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Animating suspended particle explosionsAnimating suspended particle explosions
Bryan E. Feldman et al.TOG ‐ Proceedings of ACM SIGGRAPH 2003
Copyright of figures and other materials in the paper is belongs to original authors.
Presented by Taehyeong Kim
2014. 9. 16
Computer Graphics @ Korea University
Tae‐hyeong Kim | 2014. 9. 16| # 2Computer Graphics @ Korea University
• A method for animating suspended particle explosions
• Using stable incompressible fluid model
• Combustion is modeled by the particle and fluid systems
Abstract
Tae‐hyeong Kim | 2014. 9. 16| # 3Computer Graphics @ Korea University
Result movie
Tae‐hyeong Kim | 2014. 9. 16| # 4Computer Graphics @ Korea University
• Introduction
• Simulation Methods
Gas Model
Particulate Model
Detonation, Dispersal, and Ignition
Interaction and Combustion
• Rendering Methods
• Results and Discussion
Context
Tae‐hyeong Kim | 2014. 9. 16| # 5Computer Graphics @ Korea University
• Explosions appear nearly ubiquitously in the synthetic environments Movie and television, and few video games
• Generally an explosion creates an outward-propagating pressure front or blast wave
Introduction
Tae‐hyeong Kim | 2014. 9. 16| # 6Computer Graphics @ Korea University
• The blast wave explosion’s primary effect but almost invisible
• Secondary effects bright flashes of light, flame, dust, and flying debris
• For visual effects minimize blast wave maximize secondary effects
• The goal is impressive (realistic) large fireballs
Introduction
Tae‐hyeong Kim | 2014. 9. 16| # 7Computer Graphics @ Korea University
• We model the behavior of suspended particle explosions
• The method uses stable fluid dynamics simulation to compute the motion of air and hot gases around the explosion
• Particles immersed in the fluid track the motion of particulate fuel and combustion products
• The system models combustion using a simple process governed by the particle and fluid systems
Introduction
Tae‐hyeong Kim | 2014. 9. 16| # 8Computer Graphics @ Korea University
• Our method does not attempt to model the numerically troublesome
• Incompressible fluid model and adjusts the divergence field
• Our Matlab implementation requires no more than a few seconds per frame
Introduction
Tae‐hyeong Kim | 2014. 9. 16| # 9Computer Graphics @ Korea University
• “Animating explosions” Yngve, G. D. et al. In Proceedings of ACM SIGGRAPH 2000
• “Stable fluids” Stam, J. In Proceedings of ACM SIGGRAPH 99
Background
Tae‐hyeong Kim | 2014. 9. 16| # 10Computer Graphics @ Korea University
• Suspended particle explosions burning particulates, surrounding air, and combustion products
• Type of behavior by setting initial conditions
• that will give rise to the explosion.
Simulation Methods
Tae‐hyeong Kim | 2014. 9. 16| # 11Computer Graphics @ Korea University
• Consists of
Gas(fluids) Model – Air and combustion products
Particulate Model – Heat and Mass transfer
Detonation, Dispersal, and Ignition
Interaction and Combustion
Simulation Methods
Tae‐hyeong Kim | 2014. 9. 16| # 12Computer Graphics @ Korea University
• Model the mixture of air Using a modified version of the fluid model described in [Fedkiw
et al., 2001] incompressible, inviscid fluid
• with three-dimensional grid
• Momentum conservation Navier-Stokes with zero viscosity:
where u is the fluid velocity, ρ density, p pressure, f any external forces
• include thermal buoyancy, vorticity confinement and interactions with the particles.
Simulation Methods
Gas Model
Tae‐hyeong Kim | 2014. 9. 16| # 13Computer Graphics @ Korea University
• Mass conservation that the velocity divergence be zero
Our modified version
• where Φ is zero everywhere • except for
generating additional fluid expanding by heat
Simulation Methods
Gas Model
Tae‐hyeong Kim | 2014. 9. 16| # 14Computer Graphics @ Korea University
• modified version of Poisson’s equation for eqn (2)
Simulation Methods
Gas Model
Tae‐hyeong Kim | 2014. 9. 16| # 15Computer Graphics @ Korea University
• Temperature
where T denotes the fluid temperature, Ta ambient temperature, Tmax the maximum temperature in the environment, H heat energy transfered into the fluid
Simulation Methods
Gas Model
Tae‐hyeong Kim | 2014. 9. 16| # 16Computer Graphics @ Korea University
The first term : advection by the fluid The second term : radiative
• cr is cooling constant
The third term : diffusion• set an unrealistically large value
for the thermal conductivity, ck
The final term : heat energy transfer• into the fluid from an external source
Simulation Methods
Gas Model
Tae‐hyeong Kim | 2014. 9. 16| # 17Computer Graphics @ Korea University
• We model the motion of both the particulate fuel and solid combustion products (soot) using a particle system.
• Particle consist of a position, velocity, mass, temperature, thermal mass, volume, and
type identifier.
