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CFX-5.6 Multiphase CourseFree Surface

Lecture 5

Free Surface Flow

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CFX-5.6 Multiphase CourseFree Surface

Free Surface Flow: Outline

Introduction to Free Surface Flow Homogeneous Multiphase Implementation and Examples Surface Tension Advanced Topics

Inhomogeneous Free Surface Flow

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CFX-5.6 Multiphase CourseFree Surface

What is Free Surface Flow

Free surface flow separated multiphase flow fluids separated by distinct resolvable interface examples: open channel flow, flow around ship hulls, water jet in air

(Pelton wheel), tank filling, etc.

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Free Surface Flow: Classification

Froude number

L=h (water depth) for shallow water flow L=/2 (wavelength) for sinusoidal wave train in deep water for flow around ship hulls, there is not a single wave velocity, but we

can still define a Froude number based on the ship geometry

Analogies with Mach number flow can be subcritical, transcritical, or supercritical hydraulic jump is a ‘shock’

speed wavespeed convective

gLVFr

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CFX-5.6 Multiphase CourseFree Surface

Homogeneous MPF: Concept

Homogeneous MPF model Air and water are separated by a distinct free surface interface (may

be smeared by numerics) Only one velocity at each point in space: bulk velocity

Sufficient to solve for this bulk velocity field Also valid when interphase drag is very large and body forces are

absent

iiii UUrUU

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Homogeneous MPF: Momentum

Phasic momentum equation:

Sum over phases:

Essentially a single-phase momentum equation with mixture density and viscosity

Mxr

grxpr

xUUr

tUr

jjii

ij

iji

)()()(

j

jii

ij

iji

xg

xp

xUU

tU

)()(

jiji rr

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Homogeneous MPF: Continuity

Phasic continuity:

If homogeneous:

Neglect compressibility equation is symmetric for all phases solve for (N-1) volume fractions and treat the other as a ballast

Volume continuity: Incompressibility assumed for clarity only

(not fundamental limitation)

0)()(

j

j

xUr

tr

0)()(

j

j

xUr

tr

0

j

j

xU

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Homogeneous MPF: Other equations

Bulk equations solved for other homogeneous field variables also turbulence additional variables

Energy is a special case temperature is homogeneous enthalpy is a principal variable (not shared among fluids) solution: solve two phasic equations with a large interphase heat

transfer term to force temperatures to be the same

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CFX-5.6 Multiphase CourseFree Surface

Free Surface Flow: Implementation

MPF Model usually homogeneous MPF model

Advection and transient terms compressive discretization interface typically smeared over 2-3 elements

Pressure-velocity coupling (Rhie-Chow) special treatment of buoyancy force to keep flow well-behaved at

interface

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Free Surface Flow: Maxwell’s Expt.

2-D transient problem Solved with hex and prismatic meshes Hex mesh (~10000 nodes on plane)

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Free Surface Flow: Maxwell’s Expt.

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Free Surface Flow: Wigley Hull

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Free Surface Flow: Wigley Hull

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Free Surface Flow: Jet with Adaption No adaption One step Two steps

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Free Surface Flow: Gear Box

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Surface Tension

An attractive force at the free surface interface

Normal component smooths regions of high curvature induces pressure rise within droplet:

Tangential component moves fluid along interface toward region of high often called Marangoni effect (decreases with temperature)

LFσ F

p

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Surface Tension: Wall Adhesion

Non-wetting Wetting

Wall adhesion is responsible for capillary rise in tubes

o90o90

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Dimensionless Groups

Weber number:

Capillary number:

Marangoni number:

force tension Surfaceforce InertialWe

2

LU

force tension Surfaceforce Viscous

ReWeCa

U

LTT

Ma

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CFX-5.6 Multiphase CourseFree Surface

Surface Tension: Modelling

Conceptually a surface force at interface

awkward to deal with interface topology

Reformulate as a continuum force Brackbill, Kothe, Zemach 1992

wall contact angle specifies direction of normal at wall

ss nf ˆ

rrnn

rfF

s

sss

/ˆˆ

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Surface Tension: Extreme angle

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Surface Tension: Colliding drops

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Surface Tension: Colliding drops

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Inhomogeneous Free Surface

Splashing air entrained in

water; behaves as disperse fluid

combine free surface discretization with full MPF model

use a drag law appropriate for the motion of the disperse fluid