PREDICTIVE SIMULATION OF UNDERWATER IMPLOSION: Coupling Multi-Material Compressible Fluids with Cracking Structures

Transcription

1 PREDICTIVE SIMULATION OF UNDERWATER IMPLOSION: Coupling Multi-Material Compressible Fluids with Cracking Structures Kevin G. Wang Virginia Tech Patrick Lea, Alex Main, Charbel Farhat Stanford University Owen McGarity Naval Surface Warfare Center, West Bethesda

2 MOTIVATION Underwater explosion and implosion NUWC external air-backed volumes NSWC NUWC? p = P(d, r, EOS) TNT air burned gas submarine hull water Multi-Material Fluid-Structure Interaction with Dynamic Fracture

3 PROBLEM CHARACTERISTICS Implosive collapse of underwater structures p sensor fracture t large, plastic structural deformation fluid-induced fracture flow seepage multi-phase flow high compressions and shocks in water/air * multi-material FSI with fracture * courtesy of McGarity, O., NSWC Carderock

4 Euler fluid flows, + r : F( W ) = - water: stiffened gas or Tait EOS Impermeable fluid-structure interface v f. n = v s. n no-interpenetration -p n = s s. n equilibrium Free surface / immiscible fluids v L.n L = v R.n R, p L = + v : f r = (level-set) Lagrangian equations of motion ρ S 2 u j t 2 = x i MATHEMATICAL MODEL σ ij + σ im u j x m + b j, j = 1,2,3 - J 2 plasticity, piecewise linear hardening - strain based failure criteria air before fracture f-f interface water f-s interface air water after fracture determination of crack growth (J-H Song, 28)

5 MOVING/DEFORMING BOUNDARY Arbitrary Lagrangian-Eulerian (ALE) relatively simple treatment of material interfaces accuracy and numerical stability issues well understood lack of robustness with respect to large deformations cannot handle topological changes mesh motion computation can be expensive

6 MOVING/DEFORMING BOUNDARY Embedded / immersed boundary method - operates on fixed, non body-fitted CFD grids G - no interpenetration - equilibrium v f. n = v s. n -p n = s s. n dramatically simplifies mesh generation capable of large structural deformations and fracture interface needs to be tracked with respect to CFD grid enforcing the transmission conditions becomes tricky - various names: immersed, Cartesion, fictitious domain, etc.

7 FIVER: FINITE VOLUME METHOD WITH MULTI- MATERIAL RIEMANN SOLVERS The standard finite volume spatial discretization - Euler equations W t F( W ) - integrate over a control volume (C i ) W h d t C j nei ( i) C i ij F( W h ) n ij dg i C i C ij j - evaluate one numerical flux for each facet ( C ij ) i j F ( W ) n dg Roe( W, W, n, EOS) C ij h ij h h - special treatment is required near fluid-structure and fluid-fluid interfaces ij

8 Interface flux FLUID-STRUCTURE INTERFACE S E fluid 1 i j fluid 2 - <fluid 1, structure> : fluid-structure Riemann problem W i v s. n x i * Wang, Rallu, Gerbeau, Farhat 211

9 F-S RIEMANN PROBLEM One-dimensional, fluid-structure Riemann problem rarefaction p*, r*, u x = x(t) contact s discontinuity t not involved W n L p L, r L, u L i M ij j w t x = n w(x,) = W L, if x u(x(t), t) = u (M ij ) n G s no interpenetration transmission condition could also be a shock

10 Interface flux FLUID-STRUCTURE INTERFACE S E fluid 1 i j fluid 2 - <fluid 1, structure> : fluid-structure Riemann problem --> W i * - <fluid 2, structure> : fluid-structure Riemann problem --> W j * F (1) ij = Roe (W i, W i*, EOS (1) ) (fluid 1, structure) F (2) ij = Roe (W j, W j*, EOS (2) ) (fluid 2, structure)

11 * Farhat, Rallu and Rajas, 28 Interface flux FLUID-FLUID INTERFACE S E fluid 1 i j fluid 2 - <fluid 1, fluid 2> : two-phase fluid-fluid Riemann problem W j iw i j

12 Interface flux FLUID-FLUID INTERFACE S E i j fluid 1 fluid 2 - <fluid 1, fluid 2> : two-phase fluid-fluid Riemann problem --> W i * and W j * F (1) ij = Roe (W i, W i*, EOS (1) ) F (2) ij = Roe (W j, W j*, EOS (2) )

13 COMPUTATIONAL METHODS FOR FRACTURE Element deletion - robust modeling of fracture - widely used and understood by engineers and analysts - no negative effect on time step - no defined crack path - loss of mass, momentum, and energy

14 * J-H Song et al. (28) EXTENDED FINITE ELEMENT METHOD XFEM with the Phantom Node Formulation* - each cracked element is replaced by two elements with phantom nodes - the cracking path within each element is tracked by a local signed distance function (φ(x, t)) I c e Ω S {X e φ X, t = }

15 COMPUTATIONAL FRAMEWORK Fluid-structure coupled computational framework AERO-F FIVER - FV compressible flow solver - multi-material Riemann solvers - level-set equation solver - embedded boundary method DYNA FE CSD solver fracture method XFEM element deletion interface tracker load computer embedded fluid-structure interface reference: Wang et al. (211, 212), Farhat et al. (21, 212)

16 * Performed by S. Kyriakides et al. at University of Texas at Austin Experiment* UNDERWATER IMPLOSION - implosive collapse of submerged aluminum tube (air-backed) - increased water pressure until tube collapsed. Tube collapsed dynamically essentially under constant pressure (197. psi). pressure sensors specimen water tank after sensor signal

