modeling and simulation of supercritical fluid processing ... review meeting/yang muri neem year 2...

NEEM MURI

Multi-Scale Modeling of Nano Aluminum Particle Ignition and Combustion


Modeling and Simulation of Supercritical Fluid Processing of Nano Energetic Materials


Puneesh Puri, Tao Liu, Ying, Huang, and Vigor YangThe Pennsylvania State University

University Park, PA 16802

November 7, 2006

Puneesh Puri, Tao Liu, Ying, Huang, and Vigor YangThe Pennsylvania State University

University Park, PA 16802

November 7, 2006

NEEM MURI



• Study Nano-Scale Energetic Materials (NSEM) behavior in two-phase flow environments at meso and macro scales

• Optimize NSEM fabrication techniques, especially the rapid expansion of supercritical solution (RESS) approach

• Simulate the RESS experiments of Ken Kuo at PSU

• Study Nano-Scale Energetic Materials (NSEM) behavior in two-phase flow environments at meso and macro scales

• Optimize NSEM fabrication techniques, especially the rapid expansion of supercritical solution (RESS) approach

• Simulate the RESS experiments of Ken Kuo at PSU

NEEM MURI Fabrication of Nano Energetic Materials

carrier fluid

carrier fluid

Challenges and Objectives

Injection dynamics- supercritical fluid injection and evolution

Thermodynamics and transport- nucleation and particle growth

Thermophysical properties

Challenges and Objectives

Injection dynamics- supercritical fluid injection and evolution

Thermodynamics and transport- nucleation and particle growth

Thermophysical properties

road map

homogeneous nucleation

binary system

subsonic singlespecies fluid jet

injection

transonicflow

C2H4/CH4/N2model validation

RDX

RESS Process• Material dissolves in a supercritical carrier fluid

which has liquid-like solvent power• Supercritical solution is then rapidly expanded at

subcritical condition• Abrupt decrease in dissolving capacity of the

solvent results in sudden precipitation of the solute.

RESS Process• Material dissolves in a supercritical carrier fluid

which has liquid-like solvent power• Supercritical solution is then rapidly expanded at

subcritical condition• Abrupt decrease in dissolving capacity of the

solvent results in sudden precipitation of the solute.

NEEM MURI

0)~(=

∂∂

+∂∂

jxu

tρρ

j

ijijij

j

ijijjij

xCLR

xpuu

tu

∂

++∂−=

∂

−+∂+

∂

∂ )()~~()~( τδρρ

j

jJj

j

ijij

xqQK

xuuPE

tqE

∂++∂

−=∂

−+∂+

∂+∂ )(]~)~[()~( τρρ

• Favre-filteredconservationequations

• Favre-filteredconservationequations

• Closure requirements

• Closure requirements

Large Eddy Simualtion (LES) Formulation of Supercritical Fluid Dynamics

• Thermodynamic and transport properties

• Subgrid-scale turbulence interaction

• Chemical kinetics

• Thermodynamic and transport properties

• Subgrid-scale turbulence interaction

• Chemical kinetics

, ,p imZ C Dμ λ , ,

iω &

CLR ,,

NEEM MURI Supercritical Fluid Jet Injection and Mixing

p∞ = 9.3 MPaT∞ = 300 K uin = 15 m/s Tin = 120 KDin = 254 μm

p∞ = 9.3 MPaT∞ = 300 K uin = 15 m/s Tin = 120 KDin = 254 μm

• Thermodynamic non-idealities and transport anomalies in transcritical regime- rapid property variations - large density gradient

• Diminishment of surface tension and enthalpy of vaporization• Pressure-dependent solubility • High Reynolds number

• Thermodynamic non-idealities and transport anomalies in transcritical regime- rapid property variations - large density gradient

• Diminishment of surface tension and enthalpy of vaporization• Pressure-dependent solubility • High Reynolds number

Unified CFD model has been established • Full conservation equations • Real-fluid thermodynamics & transport• Advanced numerical algorithms • LES-based turbulence closure

Unified CFD model has been established • Full conservation equations • Real-fluid thermodynamics & transport• Advanced numerical algorithms • LES-based turbulence closure

NEEM MURI Effect of Pressure on Flow Evolution(Lin & Jackson, AFRL)

Shadowgraph images of supercritical methane/ethylene jets at various Pinj/Pchm. xCH4 = 0.1, Tinj = Tchm = 300 K, and d =1.0 mm.

• Supercritical jet behaves like a highly under-expanded ideal gaseous jet at high Pinj/Pchmwith Mach disk and barrel shock visible in image.

• The shock-wave structure gradually decreases in size as Pinj/Pchm decreases.

• Supercritical jet behaves like a highly under-expanded ideal gaseous jet at high Pinj/Pchmwith Mach disk and barrel shock visible in image.

• The shock-wave structure gradually decreases in size as Pinj/Pchm decreases.

Pinj/Pc 1.38 1.29 1.22 1.17Pinj/Pchm 37.5 9.2 4.5 2.2

NEEM MURI

Shadowgraph images of supercritical methane/ethylene jets at various Pinj/Pchm. xCH4=0.1, Tinj=285 K, Tchm=300 K, and d=1.0 mm.

Shadowgraph images of supercritical methane/ethylene jets at various Pinj/Pchm. xCH4=0.1, Tinj=285 K, Tchm=300 K, and d=1.0 mm.

