Acceleration Effects on 3-D Aerodynamics of Slender Bodies

Abstract

Transient fluid dynamic effects in the transonic regime generate unique fluid behaviour during rapid acceleration when compared to a steady analysis. There is a change in the pressure load- ing upon the aerodynamic body during rapid acceleration (or deceleration) where well-known steady prediction methods for aerodynamic coefficients may not be accurate. Knowledge of changes in aerodynamic loads is valuable in obtaining increased agility and manoeuvrability. This study investigated the effect of acceleration and deceleration for a cone-cylinder at four angles of incidence, α=0◦, 5◦, 10◦, 15◦. The aerodynamic coefficients for acceleration and deceleration were compared with constant velocity to identify acceleration effects. The effects at the shoulder were tested for α=0◦, by using three cone half-angles: 10◦, 20◦ and 30◦. The computational model was three dimensional symmetric for α>0◦ and axisymmetric for α=0◦. The acceleration magnitude was constant 100g for α=0◦, and 400g for α>0◦, with straight and level flight. The Moving Reference Frame acceleration technique for one-dimensional flight was implemented in ANSYS Fluent® V.19 series and validated against Schlieren data from a free-flight ballistic range. The effects of significant axial acceleration and deceleration on an axisymmetric body was investigated in order to understand the development of the unsteady flow field and its influ- ence on drag in the transonic region. Wave and separation behaviour differed substantially between acceleration and deceleration cases. Acceleration to higher speeds was dominated by the developments of the bow, terminal, and wake shocks, which appear at higher Mach numbers than in the equivalent steady flow; due to the lag acceleration effect. Acceleration caused a shift in the transonic drag rise to higher Mach numbers with reduced maximum drag. The flow field for an accelerating cone-cylinder at incidence in the transonic Mach regime is described by downstream wave propagation and gradual wave development. The axial force coefficient for acceleration at incidence is characterized by a gradual slope in the subsonic iii Mach regime until a flight Mach number of M (t) near 1. There occurred no transonic peak and the maximum axial force was delayed to M (t)=1.1. The normal force coefficient for acceleration at incidence is characterized by a subsonic step- jump at the onset of acceleration. This is maintained until the transonic rise near M (t)=1 with an α-dependent behaviour in the supersonic Mach regime. There is an offset in the position of the primary body vortex core between acceleration and constant velocity, when measured from the cylinder surface. The position of the primary vortex core was closer to the cylinder surface during acceleration. The rear-foot of the lambda shock was classified as a weak shock, this shock was initially aft of the shoulder and propagates downstream towards the cylinder-base vertex, as the cone-cylinder accelerates from subsonic to supersonic speed. The foot of this shock locally disrupts the vortex lift, and as this shock leaves the cylinder- base vertex, the full vortex lift is then applied to the cylinder surface. This produces a step-disturbance in the normal force coefficient. The flow field for a decelerating cone-cylinder at incidence in the transonic Mach regime is characterised by upstream wave propagation and wave-surface interaction. The axial force coefficient for deceleration is characterized by a gradual reduction through M (t)=1, followed by wave-surface interactions. The cause is associated with upstream propagation of the asymmetric bow shock. The strength of this shock, the post shock pressure, and its proximity to the cone-apex modify the cone-surface pressure load in the axial direction. This gradual reduction of the axial force coefficient is maintained until the foot of the terminal and wake shocks are incident on the cone surface, the occurrence of which generates a sharp increase of the axial force coefficient. The normal force coefficient for deceleration at incidence is characterised by vortex lift flow history for deceleration through M (t)=1, from supersonic flight. The body vortices developed at supersonic flight remain in the flow field, as the cone-cylinder decelerates from supersonic to subsonic speeds. This leads to an increase in vortex lift during the subsonic Mach re- gime, compared to the constant velocity case. The elevated vortex lift during deceleration is maintained until the wake shock interacts with the body vortices at the cylinder’s aft-end. This significantly disrupts the vortex lift reducing the normal force coefficient. The upstream propagation of the terminal and wake shocks leads to shock wave boundary layer separation aft of the shoulder-vertex and with development of spiral vortex pairs around the leeward periphery of the shoulder. This raises the vortex lift, creating a temporal and sharp rise in the normal force coefficient while the terminal and wake shocks are located aft of the shoulder- vertex. This effect dissipates when the terminal and wake shocks propagate upstream and away from the shoulder vertex.