Physical Based Modeling and Animation of Fire 1/25.
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Transcript of Physical Based Modeling and Animation of Fire 1/25.
Physical Based Modeling and Animation of Fire
Physical Based Modeling and Animation of Fire
1/25
IntroductionIntroduction
Overview
Physical Based ModelPhysical Based Model
Level-set ImplementationLevel-set Implementation
Rendering of FireRendering of Fire
Animation ResultsAnimation Results
Physical Based Modeling and Animation of Fire Physical Based Modeling and Animation of Fire
2/25
Introduction
-Deflagrations : low speed events with chemical reactions converting fuel into hot gaseous products, such as fire and flame. They can be modeled as an incompressible and inviscid (less viscous) flow-Detonations: high speed events with chemical reactions converting fuel into hot gaseous productions with very short period of time, such as explosions (shock-wave and compressible effects are important)
IntroductionIntroduction
3/25
Introduction
-Introduce a dynamic implicit surface to track the reaction zone where the gaseous fuel is converted into the hot gaseous products-The gaseous fuel and hot gaseous zones are modeled separately by using independent sets of incompressible flow equations.-Coupling the separate equations by considering the mass and momentum balances along the reaction interface (the surface)
How to model?How to model?
4/25
Physically Based Model
solid fuel
gas fuel
blue core
ignition
T max
Temperature
time
gas products
gas to solid phase change
5/25
Physically Based Model
Blue coreBlue core
Hot gaseous productsHot gaseous products
Soot emit blackbody radiation that illuminates smoke
Soot emit blackbody radiation that illuminates smoke
6/25
Physically Based Model-Blue core
Reacted gaseous fuel
Reacted gaseous fuel
Implicit surfaceImplicit surface
AsAs
SS
AfAf
vfvf
Un-reacted gaseous fuel
Un-reacted gaseous fuel
Blue or bluish-green coreBlue or bluish-green core
vfAf = SAs
Vf is the speed of fuel injected, Af is the cross section area of cylindrical injection
7/25
Physically Based Model-Blue core
S is large and core is smallS is large and core is small
S is small and core is largeS is small and core is large
Blue reaction zone cores with increased speed S (left); with decreased speed S (right)Blue reaction zone cores with increased speed S (left); with decreased speed S (right)
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Physically Based Model-Blue core
Premixed flame and diffusion flamePremixed flame and diffusion flame
-fuel and oxidizer are premixed and gas is ready for combustion
-non-premixed (diffusion)
fuel fuel
premixed flamepremixed flame
diffusion flamediffusion flame
oxidizeroxidizer
Location of blue reaction zoneLocation of blue reaction zone
9/25
Physically Based Model-Hot Gaseous Products
Hot Gaseous ProductsHot Gaseous Products
- Expansion parameter f/h
f is the density of the gaseous fuelh is the density of the hot gaseous product
h=0.2 0.1 0.02
f=1.0f=1.0
10/25
Physically Based Model-Hot Gaseous Products
Hot Gaseous ProductsHot Gaseous Products
- Mass and momentum conservation require
h(Vh-D)=f(Vf-D)
h (Vh-D)2 +ph = f(Vf-D)2+pf
Vf and Vh are the normal velocities of fuel and hot gaseousD =Vf -S speed of implicit surface direction
11/25
Physically Based Model-Hot Gaseous Products
Solid fuelSolid fuel
f (Vf-D)=s (Vs-D)
Vf=Vs+(s /f-1)S
s and Vs are the density and the normal velocity of solid fuel
Solid fuelSolid fuel
Use boundary as reaction front
12/25
Implementation
-Discretization of physical domain into N3 voxels (grids) with uniform spacing
-Computational variables implicit surface, temperature, density, and pressure, i,j,k, Ti,j,k, i,j,k, and pi,j,k
-Track reaction zone using level-set methods, =+,-, and 0, representing space with fuel, without fuel, and reaction zone
-Implicit surface moves with velocity w=uf+sn, so the surface can be governed by
Level Set EquationLevel Set Equation
t= - w∙ t= - w∙ newold – Δt(w1xw2y
w3z newold – Δt(w1xw2y
w3z
13/25
Implementation
Incompressible FlowIncompressible Flow
ut= -(u ∙∇) u - ∇p/+ f
u = u* - Δt∇p/∇∙u=∇∙ u* - Δt∇∙(∇p/
∇∙(∇p/= ∇∙ u*/Δt
fbuoy = (T-Tair)zfconf = εh(Nⅹω)
∇∙u = 0
14/25
Implementation
Temperature and density
Temperature and density
Yt = −(u·∇)Y −k
T = - (u∙∇) T – Ct ( )T-Tair
Tmax-Tair
4
t = −(u·∇)
15/25
Rendering of Fire
Fire: participating medium-Light energy-Bright enough to our eyes adapt its color-Chromatic adaptation-Approaches
-Simulating the scattering of the light within a fire medium-Properly integrating the spectral distribution of the power in the fire and account for chromatic adaptation
Light Scattering in a Fire MediumLight Scattering in a Fire Medium
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Rendering of Fire
Light Scattering in a fire medium-Fire is a blackbody radiator and a participating medium-Properties of participating are described by
-Scattering and its coefficient-Absorption and its coefficient-Extinction coefficient-Emission
-These coefficients specify the amount of scattering, absorption and extinction per unit-distance for a beam of light moving through the medium
Light Scattering in a Fire MediumLight Scattering in a Fire Medium
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Rendering of Fire
Phase function p(g, ) is introduced to address the distribution of scatter light, where g(-1,0) (for backward scattering anisotropic medium) g(0) (isotropic medium), and g(0,1) (for forward scattering anisotropic medium)
Light Scattering in a Fire MediumLight Scattering in a Fire Medium
18/25
Rendering of Fire
Light transport in participating medium is described by an integro-differential equation
Light Scattering in a Fire MediumLight Scattering in a Fire Medium
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Rendering of Fire
Light transport in participating medium is described by an integro-differential equation
Light Scattering in a Fire MediumLight Scattering in a Fire Medium
T is the temperature C1 3.7418 · 10−16Wm2C2 1.4388 · 10−2moK
T is the temperature C1 3.7418 · 10−16Wm2C2 1.4388 · 10−2moK
20/25
Rendering of Fire
-Full spectral distribution --- using Planck’s formula for spectral radiance in ray machining-The spectrum can be converted to RGB before being displaying on a monitor-Need to computer the chromatic adaptation for fire --- hereby using a transformation Fairchild 1998)
Reproducing the color of fireReproducing the color of fire
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Rendering of Fire
-Assumption: eye is adapted to the color of the spectrum for maximum temperature presented in the fire-Map the spectrum of this white point to LMS cone responsivities (Lw, Mw, Sw) (Fairchild ‘s book “color appearance model”, 1998)
Reproducing the color of fireReproducing the color of fire
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Results
-Domain: 8 meters long with 160 grids (increment h=0.05m)-Vf=30m/s Af=0.4m-S=0.1m/sf=1h=0.01-Ct=3000K/s=0.15 m/(Ks2)-ε = 16 (gaseous fuel)-ε = 60 (hot gaseous products)
ResultsResults
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Results
ResultsResults
A metal ball passing through and interacts with a gas flameA metal ball passing through and interacts with a gas flame
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Results
ResultsResults
A flammable ball passes through a gas flame and catches on fireA flammable ball passes through a gas flame and catches on fire
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