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Implementation, Validation and Applications Richard Versluis, Marcel Roos, Luuk Thielen (TNO)

Moving surfaces in DSMC. Implementation, Validation and Applications Richard Versluis, Marcel Roos, Luuk Thielen (TNO). TNO is active in five core areas. Quality of Life Defence, Security & Safety Science & Industry Built Environment & Geosciences Information & Communication Technology.

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Implementation, Validation and Applications Richard Versluis, Marcel Roos, Luuk Thielen (TNO)

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  1. Moving surfaces in DSMC Implementation, Validation and ApplicationsRichard Versluis, Marcel Roos, Luuk Thielen (TNO)

  2. TNO is active in five core areas • Quality of Life • Defence, Security & Safety • Science & Industry • Built Environment & Geosciences • Information & Communication Technology Moving sufaces in DSMC

  3. Playing field of IMC/APPE Key expertise in: • Mass and heat flow • Process technology • Control Engineering • Vacuum design • Contamination control • Space applications • Semiconductor applications Moving sufaces in DSMC

  4. Rarefied gasses Flow regimes – Knudsen number • Knudsen number: Kn = λ/d • Kn < 0.01  Hydrodynamic flow • 0.01 < Kn < 0.1  Slip flow • 0.1 < Kn < 1  Transitional flow • Kn >1  Free molecular flow Moving sufaces in DSMC

  5. Flow regimes - Methods Kn Boltzmann equation Kinetic equations DSMC / Test particle MC / MD / Method of Angular Coefficients. etc 1 Grad’s 13 moments / DSMC / Empirical etc. 0.1 Navier-Stokes with velocity slip & temperature jump 0.01 Navier-Stokes / Euler Moving sufaces in DSMC

  6. DSMC overview • Flow properties are determined by simulating the movement and collisions of molecules • Movement and collision are separate steps by taking Dt << tmct • In one time step, displacement of each molecule is simply • Only a statistical representative number of molecules is simulated: Fnum ~ 1010 • Weighting factors can be applied (linear, radial, species) • Grid cell dimensions < 1/3 l • # molecules per cell N > 20 • Time step Dt < 1/10 tmct • Choice of collision models • Hard sphere • Variable soft sphere variants Moving sufaces in DSMC

  7. X-Stream General purpose CFD • Time transient • Steady state • Body-fitted • Multi-domain • Structured/collocated • Parallel • State-of-the-art solvers • Turbulence • Combustion, soot, NOx • Radiation • 3D & 1D walls • Particle trace • Boundary conditions DSMC at TNO • DSMC at TNO • Integrated in X-Stream (CFD package) • Plane 2D, 3D axi-symmetric, full 3D • Time transient or steady state • Includes gas phase and surface chemistry • Chemkin database • Surface deposition • Weighting factors (grid, species) • Various BC (wall, flow, pressure, symmetry, periodic) • Parallelized code (CRAY) • Pre- and postprocessor, also for complex geometries (non-orthogonal grids, etc.) Moving sufaces in DSMC

  8. DSMC development • Goal • To develop an algorithm to simulate moving surfaces within the calculation domain • Requirements and limitations • 3D • Arbitrary number of moving surfaces • Constant velocities (direction & time) • Same options for surface properties as stationary surface (a, g, T) Moving sufaces in DSMC

  9. Applications Moving sufaces in DSMC

  10. Source: Wikipedia commons Source:US patent 7230258 (Intel) Source: George A. Riley – Flip Chips Source: AIP news graphics Applications • Vacuum pump modeling and optimization • Rotating foil traps: debris mitigation • High-Speed Rotating deposition targets/substrates • MEMS rotors • … Moving sufaces in DSMC

  11. Implementation Moving sufaces in DSMC

  12. Implementation moving surfaces • Moving surfaces move with constant speed vb through the domain • Multiple moving surfaces are allowed • Addition of static surfaces straightforward • Method is grid independent • Surface ‘leaves’ calculation domain through a periodic boundary •  Surface re-enters on other side • Each time step (multiple) collisions between molecules and moving and stationary surfaces are calculated • DSMC Time step related to tmct as well as vb Moving sufaces in DSMC

  13. Implementation moving surfaces x = vb· t · · · · · = collision with moving surface · = no collision with moving surface · · Moving sufaces in DSMC

  14. Validation case 1: Piston flow (2D) Moving sufaces in DSMC

  15. Case 1: Piston flow (2D) Periodicbc Averaged in time, all molecules get speed vblade h Symmetric bc Symmetricbc Periodicbc • Kn = /h = 0.03; Re << 2000 • Analytical solution: Moving sufaces in DSMC

  16. Validation case 2: Plane Couette flow (2D) Moving sufaces in DSMC

  17. Case 2: Plane Couette flow (2D) U = Uw Ttop d Tbottom y x Moving sufaces in DSMC

  18. Method A Method B Uw Uw Case 2: Plane Couette flow (2D) Moving sufaces in DSMC

  19. Case 2: Plane Couette flow (2D) Post-processing artifact Sharipov ea. – Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number, J. Mech. B 23 (2004)Sone ea. – Numerical analysis of the plane Couette flow of a rarefied gas on the basis of …, J. Mech. B 9 (1999) Moving sufaces in DSMC

  20. Validation case 3: TMP rotor (3D) Moving sufaces in DSMC

  21. Case 3: TMP rotor (3D) Gas flow or compression Moving sufaces in DSMC

  22. Case 3: TMP rotor (3D) More details VT-TuM1 (Tomorrow 8am) T. Sawada, M. Suzuki, O. Taniguchi – The axial flow molecular pump, 1st report, on a rotor with a single blade row, Bulletin JSME Moving sufaces in DSMC

  23. Case 3: TMP rotor (3D) • DSMC results compare well with earlier results • T. Sawada, M. Suzuki, O. Taniguchi – The axial flow molecular pump, 1st report, on a rotor with a single blade row, Bulletin JSME • J.S. Heo & Y.K. Hwang – DSMC calculation of blade rows of a turbo molecular pump in the molecular and transitional flow regions, Vacuum 56 (2000) • S. Wang & H. Ninikota - A Three-Dimensional DSMC Simulation of Single-Stage Turbomolecular Pump Adopting Accurate Intermolecular Collisions Models, Journal of Fluid Science and Technology 1 (2006) • Method can be used to simulate rotor-stator assemblies Moving sufaces in DSMC

  24. Conclusions and future developments • Algorithm developed to simulate moving surfaces with constant speed • Results validated against well known cases • Piston flow • Plane Couette Flow (Isothermal) • TMP rotor blade (2D & 3D) • Next steps • Quantitative validation for more complex cases, such as rotor-stator assembly and complete TMP • Implementations on request (Accelerating/decelerating surfaces, rotational velocities etc) • Case studies Moving sufaces in DSMC

  25. Thank you for your attention Richard.Versluis @ tno.nl Marcel.Roos @ tno.nl Moving sufaces in DSMC

  26. Spare slides Moving sufaces in DSMC

  27. Plane Couette flow settings • 2 dimensional • Periodic BC • Isothermal (Ttop = Tbottom) • Laminar flow (Re = 0.006 … 6) • Low Ma number (Ma = 0.33 with Ma = Uwall / Usound) • Full accomodation (a=1), no sticking (g=0) • VSS collision model • Helium Moving sufaces in DSMC

  28. Case 3: TMP rotor (3D) periodic bc periodic bc fixed pressure moving element periodic bc zero flow periodic bc periodicbc periodic bc Moving sufaces in DSMC

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