Multi-tired Implementation for Near-Earth Asteroid Mitigation

Scientific Preparatory Academy for Cosmic ExplorersShen Ge, Hyerim Kim, Darkhan Alimzhanov, Neha Satak

Shen Ge, sge@spaceacad.org; Hyerim Kim, hk@spacecad.org; Darkhan Alimzhanov, da@spaceacad.org; Neha Satak, ns@spaceacad.org

2

NEO Mitigation Strategy

• Detailed three-tiered layer for exploring and mitigating Near Earth Asteroids (NEAs)

• Reference mission to asteroid 99942 Apophis is the proof of concept for this process

Ground Experiments and Simulations

LEO Flight Experiments

Apophis Exploration and Mitigation Platform

3

Apophis Exploration and Mitigation Platform (AEMP)

• Exploration and mitigation platform to Apophis. Scheduled Objectives:

1. 1. Begin a mission with precision tracking, “tagging” the asteroid with the spacecraft, and combine this with science measurements of the gravity field, material composition, and thermal properties. [2021]

2. 2. Cross-correlate the tracking data found in the initial exploration phase with SDM predictions and resolve the modeling and parameter uncertainties. [2021 – 2022]

3. 4. Perform an initial mitigation technique that depends on the least data (mass distribution, total mass, center-of-mass location, geometric envelope, spin state). [2022]

4. 5. Combine the initial mitigation phase with continued observation to map the albedo, model the thermal properties, model solar pressure, and the Yarkovsky effect. [2022-2023]

5. 6. Finally, apply some permanent mitigation technique that can eventually retire the threat completely. [2023]

2023NOV

2021FEB

4

AEMP: Mission Profile

•Launch – Feb 2021

•Cruise

•Rendezvous – Sep 2021

•Preliminary Exploration

•Long Term Mitigation – May 2023 •Short Term Mitigation – Apr 2022

•Post Mitigation Investigation

•Preliminary Analysis

•Intermediate Analysis

•End of Mission – Nov 2023

5

AEMP: Orbital Transfer• Simple 2-impulse orbit transfer• Direct launch-to-transfer orbit using a Falcon-9 vehicle• Solid kick motor provides majority of rendezvous ΔV• Upon insertion into the proximate heliocentric orbit near

Apophis, the spacecraft is to take up a 2 to 3 km stand-off position to begin exploration

• Proximity maneuvers performed by mono-propellant Hydrazine main engine and attitude control thrusters

Launch date: Feb 19-2021Rendezvous Date: Sep 14 2021

Time of flight: 208 daysC3 4.3 km2/s2

ΔVf 3 km/s

2021SEP

2021FEB

6

Why is Exploration Needed Before Mitigation?(J. D. Giorgini, L. A. M. Benner, S. J. Ostro, M. C. Nolan, and M. W. Busch. “Predicting the Earth encounters of (99942) Apophis”, Icarus 193 (2008) 1-19.)

•Errors in the Standard Dynamical Model (SDM) can produce tens of Earth radii positional errors over the period 2029 - 2036

• Uncertainties in Apophis’ thermal emission parameters (e.g. bond albedo)

can produce tens of Earth radii errors over the period 2018-2036

7

AEMP: Initial Exploration PhaseThe first actions to be performed are designed to achieve the following science objectives:

1) Determine the trajectory of Apophis 99942 with sufficient accuracy to establish the minimum trajectory change that can guarantee no Earth impact through the close approach of 2036

2) Study physical characteristicsa) to refine the orbit propagation models.

• Spin state• Asteroid mass, etc.

b) to refine intervention procedures. • Surface mapping of geometric albedo• Gravity model valid ~100m from surface

2022APR

2021SEP

8

AEMP: Instrumentation/Science Mapping

Optical Navigation Camera

Laser Range Finder

Radio Science

Inertial Measurement Unit

Star Tracker

Micro-Bolometer

Determine Absolute Position of Spacecraft     x      Determine SC to Apophis relative position x x     x  Determine mass of Apophis x x x x    Map surface geometry x x        Determine bulk volume and density x x        Model the gravity field x x        Map the albedo of the Apophis x x       xDetermine average bond albedo x x       xMap surface temperature           xDetermine spin axis x

• Optical Navigation Camera• Laser Range Finder• Radio Science• Inertial Measurement Unit• Star Tracker• Micro-bolometer

2022APR

2021SEP

9

Tracking and Mitigation Pose Conflicting Requirements

Make tracking measurements and incorporate data into

trajectory modelNominal trajectory

Suppose we launch early (2012), and acquire

tracking data over the following year.