• The jets injected at a temperature close to the critical temperature exhibit opaque shadowgraph images, indicating two-phase mixtures within the jets.

• The dome-shaped near-field jets indicate the existence of shock structures, which are masked by the opaque appearances.

• The jets injected at a temperature close to the critical temperature exhibit opaque shadowgraph images, indicating two-phase mixtures within the jets.

• The dome-shaped near-field jets indicate the existence of shock structures, which are masked by the opaque appearances.

Pinj/Pc 1.11 1.07 1.04Pinj/Pchm 34.0 8.1 2.0

Visualization of Near-Field Jets (Lin & Jackson, AFRL)

NEEM MURI

Shadowgraph images of methane/ethylene jets at various injection temperatures. xCH4 = 0.1 and d = 1.0 mm.

Shadowgraph images of methane/ethylene jets at various injection temperatures. xCH4 = 0.1 and d = 1.0 mm.

• The Tinj/Tc=1.03 jet has a large jet expansion angle and an opaque appearance due to condensation.

• The difference in jet expansion angles may come from the substantial difference in specific heat ratios and the pressure rise due to the release of latent heat during condensation.

• The Tinj/Tc=1.03 jet has a large jet expansion angle and an opaque appearance due to condensation.

• The difference in jet expansion angles may come from the substantial difference in specific heat ratios and the pressure rise due to the release of latent heat during condensation.

Pinj/Pc 1.15 1.16Tinj /Tc 1.23 1.03Pinj/Pchm 35.7 36.7γ (Cp/Cv) 1.56 5.51

Visualization of Near-Field Jets(Lin & Jackson, AFRL)

NEEM MURI

Internal structures of supercritical ethylene jets at various Tinj/Tc are shown. L/D = 4, θ = 1°, pchm = 0.2 MPa, Tchm= 300 k.

• An abrupt boundary indicating the onset of two-phase transition is located inside the injector for the fluid injected at a temperature close to the critical temperature.

• Homogeneous droplet nucleation, which is prompted through rapid expansion to reach a supersaturation state and can produce a large quantity of droplet nuclei almost spontaneously, is believed to be the mechanism for phase transition.

• Jet expansion angle and degree of opaqueness decrease as the injection temperature increases.

• Based on the relative darkness of the jet images, nucleation rate or number density of droplet nuclei decreases as the injection temperature increases.

Tinj/Tc 1.00 1.01 1.03 1.08Pinj/Pc 1.04 1.02 1.00 1.03

Internal Flow Structures in Injectors(injection from super- to sub-critical)

NEEM MURINear-Field Jet Evolution

P0/Pchm= 37

P0/Pchm= 10P0/Pchm= 5

• For a small pressure ratio, no Mach disk but a series of expansion /oblique-shock waves occur.

• For a small pressure ratio, no Mach disk but a series of expansion /oblique-shock waves occur.

• For a large pressure ratio, rapid expansion results in a dome-shaped jet boundary near the nozzle and is terminated by a Mach disk.

• For a large pressure ratio, rapid expansion results in a dome-shaped jet boundary near the nozzle and is terminated by a Mach disk.

P0/Pchm= 34P0/Pchm= 10

|∇p| (MPa/m)

NEEM MURINear-Field Jet Evolution (P0/Pchm ≈ 34)

Ma

Experiment: Ethyelen/SF6 ; P0/Pchm= 34Experiment: Ethyelen/SF6 ; P0/Pchm= 34 Simulation: Air to Air; P0/Pchm= 37Simulation: Air to Air; P0/Pchm= 37

|∇p| (MPa/m)

NEEM MURINear-Field Jet Evolution (P0/Pchm = 10)

|∇p| (MPa/m)

Ma

NEEM MURI

Entropy-pressure diagram for methane/ethylene mixture with xCH4=0.1.

• The path originated at a temperature close to the critical point can readily penetrate into the two-phase region during isentropic expansion.

• The expansion path initiated at a temperature away from the critical point may exhibit an idea gas expansion.

• Condensation phenomenon is more sensitive to injection temperaturethan injection pressure.

• The path originated at a temperature close to the critical point can readily penetrate into the two-phase region during isentropic expansion.

• The expansion path initiated at a temperature away from the critical point may exhibit an idea gas expansion.

• Condensation phenomenon is more sensitive to injection temperaturethan injection pressure.

1 2 3 4 5 6 7P (MPa)

120

140

160

180

200

220

S (J

/Mol

e/K)

T = 350 K

300 K

265 K250 K235 K220 K

200 K

CH4 - C2H4 MIXTURE, xCH4 = 0.1

BUBBLE-POINTLINE

DEW-POINTLINE

TWO-PHASEMIXTURE

VAPOR

276.5 KC.P.

SUPER-CRITICALFLUID

LIQUID

Tinj/Tc=1.23

Tinj/Tc=1.03

Isentropic Expansion Paths

NEEM MURIHomogeneous Nucleation Model

• A comprehensive model is established to obtain the dew-point pressure, saturated liquid/vapor density, and saturated liquid/vapor composition.

• Flow density and temperature are acquired by solving the 3D conservation equations for a multi-component system. Pressure can be determined by the equation of state (EOS) at given temperature and density.

