1. Physical Based Modeling and Animation of Fire 1/25

2. Introduction Overview Physical Based Model Level-set Implementation Rendering of Fire Animation Results Physical Based Modeling and Animation of Fire 2/25

3. 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) Introduction 3/25

4. 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? 4/25

5. Physically Based Model solid fuel gas fuel blue core ignition T max Temperature time gas products gas to solid phase change 5/25

6. Physically Based Model Blue core Hot gaseous products Soot emit blackbody radiation that illuminates smoke 6/25

7. Physically Based Model-Blue core Reacted gaseous fuel Implicit surface AsAs AsAs S S AfAf AfAf vfvf vfvf Un-reacted gaseous fuel Blue or bluish-green core v f A f = SA s V f is the speed of fuel injected, A f is the cross section area of cylindrical injection 7/25

8. Physically Based Model-Blue core S is large and core is small S 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) 8/25

9. Physically Based Model-Blue core Premixed flame and diffusion flame -fuel and oxidizer are premixed and gas is ready for combustion -non-premixed (diffusion) fuel premixed flame diffusion flame oxidizer Location of blue reaction zone 9/25

10. Physically Based Model-Hot Gaseous Products Hot Gaseous Products - Expansion parameter  f /  h  f is the density of the gaseous fuel  h is the density of the hot gaseous product  h =0.2 0.1 0.02  f =1.0 10/25

11. Physically Based Model-Hot Gaseous Products Hot Gaseous Products - Mass and momentum conservation require  h (V h -D)=  f (V f -D)  h (V h -D) 2 +p h =  f (V f -D) 2 +p f V f and V h are the normal velocities of fuel and hot gaseous D =V f -S speed of implicit surface direction 11/25

12. Physically Based Model-Hot Gaseous Products Solid fuel  f (V f -D)=  s (V s -D) V f =V s +(  s /  f -1)S  s and V s are the density and the normal velocity of solid fuel Solid fuel Use boundary as reaction front 12/25

13. Implementation -Discretization of physical domain into N 3 voxels (grids) with uniform spacing -Computational variables implicit surface, temperature, density, and pressure,  i,j,k, T i,j,k,  i,j,k, and p i,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=u f +s n, so the surface can be governed by Level Set Equation  t = - w∙   new  old – Δt(w 1  x  w 2  y  w 3  z  13/25

14. Implementation Incompressible Flow u t = -(u ∙ ∇ ) u - ∇ p/  + f u = u* - Δt ∇ p/  ∇ ∙u= ∇ ∙ u* - Δt ∇ ∙( ∇ p/  ∇ ∙( ∇ p/  = ∇ ∙ u*/Δt f buoy =  (T-T air )z f conf = εh(N ⅹ ω) ∇ ∙u = 0 14/25

15. Implementation Temperature and density Y t = −(u· ∇ )Y −k T = - (u∙ ∇ ) T – C t ( ) T-T air T max -T air 4  t = −(u· ∇ )  15/25

16. 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 Medium 16/25

17. 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 Medium 17/25

18. 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 Medium 18/25

19. Rendering of Fire Light transport in participating medium is described by an integro- differential equation Light Scattering in a Fire Medium 19/25

20. Rendering of Fire Light transport in participating medium is described by an integro- differential equation Light Scattering in a Fire Medium T is the temperature C1 3.7418 · 10−16Wm2 C2 1.4388 · 10−2moK T is the temperature C1 3.7418 · 10−16Wm2 C2 1.4388 · 10−2moK 20/25

21. 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 fire 21/25

22. 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 (L w, M w, S w ) (Fairchild ‘s book “color appearance model”, 1998) Reproducing the color of fire 22/25

23. Results -Domain: 8 meters long with 160 grids (increment h=0.05m) -V f =30m/s A f =0.4m -S=0.1m/s  f =1  h =0.01 -Ct=3000K/s  =0.15 m/(Ks2) -ε = 16 (gaseous fuel) -ε = 60 (hot gaseous products) Results 23/25

24. Results A metal ball passing through and interacts with a gas flame 24/25

25. Results A flammable ball passes through a gas flame and catches on fire 25/25