[american institute of aeronautics and astronautics 37th aiaa thermophysics conference - portland,...

American Institute of Aeronautics and Astronautics1

Numerical Study on Behavior of Outgas from Heat Shieldof Solar Probe

Kojiro Suzuki*

Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba, 277-8562, Japan

When a solar probe penetrates into the solar corona for the in-situ observation of thesolar wind, the temperature of the carbon-carbon heat shield is expected to rise up to over2500 K and the sublimation will occur at its surface. In the present study, the rarefied flowsof such outgas are numerically studied by the DSMC method. Consideration on the lengthscale of the phenomena shows that the interaction between the solar wind and the outgascloud will occur in much larger length scale than the spacecraft size. When the totalsublimation rate becomes high at the close approach to the sun, the velocity distributionfunction of the solar wind obtained at the probe is expected to be different from that of theundisturbed freestream. The extent of the difference is evaluated for various injection andfreestream conditions. The heat shield design to reduce the total sublimation rate is alsodiscussed and the rarefied flow environment around the probe is investigated by the nearfield analysis.

Nomenclaturecmp = most probable molecular speedd = molecular diameterD = diameter of heat shieldJ = mass loss rate per unit areakn = Knudsen numberL = length scale for interaction between solar wind and sublimation gas cloudMi = molecular weight of i-th speciesmp = particle massn = number densitypeva,i = equilibrium vapor pressure of i-th speciesq = solar radiative heating per unit areaR = universal gas constantRs = solar radiusS = area of heat shieldT = temperaturex = distance between solar probe and sun's centerλ = mean free pathSubscriptssub = sublimation gasw = condition at wall∞ = freestream condition of solar wind

I. IntroductionThe mechanism of the acceleration and heating of the solar wind in the corona is one of the most important

unsolved problems in the space science. Close-approach in-situ observations are expected to give us a key to solvethe problem. Though some design concepts of the solar probe have been studied in the past,1,2,3 technical and

* Associate Professor, Department of Advanced Energy, 5-1-5 Kashiwa-no-ha, Senior Member.

37th AIAA Thermophysics Conference28 June - 1 July 2004, Portland, Oregon

AIAA 2004-2271

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


financial difficulties have prevented us from realizing it. However, recent technological advancement in thetrajectory design, down-sizing of the spacecraft instruments, heat shield design and so on enables us to plan a low-cost small solar probe mission.4,5

One of the most critical problems on the solar probe is the design of the heat shield to protect the instruments ofthe spacecraft from severe heating of the solar radiation at close approach to the sun. Considering its scientificobjectives, the probe must penetrate into the solar corona and the minimum distance from the sun's center isexpected to be 3-5 solar radii (Rs). In the case of 4 Rs, the heat flux of the solar radiation will become about 4MW/m2, which is in the same order as the aerodynamic heating of the earth's re-entry. At present, a heat shieldfabricated from carbon-carbon (C/C) material seems promising.4 The heat shield temperature is expected to increaseup to over 2500 K and outgassing from the shield due to sublimation may affect not only the accuracy of thescientific instruments but also the properties of the solar wind around the spacecraft. Then, both durability in severeheating and reduction in contamination of the coronal environment around the probe by outgassing from the heatshield must be considered at the design of the solar probe.

Around the probe, the rarefied flow is created by the injection of the sublimation gas from the heat shield, sincethe number density of the solar wind is quite low even in the corona. The sublimation gas is expected to form thecloud around the probe and to interact with the solar wind by the molecular collision. The presence of thesublimation gas cloud will become the critical problem in two ways. First, the sublimation gas particles may causethe noise for measuring instruments. Second, the properties of the incoming solar wind may be changed by theinteraction with the cloud. In such case, the undisturbed freestream properties of the solar wind in the corona can notbe obtained by the probe. These problems will become significant when the sublimation rate becomes large.Consequently, for an appropriate design of the heat shield, it is necessary to know the characteristics of the rarefiedflows of the sublimation gas and to determine how much sublimation rate is allowable. However, the behavior of theoutgas from the heat shield of the solar probe is not well understood.