Simulation Methods
Particulate Model
Tae‐hyeong Kim | 2014. 9. 16| # 18Computer Graphics @ Korea University
• Particle’s behavior
where x is the location of a particle, f is external forces on the particle (including gravity), Y is the particle temperature, H is heat energy
• transfered to the particle or generated by combustion,
cm is the particle’s thermal mass
• If the particles have very small mass/thermal mass we treat them as massless/thermally massless
Simulation Methods
Particulate Model
Tae‐hyeong Kim | 2014. 9. 16| # 19Computer Graphics @ Korea University
• Large fireballs may result from an initial high-velocity explosion The primary result is a rapid jump
• in pressure as the explosive detonates
The high pressure region creates a shock wave and propels
• The compressible fluid method is expensive used by [Yngve et al.,2000]
Simulation Methods
Detonation, Dispersal, and Ignition
Tae‐hyeong Kim | 2014. 9. 16| # 20Computer Graphics @ Korea University
• Detonation region The divergence constraint value, Φ, rises rapidly until it reaches a
peak value Then decays back to zero, goes slightly negative, And finally stabilizes again at zero
• This schedule approximates the pressure profile typical of a high-explosive detonation
Simulation Methods
Detonation, Dispersal, and Ignition
Tae‐hyeong Kim | 2014. 9. 16| # 21Computer Graphics @ Korea University
• Eqn (1) and (2) will generate a momentum-conserving flow field with zero divergence except where Φ is non-zero incompressible flow field that moves outward (or inward if Φ < 0)
from where expansion has occurred
• The flow will correctly conform to obstacles and other divergence sources
• A detonation heat the region on nearby particles. The heat added to the fluid
• accounts for heat generated by combustion
It changes the fluid temperature according to Equation (4)
Simulation Methods
Detonation, Dispersal, and Ignition
Tae‐hyeong Kim | 2014. 9. 16| # 22Computer Graphics @ Korea University
• The result of injecting fluid at the center of a two-dimensional environment by setting a single
cell’s divergence to a positive value.
Simulation Methods
Detonation, Dispersal, and Ignition
Tae‐hyeong Kim | 2014. 9. 16| # 23Computer Graphics @ Korea University
• The particle and fluid models interact with each other through the transfer of momentum and heat energy.
• Additionally, our combustion model involves interactions between the particles and fluid.
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 24Computer Graphics @ Korea University
• The drag force on a particle is
where αd is the particle’s drag coefficient, r its radius, u is the fluid’s interpolated velocity at the particle location
• The opposite force is applied to the fluid cell containing the particle If the particle’s mass lies below a threshold, it is treated as
massless
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 25Computer Graphics @ Korea University
• Thermal transfer between the particles and the fluid is handled in a similar fashion
• The rate of heat transfer particle from the fluid around
• where αh is the coefficient of thermal conductivity• T is the fluid’s interpolated temperature at the particle location
If the particle’s thermal mass falls below a threshold, then we set Y = T and the fluid’s temperature remains unaffected.
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 26Computer Graphics @ Korea University
• Particulate fuel Once ignited, these particles generate the fiery mass of hot gases
and soot
• The actual process of combustion is quite complex, but we obtained good results with a greatly simplified model.
• The three most significant simplifications Combustion occurs irrespective of oxygen availability Combustion rate is invariant with temperature, Composition of combustion products does not depend on
temperature either
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 27Computer Graphics @ Korea University
• Fuel particle Ignite when its temperature rises above its ignition point Once ignited the particle will consume its own mass at a set rate,
its burn rate, z. Delete from the system when the particle’s mass = 0
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 28Computer Graphics @ Korea University
• Burning particle generate heat, gaseous products, and solid products
Heat is generated at a rate
• where bh is the amount of heat released per unit combusted mass of the fuel.
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 29Computer Graphics @ Korea University
• Burning particle
The gaseous products• added to the fluid system
where V is the volume of the cell and bg is the volume of gas released per unit combusted mass less the
volume of gas consumed
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 30Computer Graphics @ Korea University
• Burning particle
The solid combustion products(commonly called soot)• A fuel particle generates soot mass at a rate
where bs denotes the mass of soot produced per unit combusted mass of fuel
• When a sufficient quantity has accumulated a soot particle will be generated The initial position and velocity of the soot particle match those of
the fuel particle with a small random perturbation.
Simulation Methods
Interaction and Combustion
Tae‐hyeong Kim | 2014. 9. 16| # 31Computer Graphics @ Korea University
• The images are generated by rendering the fuel and soot particles directly Each particle receives illumination from the environment and, if sufficiently hot, glows with its own light The light emitted from the hot particles is based on blackbody
radiation • but we adjusted the mapping to match images of real explosions
One area for further work is improving the rendering method
Rendering Methods
Tae‐hyeong Kim | 2014. 9. 16| # 32Computer Graphics @ Korea University
• An efficient tool for generating motion for suspended particle explosions
• Areas for future work include burning liquid sprays, complex chemical reactions, and more realistic rendering methods.
Discussion