Review of theoretical achievements for starting flow problem for all Mach numbers

The typical behavior of unsteady flow and force evolution in a number of applications, such as aero-elastics, gust-wing interaction, flapping flight and flight maneuvering, can be understood using the starting flow model. Starting flow model is obtained either by setting rapidly an angle of attack for a wing moving at constant speed, or by accelerating a wing to a constant speed while gaining an angle of attack. In the limiting case of impulsively starting flow, the wing is assumed to gain suddenly an angle of attack in an initially uniform flow. Theories have been developed for impulsively starting flow at small angle of attack long before and at large angle of attack only recently, especially for incompressible and supersonic flow. This paper intends to provide a state-of-art overview of the typical flow phenomena, force evolution characteristics and developed theories for impulsively starting flow at any angle of attack and for both lower speed flow (vortex dominated) and high speed flow (compressible wave dominated). This review also provides some new topics that deserve further studies.