Adjoint-Based Aerodynamic Optimization of Supersonic Biplane Airfoils

Abstract

This paper addresses the aerodynamic performance of Busemann type supersonic bi-plane at off-design conditions. An adjoint based optimization technique is used to optimize the aerodynamic shape of the biplane to reduce the wave drag at a series of Mach numbers ranging from 1.1 to 1.7, at both acceleration and deceleration conditions. The optimized biplane airfoils dramatically reduces the effects of the choked flow and flow-hysteresis phenomena , while maintaining a certain degree of favorable shockwave interaction effects at the design Mach number. Compared to a diamond shaped single airfoil of the same total thickness, the wave drag of our optimized biplane is lower at almost all Mach numbers, and is significantly lower at the design Mach number.

Numerical analysis of static and dynamic performances of grid fin controlled missiles

“…Results on the drag coefficient for these two fins are presented in figure 14, along with experimental results obtained by other researchers on globally 12, 41 and locally 40 swept back grid fins with sharp leading edges. The evolution of the drag for the standard grid fin is in good agreement with the two experiments carried out by Debiasi 41 and Schuleïn and Guyot, 40 whereas the drag of the "Busemann" grid fin is consistent with the 2D numerical calculations performed by Hu et al 22 on the original Busemann biplane geometry. Although the drag is not decreased in the transonic regime due to the choking occurring in the cells in all cases, it is significantly reduced at higher Mach numbers for the "Busemann" grid fin, where a partial wave cancellation effect is observed.…”

“…However, the application of this concept has been limited due to no lift generation of such configurations and the significantly high drag generated when operating outside design conditions. 21,22 Recent studies aiming at designing an efficient and silent supersonic airplane have made use of optimization methods to improve the performance of the Busemann biplane in a wider range of operating conditions. 21,22 The performance of two geometries are compared in this work: a simple "standard" grid fin of same chord and thickness as the one studied in section IV, and a "Busemann" grid fin of similar chord and average thickness.…”

“…Moreover, another approach to reduce the wave drag is presented and consists in modifying the fin's geometry according to the Busemann biplane concept to take advantage of the "wave cancellation effect", which has recently regained in popularity in view of its application to silent and efficient supersonic airplanes. 21,22 The remainder of this paper is as follows. The numerical technique employed to calculate the pitch damping coefficient of a lattice fin missile is briefly described in the first section.…”

Transonic flow instability in the entrance region of a channel with breaks of walls

“…The calculated shock positions and drag coefficient (Fig. 2b) were undistinguishable from numerical data documented in [5,6].…”

“…Then, we analyze flow features arising at α = 0 (Sect. 5). After that we concentrate on the flow behavior at α = −2 • , when the channel is divergent along its full length (Sect.…”