AME 514 Applications of Combustionronney.usc.edu/AME514/Lecture13/AME514-S17-lecture13.pdf · AME 514 Applications of Combustion Lecture 13: ... Analogy with flames ... 0 0.05 0.1

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AME 514

Applications of Combustion

Lecture 13: Applications of combustion knowledge to other fields

2AME 514 - Spring 2017 - Lecture 13

Emerging Technologies in Reacting Flows (Lecture 1)Ø Applications of combustion (aka “chemically reacting flow”)

knowledge to other fields (Lecture 1)Ø Propagating fronts

» Frontal polymerization» Bacteria growth

Ø Inertial confinement fusionØ Astrophysical combustion

Ø New technologies (Lecture 2)Ø Transient plasma ignitionØ HCCI engines

Ø Future needs in combustion research (Lecture 3)

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Propagating fronts - motivationØ Propagating fronts are ubiquitous in nature

Ø Flames»(Fuel & Oxidant) + Heat ® More heat

Ø Solid rocket propellant fuels»(Fuel & Oxidant) + Heat ® More heat

Ø Self-propagating high-temperature synthesis (SHS) - reaction of metal with metal oxide or nitride, e.g. Fe2O3(s) + 2Al(s) ®Al2O3(s) + 2Fe(l) »(Fuel & Oxidant) + Heat ® More heat

Ø Frontal polymerization»Monomer + initiator + heat ® polymer + more heat

Ø Autocatalytic chemical reactions (non-thermal front)»Reactants + H+ ® Products + more H+

Ø Bacterial front (non-thermal front)»Nutrient + bugs ® more bugs

Ø All of these might be construed as “reaction-diffusion systems”


Reaction-diffusion systemsØ Two essential ingredients

Ø Reactive medium (e.g. fuel-air mixture) Ø Autocatalyst - product of reaction that also accelerates the reaction

(e.g. thermal energy)Ø Self-propagation occurs when the autocatalyst diffuses into the

reactive medium, initiating reaction and creating more autocatalyst, e.g.

A + nB ® (n+1)BØ Enables reaction-diffusion fronts to propagate at steady rates far

from any initiation site

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Premixed flame (SHS, solid propellant similar)

Reaction zone

TemperatureReactant

concentration

Productconcentration

2000K

300K

δ ≈ α/SL = 0.3 - 6 mm

Distance from reaction zone

Convection-diffusion zone

Direction of propagationSpeed relative to unburned gas = SL


Reaction-diffusion systems - characteristics

Ø After initial transient, fronts typically propagate at a steady rateØ Propagation speed (SL) ~ (wD)1/2

» D = diffusivity of autocatalyst or reactantw = characteristic reaction rate = (reaction time)-1

Ø D depends on “sound speed” (c) & “mean free path” (l) » D ~ cl

Ø Propagation rate generally faster in turbulent media due to wrinkling (increased surface area) of front

Ø Thermal fronts require high Zeldovich number (Ze) so that wproducts>> wreactants, otherwise reaction starts spontaneously!

Ø Flammability or extinction limits when loss rate of autocatalyst ≈ production rate of autocatalyst

Ze ≡ Tadω(Tad )

∂ω∂T T=Tad

"

#

$$

%

&

''ΔTTad

=ERTad

Tad −T∞Tad

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Instability mechanismsØ Instability mechanisms may preclude steady flat frontØ Turing instability - when ratio of reactant to autocatalyst diffusivity differs

significantly from 1 Thermal fronts: Dautocatalyst/Dreactant = LeØ Low Le: additional thermal enthalpy loss in curved region is less than

additional chemical enthalpy gain, thus local T in curved region is higher, thus reaction rate increases drastically, thus “blip” grows

Ø High Le: pulsating or travelling wave instabilitiesØ Hydrodynamics - thermal expansion, buoyancy, Saffman-Taylor

Flamefront

Burned gas

Unburned gasDirection of propagation

Heatdiffusion

Heatdiffusion

Fueldiffusion

Fueldiffusion


Polymerization frontsØ First demonstrated by Chechilo et al (1972); reviewed by Pojman et al.

