(4.2)4.4 Thermal Control of the Scientific Payload
This paragraph contains a brief description of the thermal control solutions developed by Laben in order to satisfy the scientific requirements of the GG mission.
The principal thermal requirements for the scientific P/L are concerned with the test bodies and are the following:
4.4.2 Thermal Control Solutions
The orbit of the GG satellite is such that it spends almost half of its time in eclipse (shadow of the Earth) and half in sunlight: equilibrium temperatures in the two different conditions may differ by several tenths of degrees. Due to the fast spin of the satellite, the temperature has azimuthal symmetry, but temperature gradients between the dark side and the lightened side of the spacecraft (radial gradients) may be very large. Anyway, the temperature gradients can be made negligible if the satellite is properly insulated: in fact, the temperature of the payload becomes stable if we are able to reduce the heat flowing from the inner surface of the satellite towards PGB and Test Masses. Some design solutions have been developed and are based over a ‘passive’ thermal design. These solutions have been studied considering a preliminary satellite configuration as shown in Chap. 2.
All the models and analyses developed by Laben show the feasibility of the solutions proposed for the thermal control.
The P/L thermal control is based on a thermal insulation as large as possible among test masses, PGB and S/C and on vacuum inside the satellite, so that energy is transferred only by radiation among the large surfaces inside the satellite, and not by thermal conduction. Thermal conduction is limited to the small connecting elements between Spacecraft and PGB, and between the PGB and Test masses: the smallness of the connecting elements makes it feasible to reduce the heat flux inside them. Moreover, only the preamplifiers are located at the PGB level: the rest of the electronics is located at the s/c level.
In order to reach the correct level of thermal insulation, the inner surface of the S/C and the PGB surfaces are covered by MLI with an effective emissivity eeff = 0.01 , which corresponds to about 20 layers MLI tape. Moreover, the test masses have an emissivity equal to 0.05 which is due to their polished surfaces.
The heat transfer can be schematized in the following way (note that the solar panels are located around the lateral surface of the satellite, not in the top and bottom covers). The radiation (Sun, Earth albedo and Infrared) impinges on the external surface of the satellite where it is absorbed by the solar cells; the insulating shell covering the inner surface of the spacecraft strongly reduces the amount of energy which can then be radiated towards the PGB. Assuming that x is the radial direction, the temperature across the insulating shell can be described along x by the simple model
(4.2)
with T0 the satellite initial temperature, TE the external environmental temperature, and d the penetration depth of the insulating shell (d < thickness of MLI). The temperature of the inner surface of the spacecraft depends on time as
(4.3)
with t the time scale of thermal inertia of the insulating shell, Teq the "equilibrium temperature" of the spacecraft, D T the residual orbital oscillation of the temperature due to the eclipse-sunlight transitions. The energy flow from the inner surface of the spacecraft to the external surface of the PGB can only be radiative, due to vacuum inside the satellite. The temperature difference between the inner surface of the spacecraft and the external surface of the PGB is thus minimized, having reduced to the lowest possible level the exchange of energy. In a similar way, radiative energy transfer takes place between the inner surface of the PGB and the external surface of the Test Masses. In this way thermal gradients on the test masses can be reduced and thermal stability ensured. As for the top and bottom covers of the satellite, they are coated with reflecting material in order to reduce heating, and the previous technique is applied in order to reduce thermal exchange with the inner part of the spacecraft.
Due to the high insulation of the spacecraft and to the high thermal inertia t of PGB and test masses, the time required to reach the steady state may be very long if the initial temperatures differ by several degrees from the "equilibrium temperatures" Teq. A guideline for this design is therefore for the initial temperatures of GG components to be as close as possible to the equilibrium ones to make the drift as small as possible, as shown below.
4.4.3 Estimate of the Orbital Heat Fluxes
In order to begin a quantitative study of the solutions described above, it is necessary to estimate the heat fluxes absorbed by the GG vessel while orbiting around the Earth; heat fluxes which depend on the GG orbital parameters. To perform feasibility studies of the thermal design, the GG orbit has been considered with zero declination of the Sun. This is a worst case analysis for GG because of the largest gradients between the covers and the cylindrical body of the GG vessel.
