Research ArticleInvestigation on Computing Method of Martian Dust FluidBased on the Energy Dissipation Method
Tianxiang Ding ,1 Xuyan Hou ,1 Man Li ,2 Guangyu Cao ,1 Jixuan Liu ,1
Xianlin Zeng ,1 and Zongquan Deng 1
1State Key Laboratory of Robotics and System, Harbin Institute of Technology, No. 2 Yikuang Street, Nangang, Harbin City,Heilongjiang Province, China 1500802Beijing Institute of Spacecraft Environment Engineering, China Academy of Space Technology, No. 104 Youyi Street, Haidian,Beijing, China 100094
In this paper, an initiative Martian dust fluid simulating research based on the energy dissipation method was developed to simulatethe deposition process of Martian dust fluid which was caused by surface adhesion between particles and Martian rovers. Firstly, anenergy dissipationmodel of particles based on the Discrete ElementMethod (DEM) was established because of the characteristics ofMartian dust particles such as tiny size and viscoelasticity. This model is based on the existing DMT model to analyze the collisiondeposition of dust fluid particles, including particle-spacecraft collision and particle-particle collision. Secondly, this paper analyzedthe characteristics of particles after their first collision, then, established the stochastic model of critical wind speed for the particledeposition process. Finally, a series of simulations of the Martian dust fluid particle deposition process were done based on DEM-CFD. The results verified the accuracy of the energy dissipation model and the stochastic model, which could also verify thefeasibility and effectiveness of the computing method of Martian dust fluid based on the DEM-CFD technology.
1. Introduction
A global dust storm (GDS) occurred in Mars year (MY) 34(2018). According to the observation from the MSL Curiosityrover, the daily maximum UV radiation in the Gale Craterdecreased by 90% from sols 2075 (opacity~1) to sols 2085(opacity~8.5) [1, 2]. Figure 1(a) are two views from NASA’sCuriosity rover showing that dust has significantly increasedover three days from June 7th to June 10th. Figure 1(b) showsa series of views from the Opportunity rover with darkeningMartian sky, while the right side was Opportunity’s worst vis-ibility in the MY34 GDS.
Due to the low solar radiation, the solar-powered Oppor-tunity rover (MER-B) was forced to shut down since June10th of 2018, and eventually led to the end of the MER mis-sion. In fact, local and regional dust storms are ubiquitous onMars. Every few Mars years, regional dust storms grow and
merge to become a global dust storm (GDS). Lisano andBernard created a timeline of dust storm observations, whichis shown in Figure 2. The timeline includes all major planet-encircling and regional dust storms, which were observed byMars orbiters, by Mars landers or by telescopes from theEarth, from 1971 to 2013 (the MY9 to the MY31) [3–7].According to limited GDS samples, a GDS occurred everythree Mars years on average.
Martian dust particles lifted by Martian aeolian activitiesmay cause serious challenge to Martian rovers. These finepowders, which are mainly crushed basaltic materials, maycause performance degradation and other issues of optics tothe rovers [8–16]. The Opportunity rover was hit by theMY28 GDS in 2007 when it carried on exploring operationsin the Victoria Crater. During the peak of the storm, poweroutput from the solar panels was reduced over 80%, whichled to two weeks of minimal operations, including several
HindawiInternational Journal of Aerospace EngineeringVolume 2020, Article ID 2370385, 13 pageshttps://doi.org/10.1155/2020/2370385
Figure 1: Views of the MY34 GDS from Martian rovers: (a) Curiosity’s view of the MY34 GDS; (b) Opportunity’s view of the MY34 GDS.
Oct
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Northern season Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnSp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnPlanet-encircling storm S⁎
O OS⁎ S⁎ S⁎S S r rr⁎ r⁎ r⁎ r⁎ r⁎ r⁎No No No No No
Mariner 9
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O OL L L L L L L L L L L L L L
O O O O O O O OViking orbitersViking landers
Earth year and Mars Ls (deg) on Jan 1Mars year MY17 MY18 MY19 MY20 MY21 MY22 MY23 MY24
Northern season Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnSp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnPlanet-encircling storm
O O O O O O Or⁎ r⁎ r⁎r⁎ r⁎ r⁎ r⁎ No No No No No No? ? ? ?