• When the local temperature is less than the critical mixing temperature and the local density falls between the saturation-state values, the homogeneous equilibrium model is activated and replaces the EOS to get the local pressure.

• A comprehensive model is established to obtain the dew-point pressure, saturated liquid/vapor density, and saturated liquid/vapor composition.

• Flow density and temperature are acquired by solving the 3D conservation equations for a multi-component system. Pressure can be determined by the equation of state (EOS) at given temperature and density.

• When the local temperature is less than the critical mixing temperature and the local density falls between the saturation-state values, the homogeneous equilibrium model is activated and replaces the EOS to get the local pressure.

NEEM MURI



• Development of a unified model for ignition and combustion of aluminum particles applicable at all scales

• Investigation of the essential difference in physiochemical mechanisms under micro and nano scales

• Study of the collective behavior of particle dust combustion in flow environments• Coupling the studies of the USC group at meso/micro scales

• Development of a unified model for ignition and combustion of aluminum particles applicable at all scales

• Investigation of the essential difference in physiochemical mechanisms under micro and nano scales

• Study of the collective behavior of particle dust combustion in flow environments• Coupling the studies of the USC group at meso/micro scales

Quantum Micro MesoNano Macro

Length (m)

10-12 10-9 10-6 10-3 100

USC

PSU

NEEM MURI

Hydrogen Inlet

Alum inum DustF lam e

G lass Beads

Exhaust

Linear Actuator

Piston Rod

Alum inumParticles

Aerosol GeneratorM ain Body

E jector

O xidizerInlet

O xidizerInlet

Co-F low Shroud

A lum inumAerosol

Exhaust

AluminumDust Flame

Co-Flow Shroud

Glass Beads

AluminumAerosol

EjectorOxidizer InletOxidizer

Inlet

AluminumParticles

Piston Rod

Linear Actuator

Aerosol GeneratorMain Body

Hydrogen Inlet

• Experimental apparatus– Aluminum aerosol is generated by

high velocity gas (> 100 m/s) over a bulk amount of aluminum particles which is fed by a linear actuator

– High-flow particle ejector is employed to reduced the main flow velocity without changing the equivalence ratio of the aerosol

– Particle-laden flow is ignited using a hydrogen/air diffusion flame, and thus removed subsequent to steady burning

• Experimental apparatus– Aluminum aerosol is generated by

high velocity gas (> 100 m/s) over a bulk amount of aluminum particles which is fed by a linear actuator

– High-flow particle ejector is employed to reduced the main flow velocity without changing the equivalence ratio of the aerosol

– Particle-laden flow is ignited using a hydrogen/air diffusion flame, and thus removed subsequent to steady burning

Experimental Setup

Al

airAir

NEEM MURI Laminar Premixed Flames

stoichiometric methane/air flamestoichiometric methane/air flame stoichiometric aluminum/air aerosol flame with particle size 5–8 μm

stoichiometric aluminum/air aerosol flame with particle size 5–8 μm

~ 1.28 cm~ 1 cm~ 1 cm

Adopted from Risha, et al., Penn State University

NEEM MURI

Captured images of aluminum/air dust flame as a function of volumetric flow rate; particle size5-8 μm and air flow rate of 26.3 LPM and φ=1.201

Captured images of aluminum/air dust flame as a function of volumetric flow rate; particle size5-8 μm and air flow rate of 26.3 LPM and φ=1.201

Effect of Mass Flow Rate

Qnet = 12974 [cm3/min] 12158 10660 8444

h f=4

.57

cm

h f=3

.88

cm

h f=3

.31

cm

h f=2

.85

cm

SL = 16.26 [cm/s] 16.73 17.33 20.63

NEEM MURI Laminar Flames of Mono- and Bimodal-Dispersed Aluminum Particles/Air Mixtures

100% micro particles (5–8 μm)100% micro particles (5–8 μm) 20% nano particles (100 nm) addition20% nano particles (100 nm) addition

Bimodal particle flame features increased flame speed and thicker flame zone. Bimodal particle flame features increased flame speed and thicker flame zone.

NEEM MURI Aluminum Combustion in Steam

Aluminum DustFlame

Exhaust

Linear Actuator

Piston Rod

AluminumParticles

Aerosol GeneratorMain Body

Ejector

AluminumAerosol

Steam Inlet Steam Inlet

Steam GeneratorAir

Hydrogen

Liquid WaterTC

Flame of Al/H2O/N2 mixtures

NEEM MURI Modeling of Bimodal Aluminum Dust Flame at Fuel-Lean Conditions

preheatzone

flamezone III

post flamezone

,1bx v= τ

x0x =

T

,1ignT

particles heatedby local gas

gas heated byconduction fromflame zone

burning oflarge particles

flame zone I

flamezone II

,2ignT

burning ofsmall particles

0x Z= 0 ,2bx Z v= + τ

overlappingburning

a) overlapping flame

gas heated byconduction fromflame zone

preheatzone I

flamezone II

post flamezone

,1bx v= τ

x

0x =

T

,1ignT

particles heatedby local gas

burning oflarge particles

flame zone I

,2ignT

burning ofsmall particles

0x Z= 0 ,2bx Z v= + τ

b) separated flame

preheatzone II

• Flame configuration depends on the mass concentration, particle size, ignition temperature, and burning time of each group of aluminum particles.

• Ignition temperature and burning time of aluminum particle are needed as input parameters.

