1
A Thermal Analysis of Select Materials in the Use of a CubeSat De-Orbit Device as a Membrane for an Inflatable Drag-brake Immediately Following Deployment and After Complete Inflation Utilizing Satellite Toolkit
Juan Parducci
MAE 560: Space Systems Engineering
March 9th, 2012
Introduction:
Due to the low weight, power requirement, and inherently small size of CubeSats, it is desirable to have a passive de-orbit device versus an active one. Currently, the CubeSat De-orbit Device Team, working on their senior project, has been tasked with the development of a passive de-orbit device. There are two devices which are under consideration by the team and both involve the inflation of a drag-brake through passive methods. Both of these process are temperature driven. One involves the use of a sublimating compound as a catalyst for inflation while the other exploits the properties of Shape Memory Alloys.
Purpose:
The purpose of this study was to gain an understanding of the temperatures experienced by a CubeSat inflatable de-orbit device before and after complete inflation has occurred. By varying the surface material of the inflatable membrane, different temperatures are achieved. The results of this study could determine whether a heating element would be required onboard a CubeSat in order to sustain temperature requirements for the deployment of an inflatable drag-brake.
This study was performed for two cases. In the first case, the CubeSat is in a circular Polar Orbit in which it is always in line of sight of the sun. In the other case, the CubeSat was assumed to be in a circular equatorial orbit with times in which the inflatable is not visible to the sun. The polar orbit has no eclipse compared to the equatorial orbit which has a maximum eclipse. A thermal study was conducted to determine the equilibrium temperatures of the inflatable before and after deployment had occurred in both of these orbits. STK was heavily utilized.
Equations:
Solar radiation intensity outside the Earth’s atmosphere and at the Earth’s average distance from the Sun:
where
resulting in
For the purpose of calculating albedo radiation, the Earth can be regarded as a diffuse reflecting sphere.
The intensity of the albedo radiation incident on a spacecraft:
From table 11.1 for planet Earth
(Figure 11.2)
For computations, the following values used are:
a=0.33
F=1 is assumed for all cases
Planetary thermal radiation:
Earth radiates with an intensity of and decays with altitude. The approximate value at any given altitude:
Where
where
Equilibrium Temperature for orbits with no eclipse (Polar Orbit):
Equilibrium Temperature for orbits with maximum eclipse (Equatorial Orbit)
where
f = fraction of orbit illuminated by the Sun
Values for ‘f’ are gathered through orbital analysis performed using STK
For the deployed (not inflated device)
It is assumed that the Mylar balloon is of a one dimensional nature due to packaging and folding and retaining a square shape. The faces of the square are assumed to be facing the sources of radiation directly
It is assumed that the square is of dimensions
For the fully inflated device
It is assumed that the Mylar balloon is a sphere which circular cross-sectional areas exposed to sources of radiation.
