Florida State University V. Mihalef B. Unlusu D. Metaxas M. Sussman M. Y. Hussaini Physics-Based Boiling Simulation

Abstract 물리기반 Boiling 현상을 시뮬레이션 – 액체와 기체의 상호 작용 시뮬레이션 – 여러 온도에서 시뮬레이션 – 물질전달 ( mass transfer) 현상 시뮬레이션 실제와 유사한 현상 시뮬레이션 – 액체 질량의 순환 – Roiling boil – 고체 경계에서 nucleation seeding

Introduction 온도의 gradients 방향으로 일어나는 물질 전달 현상과, 증기와 액체의 섞이는 현상을 표현하고자 함 – 경계면의 이류는 Navier-Stokes simulator 사용 – 온도는 heat dynamics 와 mass transfer mechanism 사용 – 현재까지는 bubble 이 떠오르는 것에만 초점 – [MSKG05] 최초로 온도에 초점

Introduction Introduction (Con’t) 물질 전달 률 physics-based approach – nucleation site 주변에서 mass transfer 발생 flux : facing normal : latent heat of vaporization : coefficient of diffusivity for the temperature :

Previous Work Eulerian 기반 grid elements 사용 – nodes, cell centers, face centers Navier-Stokes solvers [FM96] semi-Lagrangian techniques [Sta99] particle level set method [EMF02] generate impressive bubbles [HK05] multiple interacting fluid [LSSF06]

Lagrangian methods – the smooth particle hydrodynamics method (SPH) Temperature property to particles [MSKG05] – spring-mass system modeling heating and melting of deformable objects [TPF89]

Previous Work (Con’t) mass conservation – PLS method Hybrid particle – CIP method color field & gradient advect – CLSVOF method PLS 보다 많고 작은 Bubble 을 다루는데 유리함

CLSVOF (coupled level set and volume of fluid)

CLSVOF The level set is updated so that the new liquid volume matches the volume fraction F

Our Fluid Solver Second order extension [Sus03] – single-phase : 공기, 바람이 물에 영향을 미치지 못함 – tow-phase 기법으로 확장 First order two-phase approaches 도입 [SHS¤04] – Continuum methods

Boundary conditions for nucleation sites Bubbles form – Vortex, rise bubble, fill up emptied space nucleation sites – seeded at an arbitrary frequency

Our Fluid Solver Mass Transfer the level set equation, volume-of-fluid equation

Navier-Stokes equation

material derivative initial surface water level The density and Heaviside function H

Temperature equation

continuity condition

Outline of numerical method for gas-liquid coupling face centered density height fraction

Step 1. Calculate mass transfer rate

Step 2. update and F due to mass transfer

Step 3. calculate provisional advective states material (advective) derivative

Step 4. temperature diffusion, The discretization of a Poisson equation [GFCK02].

Step 5. velocity diffusion, [LRR00] The face centered viscosity is defined as, The velocity is defined as,

Step 6. update of surface tension, gravity and viscous terms at the cell faces,

Step 7. pressure correction step. Heaviside function is defined as,

Step update the density and height fractions using the current values of the level sets update the global velocity set the liquid and gas velocity extrapolate the liquid velocity

Animations using an Athlon 64 workstation with 2.4GHz and 3GB RAM simulations evolved to very energetic boiling, decrease in the liquid-level during boiling. – bubbles burst when they reach the liquid surface – mass is transferred to the air

Animations Circulation – bubbles rise to the surface naturally Large viscosity "straight" pattern Small viscosity mixing pattern

Animations The boiling became very energetic, with lots of circulation, what one would call a roiling boil.

Animations Interactions with heated objects The sphere temperature is 500 K before t=2.5 and 300 K afterwards

Conclusion Modeling and simulating boiling-type phenomena Using two-phase flow formulation of the CLSVOF method Future journal paper – two-way interactions with heated deformable objects