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.

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Acknowledgments

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

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Outline

• Problem• Significance• Methodology/Solution• Results/Evaluation• Conclusion• Further Research

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Outline

Problem• Significance• Methodology/Solution• Results/Evaluation• Conclusion• Further Research

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China Lake – Naval Air Warfare Center: Weapons Division*• RDT&E: Research, Develop, Test, and

Evaluate

*http://www.nawcwpns.navy.mil

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Energetics Development

• Energetics– Explosives– Rocket propellant– Fuzes– Igniters

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Rocket Propellant

• Properties (Miller 1982)– Thrust– Smoke– Exhaust signature– Heat– Burn rate

• Various rocket applications• How to optimize these properties?

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Rocket Propellant (continued)

• Currently– Research chemist– Think up new formulations– Test out best candidates

• Problems– Very expensive– Research community is limited

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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

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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

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Outline

• Problem

Significance• Methodology/Solution• Results/Evaluation• Conclusion• Further Research

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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

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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

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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)

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

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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

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Packing Fraction

• How “dense” is the pack?• Relationship between

– Volume of the particles– Volume of the empty container

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High Density Packing Example

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Medium Density Packing Example

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Low Density Packing Example

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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

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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

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High Density – Patterns Evident

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Scalability

• How do the properties change as the number of particles change?– Speed– Packing fraction

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Relation to Computer Science

• Modeling– Abstraction of reality

• Data structures• Algorithm development• Algorithm analysis• Complexity analysis

• Solving a real complex problem

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Outline

• Problem• Significance

Methodology/Solution• Results/Evaluation• Conclusion• Further Research

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How Do You Make a Rocket Motor? (Simplified)• Get a rocket

case• Pour in

propellant• Attach exhaust

nozzle

Image from http://www.aerospaceweb.org/

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What Does Propellant Look Like?• Molecules of

propellant• Essentially

spheres

Image from http://www.aerospaceweb.org/

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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?

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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

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SGMP – Visualization

• Custom tool– Particle/Primitive system (Ebert 1996)

• Demonstration

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SGMP – Collision Calculations

• Calculated many, many times• Computationally expensive• Use neighbor lists to reduce number of

checks

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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)

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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

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Generate Neighbor List

• One-time complexity– O(n)– Compare one to all the rest

• Total complexity (entire pack)– O(n2)

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Downward Drop

• One-time complexity– O(1)– Constant drop distance

• Total complexity (entire pack)– O(n)

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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

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Why log(n)?

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Outline

• Problem• Significance• Methodology/Solution

Results• Evaluation• Conclusion• Further Research

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SGMP Starting Arrangements

• Single Column• Small Dense• Large Dense• Loose Random• Number of particles tested

– 150, 300, 750, 1002, 2001, 3000, 6000, 9000

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SGMP – Single Column

• Single column of particles above control volume

• Demonstration

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Results – Single Column

• Packing fraction– 300 particles - 0.62– 9000 particles - 0.60

• Speed– 9000 particles

• 41424 seconds (~12 hours)

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Results – Single Column

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Results – Single Column

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SGMP – Small Dense

• Densely packed starting grid• Only within the control volume• Demonstration

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Small Dense – Results

• Packing fraction– 750 particles - 0.61– 9000 particles - 0.60

• Speed– 9000 particles

• 56337 seconds (~15 hours)

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Small Dense -- Results

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SGMP – Large Dense

• Densely packed starting grid• Within the expanded volume• Demonstration

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Large Dense – Results

• Packing fraction– 9000 particles - 0.59

• Other packs were very similar

• Speed– 9000 particles

• 19699 seconds (~5.4 hours)

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Large Dense -- Results

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SGMP – Loose Random

• Loosely packed random starting grid• Only within the control volume• Demonstration

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Loose Random – Results

• Packing fraction– 9000 Particles - 0.59

• Other packs were very similar

• Speed– 9000 particles

• 456715 seconds (~5.2 days)

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Loose Random – Results

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Outline

• Problem• Significance• Methodology/Solution• Results

Evaluation• Conclusion• Further Research

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Evaluation – Packing Fraction

• Packing fractions were similar

Model Packing Fraction

Single Column 0.62

Small Dense 0.61

Large Dense 0.59

Loose Random

0.59

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Evaluation - Speed

• Wildly different completion times for the various models. Why?

• Most steps “basically” the same– Number of Spin, Gap, and Move cycles

• Falling height very different from model to model

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Falling Height

• Demonstration

Model Highest distance

Time (seconds)

Large Dense 2.1 19699

Small Dense 3.4 56337

Loose Random

21.6 456715 (5 days!)

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Outline

• Problem• Significance• Methodology/Solution• Results• Evaluation

Conclusion• Further Research

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Packing Fraction – All

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Speed – All

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Conclusions – The Bad

• Packing fraction– Target -- 0.63– Result -- < 0.59

• Speed– Target -- 100,00 particles in 1 minute– Result – 9,000 particles in 5 hours

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Conclusions – The Good

• Randomness– All RDF graphs looked normal

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Outline

• Problem• Significance• Methodology/Solution• Results• Evaluation• Conclusion

Further Research

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Future Work

• Improve speed– Better downward fall algorithm– Variable spin granularity

• Improve packing fraction– Higher spin granularity– Contact model (non-zero coordination number)

• Algorithm additions– Multi-modal pack (various sphere sizes)

• Requires random ‘fall’ vectors

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Presentation References

• Balci, O. (2001), ‘A methodology for certification of modeling and simulation applications’, ACM Trans. Model. Comput. Simul. 11(4), 352–377.

• Ebert, D. S. (1996), ‘Advanced modeling techniques for computer graphics’, ACM Comput. Surv. 28(1), 153–156.

• Furka, A. (1995), ‘History of combinatorial chemistry’, Drug Development Research 36(1), 1–12.

• Hartmanis, J. & Hopcroft, J. E. (1971), ‘An overview of the theory of computational complexity’, J. ACM 18(3), 444–475.

• Knott, G. M., Jackson, T. L. & Buckmaster, J. (2001), ‘The random packing of heterogeneous propellants’, AIAA Journal 39(4), 678–686.

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Presentation References (continued)

• McGeary, R. K. (1961), ‘Mechanical packing of spherical particles’, Journal of the American Ceramic Society 44(10), 513–522.

• Miller, R. B. (1982), Effects of particle size on reduced smoke propellant ballistics, in ‘AIAA/SAE/ASME 18th Joint Propulsion Conference and Exhibit’, number AIAA-82-1096.

• Torquato, S. (2002), Random heterogeneous materials: Microstructure and macroscopic properties, 1st edn, Springer-Verlag, New York.

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End of Presentation

• Thank you• Questions are welcome