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## Mark Stockmyer October 5, 2007

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**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.**Acknowledgments**• Dr. Hossein Saiedian • Dr. Arvin Agah • Dr. Xue-Wen Chen • Dr. Travis Laker • Kristina Stockmyer • ONR – Office of Naval Research**Outline**• Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research**Outline**• Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research**China Lake – Naval Air Warfare Center: Weapons Division***• RDT&E: Research, Develop, Test, and Evaluate *http://www.nawcwpns.navy.mil**Energetics Development**• Energetics • Explosives • Rocket propellant • Fuzes • Igniters**Rocket Propellant**• Properties (Miller 1982) • Thrust • Smoke • Exhaust signature • Heat • Burn rate • Various rocket applications • How to optimize these properties?**Rocket Propellant (continued)**• Currently • Research chemist • Think up new formulations • Test out best candidates • Problems • Very expensive • Research community is limited**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**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**Outline**• Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research**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**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**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)**How Do You Measure Quality of Packing?**• Speed • Packing fraction • Randomness • Scalability**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**Packing Fraction**• How “dense” is the pack? • Relationship between • Volume of the particles • Volume of the empty container**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**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**Scalability**• How do the properties change as the number of particles change? • Speed • Packing fraction**Relation to Computer Science**• Modeling • Abstraction of reality • Data structures • Algorithm development • Algorithm analysis • Complexity analysis • Solving a real complex problem**Outline**• Problem • Significance • Methodology/Solution • Results/Evaluation • Conclusion • Further Research**How Do You Make a Rocket Motor? (Simplified)**• Get a rocket case • Pour in propellant • Attach exhaust nozzle Image from http://www.aerospaceweb.org/**What Does Propellant Look Like?**• Molecules of propellant • Essentially spheres Image from http://www.aerospaceweb.org/**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?**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**SGMP – Visualization**• Custom tool • Particle/Primitive system (Ebert 1996) • Demonstration**SGMP – Collision Calculations**• Calculated many, many times • Computationally expensive • Use neighbor lists to reduce number of checks**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)**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**Generate Neighbor List**• One-time complexity • O(n) • Compare one to all the rest • Total complexity (entire pack) • O(n2)**Downward Drop**• One-time complexity • O(1) • Constant drop distance • Total complexity (entire pack) • O(n)**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**Outline**• Problem • Significance • Methodology/Solution • Results • Evaluation • Conclusion • Further Research**SGMP Starting Arrangements**• Single Column • Small Dense • Large Dense • Loose Random • Number of particles tested • 150, 300, 750, 1002, 2001, 3000, 6000, 9000**SGMP – Single Column**• Single column of particles above control volume • Demonstration**Results – Single Column**• Packing fraction • 300 particles - 0.62 • 9000 particles - 0.60 • Speed • 9000 particles • 41424 seconds (~12 hours)**SGMP – Small Dense**• Densely packed starting grid • Only within the control volume • Demonstration**Small Dense – Results**• Packing fraction • 750 particles - 0.61 • 9000 particles - 0.60 • Speed • 9000 particles • 56337 seconds (~15 hours)**SGMP – Large Dense**• Densely packed starting grid • Within the expanded volume • Demonstration**Large Dense – Results**• Packing fraction • 9000 particles - 0.59 • Other packs were very similar • Speed • 9000 particles • 19699 seconds (~5.4 hours)