Physical Based Modeling and Animation of Fire

Physical Based Modeling and Animation of Fire

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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

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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

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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?

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Physically Based Model

solid fuel

gas fuel

blue core

ignition

T max

Temperature

time

gas products

gas to solid phase change

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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

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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

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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

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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

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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

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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

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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

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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

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Implementation

Temperature and density

Temperature and density

Yt = −(u·∇)Y −k

T = - (u∙∇) T – Ct ( )T-Tair

Tmax-Tair

4

t = −(u·∇)

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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

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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

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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

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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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