• Flame configuration depends on the mass concentration, particle size, ignition temperature, and burning time of each group of aluminum particles.

• Ignition temperature and burning time of aluminum particle are needed as input parameters.

NEEM MURI Burning Time of Single Aluminum Particles in Air as Function of Particle Diameter

Micron and larger size particles:

• Burning under diffusion-controlled conditions

• Beckstead’s particle burning time correlation based on various experimental data:

Nano size particles:

• Burning under kinetically-controlled conditions

• d1-model from theoretical prediction; However, d0.3 law based on experimental data of Parr et al., 2003


• Burning under diffusion-controlled conditions

• Beckstead’s particle burning time correlation based on various experimental data:


• Burning under kinetically-controlled conditions

• d1-model from theoretical prediction; However, d0.3 law based on experimental data of Parr et al., 2003

1.8

0.2 0.11 0

beff

dC T p X

τ =

Particle diameter, μm

Bur

ning

time,

ms

10-2 10-1 100 101 102 10310-1

100

101

102

103

104

105Wilson and Willams [27]Wong and Turns [29]Prentice [28]Olsen and Beckstead [30]Hartman [26]Friedman and Macek [21]Davis [25]Parr et al. [9] (T0=1500 K)Parr et al. [9] (T0=2000 K)Models

d0.3

d1.8

1500 K

2000 K

3500 K

NEEM MURI Ignition Temperature of Single Aluminum Particles in Air as Function of Particle Diameter


• For particles ( > 100 μm), ignition occurs at temperature near the melting point of aluminum oxide (2350 K)

• For particles (1~100μm), ignited over a wide range of temperature from 1300 to 2300 K


• Ignition reported to occur at temperature as low as 900 K

• Trunov et al. (2005) suggested that aluminum oxidation and polymorphic phase transformation of the alumina shell are responsible for these diverse ignition temperatures


• For particles ( > 100 μm), ignition occurs at temperature near the melting point of aluminum oxide (2350 K)

• For particles (1~100μm), ignited over a wide range of temperature from 1300 to 2300 K


• Ignition reported to occur at temperature as low as 900 K

• Trunov et al. (2005) suggested that aluminum oxidation and polymorphic phase transformation of the alumina shell are responsible for these diverse ignition temperatures

Particle Diameter, μm

Igni

tion

Tem

pera

ture

,K

10-2 10-1 100 101 102 103 104500

1000

1500

2000

2500

3000

3500Parr et al. [11]Bulian et al. [36]Assovskiy [35]Yusasa e tal. [33,34]Brossard et al. [32]Ermakove tal. [31]

Particle Diameter, μm

Igni

tion

Tem

pera

ture

,K

10-2 10-1 100 101 102 103 104500

1000

1500

2000

2500

3000

3500Derevyaga et al. [30]Merzhanov et al. [29]Friedman et al. [27,28]Trunov et al. [15]CurveFit

NEEM MURI Flame Speed as Function of Particle Diameter in Mono-Dispersed Aluminum/Air Mixture

Kinetic-Controlled RegionKinetic-Controlled Region Diffusion-Controlled RegionDiffusion-Controlled Region

particle diameter, m

S L,m

/s

10-7

10-7

10-6

10-6

10-5

10-5

10-4

10-4

10-2

10-1

100

101

Risha et al. [8]Boichuk et al. [6]Goroshin et al. [4]Goroshin et al. [3]Ballal [2]Cassel [1]Molecular limit (present)Theory (present)

φ = 0.85

d−0.98

d−0.59

0

preoxidatedparticles

non-preoxidatedparticles

Kn > 1 Kn < 1• For non-preoxidized particles,

particles at sub-nano scales are assumed be assumed to behave as large molecules. Maximum flame speed is achieved with particle size approaching to its molecular limit.

• For pre-oxidized particles, as the percentage of active aluminum and the energy content of the particle drop below a critical point, the flame speed of the particle-laden flow begins to decrease with decreasing particle size. At the extreme situation, the energy release from particle oxidation may not even be able to sustain a flame.

NEEM MURIAluminum Combustion Submodel Development

• Thermochemistry— Al, AlO, AlOAl, OAlO, AlOAlO, Al2O3(l), AlH, AlOH, etc.— Data from JANNAF data base or Swihart and Catoire (C&F, 2000)

• Transport Properties— Data for Al, AlO obtained from Roger A. Svehla, NASA TR R-132 (1962) — Data for AlOAl, OAlO, AlOAlO, AL2O3(l), AlH, AlOH, etc.obtained using kinetic

theory

• Chemical Kinetics— Current aluminum submodel consists of 15 species and 22 gas-phase reactions;

Sources: Al/HCl/H2O/CO2/O2 reaction mechanisms prepared by Swihart and Catoire(J.Phys. Chem., 2002; C&F, 2003; JPP, 2003)

— Model for non-aluminum containing elementary reactions obtained from GRI-MECH 3.0 mechanism.

