The vortex particle method (VPM) is a mesh-free approach to computational fluid dynamics (CFD) solving the Navier-Stokes equations in their velocity-vorticity form. The VPM uses a Lagrangian scheme, which not only avoids the hurdles of mesh generation, but it also conserves vortical structures over long distances with minimal numerical dissipation while being orders of magnitude faster than conventional mesh-based CFD. However, VPM is known to be numerically unstable when vortical structures break down close to the turbulent regime. In this study, we reformulate the VPM as a large eddy simulation (LES) in a scheme that is numerically stable, without increasing its computational cost. A new set of VPM governing equations are derived from the LES-filtered Navier-Stokes equations. The new equations reinforce conservation of mass and angular momentum by reshaping the vortex elements subject to vortex stretching. In addition to the VPM reformulation, a new anisotropic dynamic model of subfilter-scale (SFS) vortex stretching is developed. This SFS model is well suited for turbulent flows with coherent vortical structures where the predominant cascade mechanism is vortex stretching. Extensive validation is presented, asserting the scheme comprised of the reformulated VPM and SFS model as a meshless LES that accurately resolves large-scale features of turbulent flow. Advection, viscous diffusion, and vortex stretching are validated through simulation of isolated and leapfrogging vortex rings. Mean and fluctuating components of turbulent flow are validated through simulation of a turbulent round jet, in which Reynolds stresses are resolved directly and compared to experimental measurements. Finally, the computational efficiency of the scheme is showcased in the simulation of an aircraft rotor in hover, showing our meshless LES to be 100x faster than a mesh-based LES with similar fidelity. The ability to accurately and rapidly assess unsteady interactional aerodynamics is a shortcoming and bottleneck in the design of various next-generation aerospace systems: from electric vertical takeoff and landing (eVTOL) aircraft to airborne wind energy and wind farms. For instance, current models used in preliminary design fail to predict and assess configurations that may lead to the wake of a rotor impinging on another rotor or a wing during an eVTOL transition maneuver. In the second part of this dissertation, we address this shortcoming as we present a variable-fidelity CFD framework based on the reformulated VPM for simulating complex interactional aerodynamics. We further develop our meshless LES scheme to include rotors and wings in the computational domain through actuator models. A novel, vorticity-based, actuator surface model (ASM) is developed for wings, which is suitable for rotor-wing interactions when a wake impinges on the surface of a wing. This ASM imposes the no-flow-through condition at the airfoil centerline by calculating the circulation that meets this condition and by immersing the associated vorticity following a pressure-like distribution. Extensive validation of rotor-rotor and rotor-wing interactions predicted with our LES is presented, simulating two side-by-side rotors in hover, a tailplane with tip-mounted propellers, and a wing with propellers mounted mid-span. To conclude, the capabilities of the framework are showcased through the simulation of a multirotor tiltwing vehicle. The vehicle is simulated mid maneuver as it transitions from powered lift to wing-borne flight, featuring rotors with variable RPM and variable pitch, tilting of wings and rotors, and significant rotor-rotor and rotor-wing interactions from hover to cruise. Thus, the reformulated VPM provides aircraft designers with a high-fidelity LES tool that is orders of magnitude faster than mesh-based CFD, while also featuring variable-fidelity capabilities.



College and Department

Mechanical Engineering



Date Submitted


Document Type





vortex particle, interactional aerodynamics, multirotor, eVTOL, aircraft, large eddy simulation, meshless, mesh-free, CFD, LES



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Engineering Commons