Large Scale Simulation of Cloud Cavitation Collapse Ursula - PowerPoint PPT Presentation

4th Cavitation Workshop Crete, 30 May - 1 June 2016 Large Scale Simulation of Cloud Cavitation Collapse Ursula Rasthofer with: Fabian Wermelinger, Jonas Sukys, Diego Rossinelli, Panagiotis Hadjidoukas, Petros Koumoutsakos CSE lab Computational Science & Engineering Laboratory http://www.cse-lab.ethz.ch

Outline 1. Motivation 2. Cubism-MPCF 3. Modeling Approach and Governing Equations 4. Simulations 5. Conclusions 2

Outline 1. Motivation 2. Cubism-MPCF 3. Modeling Approach and Governing Equations 4. Simulations 5. Conclusions 3

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 4

Cloud Cavitation Collapse www.amc.edu.au • Thousands of bubbles • Cloud dynamics dominated by bubble interactions ‣ Experiments ‣ Theory - based on Rayleigh-Plesset equation or similar relations esource.alstrbology.com - usually assume spherical bubbles ‣ Simulations - Lagrangian approaches for bubbles - fully resolved bubbles usually restricted to small www.jotformeu.com clouds (~100 bubbles) 5

120 Collapsing Bubbles (TUM) Bubbles = 120 Np = 1.2E+08 Tw = 29.9 CSElab : 15E+03 Bubbles , Np = 1.3E+13 , Tw = 1.8 6

Outline 1. Motivation 2. Cubism-MPCF 3. Modeling Approach and Governing Equations 4. Simulations 5. Conclusions 7

Cubism-MPCF • compressible multicomponent flow solver [Rossinelli et al. 2013] • 3D structured-grid finite volume solver - m s b i u C MPCF b • a wavelet-based compression of simulation data E l S C 8

Finite Volume Method • conservation-law form U i ∂ U ( x , t ) + r · F ( U ) = 0 U i+1 ∂ t F i-1/2 F i+1/2 U i-1 U = ( α 1 ρ 1 , α 2 ρ 2 , ρ u, ρ v, ρ w, E ) T h c i-1 c i c i+1 • cell-average values x i-1/2 x i+1/2 U ijk ( t ) = 1 Z U ( x , t )d Ω c h 3 Ω c • semi-discrete form d U ijk ( t ) + 1 ⇣ ⌘ 2 + F y 2 − F y F x 2 − F x 2 + F z 2 − F z = 0 i + 1 i − 1 k + 1 k − 1 j + 1 j − 1 d t h 2 9

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] 10

Software Layout computational domain www.cscs.ch subdomain www.alcf.anl.gov Cluster Node Core block grid cell • cluster (MPI) • node (OpenMP) • core (SIMD): WENO, HLLC 11

Performance and Comparison 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 - (TUM) 1.2 E08 - 0.15K bubbles (TUM) - (Stanford) 0.4 E13 - turbulence (Stanford) 12

Outline 1. Motivation 2. Cubism-MPCF 3. Modeling Approach and Governing Equations 4. Simulations 5. Conclusions 13

Numerical Challenges • O(100) to O(10 4 ) bubbles • broad range of length and time scales • complex interface evolution due to bubble-bubble interactions • high density ratios O(10 3 ) • surface-tension effects • coupling of gas and nearly- incompressible liquid • secondary cavitation 14

Modeling Strategies single-fluid two-fluid mixture models models approches Lagrangian/Eulerian e.g., thermodynamic e.g., diffuse interface methods, e.g., based equilibrium cavitation methods on level-set description model computational efficiency complexity/fidelity 15

Di ff use Interface Method • based on two-fluid model with 7 equations [Baer & Nunziato 1986, Saurel & Abgrall 1999] - mass, momentum, energy conservation for each phase - additional topological equation for interface • reduced to 5-equation model by asymptotic analysis in limit of zero relaxation time (velocity and pressure equilibrium at interfaces) [Kapila et al. 2001, Allaire et al. 2002, Murrone & Guillard 2005, ….] 16