• Thermochemistry— Al, AlO, AlOAl, OAlO, AlOAlO, Al2O3(l), AlH, AlOH, etc.— Data from JANNAF data base or Swihart and Catoire (C&F, 2000)

• Transport Properties— Data for Al, AlO obtained from Roger A. Svehla, NASA TR R-132 (1962) — Data for AlOAl, OAlO, AlOAlO, AL2O3(l), AlH, AlOH, etc.obtained using kinetic

theory

• Chemical Kinetics— Current aluminum submodel consists of 15 species and 22 gas-phase reactions;

Sources: Al/HCl/H2O/CO2/O2 reaction mechanisms prepared by Swihart and Catoire(J.Phys. Chem., 2002; C&F, 2003; JPP, 2003)

— Model for non-aluminum containing elementary reactions obtained from GRI-MECH 3.0 mechanism.

NEEM MURI Effects of Mass Fraction of Nano-Particles in Fuel Formulation on Flame Characteristics

x, cm

Tem

pera

ture

,K

-0.05 0 0.050

1000

2000

3000

4000

5000overlapping flameseparated flame

10%

80%

30%

95%

40%

φ = 0.85

60%

pn =

pn: nano-particle mass fraction in the fuel formulationpn: nano-particle mass fraction in the fuel formulation

At lower values of pn, the flame exhibits a separated spatial structure with a wider flame regime. At higher values of pn, the flame displays an overlapping flame configuration

At lower values of pn, the flame exhibits a separated spatial structure with a wider flame regime. At higher values of pn, the flame displays an overlapping flame configuration

nano-particle addition, pn

Lam

inar

flam

esp

eed,

m/s

Z

0 0.2 0.4 0.6 0.8 10

0.4

0.8

1.2

1.6

2

10-1

100

101

102

Flame Speed, Theo.Flame Speed, Exp.Parameter Z

φ = 0.85

separatedflame

overlappingflame

φ = 1.20

NEEM MURIVarious Stages of Particle Oxidation Behavior

Stage IParticle heating with phase transformations

Stage IParticle heating with phase transformations

Stage IIIHeterogeneous reactions/healing of cracks

Stage IIIHeterogeneous reactions/healing of cracks

Stage IIMelting of core and ignition due to melting/cracking

Stage IIMelting of core and ignition due to melting/cracking

O2 Molecules

Stage IVStage IV

Detached Flame front

Oxide cap

Al (g)

oxidizer

Stage VDetached flame front (micro)

Stage VDetached flame front (micro)

Rout

Rin

δ

O Anions

Al Cations

Phase Transformations

Al2O3(s)Rout

Rin

δO2 Molecules

Al(s)Al(l)

Rout

Rin

δO2 Molecules

Particle consumed due to heterogeneous reactions (Nano)

Particle consumed due to heterogeneous reactions (Nano)

Melting of oxide layer to form cap (Micro)

Melting of oxide layer to form cap (Micro)

NEEM MURIIgnition Criteria (1/3)

2* 0heat

f

Dtα

=

20* fg

meltp f

D ht

c Tα=

Δ

2 2

2

2O O pdN P D

dt mKT

π

π=

• Ignition at nano scale occurs at much lower temperature than at micro scale• Two schools of thought on ignition criteria :

– cracking due to thermal stress– polymorphic phase transformation of oxide layer

• Characteristic time scales for heating, melting and healing

• Ignition at nano scale occurs at much lower temperature than at micro scale• Two schools of thought on ignition criteria :

– cracking due to thermal stress– polymorphic phase transformation of oxide layer

• Characteristic time scales for heating, melting and healing

Particle Diameter, nm

Mel

ting

Tem

pera

ture

,K

0 100 200 300

400

600

800

1000

Bulk AluminumTheory [23]MD Simulations [22]Experiment [21]

NEEM MURIIgnition Criteria (Cracking) (2/3)

Temperature vs. time ramp for particle heatingTemperature vs. time ramp for particle heating

• Ignition observed near melting point of aluminum~ 940K

• Melting of aluminum core and change in density due to melting of core lead to a pressure rise of 88000 atm

• Due to higher curvature in small particles, oxide coating under higher tension as compared to large particles

• This leads to rupture of the oxide shell and hence ignition

• Ignition observed near melting point of aluminum~ 940K

• Melting of aluminum core and change in density due to melting of core lead to a pressure rise of 88000 atm

• Due to higher curvature in small particles, oxide coating under higher tension as compared to large particles

• This leads to rupture of the oxide shell and hence ignition Particle size: 20-30 nm

Heating air temperature: 1173 K

Particle size: 20-30 nm

Heating air temperature: 1173 K

Adapted from Rai et al., JPC. 2004Adapted from Rai et al., JPC. 2004

NEEM MURIIgnition Criteria (3/3)

Ignition temperature as function of particle diameter. Ref: Dreizin, 2005Ignition temperature as function of particle diameter. Ref: Dreizin, 2005

• If the characteristic time scale for the growth of layer through direct oxidation is small as compared to that of melting and cracking, then the oxidation for the rest of time can be modeled as that of diffusion through the layer.

• If the characteristic time for layer growth is larger, the oxidation process has to be modeled as the direct attack of oxygen on aluminum surface with cracking.

• An ignition criteria based on melting point of alumina attained by self heating, involving phase transformations proposed by Dreizin.

• If the characteristic time scale for the growth of layer through direct oxidation is small as compared to that of melting and cracking, then the oxidation for the rest of time can be modeled as that of diffusion through the layer.

• If the characteristic time for layer growth is larger, the oxidation process has to be modeled as the direct attack of oxygen on aluminum surface with cracking.