(1996), Epstein & Pojman (1998)Ø Decomposition of the initiator (I) to form free radicals (Ri

*):I ® R1

* + R2* - highest activation energy step

e.g. (NH4)2S2O8 ® 2NH4SO4*

Ø Followed by addition of a radical to a monomer (M):M + Ri

* ® RiM* - initiates polymer chain, grows by addition:RiMn

* + M ® RiMn+1*

Ø Most of heat release occurs through addition stepØ Note not chain-branching like flamesØ Chain growth eventually terminated by radical-radical reactions:

RiMn* + RjMm

* ® RiMn+mRjØ Chain length can be controlled by chain transfer agents - affects

properties of final product

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Polymerization front

Reaction zone

Distance from reaction zone

Temperature

Monomer concentration

Density relative to reactants

Polymerconcentration

Viscosity (log scale)

0.96

1.2

500K

300K

0.01 cm2/s

0.001 cm2/s

10 cm2/s

5 mm

Polymerization front


Polymerization frontsØ Potential applications

Ø Rapid curing of polymers without external heatingØ Uniform curing of thick samplesØ Solventless preparation of some polymersØ Filling/sealing of structures having cavities of arbitrary shape without

having to heat the structure externallyØ Limitations / unknowns

Ø Thermally driven system - need significant DT between reactants and products to have wproducts >> wreactants

Ø Previous studies: use very high pressures or high boiling point solvent (e.g. DMSO) to avoid boiling since mixtures with Tad < 100˚C won’t propagate

Ø …but water at ambient pressure is the solvent required for many practical applications

Ø Idea: use a very reactive monomer (acrylic acid) highly diluted with water to minimize peak temperature, and control heat losses to avoid extinction

Ø …but nothing is known about the extinction mechanisms!

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Polymerization fronts - approachØ Simple apparatus – round tubesØ Need bubble-free model polymerization systems

Ø 2-hydroxyethyl methacrylate (HEMA) monomer in DMSO solventØ Acrylic acid (AA) monomer in water solventØ Both systems: ammonium persulfate (AP) initiator, Cab-o-sil (fumed

silica powder) viscosity enhancerØ Control thermal boundary conditions & assess heat loss

Ø Varying tube diameter Ø Water bath, ambient air or insulated tube to control external

temperatureØ Success! Extinguishment-free, bubble-free fronts observed over a

moderate range of AA & AP concentrations


Polymerization fronts - approach

0

5

10

15

22 24 26 28 30 32 34 36

Extinction limitBubbling limit

Mas

s %

am

mon

ium

per

sulfa

te

Mass % acrylic acid

Stable fronts

Bubbling fronts

Extinguished fronts

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Polymerization frontØ Typical speeds 0.01 cm/s, SL ≈ (aw)1/2 Þ w-1 ≈ 14 sØ From plot of ln(SL) vs. 1/Tad can infer E ≈ 13.5 kcal/mole, Ze ≈ 20Ø Extinction at Pe ≈ (0.004 cm/s)(1.6 cm)/(0.0014 cm2/s) ≈ 4.6 - close to

classical flame theory predictions (lower than 40 because conductivity doesn’t increase significantly with T)

Ø Plot of SL vs. “fuel” concentration approaches vertical at extinction limit as theory predicts

Ø With insulation, limiting SL and %AA much lower

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

10 15 20 25 30 35

InsulatedUninsulated

Fron

t spe

ed (c

m/s

)

Mass percent AA

16 mm tube10% AP

0.002

0.004

0.006

0.0080.01

0.03

15 20 25 30 35 40 45

5%8%10%12%15%

Fron

t spe

ed (c

m/s

)

Mass percent AA

Mass % AP

16 mm tubeUninsulated


Polymerization fronts - thermal propertiesØ Far from limit

Ø Peak T same with or without insulation, speed and slope of T profile same, uninsulated case shows thermal decay in products

Ø Close to limitØ Uninsulated case shows substantial thermal decay in products; ratio

(peak + slope)/(peak - slope) ≈ 12 ≈ 1/Ze as expectedØ Insulated case much slower, thicker flame, little or no thermal decay,

limit not well defined

20

40

60

80

100

0 100 200 300 400 500 600 700

InsulatedUninsulatedAdiabatic

Tem

pera

ture

(˚C

)

