Navier-Stokes Computations for a Spinning Projectile From Subsonic to Supersonic Speeds

Many U.S. Army projectiles are slender, spinning bodies. When flown at an angle of attack (AOA), these projectiles are then subject to Magnus forces and moments. Although these forces are generally quite small (10–100 times smaller than the normal force) and can usually be ignored, the moment produced by these forces is critical in determining the stability of the projectile. Thus, it is important to be able to accurately determine these coefficients.
Early numerical studies that have looked at spinning projectiles [1–3] have suffered from a number of problems. The supersonic flow study [1] seemed to have produced fairly good results using the Parabolized Navier-Stokes equations. However, the grid resolution was probably questionable due to the computational resources available. The 1983 transonic study [2] also produced questionable results due to inadequate grid resolution caused again by limited computational resources. While the 1991 study [3] was able to utilize a much better grid and more robust supercomputers, a very limited number of Mach number and AOA were investigated. As the computational fluid dynamics (CFD) software and computational resources improve, more complete and accurate numerical aeroballistics data can be obtained. The present study was undertaken in order to verify the ability of a relatively new CFD software package to predict this more complete aeroballistics data for a spinning projectile. This particular CFD software has been previously used to calculate the flow fields and resulting aeroballistics data on nonspinning projectiles [4], but had not yet been benchmarked for a spinning projectile and the associated force and moment (i.e., Magnus force and moment). Prior to using this software to determine aeroballistics data for new spinning projectile designs, the software must be verified against existing data and methods to determine its accuracy.
The .50 cal. projectile has been in use for almost 60 years. While a limited amount of aerodynamic data was collected during the projectile’s development and testing [5], a relatively large amount of aerodynamic data has been obtained over the years for these rounds. Most of the data have been collected within the last 15 years at the U.S. Army Research Laboratory’s (ARL) Free Flight Aerodynamics Range* [6]. Parabolized Navier-Stokes numerical aeroballistics data have also been obtained for a similarly shaped .50-cal. training round with fairly good results [7].
The numerical aeroballistics data obtained in this study are compared to existing range data as well as semi-empirically obtained aerodynamic coefficients. The flow field of the spinning projectile is then examined within each flow regime investigated.