Then as we propagate forward over a long time period using the dynamical model, the uncertainty (tube width) might grow so large

that an unambiguous prediction is impossible by 2036.

Tracking measurements

Whereas, if we launch and do tracking just before a close approach, our

uncertainty will be smaller but there will be no time for mitigation.

9

AEMP: Tracking Error vs. Deflection Effectiveness

Tracking begins

April, 2029 close approach

1/10 Earth Radius

3 Earth Radii

10

11

AEMP: Gravity Tractor• The gravity tractor is well-known and can be applied early in mission since

detailed knowledge of the physical properties of the NEO is not required.• The thrusters used are xenon Hall Effect thrusters canted Φ = 38˚off the

thrust axis and providing a net tractor force of Fhover = 4 mN.• By maintaining a position d = 270m from C.O.M. of Apophis for 1 year

(prior to the 2029 close approach), 3 Earth radii of deflection will be achieved by 2036.

Tractoring period Average Mass Distance from

CM Force imparted

1 year 560 kg 270 m 0.014 N

2022APR

2023MAY

12

Yarkovsky EffectSo

lar R

adia

tion

Cooler “dawn” side

hotter “dusk” side

Excess radiationCarries away momentum Pphoton per photon

Net force

D. Vokrouhlicky, A. Milani, and S. R. Chesley. “Yarkovsky Effect on Small Near-Earth Asteroids: Mathematical Formulation and Examples”, Icarus 148, 118-138 (2000).

sJxh

hchPphoton

3410626.6

13

AEMP: Surface Albedo Treatment System (SATS)

• SATS raises or lowers the average albedo to produce a three-Earth-radii orbit deflection by 2036.

• On the sun-facing side, the surface has a net positive charge.

• The SATS nozzle is designed to impart a negative charge to the ACPs and dispensing is performed solely on the sun lit side.

• This effect further ensures that the particles will be quickly bound to the surface and will not rebound or levitate into an escape condition.

P. Lee, “Dust Levitation on Asteroids”, Icarus 124, 181-194 (1996)

2023MAY

2023NOV

14

AEMP: Surface Albedo Treatment System (SATS)

Pressurized Inert Gas

Albedo Change Particles

Fluidization stream

ACP Chamber

Mixing Chamber

Tribo ionization tube

A secondary flow is released into the

outer portion of the selected ACP

chamber

The ACP storage chamber is double-walled; the ACPs being contained within the inner wall. The inner wall is perforated by many

small holes.

The gas flows through the holes in the inner wall, both

“fluidizing” the ACP mass (mixing up the ACPs so that the dry powder behaves like

a liquid) and expelling a steady stream of ACPs into

the mixing chamber.

The main flow out of the gas supply leads directly to

the mixing chamber.

Once mixed, the ACPs plus gas is forced through the narrow

tribo ionization tube

2023MAY

2023NOV

15

AEMP: ACP Mass Calculation

VARIABLE QUANTITY DESCRIPTIONRadius of Apophis R 105 – 165 mDensity of Apophis ρp 1.78 g/cm3

Surface Thickness W 50 μmDistance from Orbital Track by 2036 ||Δx||2036 3REarth

Bond Albedo of Treated Surface αT 0.0461-0.4149Bond Albedo of Untreated Surface α0 0.1383-0.1613Orbit Sensitivity Factor Γ 200-1450

2

2036

0 1A T

TT

R w xM

R

SCENARIO WHITE ACP MASS(kg) BLACK ACP MASS (kg) TOTAL MASS (kg)Largest Mass (165 m),

Least Reflective (0.1613)

1.35 2.98 4.33

Nominal mass (135 m), Nom. Reflective

(0.1521)

3.58 8.86 12.4

Smallest Mass (105 m), Most Reflective

(0.1383)

21.4 64.2 85.6

2023MAY

2023NOV

16

AEMP: Spacecraft Design• Mass:

• Launch mass to Earth escape = 1100 kg

• Wet mass = 570 kg• Dry mass = 415 kg

• Power:• Solar arrays• Li-Ion battery packs• Max power mode = Grav Tractor ~

1kW• Attitude control system provides 3-axis

stabilization• Reaction wheels• Attitude thrusters provide minor

translational capability• Propulsion

• Solid kick motor for rendezvous ΔV• Hydrazine monopropellant system

for proximity operations• 2 Xenon propellant Hall’s effect thrusters

• Semi-autonomous command structure• Communications

• 1 m parabolic high gain antenna• 2 omni directional low gain antenna

• Sensor suite• Star tracker• Inertial measurement unit• Optical navigation cameras• Sun sensors• Laser range finder• Micro-bolometer

Development time: ~5yrs Total cost: ~ $350 M

17

AEMP: Cost Justification

Payload

Price(US Dollars, millions)

Dawn Framing Camera 25.4NEAR Laser Range Finder 10.1Microbolometer 15.2Albedo Change 10.2Total 60.9

Element

Amount in 2009 (US Dollars, millions)

PM/SE/MA 24.5Payload 60.9

Spacecraft 102.5Hardware total 163.5MOS.GDS 18.0Development Cost, No Reserves 206.0Development reserves 61.8Total Development costs 267.8Phase E&F costs 28.0Phase E&F Reserves 8.4Total mission costs, no launch Vehicle 304.2Launch Vehicle/services 50.0

Total mission 354.2

Costing exercise was done at Ames Mission Design Center in April 2009 Spacecraft and payload cost estimated using parametric cost estimation models Other costs modeled as percentage warp-factors Phase E/F costs based on historic Discovery class missions

18

LEO Flight Experiments (LFE)

• The Apophis Mitigation Technology LEO Flight Experiments (LFE) will demonstrate feasibility of an albedo changing prototype on a target surface in a controlled environment

• Static Preliminary Albedo Demonstration Experiment (SPADE) design is a cube-shaped spacecraft 40x40x40 cm

• Static, flat SATS test surface is part of satellite and exposed to LEO environment

2012DEC

2013FEB

19

LFE: SPADE Design Powder Canister

Pressurant Gas CanisterTorque Rod (3)

Tribodispenser Tube

SunSensor (4)

Antenna

Camera

Electronics Bay

Batteries

Test Surface

20

LFE: Mission Profile

1. Orient spacecraftV∞

2. Charge test surface then remove power supply

3. Initiate tribodispenser and spray test surface

21

LFE: Mission Profile (Part 2)

4. Allow particles time to cure

5. Observe, record, and transmit data

Data

22

LFE: Orbital and Attitude Requirements

• Orient so that panel is facing sun when on sun side of earth to allow particles to cure in sunlight

• Orient so main body of the craft shields the panel while moving through LEO atmosphere

• Main body in ‘ram’ direction, panel in ‘plasma wake’Parameter Value

Altitude* 350 km

Inclination** 46o

Ballistic Coefficient 58 – 82 kg/m2

Orbit Lifetime 30 – 200 days

* To avoid excess radiation, altitude < 700 km but for 30-day mission timeline, altitude > 300 km** Communications with College Station, TX ground station requires > 31o

23

LFE: Surface Design

• Surface simulated by charged aluminum plates of varying roughness

• Surface charge from parallel plate capacitor

• Required electric field based on expected asteroid charge density

E

Plate Area 0.217 m2

Assumed Resistivity 2.82 × 10-8 Ω·m

Dielectric Constant 9.15

Distance between Plates 0.01 m

Potential Difference 0.1 V

Capacitance 1.76 x 10-9 F

Charge on top plate 1.76 x 10-10 C

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LFE: Mass Budget EELV Secondary Payload Adapter

Total Mass Budget [kg]

Albedo Change Demo 5.9

Telecommunications and Instrumentations 1.0

Propulsion and Attitude Control 2.8

Structure, Thermal, and Power 32.2

Total 41.9

Total (with 30% safety factor) 54.5

Magnetorquer (x3)Sunsensors (x4)Magnetometer

GUMSTIX Computer

Camera (Cosmos-1 adapted)