Time (seconds)

Slope = 0.056˚C/s

27.5% AA / 10% AP16 mm tube

20

30

40

50

60

70

80

0 500 1000 1500 2000 2500 3000

14.7% AA, insulated22.2% AA, uninsulated

Tem

pera

ture

(˚C

)

Time (seconds)

10% AP16 mm tube

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15

ImagingØ Free radicals destroy fluorescein - render products non-fluorescent

(chemical, not thermal effect)Ø Use Argon-ion laser sheet to image fronts

1.78% Cab-o-sil, 26% AA, 10% AP, 30 sec intervals - low viscosity, RT unstable

2.67% Cab-o-sil, 26% AA, 10% AP, 30 sec intervals - high viscosity, RT stableAME 514 - Spring 2017 - Lecture 13


Movies courtesy Prof. J. Pojman, University of Southern Mississippi

Polymerization frontØ High Lewis number - spiral & travelling-wave instabilities like flames

(middle and right videos, viscosity-enhancing agent added to suppress buoyant instabilities)

Lean C4H10-O2-He mixtures; Pearlman and Ronney, 1994

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Ø Many bacteria (e.g. E. coli) are motile - swim to find favorable environments - diffusion-like process - and multiply (react with nutrients) - see Berg, 2000

Ø Two modes: run (swim in straight line) & tumble (change direction) - like random walk

Ø Longer run times if favorable nutrient gradient (chemotaxis)Ø Suggests possiblity of “flames”

Bacterial fronts


http://www.rowland.harvard.edu/labs/bacteria/movies/index.php

Motile bacteriaØ Bacteria swim by spinning flagella - drag on rod is about twice as

large in crossflow compared to axial flow (G. I. Taylor showed this enables propulsion even though Re ≈ 10-4) (If you had flagella, you could swim in quicksand or molasses)

Ø Flagella rotate as a group to propel, spread out and rotate individually to tumble

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Flame or molecular property

Microbiological equivalent

Temperature Concentration of bacteria Fuel Nutrients Heat diffusivity ≈ cλ Diffusivity of bacteria Fuel diffusivity Diffusivity of nutrient Sound speed (c) Swimming speed of bacterium in "run" mode Mean free path (λ) c multipled by average time to switch from run

mode to tumble mode and back Reaction timescale Reproduction time Heat loss Death (of individual bacterium) Extinguishment Death (of all bacteria)

Analogy with flames

20AME 514 - Spring 2017 - Lecture 13Fronts show a steady propagation rate after an initial transient

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8

0.2% agar0.3% agar

Fron

t dia

met

er (m

m)

Time (hours)

Reaction-diffusion behavior of bacteriaØ Bacterial strains: E.coli K-12 strain W3110 derivatives, either motile or

non-motileØ Standard condition: LB agar plates (agar concentration of 0.1 - 0.4%)Ø Variable nutrient condition: Tryptone/NaCl plates (agar concentration of

0.1, 0.3%)Ø All experiments incubated at 37˚C

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21

Summary of propagation ratesØ Experiments with motile (2086) vs. non-motile (126), LB vs. glycerol/M63

(poor nutrient) suggest that glycerol affects motility more than division rate (i.e. reaction rate)

0.01

0.1

1

10

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

Agar Concentration

Fron

t Spe

ed (m

m/h

r)

2086 LB2086 Glycerol

126 LB126 M63

B. subtilis

AME 514 - Spring 2017 - Lecture 13


Propagation rates of motile bacteria frontsØ As agar concentration increases, motility of bacteria (in particular “sound

speed” (c)) decreases, decreases effective diffusivity (D) and thus propagation speed (s) decreases substantially

Ø No effect of depth of mediumØ Above 0.4% agar, bacteria grow along the surface onlyØ Very similar results for Bacillus subtilis - very different organism - E. coli

& B. subtilis evolutionary paths separated 2 billion years ago

0

2

4

6

8

10

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

E. ColiB. Subtilis

Fron

t sp

eed

(mm

/hr)

Agar concentration, %

Motile 2086 E. Coli or B. subtilis

LB nutrient broth

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1

1.5

2

2.5

3

3.5

4

4.5

0 0.2 0.4 0.6 0.8 1

Fron

t Spe

ed (m

m/h

)

Tryptone Concentration (%)

Effect of nutrient concentrationØ Increasing tryptone nutrient concentration increases propagation speed

(either due to increased swimming speed or increased division rate) but slightly decreases propagation rate beyond a certain concentration -typically motility decreases for high nutrient concentrations (detectors saturated?)

