Development of a Vortex Particle Code for the Modeling of Wake Interaction in Distributed Propulsion

Abstract

Recent developments in electric aircraft technology have enabled the use of distributed propulsion for the next generation of vertical lift vehicles. However, the ability to rapidly assess the performance of these design concepts, with sufficient fidelity, is a current weakness of this nascent industry. This paper explores the capacity of the viscous Vortex Particle Method (VPM) to model wake interactions found in distributed propulsion. The elements of the vortex particle method are summarized, and a new approach for the calculation of vortex stretching through the complex-step derivative approximation is presented. Preliminary validation is performed on vortex ring cases resembling the fundamental dynamics encountered in propeller wakes. Unsteady wake dynamics of individual propellers are successfully modeled, replicating the instabilities that lead to vortex breakdown as observed experimentally. Comparing the method with results from momentum theory, it is shown that VPM is consistent with theoretical values of near and far field induced velocities, and a notable feature is its ability to model near/far field transition. Furthermore, VPM is able to fully characterize induced velocities across the entire wake, from the stable region where momentum theory operates, through instability transition and eventual vortex breakdown. The simulation of a multirotor configuration of two tip-to-tip propellers is shown, displaying the capacity of VPM to model wake mixing. The results presented here are intermediate steps in the development of a mid-fidelity modeling tool for the early design stages of distributed-propulsion electric aircraft.

Takeoff and Performance Trade-Offs of Retrofit Distributed Electric Propulsion for Urban Transport

“…Reported error bars in the wind tunnel data are included in fig. 6b and are due to the dynamic nature of the propeller helical vorticies [26]. The two VLMs tend to follow the experimental trends except where the propeller swirl velocity induces wing upwash in the half-span regions between advance ratios 0.2 and 0.3.…”

“…Propeller wakes generally reach their far-field values within approximately one rotor radius [26]. In this conceptual design study, we model the propeller as being removed one radius or more from the wing for the far-field values to be applied on the wing.…”

Modeling Multirotor Aerodynamic Interactions Through the Vortex Particle Method

“…The FMM approximates pairwise interactions of particles through spherical harmonic functions, 40,41 reducing the original computational complexity to a problem of order O(N ). The computation of the vortex stretching is performed through an efficient complex-step derivative approximation as explained in previous work, 21 implemented in a modified version of the open-source, parallelized FMM code ExaFMM. 42,43…”

“…In a previous study 21 we have shown that the VPM is able to fully characterize the evolution of the wake, from near field to far field and transition into turbulent breakdown. Furthermore, the VPM is a direct-numerical simulation approach, requiring an increased spatial resolution in the turbulent breakdown regime to ensure convergence.…”

“…2 shows a low-fidelity simulation of a full-aircraft configuration and a high-fidelity simulation of wake mixing of two counter-rotating rotors from previous work by the authors using VPM. 21 In recent work, VPM has been coupled with a noise code based on the Ffowcs Williams-Hawkings equation, successfully predicting rotor acoustics associated to unsteady loading. 36 Furthermore, the method has been shown to be CPU and GPU parallelizable, and scalable in heterogeneous systems for high performance computing.…”