ICCS 2017 Zurich, June 11 - 14, 2017 Large Scale Simulation of Cloud Cavitation Collapse Ursula Rasthofer with: Fabian Wermelinger, Panagiotis Hadjidoukas, Petros Koumoutsakos CSE lab Computational Science & Engineering Laboratory http://www.cse-lab.ethz.ch
Power of Cavitation extracted from: Bazan-Peregrino et al. , Cavitation-enhanced http://www.forddoctorsdts.com delivery of a replicating oncolytic adenovirus to tumors using https://de.wikipedia.org/wiki/Kavitation focused ultrasound , Journal of Controlled Release Volume 169, Issues 1–2, 2013, 40-47 engineering Extracorporeal_shock_wave_lithotripsy http://www.forddoctorsdts.com biomedical https://en.wikipedia.org/wiki/ applications nature herve.cochard.free.fr extracted from: Brennen, Hydrodynamics of pumps, Oxford University Press, 1994 https://de.wikipedia.org/wiki/ Knallkrebse 2
Cloud Cavitation Collapse www.amc.edu.au • thousands of bubbles • cloud dynamics dominated by bubble-bubble interactions ‣ experiments - challenging high frequencies and microscopic length scales - risk of damage ‣ theory esource.alstrbology.com based on Rayleigh-Plesset-like equations - spherical bubbles usually assumed - ‣ simulations - Lagrangian approaches for bubbles fully resolved bubble clouds usually - restricted to small clouds www.jotformeu.com 3
Outline • Computational Approach • Simulations • Conclusions 4
Outline • Computational Approach • Simulations • Conclusions 5
Modeling Strategies single-fluid two-fluid mixture models models approches Lagrangian methods as e.g., thermodynamic well as Eulerian e.g., diffuse interface equilibrium cavitation methods, e.g., based methods model on level-set description computational efficiency complexity/fidelity 6
Di ff use Interface Method ∂α 1 ρ 1 + r · ( α 1 ρ 1 u ) = 0 ∂ t ∂α 2 ρ 2 FLUID 1 + r · ( α 2 ρ 2 u ) = 0 ∂ t ∂ ( ρ u ) + r · ( ρ u ⌦ u + p I ) = 0 ∂ t ∂ E I N ∂ t + r · (( E + p ) u ) = 0 T E R ∂α 2 F A ∂ t + u · r α 2 = K r · u C E O(h) where K = α 1 α 2 ( ρ 1 c 2 1 − ρ 2 c 2 2 ) FLUID 2 α 1 ρ 2 c 2 2 + α 2 ρ 1 c 2 1 and [Kapila et al. 2001, Murrone & Guillard 2005, Saurel et al. α 1 + α 2 = 1 2009, Tiwari et al. 2013, …] 7
Godunov-Type Finite Volume Method • reformulation of gas-volume- α 2 ρ 1 c 2 ∂α 2 1 ∂ t + r · ( α 2 u ) = r · u fraction equation α 1 ρ 2 c 2 2 + α 2 ρ 1 c 2 1 [Johnsen & Colonius 2006] W R U i • high-order reconstruction of U i+1 F i-1/2 F i+1/2 W L face values of primitive U i-1 h variables using WENO3/5 c i-1 c i c i+1 [Liu et al. 1994, Jiang & Shu 1998] x i-1/2 x i+1/2 • approximate HLLC Riemann y solver for flux reconstruction U 1 c [Toro et al. 1994] r U L* U 2 s • low-storage 3rd-order Runge- U R* U - U + Kutta scheme for time x discretization [Gottlieb e t al. 2001] 8
�������������������������� Cubism-MPCF • compressible multicomponent flow solver tailored to HPC systems [Rossinelli et al. 2013, P . E. Hadjidoukas et al. 2015] • 3D Cartesian-grid finite volume solver • wavelet-based compression of simulation data TIME TO SOLUTION (no I/O) PFLOPS (% Peak) T w = 1.8 14.4 PFLOPS (72%) T w = 29.7 (TUM) 0.1 - 3% (TUM) T w = 16.3 - 39.0 (Stanford) 1.3 - 6.4% (Stanford) I/O COMPRESSION SIZE 10-100X 1.3 E13 - 15K bubbles - 1.2 E08 - 0.15K bubbles (TUM) - 0.4 E13 - Turbulence (Stanford) 9
Cubism-MPCF: Software Layout www.cscs.ch www.alcf.anl.gov computational domain www.fz-juelich.de Cluster Node subdomain Core block • cluster (MPI) grid cell • node (OpenMP) • core (SIMD): WENO, HLLC 10
Node and Cluster Layer • OpenMP parallelization dynamic work scheduling - 1 thread exclusively processes 1 block - node i-1 node i node i+1 • MPI parallelization non-blocking P2P communication for ghost blocks - communication time ~ O(time for processing 1-2 blocks) - 11
Core Layer • block-based memory layout increases spatial locality - • instruction and data level parallelism explicit vectorization - code fusion techniques - • temporal locality ring buffers for active data slices, e.g., in - WENO, HLLC 12
Outline • Computational Approach • Simulations • Conclusions 13
