Accurate aero-structural modelling of leading-edge inflatable kites is essential for scaling up airborne wind energy systems. Yet, existing approaches make simplifications on either the wing or the bridle line system. This paper presents a fast finite element modelling framework that integrates the wing structure and bridle lines into a single model. The finite element framework captures material and geometric non-linearities using the Newton–Raphson scheme with a co-rotational formulation. The bridle line system is represented using non-compressive springs, which are also used to represent pulleys. Inflatable leading edge and strut tubes are modelled as Timoshenko beam elements, with beam properties tuned iteratively to match experimentally fitted inflatable beam equations. The canopy is represented using non-compressive spring elements, allowing for the resolving of billowing effects. The framework is applied to the V3 kite, and validation is performed against stereoscopic photogrammetry measurements obtained from static load tests under varying internal pressures and external loads. The results demonstrate good agreement with measured kite shapes for most cases, confirming the model’s ability to capture the dominant structural behaviour of leading-edge inflatable kites. The proposed framework provides a basis for aero-structural analysis in kite design, and enables future coupling with aerodynamic models for steady and quasi-steady kite simulations.

The transition to sustainable energy sources is increasingly urgent, driving innovation in renewable energy technologies. Airborne wind energy (AWE) is a promising emerging alternative to conventional wind turbines, using tethered kites to harvest wind energy at higher altitudes where wind speeds are stronger and more consistent, while requiring significantly less material. Kitepower B.V. employs a leading-edge inflatable (LEI) kite flying in crosswind patterns to generate traction force on a tether that is reeled out from a ground-based drum connected to a generator. Energy is produced through repeated reel-out and energy-efficient reel-in cycles. As Kitepower is currently in active development, the kite design process requires many iterative design cycles and extensive testing, which are time-consuming, expensive, and heavily reliant on expert knowledge. This thesis investigates the application of multidisciplinary design analysis and optimisation (MDAO) to the geometric design of a LEI kite for ground-generation crosswind AWE systems, with specific focus on the system developed by Kitepower B.V. A computational framework is propose that integrates kite shape parametrisation, aerodynamic and structural analysis, and performance modelling within an MDAO toolchain. The kite geometry is described using a set of decoupled parameters that enable systematic reshaping while maintaining consistent reference properties. Two simulation frameworks are proposed to support this concept. The first is a conceptual high-fidelity toolchain that integrates aerodynamic, structural, and dynamic performance models, intended to guide future development of a fully coupled MDAO environment. The second is a simplified, computationally efficient toolchain that was implemented to enable quantitative optimisation under realistic time constraints. Using annual energy production as the optimisation objective, the implemented toolchain is employed to verify the optimisation methods and evaluate performance improvements relative to a reference kite design within a constrained design space. The results demonstrate that MDAO can effectively support early-stage geometric kite design for AWE applications, offering a fast, systematic alternative to traditional expert-driven design iteration.

Quantitative in-flight deformation data are required to validate coupled aero-structural models of soft-wing kites. This work presents an end-to-end measurement framework that combines stereoscopic photogrammetry with ultra-wideband (UWB) ranging on an instrumented Gamma-shaped bar to reconstruct large-scale wing deformations under operational conditions. Stereo marker tracking yields a 3D point cloud that is corrected using UWB-derived span information, enabling robust shape comparison across manoeuvres. Deformation states are quantified for depowering and turning and are compared against a commonly used undeformed CAD reference employed in aerodynamic analyses. The resulting dataset improves the quantitative characterisation of soft-wing deformation and provides validation input for aero-structural models, supporting improved kite design and providing a pathway towards deformation-aware monitoring and (near) real-time control.

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.

This study investigates the aerodynamic behaviour of two-dimensional rigid leading-edge inflatable (LEI) airfoils through experiments in TU Delft’s Low Turbulence Tunnel and computational fluid dynamics (CFD) simulations. Lift and drag coefficients were measured for two steel scale models at Reynolds numbers of 5×10⁵ and 10⁶ and angles of attack between −10° and 25°. Corrections were applied for wall and wake-rake effects, and transition behaviour was analysed using infrared imaging and oil flow visualization. CFD simulations using OpenFOAM with the k–ω and 𝛾 − R̃e𝜃t models were compared to the experimental data. Fully turbulent CFD results showed the best agreement with measurements, while transition models performed inconsistently. Infrared and oil-flow data revealed fixed or moving transition zones, corner eddies, and a laminar separation bubble. This work provides the first dedicated experimental dataset for rigid LEI airfoils and validates CFD toolchains for future aerodynamic analysis of soft-wing kites.