• An ignition criteria based on melting point of alumina attained by self heating, involving phase transformations proposed by Dreizin.

NEEM MURI

• To determine the dominant combustion mechanism, a Damkohler number, Da, for surface reaction is defined as

• Small particles at low pressures burn under kinetically controlled conditions. Large particles and high pressures favor diffusion controlled mechanism

• The characteristic burning time follows d1 law and is inversely proportional to pressure under kinetically controlled mechanism and is independent of pressure, following the d2 law in a diffusion controlled mechanism.

• To determine the dominant combustion mechanism, a Damkohler number, Da, for surface reaction is defined as

• Small particles at low pressures burn under kinetically controlled conditions. Large particles and high pressures favor diffusion controlled mechanism

• The characteristic burning time follows d1 law and is inversely proportional to pressure under kinetically controlled mechanism and is independent of pressure, following the d2 law in a diffusion controlled mechanism.

Mode of Combustion (1/2)

, 0 ,

, ,4 ln(1 )b diff p o

b kin o

t MW kPd XDa

t D iYρ∞

∞

= =+

NEEM MURI

Rout

Rin

δO2 Molecules

Mode of Combustion (2/2)

Heterogeneous(diffusion controlled)

Heterogeneous(kinetically controlled)

Homogeneous (microscale)

• In case of direct oxidation, the process is kinetically controlled due to small diffusion time scales.

• In case of heterogeneous oxidation through oxide layer, the process is diffusion controlled due to slow diffusion of Al anions or O cations through the oxide layer

• Heterogeneous mode burning more favorable for nano materials as compared to a detached flame for micro particles

• The melting point and boiling point of aluminum are 933 and 2791 K respectively. For alumina the melting and boiling points are 2327 and 4000 K.

• As oxide melts Al can vaporize forming a detached flame. But if the rate of heterogeneous oxidation is very fast, particle can self heat to melting point and get consumed in a pure heterogeneous fashion

• In case of direct oxidation, the process is kinetically controlled due to small diffusion time scales.

• In case of heterogeneous oxidation through oxide layer, the process is diffusion controlled due to slow diffusion of Al anions or O cations through the oxide layer

• Heterogeneous mode burning more favorable for nano materials as compared to a detached flame for micro particles

• The melting point and boiling point of aluminum are 933 and 2791 K respectively. For alumina the melting and boiling points are 2327 and 4000 K.

• As oxide melts Al can vaporize forming a detached flame. But if the rate of heterogeneous oxidation is very fast, particle can self heat to melting point and get consumed in a pure heterogeneous fashion

Al2O3(s)Rout

Rin

δ

O Anions

Al Cations

Al(s)Al(l)

Detached Flame front

Oxide cap

Al (g)

oxidizer

NEEM MURIMolecular Dynamics Code Development

• Capable of simulating micro-canonical (NVE), canonical (NVT), isobaric isoenthalpic-isobaric (NPH), isothermal-isobaric (NPT) ensembles

• Verlet and up to fifth-order predictor-corrector algorithms implemented• Can handle multi-atom simulations• Separate algorithms implemented for calculations of different droplet sizes in

case of liquid phase• Spatial decomposition using Linked List used for separate post processing code• Lennard Jones, Glue potential, and Streitz Mintmire potential used for aluminum• Validation done using argon• Code parallelized using MPI for distributed computing facility• Thermodynamic properties: temperature, pressure, kinetic energy, potential

energy, cohesive energy, surface tension, diffusivity using velocity auto correlation functions, melting temperature, vacancy formation energy, latent heat of melting, thermal expansion coefficient

• Structural properties: radial distribution function, lattice order parameter• Mechanical properties: internal stresses, elastic constants, bulk modulus- (in

progress)

NEEM MURIMelting Temperature Calculations for Bulk Argon

Iterations

Tem

pera

ture

(K)

Tran

slat

iona

lord

erpa

ram

ater

5.0E+04 1.0E+05 1.5E+050

50

100

150

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

TemperatureT.O.P

Drop in Translational Order Parameter during melting

Iterations

Tem

pera

ture

(K)

Pote

ntia

lEne

rgy/

atom

(eV

)

5.0E+04 1.0E+05 1.5E+050

50

100

150

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02TemperatureP.E.

Jump in Potential Energy during melting

Iterations

Tem

pera

ture

(K)

Ato

mic

Den

sity

(ato

ms/

nm3 )

5.0E+04 1.0E+05 1.5E+050

50

100

150

0.016

0.018

0.020

0.022

0.024

0.026

0.028

0.030TemperatureAtomic Density

Drop in Atomic Density during melting

r(nm)

g(r)

10 20 30 40 50 600

5

10

15

20 Before Melting (FCC Lattice)After Melting (Liquid)

Micro-canonical simulation for bulk argon with velocity scaling; 864 atoms; steady temperature gradient 10-3K/step, using predictor corrector, Tm=104.8K at 55 MPa

NEEM MURICode Validation (1/4)

Isoenthalpic-isobaric ensemble

Pressure: 90 MPa

N: 256 atoms

Time step: 8.6 fs

dT/dt=0.001K/step

Tm=117 K (117)

Iterations

Tem

pera

ture

(K)

Tran

slat

iona

lord

erpa

ram

ater

5.0E+04 1.0E+050

50

100

150

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

TemperatureT.O.P

Drop in Translational Order Parameter during melting

Ref: Solca et al., Chemical Physics, 224 (1997)Ref: Solca et al., Chemical Physics, 224 (1997)

Iterations

Tem

pera

ture

(K)

Pote

ntia

lEne

rgy/

atom

(eV

)

1.0E+05 2.0E+05600

650

700

750

800

850

900

950

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94TemperatureP.E.