In the present study, the rarefied flows of the sublimation gas and the solar wind are numerically studied by theDirect Simulation Monte Carlo (DSMC) method. The research objectives are as follows:1) To show favorable configuration of the C/C heat shield for the solar probe mission from a viewpoint of reduction

in outgassing,2) To clarify the features of the rarefied flow environment around the probe,3) To investigate how much the properties of the solar wind are affected by the interaction with the sublimation gas

cloud around the probe and to clarify the effects of the sublimation rate and the freestream conditions of the solarwind on the interaction phenomena.

II. Heat Shield Design for Solar Probe MissionFor the solar probe, two types of heat shield configuration have been proposed, that is, the conical type1,3,6 and

the dish type.4,5 In the present study, we consider the heat shield consisting of two flat C/C disks as shown in Fig. 1,since its simple shape seems suitable for fabrication with smaller mass and lower cost in comparison with theconical type. The primary shield (Disk-1 in Fig. 1) is inclined to the sun's direction and set at distance h from theintermediate shield (Disk-2). Behind Disk-2, the main body of the spacecraft is located. We assume that the backside of Disk 2 is thermally insulated and that there is no radiative heat transfer to the spacecraft main body.

The radiative heating from the sun q is predicted by the relation:3

q = q0 (Rsx

) 2 , q0 = 6.24× 107 W / m2 , (1)

where Rs and x are the solar radius and the distance from the sun's center to the probe, respectively. Assuming thatthe temperature is uniform on each disk due to high thermal conductivity of the C/C material, the shield temperatureis predicted by considering the energy balance of the incoming solar flux, the radiative cooling and the radiative heattransfer between two disks. The radiative heat transfer is calculated by using the configuration factor, whichrepresents the ratio of the radiative flux reaching one disk to the total flux radiated from the other disk. Theconfiguration factor is determined by the geometric relation between the disks and calculated by numericalintegration. The heat shield is assumed to be a gray body on which the absorptivity is equal to the emissivity. Thelatent heat of sublimation is ignored, since it is much smaller than the solar radiation and the reduction in the shieldtemperature is smaller than 1% even when the sublimation rate is high at the probe location 2.5 Rs.

When the temperature of the C/C material becomes high at close approach to the sun, sublimation occurs and thegases of C, C2, C3 and so on are injected at the surface to the surroundings. The rate of outgassing from the heat


shield due to sublimation, in other words, the mass loss rate of the heat shield, is estimated from the walltemperature (Tw) by Hertz-Knudsen-Langmuir relation:7

J sub =αi peva , i

2π (R / Mi )Tw

,i

∑ i =C, C2 , C3, ... , (2)

where α, R, M, peva denote the sublimation efficiency, universal gas constant, molecular weight of sublimation gasand the equilibrium vapor pressure, respectively. In the present study, the model of graphite7 is used for sublimationof the C/C heat shield. The effect of the ambient pressure is ignored, since the wall pressure induced by themolecular collision in the vicinity of the surface is much smaller than the equilibrium vapor pressure. In fact, therarefied flow analyses show that the reduction in the sublimation rate due to the wall pressure is smaller than 3%even at 2.5 Rs.

