Adjoint Optimization for Hyperloop Aerodynamics

This work investigates how the vehicle-to-tube suspension gap governs compressible flow physics and operating margins in Hyperloop-class transport at 10 kPa. To our knowledge, this is the first study to apply adjoint aerodynamic optimization to mitigate gap-induced choking and shock formation in a full pod–tube configuration. Using a steady, pressure-based Reynolds-averaged Navier-Stokes (RANS) framework with the GEnerlaized K-Omega (GEKO) turbulence model, a simulation for the cruise conditions was performed at M = 0.5–0.7 with a mesh-verified analysis (medium grid within 0.59% of fine) to quantify gap effects on forces and wave propagation. For small gaps, the baseline pod triggers oblique shocks and a near-Kantrowitz condition with elevated drag and lift. An adjoint shape update—primarily refining the aft geometry under a thrust-equilibrium constraint—achieves 27.5% drag reduction, delays the onset of choking by ~70%, and reduces the critical gap from d/D ≈ 0.025 to ≈0.008 at M = 0.7. The optimized configuration restores a largely subcritical passage, suppressing normal-shock formation and improving gap tolerance. Because propulsive power at fixed cruise scales with drag, these aerodynamic gains directly translate into operating-power reductions while enabling smaller gaps that can relax tube-diameter and suspension mass requirements. The results provide a gap-aware optimization pathway for Hyperloop pods and a compact design rule-of-thumb to avoid choking while minimizing power.