In-pipe aerodynamic characteristics of a projectile in comparison with free flight for transonic Mach numbers

Abstract

The transient shock dynamics and drag characteristics of a projectile flying through a pipe 3.55 times larger than its diameter at transonic speed are analyzed by means of time-of-flight and pipe wall pressure measurements as well as computational fluid dynamics (CFD). In addition, free-flight drag of the 4.5-mm-pellet-type projectile was also measured in a Mach number range between 0.5 and 1.5, providing a means for comparison against in-pipe data and CFD. The flow is categorized into five typical regimes the in-pipe projectile experiences. When projectile speed and hence compressibility effects are low, the presence of the pipe has little influence on the drag. Between Mach 0.5 and 0.8, there is a strong drag increase due to the presence of the pipe, however, up to a value of about two times the free-flight drag. This is exactly where the nose-to-base pressure ratio of the projectile becomes critical for locally sonic speed, allowing the drag to be estimated by equations describing choked flow through a converging–diverging nozzle. For even higher projectile Mach numbers, the drag coefficient decreases again, to a value slightly below the free-flight drag at Mach 1.5. This behavior is explained by a velocity-independent base pressure coefficient in the pipe, as opposed to base pressure decreasing with velocity in free flight. The drag calculated by CFD simulations agreed largely with the measurements within their experimental uncertainty, with some discrepancies remaining for free-flying projectiles at supersonic speed. Wall pressure measurements as well as measured speeds of both leading and trailing shocks caused by the projectile in the pipe also agreed well with CFD.