An improved version (HLLC) of the Harten, Lax, van Leer Riemann solver (HLL) for the steady supersonic Euler equations is presented. Unlike the HLL, the HLLC version admits the presence of the slip line in the structure of the solution. This leads to enhanced resolution of computed slip lines by Godunov type methods. We assess the HLLC solver in the context of the first order Godunov method and the second order weighted average flux method (WAF). It is shown that the improvement embodied in the HLLC solver over the HLL solver is virtually equivalent to incorporating the exact Riemann solver.

A comparison between Full Potential and Euler numerical solutions for 2D transonic unsteady flow is presented. The pros and cons of the potential model are discussed and the main features of both computational methods are summarised. The comparison is done for a Naca 0012 aerofoil oscillating in pitch at a freestream Mach number ranging from 0·755 to 0·825, in order to investigate the limit of application of the potential approximation in an unsteady flow.

Unsteady pressure data from seven aerofoil models performing constant pitch rate “ramp-down” motions from the fully separated state to low incidence have been analysed. It is observed that the time delay between attachment at the leading edge and the occurrence of minimum normal force is, to a first order, independent of reduced pitch rate. As a result, at sufficiently high pitch rate, negative normal force may be generated at large positive incidence. In contrast to this, the re-establishmeht of attached flow to the upper surface is strongly dependent upon pitch rate. The paper also contains a description of smoke flow visualisation tests. These were at a much lower Reynolds number than the pressure data tests, and consequently are of qualitative interest. Results of flow visualisation show that during a ramp-down test the near wake is much larger than in the corresponding static case, and that attachment is significantly delayed.

The evolution of low Earth orbit satellites under the action of atmospheric drag and J2 oblateness perturbations has been widely investigated. Simple analyses describing the altitude decay of a circular orbit through energy arguments have also been widely available. This paper extends these simple analyses by providing compact analytic expressions for true anomaly and ascending node angle along with a more accurate expression for altitude decay. The resulting solutions then allow a fast and efficient method of investigating the orbital evolution of decaying, precessing circular orbits. Applications include the rapid evaluation of station-keeping budgets for both single platforms and the orbital evolution of satellite constellations. Passive station-keeping by continuous low thrust acceleration is investigated and shown to be naturally unstable.