Thermal model design and orbit revaluation

Of the Citizen Explorer Satellite

Jacob Boettcher

1.0 abstract

Citizen Explorer (CX) is the first in a series of small satellites to be built by students at the University of Colorado branch of the Colorado Space Grant Consortium (CSGC). CX is a program designed to educate students of all ages about space, technology, and science. CX's primary scientific goal is to increase general environmental awareness through the use of onboard instruments it will carry to measure total ozone column and solar ultraviolet radiation.

This paper will briefly present the design process for building the model of the CX thermal system and then focus on a challenge presented after the design was complete. The CX thermal system was originally designed for a sun-synchronous circular orbit at an altitude of 705km with local time 10am-10pm.1 However, the available launch window was missed and consequently, CX will no longer be inserted into this orbit. Therefore, an evaluation of what other possible sun-synchronous circular orbits would still allow CX to fulfill the science objectives was conducted. From the science constraints a general range of orbits was selected and then analyzed to see which ones would satisfy the CX thermal requirements. The orbits considered had altitudes ranging from 500-1000 km and local times between 9am-9pm and 10:30am-10:30pm. The thermal analysis suggested that any new orbit will require some modification in the thermal design of the CX satellite. However, only the science subsystem was not satisfied by the orbits with local times somewhere in the range of 10:00am to 10:30am.

2.0 Introduction- Design process for the CX Thermal System

The Citizen Explorer Thermal System (CXTS) is one of the many design teams assembled to make CX a success. The CXTS was designed to assure a safe thermal environment for all components aboard the spacecraft. Due to severe constraints on budget and schedule, the CXTS was designed in parallel with the other subsystems in CX.4 This made the design process highly interactive, with many iterations as the design changes went down through the teams to the CXTS design team. Also, due to the budgetary and power constraints of the project, there was limited funding and power available for the CXTS.4 These constraints impacted greatly the design of the CXTS and placed the requirement that CX have an entirely passive thermal control system.4 The rest of this section will briefly describe the entire design process for creating the model of the CXTS.

The thermal design process consisted of several main steps:

  • Creating a three-dimensional model of the spacecraft for radiation view-factor calculation using SUPVIEW program.4
  • Determining the Beta Angle using FINDB6 program.4
  • Calculating the thermal inputs due to Earth-shine, solar albedo, and direct solar radiation using ALBTIME2 and ALBEDO programs.4
  • Determining the overall radiation model using REFLECT program.
  • Inputting the thermal conductances and capacitances to the model to get temperature profiles of components over several orbits and under different operational conditions using TAK III software.

Each of the steps described above will now be briefly discussed.

2.1 Finding the View-factors

View-factors are defined as the area of the given surface that can affect the area of another surface.4 For example, if two identical plates were parallel to each other they would each have a view-factor of 100% with respect to the other plate. If the same plates were perpendicular to each other, the view-factor would be 0%.4 Thus, all of the interactions (view-factors) between plates and component boxes must be calculated to obtain an accurate thermal model. To help calculate all of the view-factors, there is a program called SUPVIEW. SUPVIEW is designed to take a 3-dimensional model of a spacecraft and calculate the view-factors between the various components. Each component or surface in the model is divided into nodes. A node is the subdivision used to separate the spacecraft into components and plates so that individual elements can be analyzed for temperature changes.4 Each node in the SUPVIEW program is defined by four points and each point is defined by three coordinates x, y, and z. Nodes can be rectangular or triangular. Thus, the three-dimensional model of CX was created by breaking up the spacecraft into nodes and running the SUPVIEW program to generate all of the view-factors.

2.2 Determining the Beta Angle

One of the most important inputs into a thermal model is the direct solar radiation incident on the spacecraft. A key parameter in determining this input is the beta angle, defined as the angle between the solar vector and the orbit plane. To help calculate this parameter, there is a program called FINDB6. FINDB6 generates beta angle values based on the following inputs:

  • Starting day, month, and year
  • Ending day, month, and year
  • Apogee altitude (km), perigee altitude (km), and universal time (sec)
  • Inclination, right ascension, and argument of perigee (all in degrees)

The output from FINDB6 will list the date, percent day, beta angle, true anomaly of the dawn terminator, right ascension, power factor, argument of perigee, declination, and relative solar intensity for each day from the start date indicated to the end date.4 The beta angle is the only output data that is used in the next phase of the modeling with the ALBEDO program. Although the beta angle will change with time, in a sun-synchronous orbit such as CX’s original orbit, it varies little and so an average value is used. For the original orbit the average beta angle used for CX was 30 degrees.