Data:
Select surfaces for thermal study from table 11.3:
Surface / Absorptance / Emmitance / /Goldized Kapton
(gold outside) / 0.25 / 0.02 / 12.5
Aluminized Kapton
(aluminium outside) / 0.14 / 0.05 / 2.80
Black Paint
(epoxy) / 0.95 / 0.85 / 1.12
White Paint
(silicone) / 0.26 / 0.83 / 0.31
Solar Cells
(silicon) / 0.75 / 0.82 / 0.91
Values of f gathered through orbital analysis using STK for one orbit
Orbit / Illumination / Eclipse / f200km / 10.6% / 7.8% / 0.576087
700km / 12.4% / 6.9% / 0.642487
900km / 14.1% / 7.3% / 0.658879
Solar Intensity during times of Illumination gathered through STK
Orbit / Solar Intensity200km / 100%
700km / 100%
900km / 100%
Results:
The following results for equilibrium temperatures for cases with no eclipse (polar orbit) and maximum eclipse (equatorial orbit) were computed
Deployed inflatable before inflation
200km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 398.2 / 192.6 / 102.9 / 15.7 / 85.9
Maximum Eclipse / 312.8 / 135.7 / 60.3 / -9.3 / 46.3
700km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 397.9 / 191.9 / 101.7 / 12.9 / 84.5
Maximum Eclipse / 328.4 / 145.3 / 66.4 / -8.4 / 51.6
900km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 397.9 / 191.7 / 101.2 / 11.9 / 83.9
Maximum Eclipse / 332.1 / 147.5 / 67.7 / -8.6 / 52.7
Deployed Inflatable after full inflation
200km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 291.4 / 118.5 / 43.1 / -30.2 / 28.8
Maximum Eclipse / 219.6 / 70.7 / 7.3 / -51.2 / -4.5
700km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 291.2 / 117.9 / 42.1 / -32.6 / 27.6
Maximum Eclipse / 232.7 / 78.8 / 12.4 / -50.5 / -0.1
900km Orbit
Surface Finish / Goldized Kapton/ Aluminized Kapton
/ Black Paint
/ White Paint
/ Solar Cells
No Eclipse / 291.2 / 117.8 / 41.7 / -33.4 / 27.2
Maximum Eclipse / 235.8 / 80.6 / 13.5 / -50.6 / 0.8
Conclusion:
Very high temperatures are achievable with the correct material selection for an inflatable membrane. Temperatures are calculated to be higher at the beginning of the inflation process than towards the end. It could be possible that with proper selection of materials, there would not be a need for an onboard heating element to meet temperature requirements.
Figures:
Duration of sunlight
Sunlight Duration 200km
Sunlight Duration 700km
Sunlight Duration 900km
Intensity of sunlight during times of exposure:
Solar Intensity 200km
Solar Intensity 700km
Solar Intensity 900km
Azimuth, elevation, and range reports
Azimuth, Elevation, Range 200km
Azimuth, Elevation, Range 700km
Azimuth, Elevation, Range 900km
Computational Program for the Inflatable after deployment but before inflation:
%This program conducts a thermal spacecraft systems study for the
%minimum and maximum temperatures exprienced by a an ejected cubesat
%de-orbit device which has been deployed but has not yet inflated. It will
%be assumed that the balloon has a square shape which is nearly
%1-dimensional. The deployed but not yet inflated balloon will have
%dimensions of 9cmx9cm.
%These studies will be conducted at altitudes of 900km, 700km, and 200km.
%Assuming no eclipse (polar orbit)
%-----
%First calculation at 900km altitude for the inflatable
%-----
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=900000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%length and width of a mylar inflatable is 9cmx9cm.
r=.09; %m^2
A=r.*r;
%Absorbing area facing the sun
Asol=A;
%Absorbing area facing the Earth
Aalb=A;
%Area of the inflatable surface
Asurf=2*A;
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Maximum temperatures will be evaluated for a variety of surfaces in the
%following order from table 11.3
%Goldized Kapton (gold outside)
%Aluminized Kapton (aluminum outside)
%Black Paint (epoxy)
%White Pain (silicone)
%Solar Cells (silicon)
alpha=[0.25; 0.14; 0.95; 0.26; 0.75];
eps=[0.02; 0.05; 0.85; 0.83; 0.82];
alep=[12.5; 2.8; 1.12; 0.31; 0.91]; %=alpha/eps
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 900km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 900km
ff=0.658879;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
%---
%Warmest case, 700km orbit for the inflatable
%---
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=700000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 700km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 700km
ff=0.642487;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
%Warmest case, 200km orbit, for the inflatable
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=200000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 200km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 200km
ff=0.576087;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
Program Output:
Temperatures at 900km
T =
397.9185
191.6986
101.2418
11.9219
83.9762
T =
332.0839
147.5238
67.6894
-8.5634
52.6563
Temperatures at 700km
T =
397.9946
191.9275
101.6797
12.9108
84.4806
T =
328.4365
145.3347
66.3970
-8.4250
51.5803
Temperatures at 200km
T =
398.2161
192.5921
102.9457
15.7324
85.9367
T =
312.8076
135.7124
60.2992
-9.2835
46.3065
Computational Program for the fully inflated inflatable:
%This program conducts a thermal spacecraft systems study for the
%minimum and maximum temperatures exprienced by a deployed and fully
%inflated cubesat de-orbit device with a diameter of 45cm. For
%simplicity, it will be assumed that the balloon has a spherical shape.
