Loki A Lava Lake in Rarefied Circumplanetary Cross FlowAndrew WalkerDavid Goldstein, Philip Varghese, Laurence Trafton, and Chris Moore

University of Texas at AustinDepartment of Aerospace Engineering

27th RGD Symposium July 14th, 2010

Supported by grants through the NASA Planetary Atmosphere program and Outer Planets Research

OutlineBackground informationIoLokiOverview of our DSMC codeAtmospheric modelHot spot modelGas dynamic resultsFlow featuresBoundary layer separationConvection of heatConclusions

Io is the closest satellite

of JupiterIo radius ~1820 kmIt is the most volcanically

active body in the solar systemThe primary dayside species, SO2, was detected by the Voyager IR spectrometer in 1979 (Pearl et al., 1979)

Background Information on IoSurface Temperature ~ 90 K 115 KLength of Ionian Day ~ 42 hoursMean free path near the surface:

lnoon ~ 5 m lmidnight ~ 100 km

Loki

Loki is the most powerful volcano in the solar system (Rathbun et al., 2002)

-A lava lake with periodic eruptions (540 day period) (Rathbun et al., 2002)Marchis et al. measured the emission intensity in 3 IR bands. From their observations they calculated Lokis effective area and temperature

- AHS = 10.3-11.6103 km2; THS = 325-340 K (Marchis et al., 2005) Loki

Loki

Figure courtesy of Marchis et al. (2005). Global IR intensity from Io

Figure courtesy of Rathbun et al. (2004). High res. image of the lava lake Loki.Lava LakeLand Island

Overview of our DSMC codeThree-dimensionalParallelImportant physical modelsDual rock/frost surface modelTemperature-dependent residence timeRotating temperature distributionVariable weighting functionsQuantized vibrational & continuous rotational energy statesPhoto-emissionPlasma heating

Time scalesVibrational Half-lifemillisecond-secondTime step0.5 secondsBetween Collisions0.1 seconds - hoursResidence TimeSeconds - HoursRotational Half-life~250 secondsBallistic Time (atm)~265 secondsBallistic Time (hs)~340 secondsFlow Evolution1-2 HoursSimulation Time~2.5 hoursIo Day42 Hours

yx

3DThe domain is discretized by a spherical gridDomain extends from Io surface to 400 km in altitudeEncompasses 90 of longitude and 10 ( 5 from equator) of latitudeParallelMPITested up to 360 processors; ~1 million molecules per processor; ~4,000 comp. hrs

Loki Sub-domainDSMC in 3D/ParallelFull Planet DomainGalileo observation ofLoki in visible and IR

Atmospheric Model Boundary Conditions Pt. 1SO2 residence time on rock (Sandford and Allamandola, 1994):Molecules which impact the surface stick for a period of time dependent on the rock surface temperature, TROCK:

-DHS (DHS/kB = 346040 K) : Surface binding energy of SO2 on a SO2 frost, - no (2.41012 s-1) : Lattice vibrational frequency of SO2 within surface matrix site.Model assumes rock is coated with a thin monolayer of SO2

Sublimation & condensation of SO2 frostUnit sticking coefficient Sublimation rate given by: (Wagman, 1979)

SO2 surface frost fraction from Galileo NIMS data (Dout et al., 2001):Within a computational cell, rock and frost are assumed segregated with the relative abundances determined by the frost fractionThe frost fraction also determines the probability that a molecules hits frost or rock

Dual frost/rock surface temperature:Independent thermal inertias and albedosLateral heat conduction assumed negligibleTFROST varies between ~115 K and ~96 KTFROST ~109 K near LokiDay-to-night pressure gradientPressure varies exponentially with TFROSTdP/dx peaks at x 600 km; Loki is located at x 1400 kmPressure varies from ~0.7 nbar to less than a pbar

Atmospheric Model Boundary Conditions Pt. 2

Hot Spot Model

Three-dimensionality of wind patternWinds are driven by a day-to-night pressure gradient As the boundary layer flow reaches the adverse pressure gradient formed by Loki, the flow separates and a vortex formsWinds diverts around the high pressure region formed by Loki

Cross Flow / Hot Spot InteractionCase 1 Uniform 50:50 frost/rock; Unit sticking on rock; No plasma heatingCase 2 Inhomogeneous Surface Frosts; Temp. Dep. Res. Time ; No plasma heatingCase 3 Inhomo. Surf. Frosts; Temp. Dep. Res. Time; Plasma heating (1.3 ergs/cm2s)

Translational temperature profiles at several distances from the peak pressure region1450 km is ~10 km downstream of the center of the hot spot; 1500 km is ~10 km downstream of the hot spot edgeTTRANS cools rapidly at low altitudes because:the wind speeds are lowerthe gas is sufficiently collisional (energy is transferred from translational to rotational and vibrational energy modes and then radiated)At higher altitudes, TTRANS cools less rapidly because of the higher wind speeds and lower collision rate

Effects of Plasma HeatingC2 (Case 2) does not include plasma heating.

