The Dynamic Character of the flow over a 3.5 Caliber Tangent-Ogive Cylinder in Steady and Maneuvering States at High Incidence



Introduction

From the late 1940's to early 1950's, aircraft design was rapidly evolving due to the radical changes in propulsion systems. First proven by the German Luftwaffe in World War II, the turbojet engine was to quickly drive the piston-driven propeller to extinction as the propulsion means for state-of-the-art fighters and bombers. Although piston-driven P-51 Mustangs and F-4U Corsairs would remain in service through the Korean War, their heyday was decidedly over. Besides the turbojet, the Germans also made great strides in the development of the rocket engine, which they used with great success. The V1 and V2 rockets showed that explosives mounted on a long-range rocket could be a formidable weapon.

As the amount of thrust available increased, aircraft were able to expand their performance envelope so that velocities greater than the speed of sound were possible. By the early 1960's, most of the world-class fighter aircraft were designed to cruise supersonically. Since slender bodies of revolution have relatively low drag and a predictable conical or near-conical shock pattern in supersonic flow, it is not surprising that axisymmetric bodies were used as forebodies (nose sections) in the high-speed fighter aircraft. In addition, these shapes continued to be used in the design of rockets and missiles.



The Flow as a Function of the Angle of Attack ()
The flow over a slender forebody of circular cross-section can be separated into four regimes based on : (1) No separation (< S) - At very low angles of attack, the flow does not separate from the body. (2) Symmetric flow (S <  < A) - At low to moderate angles of attack, but below the critical angle for the onset of asymmetry, the flow rolls into two symmetric vortices on the leeside of the forebody. (3) Steady asymmetric flow A <  < U) - At high angles of attack above the critical angle (A), the flow over the slender forebody and afterbody exhibit asymmetric lee vortices and a nonzero yaw force. (4) Unsteady asymmetric flow - At very high angles of attack, the vortical flow becomes increasingly unsteady, especially over the afterbody. The mean flow is still asymmetric, but the mean yaw force decreases with α. The onset angle of attack for this flow regime will be designated U and is generally between 70° and 80°, depending on the fineness ratio (caliber) of the forebody. At = 90°, the forebody produces the familiar Karman vortex street, except for cross-sections near the tip of the forebody. Flow visualization of the slender body flow variance with angle of attack which supports the division into four regimes was done by Fiechter (1966),.



Impulsively Started 2-D Cylinder Flow Analogy (IFA)
The asymmetric crossflow (flow in a plane perpendicular to the axis of symmetry) present in the wake of a slender forebody when  > 2 immediately sparks the thought of the impulsively started two-dimensional cylinder. Recall that the impulsively started flow consists of an initial symmetric growth of lee vortices, followed by the alternate shedding of the vortices, the Karman vortex street. However, a discrepancy exists between the two problems because the wake and forces on the two-dimensional cylinder vary with time, whereas the wake and forces on a slender forebody are steady phenomena, although some natural unsteadiness exists at high angles of attack.