The present paper introduces the sloshing effects on aeroelastic stability and response of flying wing configurations. Using reduced order model based on data provided by computational fluid dynamics data, the description of the slosh dynamics is introduced into an integrated modelling that accounts for both rigid and elastic behaviour of flexible aircraft. The fully unsteady aerodynamics, modelled in the frequency domain via doublet lattice method, is recast in time-domain state-space form through the rational function approximation. The reference aircraft is the Body Freedom Flutter equipped with a single tank of cylindrical geometry, partially filled with water, and located underneath the center of mass. The results of the stability and response analyses are compared with the frozen fluid case with the final aim of showing how the fluid movement affects the complete aircraft behaviour.
The aim of this work is to provide a reduced-order model to describe the dissipative behavior of nonlinear vertical sloshing involving Rayleigh–Taylor instability by means of a feed forward neural network. A 1-degree-of-freedom system is taken into account as representative of fluid–structure interaction problem. Sloshing has been replaced by an equivalent mechanical model, namely a boxed-in bouncing ball with parameters suitably tuned with performed experiments. A large data set, consisting of a long simulation of the bouncing ball model with pseudo-periodic motion of the boundary condition spanning different values of oscillation amplitude and frequency, is used to train the neural network. The obtained neural network model has been included in a Simulink® environment for closed-loop fluid–structure interaction simulations showing promising performances for perspective integration in complex structural system.
View Video Presentation: https://doi.org/10.2514/6.2022-1186.vid 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.
- Niran Ilangakoon
- A. G. Malan
This paper proposes a higher-order accurate curvature computation method for volume-of-fluid (VOF) interfaces on 3D non-orthogonal structured meshes. Analogous to the height-function (HF) method, a novel approach is introduced to identify columns of control volumes that straddle the interface. This is followed by a volume conserving piecewise-linear interface construction (PLIC). In the interest of efficiency and generality, the latter employs a novel sweep-plane algorithm with bracketing on convex-decomposed control volumes in each column. The emphasis is on the generalisation of a PLIC-based least squares polynomial surface fitting procedure owing to its invariance with respect to local coordinate rotations in 3D. The PLIC representation of the interface is then smoothed by iteratively refining the PLIC facet normals. The interface curvature is finally computed analytically by fitting either second-or fourth-order polynomial surfaces to local stencils of PLIC facets in a least squares manner. Formal second-and fourth-order accuracy of interface curvature is demonstrated by comparing numerical results with a variety of analytical interface definitions.
The present work is dedicated to the numerical investigation of three-dimensional sloshing flows inside a ship LNG fuel tank. Long time simulations, involving 3-hours real-time duration with realistic severe sea-state forcing, have been performed using a parallel SPH solver running for several weeks on a dedicated cluster. The adopted SPH method relies on a weakly-compressible approach and a Riemann Solver for the calculation of the particle interactions. The latter increases the stability of the scheme and allows for accurate predictions of the pressure during water impact stages (see also ). The intrinsic properties of mass and momenta conservation makes it well adapted for the simulation of such kind of violent free-surface flows for long-time evolution. Single phase model has been adopted with a considerable reduction of the CPU costs (for an in-depth discussion see also ). The high values of Reynolds numbers involved requires the implementation of a sub-scale model which was embedded in the SPH scheme following the recent literature (see e.g. ). Three different filling height conditions are considered. For all of them energetic sloshing flows are induced with the occurrence of several water impact events. The latter are focused on specific zones of the tank depending on the considered filling height (see also ). For some conditions the SPH pressure predictions are compared with the experimental ones provided by Hyundai Heavy Industries (HHI). A critical discussion of these predictions is performed in order to highlight in which cases the numerical solver is able to provide good local loads estimations. Conversely, when the SPH results appear to be not realistic, comments on the causes linked to the disagreements with experiments are given.
The SLOshing Wing Dynamics (SLOWD) project aims to investigate the modelling of fuel sloshing physics to reduce the design loads on aircraft structures. This goal will be achieved through investigating the damping effect of sloshing on the dynamics of flexible wing-like structures carrying liquid (fuel) via the development of experimental setups complemented by novel numerical and analytical tools. The primary focus of the project is the application of modelling capabilities to the wing design of large civil passenger aircraft (subject to EASA CS-25 type certification), which are designed to withstand the loads occurring from atmospheric gusts, turbulence and landing impacts. The timeframe of the project is three years, starting in September 2019. This paper reviews the current progress that has been made and outlines goals for the rest of the project.
