Unsteady aerodynamic effects experienced by aerofoils during acceleration and retardation

Abstract

This investigation focuses on the aerodynamic effects caused by acceleration and retardation. It shows that, when an object is accelerated in a compressible fluid, the aerodynamic forces and moments experienced by the object at any instantaneous Mach number are different to those, experienced at the same Mach number, when the object moves at constant velocity. A supersonic biconvex aerofoil was chosen, with Fluent as the computational fluid dynamic (CFD) software. Constant velocity (steady state) simulations were conducted at Mach numbers ranging from 0.1 to 1.6 for the aerofoil. The aerofoil was then accelerated at 1041 m/s 2 (106 g) and 86.77 m/s 2 (8.845 g), starting at Mach 0.1, and decelerated at −1041 and −86.77 m/s 2 , starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were shown between the steady and the unsteady cases with the greatest differences observed in the transonic region. In this region, for each specific Mach number, acceleration-dependant variations in the position of the shock wave on the upper surface of the aerofoil were also observed. This was used to explain the great differences in the aerodynamic forces and moments between the steady and the unsteady cases in the transonic region.

Theoretical treatment of fluid flow for accelerating bodies

“…It was then demonstrated that drag on an axisymmetric flare missile dropped by 20% in comparison with steady values if the flare geometry was accelerated through the transonic range at 4 500 ms -1 . Roohani and Skews have conducted detailed studies of the unsteady aerodynamics of accelerating bodies, such as aerofoils [40][41][42][43][44] and axisymmetric objects [45] undergoing unidirectional acceleration through the subsonic and transonic ranges. This was modelled numerically using source terms added to the momentum and energy equations in the code FLUENT [46].Shock wave boundary layer interaction was found to have significant effect on the shock wave position and strength in the transonic range.…”

“…At this point it is important to explain the concept of flow history as used in the present context [43]. When an object is accelerated in a compressible fluid, the unsteady flow field generated is not allowed sufficient time to reach equilibrium at any specific Mach number.…”

“…Linear acceleration The works of Roohani and Skews [41,43,44] focus on acceleration and deceleration effects when the acceleration is parallel to the velocity of the object. In this case, the conservation equations in the relative frame Σ′ are as follows, given that = 0, and therefore = .…”