cfx slide serial no 1 2003 ansys cfx cfx-5.6 multiphase course free surface lecture 5 free surface...
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CFX Slide serial no 3 © 2003 ANSYS CFX CFX-5.6 Multiphase Course Free 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.TRANSCRIPT
CFX
Slide serial no 1© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Lecture 5
Free Surface Flow
CFX
Slide serial no 2© 2003 ANSYS CFX
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
CFX
Slide serial no 3© 2003 ANSYS CFX
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.
CFX
Slide serial no 4© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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
CFX
Slide serial no 5© 2003 ANSYS CFX
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
CFX
Slide serial no 6© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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
CFX
Slide serial no 7© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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
CFX
Slide serial no 8© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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
CFX
Slide serial no 9© 2003 ANSYS CFX
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
CFX
Slide serial no 10© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Maxwell’s Expt.
2-D transient problem Solved with hex and prismatic meshes Hex mesh (~10000 nodes on plane)
CFX
Slide serial no 11© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Maxwell’s Expt.
CFX
Slide serial no 12© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Wigley Hull
CFX
Slide serial no 13© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Wigley Hull
CFX
Slide serial no 14© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Jet with Adaption No adaption One step Two steps
CFX
Slide serial no 15© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Free Surface Flow: Gear Box
CFX
Slide serial no 16© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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
CFX
Slide serial no 17© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Surface Tension: Wall Adhesion
Non-wetting Wetting
Wall adhesion is responsible for capillary rise in tubes
o90o90
CFX
Slide serial no 18© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Dimensionless Groups
Weber number:
Capillary number:
Marangoni number:
force tension Surfaceforce InertialWe
2
LU
force tension Surfaceforce Viscous
ReWeCa
U
LTT
Ma
CFX
Slide serial no 19© 2003 ANSYS CFX
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
CFX
Slide serial no 20© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Surface Tension: Extreme angle
CFX
Slide serial no 21© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Surface Tension: Colliding drops
CFX
Slide serial no 22© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
Surface Tension: Colliding drops
CFX
Slide serial no 23© 2003 ANSYS CFX
CFX-5.6 Multiphase CourseFree Surface
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