C3 (Case 3) includes plasma heating (1.3erg/cm2s)

Data are extracted at 20 km altitude

Conclusions

Rarefied atmospheric winds interact with the hot spot LokiThe rarefied atmosphere varies from KnHS 10-4 to 0.5 at low altitudesNear Loki, KnHS 10-3 near the surface and 510-3 at 20 kmRarefied boundary layer flow develops due a day-to-night pressure gradientIn Case 1 and 2, the BL separates because of the adverse pressure gradient created by the hot spotIn Case 3, the BL remains attached because the plasma heating increases the favorable pressure gradient and decreases the relative size of the adverse pressure gradient created by the hot spotHeat convection is largely controlled by d = tRADU/R where d 1 for all casesIn Cases 1 and 2, d 0.5 at ~20 kmIn Case 3, d 1.0 at ~40 km; therefore heat is convected further with plasma heating

Important Parameters

Non-dimensional ParametersConvection of Heat:

Boundary layer separation:

Equilibration of pressure:

Sheet1

Variable NameValue

dB-HSBallistic Length Scale (Hot Spot)61 km

REffective radius of Loki59 km

HHSScale Height (Hot Spot)24 km

dB-ATMBallistic Length Scale (Surrounding Sublimation Atmosphere)20 km

HATMScale Height (Surrounding Sublimation Atmosphere)8 km

lHSMean Free Path (Hot Spot)500 m

lATMMean Free Path (Surrounding Sublimation Atmosphere)50 m

UMean Wind Speed75 m/s

VNet Vertical Velocity Above Loki25 m/s

rATMNear Surface Atmospheric Density Just Upstream of Loki10-9 kg/m3

rHSNear Surface Gas Density Above Loki10-10 kg/m3

tROTRotational radiation time scale250 s

tVIBVibrational radiation time scale1 s

Sheet2

Sheet3

Number Density drop ~exponentially with altitude for both Case 2 and 3In Case 3, plasma heating inflates the upper atmosphere leading to a denser atmosphere at high altitudesWind speed shows a boundary layer profileCase 2 B.L. thickness ~20 km; Case 3 B.L. thickness ~40 kmMuch higher wind speeds at all altitudes in Case 3 compared to Case 2 Momentum flux above ~10 km is higher in Case 3 because of the higher wind speedsAt 20 km, Case 3 x-direction momentum flux is ~6x higher

Upstream Boundary Layer PropertiesC2 (Case 2) does not include plasma heating.

C3 (Case 3) includes plasma heating (1.3erg/cm2s)

Note: x-axis is altitude not x

Knudsen NumberThe atmospheric rarefaction characterized by KnHS and KnATM KnHS=l/R where l is the mean free path and R is Lokis effective radiusKnATM=l/H where H=kT/mg is the scale height, k is Boltzmanns constant, T is the translational temperature, m is the molecular mass of SO2, and g is the gravitational accelerationGenerally, KnATM > KnHS because H < R as shown on the previous slide. At high altitudes (>30 km), KnHS & KnATM > 1. Near the surface:KnHS varies between ~10-4 and 0.5KnATM varies between ~210-3 and 5Above Loki, KnHS and KnATM fall off more slowly because of the increased scale height

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R59 km

H

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Scale Height (Surrounding

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H

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Near Surface Gas Density Above

Loki

HS

ATM

ATM

Mean Wind Speed

Net Vertical Velocity Above Loki

Effective radius of Loki

Variable Name

Near Surface Atmospheric

Density Just Upstream of Loki

Ballistic Length Scale (Hot Spot)

Ballistic Length Scale

(Surrounding Sublimation

Scale Height (Hot Spot)

Rotational radiation time scale

Vibrational radiation time scale

20 km

8 km

Mean Free Path (Surrounding

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50 m

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