17 Simulation setup UNDERWATER IMPLOSION - water / thin shell / air, no fracture - modeled half of the tube length-wise (symmetry assumed) - CFD grid: 3.7M nodes, 2.1M tetrahedron elements (3 procs.) - structural model: 14K Belytschko-Tsay shell elements - stress-strain response measured by - J 2 -plasticity, piecewise linear hardening CFD domain 2D views FE structural model (shell elements)

18 UNDERWATER IMPLOSION Synchronized Output from Experiment and Simulation

19 pressure (psi) pressure (psi)

20 pressure (psi) pressure (psi)

21 pressure (psi) pressure (psi)

22 pressure (psi) pressure (psi)

23 pressure (psi) pressure (psi) not available due to limited camera frequency

24 pressure (psi) pressure (psi) not available due to limited camera frequency

25 pressure (psi) pressure (psi) not available due to limited camera frequency

26 pressure (psi) pressure (psi) not available due to limited camera frequency

27 pressure (psi) pressure (psi) not available due to limited camera frequency

28 pressure (psi) pressure (psi) not available due to limited camera frequency

29 pressure (psi) pressure (psi)

30 pressure (psi) pressure (psi)

31 pressure (psi) pressure (psi)

32 pressure (psi) pressure (psi)

33 pressure (psi) pressure (psi)

34 pressure (psi) pressure (psi)

35 pressure (psi) pressure (psi)

36 pressure (psi) pressure (psi)

37 pressure (psi) pressure (psi)

38 pressure (psi) pressure (psi)

39 UNDERWATER IMPLOSION Validation* pressure (psi) DT - p max I + I - DT + p min time (ms) characteristics of the pressure pulse Sensor No. p min (psi) DT - (ms) I - (psi-ms) p max (psi) DT + (ms) I - (psi-ms) 1 exp sim exp sim exp sim exp sim exp sim * Farhat, Wang, Kyriakides, et al. (213)

40 EXPLOSION AND IMPLOSION Underwater explosion and implosion - tapered T661-6 aluminum cylinder with 8 bulkheads - blast loading (TNT detonation) - fracture simulated by element deletion

41 PIPE FRACTURE DUE TO DETONATION Fracture of aluminum pipe driven by internal detonation detonation tube pressure gauge aluminum pipe (specimen) I beam detonation tube.89 mm notch pre-flawed aluminum pipe (specimen) Mylar diaphragm detonation wave 457 mm mm 916 mm clamp (torque applied) * Performed by J. Shepherd et al. at California Institute of Technology.

42 EXPERIMENTAL RESULT Crack propagation patterns

43 blast pressure (kpa) EXPERIMENTAL RESULT Blast pressure notch length series initial notch length (mm)

44 HIGH-FIDELITY SIMULATION MODEL Simulation setup - detonation modeled by the Chapman-Jouguet theory - three fluid materials: explosive gas (C 2 H 2 + O 2 ), detonation product, and water - CFD grid: 1.4M nodes, 8.5M elements(on 1~2 proc. cores) - CSD Model: 17K B-T shell elements; elasto-plastic - initial notch: 25.4mm / 38.1mm / 5.8mm / 63.5mm / 76.2mm

45 HIGH-FIDELITY SIMULATION MODEL Modeling the initial notch XFEM (212) element deletion (214) notch is modeled as an initial crack notch is modeled by shells with reduced thickness

46 A 2D cut-view SIMULATION RESULT with XFEM

47 Visualization of 3D result SIMULATION RESULT with XFEM

48 SIMULATION RESULT Structural deformation and stress with XFEM

49 FRACTURE RESPONSE Comparison of XFEM and element deletion - XFEM: curving in the same direction or opposite directions - element deletion: branching - all these propagation patterns are observed in XFEM, L= 25.4 mm XFEM, L= 38.1 mm ED, L= 38.1 mm

50 Peak overpressure (KPa) VALIDATION Peak blast pressure (L=38.1 mm) Experiment Simulation w/ XFEM Simulation w/ elem. del. slope = 1.5 KPa/mm 14 slope =.614 KPa/mm 12 1 slope =.96 KPa/mm Initial notch length (mm)

51 REFERENCES - Embedded boundary method K. Wang, A. Rallu, J-F. Gerbeau, and C. Farhat, Algorithms for Interface Treatment and Load Computation in Embedded Boundary Methods for Fluid and Fluid-Structure Interaction Problems, IJNMF. 67: (211). - Interface tracking K. Wang, J. Gretarsson, A. Main, and C. Farhat, Computational Algorithms for Tracking Dynamic Fluid-Structure Interfaces in Embedded Boundary Methods, IJNMF. 7: (212) - Staggered time integrators C. Farhat, A. Rallu, K. Wang and T. Belytschko, "Robust and Provably Second-Order Explicit-Explicit and Implicit-Explicit Staggered Time-Integrators for Highly Nonlinear Fluid-Structure Interaction Problems", IJNME, 84:73-17 (21) - 17 (21). - FIVER C. Farhat, J-F. Gerbeau, and A. Rallu, FIVER: A Finite Volume Method Based on Exact Two-Phase Riemann Problems and Sparse Grids for Multi-Material Flows with Large Density Jumps, JCP, 231: (212) - Validation for underwater implosion C. Farhat, K. Wang, A. Main, J.S. Kyriakides, K. Ravi-Chandar, L-H. Lea, and T. Belytschko, Dynamic Implosion of Underwater Cylindrical Shells: Experiments and Computations, IJSS, 5: (213)