Motile 2086 E. Coli Tryptone nutrient


Quenching limit of bacteria frontsØ Quenching limit: min. or max. value of some parameter (e.g.

reactant concentration or channel width) for which steady front can exist

Ø Quenching “channels” made using filter paper infused with antibiotic - bacteria killed near the wall, mimics heat loss to a cold wall in flames

Ø Bacteria can propagate through a wide channel but not the narrow channel, indicating a quenching limit

Ø Quenching described in terms of a minimum Peclet Number:Ø Pe = sw/D (w = channel width)Ø For the test case shown s ≈ 1.75 x 10-4 cm/s, D = 3.7 x 10-5 cm2/s, w

at quenching limit ≈ 2.1 cm Þ Pe ≈ 9.8 - similar to flames and polymer fronts

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6 mm wide channel 35 mm wide channelMotile E. coli, 0.1% agar, 100 µl of kanamycin per side

6.5 hours after inoculation

Quenching limit of bacteria fronts

26

Quenching limit of bacteria frontsØ UV illumination with “masks” where bacteria are not killedØ Problem: sacrificial bacteria form “shields” to allow other bacteria

to survive!


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Comparison of fronts in Mot+ and Mot- bacteriaØ Some mutated strains are non-motile but D due to Brownian

motion ≈ 104 smaller Ø Fronts of Mot- bacteria also propagate, but more slowly than Mot+

bacteria

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2 0.25

Fron

t spe

ed (m

m/h

r)

Agar %

Non-motile 126 E. Coli LB nutrient broth


Quantitative analysisØ Bacteria D as estimated from measured front speeds

Ø SL for Mot+ ≈ 5.3 x 10-5 cm/s for 0.3% agarØ Reproduction time scale (t) of E.coli ≈ 20 minØ D ≈ s2t ≈ (5.3 x 10-5 cm/s)2(1200s) ≈ 3.3 x 10-6 cm2/sØ Similarly, D ≈ 3.7 x 10-5 cm2/s in 0.1% agar

Ø Bacteria diffusivity estimated from molecular theory Ø “Mean free path” (l) estimated as the “sound speed” (c) multiplied

by the time (t) bacteria swim without changing directionØ c ≈ 21 µm/s, t ≈ 1.4 sØ l ≈ 3.0 x 10-3 cm, D ≈ 6.3 x 10-6 cm2/s, similar to value inferred from

propagation speedØ Diffusivity of Mot- E. coli due to Brownian motion (0.75 µm radius

particles in water at 37˚C) ≈ 2.9 x 10-9 cm2/s, ≈ 1700x smaller than Mot+ bacteria

Ø Fronts should be (1700)1/2 ≈ 40x slower in Mot- bacteriaØ Consistent with experiments (e.g. 8 mm/hr vs. 0.2 mm/hr at 0.1%

agar)

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Comparison of fronts in Mot+ and Mot- bacteria

Ø Dnutrient (≈ 10-5 cm2/s) close to Dbacteria, so “Lewis number” ≈ 1Ø Do bacteria choose their run-tumble cycle time to produce D

required for Le ≈ 1 and avoid instabilies???Ø Switching from Mot+ to Mot- bacteria decreases the bacteria

diffusivity (Dautocatalyst) by ≈ 1700x but nutrient diffusivity (Dreactant) is unchanged - decreases the effective “Lewis number”

Ø Mot- fronts “cellular” but Mot+ fronts smooth - consistent with “Lewis number” analogy


Mot+ 2086 5 hr 30 min after inoculation Mot- 126 50 hr after inoculation 0.1% Agar dyed with a 5% Xylene Cyanol solution (Petri dish 9 cm diameter)