Final Report Design Synthesis Exercise Spring 2024. AE3200: Design Synthesis Exercise. DSE Group 22

Computational Fluid Dynamics (CFD) simulations of objects like the Kitepower V3A Leading Edge Inflatable (LEI) kite require accurate experimental data for validation. However, for these kites, particularly in steady-state simulations, such data is scarce. LEI kites are soft and deform continuously during flight, making validation complex. To address this, a unique experiment in the Open Jet Facility (OJF) at TU Delft, testing a rigidized subscale model of the V3A kite, marking the first wind tunnel test on a rigid kite.

The rigid model was made of carbon fiber reinforced polymer and mounted on a custom support structure that allowed adjustments to the kite’s angle of attack and sideslip. Aerodynamic forces and moments were measured at different wind speeds and orientations, with and without zigzag tape to study its effects on low Reynolds number flow.

The results were compared to existing CFD simulations, including Reynolds-Averaged Navier-Stokes (RANS) and vortex step methods. The experimental data aligned well with these simulations at low Reynolds numbers, validating the setup. However, some discrepancies highlighted areas for improvement, such as reducing interference from the support structure and better matching Reynolds numbers between simulations and experiments.

The Airborne Wind Energy industry is evolving rapidly, aiming to establish its position among the major players in the conventional renewable energy sector. Since this industry is relatively young, it faces various challenges with scaling and integration into society. One aspect that can be improved is the design process of soft-wing kites. The aim is to shift from design iterations based on experience-based hardware modifications and experimental testing to design iterations based on optimization strategies using computational simulations. For optimization-based design to be a feasible option, it requires computationally efficient underlying models. This report presents the results of thesis research that aimed to develop a fast and reasonably accurate framework for structural modeling of soft-wing kites and connected tethers.

Deformation of leading-edge inflatable kites is essential for steering and controlling aerodynamic loads. Modeling of deformation is therefore indispensable, resulting in a highly non-linear fluid-structure interaction problem. Currently, a particle system model (PSM) is the preferred choice for modeling soft-wing kites because it can simulate deformations while converging faster than other methods. The existing PSM code in Java is outdated and the current academic preference has switched to developing in Python. This led to the central research question: “Can the PSM be implemented in Python, using a
mix of Object-Oriented (OO) and non-OO programming techniques, to efficiently predict deformation?”.

While a framework was implemented based on the original Java code, it was also investigated whether it is possible to modify the solution-finding method for the structural model to improve convergence times without loss of accuracy. The aeroelastic problem can be simplified into a series of form-finding problems by assuming a quasi-steady flow. Three main families of form-finding methodologies are presented that are capable of finding solutions. Based on their properties and computational efficiency, the kinetic damping algorithm was selected as having the most potential for improving the current particle system implementation.
The kinetic algorithm was originally developed for a dynamic relaxation method that used an explicit integration scheme. Kinetic damping has never been combined with an implicit integration scheme. Slight adjustments needed to be made to the algorithm’s implementation as the current particle system
employs an implicit scheme. Analysis of verification tests revealed characteristics of the utilized implicit Euler scheme. One notable effect was numerical damping, which hurt the performance of the kinetic damping algorithm. It was discovered that the algorithm’s performance was more consistent by disabling the quadratic correction.

Validation testing showed that each method is capable of accurately predicting the shape of tether and bridle line systems. To accurately simulate the deformation of membranes, more consideration must be given to the development of the PSM that represents the considered membrane continuum.
Next, the runtimes of the self-coded solver with explicit computation of Jacobian matrices and the framework with kinetic damping algorithm were compared to the performance of a black-box solver. It was found that the framework outperformed a black-box solver in runtime, demonstrating the advantage of
using the self-coded solver. Finally, benchmarking results indicated that the modified kinetic damping algorithm, despite some limitations, generally improved runtimes. Further investigation of the scaling of the runtime against increasing amounts of DOF indicated that the current framework could be fast enough for simulation in the range of 15 to 60 particles, despite the framework’s current non-optimized state.