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Level Set Method Implementation in SNUFOAM (High Speed Planing Hull) Wednesday, March 11th, 2015

Presented by Marco Polo Espinoza# IIInterface Tracking MethodIIIConclusionsIVFuture WorkIIntroductionContents# IntroductionPhaseA phase is a thermodynamic definition for the state of matter, which can be either solid, liquid or gasMultiphase flowsThe term is used to refer to any fluid flow consisting of more than one phase or component Phase:gas/solids flows, gas/liquids flows, liquid/solids flows, gas/particle flows or bubbly flows Component: e.g. oil/water flowMultiphase flows can be classified as:Continuous: consist of two or more continuous streams of different fluids separated by interfacesDisperse: finite particles, drops or bubbles distributed in a connected volume of the continuous phase

# 3IntroductionNumerical approaches for two-phases flowsEulerian - LagrangianTreat the fluid as a continuous phase and the particles (dispersed phase) as discrete entitiesThe path of a large number of particles, bubbles and droplets is tracked throughout the flow field based on a force balance on each entityThe computing time is increasing with high number particles. The modeling of fluid particle interaction, droplet evaporation, collision, wall interaction etc. is physically concrete and clear, making it as main advantages of E-L approach

# 4IntroductionNumerical approaches for two-phases flowsEulerian Eulerian (E E)E-E approach treats both phases as continuaThis approach is more suitable in case of dense two-phase flow and it has the advantages of less computational costsSolves momentum, enthalpy, and continuity equations for each phase and tracks volume fractionsUses a single pressure field for all phasesAll phases are considered incompressible

# 5IntroductionVolume fractionIn general we consider volume fraction to be the fraction of the cell volume occupied by one particular phaseThe sum of all volume fractions in every point is unity

For volume fraction of kth fluid, three conditions are possible: k = 0 if cell is empty (of the kth fluid) k = 1 if cell is full (of the kth fluid) 0 < k < 1 if cell contains the interface between the fluids

# 6IIInterface Tracking MethodIIIConclusionsIVFuture WorkIIntroductionContents# VOF - Volume of fluidThe volume of fluid method was first proposed by Hirt and Nichols. The interface is tracked using a phase indicator function (also known volume fraction)The flow equations are volume averaged using an averaging volume smaller than the bubbles/drops used in the simulationsConsidering only two phases, without mass exchange, and volume averaging the mass and momentum equations, following three cases are encountered as shown in Fig. 2:

Interface Tracking Method

# 8VOF - Volume of fluid


# 9VOF - Volume of fluid


# 10Level Set MethodThe interface is defined as a zero level set of a distance function from the interface. To distinguish between the two fluids on either side of the interface a negative sign is attached to the distance function for one of the fluids. The distance function is a scalar property and is advected with the local fluid velocity. A given curve C (the boundary of an open set , i.e. C = ) is represented implicitly, as the zero level set


# 11Level Set MethodThe equations of motion and the boundary conditions:

The boundary conditions at the interface, , between the phases are:

Where n is the unit normal of the interface drawn outwards from the gas to the liquid, = n is the curvature of the interface, and is the coefficient of surface tension


# 12Level Set MethodWhere is the domain containing both fluids and is the Dirac delta function. d is the signed distance function from the interface; which is defined as follows: at a point x in liquid d is the distance to closest point on the interface. In the gas d is the negative of this quantity. The idea of incorporating surface tension as a force concentrated on the interface

Interface Tracking Method # 13IIInterface Tracking MethodIIIConclusionsIVFuture WorkIIntroductionContents# ConclusionsLevel set can provide a way to calculate the surface normal and the curvature in an accurate mannerConceptually simpleEasy to implement

Conclusions# IIInterface Tracking MethodIIIFuture WorkIVIIntroductionConclusionsContents# Future WorkImplementation of Level Set Method in SNUFOAMDesign of Fridsma hulls mesh Future Work

Table 1. Main characteristics# BibliographyA Compact Introduction to the Numerical Modeling of Multiphase FlowsM. Wrner Institut fr Reaktorsicherheit Programm Nukleare Sicherheitsforschung Fundamentals of Multiphase Flows Christopher E. Brennen California Institute of Technology Pasadena, CaliforniaLecture 14 - Multiphase Flows Applied Computational Fluid Dynamics Instructor: Andr BakkerLecture 16 - Free Surface Flows Applied Computational Fluid Dynamics Instructor: Andr BakkerEulerian-Lagrangian Approach for Modeling and Simulations of Turbulent Reactive Multi-Phase Flows under Gas Turbine Combustor ConditionsToward free-surface modeling of planing vessels: simulation of the Fridsma hull using ALE-VMS I. Akkerman J. Dunaway J. Kvandal J. Spinks Y. BazilevsFree-Surface Flow and Fluid-Object Interaction I. Akkerman, K. Benner, and Y. Bazilevs

Bibliography# Thank you for your attention!Q&A#

level set presentation 1

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