The blended-wing body is an aircraft configuration that has the potential to be more efficient than conventional large transport aircraft configurations with the same capability. However, the design of the blended-wing is challenging due to the tight coupling between aerodynamic performance, prescription trim, cheap and stability. Other design challenges include the nature and number of the design variables involved, and the transonic flow conditions. To address these issues, we perform a series of aerodynamic shape optimization studies using Reynolds-averaged Navier–Stokes computational fluid dynamics with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. A total of 273 design variables—twist, airfoil shape, sweep, chord, and span—are considered. The drag coefficient at the cruise condition is minimized subject to lift, trim, static margin, and center plane bending moment constraints. The studies investigate the impact of the various constraints and design variables on optimized blended-wing-body configurations. The lowest drag among the trimmed and stable configurations is obtained by enforcing a 1% static margin constraint, resulting in a nearly elliptical spanwise lift distribution. Trim and static stability are investigated at both on- and off-design flight conditions. The single-point designs are relatively robust to the flight conditions, but further robustness is achieved through a multi-point optimization.
The first set of design variables consists of control points distributed on the FFD volume. A total of 240 shape variables are distributed on the lower and upper surfaces of the FFD volume, as shown in Fig. 1. The large number of shape variables provides more degrees of freedom for the optimizer to explore, and this allows us to fine-tune the sectional airfoil shapes and the thickness-to-chord ratios at each spanwise location. Because of the efficient adjoint implementation, the cost of computing the shape gradients is nearly independent of the number of shape variables .
The next set of design variables is the spanwise twist distribution. We use ten sectional twist design variables. The center of the twist rotation is fixed at the reference axis, which is located at the quarter chord of each section. The twist variables provide a way for the optimizer to minimize induced drag by controlling the spanwise lift distribution and a way to satisfy the center plane bending moment constraint.
Since optimizers tend to explore any weaknesses in numerical models and problem formulations, an optimization problem needs to be carefully constrained in order to yield a physically feasible design. We implement several geometric constraints. First, we impose thickness constraints from the 5% chord at the LE to the 95% chord near the TE. A total of 400 thickness constraints are imposed in the 20 by 20 grid. The constraints have a lower bound of 70% of the baseline thickness and no upper bound. These constraints ensure sufficient height in the centerbody cabin and sufficient fuel volume. The LE thickness constraint allows for the installation of slats, and the TE thickness is limited due to manufacturing constraints.
The total volume of the centerbody and the wing is also constrained to meet the volume re- quirements for the cabin, cargo, and systems, as well as fuel. The LE and TE shape variables are constrained such that each pair of shape variables on the LE and TE can move only in opposite di- rections with equal magnitudes, so that twist cannot be generated with the shape design variables. Instead, twist is implemented as a separate set of variables.
Because of the absence of a structural model, we use the bending moment at the center plane as a surrogate for the structural weight trade-off and to prevent unrealistic spanwise lift distributions and wing spans. This bending moment is constrained to be less than or equal to the baseline bend- ing moment. The bending constraint is necessary to capture the trade-offs between aerodynamic performance and structural weight. However, it is possible to perform these trade-offs with more accuracy by using high-fidelity aerostructural optimization, as done by Kenway and Martins .
In addition, the BWB has to be trimmed at each flight condition. Ideally, the aircraft is trimmed at the nominal cruise condition without requiring control surface deflection. Therefore, we freeze the sub-FFD, which rotates the trim control surface during the on-design optimization with the pitching moment constraint. The sub-FFD is then used in the analysis of off-design conditions. There are several ways to trim a flying wing: by unloading wingtip on a swept wing, by adding reflex to the airfoils at the TE, or a combination of both of these . Our optimization problem has all the required degrees of freedom to meet the trim constraint.
Longitudinal stability is also a particularly important design consideration for the BWB con- figuration. With the absence of a conventional empennage, it is not immediately obvious how to best achieve a positive static margin for a BWB aircraft. The goal is to maintain a positive static margin for all flight conditions. We constrained the static margin to be greater than 1%.