The sloshing motion of a confined liquid inside a vertically moving tank is analyzed in the present series of paper. The main objective of the study is to understand the multiple resulting energy dissipation mechanisms, namely wall-liquid impacts and free surface phenomena, among others. This analysis is connected to the damping effects on the aircraft wings caused by the liquid action inside the fuel tanks. Due to the complexity and nonlinearity of the flow generated inside the tank, only experiments or efficient numerical solvers are suitable for studying the problem. In this paper, the tank-fluid system is periodically excited with a prescribed law of motion and the nonlinear features are observed, the force between the wall and the fluid and the global energy balance are computed. A weakly compressible smoothed particle hydrodynamics model has been reformulated and adapted to this kind of violent and turbulent flow. The evolution of the different terms that appear in the energy conservation law are computed, and the formulation is compared to other alternatives where the advantages of the present formulation are indicated. The comparison with the experimental results and the fluid-structure interaction case is carried out in Part II [Marrone et al., Numerical study on the dissipation mechanisms in sloshing flows induced by violent and high-frequency accelerations. II. Comparison against experimental data, Phys. Rev. Fluids 6, 114802 (2021)] of this work.
In Part I of this series [Marrone et al., Numerical study on the dissipation mechanisms in sloshing flows induced by violent and high-frequency accelerations. I. Theoretical formulation and numerical investigation, Phys. Rev. Fluids 6, 114801 (2021)], a theoretical formulation and the numerical model were developed in order to obtain a complete perspective of the energy balance of a violently accelerated flow confined inside a rectangular tank. The tank-fluid system was periodically excited with a predetermined law of motion and the force between the wall and the fluid and the global energy balance were computed. In this second part, the experimental validation of the previous formulation is presented. In order to make a comparison with a previous experimental campaign, where the tank moves along a single degree of freedom mechanical guide, two numerical problems have been studied: in the first, the decaying movement of the tank is prescribed according to the experimental measurements, and in the second the tank is coupled to a mass-spring-damper equation, and the sloshing force produced by the confined fluid acts as an external force. Both problems have been studied for two different fluids, water and oil, which implies a difference of two orders of magnitude in terms of Reynolds number. A complete description of the energy balance inside the fluid tank is performed and the complexity of the fluid dynamic behavior that takes place inside the tank is explained. The results are compared to the experimental measurements in terms of fluid-wall interaction and energy dissipation.
We present the CFD based non-dimensional characterization of violent slosh induced energy dissipation due a tank under vertical excitation. Experimentally validated CFD is used for this purpose as an ideally suited and versatile tool. It is thus first demonstrated that a weakly compressible VoF based CFD scheme is capable of computing violent slosh induced energy dissipation with high accuracy. The resulting CFD based energy analysis further informs that the main source of energy dissipation during violent slosh is due liquid impact. Next, a functional relationship characterising slosh induced energy dissipation is formulated in terms of fluid physics based non-dimensional numbers. These comprised contact angle and liquid–gas density ratio as well as Reynolds, Weber and Froude numbers. The Froude number is found the most significant in characterising verticle violent slosh induced energy dissipation (in the absence of significant phase change). The validated CFD is consequently employed to develop scaling laws (curve fits) which quantify energy dissipation as a function of the most important fluid physics non-dimensional numbers. These newly developed scaling laws show for the first time that slosh induced energy dissipation may be expressed as a quadratic function of Froude number and as a linear function of liquid–gas density ratio. Based on the aforementioned it is postulated that violent slosh induced energy dissipation may be expressed as a linear function of tank kinetic energy. The article is concluded by demonstrating the practical use of the novel CFD derived non-dimensional scaling laws to infer slosh induced energy dissipation for ideal experiments (with exact fluid physics similarity to the full scale Aircraft) from (non-ideal) slosh experiments.
There is much interest in developing concepts to reduce in-flight loads resulting from gusts and atmospheric turbulence, as this will lead to lighter aircraft with improved fuel performance and reduced environmental impact. Recent work has considered using sloshing in tanks as a means to increase the effective structural damping in the wings. Experimental studies have quantified the effect that sloshing can have on simple systems, and these studies have been complemented by the development of equivalent mechanical models to efficiently model the process and provide a design capability. This paper provides an initial study to evaluate the benefits of fuel tank sloshing on the response of a simple simulated aeroelastic wing model subjected to "one minus cosine" vertical gust sequences. The effects of the filling level and tank position upon loads alleviation are explored. It is shown that the sloshing fuel can increase the damping level in the gust response, but is dependent upon the tank filling level, and tank size and position.