By using the above models, the effects of the configuration parameters indicated in Fig. 1 on the temperature andthe total sublimation rate of the heat shield are investigated. In the present study, the diameter of Disk-2 is set as 1mand the spacecraft main body is assumed to be small enough to be in the shadow of Disk-2. The temperature ofDisk-2 decreases with the increase in the distance between two disks (h in Fig. 1), since the solid angle of Disk-1viewed from Disk-2 and the radiative heat transfer from Disk-1 to Disk-2 decrease with the increase in this distance.However, large distance results in long supporting rods between two disks and causes the increase in the structuralmass of the spacecraft. In the present study, the distance h is set as 2 m. Figure 2 shows the variations of the totalmass loss rate and the temperature of Disk-1 and -2 with the inclination angle of Disk-1. It is assumed that nosublimation occurs at the back side of Disk-2. The distance from the sun's center is 4 Rs. We set the allowable solarangle of 15 degrees in order to keep the main body in the shadow of Disk-1 even when there is some error in theattitude control. The minimum diameter of Disk-1 necessary for having the allowable angle of 15 degrees is alsoplotted in Fig. 2. When the diameter of Disk-1 increases, the temperature of Disk-2 rises, since the solid angle ofDisk-1 viewed from Disk-2 becomes larger. Then, the diameter of Disk-1 should be set as the minimum allowablevalue as indicated in Fig. 2. When the inclination angle of Disk-1 increases, both the temperature of Disk-1 and thetotal mass loss rate significantly decrease, since the solar radiative flux received at Disk-1 decreases. It should benoted that the temperature of Disk-2 becomes higher when the inclination angle increases, since the distancebetween two disks decreases in part and the radiative heat transfer between them becomes larger. Considering thecontamination problem of outgassing, the total mass loss rate of the heat shield should be reduced as much aspossible. In this case, we assume that the total sublimation rate must be smaller than 2.5 mg/s after the study atNASA Jet Propulsion Laboratory (JPL).4 Figure 2 tells that the inclination angle must be larger than 45 degrees andthat larger inclination results in smaller outgassing rate. However, larger inclination angle requires larger radius ofDisk-1 and results in larger heat shield mass. Consequently, the optimum inclination angle is 45 degrees in this case.The diameter of Disk-1 is calculated as 4 m. The optimum configuration is schematically illustrated in Fig. 1. Itshould be noted that this configuration seems quite similar to that obtained by the study at JPL.4

Figure 2. Effects of Inclination Angle on Total MassLoss Rate, Temperature and Minimum ShieldDiameter.

Figure 1. Schematic View of Two Disks Type HeatShield.


III. Method of Analysis on Outgas FlowTo investigate the behavior of the outgas from the heat shield, the rarefied gas flow around the probe must be

solved, since the ambient pressure is quite low in the solar corona. There can be two length scales in the phenomenaof the outgas. In the near field phenomena with the length scale of the heat shield size, our main concern is to clarifythe rarefied gas environment around the probe, for example, the spatial distribution of the number density of thesublimation gas. On the other hand, the interaction phenomena between the solar wind and the sublimation gas cloudare expected to occur in much larger length scale than the spacecraft size, since the velocity of the solar wind isextremely high. In the present study, two types of rarefied gas simulations are conducted with two different lengthscales as follows.

A. Near Field Analysis1. Consideration on Length Scale

In the near field analysis, we only consider the rarefied flow of the sublimation gas and the presence of the solarwind particles is ignored. The reference length is set as the diameter of the heat shield. For simplicity, we assumethat the solar probe has one heat shield disk set normal to the sun's direction. By considering the solar radiationgiven by Eq. (1) and the radiative cooling from both sides of the heat shield, the equilibrium temperature iscalculated as a function of the distance from the sun's center. As the sublimation gas, only the monatomic gas of C isconsidered, since the dominant outgas species is C at the wall temperature lower than 2500 K and at highertemperature, the dominant species C2 is expected to dissociate into C immediately after injection. By assuming thatthe sublimation gas is injected with the Maxwellian velocity distribution at the wall temperature Tw, the numberdensity of the sublimation gas at the surface is predicted by using the mean injection velocity vw as:

nw =J sub / mp

vw

, vw =(R / M C ) /Tw

2π, (3)

where mp is the mass of the sublimation gas particle and the sublimation rate per unit area Jsub is given by Eq. (2). Inthe present study, the hard sphere model8 with the constant particle diameter d of 3.4X10-10 m is used for themonatomic gas of C. Then the mean free path is calculated by the relation:

λ =1

2 π d 2nw

(4)

The variations of the equilibrium walltemperature and the mean free path with the distancebetween the probe and the sun's center are shown inFig. 3. When the distance from the sun's centerbecomes smaller than 3.5 Rs, the mean free path is inthe order of or smaller than 1 m, which is the lengthscale of the spacecraft. Consequently, in closeapproach at distance smaller than 4 Rs, the Knudsennumber becomes smaller than the unity and the flowaround the spacecraft can not be taken as freemolecular. In such case, the particle collision mustbe considered in the analyses.

