Numerical Simulation of Viscous Flow in a Super-Orbital Expansion Tube

An axisymetric Gudonov scheme has been implimented to investigate the flow in a free-piston driven superorbital expansion tube. Equilibrium chemistry is assumed, and laminar viscosity is used to compute boundary layer development. The computations start at secondary diaphragm rupture, and follow the secondary shock as it traverses the test gas. An analytical solution is used for the upstream boundary conditions, which are held constant. The condition of the test gas up to the start of the unsteady expansion has been computed for a shock speed of 10 km/sec. Comparison with experimental results shows good agreement with the macroscopic flow parameters of shock speed and attenuation. A major potential role for impulse facilities lies in simulating the superorbital flow velocities which are associated with entry into planetary atmospheres. A pilot superorbital expansion tube has been commissioned at The University of Queensland to investigate one means of doing this. Whilst the design and development of such facilities is primarily driven by an analytical understanding of the dominant flow mechanisms involved, detailed numerical analysis is required to completely define their performance and limitations. Furthermore, as the velocity range of these facilities increase, the flow density has to be reduced and this in combination with high Mach numbers causes viscous effects to have a dominant influence on the flow. For this reason, a time dependent, axisymmetric, viscous flow simulation of the above superorbital expansion tube is being developed. The facility uses a compound two stage driver to produce high shock speeds in the acceleration gas. It consists of four tubular sections separated by diaphragms, with an area ratio of 7.2 between the first and second sections. The conditions in the first helium region are chosen to drive an over tailored shock in the second tube. This creates secondary driver gas capable of driving a stronger shock in the tertiary tube than would be possible by directly coupling the first stage to the third without the intermediate section. The use of helium accelerator gas maximizes the energy addition which occurs across the unsteady expansion.