Thermal Regulation and Temperature Control. Having settled on a baseline configuration for the probe it was important to see if it lent itself to reasonably easy thermal control. Thermal regulation of spacecraft is always a difficult problem for a number of reasons, notably:

• Direct exposure of spacecraft surfaces to solar heating unshielded by atmosphere.
• Direct radiation of heat from space-facing surfaces to a sink effectively at 0K.
• The absence of ambient atmosphere to equalise internal temperatures by conduction and convection.

These factors tend to lead to extremes of temperatures on satellites, with sun-facing surfaces becoming very hot and permanently sun-shielded surfaces becoming extremely cold.

Many components and systems used on board spacecraft can only operate over a limited temperature range. Even space-specified electronic components are often limited to an operating temperature range of -10 to +40 °C [Larson92, Fortescue95] whilst batteries and monopropellant fuel tanks can be even more tightly limited, e.g. 5 to 20 °C. In order to keep such components and systems within their acceptable temperature ranges given the temperature-extreme inducing factors described above, some form of thermal control is often needed. Such thermal control measures can be divided into active and passive measures.

Active Measures. involve the use of heaters to raise temperatures or radiators and coolant loops to conduct excess heat away. They allow accurate thermostatic temperature control of particular areas of a satellite but add to weight and power budgets. Furthermore, active cooling systems are often mechanically complex, although for small-scale applications solid-state Peltier effect coolers can be used [Fortescue95].

Passive Measures. involve configuring the spacecraft's balanced of absorbency and emissivity such that it maintains a natural radiative thermal balance at the desired temperature. Passive internal temperature control is achieved by using matt-black paint and thermal doublers to maximise radiative and conductive heat transfer between sub-units.

On a simple, low cost mission such as this one it is best to make as much use of passive thermal control as possible. To see if this was feasible a first-order approximation thermal model of the probe was used to see if the probe's average temperature could be passively maintained within a reasonable range. Detailed thermal modelling of spacecraft is an extremely complex undertaking as it involved describing the spacecraft as an array of elements that exchange heat by mutual radiation and conduction. Extensive finite-element simulation is then used to determine the temperature distribution within the model. Such detailed modelling was considerably beyond the scope of this project; instead, as mentioned, a very simplified modelling method was used to determine approximate average temperatures.

Probe Thermal Model

The first thermal model of the probe was set up as per Fig 16.1. This was an intermediate stage in probe configuration when it featured solar arrays on only the front and side faces. Furthermore, at this stage it had been assumed that the maximum sun angle from the spin axis would be 60°. Three surface finishes were assumed:

• Antenna: modelled as white epoxy paint.
• Solar Arrays: modelled as average solar cells.
• Rear Face: modelled with variable emissivity.

Fig 16.1 shows the absorptivity alpha and emissivity epsilon of these finishes.

The purpose of the variable-emissivity rear face was to allow for some tuning of the passive model. Given the requirement that the maximum sun angle from the antenna boresight would be 60° the rear face would always be facing cold space during the cruise phase of the mission. By selecting its emissivity (from 0 for a perfectly non-radiating surface to 1 for a black-body radiator) the amount of heat radiated to space from the probe, and thus its average temperature, could be varied.

The model was set up (via a Mathcad worksheet) as follows:

a. The projected area of the antenna (approximating it as a flat disc) and the front and side solar arrays was calculated as a function of sun angle. Each projected area was then multiplied its absorptivity to find alpha_tot(theta), the total overall absorptivity of the probe as function of theta.

b. The areas of the antenna, front and side arrays and rear face were multiplied by their emissivities to give epsilon_tot(_r), the total overall emissivity of the probe as a function of the rear face emissivity epsilon_r. Note that this is an emissivity rather than an absorptivity function so total rather than projected area towards the Sun is used.

c. The equilibrium average temperature of the probe as a function of theta and epsilon_r was then calculated via the Stefan-Boltzmann relationship:

(16-1)

where P_sol is the solar irradiance per m² and sigma the Stefan-Boltzmann constant.

d. T(theta,_r) was then plotted for values of epsilon_r from 0 to 1 in steps of 0.2 and theta from 0° to 60°. This calculation was carried out twice with values of P_sol representing the solar irradiance at 1 AU and 1.05 AU.

Figs 16.2 and 16.3 show probe average temperature as a function of sun angle and rear-face emissivity for this probe design at solar distances of 1 and 1.05 AU.

For any combination of rear face emissivity and sun angle in the range 0° - 60°, the average temperature is always in the range 250K to 295K (-23°C to 22°C) between 1 and 1.05 AU from the Sun. If we chose a rear-surface emissivity of 0.6 (equivalent to silvered Teflon [Larson92])the range is 260K to 275K (- 13°C to 2°C) over this distance range.

