Thermal Design of DINO
Josh Stamps
March 26, 2004
Abstract
The thermal model of a satellite project is commonly referred to as a black art in the aerospace industry. The entire thermal design depends on the completion of an accurate thermal model of the satellite. In turn, the thermal model depends on the finalization of the satellites physique as well as its modes of operation. Many of these decisions are made only a few deadlines before the integration stages of the satellite. In the meantime, thermal engineers must abide by the laws of thermodynamics and materials science to predict potential problems in their design while faithfully developing their analytical model, which hopes to merely confirm the engineers’ intuition. This paper provides an overview of the thermal model of a satellite known as DINO. At this point in the development of DINO, the thermal model is beginning to manifest its strategy. With a sound strategy, the thermal design of DINO will ensure that all components will endure thermal environments well within their prescribed temperature limits.
1.0 Modeling Concepts
1.1 Focus
DINO stands for Deployment and Intelligent Nanosatellite Operations. As the name suggests, this satellites purpose is to exhibit deployment technology as well as intelligent operations. These processes are achieved by use of a network of components, which together are able to accomplish the desired task. In a sense, the satellite itself is just a collection of components connected in a certain way. These components consist of materials with desirable properties for their application. Electrical devices, for example, take advantage of materials with specific electrical properties. Alternatively, a structural component depends on the mechanical properties of the materials it employs to provide a stable satellite structure. All components of DINO have a certain utility whether it is of a structural, electrical, or optical nature. In order to perform this utility in a given environment, materials are selected carefully when designing the components’ hardware. The challenge for a thermal design is to consider the design limitations of each component, and control the thermal environment it will be subjected to so as to keep it safe from thermal damage for the duration of the satellites lifetime. The goal sounds simple enough, but becomes more complex when considering the environment of DINO as a whole. The satellite orbits Earth and thus alternates between periods of direct sunlight exposure and periods in the shadow of Earth. A closer look into the satellite also reveals electrical devices, which produce heat, that are being operated randomly rather than on a continual basis. In the overall picture, the variable radiation exposure and internal heat generation makes for a challenge in creating an isothermal environment for the component onboard DINO. An ideal thermal design for DINO would allow for a balance between the rate at which DINO dumps heat into cold space and the rate at which radiation heat and heat generated by onboard devices is being introduced to the satellite. Before discussing current progress on overcoming these challenges, a brief background on some thermodynamic concepts as well as the theoretical analysis utilized will be given.
1.1Thermodynamics Background
1.1.1 Temperature
The main thermal requirements are temperature ranges. Each team working on DINO depends on hardware to some extent in their respective designs. These hardware components are sometimes homogenous materials, and other times are composites of multiple materials. Depending on the thermal properties of all materials utilized in a component and the interfaces between them, a specific temperature range can be assigned so as to guarantee its desired performance. There are many factors which go into making such a guarantee and that will be covered shortly. First, it is appropriate to stress the significance of being able to generalize the thermal stability of a system by a single variable, namely temperature.
Temperature is an often-misconceived measurement. What temperature tells an engineer is whether there will be an exchange of thermal energy between two subjects in contact. If the two objects are at the same temperature, there will be no heat exchange between them and they are said to be in thermal equilibrium. This is a more specific version of the fundamental law of thermodynamics. Originally formulated in 1931 by R.H. Fowler, the zeroth law of thermodynamics states: “If two bodies are in thermal equilibrium with a third body, they are also in thermal equilibrium with each other (Cengel).” In today’s world this idea is almost intuitive.
What is often taken for granted is the idea that temperature is not a measurement of what is directly perceived through touch. There are other variables independent of temperature that contributes to how warm or cold and object feels. Consider the use of a glass thermometer in measuring boiling water. The boiling water transfers thermal energy to the thermometer until it is at the same temperature as the water. Although it would be unwise to touch the boiling water directly, its no problem to grab the glass thermometer and read the temperature of the water. The water obviously would feel much hotter than the thermometer but they are at the same temperature. This problem must have troubled the human race until Anders Celsius devised a universal temperature scale in 1741. Perhaps a strong reason his scale caught on is because it was based on the most vital human resource, which also happens to have possibly the most obvious thermal side affects. Water can freeze or evaporate with a small fluctuation in temperature with respect to other common substances. Celsius observed this convenience and created a centigrade scale, meaning 100 grades, between the freezing and evaporating points of water. According to the original scale: at 100C water freezes and at 0C it will evaporate.