The effect of the sloshing motion of liquid in a tank on the vertical transient motion of a single degree of freedom system is investigated. Step release tests of a vertically vibrating structure, including a tank containing liquid, demonstrate that added damping from the sloshing motion depends upon the amount of fluid in the tank and the maximum acceleration. The maximum amount of damping was observed at a 50% fill level and the system showed three distinct response regimes during the transient decay, all related to different motions of the fluid. The first response regime, immediately at the start of the transient, is considered to be the most important to exploit for aircraft gust loads alleviation due to its dominant role in the overall energy dissipation balance. Further, to advance the understanding of the modelling and predictive capabilities, coupled fluid-structure models of two opposing levels of fidelity were developed and evaluated. Namely, smoothed particle hydrodynamics (SPH) and an equivalent mechanical model (EMM) based on a bouncing ball model were considered to represent the fluid motion in the tank during the experiment. Both models are shown to provide good predictive capability in the initial impacting sloshing mode while the subsequent flow regime can be predicted with the SPH model only. The findings in this paper open routes towards improved coupled fluid-structure models and their use in improved aeroelastic wing design.
All aircraft are subject to a range of loading throughout ground and flight operations, which ultimately define the sizing and weight of the aircraft structure. Active and passive loads alleviation technologies provide an approach to reduce dynamic loads arising from atmospheric gusts and turbulence, leading to more fuel-efficient aircraft designs. Within the H2020 SLOWD project, fuel sloshing is being considered as a method for alleviating loads in aircraft wings via an increase in effective damping. Recent work has considered the transient response of a vertically vibrating, single degree of freedom system coupled to a rectangular liquid-filled tank. This research revealed identifiable dissipation regions in the free vibration responses characterised by their own distinct equivalent damping ratio values. In this work, free surface displacement has been extracted from high-speed camera footage during the chosen sloshing regimes, which are representative of a decaying parametrically excited fluid. These results are compared against a fluid-structure coupled numerical model based upon smoothed particle hydrodynamics, previously shown to have good agreement with the experimental damping response. Further analysis of the free-surface response of the numerical solution notes a presence of an undesired travelling longitudinal wave. The analysis of this discrepancy between the model and experiment is then used to improve the numerical formulation, showing a requirement for modelling surface tension.
All aircraft are subjected to dynamics loads resulting from in-flight atmospheric gusts and turbulence, with the resulting stresses determining the sizing, and hence weight, of the resulting structure. There is much interest in studying active and passive approaches to alleviate these loads, leading to more fuel-efficient and environmentally friendly airplane designs. Recent work, as part of the H2020 SLOW-D project, has considered the use of fuel sloshing as a means of loads reduction, with fundamental transient response experiments, performed using a single degree of freedom system coupled to a liquid filled tank, demonstrating a multi-regime piecewise linear damping behaviour dependent on the amount of tank fill and the size of the excitation. This work continues the effort to improve the development of coupled fluid-structure sloshing models through investigation of the 2nd and 3rd transient response regions. Experimental measurements based on high frame-rate videos of the fluid surface motion and the tank vibration are used to further develop coupled structure / sloshing fluid computational models based on an SPH approach. A good comparison between the numerical model and the experimental measurements is found.
The research on fuel loads at the Airbus Loads department will be put in context with the broader view and needs of the aerospace sloshing community. The application of a novel methodology for free surface modeling, developed in partnership with the University of Cape Town will be presented. An overview of the "Validation and Verification" process undergone by the method will be shown, with comparison of numerical simulation and experimental results. Further analysis of dynamic loads on the walls of fuel containers will be discussed for certain cases of interest for large aircraft. The industrial applications of a Reduced Order Model (ROM) developed to cover the design space of the fuel tanks will also be presented.
The SLOshing Wing Dynamics (SLOWD) project aims to investigate the modelling of fuel sloshing physics to reduce the design loads on aircraft structures. This goal will be achieved through investigating the damping effect of sloshing on the dynamics of flexible wing-like structures carrying liquid (fuel) via the development of experimental setups complemented by novel numerical and analytical tools. The primary focus of the project is the application of modelling capabilities to the wing design of large civil passenger aircraft (subject to EASA CS-25 type certification), which are designed to withstand the loads occurring from atmospheric gusts, turbulence and landing impacts. The timeframe of the project is three years, starting in September 2019.
This study details the development of a computational full aircraft model (FAM) to assess the non-linear response of an aircraft during an aerodynamic gust. A FAM comprises numerous components viz., the structure, aerodynamics and inertial loads. The focus of this study is to implement a geometrically non-linear reduced-order model (ROM) for the wing and assess its aeroelastic response against standard linear approaches. The NASA common research model (CRM) wing is modeled by three-dimensional Timoshenko beam elements in both the linear and non-linear regime. Linear responses are derived from standard linear modal analysis procedures. The geometrically non-linear beam element ROM is solved via quadratic mode shape components in the modal domain. These components are extracted from linear mode shapes in a novel approach for elastic beam elements. A representative gust load is applied to the structure and the responses are compared to the linear approach. It was found that QMS modal methodology offers improved accuracy by retaining the overall wing length even when loading produces a vertical displacement of 35% with respect to wing span. The extension caused by linear modeling exceeds 14%, while the QMS approach reduces it to less than 3%.