Mars Global Surveyor
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LMars Pathfinder (Jul − Sep 97)
Earth year and Mars Ls (deg) on Jan 1Mars year MY25 MY26 MY27 MY28 MY29 MY30 MY31 MY32
Northern season Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnSp Su Fa Wn Sp Su Fa Wn Sp Su Fa Wn Sp Su Fa WnPlanet-encircling storm S⁎
⁎
No No No No No No No No No No ?S rMars Global Surveyor
Mars OdysseyO O O O O O O O O O O O O O
O
?rS
O O O O O
L L L L L L L L L L LL L
L L LL L L L L L L L L L L L L L L L L L L L L
L L L
O O O O O O O O O O O O O O O O O O O O
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Mars Pathfinder (Jul − Sep 97)Phoneix (May − Nov 08)
Spirit roverOpportunity rover
Curiosity roverStorm optical depth in visible spectrum not measured directly on surface by optical instrumentStorm presence unknownRegional storm only
InSight Dust Storm Historic Timeline, V2.0 Custodian: Mike Lisano, JPL Date: 2013 Jun 07
Planet-encircling or global dust storm
Figure 2: The Dust Storm Historic Timeline from the MY9 to the MY31 [3]
2 International Journal of Aerospace Engineering
days with no contact from the rover to save power [17].Figure 3 shows the comparison of Opportunity’s solar panelsbefore and after the dust storm. The suspended dust droppedonto solar panels and polluted solar panels seriously, whichcaused a serious challenge to the rover’s power supply [18].
The deposition process of Martian dust is a typical two-phase flow process, but it is difficult to solve the equationsof these phenomena directly. Therefore, the numericalapproach has become an effective tool to study the gas-solidtwo-phase flow. In recent years, the numerical approachbased on DEM-CFD is widely used for the industrial two-phase flow process, such as pneumatic conveying and gas-solid fluidization [19–32]. Thus, the numerical approachbased on DEM-CFD is applicable for the research on theeffect of the Martian dust storm. In this paper, an initiativeMartian dust fluid simulating research based on the energydissipation method was developed to simulate the depositionprocess of Martian dust fluid which was caused by surfaceadhesion between particles and Martian rovers. Importantly,this study provides a theoretical basis for Martian dust pro-tection and the Martian exploration mission.
2. Materials and Methods
2.1. Energy Dissipation of Martian Dust Collision Process. Theenergy dissipation of collision is the major cause of the depo-sition process of Martian dust particles. The deposition pro-cess can be divided into two categories: the collision with theMartian rover’s surface and the collision with the grain bed,which is shown in Figure 4. In this paper, the energy dissipa-tion of collision is defined as the combined effect of adhesionenergy loss and damping energy loss, and the contact statusof Martian dust particles is analyzed based on the DMT con-tact model [33].
According to the DMT contact model, the contact pro-cess is divided into two parts: the loading process and theunloading process. The loading process starts from the gen-eration of the normal displacement until the normal dis-placement reaches the maximum. The unloading processstarts from the maximum normal displacement until the nor-mal displacement goes back to 0. However, due to the effectof the Van der Waals force, the Martian dust particle isapplied to a negative contact force in the unloading processwhen the normal displace is 0. Figure 5 shows the contact
force in the loading-unloading process, while the shaded partin Figure 5 is the adhesion energy loss of the collision process.
According to the DMT contact model [34, 35], theparticle contact force in the loading process meets the fol-lowing rule.
a3 =3R∗
4E∗ F: ð1Þ
In equation (1), F is the normal contact force, a is thecontact surface radius, and δ is the normal displacement.
The particle contact force in the unloading process meetsthe following rule.
a3 =3R∗
4E∗ F + 2πΔγ∗R∗ð Þ: ð2Þ
While the contact surface radius a and the normal dis-placement δ meet the following rule.
δ =a2
R∗ : ð3Þ
In the above equations, R∗ = ½1/R1 + 1/R2�−1 is the com-bined radius of contacted spheres, E∗ = ½ð1 − v21Þ/E1 + ð1 −v22Þ/E2�−1 is the combined elastic modulus of two contactedspheres, where vi and Ei are Poisson’s ratios and elastic mod-ulus of two particles, respectively.
