An immersed lifting and dragging line model for the vortex particle-mesh method

Abstract

The numerical study of the wake of full-scale slender devices such as aircraft wings and wind turbine blades requires high-fidelity large eddy simulation tools. The broad spectrum of scales involved entails the use of coarse-grain models for the devices. Actuator disk or line methods have been developed for that purpose, and are to date the most employed in that context. These methods transfer the force from the device to the fluid using 3D mollification functions. A novel immersed lifting and dragging line method is here presented, together with its implementation in a hybrid vortex particle-mesh flow solver. The line models the effect of blades or wings on the flow through the generation of vorticity, in a Lagrangian manner. This has several advantages over the treatment inherent to actuator methods: The absence of mollification in the spanwise direction and the relaxation of the classical Courant-Friedrichs-Lewy condition contribute to keeping the accuracy and the efficiency at a high level. The method is thoroughly verified against theory using results on various airfoils and wings. Finally, the efficiency of the approach is illustrated with the simulation of the wake of an elliptical wing. The role of parasitic drag in the development of wake instabilities is pointed out, by comparing configurations with none, moderate and high profile drag. In the last case, the simulation captures the fine scales vortex dynamics and the establishment of a turbulent wake over a length of 30 wing spans.

Unsteady lifting-line theory and the influence of wake vorticity on aerodynamic loads

“…Sugar-Gabor et al [59] suggested a method where the unsteady wake was only accounted for in the outer 3D problem, allowing for roll and yaw kinematics. Lifting-line theory has also been used to model wings in large-scale simulations where resolving the chord-scale would be prohibitively expensive, for example, in Caprace et al [11].…”

A Review of Vortex Methods and Their Applications: From Creation to Recent Advances

“…The simulations performed in this study allowed, in particular, to precisely describe the vortex dynamics involved in the generation of the two main wake vortices of the rotorcraft thanks to thorough 3-D visualizations. For further details about the ILL approach in a VPM framework, one also refers to [99], by the same authors.…”

“…An important difference between the diverse existing VIC schemes concerns the remeshing procedure in step 2. For example, in Caprace et al [99], the particles are remeshed on the underlying Cartesian grid only every 5 times steps, while in Mimeau et al [100] the remeshing procedure relocate the particles on the grid points every time steps, implying the presence of a particle at each node of the Cartesian mesh, at any time. In this particular latter case, one talks about "Semi-Lagrangian Vortex methods".…”

“…However, this approach is limited because of its low order and accuracy. The very recent introduction of immersed interface method (IIM) [131,132] and immersed lifting line approach (ILL) [12,99] introduced a real improvement and allows us to start a real progress in the challenging field of FSI. • Environmental and industrial particular flows.…”

Vortex-to-velocity reconstruction for wall-bounded turbulence via the field-based linear stochastic estimation

“…It should be addressed that the current work mainly considers the kinematic representation of wall turbulence. The current V2V reconstruction is also different from the vorticity-based velocity reconstruction involved in the vortex method for simulating the Navier–Stokes equations (Leonard 1985; Koumoutsakos & Leonard 1995; Bernard 2013; Caprace, Winckelmans & Chatelain 2020). In those works, the velocity field is reconstructed based on the vorticity field.…”