progress with high-resolution amr wetted-foam simulations
Post on 08-Feb-2016
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Progress with high-resolution AMR wetted-foam simulations.
• Two issues are central: the role of density fluctuations at the ablation surface, shock speed.
• The new material tracking routines show a short mixing length.
• Simulations modeling the CH ablator show agreement with Rankine-Hugoniot jump conditions.
DDI 3.3: High-gain wetted-foam target design
A single fiber is subject to the Richtmyer-Meshkov and Kelvin-Helmholtz instabilities
• The primary instability is Richtmyer-Meshkov, which generates a pair of vortices as the shock passes the fiber.
A lone fiber is “destroyed” in ~13 ps, or about 3 fiber-crossing times.
Time (ps)
Ce
nte
ro
fm
ass
po
sitio
n(
m)
0 10 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
singlefiber9 / singlefiber9_com.lpkTime (ps)
Ce
nte
ro
fm
ass
po
sitio
n(
m)
0 10 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
singlefiber9 / singlefiber9_com.lpk
Fiber-crossing time
Time (ps)
%fib
er
ma
ssw
ithin
on
efib
er
rad
ius
0 10 200
25
50
75
100
singlefiber9 / singlefiber9_massfrac.lpk
• A characteristic hydrodynamic time scale is the shock-crossing time tc
of the fiber.
• The fiber is accelerated to the speed of the DT in about ~2tc, or ~8 ps.
• 75% of the fiber mass lies outside its original boundaries after ~3tc, or ~13 ps.
The fiber destruction time depends on the ratio of fiber density to fluid density
• For a larger density ratio: – the Atwood number is higher and the Richtmyer-Meshkov instability
is increased– The velocity shear between the fiber and DT is greater, resulting in
greater Kelvin-Helmholtz instability
Time (ps)
%fib
er
ma
ssw
ithin
on
efib
er
rad
ius
0 10 200
25
50
75
100
4:140:1
singlefiber9 / singlefiber9_massfrac.lpk
The fiber destruction time depends onthe fiber : DT density ratio40:1 density ratio
Identification of the CH as a second material type provides a measure of mixing
Tagging a single fiber as a third material shows the degree of mixing
• Any cell with over 10 mg/cc of the “tagged” material is colored red.
Fourier decomposition of the tracer mass fraction shows a mixing length of ~1.3 m
• The average e-folding distance for decay of the mass-fraction fluctuations is ~1.3 m.
Mix region depth (m)
Fo
uri
er
de
com
po
sitio
no
ffib
er
ma
ssfr
act
ion
(%)
0 1 2 3 410-2
10-1
100
101
n=1n=2n=3n=4n=5n=6
150.2.long.8, 150.2.long.a, 150.2.lr.6
Shocks reflected from the fibers raise the pressure, elevating the post-shock pressure
• The higher pressure results in an elevated shock speed relative to a shock in a uniform field of the same average density, with the same inflow pressure.
x (m)
p(M
ba
r)
0 10 20 30
0.5
1
1.5
2
2.5
3
3.5
4
mixregionreflected
shocks
sho
ck
x (m)
p(M
ba
r)
0 10 20 30
0.5
1
1.5
2
2.5
3
3.5
4
150.2.long.6; 150.2.long.6_fr72_p.lpk
homogeneous densityfield, 3-Mbar shock
x (m)
(g
/cc)
0 10 20 30
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 mixregion
un-shocked
fibers
sho
ck
x (m)
(g
/cc)
0 10 20 30
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 mixregion
un-shocked
fibers
sho
ck
150.2.long.6; 150.2.long.6_fr72_rho.lpk
reflectedshocks
homogeneous densityfield, 3-Mbar shock
When the CH ablator is included, the Rankine-Hugoniot jump conditions are satisfied
• These targets will be fabricated with a thin plastic overcoat.• The post-shock conditions are the same as in the average case with the
same pusher.• On average the Rankine-Hugoniot conditions are obeyed, and the shock
speeds are the same.• An average treatment of density, as in LILAC, is accurate.
x (m)
De
nsi
ty(g
/cc)
0 1 2 3 4 5 6 70
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
CH
foam
rarefactionwave
shock
homogeneousfiber-resolved
x (m)
p(M
ba
r)
0 2 4 60
2
4
6
8
10
12
14
16
18homogeneous
inhomogeneous
rarefactionwave
shock
CH foam
Time (ps)
Sh
ock
po
sitio
n(
m)
0 20 40 60 80
0.5
1
1.5
2
2.5
3
3.5
4
4.5 homogeneousinhomogeneous
The fiber destruction time depends on the ratio of the fiber density to the fluid density
40:1
4:1
4 ps 8 ps 12 ps
The fiber-resolved simulations behave, on average, like the equivalent 1-D simulation
x (m)
de
nsi
ty(g
/cc)
0 2 4 6 8 100
0.25
0.5
0.75
1
1.25
1.5
1.75
2
inhomogeneoushomogeneous
x (m)
pre
ssu
re(M
ba
r)
0 2 4 6 8 100
1
2
3
4
5
x (m)
inte
rna
len
erg
y(M
ba
r)
0 2 4 6 8 100
1
2
3
4
5
6
7
x (m)
velo
city
(m
/ns)
0 2 4 6 8 100
5
10
15
20
25
30
35
Shocks reflected from the foam fibers elevate the post-shock pressure.
• The main shock is partially reflected off the foam fibers.• The reflected shocks make their way though the mix region, eventually
crossing the ablation surface and entering the corona.• Conservation of mass requires the density in the mix region match the
post-shock speed.• Since ~ log(p / 5/3), the post-shock adiabat is higher by p / p ~ ??.
x (m)
(g
/cc)
0 10 20 30
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 mixregion
reflectedshocks
un-shocked
fibers
sho
ck
x (m)
(g
/cc)
0 10 20 30
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8 mixregion
reflectedshocks
un-shocked
fibers
sho
ck
150.2.long.6; 150.2.long.6_fr72_rho.lpk
x (m)
p(M
ba
r)
0 10 20 30
0.5
1
1.5
2
2.5
3
3.5
4
mixregionreflected
shocks
sho
ck
x (m)
p(M
ba
r)
0 10 20 30
0.5
1
1.5
2
2.5
3
3.5
4
150.2.long.6; 150.2.long.6_fr72_p.lpk
The fiber destruction time depends on the ratio of fiber density to fluid density
• For a larger density ratio: – the Atwood number is lower and the Richtmyer-Meshkov instability
is increased– The velocity shear between the fiber and DT is greater, resulting in
greater Kelvin-Helmholtz instability
Time (ps)
%fib
er
ma
ssw
ithin
on
efib
er
rad
ius
0 10 200
25
50
75
100
4:140:1
singlefiber9 / singlefiber9_massfrac.lpk
The fiber destruction time depends onthe fiber : DT density ratio
Artificial viscosity is modeled in BEARCLAW by splitting the contact discontinuity
• The Riemann problem at a cell boundary is solved with three waves: shock, rarefaction (collapsed to a midpoint line) and contact discontinuity (CD).
• Eulerian codes are subject to the growth of noise due to discretization.• These are eliminated in BEARCLAW by splitting the CD from a sharp
transition to a smooth transitional region.• For appropriate values of the artificial viscosity, the shock speed is not
affected.
Time (ps)
Sh
ock
po
sitio
n(
m)
0 2 4 60
1
2f=0.95f=0.1
150.2.long.g_150.2.long.f_xs.plt
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