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On The Dynamics of Mercury Target Delivery and Dump

On The Dynamics of Mercury Target Delivery and Dump. By. Foluso Ladeinde Stony Brook University Stony Brook, New York 11794-2300. Muon Collider Design Workshop December 1-3, 2009; at BNL. Outline.

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On The Dynamics of Mercury Target Delivery and Dump

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  1. On The Dynamics of Mercury Target Delivery and Dump By Foluso Ladeinde Stony Brook University Stony Brook, New York 11794-2300 Muon Collider Design Workshop December 1-3, 2009; at BNL

  2. Outline • A Mechanical/Aerospace Engineer’s viewpoints on delivery, jet exhaust, and dump of Hg target • Whither Moody chart (friction factor) or system curve? - A different kind of pipe analysis • Whither the familiar decay laws for jet flows? – A different kind of jet analysis • Relevant analytical work on jet exhaust • CFD Analysis • Scope • Governing Equations • The internal flow • The jet exhaust • The Dump • The integrated model pipe-jet flow • Hybrid CFD-CSM-CFA Analysis

  3. The internal flow problem Whither Moody Chart (friction factor) and system curve? Moody Chart Pump/System Curve

  4. Whither the familiar jet decay laws?

  5. Analysis Options • Data from physical experiments • Exact, closed-form analysis • Approximate methods • Computational fluid dynamics (fluid flow problems) • Computational solid mechanics (solid mechanics problems) • Computational material science (material science problems) • Computational dynamics analysis (dynamics problems) • Etc… • Some advantages of numerical methods • Focus on computational fluid dynamics (CFD)e • Procedures for CFD analysis

  6. CFD-Governing Equations

  7. CFD-Governing Equations

  8. CFD-Governing Equations

  9. Turbulence Modeling Options in CFD • RANS • Spalart-Allmaras • k-e (Launder-Sharma) • k-e (Abid model) • High Re No. k-e • k-w (Menter’s SST model) • LES • Smagorinsky model • Dynamic SGS model • Implicit LES (Filtering) • DES • Based on Spalart-Allmaras • PRNS • Based on Abid k-e • Based on high Re No. k-e • RANS/LES Hybrid

  10. CFD - Numerical Approach • Spatial Discretization • MUSCL (2nd-order) • WENO (5th-order) • COMPACT (6th-order) • Time Marching • 2nd order Beam-Warming • 4th order Runge-Kutta • TVD Runge-Kutta

  11. L R CFD - MUSCL

  12. - + - + CFD - WENO Transform to characteristic form: Lax-Friedrichs Flux-splitting WENO Reconstruction Back to physical space, Numerical flux

  13. CFD - WENO… • WENO Evaluation: Smoothness Indicator Robustness Factor • Modifications Made:

  14. COMPACT • 6th order theoretical accuracy: • Filter high-frequency noise:

  15. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  16. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  17. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  18. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  19. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  20. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  21. The internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

  22. Jet Flow • Relevant analytical work on jet exhaust in a magnetic field • Osima et al. (1987) • Field: 1/2 (1-tanh(z-15)/6.2) – inverted “S” • Determination of the shape of the free surface • Stuart number, Weber number, and εm=a/Lm determine shape of jet • Round, elliptical, lobe-shaped • Gallardo et al. 2002 • Field: Gaussian and other distributions (in z-) • Changes in jet cross section and velocity assumed small! • If jet enters field close to the axis, induced forces are compressive and retarding. Hydrostatic pressure and jet diameter increases, then re-accelerates and elongates. • Hydrostatic pressure becomes negative and cavitation occurs as jet leaves field

  23. Instability wave Ansatz • Circular nozzle • Parallel • Weakly non-parallel • Leads to ODE eigenvalue problem (in radial coordinate) • Efficient solution by shooting method • Chevron nozzle • Parallel • Weakly non-parallel Leads to PDE eigenvalue problem in r, q

  24. Pipe/Jet, RANS/LESHybrid • Pipe/Jet • RANS/LES,

  25. CFD – Jet Exhaust No MHD, energy input JET CFD ANALYSIS – TTC (AEROFLO)

  26. CFD – Jet Exhaust No MHD, energy input JET CFD ANALYSIS – TTC (AEROFLO)

  27. CFD – Turbulence Modeling LES / RANS LES / RANS

  28. CFD- Level-Set Equation Free Surface Calculation (Peters) - Distance to the Flame Surface Flame Curvature Turbulent Flame Speed (Peters, Pitsch) Numerical Approach Spatial Discretization: ENO (up to 6th order) Time Marching: TVD Runge-Kutta (2nd, 3rd order)

  29. Re-initialization Procedure • G-transport equation: • Valid only at the flame surface • Does not preserve the distance •  - pseudo-time • is preserved • numerical approach • Sussman, Smereka, & Osher (1994) • Russo & Smereka (2000) • Sussman & Fatemi (1999) (for narrow-band method)

  30. Re-initialization Procedure Curvilinear Coordinates Central Finite Differences Upwinding based on Wi

  31. CFD-Level set/VOF By Others LEVEL SET METHOD – UCLA (HIMAG)

  32. CFD-Level Set LEVEL SET – TTC (AEROFLO)

  33. DUMP: CFD – LEVEL SET By Others – Tristan Davenne LEVEL SET – RUTHERFORD APPLETON LAB(CFX)

  34. Dynamic Analysis – Dump material By Others – Tristan Davenne DYNAMIC ANALYSIS – RUTHERFORD (AUTODYNAMICS)

  35. Concluding Remarks • Discussed delivery, jet exhaust, and dump of Hg target, from a mechanical/aerospace engineer viewpoint • No Moody chart, friction factor data, or system curves for operating point determination • A different kind of jet exhaust! • Couple of relevant analytical work on jet exhaust • CFD holds promise for the hybrid analysis • Level set (VOF) useful in determining free surface; thermal energy not built into procedures • Hybrid CFD-CSM-CFA Analysis • More theoretical analysis needed for the internal flow and jet flow; extend with numerical procedures • Dump analysis will most likely be numerical

  36. The Internal flow problem DELIVERY SYSTEM CFD ANALYSIS – SBU (AEROFLO)

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