2. Method of Numerical SimulationTo simulate the rarefied flow of the sublimation

gas around the spacecraft, we use the DSMCmethod8 with the modified Nanbu scheme.9 In theDSMC method, the calculation at each time step isdivided into two procedures, that is, update of theparticle position by the translational motion andupdate of the molecular velocity by the collisionsbetween particles. In the modified Nanbu scheme,

Figure 3. Variations of Equilibrium Wall Temperatureand Mean Free Path with Distance from Sun's Center.


the velocity of all the test particles is updated at once in each time step after all the collisions in the computationaldomain are calculated. Such explicit procedure in the collision calculation seems suitable for the case in which theoverset grid system is used to describe a multi-body configuration like the heat shield of two disks type as shown inFig. 1.

Before the three-dimensional calculation around the whole configuration of the heat shield system shown in Fig.1, two-dimensional calculations are made to clarify the fundamental features of the rarefied flow of the sublimationgas. In the two-dimensional analyses, the heat shield is described as a plate with width D. The size of thecomputational domain is 10D X 10D and the heat shield is located at the center of the computational domain. At theheat shield surface, the sample particles for the sublimation gas are injected with the Maxwellian velocitydistribution at the wall temperature. The diffusive reflection is assumed for the collision between the wall andparticles. On the outer boundary of the computational domain, the outflow condition, in which the test particlesgoing out of the computational domain are deleted from the calculation, is used. The time step size is specified as40% of the mean collision time. The total number of the test particles in the computational domain is about 50,000.

In the three-dimensional calculation, the oversetgrid system shown in Fig. 4 is used to describe thetwo disks configuration of the heat shield of thesolar probe. Two cylindrical sub-grid systems areseparately generated around Disk-1 and Disk-2 andinserted in the background grid with uniform andorthogonal spacing. The Disk-1 is put at 45 degreesincidence to the sun's direction. To avoid the doublecounting of the collision both in a sub-grid and inthe background grid, the collisions of particleslocated in the overlapped region are calculated onlyonce in a sub-grid system. The boundary conditionsare the same as the two-dimensional calculations. Tosave the computational time and storage, only thehalf portion is calculated and the symmetriccondition is applied on the plane of symmetry. Thetotal number of the test particles in thecomputational domain is about 150,000.

B. Far Field Analysis1. Consideration on Length Scale

In the far field analysis, the interaction between the solar wind particles and the sublimation gas particles isconsidered. Though the properties of the solar wind10 in the corona is not well understood, the velocity, temperatureand number density are assumed to be 100 km/s, 106 K and 1014 m-3, respectively, as the nominal values in thepresent study.

To begin with, the length scale of the phenomena must be determined. The sublimation gas injected from theheat shield widely spreads around the spacecraft and forms a cloud. When the size of the cloud and the numberdensity in it are large, the solar wind particles will collide with the sublimation gas particles many times until theyhave passed through the cloud. Though the solar wind is plasma flow, the neutral atomic hydrogen is assumed as thecomponent of the solar wind. The effects of charged particles and the presence of the electrons are ignored. Themonatomic gas of C is considered as the sublimation gas in the same way as in the near field analysis. For simplicity,the hard sphere model with diameter of 3.4X10-10 m is assumed for both particles.

