Surrogate-assisted airfoil optimization in rarefied gas flows

Abstract

With growing interest in space exploration, optimized airfoil design has become increasingly important. However, airfoil design in rarefied gas flows remains underexplored because solving the Boltzmann equation formulated in a six dimensional phase space is time consuming. To address this problem, a solver-in-the-loop Bayesian optimization framework for symmetric, thickness-only airfoils is developed. First, airfoils are parameterized using a class shape transformation that enforce geometric admissibility. Second, a Gaussian process expected improvement surrogate is coupled in batches to a fast converging, asymptotic preserving Boltzmann solver for sample efficient exploration. Drag minimizing airfoils are identified in a wide range of gas rarefaction. It is found that, at Mach numbers Ma=2 and 4, the streamwise force increases with the gas rarefaction and shifts from pressure dominated to shear dominated drag, while optimization reduces drag at all conditions. The benefit of optimization peaks in the weakly rarefied regime, about 30% at Ma=2 and 40 to 50% at Ma=4, and falls to a few percent in transition and free-molecular flow regimes. Drag decomposition shows that these gains come mainly from reduced pressure drag, with viscous drag almost unchanged. The optimal airfoils form a coherent rarefaction-aware family: they retain a smooth, single-peaked thickness profile, are aft-loaded at low gas rarefaction, and exhibit a forward shift of maximum thickness and thickness area toward mid-chord as gas rarefaction increases. These trends provide a physically interpretable map that narrows the design space.

Figures (12)

• Figure 1: Representative meshes for the four endpoint topologies.
• Figure 2: Surrogate-assisted optimization workflow at a fixed operating condition $(M_\infty,\mathrm{Kn})$.
• Figure 3: Flowfield comparison at $\mathrm{Ma}=2$ between the initial (left column) and optimized (right column) airfoils. The Knudsen numbers are 0.01 and 0.50 in the top and bottom rows, respectively.
• Figure 4: Geometry-only comparison between our optimized thickness distributions and the shape optimization method yuan2025adjoint at $\mathrm{Ma}=2$. First row: physical-scale view at $\mathrm{Kn}=0.01$ (left) and $\mathrm{Kn}=0.50$ (right). Second row: vertically magnified view.
• Figure 5: Optimized airfoil shapes at $M_\infty=2$ at 11 different Knudsen numbers. The flow is from left to right.