Investigation of sloshing effects on flexible aircraft stability and response

The present paper provides an investigation of the effects of linear slosh dynamics on aeroelastic stability and response of flying wing configuration. The proposal of this work is to use reduced order model based on the theory of the equivalent mechanical models for the description of the sloshing dynamics. This model is then introduced into an integrated modeling that accounts for both rigid and elastic behavior of flexible aircraft. The formulation also provides for fully unsteady aerodynamics modeled in the frequency domain via doublet lattice method and recast in time-domain state-space form by means of a rational function approximation. The case study consists of the so-called body freedom flutter research model equipped with a single tank, partially filled with water, located underneath the center of mass of the aircraft. The results spotlight that neglecting such sloshing effects considering the liquid as a frozen mass may overshadow possible instabilities, especially for mainly rigid-body dynamics

Experimental data-driven reduced-order modeling of nonlinear vertical sloshing for aeroelastic analyses

This thesis focuses specifically on the study of nonlinear sloshing effects caused by large tank motions in a direction perpendicular to the free liquid surface with emphasis on aeronautical applications. Sloshing is a phenomenon that typically occurs in aircraft tanks as they are subjected to loads caused by gusts, turbulence and landing impacts. This type of sloshing leads to a noticeable increase in overall structural damping, yet it is generally not modeled in the design phase of modern aircraft. The identification and study of such dissipative effects may enable the development of less conservative aircraft configurations in the future, allowing for increasingly lighter structures and reduced environmental impact. The present thesis proposes a combined experimental and numerical approach aimed at obtaining reduced-order models for vertical sloshing, to be subsequently integrated into aeroelastic modeling and applications for the assessment of their effects on overall performance. An experimental campaign is first carried out to characterise the nonlinear dissipative behaviour of vertical sloshing for different filling levels. Specifically, a controlled electrodynamic shaker is employed to provide vertical displacement by means of sine-sweep excitation. By exploiting vertical harmonic motion, it is shown how the frequency and amplitude of the imposed excitation significantly influence the dissipative capabilities of the sloshing liquid. The same experiment is used to create a database - with an acquisition phase that considers vertical sloshing as an isolated system - to build a neural-network-based reduced-order model. The dynamics to be modeled is considered as a black box process, leading to the identification of a surrogate model driven only by input/output signals, regardless the knowledge of the internal dynamics. In order to assess the capability of the identified reduced order model for sloshing, the same tank used to generate the training data is mounted at the free end of a cantilever beam to create a new experimental setup in which a fluid-structure interaction scenario is expected. Indeed, this experiment provides experimental data for the validation of the identified dynamic model by comparison with numerical data. The comparison is carried out using a dynamic virtual simulation model corresponding to the experiment, in which the numerical model of the beam interacts with the reduced-order model simulating the sloshing dynamics. Finally, the experimentally validated reduced-order model is used in two different aeroelastic applications - wing prototype and flying wing model - to finally predict the dissipative effects induced by vertical sloshing on the aeroelastic response. Aeroelastic response analyses under pre- and post-critical conditions showed how the vertical sloshing dynamics helps to alleviate the dynamic loads due to severe gusts while providing limit cycle oscillation beyond the flutter margin

Experimental Validation of Neural-Network-Based Nonlinear Reduced-Order Model for Vertical Sloshing

In this paper, a nonlinear reduced order model based on neural networks is introduced in order to model vertical sloshing for use in fluid-structure interaction simulations. A box partially filled with water, representative of a wing tank, is first tested to identify a neural network model and then attached to a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the structure. The experimental set-up is equipped with accelerometers and load cells at the interface between the tank and an electrodynamic shaker, which provides vertical acceleration to the tank. Accelerations and interface forces measured during the experimental tests are employed to identify a recurrent network able to return the vertical sloshing forces when the tank is set on vertical motion. The identified model is then experimentally tested and assessed by its integration on the tip of a cantilever beam. The free response of the experimental setup are compared with those obtained by simulating an equivalent virtual model in which the identified reduced-order model is integrated to account for the effects of vertical sloshing

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing

Sloshing reduced-order model trained with Smoothed Particle Hydrodynamics simulations

The main goal of this paper is to provide a Reduced Order Model (ROM) able to predict the liquid induced dissipation of the violent and vertical sloshing problem for a wide range of liquid viscosities, surface tensions and tank filling levels. For that purpose, the Delta Smoothed Particle Hydrodynamics (δ-SPH) formulation is used to build a database of simulation cases where the physical parameters of the liquid are varied. For each simulation case, a bouncing ball-based equivalent mechanical model is identified to emulate sloshing dynamics. Then, an interpolating hypersurface-based ROM is defined to establish a mapping between the considered physical parameters of the liquid and the identified ball models. The resulting hypersurface effectively estimates the bouncing ball design parameters while considering various types of liquids, producing results consistent with SPH test simulations. Additionally, it is observed that the estimated bouncing ball model not only matches the liquid induced dissipation but also follows the liquid center of mass and presents the same sloshing force and phase-shift trends when varying the tank filling level. These findings provide compelling evidence that the identified ROM is a practical tool for accurately predicting critical aspects of the vertical sloshing problem while requiring minimal computational resources

Linear and Nonlinear Reduced Order Models for Sloshing for Aeroelastic Stability and Response Predictions

This paper makes use of sloshing reduced-order models to investigate the effects of sloshing dynamics on aeroelastic stability and response of flying wing structure. More specifically, a linear frequency-domain operator derived by an equivalent mechanical model is used to model lateral (linear) sloshing dynamics whereas data-driven neural-networks are used to model the vertical (nonlinear) sloshing dynamics. These models are integrated into a formulation that accounts for both the rigid and flexible behavior of aircraft. A time domain representation of the unsteady aerodynamics is achieved by rational function approximation of the fully unsteady aerodynamics obtained via the doublet lattice method. The case study consists of the so called Body Freedom Flutter research model in two different configurations with one or two tanks partially filled with liquid with a mass comprising 25% of the aircraft structure. The results show that linear sloshing dynamics are able to change the stability margin of the aircraft in addition to having non-negligible effects on rigid body dynamics. On the other hand, vertical sloshing acts as a nonlinear damper and eventually provides limit cycle oscillations after flutter onset