Computation of transonic flow past projectiles at angle of attack

Numerical Calculation of Three-Dimensional Displacement Effect on Bodies of Revolution

“…The Mach number is transonic at M = .94 with a well developed shock aft of the corner where the ogive and the tail sections join. The inviscid transonic flow about this body was obtained from a small disturbance potential technique developed by Reklis, Sturek, and Bailey 5 , In both Figures 8 and 9, the angle of attack is 4° and the boundary layer is turbulent. The body used for Figure 8 was not spinning while the body used for Figure 9 was spinning at 10,000 rpm.…”

“…In order to produce a stable numerical scheme for the solution of Equation 5it is necessary to understand the nature of these characteristic paths. The characteristic paths of Equation (5) may be obtained if it is rewritten in the form 9 (A-6 )/3x + (w /Ru )9(A-6 )/9e = AfA-fi )+B The partial differential Equation (5) has been transformed into the ordinary differential Equation (8). The lines along which d9/dx = w /Ru e e are thus characteristic paths of Equation (5).…”

“…The characteristic paths of Equation (5) may be obtained if it is rewritten in the form 9 (A-6 )/3x + (w /Ru )9(A-6 )/9e = AfA-fi )+B The partial differential Equation (5) has been transformed into the ordinary differential Equation (8). The lines along which d9/dx = w /Ru e e are thus characteristic paths of Equation (5). Equation (8) was written in terms of (A-6 ) as A is approximately equal to 6 for X X slender bodies of revolution at small angles of attack and this form emphasizes the difference between A and 6 .…”

A Theoretical and Experimental Investigation of a Transonic Projectile Flowfield

“…The inviscid flow region is treated by the method developed by Reklis et al 4 involving a numerical solution of the transonic small-disturbance equation for the velocity perturbation potential </ > which, in cylindrical coordinates, is…”

“…Inviscid transonic computational results have been obtained by Reklis et al 4 for a secant-ogive-cylindrical boattail shape. This work was then extended to include the viscous boundary layer and modeling of the shock/boundary-layer interaction regions.…”