While analyzing the collision between the Martian dustparticle and the Martian rover’s surface, R1 = r1 is the curva-ture radius of the contact point A, R2 is the curvature radiusof the surface. Thus,
R1∗ =
R1R2R1 + R2
����R1=r1,R2=+∞
= r1: ð4Þ
According to equation (2), the adhesion energy loss is notrelated to the magnitude and direction of the particle veloc-ity, but related to the contact surface energy Δγ∗, the com-bined elastic modulus E∗, and the combined radius ofcontacted spheres R∗. Thus, the adhesion energy loss at thecontact point A of the first collision (as shown in Figure 4)can be calculated as follows.
WAv =ðδAmax
δ0
4E∗
3r1a3
∂δ∂a
da
+ðδ0δAmax
4E∗
3r1a3 − 2πΔγ∗r1
� �∂δ∂a
da
= 2πΔγ∗r13πr21Δγ∗
2EA∗
� �2/3
= 17:66Δγ∗5/3EA∗−2/3r1
4/3:
ð5Þ
According to the collision theory, the damping force dur-ing the collision is proportional to the instantaneous velocityof the particle. If we only consider the damping energy loss,the damping force is greater due to the higher particle
Figure 3: Comparison of Opportunity’s solar panels before andafter the MY28 GDS.
3International Journal of Aerospace Engineering
velocity at the beginning of the collision process, whichcauses a lower deceleration rate during the collision process.If we only consider the adhesion energy loss, the adhesionforce is smaller due to the smaller normal displacement atthe beginning of the collision process, which causes a higherdeceleration rate during the collision process. Considering
the coupling effect of the adhesion energy loss and the damp-ing energy loss, the relationship between the particle velocityand the normal displacement can be simplified as a linearcurve, which is shown in Figure 6.
Thus, the damping energy loss at the first contact point Acan be calculated as follows.
WAd =ðδAmax
δ0
CVidδ =12CV0
3πr21Δγ∗
2EA∗
� �2/3
= 1:41CΔγ∗2/3EA∗−2/3r1
1/3V0:
ð6Þ
In equation (6), C is the damping coefficient, and V0 isthe initial particle velocity during the collision process.
According to equation (5) and equation (6), the totalenergy dissipation of the Martian dust particle at the firstcontact point A can be calculated as follows.
WA =WAv +WAd = 17:66Δγ∗5/3EA∗−2/3r1
4/3
+ 1:41CΔγ∗2/3EA∗−2/3r1
1/3V0:ð7Þ
According to Figure 4, the particle collides with theMartian rover’s surface at the second contact point B afterrotating a certain angle. R1 = r2 is the curvature radius ofthe contact point B, and R2 is the curvature radius of thesurface. Thus,
R1∗ =
R1R2R1 + R2
����R1=r2,R2=+∞
= r2: ð8Þ
The adhesion energy loss at the contact point B of thesecond collision can be calculated as follows.
WBv =ðδBmax
δ0
4E∗
3r2a3
∂δ∂a
da
+ðδ0δBmax
4E∗
3r2a3 − 2πΔγ∗r2
� �∂δ∂a
da
= 2πΔγ∗r23πr22Δγ∗
2EA∗
� �2/3
= 17:66Δγ∗5/3EB∗−2/3r2
4/3:
ð9Þ
Fall
A B
Fall
Rotate
RotateBounce Bounce
Energy dissipationCD
Figure 4: Deposition process of Martian dust particles.
Loading
F
A
B 𝛿O
C
Unloading
Figure 5: Comparison of Opportunity’s solar panels before andafter the MY28 GDS.
𝛿max𝛿
Vi
Vo
Adhesion effect only
Simplified curve
Damping effect only
Figure 6: Simplification of the velocity-normal displacement curve.
4 International Journal of Aerospace Engineering
The damping energy loss at the second contact point Bcan be calculated as follows.