Cloud Setup R B R C y d G r B R B x z • gas-volume fraction • cloud generation n B 1 X R 3 locations: random - α = B ,i R 3 C i =1 - radii: constant or random • cloud interaction parameter ✓ R eq • collapse driven by increase ◆ 2 β = α of ambient pressure R avg 14
50K Bubbles, 64 Billion Cells 25K time steps, 72h x 32K cores 15
Micro-Jet Formation • due to pressure gradient along interface • directed toward cloud center 12 8 4 0 y − 4 − 8 − 12 − 12 − 8 − 4 0 4 8 12 x 16
Bubble Reconstruction Γ int ( t ) = { x ∈ Ω | α 2 ( x , t ) = 0 . 5 } Ψ = 1 . 00 φ = 1 . 00 α 2 > 0 . 5 α 2 < 0 . 5 ⌘ 2 Ψ = 0 . 96 ⇣ 3 1 2 V B 6 π φ = 0 . 98 sphericity Ψ = S B φ = V B porosity V h B Ψ = 0 . 60 φ = 0 . 67 17
Sphericity and Porosity 1 1 φ Ψ increasing cloud interaction parameter 0 . 99 0 . 99 1 1 0 . 98 0 . 99 φ Ψ 0 . 96 0 . 98 1 1 0 . 80 0 . 90 φ Ψ 0 . 60 0 . 80 0 0 . 2 0 . 4 0 . 6 0 . 8 1 0 0 . 2 0 . 4 0 . 6 0 . 8 1 t/t C t/t C 18
Keller-Miksis Equation for Clouds • spherical bubble collapses assumed • weakly compressible liquid flow • extended form including bubble translation ! ! ! ˙ ˙ ˙ 3 B i = 1 d t ( p B i − p 1 ) + 1 d R B i R B i R B i ( p B i − p 1 ) + R B i R B i ¨ ˙ R 2 x 2 1 − R B i + 1 + 4 ˙ 2 − B i 2 c 1 c 1 c 1 ρ 1 c 1 ρ 1 radius n B " R 2 1 ⇣ ⌘ ⇣ ⌘ B j B j ¨ R B j + 2 R B j ˙ x B j + ˙ x B i + 5 ˙ X R 2 R 2 � � + R B j ¨ R B j ˙ R B j ˙ x B i − x B j x B j − · B j 2 d 3 d ij ij j =1; j 6 = i !# R 3 � ˙ � ˙ � ˙ + 3 B j � � � �� � � � � ˙ x B i + 2 ˙ x B i + 2 ˙ x B j · x B j x B j · x B j − x B i x B i − x B j x B j − · 4 d 3 d 2 ij ij N " 1 1 � ⇣ ⌘ x B i + ˙ X B j ¨ R B j + 2 R B i R B j ˙ B j + ˙ R B i ˙ R B i R 2 R 2 R B j R 2 � 3 R B i ¨ R B i ˙ x B i = x B i − x B j B j d 3 ij j =1; j 6 = i position R 2 ⇣ ⇣ ⌘ ⌘ B j R B i R B j + 5 R B i ˙ ˙ R B i R B j ¨ x B j + ˙ R B j x B j − 2 d 3 ij ◆!# 3 R 2 ✓ ⇣ ⌘ B j R B i R B j + 5 R B i ˙ ˙ � � � � + R B i R B j ¨ x B j + ˙ R B j x B i − x B j x B i − x B j x B j · 2 d 5 ij ◆ 3 γ 2 ✓ R B i (0) p B i = p B i (0) R B i 19 [Keller & Miksis 1997, Mettin et al. 1997, Doinikov 2004]
Bubble Radius increasing cloud interaction parameter 0 . 8 0 . 8 0 . 8 A A A 0 . 7 0 . 7 0 . 7 R B [mm] R B [mm] R B [mm] C C C 0 . 6 0 . 6 0 . 6 B B B 0 . 5 0 . 5 0 . 5 0 10 20 30 40 50 0 20 40 60 0 20 40 60 80 t [ µ s] t [ µ s] t [ µ s] • A: center-most solid: 3D simulations • • B: closest to R C /2 dashed: without bubble translation (KM) • • C: outer-most dash-dot-dot: with bubble translation (DK) • • increasing deviations with increasing cloud interaction parameter, in particular, if bubble translation is neglected 20
Large-Scale Cloud • 12500 air bubbles in water • p C = 1 bar • p ∞ = 10 bar • cloud radius: 45 mm • average bubble radius: 0.69 mm • gas-volume faction: 5% • cloud interaction parameter: 28 21
Cloud Collapse p S V 2 p S,max V 2 (0) 1 0 . 8 0 . 6 0 . 4 0 . 2 0 0 100 200 300 400 t [ µ s] 22
Collapse Wave simulation Morch model 0 . 6 u W [km / s] 0 . 4 0 . 2 0 0 50 100 150 200 250 300 t [ µ s] • Morch model: collapse wave in cloud of vapor bubbles R 2 = − p ∞ − p vapor R !! 2 (1 − γ )(1 − α C )) ! R + ( 3 2 − 1 [Morch 1989] ρ liquid α C 23
Erosive Potential • pits: plastic deformations in simulation fit form of small indents probability density function of coverage rate cumulative impact rate • due to impulsive load 10 5 cm 2 s ] generated by bubble collapses 1 10 4 cpr [ shell 1 shell 2 10 3 shell 3 0 1 2 3 4 d P [mm] shell 1 shell 2 shell 3 · 10 4 8 1 6 cm s ] 3 pcr [ 1 2 4 2 0 0 1 2 3 4 d P [mm] 24
Outline • Computational Approach • Simulations • Conclusions 25
Summary & Outlook • diffuse interface method and Cubism-MPCF ✓ important to account for gas expansion and compression in interface ✓ compressible multicomponent flow solver capable of processing up to 7x10 11 cells per second • HPC for collapsing clouds with up to 50K bubbles ✓ comparison with bubble-particle approaches ✓ insights into induced pressure and velocity fields, wave dynamics, bubble shape evolution as well as erosive potential ➡ integration of mass transfer and application to turbulent cavitating flow 26
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