Governing Equations ∂α 1 ρ 1 + r · ( α 1 ρ 1 u ) = 0 ∂ t ∂α 2 ρ 2 + r · ( α 2 ρ 2 u ) = 0 ∂ t ∂ ( ρ u ) + r · ( ρ u ⌦ u + p I ) = 0 ∂ t ∂ E ∂ t + r · (( E + p ) u ) = 0 O(h) ∂α 2 ∂ t + u · r α 2 = K r · u where K = α 1 α 2 ( ρ 1 c 2 1 − ρ 2 c 2 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, …] 17

Thermodynamic Closure • stiffened equation-of- p k = ( γ k − 1) ρ k e k − γ k p c ,k state (EoS) for pure fluids [Menikoff & Plohr 1989, …] ρ = α 1 ρ 1 + α 2 ρ 2 • mixture relations ρ e = α 1 ρ 1 e 1 + α 2 ρ 2 e 2 • pressure equilibrium p=p k • mixture speed of sound 1 ρ c 2 = α 1 + α 2 ρ 1 c 2 ρ 2 c 2 1 2 [Wood 1930] 18

Further Variants • source term of gas-volume-fraction equation neglected • mixture mass conservation • equation-of-state must be valid in all flow regions (pure fluids and artificial mixing zone) ∂ρ [Shyue 1998, Johnsen & Colonius 2006,…] ∂ t + r · ( ρ u ) = 0 ∂ ( ρ u ) + r · ( ρ u ⌦ u + p I ) = 0 ∂ t ∂ E ∂ t + r · (( E + p ) u ) = 0 ∂φ ∂ t + u · r φ = 0 where φ 2 { Γ , Π } and α 1 ρ 1 c 2 γ 1 − 1 + α 2 ρ 2 c 2 1 2 1 ρ c 2 = γ 2 − 1 γ p c Γ = and Π = γ − 1 . α 1 α 2 γ − 1 γ 1 − 1 + γ 2 − 1 19

Model Properties ���� ������� ��� ���� ��� • non-monotonic speed of sound with ���� ���� ���� respect to gas volume fraction ���� � ��� ��� ��� ��� � � ��� ��� ��� ��� � � � • right-hand-side term of gas volume α 1 α 2 ( ρ 1 c 2 1 � ρ 2 c 2 2 ) r · u fraction equation α 1 ρ 2 c 2 2 + α 2 ρ 1 c 2 1 - increase of gas volume fraction across rarefaction waves - decrease of gas volume fraction across compression waves 20

Key Issue I: Negative Pressure • High Pressure Ratios ��� � • Large Clouds ��� ��� - amplification of waves due to ��� � ��� �� ���� ��� many bubble layers � ���� ‣ high peak pressures in cloud ���� ���� resulting in strong rarefaction in ���� � � � � � �� �� �� �� � ���� cloud interior 21

Key Issue I: Negative Pressure p k = ( γ k − 1) ρ k e k − γ k p c ,k • effects of choice for EoS for pure fluids negative pressure in liquid due to stiffened EoS - - tensile stresses appearing as negative pressure regions due to strong rarefaction waves - indications of secondary cavitation? - other? Note: Negative pressures also observed by other groups (private communication) 22

Negative Pressure - Remedies? • right-hand-side term of gas volume fraction equation - dynamic creation of interfaces by mechanical relaxation if small portion of gas available [Saurel et al. 2008] ∂ t + u · r α 2 = α 1 α 2 ( ρ 1 c 2 1 � ρ 2 c 2 2 ) ∂α 2 r · u α 1 ρ 2 c 2 2 + α 2 ρ 1 c 2 1 • integration of mass transfer directly enabled by separate continuity equation for each fluid [Saurel et al. 2008] 23

Cavitation Tube - Setup • two diverging rarefaction waves in water with small amount of air volume fraction content stationary contact wave t rarefaction wave rarefaction wave W L W R x • initial conditions (1150 . 0 kg / m 3 , − 100 . 0 m / s , 1 . 0 · 10 5 Pa , 1 . 0 · 10 − 2 ) ( for 0 m ≤ x ≤ 0 . 5 m ( ρ , u, p, α 2 ) 0 = (1150 . 0 kg / m 3 , 100 . 0 m / s , 1 . 0 · 10 5 Pa , 1 . 0 · 10 − 2 ) for 0 . 5 m < x ≤ 1 . 0 m 24