This study aims to develop a regression model of the aerodynamic coefficients for leading edge inflatable (LEI) kite profiles. Aerodynamic data is obtained by 2D computational fluid dynamics (CFD) simulations for different Reynolds numbers, angle of attack and profile configuration, leading to the following: lift, drag and moment coefficients, as well as the surface distribution of pressure and skin friction coefficients. The machine learning regression model is trained on this multidimensional dataset to generate accurate 2D aerodynamic predictions, which serve as essential input for the vortex step method (VSM), a fast aerodynamic solver used in kite fluid-structure interaction (FSI) simulations.

The profile geometry parameterisation forms the backbone of the automated CFD toolchain. It provides an advanced and robust design framework for LEI kite profiles. The geometry is defined by its main components: a circular leading edge (LE) tube and a canopy, which is subdivided into two splines. The front spline connects the LE tube seam (i.e., the LE tube–canopy stitching connection) to the maximum camber point, while the rear spline extends from this point to the trailing edge (TE). Both splines are modelled as cubic Bézier curves with four control points, where the first and last points define the connection boundaries, enabling smooth and flexible surface shaping. The seam angle on the LE tube is dynamically calculated to ensure a smooth transition for any given configuration. The positions of the control points are governed by the following non-dimensionalised profile parameters, defined relative to the chord: LE diameter t, maximum camber chordwise position η, camber height κ, reflex angle δ, camber tension λ, and LE curvature φ. For meshing purposes, a finite thickness is assigned to the canopy to separate the upper and lower flow regions. Additionally, a LE fillet is added to the underside of the canopy to facilitate mesh smoothing at the sharp corner connection with the LE tube.

Aerodynamic data is collected from steady Reynolds-averaged Navier–Stokes (RANS) simulations, employing the k-omega shear stress transport (SST) turbulence model. The simulations are performed with the open-source CFD software OpenFOAM, using structured meshes generated in Pointwise. An extensive mesh sensitivity analysis was conducted, focusing on the effects of canopy thickness, the LE fillet, and the resolution of the fully structured grid in both normal and tangential directions. Transition modelling was omitted based on the assumption that the boundary layer undergoes forced transition at the LE tube seams. This includes the LE tube-canopy connection on the upper side and the LE closing seam on the lower side, where numerical results indicated that the flow transitions due to seam-induced roughness. Since the region upstream of the seams is small, its impact is considered negligible, justifying the simplification.

Due to the large number of simulations required, computational resources from the high-performance computing (HPC) cluster of the Faculty of Aerospace Engineering at TU Delft were utilised. To define the parameter configurations for data collection, a trade-off was made between parameter resolution and computational cost. Parameters were sampled across the following ranges for three Reynolds numbers (Re = 1 x 10^6, 5 x 10^6, and 2 x 10^7): α from -22° to -10° (13 values), t from 0.03 to 0.12 (5 values), η from 0.08 to 0.4 (8 values), κ from 0.04 to 0.16 (7 values), δ from -8° to 0° (4 values), and λ from 0.1 to 0.4 (4 values). The LE curvature φ was held constant at 0.65.

The flow fields were analysed for the effects on the newly introduced parameters in the updated profile geometry model: δ, λ, and φ. Downward deflections of the profile TE due to negative δ resulted in reduced lift and increased drag performance, while enhancing longitudinal pitching moment stability. In contrast, variations in λ showed the opposite effect; increased camber tension resulted in higher lift and drag values but diminished longitudinal stability. The parameter φ, having minimal geometric influence, caused negligible changes in aerodynamic performance, only slightly altering the pressure distribution. Consequently, φ was fixed in the regression model. Among all tested algorithms, the extra trees (ET) model achieved the highest predictive accuracy, with R2 scores of 0.987 for Re = 1 x 10^6, 0.988 for 5 x 10^6, and 0.989 for 2 x 10^7.