When the probe is taken as a point-source of gas injection, the number density of the sublimation gas at distancer on the center line from the sun is predicted as:

n =J subS

4π mp r 2

2π (R / M C )Tw

, (5)

where the free molecular flow is assumed and S is the area of the heat shield. We define the length scale L as thedistance where the number density of the sublimation gas cloud becomes the same as that of the incoming solarwind. Then the length scale L is given by:

Figure 4. Overset Grid around Heat Shield of TwoDisks Type for Three-dimensional Calculation.


L =J subS

4π n∞mp

2

π (R / M C )Tw

, (6)

where n∞ denotes the number density of the solar wind. To evaluate the effective mean free path, we must considerthe collision between the high speed dilute gas (solar wind) and low speed dense gas (sublimation gas cloud). Forthe mean collision time, the velocity of the solar wind particle should be used in place of that of the sublimation gas,since the former is much higher and the sublimation gas particle is expected to collide much more frequently withthe solar wind particles than with the sublimation gas particles. By using the most probable molecular speed of thesublimation gas at temperature Tw, the mean collision time based on the number density and velocity of the solarwind, and the length scale given in Eq. (6), the Knudsen number for the far field analysis is given as:

kn =λL=

cmp

π d 2 n∞V∞L=

2(R / M C )Tw

π d 2n∞V∞L. (7)

Figure 5 shows the variations of the total mass loss rate, length scale and the Knudsen number with the distancebetween the sun's center and the probe. The area of the heat shield is 10 m2. The heat shield is assumed to be a flatplate and to be set normal to the sun's direction. When the probe gets closer to the sun, the total mass loss rate andlength scale becomes larger and the Knudsen number decreases. At 2.5 Rs, the length scale is about 1 km, which ismuch larger than the spacecraft size. In this case, the Knudsen number is about 1.0 and the collision between thesolar wind particles and the sublimation gas particles can not be neglected.

As seen in Eqs. (6) and (7), the length scale and the Knudsen number depend on the temperature of the heatshield, the number density of the solar wind and the total mass loss rate, which is given by the product of thesublimation rate Jsub and the heat shield area S. Figure 6 shows the variations of the length scale and the Knudsennumber with the total mass loss rate of the heat shield. The most dominant factors with respect to the interactionbetween the solar wind and the sublimation gas cloud are the total mass loss rate and the number density of the solarwind. The effect of the heat shield temperature is negligibly small. It should be noted that the Knudsen number forthe number density 1014 m-3 and the total mass loss rate 10-2 kg/s is the same as that for 1016 m-3 and 10-4 kg/s. Whenthe number density of the solar wind is unexpectedly large, the interaction effect may become intolerably significantfor the solar wind observation even when the total mass loss rate is smaller than the maximum allowable value forthe nominal freestream condition of the solar wind.

Figure 6. Variations of Length Scale and KnudsenNumber with Total Mass Loss Rate of Heat Shield.

Figure 5. Variations of Total Mass Loss Rate,Length Scale and Knudsen Number with Distancebetween Sun's Center and Probe.


2. Method of Numerical SimulationTo simulate the interaction between the solar wind and the sublimation gas, the DSMC method with the modified

Nanbu scheme is also used. The difference in the particle mass between the solar wind (H) and the sublimation gas(C) is taken into account at the collision calculation. In the far field analysis, only the three-dimensional calculationsare made. The size of the computational domain is 10L X 10L X 10L. The solar probe is described as the point-source located at the center of the computational domain except the merged length scale case which will bediscussed later. The sample particles for the sublimation gas is injected from the point-source in both upstream anddownstream directions with the specified total mass loss rate. The solar wind particles coming into thecomputational domain are given by the Maxwellian velocity distribution function at the freestream velocity andtemperature. The test particles going out of the computational domain are deleted from the calculation. The time stepsize is determined with the Courant number for the freestream velocity at 0.6, which corresponds to about 20-60%of the mean collision time. The total number of the test particles in the computational domain is about 500,000-700,000.