25

LFE: Cost Budget Cost Component Parameter X (Unit) Parameter Value RDT&E Cost 1st Unit Cost SubTotal Cost1 Payload Spacecraft Total Cost 1.68 x 104 $4.00 $2.70 $6.702 Spacecraft Satellite bus dry wt. (kg) 3.57 x 10 $0.00 $0.00 $0.002.1 Structure Structures wt. (kg) 1.99 x 10 $1.05 $0.45 $1.502.2 Thermal Thermal control wt. (kg) 1.00 $0.20 $0.20 $3.25 Average power (W) 1.50 $0.01 $0.01 $0.022.3 Electrical Power System (EPS) Power system wt. 1.48 x 10 $1.50 $0.90 $2.40 Battery capacity (A-hr) 2.27 x 10 $4.50 $2.75 $7.25 BOL Power (W) 1.80 x 102 $3.50 $2.10 $5.50 EOL Power (W) 1.00 $3.00 $1.70 $4.402.4a Telemetry Tracking & Command (TT&C) TT&C / DH (W) 3.00 *** $0.20 $0.20 Downlink data rate (Kbps) 5.60 x 10 *** $0.92 $9.152.4b Command & Data Handling (C&DH) TT&C + DH wt. (kg) 9.00 x 10-1 $0.50 $0.20 $7.00 Data Storage Capacity (MB) 1.40 x 102 $3.00 $1.25 $4.30

2.5 Attitude Determination & Control Sys. (ADCS) ADCS dry wt. (kg) 1.50 *** $1.15 $1.15 Pointing accuracy (deg.) 1.00 *** $2.45 $3.45 Pointing knowledge (deg.) 1.00 *** $2.20 $2.202.6 Propulsion Satellite Bus dry wt. (kg) 3.57 x 10 *** $0.00 $0.00 Satellite volume (m^3) 9.87 x 10-2 *** $0.00 $0.00 Total: $23.5 M3 Integration, Assembly & Test (IA&T) Spacecraft total cost 1.68 x 104 $0.00 $3.00 $3.004 Program Level Spacecraft total cost 1.68 x 104 $2.50 $2.50 $5.005 Ground Support Equipment (GSE) Spacecraft total cost 1.68 x 104 *** $1.50 $1.506 Launch & Orbital Operations Support (LOOS) Spacecraft total cost 1.68 x 104 *** $1.35 $1.35

Inflation Factor 1.30 Total

Satellite Cost: $34 M

26

Ground Experiments (GE)• Ground tests to determine optimal parameters for design of

tribodispenser through repeated experiments with combinations of varying inputs.

• Outputs to be maximized:– Charge-mass ratio (Q/M). This is immediately out of tube. will not be

the same for each particle but we want the charge to be +/- 10-6 Coulombs (C) within 1 standard dev (σ).

– Albedo Change (AC). Difference between albedo after treatment with albedo before treatment. This will mostly depend on the pigmentation of the powder.

– Coverage area-mass ratio (A/M). – First pass transfer efficiency (FPTE). Mass of powder on surface over

total mass after one trial.

2012

2010

27

GE: Experimental Parameters COMPONENT Q/M AC A/M FPTE

Tube length X X X

Tube material X

Tube radius X X X

Gas Pressures (injection,

dilution, vortex)

X X X X

Particle/Gas Ratio X X X X

Surface albedo X

Nozzle choice X X X X

Comment: This chart only shows direct correlation. Obviously there’s indirect correlations as well. For instance, particles that have greater charge/mass ratio (Q/M) are more likely to “stick” to the surface and hence produce a larger albedo (AC).

ASSUMED CONSTANTS:1. Powder (developed by PCRG for our application)2. Surface temperature (400K)3. Surface roughness (distributed according to asteroid)4. Surface material (LL Chondrite mod)5. Surface charge (5 V)

Secondary variables affecting the experiment are not shown!

28

GE: Objective Hierarchy Q/M AC A/M FPTE

Q/M 1 ½ 3 2

AC 2 1 4 3

A/M 1/3 ¼ 1 ½

FPTE ½ 1/3 2 1

Q/M AC A/M FPTE

.2771 .4658 .0960 .1611

Weights:

AHM:

Albedo change is the most important objective criteria. Coverage area-mass ratio is the least important.

29

GE: Optimization of Design

1. Conduct multiple runs of experiments with varying input parameters.

2. Obtain average and standard deviation of runs.3. Give a measure of “goodness” to each output result

(Q/M, AC, A/M, and FPTE) of each set of input parameters.

4. Multiply each “goodness” by the weights defined in objective hierarchy and sum them to obtain one number for each setup. The setup with the maximum number is the one to use.

30

GE: Minimizing Experiment Runs

• A full factorial experiment assuming two levels of factors, 2n runs are necessary where n is the number of independent parameters.

• Using Taguchi methodology, this can be cut to 2(n+1) runs depending on number of considered interactions.

