Gradient-Based Internal–External Flow Coupling Optimization for Embedded-Inlet Aircraft

As aerodynamic configurations become increasingly integrated with propulsion systems, internal–external flow coupling has become a key issue in airframe–engine integration. For embedded-inlet configurations, however, the airframe and inlet/exhaust system have different geometric shaping requirements, making their design variables difficult to represent within a unified gradient-based optimization framework. This study develops a continuous parameterization method for embedded inlets that simultaneously controls cross-sectional profiles, area distribution, and centerline under large cross-sectional rotation angles. The method combines B-spline curves, shape blending functions, quaternion-based transformations, and free-form deformation (FFD) to establish a hybrid parameterization framework for coupled internal–external flow optimization. Analytical geometric sensitivities of the inlet surface mesh with respect to profile, area-distribution, and centerline variables are derived through the complete parameterization chain and coupled with discrete-adjoint flow sensitivities, enabling gradient evaluation for both external aerodynamic-shape and internal inlet-geometry variables. The framework is applied to full-configuration multipoint optimization of an aircraft with an embedded inlet. Aerodynamic drag is reduced by 2.82% and 2.36% at the two design points, while inlet drag decreases by 4.44 and 4.63 counts (1 count = 0.0001). Under distortion-coefficient and mass-flow-rate constraints, the inlet-exit total pressure recovery coefficient increases by 0.54% and 0.41%, respectively. These results demonstrate the effectiveness of the proposed method for integrated internal–external flow optimization and its potential for airframe–engine integrated design.