2.3 Calculating the thermal inputs due to Earth-shine, solar, albedo, and direct solar radiation

There are three primary thermal inputs for the CX thermal model: direct solar flux, Earth albedo, and Earth infrared radiation.4 These three inputs are important and their values are based heavily on where the satellite is in its orbit and how it is orientated. Therefore, the variations in solar flux, Earth albedo, and Earth IR must be calculated with respect to position and time in CX’s orbit.4 The program that will determine these variations for CX is called ALBEDO.

Before ALBEDO can be used, the time and position of when the satellite is in sunlight and when it is in eclipse must be determined. To determine this information, the program ALBTIME2 is used and requires the following inputs:

  • Altitude at apogee (km)
  • Altitude at perigee (km)
  • Alpha at perigee (degrees)
  • Beta angle (degrees)
  • Desired alpha increment (degrees)

The output from ALBTIME2 will be given such that shadow and sunlit portions of the orbit will be given in terms of true anomaly. Based on this output, the desired resolution of the analysis can be determined and the orbit is divided into a distinct number of sections as needed (12 for CX).4 Next, a value for the true anomaly is selected that is right before the dusk terminator (when the satellite goes into eclipse) and a value is selected that is right before the dawn terminator (when the satellite enters sunlight). The rest of the orbit is defined by other true anomaly values that are divided evenly throughout the remaining sections of the orbit. These values are then input into ALBEDO so that the program can take into account the change in thermal input at the proper time.

ALBEDO requires the following user-defined constants to be entered into the program: Solar constant, Earthshine constant, Albedo constant, Earth radius, altitude, eccentricity, alpha of perigee, beta angle, maximum number of subelements per surface, number of orbital positions (the sections defined using the output from (ALBTIME2), number of rings for Earth subdivision, and designation of space-oriented spacecraft or nadir pointing.4 ALBEDO also requires the same corner and node format that was used in SUPVIEW, with two exceptions. The axis used in SUPVIEW is not important as long as it is a right-handed system. ALBEDO, however, requires that the +Z axis be pointing away from Earth, and the +Y direction be the direction of spacecraft flight.4 This is important so ALBEDO knows the orientation of the spacecraft in flight. The second exception is that the SUPVIEW model is an internal view-factor model. ALBEDO is an external model, consequently, an external nodal model must be created. Usually the same set of corners can be used but now the surfaces must be defined to be facing out rather than into the satellite. Finally, the outputs from ALBEDO will be used in the REFLECT program to determine the overall radiation budget for CX.

2.4 Determining the overall radiation model

Once the ALBEDO portion of the model is complete, the space inputs and internal view-factors are known. To finalize the radiation budget for CX, the thermal finishes of each of the nodes needs to be defined. The program REFLECT takes the thermal finishes and calculates the radiation budget for the model. However, in order to complete the entire radiation budgets for CX two models need to be run: one external and one internal. The external model uses the background of space at 4 degrees Kelvin and the external node thermal finishes to perform the calculations.4 Since the external nodes are facing space, each external node will have a 100% view factor of space. 4 The internal model uses the view factors calculated by SUPVIEW to calculate the radiation influence of each node on all others. The REFLECT program requires the following inputs: maximum number of iterations for radiation balance, error allowed in balance, default value for emissivity, default value for absorptivity, and non-default values for emissivity and absorptivity for any given surface.4

Each output file contains a list of surfaces, the surfaces they can see, and the radiation exchanged between them.4 The combined output of the internal and external models are used in the final program Thermal Analysis Kit III (TAK III).

2.5 Inputting the thermal conductances and capacitances to the model to get temperature profiles of components over several orbits

The final step in the thermal modeling procedure requires that all of the thermal conductances and capacitances be calculated for all the interactions between nodes. The thermal capacitance for each component of the satellite can be calculated from the following equation:

Equation (1)4

Thus, if the mass of a specific component and its material properties are known (so CP can be determined), then the thermal capacitance can be found.

Calculating conductances is more difficult and involves three different procedures: one for the conductance between two parts of the same thickness, one for the conductance between two parts of equal thickness, and a third for the conductance between components using fasteners. The equations to determine the conductances for each of these different scenarios are involved and will not be presented in this paper. For additional information on this section, the reader is referred to Reference 4.

Assuming that all of the capacitances and conductances are known for the satellite, the final step in completing the TAK III model is to add the dissipated power for each node that has power associated with it. The power dissipation can be represented at a constant rate or with a timing sequence that is associated with the satellite’s functions at different times in the orbit. For CX most of the components are powered-on all the time; only the transmitter and spectrometer are turned on and off during nominal operations.4 By adding power dissipation to the program, the TAK III model is ready to calculate the temperatures of each node. TAK III can be run in two modes: steady state where the temperature of each node is found at a time equal to infinity, and transient where the temperature of each node is found with respect to time. TAK III allows this data to be output and plotted versus time so that the thermal performance of the satellite along its orbit can be analyzed.