Pressure: 44.56 kbar

Isoenthalpic-isobaric ensemble

Velocity scaling

Tm=837.7 K (840.9 K)

Average atomic density: 0.03236 atom/A3

(0.03403)

Energy per atom: 0.1356 eV (0.1317)

Ref: Agarwal et al., J. Chem. Phys. , 118, 21 (2003)Ref: Agarwal et al., J. Chem. Phys. , 118, 21 (2003)


A 16384 atom droplet of liquid Argon at 98K in equilibrium with its saturated vapor using NVE simulationsA 16384 atom droplet of liquid Argon at 98K in equilibrium with its saturated vapor using NVE simulations

Ref: Dr. Little, PhD Thesis, Penn State UniviersityRef: Dr. Little, PhD Thesis, Penn State Univiersity

Density contour (kg/cm3)

r/σ

g(r)

1.0 2.0 3.0 4.0

0

1

2

3Ref. 69 (Allen & Tildesley)Current Study

Radial distribution function at ρ*=0.844 and T*=0.71

Solid state ArgonSolid state Argon


Pressure: 0.25 kbar

Rcutoff: 10 Angstroms

Epsilon: 125 K

Sigma: 3.446 A

Isothermal-isobaric ensemble

Tm=105 K (105 K)

Iterations

Vol

ume

(cm

3 /mol

)

Tem

pera

ture

(K)

200000 300000 400000 500000

25

30

35

40

60

80

100

120

140

160

180Temperature (K)Volume (cm3/mol)

Ref: Nose et. al, J. Chem. Phys., 84, 3 (1986) Ref: Nose et. al, J. Chem. Phys., 84, 3 (1986)


Pressure (Pa)

Mel

ting

Tem

pera

ture

(K)

2.0E+09 4.0E+09

200

400

600

800

ExperimentalThermodynamic Tm(Zha et al.)Structural Tm(Thompson et al.)Thermodynamic Tm(Thompson et al.)Structural Tm(Current study)

Melting temperature of Argon vs. pressure

• Simulations for melting of argon as a function of pressure• Comparisons with melting studies performed by Solca et al. and Thompson et al.

• Simulations for melting of argon as a function of pressure• Comparisons with melting studies performed by Solca et al. and Thompson et al.

Ref: Zha et al., J. Chem. Phys., 85, 1034 (1986), Thompson et al., J. Chem. Phys., 118, 21 (2003), Hardy et al., J. Chem. Phys., 54, 1005 (1971)

Ref: Zha et al., J. Chem. Phys., 85, 1034 (1986), Thompson et al., J. Chem. Phys., 118, 21 (2003), Hardy et al., J. Chem. Phys., 54, 1005 (1971)

NEEM MURIDefect nucleated melting

Ref: Solca et al., Chemical Physics, 224 (1997)Ref: Solca et al., Chemical Physics, 224 (1997)

• Melting of an ideal crystal takes place at temperature higher than experimental melting point

• Melting point initially decreases with void size

• Melting temperature constant in a range of void size called plateau region

• Beyond critical void size, melting temperature drops significantly

• Critical void size decreases with an increase in pressure

• Structural melting point (Ts) ~200K higher than thermodynamic melting point (Tm)

• Study by Lutsko et al. shows a ratio of 0.81 for Tm/Ts for Cu using Embedded atom potential

• Melting of an ideal crystal takes place at temperature higher than experimental melting point

• Melting point initially decreases with void size

• Melting temperature constant in a range of void size called plateau region

• Beyond critical void size, melting temperature drops significantly

• Critical void size decreases with an increase in pressure

• Structural melting point (Ts) ~200K higher than thermodynamic melting point (Tm)

• Study by Lutsko et al. shows a ratio of 0.81 for Tm/Ts for Cu using Embedded atom potential

Void sizeM

eltin

gTe

mpe

ratu

re(T

m)

0 20 40 60 80900

950

1000

1050

1100

1150P= 1 atmN= 2048 atoms

Solca et al.

Present Study

NEEM MURIMelting of Bulk-Aluminum

• Constant Pressure NPH Simulation done at 1000 MPa using 2048 particles

• Bulk Aluminum simulated using periodic boundary conditions and an fcc lattice with lattice constant 4.032 Angstroms

• Melting characterized by sharp increase in Potential Energy per atom spent as latent heat and also a sharp increase in Atomic density

• Lattice order parameter characteristic of structure reduces by an order of magnitude near melting

Iterations

Tem

pera

ture

(K)

Pote

ntia

lEne

rgy/

atom

(eV

)

5.0E+05 1.0E+06 1.5E+06

0

500

1000

1500

-3.40

-3.30

-3.20

-3.10

-3.00TemperatureP.E.


