Evaluation on Piezoaeroelastic Energy Harvesting Potential of A Jet Transport Aircraft Wing with Multiphase Composite by means of Iterative Finite Element Method

This paper presents new insight on the potential of piezoaeroelastic energy harvesting on the transport aircraft wing structure. A novel numerical investigation is conducted in the present study. An advanced iterative finite element method (FEM) is applied to estimate the amount of harvested energy. Currently, FEM-based commercial software has a limited application on piezoelectric structures, i.e., actuator and sensor. The iterative FEM algorithm extends the commercial software implementation for the energy harvesting analysis. The multidisciplinary issue of the aeroelastic phenomenon and piezoelectric energy harvesting is evaluated in the present case. Likewise, interestingly, stress and failure analysis of a lifting surface with an active energy harvesting component could be enabled. Implementation of a wing with an embedded piezoelectric layer is concerned. A cruise flight condition and gust disturbance are evaluated. The analysis concerning the occurrence of gust also provides a more realistic insight into the power harvested during a flight operation.

Aircraft wing; Energy harvesting; Gust load; Iterative FEM; Piezoaeroelastic

Many researchers have been attracted by multifunctional material systems in the past few decades (Ferreira et al., 2016; Sairajan et al., 2016). The article by Christodolou and Venables (Christodoulou & Venables, 2003) is one of the earliest publications on this subject. They highlighted the combination of structural functions, i.e., load-bearing, with power generation, the so-called structural-power system.
    In the new and renewable energy topic, many studies and technologies rely on ambient sources, i.e., wind, thermal, and solar (Krasniqi et al., 2022; Brazovskaia & Gutman, 2021; Guenther, 2018; Hafizh et al., 2018; Selvan & Ali, 2016; Thomas et al., 2006). In terms of structural-power systems, piezoelectric energy harvesting has been one of the promising subjects (Anton & Sodano, 2007). In a lifting structure, i.e., aircraft, the vibration exerted by the fluid-structure interaction is one of the sources to harvest the  energy (Abdelkefi, 2016; Li et al., 2016; Rostami & Armandei, 2017).

Anton and Inman (2008) pioneered the experimental study on piezoelectric energy harvesting from aircraft structures. They have successfully flight-tested a remote control aircraft with active piezoelectric energy harvesters attached to the wing spars and fuselage. Numerous mathematical and computational methods have also been studied.

One of the first mathematical models on this topic was developed by Erturk et al. (2010). They coined the term piezoaeroelastic energy harvesting, which defines the energy harvesting from aeroelastic vibration of the piezoelectric-based structure. Their proposed mathematical model concerns a flutter-based energy harvesting from 2 Degree-of-Freedoms (DoF) airfoil. They have also performed a wind tunnel test for validation.

Following the success of the airfoil model, higher fidelity computational models have been developed. Planar lifting structure models were proposed for time-domain ( De-Marqui et al., 2010) and frequency-domain ( De-Marqui al., 2011) problems. The models utilized the electromechanical shell element  ( De-Marqui et al., 2009).

Although a significant number of studies involved with experimental fluid-structure interaction tests, there is a lack of investigation concerning more functional aerodynamic conditions (Abdelkefi, 2016). Most of studies focused on instability and resonance conditions, i.e., flutter, galloping, and vortex induced vibration (Rostami & Armandei, 2017). However, an instability or resonance phenomenon could lead to a structural failure.

To the authors' knowledge, only a few publications discussed the development of models concerning piezoaeroelastic energy harvesting from operational aerodynamic conditions. The investigation on energy harvesting from discrete gust loads, i.e., 1-cosine and square gusts, were discussed by Xiang et al. (2015), Bruni et al. (2017), Cheng et al. (2019), Saporito and Da-Ronch (2020). Tsushima and Su (2016) presented a computational model to evaluate turbulence conditions. They  extended their model in combination with an active control system (Tsushima & Su, 2017).

Akbar and Curiel-Sosa investigated the cruise flight condition of a civil jet transport aircraft in (Akbar & Curiel-Sosa, 2016). Akbar and Curiel-Sosa (2018) discussed the extension of this study in their article. By implementing multiphase piezoelectric composites, it was claimed up to 40 kW of power can be harvested and may be used as an alternative for reducing the fuel consumption (Akbar & Curiel-Sosa, 2018). However, the computational tools were limited on a harmonic bending motion. Furthermore, the studies neglected the two-ways coupling between the aerodynamic loads and the structural deformation. Therefore, one of the research gaps is on the investigation of a more realistic load case, i.e., involved a more sophisticated interaction concerning aerodynamics, structures and electrical domains. In the present work, thus, the main problem statement is how to evaluate a more realistic load case using numerical methods.

A so-called iterative finite element method (FEM), was proposed by Akbar and Curiel-Sosa (2019). The iterative FEM was developed to use FEM-based commercial software with augmentation of a simple computational program to evaluate electromechanical coupling of energy harvesting cases. This method has been validated and proven to estimate the energy harvested from lifting structures, i.e., bimorph plate and UAV wing.

In the present work, for the first time, the iterative FEM is utilized to investigate the energy harvesting potential of a jet transport aircraft wing. Hence, enabling the evaluation for a more practical flight condition, i.e., aeroelastic condition concerning a cruise flight and discrete 1-cosine gust disturbance. Various gust velocities considering the occurrence probability are concerned. The following sections present the fundamental of the iterative FEM and the results of the aircraft wing numerical investigation. 

The iterative FEM scheme implementation provides a more realistic flight loading approach to the wing structure of a jet transport airplane imposed by cruise load and gust disturbance. The analyses discussed in this paper have integrated the aeroelastic aspects with structural dynamic and unsteady aerodynamic numerical model. The use of commercial software in iterative FEM has allowed for the evaluation of numerous forms of structural analyses, such as gust and failure modules. The stress and failure studies of the wing, when subjected to the gust load and harvesting the energy, were undertaken in this work. The wingbox is safe even when confronting a high wind while generating the electrical power, according to the failure study. Thus, the multidisciplinary problem concerning structural strength, aeroelastic vibration, and energy harvesting, can be solved with this iterative FEM scheme. This study depicted a more practical result by utilizing a more realistic load model for gust and cruise loads. The gust's response pointed out that structural vibration was quickly damped during a cruise flight; thus, the maximum gathered power being attained in a relatively short time. Furthermore, a significant amplitude gust may only occur once at a given distance, preventing continuous power harvesting via structural vibration owing to aeroelastic gust throughout a typical flight. According to the data presented in this paper, the energy captured during a typical cruise flight under gust perturbation is likely low compared to the energy delivered by the aircraft system, such as the Auxiliary Power Unit. Therefore, the piezoelectric energy harvesting structure is not feasible to support the aircraft's main power supply. The gathered energy, on the other hand, might be utilized to improve the efficiency of other aircraft systems, i.e., active disturbance control, such as a gust alleviation system.

The authors would like to thank Mr. Nanda Wirawan (National Research and Innovation Agency of Indonesia) for his assistance with the computational work. We also appreciate the support offered by the ITB Research, Community Service, and Innovation Program (P2MI ITB) under grant no. 2C/IT1.C04/SK/KP/2021.

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