超低轨卫星减阻多目标伴随优化设计

Multi-objective adjoint optimization for drag reduction of very low Earth orbit satellites

  • 摘要: 针对超低轨卫星在稀薄大气环境下的气动外形优化设计需求,发展了气体动理学伴随优化方法,开展了卫星主体三维外形的多目标伴随优化研究。优化对象为与“GOCE”和“SLATS”尺寸相当、运行于海拔150~300 km高度的迷你型卫星主体。优化中以CST参数化方法描述旋成体外形母线,以减小气动阻力和增大体积为优化目标,考虑卫星长度、最大直径及长细比的多重几何约束。卫星稀薄气体绕流采用BGK模型方程结合漫反射边界条件描述,并构建相应的伴随方程以实现设计敏感度的高效计算,最终通过梯度下降算法获得Pareto前沿上的优化外形集。优化结果显示:所发展的伴随优化方法可在10步左右收敛(20次左右动理学方程求解),单个Pareto点求解耗时约42 min;优化外形随体积增大主要呈现“水滴”形和钝前后缘柱体两类特征,其间存在独特的外形过渡区并存在膝点法决策的最终解;相比于同体积同约束圆柱体,优化外形减阻效果约11.0%~22.6%;并且150 km和300 km高度最优外形差异较小。该研究为超低轨卫星气动外形设计积累了经验,验证了伴随优化在稀薄流设计问题中的高效性、有效性以及应用潜力。

     

    Abstract: To optimize aerodynamic shapes of very low Earth orbit (VLEO) satellites operating in rarefied atmospheric environments, a gas-kinetic adjoint optimization method is developed, and multi-objective adjoint optimization research is conducted on the three-dimensional shape of the satellite body. The optimization targets the main body of mini-satellites with dimensions comparable to "GOCE" and "SLATS", operating at altitudes of 150~300 km. In the optimization, the generatrix of the axisymmetric body is parameterized using the CST method, with the objectives of reducing aerodynamic drag and increasing volume, while considering multiple geometric constraints on satellite length, maximum diameter, and slenderness ratio. The rarefied gas flow around the satellite is described by the BGK model equation combined with the diffuse reflection boundary condition. The corresponding adjoint equations are constructed to enable efficient computation of design sensitivities, and the set of optimal shapes on the Pareto front is finally obtained via a gradient descent algorithm. Optimization results show that the developed adjoint optimization method converges within about 10 optimization steps (20 solutions of kinetic equations), and the solution for a single Pareto point takes approximately 42 minutes. As the volume increases, the optimal satellites mainly exhibit two classes of shapes: "water-drop" shapes and cylindrical shapes with blunt leading and trailing edges, with a distinct shape transition region in between, where the final solution is determined by the knee point method. Compared to a cylindrical baseline of equal volume and constraints, the optimized shapes achieve drag reductions of approximately 11.0%~22.6%. Moreover, the optimal shapes at altitudes of 150 km and 300 km show little difference. This study provides valuable experience for the aerodynamic shape design of VLEO satellites, validating the high efficiency, effectiveness, and application potential of adjoint optimization in rarefied flow design problems.

     

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