• Orthogonal array/Taguchi Method assumes interactions between variables are negligible unless otherwise stated.

31

GE: Experimental Schematic

Gas Tank

SATS Triboiontube of SATS

Faraday cages

Electrometers

Aluminum plate

Lamp

Nozzle

Faraday cage

Electrometer

Vacuum Chamber

Not shown:- DAQ + Computers- Scale (to measure mass of SATS before and after each run as well as mass of plate before and after each run)- Cameras (to take photos of plate before and after each run for albedo and coverage area analysis AND flow)-Thermistors (measure temperature of plate)

Infrared heater

32

Simulation Outline

• Particle deposition simulator simulates particle dynamics from spacecraft to surface

• Inputs are design parameters such as tribodispenser length, particle size, spacecraft hovering height, etc

• Outputs are particle trajectories, charge-mass ratio, albedo change, etc

• Works concurrently with ground experiments to optimize design

33

Simulation Outline

• Nine sections, split into two groups• Sections 1-4 focus on gas-particle flow where

pressurized gas forces dominate• Sections 5-9 focus on interspatial and asteroid

based forces where these forces dominate

34

Sim: Near Field

• Mass flow rate• ACP charge

• Gas Pressure• Particle Positions, Velocities, Accelera-

tions-> Distribution

Input Parameters Output Parameters

Materials - Average particle size and density, particle volume fraction, particle velocityConfiguration- Length and Diameter of the tubePressurant application- Injection pressure, dilution pressure, vortex pressure

Sim: Near Field

- Governing Equations: 1) Mass conservation eqn. 2) Momentum Conservation eqn.

Turbulent air flow - The standard κ-ε model

1. a) ACP/Gas Flow

Design procedure

1) Models for Tribocharging Tube a) ACP/Gas flow (+ turbulence) b) Electrostatic Charging

2) Models for Dispensing a) Solid particle motion b) Electrostatic Field

35

- Rate of particle collisions with tube walls For Charge per mass:

Sim: Near Field

0

max

3

314

g c

p p

gp

p p

VD zqDum mD v

Dielectric constant of gas - usually close to vacuum constant

Effective contact potential (Volta potential) Mass density of particle material

Mass density of gas

Diameter of tribo

g

c

p

g

V

D

0

4

tube Diameter of powder particles

Seperation distance, a few angstroms according to paper Axial gas velocity Mean axial particle velocity Gas/Particle mass flow ratio

pD

zuvm

WD

2

Powder mass flow rategu

W

1. b) Electrostatic Charging

36

Sim: Near Field

37

2. a) Solid particle motion-> predicts the trajectories of the

particles -> stepwise integration over discrete

time steps-> solved in each coordinate direction to

predict the velocity and position of the particle at given time.

- Lagrangian Approach the equation of motion for the particles

2. b) Electrostatic Field-Consider the space charge from nozzle to near field, and interactions between particle - particle. Laplace equation

38

Sim: Near FieldFirst Tribo dispenser Model (Solidworks)

39

Sim: Near FieldTribo dispenser Model (Gambit)

Volume Meshes

Set Boundary conditions

40

Sim: Far Field IO

utputs

Spacecraft Height

Asteroid Size and Shape

Position

Asteroid Mass Density

Forces (acceleration)

Inputs

Asteroid Surface Charge

Density

ACP Charge

ACP Density

ACP Radius

ACP Position

ACP Velocity

ACP Acceleration

ACP Position

ACP Velocity

ACP Acceleration

From outputs of near-field

ACP Charge

Numerical integration of force equations propagated

Note: All variable constants are outlined in red.

41

Sim: Far Field IGravitational Force (Fg)G – gravitational constantM – mass of Apophism – mass of ACPr – distance between mass centers of Apophis and ACP

Electrostatic Force (FE)q – charge of ACPσ – surface charge density of ApophisA – incremental surface area

Solar Radiation Force (Fr)S – solar fluxA – surface area of Apophisc – speed of lightv – velocity of ACPQpr – radiation pressure coefficient

42

Sim: Far Field I

1. Starting at t=0, n powders are ejected from spacecraft at an altitude h with some velocity and acceleration. Eject more n powders every tint seconds.

2. Velocity and position is propagated forward in time using Newton-Euler equations and Runge-Kutta integration with time step Δt.