Comparison of fronts in Mot+ and Mot- bacteria

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31

Patterns in Mot- bacteria



Summary

PropertyGas flame

(e.g. CH4-air)SHS Autocatalytic

aqueous front Polymer

frontBacterial

frontReactant(s) Fuel, oxidant Reductant,

oxidantReactants (e.g. IO3

- - S2O42-)

Monomer & initiator (e.g. IO3

- - S2O42-)

nutrient

Product(s) CO2, H2O, thermal energy

Metal, metal oxide or nitride

product polymer bacteria

Autocatalyst Thermal energy, free radicals

Thermal energy

H+ Thermal energy

bacteria

Flame speed (S) 400 mm/s 10 mm/s 0.2 mm/s 0.1 mm/s 0.001 mm/s

Zeldovich # (Ze) 10 - 20 10 - 20 0.05 20 0Heat loss Important Important Unimportant

(Ze<<1)Important None

Prandtl # (Pr) 1 ∞ 7 1000 1000

Lewis # (Le) 1 ∞ 70 (but irrelevant) nearly infinite 1 (Mot+); 10-4 (Mot-)

Density ratio d º (r¥-ra)/r¥

6 (monotonic) 0.1 0.0006 (monotonic)

-0.2 (non-monotonic)

?

Viscosity ratio (na-n∞)/n¥

25 ∞/∞ 0.1 1 - ∞ 1

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Inertial confinement fusion (ICF)Ø Fusion power, e.g. by inertial confinement, is the holy grail of

power generationØ Need to obtain high r & T near center of deuterium-tritium

spherical (probably plastic) shellØ “Direct drive” approach - laser irradiation used to obtain mass

ablation of shell; laser energy absorption occurs at a “critical surface” (equivalent to a “reaction zone” in flames) within ablating plasma surrounding the shell

Ø Imploding shell accelerated inward due to outside high pressure resulting from ablation

http://www.nuc.berkeley.edu/thyd/icf/target.html


Inertial confinement fusion (ICF)

Clavin & Almarcha, 2005

Laser source (1 of many)

ShellNuclear fuel

Ablated shell vapor

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Inertial confinement fusionØ Low Mach number - ablation front speed << local sound speedØ Similar to buoyantly-unstable upward-propagating flame with ablation

front velocity Va!Ø Rayleigh-Taylor like instabilities disrupt spherical symmetry, thus limit “compression ratio” & may prevent “ignition”

Ø Density ratio very high since T ratio very high (≈105)Ø Different from flames because thermal conductivity of plasma varies

rapidly with temperature (~Tn, n ≈ 2.5)

Clavin & Masse, 2004


Inertial confinement fusion (ICF)Ø ICF: growth rate of instability (s) encouraged by acceleration (g),

discouraged by mass ablation (negative Darrieus-Landau effect)

Ø Flames: growth rate encouraged by both acceleration and thermal expansion (Darrieus-Landau) effect:

Ø Need to include “diffusive-thermal” effect - damping at large wavenumbers (k) due to thermal conduction with length scale = flame thickness dc; for flames:

k = wavenumber; r = density; a = ablating (solid) material; * = gas adjacent to ablating solid, c = at critical surface (where laser energy is absorbed)

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Ø With large thermal conductivity ratio, a wide range of characteristic diffusive lengths occurs - not just a single thickness as in flames)

Ø Simplest result, large density ratio

Ø Froude numbers (Fr) typically O(1) in flames; much smaller in ICFs (large acceleration)

Inertial confinement fusion (ICF)

Clavin & Masse, 2004


Inertial confinement fusion (ICF)Ø This is linear stability analysis, what about non-linear evolution?

Superficially similar to Rayleigh-Taylor…

Clavin & Almarcha, 2004

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Inertial confinement fusion (ICF)Ø “Spikes” of cold material penetrating plasma can be studied analytically;

result shows spikes overshoot “free-fall” velocity & approach free-fall with power-law form

Ø Results show sufficiently large shells are highly unstable - can use small shells, but then heat losses (radiation!) are likely to prevent ignition

Ø What is optimal size of fusion shell to avoid instabilities yet allow ignition?

