GSMMC 2009 Fuel Tanks problem

Design of fuel tanks for high-speed vehicles

Thomas Witelski, Department of Mathematics, Duke University

Vehicles powered by liquid fuel pose many engineering challenges. Predicting the motion of the vehicle (cars, planes, ships, missiles, rockets) follows from the equations of mechanics and the information known on the rigid structure of the vehicle. If the vehicle's fuel tank is completely filled, then the mass of the fuel can be incorporated into the total as if the fuel were solid. However, as the fuel gets used up, or if the tank were originally only partially filled, the liquid fuel will move subject to the forces imposed by the motion of the container; this is called sloshing. In addition to shifting the balance of mass in the vehicle in a dynamic manner, sloshing may generate large forces as the fluid slams against the container walls (especially at resonant forcing frequencies); this can have a significant effect on the stability of the moving vehicle. Different designs for the shapes of fuel tanks (and interior structures called baffles) can reduce sloshing but can produce other side-effects.

Our focus will be on geometric aspects of fuel tank design for highly maneuverable high-speed vehicles (race cars, jet planes, satellites) that may experience a wide range of orientations and forces. Analysis of the inviscid fluid dynamics will begin with hydrostatic solutions, with surface tension included for micro-gravity environments. Limiting situations involving nearly-empty tanks and drain choking phenomena will be important.

References

The new "dynamic behavior of liquids in moving containers" by F. T. Dodge