3. Detect when powders are ~1 meter above the surface and pass the simulation of Far-Field 1 to Far-Field 2.

43

Sim: Far Field II

Plasma Sheath Thickness

Position

Solar Wind Mach Number

Forces (acceleration)

Inputs

Plasma Sheath Potential

ACP Charge

ACP Density

ACP Radius

Outputs

ACP Position

ACP Velocity

ACP Acceleration

ACP Position

ACP Velocity

ACP Acceleration

From outputs of Far-Field 1

ACP Charge

Numerical integration of force equations propagated

44

Sim: Far Field II• A plasma sheath of negatively charged

particles floats right above the surface and screens out the positive charges on the surface.

• The powder particles must be able to “punch” through this cloud.

• Once the ACP enters the sheath, its ultimate fate can only be one of three possibilities:1. It falls to the surface. GOOD2. It gets deflected and totally escapes.

NOT GOOD3. It becomes suspended in the sheath.

NOT GOODAsteroid

Powder Paths

Layer of charged electrons

45

Sim: Far Field II

• Solve two pairs of equations:

mgdzdYY

ekT

enadtzdm d

ed

2/3

002

2

4

ie IIdtdQ

0),1exp(exp8

0),exp(exp8

2/12

0

2/12

0

UYkTeV

mkTaenI

UYkTeV

mkTaenI

dee

ee

dee

ee

e

e

i

ei kTeVM

kTeUmkTMaenI

/2/21 2

2/12

0

Force

Current

46

Sim: Far Field II

1. Take position, velocity, and acceleration of particles from FF1.

2. Propagate positions and velocities of particles through FF2 forces.

3. Relay outputs to FF3 as inputs after undergoing a certain plasma sheath thickness.

47

Sim: Far Field III

• After passing through the sheath, the particles will hit the ground.

• But will the ground be – Shadowed (negatively charged) or sunlit (positively

charged)? (Will the particle be repelled or attracted at certain places?)

– Hilly or flat? (Will the particle bounce upon impact? How will this affect coverage area?)

– Rocky or soft? (Will the particle bounce upon impact?)– Light or dark? (Will the particle create much albedo

change?)

48

Sim: Far Field III• Current simulation efforts take into account a distribution of albedo

and heights on surface generated by:1. Create a realistic needle map n(i, j) of the surface where (i, j) is a particular

pixel in the MxN image matrix. A needle map is just a matrix of normal vectors to the surface.

2. Assume a solar position relative to the surface. This determines the direction of the lighting.

3. Create an intensity map of an asteroid dependent on the needle map.4. Find the geometric albedo at every pixel by assuming a Lambertian model.5. Apply ACP positions from outputs of FF2 for both colors. Find the amount

of albedo change detected for either case.• Currently just using a rough probability of landed particles for

generating the normal distribution of ACP landings for particles.

49

Sim: Far Field III

• Assuming 500 m2 coverage, i.e. 1.4% area coverage for the smallest possible sizeSCENARIO ALBEDO BEFORE (AVG) ALBEDO AFTER (WHITE) ALBEDO AFTER (DARK) Light 0.6947 0.7862 0.5795Mid 0.4228 0.5682 0.3617Dark 0.2205 0.4276 0.2451

50

Conclusion

• Three-tiered design process of AEMP mission, LEO test flight satellite mission, and ground experiments with simulations is progressing concurrently providing insight on all three layers of design

• Continued collaboration between the three design layers will culminate in the launch of a fully functioning spacecraft to the near earth asteroid Apophis early 2022

51

Questions?

52

EXTRA SLIDES

53

EELV Secondary Payload Adapter (ESPA) Small Launch scaled version

38.8” primary interface diameter Sized for:

Minotaur IV Falcon 1e Taurus Delta II

Fits CubeSats up to 180 kg Flight validation costs are low

Use existing test facilities

ESPA Contraints

List of Parameters for MethodSymbol Parameter Secondary

VariablesOption 1

(-)Option 2

(+)

L Length of tube Charge on particle

521 mm (default)

1000 mm

r Radius of tube Mass flow rate through tribogun

~35 mm diameter (default)

