Understanding Heat and Mass Transport at Liquid/Vapor Interfaces and Interfaces with Programmable Surface Properties
PIs: Lois Gschwender (RXBT), Larry Byrd (RZPS), Alex Briones(UDRI), Jamie Ervin,(UDRI) Shawn Putnam (UTC)
Grant No. 2303BR5P FY09-FY12
Outline
• Introduction
– Objectives/Goals/Impact
– Approach
• RX Experimental
• RZ Continuum modeling of the liquid with molecular dynamics level modeling for enhanced surfaces
– Science
– Accomplishments
– Next years work
Objective
Develop a fundamental understanding of heat and mass transfer during liquid/vapor phase change:
1. Outline the key physical mechanisms that limit thermal transport across solid/liquid/vapor interfaces .
2. Validation of theoretical models that incorporate surface effects such as van der Waals forces to predict heat and mass transport during non-equilibrium processes.
3. Explore two-phase heat and mass flow at interfaces with programmable surface properties (e.g. photosensitive SAMs and synthetic proteins with switchable properties such as hydrophobicity, conductivity, and charge).
• Understanding phase change at the micro-scale will allow better prediction and control of – Critical heat flux
– Static and dynamic flow instabilities
– Limitations to heat transfer
• Single droplet evaporation provides a starting point with the smallest impact from bulk fluid mechanics that interact during phase change.
• This work will also aid in the development of better multi-scale models.
Figure 1: Baker (1954) Flow Map for Horizontal Two-Phase Flow
Relevance to Basic Science
Impact
The need for better performance led to unstable designs that were made possible by computer control.
YB-49 project was cancelled in 1948 following an accident that killed two test pilots and three engineers.
Forty years later the B2 bomber made its public debut in 1988
Impact
•INVENT studies have shown weight savings and better thermal management is possible with vapor cycle systems. •Two phase heat transfer requires less coolant flow and can minimize temperature differences in the presence of high heat fluxes for applications such as electronics, radar, DEW
1
10
100
1000
0 10 20 30
m1/m
2
DT (C)
H2O
NH3
R22
FC72
To optimize two phase systems such as pumped loops and vapor compression cycle refrigeration, it may be necessary to avoid or recover from instabilities using computer control.
m1 = single phase flowrate m2 = two phase flowrate
10mm ≤ Rdrop ≤ 200mm
hydrophobic: q > 90o (low surface energy)
hydrophillic: q < 90o (high surface energy)
Why small droplets? •This helps isolate the interfacial phenomena from bulk fluid motion • increased computational
throughput (↓Rdrop → ↓tsimulation) • increased experimental throughput ↑(#drops/sample) • experiments may bridge multi-scale
modeling of two-phase systems
RX: high-speed photography,
high-speed IR thermal mapping, &
time-domain thermoreflectance (TDTR)
q
heat
heat
probe pump
substrate
droplet
Approach
Microdroplet evaporation on heated surfaces
RZ: numerical simulations of experiments
elapsed time = 300 μs
Droplet velocity = 5 mph
Experimental Apparatus for Microdroplet Studies*
heat
probe pump
substrate
droplet
• Phantom V12 high-speed camera (8x32 pixels → 1,000,000 fps) • FLIR SC4000 IR camera (8x32 pixels → 5,000 fps) • Microdroplet Fluid Dispenser (not shown above) • Two-Color Time-Domain Thermoreflectance (TDTR)
• multifunctional studies of heat and mass transfer of coolants with nano- & macro-structured thin-film interfaces
*built in-house
John Bultman Art Safriet
Picoseconds
0 50 100 150 200
Vin
(n
orm
ali
zed
)
0.0
0.5
1.0
1.5
2.0
Al/Si from UIUC
UIUC
AFRL
Time-Domain Thermoreflectance (TDTR)
Picoseconds
0 50 100 150 200
Vin
(n
orm
ali
zed
)
0.0
0.5
1.0
1.5
2.0
Al/SiO2/Si from UIUC
UIUC
AFRL
Picoseconds
0 500 1000 1500 2000
-Vin
/Vou
t
0.0
0.5
1.0
1.5
2.0
Al/Si from UIUC
Model
Experiment
a-SiO2 (500 nm)
Pump (f ≈ 1.11 MHz)
Probe
