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Jana R. Fetzer, A. Class (May 21, 2014)

Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach. Jana R. Fetzer, A. Class (May 21, 2014). Outline. Motivation Multiple Pressure Variables Approach Implementation in OpenFOAM Validation Aero acoustic

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Jana R. Fetzer, A. Class (May 21, 2014)

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  1. Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach Jana R. Fetzer, A. Class (May 21, 2014)

  2. Outline • Motivation • Multiple Pressure Variables Approach • Implementation in OpenFOAM • Validation • Aero acoustic • Liquid metal • Conclusion J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  3. Motivation nozzle outflow proton beam inflow • European Spallation Source (ESS) proton beam keyfigures • Proton beam power 5 MW • Proton beam mean current 2 mA • Long-pulse 2.86 ms • Repetition rate 14 Hz • MEgawattTArget: Lead bIsmuthCooled • Nozzle for flow conditioning and elimination of cavitation • Successive beam pulses interact with fluid not subjected to the beam previously • Pressure ~ 1bar • Flow velocity 1.5-2 m/s • LBE J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  4. Motivation spoilerfor forceddetachment expansion volume • Dedicated design measures to counteract the effects of pressure waves • Expansion chamber in Ubend • Spoiler enforcing flow detacement Two internal free surfaces J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  5. Motivation - grid size - flow velocity - speed of sound ~ 1700 m/s (LBE) • Transient incompressibleflow simulation • Time step approx.: • Transient simulation resolving flow phenomena and acoustic phenomena • Time step approx.: J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  6. Multiple PressureVariables Approach • Multiple PressureVariables Approach • Klein (1995) performed an asymptotic analysis using two spatial scales and one time scale to capture long wavelength phenomena • Basic non- dimensionalized variables , , , , - global Mach number • Non-dimensionalizedcompressible Navier Stokes equations in primitive variables for the equation of state of a perfect gas J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  7. Multiple Pressure Variables Approach • AsymptoticConsiderations • Vector of the primitive variables • – local variable associated with convective phenomena • – large scale coordinate associated with acoustic wave propagation • Asymptoticexpansion J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  8. AsymptoticLimit Equations Leading order continuity equation: : Leading, first and second order velocity equation: : Leading order pressure equation J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  9. Interpretation ofasymptoticequations compression heattransfer • Fromthe leading and first order velocityequationfollows • Temporal evolution of fromleading order pressure equation • Integration with respect to over the domain • Applying Gauß-Green theorem with – outward directed unit normal on the boundary of J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  10. Interpretation ofasymptoticequations “ - “ average over local structures Large scaleaverageof second order velocity equation First order pressure equation Evolution equations for the large wavelength acoustics J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  11. Interpretation ofasymptoticequations mathematical model of an incompressible flow with variable density • Formal limit of asymptotic equations for in a bounded domain without heat conduction and global compression from the boundary J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  12. Implementation in OpenFOAM multiregionsolver pisoMPVFoam map variables acousticsolver decomposepressure thermodynamicpressureevolution caclulatenewpressureestimate p solveacousticsystem Interpolate & mom velocitypredictor → intermediate velocity field solve solve solveenergyequation calculatematerial properties f(T) pressure-velocitycorrector → new correctvelocity outer Iteration inner Iteration J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  13. Implementation ofthe MPV Method in OpenFOAM M=0.125 • Implementation is based on Munz et al. (2003) • Pressure decomposition • Thermodynamic pressure: • Acoustic pressure • constant on small spatial scale andvaries on large scale • Reference length hydrodynamic scale: • Reference length acoustic scale: • Hydrodynamic pressure J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  14. Validation liquid metal aero acoustic Validation Matrix J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  15. Test Cases – Aeroacoustic Stream tracer visualization • Lid Driven Cavity • Laminar, Re=1000 • M = 0 • Mesh: 129 x 129 nodes J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  16. Test Cases – Aeroacoustic Horizontal velocity at vertical cross-section Vertical velocity at horizontal cross-section • Horizontal and vertical velocity along vertical/horizontal cross-section • pisoFoam and benchmark (Ghia et al.) comparison J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  17. Test Cases – Aeroacoustic slip Initial density distribution • „Vortex in a box“ – generation of acoustic waves due to a rotating vortex • Initial Conditions • Mesh: • Hydrodynamic 32x32 cells • Acoustic 4x4 cells J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  18. Test Cases – Aeroacoustic J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  19. Test Cases – Aeroacoustic • Generation of Acoustic waves by „Co-rotating vortex pair“ • Initial conditions • p=1 bar • M = 0.095 • Mesh • Hydrodynamic: 100 000 cells • Acoustic: 5184 cells J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  20. Test Cases – Aeroacoustic t =0.9 s t = 1.2 s t = 1.5 s Vortex merging t = 1.8 s t = 2.1 s J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  21. Test cases liquid metal x = 0.2m Inletux =10 m/s noslip x-velocitycomponent at x = 0.2m verticalcut • Backwardsfacingstep • Inletvelocity 10 m/s • k-εturbulencemodel • LBE @ T=450K J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  22. Conclusion & Outlook MPV approach proposed for simulation of pulse-induced pressure wave/ hydrodynamics interaction Low extra numerical effort for solving acoustics Suitable for design optimization Implementation based on OpenFOAM architecture (pisoFoam) Extensive ongoing validation Design measures to limit effects of pressure waves in META:LIC target will be analyzed Input on experimental data on pressure waves is appreciated for validation J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

  23. References R. Klein, „Semi-implicitextensionof a Godunov-type schemebased on low Mach numberasymptotics I: One dimensional flow“ Journal ofComputationalPhysics, 121, p 213-237, 1995 C.-D. Munz, S. Roller, R. Klein, K.J. Geratz, „The extensionofincompressibleflowsolverstotheweaklycompressibleregime“ Journal of Computers andFluids, 32 (2003) 173-196 J. R. Fetzer - Towards the simulation of proton beam induced pressure waves in liquid metal using the Multiple Pressure Variables (MPV) approach

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