This trend of decreasing temperature with increasing warmth was reversed in 1887, by the International Commission on Weights and Measures who adopted the scale and reversed the order so that 100C corresponded to the warmer temperature where water begins to evaporate and 0C corresponds to the colder state of water where freezing takes place. As the world of science evolved, Lord Kelvin mathematically projected the temperature corresponding to zero pressure with respect to 0C. He determined this value to be –273.15C. This corresponds to the absolute lowest possible temperature in the universe and corresponds to 0K on the newly devised Kelvin scale. This scale became known as the absolute temperature scale. Both temperature scales will be utilized throughout the analysis of DINO depending on the circumstance.
In reality, temperature is a measurement of the average molecular kinetic energy of a substance. At every level from sub-atomic to molecular, particles in a system can vibrate, rotate, or translate. The particles in motion have mass and their motion can be quantified as a form of kinetic energy. The average energy of all motion is what temperature is a measurement of. With this in perspective it makes a bit more sense why heat transfer does not occur between objects with the same temperature. The particles of each object possess the same kinetic energy so there can be no transfer of momentum from one object to the other by direct contact.
The temperature of the components that make up DINO is vastly important, as it is the beginning and the end to the analysis. We are given initial temperatures, as well as temperature restrictions for each component, and in the end will provide the maximum and minimum temperatures each component will see for any possible mode of operation DINO could endure. In order to get from beginning to end, an analysis of heat transfer between all components is performed. Temperature differences drive heat transfer throughout the satellite and heat transfer leads to changes in temperature.
1.1.2 Temperature Change
As was just established, temperature is a measure of the internal kinetic energy of a system. Changes in this energy, or changes in temperature, are the result of transfers of this kinetic energy to and from the system. This type of energy transfer is called heat transfer. The driving force that activates heat transfer is temperature. In a system, kinetic energy is distributed throughout so as to reach equilibrium, at which point the system is said to be in steady state. In a steady state system, all components are in thermal equilibrium with each other and there is no transfer of heat. DINO will be in steady state only while it is stored in the payload of the shuttle that transports it to orbit. This is because the satellite is in a controlled environment while in the shuttle, allowing it to reach a uniform temperature. There are no temperature differences to drive the transfer of heat to or from the satellite. Once in orbit, however, the satellite is subjected to cold space as well as warm bodies such as the Sun and the Earth resulting in periodic fluctuations of heat gain and loss while orbiting. Furthermore, electrical devices onboard DINO are activated, generating heat that is dumped into the satellite.
In order to predict temperatures of components onboard DINO, it is necessary to quantify how much is transferred as a result of temperature differences as well as how much heat is required to change the temperature of each component. A thermal engineer works in the macroscopic realm of thermodynamics. Meaning, the engineer is concerned with properties of materials rather than the microscopic processes that determine these properties.
1.1.3 Heat
Originally, heat was thought of as a massless substance called calorie. It was quantified with the Celsius temperature scale in mind. One calorie of heat is enough to raise the temperature of 1 gram of water by 1C. 1000 calories are equivalent to a Calorie, as seen on the side of food and drink boxes today. However, since discovering that heat transfer is literally the transfer of internal energy rather than the transfer of a massless substance, heat energy has been more conveniently quantified on the same scale as many other forms of energy, Joules or BTU’s (British Thermal Units).
Different materials of identical mass require different amounts of heat to change the temperature by 1C. This is a result of the structure of the material. A rigid structure such as iron, for example, requires 4.5 Joules of heat to change the temperature of 1 gram of the substance by 1C. Alternatively, liquid water requires 41.9 Joules to change the temperature of 1 gram of water by 1C. The amount of heat required to change the temperature of a specific material is a property of that material. This property is called specific heat, Cp. With knowledge of a materials specific heat, comes knowledge of how much heat is required to change its temperature. Equation 1 gives the relation for the change in temperature, as a result of heat transfer for a specific material.
Equation 1
1.1.4 Heat Transfer
With the thermal analysis of DINO, the initial temperature of all components is known as being equal to the steady state temperature of the payload onboard the shuttle. From the moment the satellite is placed into orbit, and its instruments are initiated heat is being gained and lost by components on the satellite simultaneously. This begins a cycle of non-homogenous temperature distribution throughout the satellite that must be predicted continuously through the end of DINO’s lifetime. The amount of heat created by onboard devices can easily be predicted, as well as the magnitude of heat provided by celestial bodies. However, this information along with equation 1 is inadequate it analyzing a complex network of components such as with DINO. Once one component onboard DINO gains or loses heat energy it begins exchanging energy with all components it is in contact with. If it gains heat, it immediately transfers enough of this heat so its neighboring components so as to maintain thermal equilibrium. In effect, the satellite is constantly distributing heat so as to reach steady state. So in order to change the temperature of a single component, enough heat must be provided so as to change the temperature of all components in contact with it, and the components in contact with them and so on. This is where the calculation becomes tricky, and it becomes necessary to quantify how heat travels through DINO as well as how it is deposited in equation 1.