3.0 Reason for Orbit revaluation

Citizen Explorer (CX) was designed for a circular 705 km, sun synchronous orbit with a local time of 10:00 am at the descending node.1 This orbit was forfeited when the launch of the satellite was delayed. Thus, a revaluation of what possible orbits would satisfy all of the subsystems requirements was conducted. Presented here is the analysis performed to verify what types of orbits could satisfy the thermal requirements imposed by the different subsystems.

Before the thermal portion of the orbit revaluation was begun, certain orbit limits were already defined by other subsystems. First of all, non-sun synchronous orbits were eliminated from the possible orbit scenarios for the following reasons: these orbits would not allow the spacecraft to collect sufficient power for operation and they would require active pointing of the satellite to keep the solar panels at a constant angle to the sun.1 In addition, the science instruments placed a requirement that the local pass times of the orbit fall between 9 am-9 pm and 12 am-12 pm.1 Also, a minimum altitude constraint of 500 km was imposed based upon the significant atmospheric drag effects that were predicted to occur at lower altitudes.1 Lastly, the power subsystem required that the orbit have local times of 10:30 am-10:30 pm or earlier in order to collect sufficient energy with the solar arrays to power the satellite.1

From the constraints that are described above, six different orbit scenarios were investigated to see which would satisfy the thermal requirements of CX.

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4.0 Thermal Analysis

To analysis the thermal environment of the CX satellite in six different orbits the Thermal Analysis Kit III (TAK III) was used.2 Table 1 below displays the altitudes and Local Time for each of these orbits.

Table 1: Orbit Altitudes and Local Times

1 / 2 / 3 / 4 / 5 / 6
Altitude (Km) / 500 / 1000 / 500 / 1000 / 500 / 1000
Local Time / 9am-9pm / 9am-9pm / 10am-10pm / 10am-10pm / 10:30am- 10:30pm / 10:30am- 10:30pm

For each of the six orbit scenarios a hot and cold case was run using the maximum and minimum values of Solar flux, Earth IR Emission, and Direct Solar Albedo. The values used are presented in Table 2 below.3

Table 2: Values of Solar Flux, Earth IR Emission, and Albedo

Solar Flux (Wm-2) / Earth IR Emission (Wm-2) / Direct Solar Albedo
(%)
Maximum / 1428 / 238 / 50
Minimum / 1371 / 194 / 34

Each of the models was run with the nominal power mode. In addition, for each different orbit scenario a new beta angle was found with the use of the FINDB6 program. From the FINDB6 program the maximum and minimum beta angle values were used to run with the hot and cold cases respectively. The values that were used for the six different orbit scenarios can be found in Appendix D. In order to make the processing of the data easier the five temperature sensitive subsystems were analyzed separately and are described below.

4.1 ADCS

For the Attitude Determination and Control System there were eight components that were modeled in the thermal program. These eight components were: five Coarse Sun Sensors (CSS), two Magnetometers, and the ADCS Microcontroller. The thermal requirement imposed by this subsystem was that each component must be kept between 0 and 30 degrees Celsius.4 In order to present the data from the analysis in a more condensed manner, the maximum and minimum temperatures for each of the components listed above were averaged to get a general high and low temperature for the ADCS subsystem. Figure 1 in Appendix C displays the averaged maximum and minimum temperature for the ADCS subsystem that was obtained in each of the six orbit scenarios. All of the thermal data taken can be found in Appendix A and the average maximum and minimum temperature data can be found in Appendix B.

In Figure 1 in Appendix C, the two straight lines represent the temperature limitations imposed by the subsystem. From this figure several observations can be made. The maximum temperature limit for ADCS was exceeded for both orbit scenarios 1 and 2. In orbit scenarios 3 and 4, the ADCS maximum and minimum limits were approached, but both appear to satisfy the requirements. The minimum temperature limit was exceeded in the fifth orbit scenario, but the sixth orbit scenario satisfied all of the temperature requirements. Thus, orbit scenarios 3, 4 and 6 appear to satisfy the ADCS thermal requirements. This suggests that the closer that the new orbit is to the original local time of 10:30 am-10:30 pm the better chance that it will satisfy the temperature requirements of the ADCS subsystem.

4.2 Science

For the Science subsystem there were two components that were modeled in the thermal program. These two components were a Photometer and a Spectrometer. This subsystem had the most stringent thermal requirements. For these two instruments to perform at an optimal level they must be kept between 7 and 12 degrees Celsius.6 However, they will function as long as they are kept between 0 and 16 degrees Celsius.6 In order to analyze the Science subsystem, the maximum and minimum temperatures of the photometer and the spectrometer were averaged to get general values for the Science subsystem. The temperatures obtained by the Science subsystem are presented in Figure 2 in Appendix C.