Fluid-Structure Interaction Calculations With Breakage and Dust

1. Fluid-Structure Interaction Calculations With Breakage and Dust Rainald Löhner, Joseph D. Baum, Orlando A. Soto and Fumiya Togashi Center for Computational Fluid Dynamics SPACS, George Mason University, Fairfax, VA, USA SAIC, McLean, VA, USA cfd.gmu.edu/~rlohner www.scs.gmu

2. Overview • Motivation / Applications Targeted • Particle/Flow Interaction • Examples • Shock/Dust Interaction • Conclusions and Outlook

3. Motivation/Applications Targeted

4. Motivation/Applications Targeted • Fine Particles • Suspensions • Dust • Mist/Droplets • Enhancement of Combustion • Aluminum in Solid Rocket Motors • Shock/Dust Interaction

5. Adapted CFD mesh and Pressure Contours at 125 ms Pressure Contours, t=244 ms CSD Velocity, t=244 ms Cased Weapons

6. Basic Phenomena a) Detonation/Fragmentation b) Fragment Transport c) Frags Hit/Pulverize Walls d) Dust/Shock Interaction

7. Physics

8. Physics • Eulerian • Treat As Dilute Phase • Concentration: Transport (Advection, Diffusion, Reaction) Eqns. • Lagrangian • Treat As `Particle in Fluid’ • Individual (or Group): Movement, Evaporation, Heat, …Eqs. • Focus Here: Lagrangian Treatment

9. Flow: Euler/Navier-Stokes Equations

10. Momentum Transfer • Drag Force of Each Particle • Drag Coefficient and Reynolds-Number

11. Heat Transfer • Heat Flux For Each Particle • Film Coefficient, Nusselt- and Prandtl-Number

12. Numerics

13. Conservation Laws… • Conservation Law: • Galerkin FEM: • Consistent Numerical Flux: • k-Step Runge-Kutta Scheme:

14. Particle Motion and Temperature (1) • Velocity and Position • Temperature • Integrated Explicitly; 4th Order Runge-Kutta

15. Particle Motion and Temperature (2) • Position, Velocity and Temperature: • Integrated Explicitly; Typically: 4th Order Runge-Kutta

16. Particle Tracking • Need: Flow Variables At Location of Particle •  Need Host Element for Each Particle • Initialization: Bins + Near-Neighbour Search • Incremental: Near-Neighbour Search • Vectorized and Parallelized for OMP • Also Running in MPI

17. Walls: Boundary Conditions • Walls: Bouncing, Sticking, Gliding, … • Embedded Surfaces Bouncing Sticking Gliding

18. Numerical Issues (1) • Suppose: Very Small Particle • Low Re-Nr  High Relative Drag • Drag: ~ r2 • Mass: ~ r3 • Large CFD Timestep •  In One Timestep, Velocity Can Exceed Flow Veloc •  Physically Wrong (!) • Solutions: • Substepping (Expensive, Load Balance Issues) • Limiting

19. Numerical Issues (2) • Suppose: Very Small Particle • Low Nu-Nr  High Relative Heating • Heat Flux: ~ r2 • Heat Capacity: ~ r3 • Large CFD Timestep •  In One Timestep, Temperature Can Exceed Flow Temp •  Physically Wrong (!) • Solutions: • Substepping (Expensive, Load Balance Issues) • Limiting

20. Numerical Issues (3) • Assume 1-D: Difference in Velocities at tn: Δvn = vf - vnp • If Δvn > 0 : Δvn+1 ≥ 0 • If Δvn < 0 : Δvn+1 ≤ 0 • Same Applies to Temperatures • Imposed at Every Runge-Kutta Stage

21. Particle-Flow Interaction • Change in Momentum for 1 Particle • Change in Energy for 1 Particle • Multiply By Number of (True) Particles in Packet

22. Particle-Flow Interaction • Need: • Conservative Transfer of Mass, Momentum and Energy •  Use Shape-Functions to Project Mass, Momentum and Energy Increments to Flow Grid Ni

23. Accurate Flow  Particle ; Particle  Flow • Need Sufficient Particles Per Element •  Split Up Particles If Too Few/Element Size Increases •  Agglomerate Particles If Too Many in One Element •  Refine Mesh If Too Many Particles in One Element

