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Transient Mixed Flow Modeling Capability in SRH-2D for Culverts and Bridges
Yong G. Lai
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Outline Background Equations/Numerical Methods
Verification/Demonstration Concluding Remarks
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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
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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
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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.
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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
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Preissmann Slot Concept
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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
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2D Preissmann Slot Method
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Our Extension to Polygons
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Governing Equations
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Discretization: Continuity Eqn
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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
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Model Verification: Fast Transient Cases
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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
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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)
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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
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Test 2: Comparison Solid: Exact Solution at time=0.3 s Symbol: SRH-2D
Slot_Ratio:
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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
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Test 3: Dam-Break Animation
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Test 3: Comparison Solid: SRH-2D Solution from 2D Triangular Mesh
Dash: Reference “Exact” Solution from 1D Radial Solution
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Demonstration: Dam-Break Flood through a Bridge
Dam Water Depth: 15 m; Channel Water Depth: 1.5m
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Results at Time = 10 s Dam Water Depth: 15 m; Channel Water Depth: 1.5m
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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
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THANK YOU QUESTIONS ?
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