WBd =ðδBmax
δ0
CVidδ =12CVB0
3πr22Δγ∗
2EB∗
� �2/3
= 2CΔγ∗2/3EB∗−2/3r1/32 m−1/2ΔWB
1/2:
ð10Þ
In equation (10), ΔWB = 1/2mV20 −WA is the initial
kinetic energy at the contact point B.According to equation (9) and equation (10), the total
energy dissipation of the Martian dust particle at the secondcontact point B can be calculated as follows.
WB =WBv +WBd = 17:66Δγ∗5/3EB∗−2/3r2
4/3
+ 2CΔγ∗2/3EB∗−2/3r1/32 m−1/2ΔWB
1/2:ð11Þ
Therefore, the total energy dissipation of the particle-Martian rover collision is
WAB =WA +WB: ð12Þ
While analyzing the collision between the Martian dustparticle and the grain bed, R1 = rC1 is the curvature radiusof the depositing particle at the first contact point C, andR2 = rC2 is the curvature radius of the grain bed particle atthe contact point C. Thus,
RC∗ =
R1R2R1 + R2
����R1=rC1,R2=rC2
=rC1rC2rC1 + rC2
: ð13Þ
The adhesion energy loss at the contact point C of thefirst collision can be calculated as follows.
WCv =ðδCmax
δ0
4E∗
3R∗Ca3
∂δ∂a
da
+ðδ0δCmax
4E∗
3R∗Ca3 − 2πΔγ∗R∗
C
� �∂δ∂a
da
= 2πΔγ∗R∗C
3πR∗C2Δγ∗
2Ep∗
!2/3
= 17:66Δγ∗5/3Ep∗−2/3R∗
C4/3:
ð14Þ
The damping energy loss at the first contact point Ccan be calculated as follows.
WCd =ðδCmax
δ0
CVidδ = 1:41CΔγ∗2/3Ep∗−2/3R∗
C1/3V0: ð15Þ
According to equation (14) and equation (15), the totalenergy dissipation of the Martian dust particle at the firstcontact point C can be calculated as follows.
WC =WCv +WCd = 17:66Δγ∗5/3Ep∗−2/3R∗
C4/3
+ 1:41CΔγ∗2/3Ep∗−2/3R∗
C1/3V0:
ð16Þ
According to Figure 4, the particle collides with the grainbed at the second contact point D after rotating a certainangle. The adhesion energy loss WDv and the dampingenergy loss WDd at the second contact point D can be calcu-lated as follows.
WDv =ðδDmax
δ0
4E∗
3R∗Da3
∂δ∂a
da
+ðδ0δDmax
4E∗
3R∗Da3 − 2πΔγ∗R∗
D
� �∂δ∂a
da
= 2πΔγ∗R∗D
3πR∗D2Δγ∗
2Ep∗
!2/3
= 17:66Δγ∗5/3Ep∗−2/3R∗
D4/3,
ð17Þ
WDd =ðδDmax
δ0
CVidδ
= 2CΔγ∗2/3EP∗−2/3R∗
D1/3m−1/2ΔWD
1/2:
ð18Þ
In equation (18), ΔWD = 1/2mV20 −WC is the initial
kinetic energy at the contact point D.
Table 1: Parameters of Martian dust materials and Martian rovermaterials.
Parameters Value
Curvature radius of the contact point r 10-7m
Combined radius of Martian dust particles R∗ 5~100 μmShear modulus of Martian dust particles 20GPa
Poisson’s ratio of Martian dust particles 0.25
Shear modulus of Martian rover materials 70GPa
Poisson’s ratio of Martian rover materials 0.3
Surface energy between the particles and theMartian rover Δγ∗ 0.04 J/m2
1
0.8
0.6
0.4
0.2
00 2 4 6
Particle velocity V0 (m/s)
R⁎ = 5𝜇m
R⁎ = 10𝜇m
R⁎ = 50𝜇m
R⁎ = 100𝜇m
Loss
coef
ficie
nt 𝜂
8 10
Figure 7: The effect of the combined radius R∗ to the critical windspeed Vc1.
5International Journal of Aerospace Engineering
According to equation (17) and equation (18), the totalenergy dissipation of the Martian dust particle at the secondcontact point D can be calculated as follows.
