Small Satellite Thermal Modeling and Design at USAFA: FalconSat-2 Applications[1]
C1C Richard Lyon2
LtCol Jerry Sellers2
Craig Underwood3
2USAF Academy Small Satellite Research Center
USAF Academy, CO
3Surrey Space Centre, University of Surrey,
Guildford, Surrey, UK
Abstract—The US Air Force Academy FalconSat program is one in which undergraduate cadets design, build, test, and operate satellites to carry Air Force and Department of Defense payloads for scientific missions. Currently, cadets are working on FalconSat-2, designed to carry the Micro Electro-Static Analyzer (MESA) payload that will investigate the morphology of plasma depletions in the ionosphere. The Engineering Model was completed and tested in April 2001, and cadets will construct the Qualification and Flight Models in the fall of 2001. To aid in the development of the satellite, behavioral models of various spacecraft subsystems have been created using MatLab and used to simulate projected operational modes of the satellite and the effects on major satellite subsystems. One major subsystem that had been overlooked until this summer was the thermal subsystem. We require a detailed thermal model to aid in the development and testing of FalconSat-2 for several reasons. First, we wish to predict the thermal behavior of the satellite in the various thermal tests it will undergo in the development process. We also wish to predict the thermal behavior of the satellite in various expected operational modes and attitudes. This will in turn enable us to design and implement any required thermal control for the satellite. Over the summer, during research performed at the University of Surrey, a thermal model of FalconSat-2 was created in MatLab using finite differential analysis and a lumped-parameter approach. The FalconSat-2 model was adapted from models developed by Dr. Craig Underwood, which have been used over the years in the design and analysis of Surrey’s small satellites – including, most recently, the UK’s SNAP-1 nano-satellite. This paper will detail the development process undergone in creating the FalconSat-2 thermal model, will demonstrate how the model works, and will validate the results. Additionally, the paper will describe the thermal control solutions implemented for FalconSat-2 and how the model is used in the development process.
Table of Contents
- Introduction
- Model Description
- Model Verification
- Thermal Design Discussion
- Conclusion
1. Introduction
The capstone of the United States Air Force Academy Astronautics curriculum is the FalconSat Program. One goal of the program, housed within the Academy’s Small Satellite Research Center, is to give undergraduate cadets the unique opportunity to “learn space by doing space.” The program facilitates cadet development of small satellite mission design through instructor guidance and mentorship. It allows cadets to gain real-world experience with satellite design, assembly, integration, testing, and operations within the context of a two-semester engineering course sequence. A second goal of the program is to provide a useful nanosatellite platform for Air Force and Department of Defense space experiments. Through FalconSat participation, cadets receive the hands-on opportunity to apply the tools developed in a classroom to a real program, ideally preparing them for the situations they may encounter as officers and as engineers after they graduate.
The current project, FalconSat-2, is the third satellite to be developed within the Academy’s program. The satellite’s primary payload is the Micro Electro-Static Analyzer (MESA) sensor suite, designed to study plasma depletions in the F region of the ionosphere. It will be launched on the Space Shuttle as part of the small payloads Hitchhiker project. FalconSat-2 will be mounted in a Get Away Special (GAS) canister with the Hitchhiker Motorized Door Assembly (HMDA) and will use the Pallet Ejection System (PES). The satellite is built around a “FalconSat-N” approach, meaning the spacecraft bus is designed so that it will be easily adaptable to carry future payloads. As such, the basic design is one of an outer structural shell upon which the solar panels and MESA sensors are mounted, and an inner column around which the other subsystems are placed in module boxes. The satellite is a 12.5-inch cube, with the solar panels placed on the +X, -X, +Y, and –Y facets, the MESA sensors, S-band antenna, and whip antenna placed on the +Z facet, and the interface ring placed on the –Z facet for attachment with the Space Shuttle’s Get Away Special (GAS) canister. Figure 1a shows an external view of FalconSat-2, and Figure 1b shows an exploded view detailing key features and components.
Figure 1a: FalconSat-2 external view
Figure 1b: Exploded view of FalconSat-2 showing key features and components
FalconSat-2 has been in development since Fall 2000, with the Engineering Model completed and tested in Spring 2001. Prior to Summer 2001, however, no work had been done on the thermal subsystem of FalconSat-2. This need was addressed over the summer of 2001 through research conducted at the University of Surrey.
The basic purpose of thermal design is to maintain the temperature of all spacecraft components within desired limits. We also wish to minimize the temperature fluctuation (thermal cycling) that the spacecraft components are subjected to. FalconSat-2’s internal components, which are the most thermally sensitive parts of the satellite, are fairly thermally decoupled from the external heat flux the satellite is subjected to. This is due to the design with the inner column and outer structural shell. This allows us to control the temperature with a passive thermal design approach. We will modify the thermo-optical properties (absorptivity and emissivity values) of the external facets of the satellite so that the satellite and all components are maintained within the optimal temperature range.