< 0.3 ps Al (106 nm) 2wo
Si
Dr. Jim Gord Group (RZ), Dr. Sukesh Roy1(contractor), & Dr. Jamie Gengler1,2 (contractor)
IR images of 1mm water droplet evaporating on Al thin-film at room temperature
IR Thermal Mapping of
Evaporating Water Droplet
t=0s t=6s t=12s t=18s t=24s t=30s t=36s
microdrop dispenser
q
water droplet
q = 58o
RH = 30% Dia. = 1mm
12x IR objective
sample
spLs
m
t
Vdrop/1.0
2
)1( 3
D
D
m
m
t=-10.4us t=4.7us t=19.9us t=35.0us t=50.2us t=65.3us t=80.5us t=95.6us t=171.3us
High-speed images of a water microdroplet on an aluminum thin-film at room temperature
High-speed photography of Impinging Microdroplets: Unheated Surface
Quantitative mass flux (fluid dynamics) characterization at microsecond time-scales
q
water droplet:
q = 46.4o
RH = 30%
Rdrop = 27.7um
vdrop = 2.45 m/s
We = 4.5
High-Speed Image (70,000 fps)
Fluid Dynamics of Impinging Microdroplets: Unheated Surface
-50 0 50 100 150 200
time (us)
0
20
40
60
80
100
120
dro
ph
eig
ht
(um
)
- fitdamped oscilator
Droplet Height as a Function of Time
Rdrop= 17.7 mm
vdrop= 3.09 m/s
qEq.= 73.78o
We= 4.61
A= 15.33 mm
= 60.77 khz
-1
= 20.47 ms
ForcesTensionSurface
Inertia
EnergySurface
EnergyKineticWe )cos()( 2/ tAetH t
solution for damped oscillator
Fluid Dynamics of Impinging Microdroplets: Unheated Surface
ForcesTensionSurface
Inertia
EnergySurface
EnergyKineticWe )cos()( 2/ tAetH t
solution for damped oscillator
0 50 100 150
time (us)
0
50
100
150
dro
ph
eig
ht
(um
)
- fitdamped oscilator
Droplet Height as a Function of Time
Rdrop= 22.01 mm
vdrop= 7.78 m/s
qEq.= 57.05o
We= 36.23
A= 17.50 mm
= 43.97 khz
-1
= 13.40 ms
Impinging Droplet Dynamics: Unheated Surface
t=-10.4us t=4.7us t=19.9us t=35.0us t=50.2us
t=65.3us t=80.5us t=95.6us t=171.3us
Microdroplet impinging on Al thin-film at room temperature (54 mm dia.)
Liquid-Gas Phase Numerical Model
• Liquid water constant properties.
• Temperature and species dependent thermodynamic properties.
Continuity Equation
Momentum Equation
Energy Equation
Species Equation
2/12/1
2/1
lg22
2
g
g
l
l
T
P
T
P
R
MWm
gsat PPRT
MWm
2/1
lg22
2
Schrage Evaporation Model:
ggll ggll kkk
ggll mmm 371.01095.9 4 T
Mixture properties:
Wall Adhesion:
www tnn qq sinˆcosˆˆ
Evaporation mechanism
• Schrage’s equation is based on the kinetic theory of gases for a flat interface, corrections have been suggested for a number of possible physical phenomena.* We will study the use of this approach and the appropriate value for the accommodation coefficient
2/12/1
2/1
lg22
2
g
g
l
l
T
P
T
P
R
MWm
Note since the measured accommodation coefficient is often quite small, this could imply that 1) The largest resistance to heat transfer is in the fluid
mechanics 2) The model is overly simplistic and is just a correction
factor for multiple effects
* Marek, R. and Straub, J., “Analysis of the evaporation coefficient and condensation of water” , Int. J. of Heat and Mass Transfer, 44 (2001, 39-53
Q
R1 R2 R3
T2 T1 Ts Tg
Q
Liquid
Tg T2
T1 Ts
Mechanisms to capture with modeling
• Dynamics of normal and glancing droplet impingement on surfaces.
• Impact of vaporization models such as Schrage’s on evaporation from surfaces.
• The effect of curvature on droplet vaporization.
• The mechanism of droplet de-pinning during vaporization.
• Contact line dynamics on surfaces at various range of conditions (We, Ca, Re, Bo, Ma, Ja, … someone’s last name number etc.
• Droplet evaporation from hydrophilic, patterned, and continuous gradient surfaces upon impingement.
2/12/1
2/1
lg22
2
g
g
l
l
T
P
T
P
R
MWm
Cases Investigated
• Comparison with literature
– Pinned droplet evaporation on hot surface
– Large droplet with advancing = static contact angle
– Static vs Dynamic contact angle
• Comparison with in-house experiments
– Impinging droplet on unheated surface
Pinned Droplet Evaporation from a Hot Surface Temperature Profiles
Geo-Reconstruct, Dynamic Mesh Adaptive, NITA, and Variable-time Stepping.