WD =WDv +WDd = 17:66Δγ∗5/3Ep∗−2/3R∗
D4/3
+ 2CΔγ∗2/3EP∗−2/3R∗
D1/3m−1/2ΔWD
1/2:ð19Þ
Therefore, the total energy dissipation of the particle-grain bed collision is
WCD =WC +WD: ð20Þ
2.2. Critical Wind Speed for Martian Dust Particle DepositionProcess. If the initial energy of the Martian dust particle isgreater than the energy dissipation during the collision pro-cess, the falling particle will bounce from the Martian rover’ssurface or the grain bed after the collision process. In thispaper, we define the critical wind speed for the depositionprocess is the maximum velocity for the particle that restson the Martian rover’s surface or the grain bed after the col-lision process. Thus, the critical wind speed for the deposi-tion process on the Martian rover’s surface Vc1 should meetthe following rules.
We assume g1 = 17:66Δγ∗5/3EA∗−2/3r1
4/3, g2 = 1:41CΔγ∗2/3 EA
∗−2/3r11/3, g3 = 1/2m, g4 = 17:66Δγ∗5/3EB
∗−2/3r24/3,
g5 = 2CΔγ∗2/3EB∗−2/3r1/32 m−1/2, then, Vc1 can be calculated
In the above equations, g1 is the coefficient of theadhesion energy loss at the contact point A, g2 is the coef-ficient of the damping energy loss at the contact point A,g3 is the coefficient of the kinetic energy, g4 is the coeffi-cient of the adhesion energy loss at the contact point B,and g5 is the coefficient of the damping energy loss at thecontact point B.
Similarly, the critical wind speed for the deposition pro-cess on the grain bed Vc2 should meet the following rules.
1
0.8
0.6
0.4
0.2
00 1 2 3
Loss
coef
ficie
nt 𝜂
4 5
(a)
1
0.8
0.6
0.4
0.2
00 1 2 3
Loss
coef
ficie
nt 𝜂
4 5
(b)
Figure 8: The effect of the curvature radii to the critical wind speed Vc1: (a) The effect of r1 to the Vc1; (b) The effect of r2 to the Vc1.
Combined radius of Martian dust particles R∗ 5~100μmShear modulus of Martian dust particles 20GPa
Poisson’s ratio of Martian dust particles 0.25
Surface energy between the falling particlesand the grain bed particles Δγ∗ 0.04 J/m2
4020
0
1.5
Criti
cal w
ind
spee
d fo
r par
ticle
dep
ositi
on p
roce
ss V
c2 (m
/s)
Contact parameters (𝜇m)0
10.5
1.51
0.5
1.51
0.5
1.51
0.52 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
0 20 40 60 80 100
Vc2 R⁎
Vc2 rc1
Vc2 rc2
Vc2 rD1
rD2Vc2
Figure 11: Effects of the contact parameters to the critical windspeed Vc2.
525
r(𝜇m)
4
3
2
1
1 2 3 4 5
20
15
10
5
Vc1(m/s)
R⁎(𝜇m)
R⁎: 0~5𝜇m
500.8
r(𝜇m)40
30
20
10
20 30 40 50
0.6
0.4
0.2
Vc1(m/s)
R⁎(𝜇m)
R⁎: 20~50𝜇m
r(𝜇m)0.3
150
100
50
50 100 150 200
0.25
0.2
0.15
0.1
0.05
Vc1(m/s)
R⁎(𝜇m)
R⁎: 50~200𝜇m
r(𝜇m)4
15
10
5
5 10 15 20
3
2
1
Vc1(m/s)
R⁎(𝜇m)
R⁎: 5~20𝜇m
Figure 10: Contour map of the critical wind speed Vc1.
30 2
1.5
1
0.5
020 40 60 80 100 100
50
25201510
501 3 5 7 11 11
61
Vc1(m/s)Vc1(m/s)
R⁎(𝜇m)
r(𝜇m)r(𝜇m)
2
1.5
1
0.5
03 56
1
s)Vc1(m/s)
R⁎(𝜇m) R⁎(𝜇m)
Figure 9: Surface diagram of the critical wind speed Vc1.
