Comparison of panel method formulations and its influence on the development of QUADPAN, an advanced low-order method

A spinning two-dimensional cylinder experiences a negative Magnus lift force at small spin ratios (peripheral speed/freestream speed) in the critical Reynolds number regime in steady incompressible flow. A comprehensive explanation of this phenomenon is offered. A negative Magnus side force at a small spin ratio has been measured on an inclined, spinning ogive-cylinder at a certain subcritical cross-flow Reynolds number. Through use of the impulsive flow analogy, the two-dimensional explanation can be applied to the negative side force experienced by the inclined spinning ogive-cylinder if the effect of the body vortices is allowed for. At both critical and subcritical cross-flow Reynolds numbers, the body vortices produce a side force which is opposed to, and larger than, the side force associated with the cross-flow separation positions. The cross-flow separation positions are similar to those on a spinning two-dimensional cylinder. Starting with the measured separation and body vortex positions, a simple potential flow model is developed, which predicts total side forces in qualitative agreement with those measured.

Negative Magnus forces in the critical Reynolds number regime.

An analysis of recent wind-tunnel results is presented describing the influence of Mach number, Reynolds number, and body geometry on asymmetric vortex development and associated forces on slender missile configurations at high angles of attack. Experimental force and moment coefficients, load distributions, and surface-pressure distributions (steady and unsteady) are presented for several ogive and triconic nose configurations for angles of attack up to 90°, subsonic to low supersonic Mach numbers, and Reynolds numbers (based on body diameter) from 3.17X10 5 to 3.17X106. Asymmetric vortex locations and strengths, boundary-layer separation lines, and side-force coefficients are predicted using the unsteady cross-flow analogy and a discrete vorticity cross wake. Predictions of side force coefficients compare well with the force test data for angles of attack up to 40°. A a CN CY

Asymmetric Vortex Wake Development on Missiles at High Angles of Attack

An array of experiments have been conducted on a finless, slender body with a rotating nose tip having up to three nose tip strakes The model had a fineness ratio of 200 and a 27 tangent ogive nose The experiments were performed at a Mach number of 015 and a Reynolds number of 993 X 10 The results show that the use of a rotating nose tip on a slender body can significantly reduce (up to 80%) the out-of-plane loading on the body The amount of reduction is dependent upon the rotation rate and the number of strakes on the rotating nose As the number of strakes increased, the effect of the rotation rate became less evident The results show that a reduction in the side force did not necessarily coincide with a corresponding reduction of the yawing moment In virtually all cases, the spinning tip worked best in reducing the out-of-plane loading below some critical angle of attack where the flow appears to behave with a convective instability Tests above the critical angle of attack showed less dependence on the effects of the nose tip disturbances These effects argue that above this critical angle the flow is controlled by an absolute instability

Rotating nose tip effects on slender body aerodynamics at high angles of attack

Separated flow over bodies of revolution using an unsteady discrete-vorticity cross wake

A method is developed to determine the flowfield of a body of revolution in separated flow. The technique employed is the use of the computer to integrate various solutions and solution properties of the sub-flowfields which make up the entire flowfield without resorting to a finite difference solution to the complete Navier-Stokes equations. The technique entails the use of the unsteady cross flow analogy and a new solution to the required two-dimensional unsteady separated flow problem based upon an unsteady discrete-vorticity wake. Data for the forces and moments on bodies of revolution at high angle of attack (outside the range of linear inviscid theories) such that the flow is substantially separated are produced which compare well with experimental data at low speeds. In addition, three-dimensional steady separation regions and wake vortex patterns are determined.

F. J. Marshall

Papers

Separated flow over a body of revolution

Iterative techniques for the solution of large linear systems in computational aerodynamics

Impulsive motion of a cylinder and viscous cross flow