Clavin & Williams, 2005


Supernovae explosionsØ See Oran (2005)Ø Red Giant stars burn H and He, form C and O atomsØ White Dwarf stars burn for billions of years, then end in a self-

propagating thermally-triggered thermonuclear explosion Ø Principal reactants 12C and 16O nuclei; 56Ni and other iron-group

elements are principal productsØ Explosion time on the order of seconds, but brightness peaks ≈ 20 days

after explosion, lasts for months - brightness vs. time VERY similar for different supernovae when scaled by time and intensity of peak intensity

Ø Large-scale, three-dimensional numerical simulations predict formation of highly wrinkled turbulent fronts whose burning rate is controlled by the Rayleigh-Taylor instability

Ø Initial speed less than the local sound speed, i.e., a “deflagration,” but may transition to “detonation”

Ø Whether transition occurs affects the composition of the supernova remnants in observable ways (e.g. spectrum of radiation)

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Supernovae explosions

Oran, 2005

/s



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DeflagrationGamezo et al., Science 2003

DetonationGamezo et al., PRL 2004


ReferencesØ Berg, H. C., "Motile Behavior of Bacteria," Phys. Today 53, 24 (2000).Ø Budrene E.O., Berg H. C., "Complex patterns formed by motile cells of E. coli," Nature 349, 630

(1991).Ø Chechilo, N. M., Khvilivitskii, R. J., Enikolopyan, N. S. (1972). “On the Phenomenon of

Polymerization Reaction Spreading,” Dokl. Akad. Nauk SSSR 204:1180-1181.Ø Clavin, P., Masse, L. (2004). “Instabilities of ablation fronts in inertial confinement fusion: A

comparison with flames,” Physics of Plasmas 11:690-705.Ø Clavin, P., Williams, F. A. (2004). “Asymptotic Spike Evolution in Rayleigh-Taylor Instability,”

J. Fluid. Mech. 525:105-113.Ø Clavin, P., Almarcha C. (2005). “Ablative Rayleigh-Taylor instability in the limit of an infinitely

large density ratio,” Comptes Rendus Mechanique 333:379-388.Ø Costerton, J. W. (1995). “Overview of microbial biofilms,” J. Indus. Microbiol. 15:137-140.Ø Epstein, I. R., Pojman, J. A. (1998). An introduction to nonlinear chemical dynamics, Oxford.Ø Gamezo, V. N., Khokhlov, A. M., Oran, E. S., Chtchelkanova, A. Y., Rosenberg, R. O. (2003).“Thermonuclear supernovae: Simulations of the deflagration stage and their implications,” Science299, 77-81.

Ø Gamezo V. N., Khokhlov A. M., Oran, E. S. (2004). “Deflagrations and Detonations inThermonuclear Supernovae,” Phys. Rev. Lett. 92, Art. No. 211102.

Ø Gjaltema, A., Arts, P.A.M., Loosdrecht, M.C.M., van Kuenen, J.G., Heijnen, J.J. (1994). “Heterogeneity of biofilms in rotating annular reactors: Occurrence, structure, and consequences,”Biotechnol. Bioeng. 44:194–204.

Ø Heydorn, A., B. K. Ersboll, M. Hentzer, M. R. Parsek, M. Givskov, and S. Molin (2000). Experimental reproducibility in flow-chamber biofilms. Microbiology 146:2409-15.

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ReferencesØ Mah, T. F. C., O'Toole, G. A. (2001). “Mechanisms of biofilm resistance to antimicrobial agents,”

Trends in Microbiology 9:34-39.Ø O'Toole, G. A., H. Kaplan, and R. Kolter (2000). “Biofilm formation as microbial development,”

Ann. Rev. Microbiol. 54:49-79.Ø Oran, E. S. (2005). “Astrophysical Combustion,” Proc. Combust. Inst. 30, 1823 - 1840.Ø Pojman, J. A., Hyashenko, V. M., Khan, A. M. (1996). “Free-radical frontal polymerization: self-

propagating reaction waves,” J. Chem. Soc., Faraday Trans. 92, 2825.

Documents

AME 514 Applications of Combustionronney.usc.edu/AME514/Lecture13/AME514-S17-lecture13.pdf · AME 514 Applications of Combustion Lecture 13: ... Analogy with flames ... 0 0.05 0.1