Development and Analysis of a Gravity-Simulated Particle-Packing Algorithm for Modeling Optimized Rocket Propellants

1. Development and Analysis of aGravity-Simulated Particle-Packing Algorithm for Modeling Optimized Rocket Propellants Mark Stockmyer October 5, 2007 Approved for public release; distribution is unlimited.

2. Acknowledgments • Dr. Hossein Saiedian • Dr. Arvin Agah • Dr. Xue-Wen Chen • Dr. Travis Laker • Kristina Stockmyer • ONR – Office of Naval Research

3. Outline • Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research

4. Outline • Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research

5. China Lake – Naval Air Warfare Center: Weapons Division* • RDT&E: Research, Develop, Test, and Evaluate *http://www.nawcwpns.navy.mil

6. Energetics Development • Energetics • Explosives • Rocket propellant • Fuzes • Igniters

7. Rocket Propellant • Properties (Miller 1982) • Thrust • Smoke • Exhaust signature • Heat • Burn rate • Various rocket applications • How to optimize these properties?

8. Rocket Propellant (continued) • Currently • Research chemist • Think up new formulations • Test out best candidates • Problems • Very expensive • Research community is limited

9. Combinatorial Chemistry • Computer simulation • Input millions of random combinations • See what the results are • Used in drug synthesis (Furka 1995) • Very difficult • Not currently feasible for energetic materials • More complex than drugs

10. Steps to Combinatorial Chemistry • PEP (Propellant Equilibrium Program) • Optimizing version written last year at C/L • Determine internal structure of propellant (Knott, Jackson, & Buckmaster 2001) • Done, but slow • Simulate burning of the propellant • Still in progress; very slow

11. Outline • Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research

12. Packing: State of the Art • Physical simulation is difficult (Agarwal 2002) • Requires “plausible” motion • Momentum • Parallelization • In a word: Slow • CSAR (Center for Simulation of Advanced Rockets) (Knott et al. 2001) • Kinematic model • 100,000 particles • 64 processors • 100 hours

13. Kinematic Modeling Is Too Slow • Assembly algorithms are faster • Place particles in best location • Final location is fixed (sticky) • Get close to modeling reality • Without all the slowness • Problem: Can be algorithm specific • Too specific to be of use

14. What Is a Good Simulation?* • DOD method/modeling and simulation • Subject matter experts • Hierarchy of indicators • Weighting of indicators • Rule-based knowledge base *(Balci 2001)

15. How Do You Measure Quality of Packing? • Speed • Packing fraction • Randomness • Scalability

16. Speed • How long does it take? • 100 hours is too long • Faster the better • Target: 100,000 particles in a minute • 86,000 runs/processor/day • 1 Million runs in 12 days

17. Packing Fraction • How “dense” is the pack? • Relationship between • Volume of the particles • Volume of the empty container

18. High Density Packing Example

19. Medium Density Packing Example

20. Low Density Packing Example

21. How Dense Is Dense? • Ball bearing experiments (McGeary 1961) • Drop a few ball bearings in graduated cylinders • Shake and vibrate • Repeat until the cylinder is full • Final packing fraction: 0.625 • Kilgore and Scott (1969) • 0.6366 • Our target: 0.63

22. Randomness • Difficult to measure • Looking for patterns • How far are particles from one specific particle? • RDF (Radial Distribution Function) • Statistical tool • Can be used to measure particle relationships • Direct RDF example later

23. High Density – Patterns Evident

24. Scalability • How do the properties change as the number of particles change? • Speed • Packing fraction

25. Relation to Computer Science • Modeling • Abstraction of reality • Data structures • Algorithm development • Algorithm analysis • Complexity analysis • Solving a real complex problem

26. Outline • Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research

27. How Do You Make a Rocket Motor? (Simplified) • Get a rocket case • Pour in propellant • Attach exhaust nozzle Image from http://www.aerospaceweb.org/

28. What Does Propellant Look Like? • Molecules of propellant • Essentially spheres Image from http://www.aerospaceweb.org/

29. How Do Things Fall? • Gravity • Falling • Collision • How does a falling particle know where to go? • Simple to the human eye • How do I create an algorithm to do the same thing?

30. SGMP: Spin Gap Move Protocol • Move a particle downward until there’s a collision • Spin - Move the particle in a circle • Gap - Find out where there’s no collision • Move - Move the particle in the direction of non- collision

31. SGMP – Visualization • Custom tool • Particle/Primitive system (Ebert 1996) • Demonstration

32. SGMP – Collision Calculations • Calculated many, many times • Computationally expensive • Use neighbor lists to reduce number of checks

33. SGMP– Neighbor Lists* • Find a small number of particles • The neighbors • Near the object particle • List will always contain fixed (or less) number of particles • Around 10-20 • A computationally expensive process *(Torquato 2002)

34. SGMP – Complexity • Specify all possible computations (Hartmanis and Hopcroft 1971) • Repeated steps • Generate neighbor list • Downward drop • Circular sweep • Find largest gap • Move particle into gap • Sweep, Gap, and Move can be grouped

35. Generate Neighbor List • One-time complexity • O(n) • Compare one to all the rest • Total complexity (entire pack) • O(n2)

36. Downward Drop • One-time complexity • O(1) • Constant drop distance • Total complexity (entire pack) • O(n)

37. Spin, Gap, and Move • One-time complexity • O(1) • Remember, fixed # of particles in the neighbor list • Total complexity (entire pack) • O(n log(n)) • n – all particles • log(n) – cross section of pack • Example

38. Why log(n)?

39. Outline • Problem • Significance • Methodology/Solution • Results • Evaluation • Conclusion • Further Research

40. SGMP Starting Arrangements • Single Column • Small Dense • Large Dense • Loose Random • Number of particles tested • 150, 300, 750, 1002, 2001, 3000, 6000, 9000

41. SGMP – Single Column • Single column of particles above control volume • Demonstration

42. Results – Single Column • Packing fraction • 300 particles - 0.62 • 9000 particles - 0.60 • Speed • 9000 particles • 41424 seconds (~12 hours)

43. Results – Single Column

44. Results – Single Column

45. SGMP – Small Dense • Densely packed starting grid • Only within the control volume • Demonstration

46. Small Dense – Results • Packing fraction • 750 particles - 0.61 • 9000 particles - 0.60 • Speed • 9000 particles • 56337 seconds (~15 hours)

47. Small Dense -- Results

48. SGMP – Large Dense • Densely packed starting grid • Within the expanded volume • Demonstration

49. Large Dense – Results • Packing fraction • 9000 particles - 0.59 • Other packs were very similar • Speed • 9000 particles • 19699 seconds (~5.4 hours)

50. Large Dense -- Results