Brigham Young University BYU ScholarsArchive Faculty Publications 2020-8 High-Fidelity Modeling of Multirotor Aerodynamic Interactions for Aircraft Design Eduardo Alvarez Brigham Young University, [email protected] Andrew Ning Brigham Young University, [email protected] Follow this and additional works at: https://scholarsarchive.byu.edu/facpub Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Alvarez, Eduardo and Ning, Andrew, "High-Fidelity Modeling of Multirotor Aerodynamic Interactions for Aircraft Design" (2020). Faculty Publications. 4179. https://scholarsarchive.byu.edu/facpub/4179 This Peer-Reviewed Article is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Faculty Publications by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Postprint version of the article published by AIAA Journal, Aug 2020, DOI: 10.2514/1.J059178. The content of this paper may differ from the final publisher version. The code used in this study is available at github.com/byuflowlab/FLOWUnsteady. High-fidelity Modeling of Multirotor Aerodynamic Interactions for Aircraft Design Eduardo J. Alvarez ∗ and Andrew Ning.† Brigham Young University, Provo, Utah, 84602 Electric aircraft technology has enabled the use of multiple rotors in novel concepts for urban air mobility. However, multirotor configurations introduce strong aerodynamic and aeroacoustic interactions that are not captured through conventional aircraft design tools. In this paper we explore the capability of the viscous vortex particle method (VPM) to model multirotor aerodynamic interactions at a computational cost suitable for conceptual design. A VPM-based rotor model is introduced along with recommendations for numerical stability and computational efficiency. Validation of the individual rotor is presented in both hovering and forward-flight configurations at low, moderate, and high Reynolds numbers. Hovering multirotor predictions are compared to experimental measurements, evidencing the suitability of the proposed model to capture the thrust drop and unsteady loading produced by rotor-on- rotor interactions. I Introduction Technology convergence in the past ten years has opened a new design space in electric aircraft, enabling the use of distributed propulsion and electrical vertical takeoff and landing (eVTOL) for urban air mobility [1–4]. The concept of eVTOL in an urban setting is forecasted to evolve into a $1.5 trillion “flying car" industry by the year 2040 [5]. However, this unconventional aircraft configuration poses technical challenges that still remain to be solved [6]. A strong noise signature [7, 8] and a complicated transition maneuver [9, 10] are examples of the challenges encountered in eVTOL aircraft, both stemming in some degree from the aerodynamic interactions between rotors and lifting surfaces [11]. Furthermore, these interactions are common across quadrotor, tilt-rotor, tilt-wing, and distributed propulsion concepts making use of multiple rotors. As an example of eVTOL configuration, Fig. 2 shows NASA’s GL-10 tilt-wing prototype aircraft during vertical takeoff, prior to transitioning into wing-borne forward flight. The use of multiple rotors operating in close proximity introduces strong aerodynamic interactions that are not well understood, are not captured through conventional design tools, and need to be addressed in the conceptual design stage [12–15]. Experimental studies of side-by-side rotors in hover show a drop in thrust of 3–4% [16–19] due to rotor-on-rotor interactions. More remarkably, Zhou et al. [20] and Ning [21] measured a noise increase of 3 dB associated with unsteady loading as the distance between rotors is decreased. In edgewise forward flight, Stokkermans et al. [22] found that the interactions can become as drastic as to drop the thrust by 30%. Wake mixing and the unsteady Fig. 2 NASA GL-10 eVTOL prototype aircraft during vertical takeoff. Credits: NASA Langley/David C. Bowman. ∗Doctoral Candidate, Department of Mechanical Engineering, [email protected], AIAA Member. †Assistant Professor, Department of Mechanical Engineering, [email protected], AIAA Senior Member. 