Pinned Droplet Evaporation from a Hot Surface: Numerical Comparison
•Ts= 373.15 K • Experimental results indicate that droplet lifetime is 14 s (Crafton, E. F., 2001, ‘‘Measurements of the Evaporation Rates of Heated Liquid Droplets,’’ M.S. Thesis, Georgia Institute of Technology, Atlanta, GA)
Impinging Droplet on a Hot Surface
• We = 220, Ts=180°C, 60° advancing contact angle, •Accommodation coefficient set to 0.03
0.03
Bernardin, J.D., Stebbins, C.J., Mudawar, I., Mapping of Impact and Heat Transfer Regimes of Water Drops Impinging on a Polished Surface, Int. J. Heat Mass Trnsfr. 40 (1997) 247-267.
Summary
• Pinned Droplet (1mm diameter) – Reasonable agreement between predicted and measured volume as a
function of time over most of the lifetime of the drop
• Impinging Droplet (3 mm diameter) – Reasonable agreement during the early spreading stage of the droplet
• Comparison with in-house – Reasonable agreement for short times at room temperature with
unheated surface
• The experimental and numerical foundations have been set for future two phase flow studies
Future Work
• In-house experiments with heated surfaces using TDTR.
• Characterize the effect of curvature on droplet vaporization.
• Implement other strategies such Blake’s molecular kinetics-based contact line velocity to improve accuracy of numerical simulations.
• Explore the dependence of interfacial thermal conductance on surface energy using molecular dynamics modeling
Surface enhancements:
hydrophilic patterned Continuous gradient
Programmable through the use of the appropriate wavelength of light from hydrophilic to hydrophobic.
Thermal Characterization of Solid-Liquid, Solid-Vapor, & Liquid-Vapor Interfaces
Temperature Discontinuity at Interfaces:
hydrophobic hydrophilic
GAl ~ 180 MW m-2 K-1
GAu ~ 100 MW m-2 K-1
GAl ~ 60 MW m-2 K-1
GAu ~ 50 MW m-2 K-1
Au Au
1 2 3
4
Metal-Surfactant-Water Interfaces
1) OTS modified Al surface
2) C18-modified Au surface
3) PEG-silane modified Al surface
4) C11-OH modified Au surface
Interfacial Conductance (G)
JQ = G DT
Vapor Pressure: ~195 Pa, Evaporation Rate: ~ 0.5 g m-2 s-1, Tliquid = 35oC, Heat Flux: JQ ≈ 1200 W m-2
Temperature Discontinuity during Steady-State Evaporation
JQ ~ 100 MW m-2
G ~ 100 MW m-2 K-1
∆T ~ 1 K
Equilibrium Thermodynamics
phase changes - Tl = Tv, pl = pv, μl = μv
vapor
liquid
Steady-state Evaporation
JQ
DT
x
T
Conclusions for numerical modeling
• The computational domain needs to be about 10 times larger than the droplet radius to avoid B.C. disturbances.
• Grid independence analyses indicate that the grid needs to be ~0.5 mm. Below this grid size the continuum mechanics are not applicable.
• Non-uniform mesh with grid adaption needs to be used for slow droplet vaporization due to numerical stiffness.
• NITA needs to be used for slow evaporation since it speeds up the calculations.
• Variable time stepping must be used with NITA.
• Scalability was tested with 3, 6, and 12 processors. By increasing the number of processors above 3 the computational time increased.
• Geo-Reconstruct Scheme for discretization of volume of fraction equation exhibits superior results than the CICSAM scheme.
Numerical Procedure using Fluent
• Explicit VOF.
• 1st order temporal and 2nd order spatial discretization.
• Second order upwind scheme discretization is used for species mass fraction and energy equations.
• Quick is used for discretization of the momentum equation.
• CICSAM, Compressive, and Geo-Reconstruct schemes are used for discretization of the volume of fraction equation.
• Non-adaptive and dynamic adaptive meshing are used.
• Fixed and variable time stepping methods are used.
Static (qS) vs. Dynamic (qD) Contact Angle
Experimental results from Šikalo, S., Tropea, C., and Ganić, E.N., “Dynamic Wetting Angle of a Spreading Droplet,” Exp. Thermal & Fluid Sci. 29 (2005) 795-802. Numerical results match the spreading factor (d/Do) very well when the dimensionless time t×Vo/Do is less than 1.0 with both qS and qD methods. For t×Vo/Do>1.0, calculations with qS and qD method over-predict and under-predict,
respectively.