7International Journal of Aerospace Engineering
In the above equations, h1 is the coefficient of theadhesion energy loss at the contact point C, h2 is the coeffi-cient of the damping energy loss at the contact point C, h3is the coefficient of the kinetic energy, h4 is the coefficientof the adhesion energy loss at the contact point D, and h5is the coefficient of the damping energy loss at the contactpoint D.
According to equation (22) and equation (24), the criticalwind speed for the deposition process is the function of thecombined radius of particles and the curvature radius of con-tact points. Due to the irregularly shaped characteristics ofMartian dust particles, the combined radius and the curva-ture radius are diverse for different particles. Thus, the criti-
cal wind speed for the deposition process should be therandom variable related to the combined radius and the cur-vature radius.
Vc1 is the function of the combined radius R∗, the curva-ture radius of the falling particle at the contact point A r1 andthe curvature radius of the falling particle at the contact pointB r2. X = ½R∗, r1, r2�T is defined as the random vector of Vc1, fis the probability density function, Z = ½Vc1, R∗, r1, r2�T, thus,
f Z Zð Þ = f X Xð Þ 1JZ Xð Þj j ,
f X Xð Þ = f R∗ R∗ð Þf r1 r1ð Þf r2 r2ð Þ:
8><>: ð25Þ
30 2
1.5
1
0.5
00 25 50 75100 0
2040 50
20
10
00
2.55
7.5 10 02
4 5
Vc2(m/s) Vc2(m/s)
R⁎(𝜇m) R
⁎(𝜇m)r(𝜇m)r(𝜇m)
Figure 12: Surface diagram of the critical wind speed Vc2.
2.5 20r(𝜇m)2.1
1.6
1.1
0.6
10.1
2 3 4 5
15
10
5
R⁎(𝜇m)
r(𝜇m) 38.5
6.5
4.5
2.5
50.5
10 15 20
2.5
2
1.5
1
0.5
r(𝜇m) 2522
17
12
7
202
30 40 50
0.6
0.5
0.4
0.3
0.2
r(𝜇m)85
65
45
25
505
100 150 200
0.2
0.15
0.1
0.05
Figure 13: Contour map of the critical wind speed Vc2.
Table 3: CFD simulation parameters of Martian airflow in Fluent.
Simulation parameters Value
Operating pressure 690 pa
Gravity 3.73m/s2
Temperature 220K
Density 0.0167 kg/m3
Viscosity 1:35 × 10−5 kgm−1 s−1
Inlet velocity magnitude 0.5~10m/s
Gauge pressure 0 paFigure 14: Mesh for the simulation of the Martian dust depositionprocess.
8 International Journal of Aerospace Engineering
In equation (25), f XðXÞ is the joint probability density ofrandom independent variables, JZðXÞ is the Jacobian deter-minant of the random vector Z which is related to the ran-dom vector X. JZðXÞ can be calculated as follows.
Vc2 is the function of the combined radius R∗, the curva-ture radius of the falling particle at the contact point C rC1,the curvature radius of the grain bed particle at the contactpoint C rC2, the curvature radius of the falling particle at
the contact point D rD1, and the curvature radius of the grainbed particle at the contact point D rD2. Thus, the probabilitydensity of Vc2 can be calculated as follows.
3. Results and Discussion
3.1. Influence Factors of Critical Wind Speed for Martian DustParticles Deposition Process. While analyzing the collisionbetween the rover’s surface and the Martian dust particle,we use the Matlab to plot the Vc1 curves in different com-bined radii R∗. Parameters of Martian dust materials andMartian rover materials are shown in Table 1. The coefficientof energy loss ηð0 ≤ η ≤ 1Þ is defined as the ratio of the parti-cle velocity after collision to the particle velocity before thecollision. It is obvious that the particle has a deposition pro-cess while η = 0.
The effect of the combined radius R∗ to the critical windspeed Vc1 is shown in Figure 7. It can be seen from Figure 7that the Vc1 grows substantially with the declining R∗. Thecoefficient of energy loss η shows a truncation effect aroundthe related critical wind speed.
The effect of the curvature radii r1, r2 at the contact pointA and the contact point B to the critical wind speed Vc1 areshown in Figure 8. It can be seen from Figure 8 that the Vc1rises with the growing curvature radius, while the adhesionenergy loss is greater during the collision process.