Iterations

Tem

pera

ture

(K)

Ato

mic

Den

sity

(ato

ms/

nm3 )

5.0E+05 1.0E+06 1.5E+06

0

500

1000

1500

0.048

0.050

0.052

0.054

0.056

0.058

0.060

0.062

TemperatureAtomic Density

Sudden drop in Atomic Density during melting

NEEM MURINano-Aluminum

3

3 3

4 / 3

~ 0.25229 0.03154

5 ~ 4,000

10 ~ 31,540

20 ~ 252,320

Al Al

p

p p

p

p

p

m N m NV r

N r d

d nm N

d nm N

d nm N

ρπ

= =

⇒ =

= →

= →

= →

2048 Al Atoms equilibrated at 900 K to form a 4 nm nano particle

2048 Al Atoms equilibrated at 900 K to form a 4 nm nano particle

NEEM MURISimulation Results for Aluminum

• Comparison between potentials made, using the thermo-physical properties of bulk/nano aluminum particle as a benchmark

• Lennard-Jones, Glue and Streitz-Mintmire implemented so far• Sutton-Chen, Finnis Sinclair and Johnson potentials to be implemented• Two body potentials like L-J Potential fail to predicting thermodynamic properties• Embedded atom part of Streitz Mintmire used so far for melting studies of

Aluminum; Electrostatic part also implemented for particle and oxidation studies• Cohesive energy very close to -3.36 eV/atom and equilibrium lattice spacing of 4.05

A for Aluminum• Density of 4 nm aluminum particle close to 2700 kg/m3 for solid aluminum• Melting temperature of 945 K predicted using defect nucleated melting of aluminum• Similar results through Glue and S-M potentials for bulk aluminum

• Comparison between potentials made, using the thermo-physical properties of bulk/nano aluminum particle as a benchmark

• Lennard-Jones, Glue and Streitz-Mintmire implemented so far• Sutton-Chen, Finnis Sinclair and Johnson potentials to be implemented• Two body potentials like L-J Potential fail to predicting thermodynamic properties• Embedded atom part of Streitz Mintmire used so far for melting studies of

Aluminum; Electrostatic part also implemented for particle and oxidation studies• Cohesive energy very close to -3.36 eV/atom and equilibrium lattice spacing of 4.05

A for Aluminum• Density of 4 nm aluminum particle close to 2700 kg/m3 for solid aluminum• Melting temperature of 945 K predicted using defect nucleated melting of aluminum• Similar results through Glue and S-M potentials for bulk aluminum

NEEM MURIMD Simulations in Multi Scale Modeling

• Investigate essential differences between physiochemical mechanisms under micro and nano regimes and develop a link between the two

• Extend/Apply theories and correlations established at macro level to nano scales• Propose new theories for nano scales, if required

• Investigate essential differences between physiochemical mechanisms under micro and nano regimes and develop a link between the two

• Extend/Apply theories and correlations established at macro level to nano scales• Propose new theories for nano scales, if required

Major ObjectivesMajor Objectives

Quantum Micro MesoNano Macro

Length (m)

10-12 10-9 10-6 10-3 100

USC

PSU

NEEM MURISummary of Work

• Molecular Dynamics code developed to understand the phenomena at nano scale in detail as a part of overall five stage model

• Code validated for thermodynamic properties using experimental results of Argon• Comparison between potentials made, using the thermo-physical properties of

bulk/nano aluminum particle as a benchmark• Lennard Jones potential fails to predict thermodynamic melting of aluminum• Similar results obtained through Glue and S-M potential• Aluminum melting studied using defect nucleated melting • Nano particle melting studies for aluminum to be used in first two stages of the five

stage model

• Molecular Dynamics code developed to understand the phenomena at nano scale in detail as a part of overall five stage model

• Code validated for thermodynamic properties using experimental results of Argon• Comparison between potentials made, using the thermo-physical properties of

bulk/nano aluminum particle as a benchmark• Lennard Jones potential fails to predict thermodynamic melting of aluminum• Similar results obtained through Glue and S-M potential• Aluminum melting studied using defect nucleated melting • Nano particle melting studies for aluminum to be used in first two stages of the five

stage model

• Nano particle melting studies in future - first two stages of the five-stage model• Parametric studies on the affect of ambient conditions (temperature, pressure),

particle size, and thickness of oxide layer on melting• Simulation of oxidation of nanoparticle - final three stages of the five-stage model

• Nano particle melting studies in future - first two stages of the five-stage model• Parametric studies on the affect of ambient conditions (temperature, pressure),

particle size, and thickness of oxide layer on melting• Simulation of oxidation of nanoparticle - final three stages of the five-stage model

NEEM MURIFuture Work

• Simulation the RESS experiments of Ken Kuo at PSU, and optimize the nano particle fabrication process

• Validation of theoretical modeling and simulation of single nano particle incorporating all observed phenomena

• Study of effects of ambient conditions, particle size, particle number density, oxidizer and chemical kinetics on the burning characteristics of nano particles

• Investigation of particle dust combustion in flow environments

• Simulation the RESS experiments of Ken Kuo at PSU, and optimize the nano particle fabrication process

• Validation of theoretical modeling and simulation of single nano particle incorporating all observed phenomena

• Study of effects of ambient conditions, particle size, particle number density, oxidizer and chemical kinetics on the burning characteristics of nano particles

• Investigation of particle dust combustion in flow environments

NEEM MURI

THANKS !

modeling and simulation of supercritical fluid processing ... review meeting/yang muri neem year 2...

Documents