This paper presents the results of research conducted by Alenia (Italy), Dasa (Germany), DERA (United Kingdom), NLR (The Netherlands), and DLR (Goettingen, Germany) as part of the Western European Armaments Group (WEAG) TA15 program, Common Exercise V. The WEAG TA15 program was a collaborative program concerned with the investigation of steady and unsteady vortical flows over military aircraft configurations. An important component of the program were the Common Exercises (CE), which promoted the exchange of knowledge between the participating nations and aided the development of computational methods to predict vortical flows. As the analysis of flow fields about rolling delta wings is of high interest, the last CE of this group concentrated on the numerical and experimental investigation of unsteady flow over a 65 degree swept delta wing in rolling motion at transonic speed. Guided by previous work on unsteady motions, the numerical investigation was again restricted to unsteady Euler methods. Each participant for the numerical calculations was asked to perform unsteady Euler calculations for given test cases using a mandatory grid and a given number of physical time steps per period. Numerical calculations with different unsteady Euler methods using a common grid were performed at a constant rolling rate of omega(r)=0.0762 for different angles of incidence: alpha(sub 0)=0 degrees, alpha(sub 0)=10 degrees, and alpha(sub 0)=17 degrees. The numerical results reveal that the different spatial discretizations lead to characteristic differences mainly in the magnitudes of the vortex-induced suction peaks in the unsteady pressure distributions and in the prediction of vortex breakdown. The results should finally result in the development of a data base for further code validation. (13 figures, 14 refs.).

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling, highly swept delta wings undergoing either forced motions or free-to-roll motions that include active roll suppression. The flow solver of the code involves a multistage, Runge-Kutta time-stepping scheme that uses a cell-centered, finite-volume, spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free to-roll case by simultaneously integrating in time the rigid-body equation of motion with the governing flow equations. Results are presented for a delta wing with a 75 deg swept, sharp leading edge at a free-stream Mach number of 1.2 and at 10 deg, 20 deg, and 30 deg angle of attack alpha. At the lower angles of attack (10 and 20 deg), forced-harmonic analyses indicate that the rolling-moment coefficients provide a positive damping, which is verified by free-to-roll calculations. In contrast, at the higher angle of attack (30 deg), a forced-harmonic analysis indicates that the rolling-moment coefficient provides negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation, which is characteristic of highly swept delta wings. This limit cycle oscillation may be actively suppressed through the use of a rate-feedback control law and antisymmetrically deflected leading-edge flaps. Descriptions of the conical Euler flow solver and the free-to roll analysis are included in this report. Results are presented that demonstrate how the systematic analysis of the forced response of the delta wing can be used to predict the stable, neutrally stable, and unstable free response of the delta wing. These results also give insight into the flow physics associated with unsteady vortical flows about delta wings undergoing forced m...

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon. Lee, Elizabeth M. and Batina, John T. Langley Research Center RTOP 505-63-21-01...

This report presents computations of the flowfield around an 80 degree sweep delta wing undergoing a constant roll-rate maneuver from 0 to 45 degrees. The governing equations for the problem are the unsteady, three- dimensional Navier-Stokes equations. The equations are solved using the implicit, approximately-factored algorithm of Beam-Warming. Fixed roll angle results are also presented and compared with experimental measurements to demonstrate the ability of the numerical technique to accurately capture the flowfield around a rolled delta wing. The dynamic behaviors of the vortex position and strength, as well as their corresponding effect on surface pressure, lift and roll moment, are described. A simple, quasi-static explanation of these vortex behaviors based on effective angle-of-attack and sideslip angle is proposed ... Delta wing roll, Vortex dynamics, Vortical flow, Unsteady maneuver.