US 10,380,219 B2 · Method for computing self-contamination processes of a spacecraft

Abstract

A method for computing self-contamination processes of a spacecraft by means of a data processing device comprising the following steps: receiving a first set of input parameters comprising general definitions of the spacecraft, receiving a second set of input parameters comprising control parameters for the spacecraft orbital data, physics, numeric, and a predetermined accuracy requirement of the computation, computing a self-contamination process of the spacecraft based on the received first and second sets of input data by either evaluating the analytical solution of a basic equation of emission or numerically solving the basic equation of emission for calculating a deposit of molecules outgassed from surfaces of the spacecraft with a numerical solver with the data processing device, wherein the numerical solver applies an adaptive stepsize control based on the preset accuracy requirement of the computation, and outputting the calculated deposit.

A method for computing self-contamination processes of a spacecraft by means of a data processing device comprising the following steps:

receiving a first set of input parameters comprising general definitions of the spacecraft,
receiving a second set of input parameters comprising control parameters for the spacecraft orbital data, physics, numeric, and a predetermined accuracy requirement of the computation,
computing a self-contamination process of the spacecraft based on the received first and second sets of input data by either evaluating the analytical solution of an equation of emission or numerically solving the equation of emission
W
.
dep
,
⁢
i
=
(
F
ji
-
δ
ij
τ
r
,
⁢
j
)
⁢
W
dep
,
⁢
j
+
F
ji
⁢
W
.
emitted
,
⁢
j
for calculating a deposit of molecules outgassed from surfaces of the spacecraft with a numerical solver with the data processing device, wherein the numerical solver applies an adaptive stepsize control based on the predetermined accuracy requirement of the computation, wherein Fji denotes a view factor from node j, first surface mesh element, to node i, second surface mesh element, δij denotes the Kronecker delta from node i to node j, τrj denotes the temperature-dependent reemission time of node j, τej denotes the temperature-dependent emission time of node j, and wherein calculation of a deposit of molecules outgassed from surfaces of the spacecraft with a numerical solver comprises a stepwise analytical integration of the emission term Wemittable of the equation of emission according to the following equation:
Δ
⁢
⁢
W
emittable
,
j
=
W
emittable
,
j
⁡
(
t
n
)
⁢
(
1
-
(
τ
e
,
j
⁡
(
t
n
)
τ
e
,
j
⁡
(
t
n
)
+
α
j
⁢
h
)
1
α
j
)
,
with αj being the secant slope defined by
α
j
=
τ
e
,
j
⁡
(
t
n
+
1
)
-
τ
e
,
j
⁡
(
t
n
)
t
n
+
1
-
t
n
,
τe designating time dependent material parameters, and h designating the time interval h=tn+1−tn, and
outputting the calculated deposit;
wherein the numerical solver applies a theta-method for calculating an analytical solution of the equation of emission for calculating a deposit of molecules outgassed from surfaces of the spacecraft and adapts the stepsize of the theta-method by performing the following steps:
a) choosing an initial stepsize hlte and setting it as actual stepsize,
b) calculating the local truncation error LTE of the theta-method for one step with the actual stepsize,
c) calculating the stepsize for the next step depending on the calculated local truncation error LTE and setting the calculated stepsize for the next step as actual stepsize,
d) repeating steps b) and c);
and
wherein calculating of the stepsize htol for the next step depending on the calculated local truncation error is performed according to the following equation:
h
tol
=
min
(
h
lte
⁢
TOL
m
LTE
m
⁡
(
Θ
prop
)
)
with hlte designating the chosen initial stepsize, Θprop being either Θ1 or Θ2 depending on which one is selected as a propagator, LTEm(Θprop) designating the local truncation error calculated for a pair of nodes Wm, Vm for the selected theta-method Θprop, wherein TOLm designates the predetermined accuracy requirements or tolerances that are applied at time tn+1 in the calculation of the next timestep and are selected from two predetermined values TOLm,abs and TOLrel according to the following rule:
if Um(tn+1,Θprop)>TOLm,abs
TOLm=TOLrelum(tn+1,Θprop)
else
TOLm=TOLm,abs
where Um(tn+1,Θprop) is either Wm(tn+1,Θ1) or Vm(tn+1,Θ2) depending on which one is selected as propagator, and wherein
w
⁡
(
t
n
+
1
,
Θ
1
)
=
y
⁡
(
t
n
)
+
h
⁡
[
Θ
1
⁢
f
⁡
(
t
n
+
1
,
y
⁡
(
t
n
+
1
)
)
+
(
1
-
Θ
1
)
⁢
f
⁡
(
t
n
,
y
⁡
(
t
n
)
)
]
;
v
⁡
(
t
n
+
1
,
Θ
2
)
=
y
⁡
(
t
n
)
+
h
⁡
[
Θ
2
⁢
f
⁡
(
t
n
+
1
,
y
⁡
(
t
n
+
1
)
)
+
(
1
-
Θ
2
)
⁢
f
⁡
(
t
n
,
y
⁡
(
t
n
)
)
]
;
and
LTE
m
⁡
(
Θ
prop
)
=
(
1
2
-
Θ
prop
)
⁢
w
m
⁡
(
t
n
,
Θ
1
)
-
v
m
⁡
(
t
n
,
Θ
2
)
Θ
1
-
Θ
2
,
wherein y(tn) denotes the exact solution of the LTE at a time tn, wherein y(tn+1) denotes the exact solution of the LTE at a next time tn+1 and wherein
f(tn+1,y(tn+1))={dot over (y)}(tn+1).

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Method for computing self-contamination processes of a spacecraft

Life of this patent

Method for computing self-contamination processes of a spacecraft

Life of this patent

Abstract

Claims7