firstflames

8/14/2019 firstflames

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First Flames:

Burning, Turbulence and Buoyancy Jonathan Dursi (CITA), Frank Timmes (LANL),

Mike Zingale (SUNY SB)


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Flame Ignition

Highly nonlinear,transient

phenomenon

Interaction of nuclear reactions,conductivity,

hydrodynamics

Difcult to model

Nigel Gorbold, Univ. Colorado


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Ignition

Turbulentconditions

Many potential`ashpoints Important to

understand where/when points doignite

Niemeyer, Hillebrandt &Woosley (1996):

success of explosioncan depend sensitivelyon number, location ofignition points


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Early Burning

Ignition can occur on ~cm scales

Not resolved by large-scalesimulation

For initial conditions in large-scale simulations, need to map

turbulence ignition points ignition early ame bubbles


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Outline

Some notes on ignition One-zone Flame (ongoing) Detonation

Early burning: what happens next? Characteristic size of ame bubbles Flame model?


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Flame vs Detonation

Flame/Deagration

Subsonic

Heat propagates byconduction

Detonation Supersonic

Shock-driven heating


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Our contributions

Dursi & Timmes 2006: One-zone ignition times Very hard to ignite det n at low densities:

need much more than local supersonicow. Geometric constraint.


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Our contributions

Zingale & Dursi 2007:

Under given conditions, there is acharacteristic size of a ame bubble -larger is shredded by motions, turbulence

This characteristic size may lead to newame model


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One-zone ignition

Ignition: interactionof:

`chemistry

hydrodynamics

conduction

Even in one-zonemodel (no hydro,cond n) not trivial

1e+09

2e+09

3e+09

4e+09

5e+09

6e+09

7e+09

8e+09

9e+09

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

T e m p

( K )

Time (s)

Ignition Delay Time


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One-zone ignition

`map out ignition timesfor various conditions

Density, temp, comp.

Measurement of a`burning time

ignition if burning timefaster than ow,conduction times

8.0 8.5 9.0 9.5log10(dens)

8.6

8.8

9.0

9.2

9.4

9.6

9.8

10.0

l o g 1 0 ( t e m p )

m illio n s e c1 0 0 0 s e c

1 s e c

1 m il l is e c

1 m ic r o s e c

1 n a n o s e c

1 p i c o s e c


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One-zone ignition ~7000 calculations

Can build ignition timetting function

Quite good over ~15orders of magnitude inignition time

Surprising dependence oncomposition - eg, evenmodest amount of Ne

10 -15 10 -10 10 -5 10 0 10 5 10 10

Computed Ignition Time (s)

10 -15

10 -10

10 -5

10 0

10 5

10 10

F i t I g n

i t i o n

T i m e

( s )


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One-zone ignition time Necessary input into

ignition models

Ignition time must becompared to ow ( )and conduction ( )time scales

Also directly givesdetonation thickness -distance behind shock where burning occurs

-0.001 0.000 0.001 0.002 0.003Position behind shock (cm)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

P r e s ,

E n e r g y

R e

l e a s e

Pred. Width

i

h c


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Flame ignition

Only a small part of thequestion we really wantanswer to:

Given a particularturbulent hotspot, canthat point ignite beforeeddies/conduction diffuseit away?


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Spark-ignited counterow ames:Mastorakos, Marchione, Ahmed, Balachandran, Cambridge


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Flame ignition Simplied setup:

Spherical gaussianhotspot, quiescent ow

Even still, huge parameterspace

Work withundergraduate studentsDoucette, Hiratsuka,ongoing


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Detonation Ignition Ignition at a point --

drives hot shock

Shock must slow down todetonation speed fordetonation to ignite

How big a region?Naively, about a shock thickness ( )

About a factor of 5000too small!

ignitionpt

shock

cold fuel

ashD i


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Detonation Ignition Curvature strongly

modies detonation

Speed drops withcurvature

Beyond certain point, nosteady detonation.

Size of region must be~5000 detonationthicknesses

Detonation Curvature (10km) -1

D e t o n a t

i o n

S p e e

d ( 1 0 7

k m

/ s )


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Detonation Ignition Corresponding physical

size of region growsrapidly with decreasingdensity

By 5x10 7, already ~km forlow carbon fraction

Hard for purely localprocess to ignitedetonation

But very easy tospuriously numerically

ignite detonation


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Outline

Some notes on ignition One-zone Flame (ongoing) Detonation

Early burning: what happens next? Characteristic size of ame bubbles Flame model?


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First Burning

Once a pointignites, what canhappen?


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First Burning


Spherical ameburningoutwards


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First Burning


Buoyant rise


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First Burning


Distortion byturbulence


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First Burning

Each hascharacteristic

velocity Flame speed xed

at given dens

Others bubble-sizedependent Flame speed always

wins until grows


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Size where ame speed

stops dominating


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What happens then?

Robinson,Dursi et al

(2003)


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What happens then?

Robinson,Dursi et al

(2003)


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Iapichino et al, (2006)


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Buoyant rise

Vortical motionsof bubbles own

rise tear it apart Unless ame

speed is faster

Balance setscharacteristicame bubble size


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Balance between two

sets bubble size


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Characteristic bubble

Size

Sets initial condition`ame bubble sizefor large-scalesimulation (~0.5 km)


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Compared against

simulations Semi-analyticcalculations

comparisons of velocities checkedwith `real amecode developed at

LBNL (Zingale, Bell,Day, Rendleman)

Note non-constantame properties!


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Simple semi-analytic model forthis case: amespeed ~ risespeed between30-50 ame

thicknesses in size


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Flame modeling Flame modeling

based on planarpicture of ame

Simulations w/ ~50ame thicknesses

Turbulent, RTcorrugation

But much largerrange of scales

Zingale et al, (2005)


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`Fragmenting Bubbles

Flame Model Volume V burning

outwards,fragmenting intocharacteristicvolumes


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Rapid decrease in bubble size just where increased burning needed?


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Conclusions One zone ignition times - changes w/ Ne Hard to ignite detonations

Flames burn out signicantly (~km) beforethey start to rise Initial conditions need roughly this res

Found typical burning bubble size Rapid decrease in size - increased burning? Is planar ame model appropriate?


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Conclusions One zone ignition times - changes w/ Ne Hard to ignite detonations

Flames burn out signicantly (~km) beforethey start to rise Initial conditions need roughly this res

Found typical burning bubble size Rapid decrease in size - increased burning? Is planar ame model appropriate?


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Characteristic Bubble

Size Can also predict if

burns through centre

If ignites within ~25km will certainlyburn through centre

No remaining poolof fuel


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Zingale et al, (2006)


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Sedov ignition of a

detonation

0.1 1.0 10.0 100.0 1000.0Shock Position (cm)

0.1

1.0

10.0

100.0

S h o c

k V e

l o c

i t y

( V 0

)

90 100 110 120Shock Position (cm)

0.900.95

1.00

1.051.10

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