ICHS 2011 HighOrder Perturbation Solutions To A LH

ICHS 2011 High-Order Perturbation Solutions To A LH 2 Spreading Model With Continuous Spill Sep 13, 2011 Myungbae Kim KOREA INSTITUTE OF MACHINERY & MATE

Contents Introduction Formulation Results & Discussion Conclusions KOREA INSTITUTE OF MACHINERY & MATE

Introduction - 1 Leak of flammable liquid § Most common undesirable event in several plants, especially offshore production installations § Initiating event in almost all Event Tree Analysis § Top event of almost all Fault Tree Analysis § Makes a pool or a puddle The pool radius is important for determining a fire size. KOREA INSTITUTE OF MACHINERY & MATE

Introduction - 2 Leak model § Instantaneous Release § Continuous Release Spread model § Simple Physical Model § Shallow Layer Model § Full Navier-Stokes Equation KOREA INSTITUTE OF MACHINERY & MATE

Simple Physical Model - Briscoe & Shaw Spill source rate, Evaporation, E R(t) Hydrostatic Pressure § Radius always tends to increase § Neglecting viscosity and surface tension KOREA INSTITUTE OF MACHINERY & MATE

Formulation ▣ Governing Equations ▣ Initial Conditions and KOREA INSTITUTE OF MACHINERY & MATE

Previous Results The 1 st order solution for the pool volume due to the non-uniform expansion by secular terms as time increases KOREA INSTITUTE OF MACHINERY & MATE

Non-dimensionalization ▣ Characteristic Time & Length ▣ Dimensionless Variables KOREA INSTITUTE OF MACHINERY & MATE

Dimensionless Governing Equations Dimensionless evaporation rate ; an unique governing parameter with KOREA INSTITUTE OF MACHINERY & MATE

3 rd Order Expansion for Solutions KOREA INSTITUTE OF MACHINERY & MATE

Perturbation Equations Initial conditions; All variables is zero at t=0 KOREA INSTITUTE OF MACHINERY & MATE

Perturbation Solutions KOREA INSTITUTE OF MACHINERY & MATE

Results and Discussion -1 LH 2 Spill on wax E=4. 2 10 -4 m/s (Verfondern & Dienhart) KOREA INSTITUTE OF MACHINERY & MATE

Results and Discussion -2 LH 2 Spill on concrete E=4. 2 10 -4 m/s KOREA INSTITUTE OF MACHINERY & MATE

Conclusions § The unique governing parameter by nondimensionalization. § For the pool volume, improvement of the 3 rdorder solutions is shown. § For the pool radius, the 3 rd-order and 2 nd-order solutions are nearly identical, and the improvement by high order solutions is not so large compared to 1 st-order solutions. KOREA INSTITUTE OF MACHINERY & MATE

Thank you for your attention!! KOREA INSTITUTE OF MACHINERY & MATE