1 dynamics responsible for these effects are not captured through low-fidelity models used in conventional design tools. Multiple panel and filament methods have been developed for the modeling of unsteady free wakes, but experience shows that the requirement of preserving wake connectivity makes them ill-conditioned for the modeling of wake mixing [23]. These interactions can be analyzed through conventional computational fluid dynamics (CFD) approaches, like Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulations (LES) [24–29], but computational cost makes them prohibitive for design space exploration. Hence, the ability to rapidly assess the performance of these design concepts, with sufficient fidelity, is a current weakness of the nascent eVTOL industry. In this study we investigate the accuracy of the viscous vortex particle method [31, 32] (VPM) in modeling rotor-on-rotor aerodynamic interactions in a side-by-side configuration as encountered in tilt-wing, quadrotor, and distributed propulsion aircraft. The viscous VPM is a mesh-free CFD method for the numerical solution of the Navier-Stokes equations in their vorticity form. The VPM is a direct numerical simulation that efficiently preserves vortical structures in a Lagrangian scheme, eliminates the complexities of mesh generation, is absent of the numerical dissipation associated with mesh-based CFD, and is one to three orders of magnitude faster than RANS or LES∗. This method has been shown to achieve a continuum of fidelity levels across resolved scales, from medium fidelity apt for conceptual-design [33–40] to high fidelity apt for fundamental fluid dynamics research [41–43]. Fig. 3 shows a mid-fidelity simulation of a full-aircraft configuration and a high-fidelity simulation of wake mixing in side-by-side propellers from previous work by the authors [30]. Furthermore, the method has been shown to be CPU and GPU parallelizable, and scalable in heterogeneous systems for high performance computing [44–46]. In previous work by the authors, the computational speed of the VPM has been demonstrated in a parametric study comprised of 1000+ multirotor simulations, requiring a wall-clock time of less than four days on a desktop computer with an average of four minutes per simulation [47]. Thus, coupled with an acoustics solver, the VPM approach could enable high-fidelity aerodynamic and aeroacoustic predictions capturing multirotor interactions during conceptual design. The viscous VPM has been used in the rotorcraft community for the past two decades [48–52] demonstrating its efficiency in modeling wake-dominated problems, especially in the cases of coaxial rotors [53–55] and edgewise forward flight [42, 50, 56–60]. More recently, Tan et al. modeled the interactions between tandem rotors subjected to ground effect [61] and simulated the interactions between a tilt-rotor aircraft and a tandem-rotor helicopter while simultaneously landing on a ship deck [62], demonstrating the capacity of the VPM to capture intricate aerodynamic interactions. When coupled with the acoustic Ffowcs Williams-Hawkings equation, VPM-based simulations of isolated rotors have shown good agreement between experimental and predicted noise radiated from unsteady airloads, high-speed impulsive effects, and blade-vortex interactions [49, 63, 64]. Even though VPM has been extensively used in coaxial rotors and rotorcraft forward flight, little work has been done in modeling the side-by-side multirotor configuration encountered in eVTOL. This case is especially challenging because it needs to capture rotor-on-rotor interactions across the entire flight envelope of the eVTOL aircraft, from hover during takeoff to low and high advance ratios during transition and cruise, at both low and high Reynolds numbers [10]. In addition to performance predictions, it is also crucial to capture the unsteady loading introduced by rotor-on-rotor interactions in order to lay the groundwork for future noise predictions [65]. In this study we introduce Fig. 3 Mid-fidelity VPM simulation of eVTOL aircraft (left) and high-fidelity VPM simulation of multirotor wake mixing [30] (right). ∗In the author’s experience, a RANS simulation of two side-by-side rotors in STAR-CCM+ requires about 1000 processor hours. Meanwhile, a VPM simulation with FLOWVPM, at a comparable resolution, requires only 3 processor hours. 2 a VPM-based multirotor model and present extensive validation across the flight envelope. A summary of VPM theory and the numerical schemes used in this study are presented in Section II. The multirotor model is introduced in Section III along with a convergence study and recommendations for numerical stability and computational efficiency. In Sections IV.B and IV.C, validation of the individual rotor is presented in both hovering and forward-flight configurations at low, moderate, and high Reynolds numbers. Validation of the hovering multirotor is presented in Section IV.D, comparing predictions to experimental measurements of thrust drop and unsteady loading associated with rotor-on-rotor interactions. Alongside the multirotor model validation, this paper presents the following contributions to the viscous vortex particle method: • A simplistic, efficient, and accurate approach for the computation of vortex stretching through a complex-step