This model indicated that for the general configuration of probe being considered it would be possible to keep the average temperature within reasonable limits using fairly simple passive thermal control measures.

Subsequent redesign of the probe (see Section 14) lead to a design with identical annular solar arrays on both front and back panels. The maximum sun angle limit was removed as it was decided that the probe should be able to operate under any angle of illumination. Also, solar array power analysis (supported by initial thoughts on structural design) suggested that a less oblate cylindrical design would be desirable. The probe thermal model was thus amended as in Fig 16.4.

This model was arrived at after a series of intermediate models. It was found that the original design had poor thermal as well as power properties for sun angles approaching 90°. This was due to its very oblate design; heat absorbed by the side array was easily radiated out of the space-facing front and back faces. Even when the design had been made less oblate for power and structural reasons, it proved difficult to keep the probe temperature within reasonable limits at high sun angles. The problem was exacerbated by the decision to use an array on both the front and back face, as the high emissivity of solar cells meant that heat was lost even more readily from the rear face. Another factor to be borne in mind is that with a rear solar array the probe may be operating sunwards from Earth, under an increased solar flux.

This problem was addressed in two ways. Firstly, the absorptivity/emissivity ratio of the side arrays was increased to allow the probe to absorb more heat at high sun angles. This was done by replacing the uniform covering of solar cells with a mixed covering of solar cells and gold-faced surface finish. Gold has a very high absorptivity/emissivity ratio (0.3/0.03) and so is a much better absorber of near-IR wavelengths than it is a radiator of thermal ones. Power modelling had suggested a probe radius/depth ratio of for optimum power production at all sun angles. By increasing this to 1 (i.e. a probe twice as wide as it was deep) but using a side array fill factor of only 80% the same power-collecting area could be achieved whilst leaving space for gold finish to lower the average absorptivity/emissivity ratio. This 4:1 array/gold mix gave an average absorptivity/emissivity ratio of 0.704/0.666, significantly higher than the 0.805/0.825 assumed for solar cells alone. Note that for this model an evenly-distributed pattern of the two surfaces was assumed. A deliberately uneven pattern could be used to increase or decrease the absorptivity/emissivity ratio over particular areas should detailed thermal modelling indicate it would be desirable.

The second measure adopted was to reduce the heat radiated via the front and rear faces central regions (i.e. the antenna on the front face and the area around the main thruster on the rear face). This was done by thermally isolating these areas using low-emissivity surfaces. For simplicity, a gold covering was again assumed.

An additional factor taken into account in this model was the heat dissipated within the probe by its own power consumption. This was taken into account as an extra thermal power contribution P_dis in the thermal balance equation:

(16-2)

Fig 16.5 shows the average temperature for the final configuration. As this design is thermally symmetrical, it covers both the case of both the front and back faces being towards the Sun. Temperature curves for solar distances of 0.93 AU, 1 AU and 1.07 AU are shown; the increased margins over earlier models reflect the fact that the probe may be launched to encounters 0.05 AU from the Earth both at perihelion (0.98 AU) and aphelion (1.02 AU). As can be seen the probe average temperature is maintained between 267K - 315K (-6°C - 42°C) over this range.

Areas for Further Study. It should be noted that the temperature calculated via these models is an average for the entire spacecraft. In actual fact the temperature distribution within the spacecraft will depend on a number of factors such as thermal conductivity of major components, the degree to which heat is distributed by radiation and details of power dissipation and any particular passive measures (such as extra insulation) used. A much more detailed model would be required to take all these factors into account; however, such a model would require a more detailed probe design to be carried out and is thus beyond the scope of this feasibility study. However, a number of general thermal design points can be made that would be appropriate to this probe.

• Fuel Tank and Line insulation would be desirable to ensure that hydrazine fuel did not freeze, particularly towards the spacecraft skin where temperatures could be lower, although the spin-stablized design should ameliorate this.
• High-conductivity Thermal Doublers could be used to redistribute heat from on-board electronic equipment to areas at risk of becoming too cold.
• Substitution Heaters could be used to mimic the heat dissipated from systems such as the science payload that are not powered for all phases of the mission.

Thermal Design Summary. Thermal modelling of the basic design concept for the probe indicated that it would probably be possible to maintain a reasonable level of average temperature control using only passive measures. A slightly more detailed thermal model of the final design study configuration confirmed that average internal temperatures could be maintained with the range 267 K - 315 K over the environment in which the probe would be required to operate. A more detailed design study should examine the temperature distribution within the probe to ensure that it was consistent with the operating ranges of relevant sub-systems.