Micromaps host Satellite Design Proposal

2.5 Thermal

A preliminary thermal analysis determines the temperature variations the satellite experiences on orbit. This analysis is presented in Table 20. It assumes a spherical satellite with uniform surface properties. The minimum and maximum power dissipations are estimates from the preliminary power budget. The other values presented are discussed in more detail later in this section chapter.

Table 20: Design parameters for preliminary VASCAT thermal analysis

Generalized component temperature limits are given in Table 21.

2-174

Nodes transfer heat between themselves by conduction. Conduction couplings are a measure of how a node transfers heat to another node that is touching it. The following equation is the governing conduction heat transfer equation:

2-184

Radiation heat exchange takes place between nodes and space. For the purposes of this analysis, internal radiation between components is neglected. The internal surfaces of the satellite are painted black, which minimizes internal radiative heat transfer. Only radiation from the bus external surfaces to space is considered. Radiation heat transfer is given by:

2-194

Generation of a thermal model requires knowledge of the heat fluxes (see Equation 2-17) in addition to the heat transfer paths. Nodal heat fluxes are determined from the internal component dissipations and environmental inputs. Hot and cold cases are considered. The hot case includes the maximum or peak power dissipations from each of the components and the maximum orbit averaged fluxes on the satellite. Likewise, the cold case includes the minimum operational power dissipations and the minimum orbit averaged fluxes.

The internal dissipations are determined by the mission operation requirements and are obtained from the power subsystem. The component dissipations used for each of the cases are given in Table 22.

Table 22: Component internal power dissipations

The orbit averaged fluxes are calculated from information about the satellite’s orbit. The external heat sources are direct solar energy, Earth infrared (IR) and albedo. Albedo is a measure of how much of the sun’s energy is reflected from the Earth’s atmosphere and surface back into space, and is usually given as a percentage.⁶ The cold case analysis assumes the satellite is in eclipse and the only external heat source is from the Earth. The environmental fluxes are shown in Table 23.

The actual heat input depends on the surface properties of the satellite. Absorbtivity, , is a measure of how much external radiation is absorbed by the surface in question and is dependant upon the thermal coating applied. Emissivity characterizes how much heat the surface radiates according to Equation 2-19.²⁰ The surface properties of various VASCAT external components are given in Table 24.⁶

Table 24: Surface properties

The total input power is determined by:

2-20

View factor is a parameter that varies depending upon the position of the satellite relative to the orbital frame. For example, the nadir panel of the satellite is Earth-pointing, and therefore rarely has a full view of the sun. Therefore, the nadir panel view factor is approximately 0.2. The view factor is determined by the MATLAB code in Appendix A. This code determines the power output from body-mounted solar cells on a hexagonal cylinder at various positions in an orbit. It outputs the projected area that a surface will ‘see’ relative to the solar vector. This projected area is then used to determine the view factor for the external bus surfaces.

The thermal model is assembled after the heat transfer paths are identified and internal and external heat sources are considered. The thermal analysis requires simultaneous evaluation of Equations 2-17, 2-18, and 2-19 at each node. This evaluation is complex due to the nonlinear relationship between the temperature of a node and its resulting heat flux.⁹

The Systems Integrated Numerical Differential Analyzer (SINDA), a thermal analysis package commonly used in industry, analyzes the VASCAT thermal model.³ This software package calculates nodal temperatures based on user-generated conduction and radiation couplings and input fluxes. The program then uses an explicit forward solution method to evaluate the governing heat transfer equations. The explicit forward method uses the conditions at the current time step, or iterative loop, to calculate the temperature of each of the nodes in the system. It then performs an energy balance check on each of the nodes and varies the time step accordingly. The result is a steady state solution for nodal temperatures.

The MAPS instrument is the mission driver for the VASCAT, so several steps are taken to thermally control it. The instrument is conductively coupled to the nadir and zenith panels of the satellite. Additionally, the nadir and zenith panels are coated with white paint to increase their dissipation to space and reduce their incident heat flux.

The hot and cold case temperatures of the VASCAT components are listed in Table 25. Almost all component temperatures are within their specified limits. The exception is the MAPS instrument. In hot case conditions, MAPS operates at about 0.5 degrees over its hot limit. The model has temperature accuracy limits of ±1 degrees. Therefore, a 0.5 degree temperature violation is deemed acceptable within the scope of this analysis. However, the analysis shows that MAPS is a primary constraint driver for further design.

The exterior of the VASCAT is covered in solar cells. Therefore, it is not possible to incorporate a radiator into the design to help dissipate heat from MAPS. However, it may be possible to use conductive straps or fasteners to better transfer heat from the instrument to the satellite. Additionally, a doubler or cold plate might be used to thermally isolate the MAPS instrument from the rest of the satellite. These modifications are detailed design parameters and are therefore outside the scope of this analysis.

This analysis is preliminary and is based upon estimated values. A more in-depth analysis should be performed on the VASCAT to determine if a passive thermal control system is indeed accurate. No detailed internal structural configuration has yet been defined. Therefore, the conduction paths are estimated from HokieSat’s internal configuration. In addition, the thermal masses of each of the components are estimates. Finally, a transient analysis, which takes into account the change in variations in temperature of the satellite over the course of an orbit, should be performed to ensure that a passive TCS is adequate.