On FalconSat-2, the operational temperatures are limited by the electronic components within the satellite, and specifically by the battery. The battery is the most thermally sensitive of the satellite subsystems because it cannot be recharged below 0˚C. As a result, the nominal temperature range targeted for the batteries and internal components of FalconSat-2 is +5 to +30 deg C. The other commercial electronics within the satellite have temperature limits of –40 and +85 deg C. The structural components and solar panels have much more relaxed temperature limits. Table 1 lists the temperature limits for FalconSat-2.
Table 1 – Temperature limits for FalconSat-2 subsystems
Subsystem / Minimum Temperature (˚C) / Maximum Temperature (˚C)Battery / 0 / 50
EPS / -30 / +50
MESA / -40 / +85
Data Handling / -40 / +85
Comm / -40 / +85
Solar Panels / -100 / +110
Structure / N/A / N/A
To design the thermal subsystem and ensure that FalconSat-2 will meet these temperature limits, we had to first simulate the thermal behavior of the satellite. This will allow us to see how the satellite will behave without any thermal control implemented, which will in turn show us what design we must implement to meet the temperature range requirements. In order to simulate the satellite’s thermal behavior, a model had to be created.
We require a detailed thermal model of FalconSat-2 for several reasons. Primarily, we need to simulate expected on-orbit thermal behavior of the satellite and ensure that no spacecraft components exceed their maximum or minimum temperature limits. We also need to ensure that the temperature fluctuation (thermal cycling) of all spacecraft components is minimized. By simulating varying on-orbit scenarios, including varying attitude modes and varying subsystem operation modes, we can also simulate worst-case hot and worst-case cold temperature scenarios. Furthermore, we wish to use the thermal model to simulate testing environments that we will subject the satellite to at various phases throughout the development. Furthermore, we wish to integrate the thermal model into an overall behavioral model of the satellite to assess the interaction of the thermal design with the rest of the satellite.
2. Model Description
The computer thermal modeling tool was created in MatLab using Simulink to coordinate the programming. It uses finite difference analysis to calculate the change in temperature at each node at every time step. The overall thermal model is broken up into two parts. The first part compiles a history of the external flux inputs to the satellite for a single orbit. The second part of the model then uses these flux inputs along with the physical makeup of the satellite to actually perform the finite difference analysis to calculate the thermal behavior of the satellite throughout the orbit.
Flux History Calculation Model
The flux history calculation model calculates the heat flux coming into the satellite due to insolation (direct solar radiation), Earth infrared radiation, and albedo (solar radiation reflected off of the Earth). The model calculates this flux and compiles a history as a function of time for each of the six faces of the spacecraft.
The inputs to the flux history calculation routine are the satellite’s epoch classical orbital elements, epoch date and Universal Time, the satellite’s attitude control method (Sun-tracking, velocity tracking, tumbling, or quaternions), and the time of flight taken from the simulation clock. The outputs are insolation, Earth infrared, and albedo fluxes for each face with respect to time for an entire orbit.
The flux history calculation model is broken into five modules within MatLab. These modules, along with their inputs and outputs, are discussed here:
COE Update--This module updates the classical orbital elements (COEs) from the epoch time to the current simulation time. Inputs are the epoch COEs, the epoch date and time, and the time of flight, taken from the MatLab simulation clock. This module outputs updated COEs for the satellite and the current Julian date.
Light--This module calculates the sun position vector, the satellite position and velocity vectors, and whether or not the sun currently illuminates the satellite. Inputs are the current COEs and Julian date. Outputs are the satellite position vector (R), satellite velocity vector (V), sun position vector (Rsun), illumination flag (Vis) and satellite/sun Beta angle.
Surface Normals--This module calculates the surface normal vectors of each of the six faces of the satellite. This routine is used if the satellite is sun-tracking, velocity-tracking, or randomly tumbling. There is a switch where the user can choose which tracking mode to use. Alternatively, the surface normal vectors can be calculated using quaternions from an interface with Satellite Tool Kit. There is a switch that allows the user to choose which method of calculating the surface normal vectors they would like to use. Inputs are the satellite position vector (R), satellite velocity vector (V), sun position vector (Rsun), illumination flag (Vis) and satellite/sun Beta angle. Outputs from the module are the surface normal vectors for each face of the satellite, the angle from the +K axis to the satellite R vector (phi), and the angle from the +I axis to the satellite R vector (theta).
Insolation--This module calculates the insolation flux on each of the six faces of the. Its inputs are the surface normal vectors, sun position vector, and illumination flag. It outputs the insolation flux on each face in Wm-2 in both graphical and matrix form.