As stated previously, heat transfer is a result of temperature. In practice, a temperature difference is required to drive heat from one point to another so it is a temperature difference that activates heat transfer. Since temperature differences drive heat transfer and the result of heat transfer is a change in temperature, heat transfer is calculated as a time rate. As the process of heat transfer progresses, the driving temperature difference decreases and the rate at which heat is transferred decreases accordingly.
The three mechanisms of heat transfer are conduction, radiation, and convection. Thermal conduction is heat transfer as a result of momentum transfer at a molecular level thru a medium. Radiation heat transfer is a result of electromagnetic waves driven by temperature differences between objects not in contact. Radiation heat transfer is a much faster process than the other mechanisms of heat transfer, as energy it is not hindered by a medium thru which to travel as in the case of conduction. Convection is a form of conduction in which case a moving fluid is in contact with an object. The rate of heat transfer in a convective process depends on the surface properties of the fixed object. In the case of DINO, convection is neglected as space can be considered a vacuum.
1.1.5Heat Conduction
The most common form of heat transfer is thermal conduction. At a microscopic level it is the transfer of momentum through an object or between objects in contact. This type of heat transfer is what allows heat to be distributed through an object when applied at a specific point. The rate at which heat propagates from one point to another through a medium is given by equation 2.
Equation 2
In 1822, J. Furier first expressed equation 2 quantifying the rate of heat transfer via conduction. It states that the time rate of heat transfer is equal to the product of the cross sectional area thru which heat is transferred, the thermal conductivity of the material in the direction of heat transfer, x, and the temperature gradient, dT/dx, which drives the process. Thermal conductivity, k, is a measure of how quickly heat can travel through a material. It depends mainly on the molecular structure of the material, but also on the instantaneous temperature of it. If the structure is rigid in all directions, then internal kinetic energy can travel with ease through the material. This explains in large part why metals, typically with rigid crystal structures, can more easily pass heat than say polymers, which have strong bonds in one direction along chains but have weak vander-waals bonds between chains. The thermal conductivity of a material also varies with the temperature of the material. If there is already a relatively large amount of kinetic energy stored by the structure of a given material, its ability to pass excess kinetic energy is hampered. Thus thermal conductivity is higher for rigid structures and decreases with temperature.
In order to apply this equation to the satellite, DINO is broken up into discrete rectangular elements. Each element, called a node in modeling the satellite, has a temperature that is assigned at its center of mass. Of interest to the thermal model of DINO, is the rate at which heat can conduct from node to node. If the nodes are of the same material, then equation 2 can be applied directly with the temperature gradient determined by the temperature difference and the distance between the centers of each node. If the nodes are different materials, the average rate of heat conduction is calculated depending on the temperature gradient from the center of each node to the interface between them.
Creating a thermal conduction model of DINO is the fundamental step in the overall analysis. By breaking the satellite up into nodes, a network of potential heat paths and depositories is established. The accuracy of this model depends on its resolution, as determined by selecting nodes. The temperature of a node is an average of the mass it represents. Therefore decreasing the size of the nodes and thus increasing the number of nodes representing the physical satellite results in an accurate representation of thermal activity throughout the satellite. Each node represents a quantity of mass that can gain or lose energy with interfacing nodes according to equation 2. In so doing, the temperature of this node changes with the relation shown in equation 1. The next step in building the thermal model of DINO is including all sources of heat transfer to and from the satellite.
1.1.6 Thermal Radiation
Heat transfer to and from the satellite is a result of radiation heat transfer. It is also a mechanism that allows heat transfer between nodes as with conduction. In practice it is calculated as if it were driven by a temperature difference between surfaces that are in view of one another. In reality radiation transfer is a combination of radiation being emitted from a surface as result of its temperature, and energy incident on a surface that was emitted by others.
Joseph Stefan first quantified the rate at which heat is transferred via radiation in 1879. Stefan discovered that the energy at which a blackbody emits radiation is the product of the Boltzmann constant, , and the temperature of the emitting surface to the fourth power. This law became known as the Stefan-Boltzmann equation and is included as equation 3.
Equation 3
The Stefan-Boltzmann equation assumes an ideal surface known as a blackbody, in which heat is radiated at a maximum rate. A real surface, however, has a color which limits the wavelength at which heat is radiated, as well as a rough surface which alters the direction in which radiation is emitted. To account for these variables, the total amount of radiation emitted from a given surface at a specific temperature is found by multiplying a constant by the Stefan-Boltzmann equation known as emissivity, . Emissivity is a property that determines what fraction of thermal energy is radiated by a surface with respect to an ideal blackbody. So, if the surface property and temperature of a material are known, the amount of heat lost thru radiation can be quantified.