~15 mm diameter

ηm Tube material Charge on particle

Teflon Nylon

ηn Tube nozzle Particle distribution

Straight Fan-shaped

φ Particle-gas ratio

Charge on particle

TBD TBD

ρinj Pressure – injection

Mass flow rate through tribogun

140 kPa ? TBD

Ρdil Pressure – Dilution

Particle concentration

in gas

110 kPa ? TBD

ρvor Pressure – Vortex

Turbulence of motion in gas

80 kPa ? TBD

Experimental TrialsC

F

L

ηnΦ

ρinj ρdil

ηmr

ρvo

r

A

D E

B

G H

T A C AC D AD B BD E F G FG H GH AG e

1 - - - - - - - - - - - - - - -

2 - - - - - - - + + + + + + + +

3 - - - + + + + - - - - + + + +

4 - - - + + + + + + + + - - - -

5 - + + - - + + - - + + - - + +

6 - + + - - + + + + - - + + - -

7 - + + + + - - - - + + + + - -

8 - + + + + - - + + - - - - + +

9 + - + - + - + - + - + - + - +

10 + - + - + - + + - + - + - + -

11 + - + + - + - - + - + + - + -

12 + - + + - + - + - + - - + - +

13 + + - - + + - - + + - - + + -

14 + + - - + + - + - - + + - - +

15 + + - + - - + - + + - + - - +

16 + + - + - - + + - - + - + + -

NOTE:For experiments not requiring all 8 factors here, simply ignore respective column in chart.

Comment:e may be useful for error estimation

Determining Interrelationships

• To find the optimal configuration, an equation can be written,

16/

16/0

6

1,

8

10

kiki

k

jjiji

iiik

yxa

ya

xxaxaay

where yk = kth trial result of output (can be Q/M, albedo, FPTE, A/M)a = coefficients to be determined. Note that ai also applies to double coefficientsxi = 1 (for maximum input value) or -1 (for minimum input value)

Experimental Trials

• In addition to the 16 trials necessary, 3 repeated trials of conditions at the midpoint of the high and low levels for all 8 factors need to be conducted to determine the validity of the measurements.

Equipment RequiredSYSTEM COMPONENTS

Surface Albedo Treatment System

(SATS)

- Tribogun- Powder- Hopper (will contain powder)- Control electronics- Valves- Pipes- Pressurant Tank (will contain neutral gas)- Neutral gas

Heat/Light Source + Heat Detector

- Modified projector lamp(simulates solar radiation)- Infrared heater (continually heats the surface with IR)- Thermistors

Surface - 0.22 m2 Aluminum plate with varying albedo and roughness (or multiple plates with differing albedo/roughness)

Charge Detector (CD) - Faraday Cup Electrometer (connected to DAQ)

Mass Measurer (MM) -Scale

Cameras - High speed to Look at flow and curing- Webcam to look at surface after treatment

Environment - Vacuum chamber (eliminates charge interaction with air)

Debye Length

• Solid body in a plasma will be surrounded by a plasma sheath.

• Minimum distance scale over which the particles may be considered in its collective behavior. Any smaller than this and the interactions between individual particles have to be considered.

• Two Debye length:– Solar wind– Photoelectron layer (from photoelectric effect)

Comparisons of Debye Lengths

• The spatial scale at which solar wind interacts at 1 AU: 12 m.

• Spatial scale at which the near-surface electron cloud interacts at 1 AU: 0.1 m

• The more significant Debye length is the shorter one.

ForcesCharged dust particle in sheath will be subjected to

electric and gravitational forces.

Constantsm = mass of particleg = gravitational constant (assume radius of asteroid is much larger than Debye length)λd= Debye length (assume much smaller than radius of asteroid)a = particle radius (assume much smaller than Debye length)n0 = ion density far from surfaceε0 = permittivity constant in vacuume = electron chargek = Boltzmann constantTe = electron temperatureNon-dimensional variables:z = x/ λdY = eV/kTe

mgdzdYY

ekTena

dtzdm d

ed

2/3

002

2

4

Secondary Equation

Besides the force equation, the other key differential equation to solve to find z is the net current equation. This is the total current that runs through the particle:

whereQ = charge of particleIe = electron currentIi = ion current

ie IIdtdQ

Electron Current Equation

Assuming a Maxwellian distribution of electrons having gone through potential V,

0),1exp(exp8

0),exp(exp8

2/12

0

2/12

0

UYkTeV

mkTaenI

UYkTeV

mkTaenI

dee

ee

dee

ee

Ion Current equation

Similarly,

e

e

i

ei kTeVM

kTeUmkTMaenI

/2/21 2

2/12

0

65

Solidworks Model

66

Fluent Simulation: velocity, mass flow rates

Future Work

Develop User Defiened Function to allow Fluent to account for Charges of particle