School of something

1
School of something FACULTY OF OTHER
School of Mechanical Engineering FACULTY OF
ENGINEERING
Flow Simulation for Improved Engineering
Design Dr Harvey Thompson Colleagues Institute
of Engineering Thermofluids, Surfaces
Interfaces (iETSI) (Particularly Dr Nik Kapur,
Dr Jon Summers, Dr Mark Wilson, Dr Sergii
Veremieiev, Dr Yeawchu Lee, Prof. Phil Gaskell)
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Summary
School of something FACULTY OF OTHER

• Current Capabilities of Computational Fluid
  Dynamics (CFD) in Design of Engineering Systems
  with Free Surface Film and Droplet Spreading
  Flows
• 2D Simulations Industrial Coating
• 3D Simulations Flows over real surfaces
• Bio-pesticide
  application methods

3
2D Simulations Industrial Coating Flows
Slot Coating

• Several different precision coating processes
• produce a range of important products,
• including
• Polymer films and packaging materials
• Ink-jet printing and imaging media
• Large Area Printed Electronic Devices

Roll Coating
4
2D Simulations Industrial Coating Flows
Key Problem for Coating Engineers avoid
formation of streak-lines which destroy product
quality caused by eddies in the flow
Coating web direction
Thin streak-line destroys product quality
5
2D Simulations Industrial Coating Flows

• Industrial Coating Flows Difficult to Simulate
• (even in 2D!)
• Surface-tension dominated, free surface flows
• Static and dynamic wetting lines where
• coating is formed
• Highly curved flow domains
• Finite Element (FE) Methods suitable
• for such problems

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2D Simulations Industrial Coating Flows
Avoidance of Streak-lines (1) Classic Moffatt
1964 JFM paper strong effect of static contact
line on eddy size and strength Increase static
angle to reduce streak-lines Practical solution
coat cascade surface with PTFE reduced wastage
by 4M over three years!
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2D Simulations Industrial Coating Flows
Avoidance of Streak-lines (2) Slot exit
flow. Slot exits often used to supply pre-metered
coatings such as slide and curtain
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2D Simulations Industrial Coating Flows
Avoidance of Streak-lines (2) Slot exit
flow. Back-wetting of uppermost slot may occur
during start-up can lead to defect-causing
solids deposits due to degradation in
recirculation regions. Back wetting at the upper
slot (a) experimental, (b) CFD prediction
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2D Simulations Industrial Coating Flows
Avoidance of Streak-lines (2) Slot exit
flow Merging flow out of slot exits effect of
chamfering lower corner Chamfer can remove
eddies in both liquid layers simultaneously!
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2D Simulations Industrial Coating Flows
Mass Transfer into Eddies and Residence Times in
Forward Roll Coating, Wilson et al, JFM, give
date.
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2D Simulations Industrial Coating Flows
Tracer particle trajectories Runge-Kutta
scheme trigonometric interpolation of nodal and
spinal data allows evaluation of u,v at arbitrary
t
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2D Simulations Industrial Coating Flows
Mass Transfer into Eddies and Residence Times in
Forward Roll Coating, Wilson et al, JFM, give
date. Enables residence times and effects of
time-dependent forcing to be analysed, e.g. Roll
eccentricity or variable roll speeds.
Experiment
CFD
13
3-D Film and Droplet Flows over Topography
Several important practical applications e.g.
film flow in the eye, electronics cooling, heat
exchangers, combustion chambers, etc... Focus
on precision coating of micro-scale displays
and sensors, Tourovskaia et al, Nature
Protocols, 3, 2006. Pesticide flow over
leaves, Glass et al, Pest Management Science,
2010.
Plant disease control
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3D Film Flow over Topography
For displays and sensors, coat liquid layers over
functional topography light-emitting species on
a screen Key goal ensure surfaces are as planar
as possible ensures product quality and
functionality BUT free surface disturbances are
persistent!
Stillwagon, Larson and Taylor, J. Electrochem.
Soc. 1987
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3D Film Flow over Topography

• Key Modelling Challenges
• 3-D surface tension dominated free surface flows
  are very complex Navier-Stokes solvers at early
  stage of development (see later)
• Surface topography often very small (100s nm)
  but influential need highly resolved grids?
• No universal wetting models exist
• Large computational problems adaptive
  multigrid, parallel computing?
• Very little experimental data for realistic 3D
  flows.

