1. Tasks 4.1 4.2 Department of Civil and Environmental Engineering University of Trento Wallingford (UK), May 16 th -17 th 2002 IMPACT Investigation of Extreme Flood Processes & Uncertainty Composition of the group: a.armanini l.fraccarollo m.larcher g.rosatti e.toro c.dalrì e.zorzin

2. A Godunov method for the computation of erosional shallow water transients L. Fraccarollo, H. Capart, and Y. Zech submitted to the Int. Journal of Numerical Methods in Fluids, 2002.

3. Equations

5. n 1D with sections having varying shape and dimensions n inclusions of non-erodible sections at assigned positions Undergoing Advancements n Adaptation processes n Selection processes n Boundary conditions n True two phase flows

6. 2D model for flows over mobile bed during extreme events

7. Governing equations

8. A splitting technique is adopted, spanned over two steps for each direction. First step. The numerical integration in the time-space domain concerns the following PDE Second step. The numerical integration in the same domain of the following ODE:

9. X-splitting

10. Non conservative flux + Source terms

11. 2D Numerical model

13. n inclusions of non-erodible sections at assigned positions Undergoing Advancements n Adaptation processes n Selection processes n Boundary conditions n True two phase flows n Rheological model n mesh-cells fitting to boundaries (I.e.:cut-cell methods)

14. OBLIQUE FRONT DEVIATION ANGLE DEFLECTION ANGLE

16. Task 4.2 belt flumeslit 6.0 m Recirculating experimental channel for uniform granular flow uniform granular flow uniform mud flow

17. Recirculating experimental channel for uniform granular flow

19. Flow regimes

20. n Voronoï 2D (Capart et al., 2002) n Voronoï 3D (Spinewine et al., 2002) n PIV (Lorenzi et al., 2002) Measurement Techniques

21. Local stress relations Normal stress local equilibrium Deriving along y direction: Tangential stress local equilibrium Deriving along y and substituting dc/dy we obtain: Second order equation to get velocity profile

22. No added mass effect on velocity profile

23. Feed pipe Pneumatic piston (23° max) flume inflow outflow Valve Pump hopper Forced flux between pump and hopper Experimental installation for mud-flow

24. Mud-flow (Sarno material) steady condition

25. n Ultrasound doppler velocimeter n Particle tracking n High-frequency radar Measurement Techniques

26. Ultrasound Doppler Velocimeter It has been used for medical applications in the 60es; Cardiovascoular surgery Food industry Metallergic industry Ultrasound beam survey Acoustic field intensity along the transducer Divergence of ultrasonic beam Near field (blind zone) Far field Sampling volume Burst lenght Beam geometry

27. Working scheme Frequency difference between the sent and the received signal Pulsed doppler ultrasound Doppler effect Shift phase of the received echo Particle velocity

28. Sound celerity measure Sound celerity geometric field kinematic field determines Micrometer 2MHz probe water1498 m/s mud 30 % mud 40 % 2100 m/s 2790 m/s mud 50% Signal Completely absorbed Steel plate

29. Operative procedure X Y Z Flow direction Side measurements Bottom measurements Motion along Z Motion along X Doppler angle Ultrasonic Gel Y is constant Doppler Angle 500 kHz probe Partial ultrasound beamComplete ultrasonic beam

30. Experiemntal measurements Instrument setting parameters Side measurements3D velocity profile Concentration variation along the section? Wall reflection effect? Other effects? Mean value over 1000 profiles

31. Experimental measurements Conclusions about the velocimeter Advantages: - Opaque fluids measurement - Instantaneous geometric-kinematic information Disadvantages: - Distruction of the ultrasonic beam with d> 1.5 mm - Rapid absorption, power increase - High divergence of the sonic field - Invalid data - High Signal Noise Ratio - Sound celerity constant for every fluid