24. Numerical Issues (1) • Suppose: Very Heavy / Large / Many Particles • Outside Limits of Theory, But Sometimes Encountered In Runs • Large CFD Timestep •  In One Timestep, Force Exerted By Particles May Lead To Flow Velocity That Exceeds Particle Velocity •  Physically Wrong (!) • Solutions: • Substepping  Expensive, Reduction of Timestep • Limiting  Non-Conservative

25. Numerical Issues (2) • Suppose: Very Heavy / Large / Many Particles • Outside Limits of Theory, But Sometimes Encountered In Runs • Large CFD Timestep •  In One Timestep, Energy Flux From Particles May Lead To Flow Temperatures That Exceeds Particle Temperature •  Physically Wrong (!) • Solutions: • Substepping  Expensive, Reduction of Timestep • Limiting  Non-Conservative

26. Numerical Issues (3) • Add Momentum/Energy From Particles • Compare Velocities/Temperatures • Limit to Physically Reasonable Values • Add to Source-Terms

27. Particle Contact (1) • Volume of np Particles: •  Equivalent Radius: • Overlap Distance: • Average Overlap Distance of Particles:

28. Particle Contact (2) • Define Unit Normal: • Define Tangential Direction from Velocity:

29. Particle Contact (3) • Normal and Tangential Forces • Limit Tangential Force to Avoid Reversal of Velocities • Add Velocity-Based Damping Force in Normal Direction • Limit:

30. Particle Contact (4) • Complete Force: • Estimation of Contact Stiffness: • Assume Particle At Rest in Incoming Flow • Another Particle Behind • Penetration Factor ξ

31. Particle Contact (5) • Spatial Neighbour Information Options: • Bins • Octrees • Element Neighbour Lists • Used Here: Bins

32. Particles and MPI

33. 1 Layer of Overlap Ω1 Ω2 Particles and MPI (1) • Approach Based on Passing Particle Info Across Overlapping Elements • If Mesh Is Changed/Read In: • Obtain All Elements That Overlap Domains • Order Border Elements According to Communication Schedule

34. Particles and MPI (2) • For Each Timestep: • Obtain Particles in Each Element • For Each Exchange Pass: • From List of Border Elements: Get Particles That Need to be Sent to Neighbouring Domain • Exchange Info Of How Many Parts Sent/Received • Exchange (Send/Receive) Particles

35. Particles and MPI (3) • Duplicate Particles: • Reason: CFL < 1 • Best Solution: Universal Unique Number • Integer Filter of Duplicate Particles • Particles With Same Location • Reason: Flow Physics, Geometric Singularities (e.g. Corners) • Best Solution: Traverse Elements, Remove/Separate Particles With Same Location

36. Particles and MPI (4) • Further Improvements: • Extensive OMP Parallelization of Particle Subs/Modules • Extensive Timing/Optimization of All Particle Subs/Modules • Improvements in MPI Send/Receive Modules • Before Improvements: 2-3 Min/Timestep • After Improvements: 2-3 Seconds/Timestep

37. Link to CSD

38. CSD to Particles (1) CSD CSD Faces Passed to CFD CFD CFD Before Failure After Failure

39. CSD to Particles (2) • Model Pulverization • Main Steps • Take Failed CSD Element (Hexahedron, Tetrahedron) • Pass These to CFD via FEMAP • User Specifies Particle Size/Density/… Distribution • Initial Velocity of Particles • From CSD • From Experimental Evidence [Can Be O(400-100 m/sec)] • CFD Updates Flowfield and Particles

40. Examples

41. WEPACT-4

42. WEPACT-4 Initial Conditions The air in z >0: p = 1.01E6 dynes/cm2 and T = 15.15 °C = 288.3 °K. The air in z < 0: p = 4000 psi = 2.7579E8 dyne/cm2 and T = 1430.6 °K. Z>250cm: filled with air and dust (0.1g/cc) Dust particle: 2.3g/cc, D=100mm

43. Computed Gas Density & Velocity

44. Computed Gas Pressure & Mach-Nr.

45. Computed Gas Energy & Temperature

46. Computed Dust Density & Velocity

47. 3D Plot of Dust Density Profile Dust Density x Time

48. Movies – Gas Velocity & Dust Velocity

49. WEPACT-5

50. WEPACT-5 Initial condition 430cm > Z >250cm: filled with air and dust (0.1g/cc) Dust particle: 2.3g/cc, D=100mm