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3D Film Flow over Topography
Finite Element methods not as well-established
for 3-D free surface flow. Promising alternatives
include Level-Set, Volume of Fluid (VoF), Lattice
Boltzmann etc but still issues for 3D surface
tension dominated flows grid resolution
etc... Fortunately thin film lubrication low
assumptions often valid provided eH0/L0 ltlt1 and
capillary number Caltlt1 Enables 3D flow to be
modelled by 2D systems of pdes.
gravity
H0
inflow
y
s(x,y)
h(x,y)
L0
x
outflow
a
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3D Film Flow over Topography
Decre Baret, JFM, 2003 Flow of Water Film over
a Trench Topography
Comparison between experimental free surface
profiles and those predicted by solution of the
full Navier-Stokes and Lubrication
equations. Agreement is very good between all
data. Lubrication theory is accurate for thin
film flows with small topography and inertia!
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3D Film Flow over Topography
Thin Film Flows with Significant Inertia Free
surfaces can be strongly influenced by inertia
e.g. free surface instability, droplet
coalescence,... standard lubrication theory can
be extended to account for significant inertia
Depth Averaged Formulation of Veremieiev et al,
Computer Fluids, 2010. Film Flows of Arbitrary
Thickness over Arbitrary Topography Need full
numerical solutions of 3D Navier-Stokes
equations!
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Depth-Averaged Formulation for Inertial Film Flows

1. Reduction of the Navier-Stokes equations by the
   long-wave approximation

Restrictions
2. Depth-averaging stage to decrease
dimensionality of unknown functions by one

,

Restrictions no velocity profiles and internal
flow structure
3. Assumption of Nusselt velocity profile to
estimate unknown friction and dispersion terms
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Depth-Averaged Formulation for Inertial Film Flows
DAF system of equations
For Re 0 DAF LUB

• Boundary conditions
• Inflow b.c.
• Outflow (fully developed flow)
• Occlusion b.c.

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Flow over 3D trench Effect of Inertia
Gravity-driven flow of thin water film 130µm
H0 275µm over trench topography sides 1.2mm,
depth 25µm
surge
bow wave
comet tail
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Accuracy of DAF approach
Gravity-driven flow of thin water film 130µm
H0 275µm over 2D step-down topography sides
1.2mm, depth 25µm Max
Error vs Navier-Stokes (FE)
Error 1-2 for Re50 and s0 0.2
s0step size/H0
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Free Surface Planarisation

• Noted above many manufactured products require
  free surface disturbances to be minimised
  planarisation
• Very difficult since comet-tail disturbances
  persist over length scales much larger than the
  source of disturbances
• Possible methods for achieving planarisation
  include
• thermal heating of the substrate, Gramlich et al
  (2002)
• use of electric fields

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Electrified Film Flow

• Gravity-driven, 3D Electrified film flow over a
  trench topography
• Assumptions
• Liquid is a perfect conductor
• Air above liquid is a perfect dielectric
• Film flow modelled by Depth Averaged Form
• Fourier series separable solution of Laplaces
  equation
• for electric potential coupled to film flow by
  Maxwell free
• surface stresses.

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Electrified Film Flow

• Effect of Electric Field Strength on Film Free
  Surface
• No Electric Field
  With Electric Field
• Note Maxwell stresses can planarise the
  persistent, comet-tail disturbances.

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Computational Issues

• Real and functional surfaces are often extremely
  complex.

Multiply-connected circuit topography
Lee, Thompson and Gaskell, International Journal
for Numerical Methods in Fluids, 2008
Need highly resolved grids for 3D flows
Flow over a maple leaf topography
Glass et al, Pest Management Science, 2010
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Adaptive Multigrid Methods

• Full Approximation Storage (FAS) Multigrid
  methods very efficient.
• Spatial and temporal adaptivity enables fine
  grids to be used only where they are needed.
• E.g. Film flow over a substrate with isolated
  square, circular and diamond-shaped topographies
  
• Free Surface
  Plan View of Adaptive Grid

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Parallel Multigrid Methods

• Parallel Implementation of Temporally Adaptive
  Algorithm using
• Message Passing Interface (MPI)
• Geometric Grid Partitioning
• Combination of Multigrid O(N) efficiency and
  parallel speed up very powerful!

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3D FE Navier-Stokes Solutions
Lubrication and Depth Averaged Formulations
invalid for flow over arbitrary topography and
unable to predict recirculating flow regions As
seen earlier important to predict eddies in many
applications E.g. In industrial coating
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3D FE Navier-Stokes Solutions
Mixing phenomena E.g. Heat transfer enhancement
due to thermal mixing, Scholle et al, Int. J.
Heat Fluid Flow, 2009.
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3D FE Navier-Stokes Solutions

• Commercial CFD codes still rather limited for
  these type of problems
• Finite Element methods are still the most
  accurate for surface tension dominated free
  surface flows grids based on Arbitrary
  Lagrangian Eulerian Spine methods
• Spine Method for 2D Flow
  Generalisation to 3D flow

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3D FE Navier-Stokes vs DAF Solutions
Gravity-driven flow of a water film over a trench
topography comparison between free surface
predictions
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3D FE Navier-Stokes Solutions
Gravity-driven flow of a water film over a trench
topography particle trajectories in the
trench 3D FE solutions can predict how fluid
residence times and volumes of fluid trapped in
the trench depend on trench dimensions
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Droplet Flows Bio-pesticides

• Droplet Flow Modelling and Analysis

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Application of Bio-pesticides
Changing EU legislation is limiting use of
chemically active pesticides for pest control in
crops. Bio-pesticides using living organisms
(nematodes, bacteria etc...) to kill pests are
increasing in popularity but little is know about
flow deposition onto leaves Working with Food
Environment Research Agency in York and Becker
Underwood Ltd to understand the dominant flow
mechanisms
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Nematodes

• Nematodes are a popular bio-pesticide control
• method - natural organisms present in soil
• typically up to 500 microns in length.
• Aggressive organisms that attack the pest by
  entering body openings
• Release bacteria that stops pest feeding kills
  the pest quickly
• Mixed with water and adjuvants and sprayed onto
  leaves

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What do we want to understand?

