Lai. Background Equations/Numerical Methods Verification/Demonstration Concluding Remarks. Outline. Transition between free surface open channel flows and pressurized conduit flows

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

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

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

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

  4. Large body of literature 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 Numerical Methods

  5. 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. Existing Numerical Methods

  6. A 2D Mixed Flow Model 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 Present Objective

  7. Preissmann Slot Concept

  8. Advantages: 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 Key Advantages & Limitations

  9. 2D Preissmann Slot Method

  10. Our Extension to Polygons

  11. Governing Equations

  12. Discretization: Continuity Eqn

  13. 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 Numerical Algorithm

  14. Model Verification:Fast Transient Cases

  15. 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 Test 1: Colliding Flows

  16. 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) Test 1: Comparison

  17. 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 Test 2: Dam-Break

  18. Solid: Exact Solution at time=0.3 s Symbol: SRH-2D Slot_Ratio: 0.005 Test 2: Comparison

  19. 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 Test 3: 2D Circular Dam-Break

  20. Test 3: Dam-Break Animation

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

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

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

  24. 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 Concluding Remarks

  25. THANK YOU QUESTIONS ?

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