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

Mesh and Boundary Conditions

Pinned Droplet Evaporation from a Hot 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 Velocity Profiles

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.

Backup

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.

Fluid Dynamics of Impinging Microdroplets: Unheated Surface

)cos(2/

)( tt

AetH

0 10 20 30 40

Weber #

0

10

20

30

40

-1(m

s)

0 10 20 30 40

Weber #

20

40

60

80

(k

Hz)

Comparison of damped oscillator fit data for impinging water droplets of different kinetic energies

q

solution for damped oscillator