IV. Results and Discussion

A. Near Field AnalysisFirst, the two-dimensional analyses on the behavior of the outgas are made to understand the characteristics of

the rarefied flow of the sublimation gas cloud around the probe. Figure 7 shows the number density distribution ofthe sublimation gas at distance 2.5 Rs. The upper half of the figure is the result considering the molecular collisionsand the lower half is that of the collisionless calculation. As already shown in Fig. 3, when the probe is located at 2.5Rs, the Knudsen number becomes small and the effects of the molecular collisions can not be neglected. It is clearlyseen that the cloud of the sublimation gas in the collisionless case spreads wider than the collisional case.

The molecular collision produces the pressure on the wall of the heat shield. The wall pressure is compared withthe solar radiation pressure, thrust due to the mass injection of sublimation, and the dynamic pressure of the solarwind in Fig. 8. The width of the heat shield is 1 m. The dynamic pressure of the solar wind is negligibly small incomparison with the other types of forces. When the distance from the sun's center is smaller than 3 Rs, the injectionthrust becomes the largest force. The wall pressure is smaller than the injection thrust but their difference decreaseswith the decrease in the distance from the sun. The wall pressure also depends on the size of the heat shield. Largerwall pressure will be generated for larger heat shield, since the Knudsen number decreases and the molecularcollision becomes more frequent.

Figure 8. Comparison of Various Types of Forcesacting on Heat Shield.

Figure 7. Number Density Distribution ofSublimation Gas by Two-dimensional Analysis.


Figure 9 shows the number density distributionof the sublimation gas around the solar probe on theplane of symmetry by the three-dimensionalanalysis. The temperature of Disk-1 and Disk-2 isassumed to be 2700 K and 2000 K, respectively.The amount of the sublimation gas reaching themain body of the spacecraft behind Disk-2 isnegligibly small. To avoid the noise at scientificobservation, the measurement instruments shouldbe located in the region where the density of thesublimation gas is low, that is, in the region behindDisk-2.

B. Far Field Analysis

Figure 10 shows the number densitydistributions of the solar wind and the sublimationgas on the plane of symmetry by the three-dimensional far field analysis. The total mass lossrate of the heat shield is 0.01 kg/s, which corresponds to the distance from the sun's center at 2.5 Rs for the heatshield area 10 m2. From this figure, the length scale of the flow phenomena seems to be about 1 km, which is almostthe same as predicted in Fig. 6. Due to the presence of the sublimation gas cloud, the number density of the solarwind increases by about 5% in front of the probe. In the wake region behind the probe, decrease in the numberdensity by 7-8% is observed. On the other hand, the number density distribution of the sublimation gas is not sostrongly affected by the incoming solar wind.

The velocity distribution functions, in other words, theenergy spectrum, of the solar wind is one of the mostimportant measuring items to understand the mechanism of the corona heating. Figure 11 shows the velocitydistribution function of the solar wind for the velocity component in the direction to the sun calculated at the probelocation for various total mass loss rate. The wall temperature of the heat shield is fixed as 3000 K. At the mass lossrate 10-4 kg/s, the obtained distribution function is almost the same as that of the freestream, which is indicated bythe thick solid line in the figure. When the total mass loss rate increases, the difference between the profile of thefreestream and that obtained at the probe location becomes large. At the mass loss rate 0.01 kg/s, the solar wind

Figure 9. Number Density Distribution of SublimationGas around Heat Shield of Dual Disks Type on Plane ofSymmetry by Three-dimensional Analysis.

Figure 11. Effect of Total Mass Loss Rate onVelocity Distribution Function obtained by SolarProbe.

