WEST LAFAYETTE, Ind. – A computer model originally applied to such theoretical problems as understanding the mathematics behind soap bubble formation could be worth millions of dollars for companies that operate communications satellites.
Engineers recently have used the model to develop an innovative method for better gauging how much fuel is left in the expensive satellites. Moreover, the technique uses temperature data that are already routinely collected, meaning it requires no additional satellite hardware and can be applied to existing spacecraft.
The satellites, which are maintained in the proper position about 22,500 miles above Earth by firing small rocket thrusters, must be replaced shortly before they run out of fuel. Enough fuel must remain to get the satellites out of orbit to make room for their replacements.
The net annual revenues for a single satellite may be in the billions of dollars, so the premature retirement of a space vehicle is no small matter, said Steven Collicott, an associate professor of aeronautics and astronautics at Purdue University. More accurate fuel-gauging methods are needed so that companies can better determine when to replace a satellite.
Every drop of the hydrazine rocket fuel is worth more than its weight in gold. For satellites that send signals to pagers or residential TV dishes, just one pound of hydrazine translates into about $2.5 million in revenue.
"If it's so expensive to get a pound up there, then you better do everything you possibly can to use it efficiently," Collicott said. He was one of three engineers who wrote a research paper demonstrating how the computer model is used in a new method for gauging the quantity of propellant in a satellite's fuel tank.
The paper appeared in the November-December issue of the Journal of Spacecraft and Rockets, published by the American Institute of Aeronautics and Astronautics. It was written by Jay Ambrose, an engineer at Lockheed Martin Corp.'s Advanced Technology Center; Collicott; and former Lockheed Martin engineer Boris Yendler.
Although it may sound like a simple task, precisely monitoring the quantity of propellant in a satellite's fuel tank is not so easy. The problem's complexity is perhaps illustrated by the level of skills needed for the research, said Collicott, adding that all three researchers have doctoral degrees in aerospace engineering.
"It's not like a car's fuel tank, which has a little float that floats on top of the gasoline and moves a lever," Collicott said. "Floats don't work in space because everything is floating."
Conventional gauging methods include calculating fuel consumption based on the number and duration of all rocket firings since launch. Because engineers know how much fuel the rockets consume, they can estimate how much is left. Another technique is to use the ideal gas law, in which the temperature and pressure of gas in a container can be used to calculate how much gas is present. Knowing how much gas is contained in the tank, in turn, reveals information about how much liquid fuel is present.
"These methods have worked, but the quest for improvements and redundancy led to the new technique," Collicott said.
The engineers used a model created in the early 1990s by Kenneth Brakke, a mathematics professor at Susquehanna University, to help improve fuel gauging. The model was initially used to describe the mathematics behind such phenomena as the formation of soap bubbles. It also helped to solve the following problem: When a straw is placed inside a glass of water, why does the water level inside the straw rise higher than the level in the glass?
"The exact same physics, the wicking action, is responsible for positioning fuel inside the tank," Collicott said. "Here on Earth we see this capillary action only on very small length scales because gravity generally overwhelms it.
"But in space the weight of the liquid is irrelevant."
Consequently, the effect is exaggerated in space, making it more difficult to predict the liquid's movement and its location inside the tank.
However, Collicott's application of the model makes it possible to use routine temperature data from the satellite to monitor how much fuel is left in the tank. Those data come from heaters, which are needed to keep the fuel from freezing, and temperature sensors located on the outside of the fuel tank.
Areas of the tank that contain fuel take longer to heat, while portions of the tank that are empty heat up faster. The more fuel that is present, the longer it takes to heat.
"The same principle applies to a pot of water on a stove," Collicott said. "The less water there is in the pot, the faster it heats up."
Information returned to Earth from satellites reveals how fast different areas of the tank are heating up, indirectly indicating where the most fuel is located. The model uses the temperature information to provide a detailed, three-dimensional understanding of where fuel is located inside the tank. That information can, in turn, be used to calculate how much fuel remains in the tank.
"One practical benefit of this gauging method is that it makes use of hardware that is already a standard part of these satellites," Collicott said. "As such it can even be applied to satellites launched before this work began."
Lockheed Martin uses the technique on some commercial communications satellites, such as those for digital television broadcast to homes. The technique may be improved in the future, as researchers gain a better understanding of how fluids behave in weightlessness.
"Propellant gauging has long been a problem," Collicott said. "I am not saying by any means that this has the whole thing solved."
The technique also might be used to help design satellite fuel tanks that better control the position of liquid propellants. An unbalanced load can cause a satellite to wobble, which requires a greater use of thrusters to control the spacecraft. Designs that better control the fuel's movement would result in less fuel consumption and increased revenue, Collicott said.
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