Figures 9 and 10 are the surface diagram and the contourmap of the Vc1, respectively. According to these two figures,we can estimate and compare the Vc1 in different combinedradii R∗ and curvature radii r.
While analyzing the collision between the grain bed andthe Martian dust particle, we use the Matlab to plot the Vc2curves in different combined radii R∗ and curvature radii r.Parameters of Martian dust materials are shown in Table 2,while the effects of the contact parameters to the Vc2 areshown in Figure 11. According to Figure 11, the combinedradius of the particle shows a dominant influence on the crit-ical wind speed Vc2 while the curvature radii show similarinfluence on the Vc2.
Figures 12 and 13 are the surface diagram and the con-tour map of the Vc2, respectively. According to these two fig-ures, we can estimate and compare the Vc2 in differentcombined radii R∗ and curvature radii r.
3.2. Simulation of Martian Dust Deposition Process Basedon DEM-CFD. A series of simulations of the Martian dustdeposition process are performed by using the couplingmodule of EDEM-Fluent. Table 3 shows the CFD simulation
Table 4: DEM simulation parameters of Martian dust particles inEDEM.
Simulation parameters Value
Poisson’s ratio of the particles υ1 0.25
Shear modulus of the particles G1 2 × 1010 paDensity of the particles ρ1 1300 kg/m3
Poisson’s ratio of the Martian probe υ2 0.3
Shear modulus of the Martian probe G2 7 × 1010 paDensity of the Martian probe ρ2 2719 kg/m3
Coefficient of friction between the particlesand the Martian probe f 0.5
Coefficient of rolling friction between theparticles and the Martian probes f R
0.01
Recovery coefficient between the particlesand the Martian probe k0
0.1
Surface energy between the particles andthe Martian probe γ 0.04 J/m2
parameters of Martian airflow in Fluent. The velocity inletand the pressure outlet are selected in the Fluent, and thesimulation temperature is constant. The turbulence modelis the RNG k—ε model. The mesh for the simulation isshown in Figure 14.
Martian dust particles are modeled in the Discrete Ele-ment Method (DEM) software EDEM, and simulationparameters of these particles are shown in Table 4. SinceMartian dust particles have characteristics of irregular shapeand tiny size, 4 kinds of particle models are modified with thefractal dimension of 2.2, 2.3, 2.4, and 2.5, respectively, whichare shown in Figure 15 [36]. All these particles have the cur-vature radii of 1.78μm~4.58μm.
A series of simulations for the particle-rover collision andparticle-particle collision are carried out for the study on theMartian dust deposition process, as shown in Figure 16. Theparticle factory is modified as the dynamic factory in order togenerate new falling particles during the simulation process.In the simulation of particle-particle collision, particles arepreplaced on theMartian rover’s surface to simulate the grainbed, while these particles have a speed of less than 10-6m/s.
The particles of fractal dimension 2.2 are used for analyz-ing the effect of the combined radius R∗ to the critical windspeed Vc1 and Vc2. The collision process between the 20μmsized particle and the Martian rover’s surface is shown inFigure 17. According to the simulation result shown inFigure 17(a), the particle bounced back to the airflow afterthe collision process while the wind speed is 0.75m/s. It can
Figure 16: Simulation model for Martian dust deposition process:(a) Simulation model for particle-rover collision; (b) Simulationmodel for particle-particle collision.
10 International Journal of Aerospace Engineering
be seen from Figure 17(b) that the particle deposited on thespacecraft surface after the collision process while the windspeed is 0.65m/s. Therefore, the critical wind speed Vc1 ofthis particle should be between 0.65m/s and 0.75m/s. Basedon this, we carried out a series of simulations with differentwind speed conditions (from 0.65m/s to 0.75m/s). Hence,the critical wind speed was defined as the maximum of thesewind speed conditions based on DEM-CFD simulationresults, in which the falling particle did not bounce back tothe airflow. According to the simulation results, the criticalwind speed Vc1 of this particle is 0.68m/s, which has a 7%error with the theoretical result (0.73m/s).
