Adjoint-based optimization method for aerodynamic-stealth of aircraft considering the scattering characteristics of absorbing materials

With the continuous advancement of radar detection and counter-detection technologies, relying solely on stealth shaping can hardly meet the stealth performance requirements of advanced aircraft in a wide electromagnetic frequency domain. Meanwhile, stealth materials have evolved from the initial large-area spray-on absorbing coatings on the airframe to systematic stealth coatings and multifunctional stealth structures, with increasing specificity of application. Establishing an aerodynamic-stealth optimization design method for aircraft that accounts for the scattering characteristics of radar-absorbing materials can mitigate the adverse effects of shape design driven by stealth requirements on aerodynamic and flight performance, while ensuring stealth performance under wideband conditions. Therefore, to address the wideband omnidirectional stealth challenges of advanced aircraft, this study integrates the impedance boundary condition (IBC) theory and the S-parameter inversion method based on effective medium theory (EMT) to construct a calculation method for electromagnetic scattering characteristics of targets with electromagnetic metamaterials and coated media. Furthermore, an adjoint equation for the electromagnetic field for metal-dielectric hybrid targets is established, and the multi-level fast multipole expansion of the adjoint equation is derived. On this basis, an adjoint optimization method for aircraft aerodynamic-stealth design considering the scattering characteristics of absorbing materials is proposed. This adjoint method enables fast calculation of the gradients of aerodynamic and stealth objectives in the design problem, and the sequential quadratic programming (SQP) algorithm is then applied for optimization search. Optimization design is carried out on a typical flying wing configuration with local absorbing coating. The results show that the pressure drag of the optimized shape is significantly reduced under subsonic conditions at Ma = 0.8 and Ma = 0.85, decreasing by 33% and 35%, respectively. Meanwhile, the mean radar cross section (RCS) within the target angular domain θ = 85°–95°, φ = 135°–225° is reduced by approximately 18%. The proposed method can improve the aerodynamic-stealth performance of the aircraft to a certain extent and can serve as a reference for the shape and coating design of aircraft incorporating radar-absorbing materials.