Figure 10. Number Density Distribution of SolarWind and Sublimation Gas Cloud by Far FieldAnalysis.


particles are significantly decelerated by the collision with the sublimation gas cloud. In this case, the properties ofthe solar wind obtained by the probe are expected to be much different from those of the undisturbed freestreamcondition. The result for the heat shield inclined at 45 degrees to the freestream direction is also plotted in Fig. 11. Itis almost the same as the result for the heat shield set normal to the freestream. As for the interaction with the solarwind, the most dominant factor is the total mass loss rate and it must be smaller than 10-4 kg/s to observe theundisturbed freestream properties of the solar wind by the solar probe.

As already discussed in Fig. 6, the number density ofthe freestream solar wind has also significant effect onthe interaction phenomena. Figure 12 shows that thedistribution function at the total mass loss rate 10-4 kg/sand the number density of the solar wind 1016 m-3 is quitesimilar to that at 0.01 kg/s and 1014 m-3. This factindicates that the evaluation method of the length scalegiven in Eqs. (5)-(7) is appropriate for the interactionphenomena between the solar wind and the sublimationgas cloud. Considering the case that the number densityof the solar wind in the corona is much higher thanexpected, the total mass loss rate should be much smallerthan 10-4 kg/s. In this sense, it seems reasonable that themaximum allowable value for the total mass loss rate isset at 2.5 mg/s in the solar probe study of JPL.4

C. Merged Length Scale CaseWhen the number density of the solar wind increases,

both the length scale and the Knudsen number decreaseas shown in Fig. 6. At the total mass loss rate 10-4 kg/sand the freestream number density 1016 m-3, respectively,the length scale is predicted as 4 m, which is in the sameorder as the heat shield diameter. In such case, thephenomena in the far field analysis and those in the nearfield analysis are expected to be merged and the heatshield can not be described by the poit-source as in the

Figure 12. Effect of Freestream Number Density ofSolar Wind on Velocity Distribution Functionobtained by Solar Probe.

Figure 14. Effect of Measuring Location onVelocity Distribution Function in Merged LengthScale Case.

Figure 13. Number Density Distribution of SolarWind in Merged Length Scale Case.


far field analysis. The number density distribution of the solar wind in the merged length scale case is shown in Fig.13. The strong compression in front of the heat shield, which is not observed in the far field interaction, is seen.Figure 14 shows the velocity distribution function of the solar wind particles at five different locations A-E indicatedin Fig. 13. The spike at the velocity around 0 km/s is caused by the diffusive collision at the heat shield wall. In thiscase, the point E seems to be the beat position for measurement of high energy particles in the solar wind, since thevelocity distribution function is almost the same as the freestream profile in the velocity range higher than 200 km/s.The sensors for the solar wind measurement should be located in the shadow of the heat shield near its boundary andfar downstream of the heat shield.

V. ConclusionThe major conclusions of the present study are as follows:

1) The multiple-stage C/C disks with the most forward primary disk inclined to the sun's direction is promising forthe heat shield configuration of the solar probe from a viewpoint of reduction in the shield mass and total massloss rate.

2) The effects of the rarefied flow of the sublimation gas from the heat shield should be considered not only in thenear field around the spacecraft but also in the far field. The interaction between the solar wind and the cloud ofthe sublimation gas may occur in much larger scale than the size of the spacecraft. The method to evaluate thelength scale and the Knudsen number for the interaction phenomena is proposed.

3) The number density distribution of the outgas around the probe is predicted by the DSMC analysis. Themeasurement instruments should be located in the region where the density of the sublimation gas is low.

4) The properties of the solar wind measured at the solar probe may be disturbed due to the interaction with thesublimation gas cloud injected from the probe itself. The DSMC analyses show that the velocity distributionfunction of the solar wind obtained by the probe may be different from that of the undisturbed freestream. Thedifference becomes significant when the total mass loss rate of the heat shield and the freestream number densityof the solar wind are large. Consequently, the total mass loss rate must be strictly limited and the location of thesensors should be carefully determined for accurate measurement of the solar wind in the corona.

AcknowledgmentsThis work is supported in part by Grant-in-Aid for Scientific Research No. 14350508 and No. 15360450 of

Japan Society for the Promotion of Science.

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