A series of simulations are carried out for analyzing thedeposition process on the Marian rover’s surface by usingthe fractal dimension 2.2 particles with the combined radii
of 5μm, 10μm, 40μm, 60μm, 80μm, and 100μm, respec-tively. The simulation results and the theoretical results ofthe Vc1 are shown in Figure 18. According to Figure 18, thecritical wind speed Vc1 drops significantly with the increasingcombined radius, which proves that the smaller particles aremore likely to be deposited on the Martian rover’s surface.Besides, the errors between the simulation results (discretedata point) and the theoretical results (continuous curve)are less than 10%, which proves the reliability of the theory.
The simulation results (discrete data point) and the theo-retical results (continuous curve) for analyzing the deposi-tion process on the grain bed by using the different sizedfractal dimension 2.2 particles are shown in Figure 19. Theresults of the Vc2 has a similar trend with the results of Vc1,which also proves the reliability of the theory.
The 20μm sized particles in different shapes are used foranalyzing the effect of different curvature radii to the criticalwind speedVc1. Since curvature radii of the fractal dimension2.2 particle and the fractal dimension 2.4 particle are tooclose, the fractal dimension 2.3 particle and the fractaldimension 2.5 particle are used for the simulation. The distri-bution probabilities of the Vc1 of these two particles are
Table 5: Distribution probability of the Vc1 of the fractal dimension2.3 particle.
NumberCurvatureradius (μm)
Critical windspeed (m/s)
Probability (%)
1 1.8 0.67 36
2 2.5 0.78 35
3 3.1 0.86 29
Table 6: Distribution probability of the Vc1 of the fractal dimension2.5 particle.
NumberCurvatureradius (μm)
Critical windspeed (m/s)
Probability (%)
1 1.8 0.53 14
2 2.5 0.67 15
3 2.7 0.79 21
4 3.2 0.96 35
3
2
2.5
1.5
1
0.5
00 20 40
Combined radius of the particle (𝜇m)
Criti
cal w
ind
spee
d fo
r par
ticle
depo
sitio
n pr
oces
s Vc2
(m/s
)
60 80 100
Figure 19: The simulation results and the theoretical results of thecritical wind speed Vc2.
4
3
2
1
00 20 40
Combined radius of the particle (𝜇m)
Criti
cal w
ind
spee
d fo
r par
ticle
depo
sitio
n pr
oces
s Vc1
(m/s
)
60 80 100
Figure 18: The simulation results and the theoretical results of thecritical wind speed Vc1.
0.75m/s
0.60
0.45
0.30
0.15
0
(a)
0.65m/s
0.52
0.39
0.26
0.13
0
(b)
Figure 17: The collision process between the 20μm sized particle and the Martian rover’s surface: (a) Bouncing process of the collision; (b)Deposition process of the collision.
11International Journal of Aerospace Engineering
shown in Tables 5 and 6, respectively. It can be seen fromTables 5 and 6 that particles with a higher fractal dimensionhad a more dispersed probability of critical wind speed.
4. Conclusions
Based on the Discrete Element Method (DEM), the presentstudy has established a contact model that includes the colli-sion energy loss. This paper for the first time developed amethod to study the energy dissipation of Martian dust par-ticles after colliding with Martian rovers or the particle bed,which played an important role in the deposition process.Through the numerical approach, the combined radius ofthe particle showed a dominant influence on the critical windspeed for the particle deposition process, followed by curva-ture radii of contact points. Besides, particles with a higherfractal dimension had a more dispersed probability of criticalwind speed. Importantly, this study provides a theoreticalbasis for Martian dust protection and the Martian explora-tion mission.
Data Availability
The data used to support the findings of this study areincluded within the article.
Disclosure
The extensive abstract of this paper was presented to TheInaugural International Symposium on Water Modelling(iSymWater2019) for an oral presentation. Thanks especially.
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper.
Acknowledgments
This research was funded by the National Nature ScienceFoundation of China (No. 51575123, No. 51902026), theSelf-Planned Task (No. SKLRS201801B) of State Key Labora-tory of Robot Technology and System (HIT), and the QianXuesen Laboratory of Space Technology Seed Fund (No.QXSZZJJ03-03).
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