Earth Effects--This module calculates the Earth Infrared and Albedo flux on each of the six faces of the satellite. This part of the model takes the longest time, as there is a double discrete summation to calculate the Earth IR and Albedo view factors for each face of the satellite. Inputs are the surface normal vectors for each face of the satellite, the satellite position vector (R), the sun position vector (Rsun), the angle from the +K axis to the satellite R vector (phi), and the angle from the +I axis to the satellite R vector (theta). It outputs the Earth infrared and Albedo flux on each face in Wm-2 in both graphical and matrix form.
Figure 2a shows the Simulink interface of the flux history calculation model. It takes approximately thirty minutes of computation time to calculate the flux history for the 92-minute orbit of FalconSat-2.
Figure 2a – MatLab Flux History Calculation Model Interface
Figure 2b – MatLab Nodal Temperature Calculation Model Interface
Nodal Temperature Calculation Model
The second main part of the overall thermal model is the nodal temperature calculation portion. This part of the model actually conducts the finite difference analysis and calculates the temperature of each node of the satellite versus time for the entire orbit. The MatLab interface for this portion of the model is shown in Figure 2b.
The inputs to the nodal temperature calculation routine are the flux histories for the satellite calculated in the first part of the thermal model as well as the lumped parameter definitions of the thermal nodes throughout the satellite and the conduction links between the nodes. These lumped parameters include the mass (m), specific heat capacity (c), cross-sectional area (A), absorptivity (α), emissivity (ε), and thermal conductivity values (k). The output from the model is a temperature profile for each node in the satellite.
The nodal temperature calculation model is broken down into five modules within MatLab. These modules are described here:
External Qin--This module calculates the external heat transfer into each node due to insolation, Earth infrared, and albedo. The inputs are the flux history matrices compiled in the previous model. The flux on each facet is then multiplied by the appropriate surface area and absorptivity or emissivity value for each node to calculate the external heat transfer into each node in watts, designated as Qext.
Fourier Conduction--This module calculates the heat transfer between nodes due to Fourier conduction. It iterates through each node in the satellite and calculates the heat transfer to or from every other node. The key equation in this subsystem, with “i” being the current node of interest, is equation 1, with the subsystem performing this summation for each of the nodes in the satellite:
(1)
Inputs are the temperature of each node and the conductivity between each node. The module outputs the heat transfer into each node due to conduction in watts, designated as Qcond.
Black Body Radiation From Space--This module calculates the black body radiation coming into each node from the background of space. Of course, heat is actually transferring out of each node to space, so the outputs from this subsystem will be negative. The heat transfer from each node to space is calculated using the black body radiation equation, with the background heat of space assumed to be 4K.
Internal Power Dissipation--This module puts the internal power dissipated at each node into the matrix form the model requires. These internal power dissipations are an input to the overall thermal model.
Finite Difference Analysis--This module calculates the temperature of each node using finite difference analysis. The key equation in this subsystem is equation 2:
(2)
Once the Delta T at each node is calculated, the temperature at each node is calculated by adding the Delta T to the previous nodal temperature.
3. Model Verification
The MatLab thermal model was verified in two ways. First, over the summer while it was being developed, it was used to model Surrey Satellite Technology, Ltd.’s SNAP-1 nanosatellite. The results were then compared to a SNAP-1 thermal model created in Pascal by Dr. Craig Underwood of SSTL. The model results match exactly. This is to be expected because the same assumptions, including the epoch COEs, epoch date/time, tracking mode, and SNAP-1 geometry, were used for both models. Figures 3a – 3b show the temperature vs. time of each node in SNAP-1 results from the MatLab model compared with Dr. Underwood’s Pascal model.
Figure 3a: All 30 SNAP-1 Nodal Temperatures Over 1 Orbit from MatLab Model
Figure 3b: All 30 SNAP-1 Nodal Temperatures Over 1 Orbit from Dr. Underwood’s Pascal Model
The MatLab thermal model was further verified by modeling the FalconSat-2 Engineering Model configuration. This model simulates the Thermal/Vacuum test of the FalconSat-2 Engineering Model conducted at Kirtland AFB in Spring 2001. The model uses a 25-node finite differential analysis model to simulate the thermal vacuum test. A description of the 25 nodes can be found in Table 2.
Table 2 – FS-2 Engineering Model Nodal Definitions
Two main assumptions were used in this model. First, the aluminum structural facets were assumed to be a single average thickness (the different thicknesses due to the actual orthogrid pattern were ignored). This average thickness was determined from the mass of aluminum in each facet divided by the density and surface area. The second assumption was that the heat flux inputs used for the model were the actual temperature measurements of the thermal vacuum chamber. The temperature of the chamber was assumed to be an infinite well at the average temperature of the eight temperature measurements in the chamber.