%These studies will be conducted at altitudes of 900km, 700km, and 200km.
%Assuming no eclipse (polar orbit)
%-----
%First calculation at 900km altitude for the inflatable
%-----
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=900000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%Diameter of a mylar inflatable is 45cm
r=.225; %m
A=pi*r^2;
%Absorbing area facing the sun
Asol=A;
%Absorbing area facing the Earth
Aalb=A;
%Area of the inflatable surface
Asurf=4*A;
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Maximum temperatures will be evaluated for a variety of surfaces in the
%following order from table 11.3
%Goldized Kapton (gold outside)
%Aluminized Kapton (aluminum outside)
%Black Paint (epoxy)
%White Pain (silicone)
%Solar Cells (silicon)
alpha=[0.25; 0.14; 0.95; 0.26; 0.75];
eps=[0.02; 0.05; 0.85; 0.83; 0.82];
alep=[12.5; 2.8; 1.12; 0.31; 0.91]; %=alpha/eps
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 900km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 900km
ff=0.658879;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
%---
%Warmest case, 700km orbit for the inflatable
%---
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=700000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 700km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 700km
ff=0.642487;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
%Warmest case, 200km orbit, for the inflatable
%Boltzman Constant
s=5.67*10^-8; %Wm^-2K^-4
%Total power output from the sun
P=3.856*10^26; %W
%Average distance from the Earth to the sun
d=149597870.7*10^3; %m
%Solar radiation Intensity
%From table 11.1 solar radiation intensity at 1AU = 100%, also confirmed
%from STK
Js=P/(4*pi*d^2);
% Radius of Earth can be assumed to equal Rrad page 362.
Rrad=6.38*10^6; %m
%Orbit radius, first study will be conducted at 900km
Rorb=200000+Rrad; %m
%Planetary radiation (Falls with altitude)
Jp=237*((Rrad/Rorb)^2);
%----
%Warmest Case
%It will be assumed that half of the sphere is facing the sun and the other
%half is facing the earth
%----
%Intertially dissipated power will be assumed to be small
Q=0;
%Fmax is equal to 1 from page 360 table 11.1;
F=1;
%Earth albedo
a=0.33;
Ja=a*F*Js;
Aplan=A;
%Equation governing temperature equillibrium
% T^4=
% (Aplan*Jp)/(Asurf*s)+Q/(Asurf*s*eps)+(Asol*Js+Aalb*Ja)/(Asurf*s)*(alep)
%Q was assumed to be small so the term goes away resulting in
'Temperatures at 200km '
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)).^(1/4); %Kelvin
T=T-273 %Celcius
%And for the coolest case where ff is equal to the fraction of the orbit
%which illuminated by the sun. This data is known from data obtained
%through STK. A value of F=1 will be assumed again.
%At an orbit of 200km
ff=0.576087;
T= ((Aplan.*Jp)/(Asurf.*s)+(Asol.*Js+Aalb.*Ja)/(Asurf.*s).*(alep)*ff).^(1/4); %Kelvin
T=T-273 %Celcius
Program Output:
Temperatures at 900km
T =
291.1730
117.7634
41.6986
-33.4102
27.1800
T =
235.8129
80.6170
13.4845
-50.6363
0.8432
Temperatures at 700km
T =
291.2370
117.9559
42.0668
-32.5786
27.6041
T =
232.7458
78.7761
12.3977
-50.5198
-0.0616
Temperatures at 200km
T =
291.4232
118.5147
43.1314
-30.2059
28.8286
T =
219.6035
70.6848
7.2701
-51.2418
-4.4963