• Why do adjuvants improve effectiveness reduced
• evaporation rate?
• How do nematodes affect droplet size
  distribution?
• How can we model flow over leaves?
• How does impact speed, droplet size and
  orientation affect droplet motion?

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Droplet spray evaporation time effect of adjuvant
Size of droplets Concentration () Initial mass (mg) Mass fraction left after 10 min () Evaporation time (min)
large 0 130.3 36.3 26.3
large 0.01 138.0 36.6 24.0
large 0.1 161.0 48.7 36.0
small 0 87.3 13.3 16.3
small 0.01 92.5 9.7 16.0
small 0.1 138.3 33.3 25.7
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Droplet size distribution for bio-pesticides
Teejet XR110 05 nozzle with 0.8bar
Matabi 12Ltr Elegance18 knapsack sprayer
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VMD of the bio-pesticide spray depending on the
concentration of adjuvant
addition of bio-pesticide does not affect Volume
Mean Diameter of the spray
Substance Dv50 (µm) Dv50 (µm) Dv50 (µm) Dv50 (µm) Dv50 (µm)
Substance c 0 c 0.01 c 0.03 c 0.1 c 0.3
wateradjuvant 273.3 275.1 269.4 330.5 352.9
watercarrier material 285.9 276.1 297.3 329.2 360.8
watercommercial product (biopesticide) 271.0 272.8 282.6 307.5 360.6
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Droplet flow over a leaf simple theory
2nd Newtons law in x direction
theoretical expressions from Dussan (1985)
Stokes drag
Contact angle hysteresis
Velocity
Relaxation time
Terminal velocity
Volume of smallest droplet that can move
42
Droplet flow over a leaf simple theory vs.
experiments



47V10 silicon oil drops flowing over a
fluoro-polymer FC725 surface


Dussan (1985) theory
Podgorski, Flesselles, Limat (2001) experiments
droplet flow is governed by this law
Le Grand, Daerr Limat (2005), experiments
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Droplet flow over a leaf (?60º) effect of
inertia
For V10mm3, R1.3mm, terminal
velocity0.22m/s Lubrication theory
Depth averaged formulation
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Droplet flow over a leaf (?60º) effect of
inertia
For V20mm3 R1.7mm terminal velocity0.45m/s Lu
brication theory Depth
averaged formulation
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Droplet flow over a leaf (?60º) summary of
computations
V, mm3 R, mm Bosin? Ca a, m/s Ca a, m/s Ca a, m/s
V, mm3 R, mm Bosin? Experiment Experiment Computation Re0 Computation Re0 Computation Re10 Computation Re10
0.27 0.4 0.06 0 0 0.0003 0.02 0.0001 0.007
10 1.3 0.62 0.003 0.13 0.005 0.21 0.005 0.22
20 1.7 0.99 0.006 0.24 0.010 0.42 0.009 0.40
30 1.9 1.30 0.008 0.33 0.012 0.54 0.011 0.48
40 2.1 1.57 0.011 0.48 0.014 0.62 0.012 0.55
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Droplet flow over a leaf theory shows small
effect of initial velocity
Velocity
Initial velocity
Relaxation time
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Droplet flow over a leaf computation of
influence of initial condition
V10mm3 R1.3mm a0.22m/s Bosin?0.61 v00.69m/s B
osin? init 1.57
V10mm3 R1.3mm a0.22m/s Bosin?0.61 v01.04m/s B
osin? init 2.49
this is due to the relaxation of the droplets
shape
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Droplet flow over (?60º) vs. under (?120º) a
leaf computation
V20mm3 R1.7mm a0.45m/s Bosin?0.99 ?60º
V20mm3 R1.7mm a0.45m/s Bosin?0.99 ?120º
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Bio-pesticides initial conclusions

• Addition of carrier material or commercial
  product (bio-pesticide) does not affect the
  Volume Mean Diameter of the spray.
• Dynamics of the droplet over a leaf are governed
  by gravity, Stokes drag and contact angle
  hysteresis these are verified by experiments.
• Droplets shape can be adequately predicted by
  lubrication theory, while inertia and initial
  condition have minor effect.
• Simulating realistically small bio-pesticide
  droplets is extremely computationally intensive
  efficient parallelisation is needed ( see e.g.
  Lee et al (2011), Advances in Engineering
  Software) BUT probably does not add much extra
  physical understanding!