In order to determine quantitative results, an Esarad model of the GG vessel has been developed. The model contains 24 nodes:
The orbital data used in the calculations are:
Esarad provides the power absorbed by each node of the model at various orbital positions of the satellite along its orbit (11 in our case). It is found that the power absorbed is highly uniform, as it was expected because of the fast spin.
In order to evaluate the performances of the proposed thermal design, thermal mathematical models (TMM) and analyses were developed with the Esatan software tool using the data obtained by Esarad.
With the satellite structure shown in Chap. 5, a detailed thermal model with
79 nodes was developed. By transient analyses results, a high uniformity of the temperature both for the PGB and the test masses was found, as expected. Therefore, it was decided that a less detailed (reduced) model could be used instead.The reduced thermal mathematical model includes 17 nodes plus 1 boundary node:
The total electrical power considered in these simulations is
106 W. The nodal thermal couplings are computed taking account the estimated coupling for the detailed TMM (the detailed TMM radiative couplings were calculated by Esarad, running the Monte Carlo ray tracing module).The conductive coupling between the PGB and the GG vessel by means of the PGb tiny springs is negligible due to the spring dimensions (see Fig. 2.5).
Both transient and steady state analyses were addressed.
Using the average heat absorbed by GG during one orbit, the equilibrium temperatures of nodes,
Ti-eq , are calculated (steady state analysis). The meaning of these values is: once thermal equilibrium has been reached, the nodal temperatures Ti(t) oscillate around the corresponding equilibrium values Ti-eq (thermal equilibrium may be reached after a long time since the bodies are well insulated). The test masses have equal T i-eq = –2.7 °C.Another steady state analysis was performed in order to estimate the range of variation of
Ti-eq values, due to different seasonal and climatic conditions. To do this, the following variations in the average heat flux data have been inserted in the model:The results show that the maximum excursion over
Ti-eq due to variations of the incoming energy flux on the satellite is less than 7.5 °C . As consequence of this, it is reasonable to demand that the GG satellite be launched with an initial temperature: |T0 - Ttm-eq| < 10 °C ; where Ttm-eq is the test masses equilibrium temperature and T0 satisfies: T0 = Ti (t=0) " i.This condition shortens all the initial transient times and makes all drifts in temperature small. In order to verify the compliance of the design with the thermal requirements, a transient analysis is needed. Since the temperature drift is proportional to the difference between the initial and the equilibrium temperatures, a worst case condition for the analysis is to require:
|T0 - Ttm-eq| = 10 °C (4.4)
Using data obtained from the steady state analysis, the above condition means
: T0 = +7.3 , (i.e.: -2.7 + 10.0). The time span chosen for the simulation is 30 days. Fig. 4.17 shows the temperature evolution of the nodes corresponding to the PGB and the test masses; Fig. 4.18 shows a detailed view of the evolution of the test masses temperatures.
Figure 4.17 Nodal temperature drift to equilibrium
Figure 4.18 Detailed view of the time evolution of the test masses temperatures
The results of this analysis can be summarized as follows:
The results show that after the 21st day the test masses temperature drift is less than
0.2°C/day. Another case has been analyzed in which: |T0 - Ttm-eq| = 5 °C. The results are reported in Fig. 4.19 and show that the test masses drift fulfills the requirements for the entire 30 days duration of the simulation. 
Figure 4.19 Time evolution of P/L Temperatures in the case |T
0 - Ttm-eq| = 5 °CThe results reported here show that the performances of the passive thermal control proposed for the GG payload are such that the mission requirements can be met. However, there are severe limits to the maximum power that can be dissipated by the payload electronics. For this reason, only the preamplifiers are allowed at the PGB level (on the PGB tube). It is also found that - as expected- the initial deviation from equilibrium of the temperature distribution inside the PGB, rules the steepness of the temperature drift. It is therefore recommended that the initial model temperatures be as close as possible (within less than
10 degrees) to their equilibrium values, which is doable. As for temperature gradients along the z axis, across the test bodies and the coupling arms (shown in Fig. 2.1), a detailed numerical simulation was not carried out but conservative estimates show that the requirement for them not to exceed about 1 degree can be met.