Characterization of nonlinear slosh loads in aircraft remains a challenging problem. This work benchmarks a frozen fuel mass model against computational fluid dynamics data across a complete flight envelope. Thereafter, a novel surrogate reduced-order model aimed at improving on frozen fuel mass predictions is proposed. For a given tank geometry, the surrogate reduced-order model employs computational fluid dynamics simulations from which limit state slosh loads may be computed. These are calculated as a function of the mode of excitation (vertical or lateral), fill level, excitation frequency, and excitation amplitude. The resulting response surface is then described via a kriging interpolation-based surrogate reduced-order model. The surrogate is combined with a novel metric for the amplification factor (the ratio of the actual load to that induced by a frozen fuel mass) to predict the transient slosh-induced force due to arbitrary gust-type excitations. The latter is characterized as a priori in terms of acceleration amplitude and frequency via Fourier decomposition. It is demonstrated that the proposed surrogate reduced-order model improves the accuracy in predicting lateral slosh-induced loads by an average of 150% as compared to a frozen fuel mass model for a range of excitations, while being conservative. © 2017 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
This paper will propose Reduced-Order Models (ROM) based on data provided by high-fidelity and highly efficient CFD codes, for the study of sloshing-integrated aeroelas-tic systems. A sloshing-addressed CFD code, ELEMENTAL R , is employed to generate data set to be used for the ROM synthesis. The developed sloshing ROM, based on a Linearized Frequency Domain (LFD) approach, uses an Input/Output system identification technique from CFD transient simulations to construct an unsteady Generalized Sloshing Force (GSF) matrix in analogy with the Generalized Aerodynamic Force (GAF) matrix used to model the aircraft external unsteady aerodynamics. The approach is assessed with experimental results performed at the Airbus Protospace Lab. (Filton, Bristol UK) on an actual beam-like structure carrying a series of tanks. The obtained state-space form for the sloshing ROM has been suitable developed for applying it within aeroelastic framework for perspective integrated stability analyses and design.
We provide an overview of the activities at the Loads and Aeroelastics department at Airbus in support of the design of the wing fuel tanks for large passenger aircraft. Particular focus is given to a recent design modification of the best-selling Single Aisle family, which required the estimation of "local" fuel loads (pressure distribution and forces) under dynamic excitations. In addition, we present a series of recent experimental tests, which looked at the effect of sloshing on the "global" dynamic response of the aircraft. The campaign was performed with the aim of validating numerical fluid-structure interaction models for discrete gust and continuous turbulence encounters.
The wings of large civil passenger aircrafts, which are designed to withstand the loads occurring from atmospheric gusts and turbulence to landing impacts, still demand further research. This goal will be achieved through investigating the damping effect of sloshing on the dynamics of flexible wing-like structures carrying liquid via the development of experimental setups complemented by numerical models. The aim of this work is to analyze the effect of sloshing in reducing the design loads on aircraft structures using SPH as the main numerical tool. The first step of this research was performed inside the Airbus Protospace Lab in Filton (UK), where a scaled model of the problem was tested. The wing is represented by a cantilever with a liquid tank attached at its tip. The behaviour of the system once deformed and released and the accelerations at the free end of the beam were registered for different configurations. In this work, a numerical model of a fully coupled fluid-structure interaction problem is developed. In order to understand and analyse the damping mechanisms, the structure is modelled through beam theory and solved by two different methods: a mass-spring-damper system and modal analysis. For the fluid, the δ-LES-SPH model is used, which has been implemented for the boundary integrals methodology in order to simulate complex geometries. A set of cases are simulated in order to reproduce trends noticed in the experiments, including different inner tank configurations , for the two beam models tested. SPH as numerical tool demonstrates that the presence of liquid in tanks attached to flexible structures introduces a damping effect.
We provide an overview of a series of experimental tests performed by the Loads & Aeroelastics department at Airbus in support of a broader research activity, aiming at modelling the dissipative effects of fuel sloshing on the dynamic behavior of wing-like structures. We describe the test setup, its similarity with the actual wing-structure of a large civil aircraft, the scaling rules applied, the measuring equipment and the practical considerations which drove the design of the test rig. The free vibration of this wing-like structure is compared for cases with and without sloshing, showing the potential of exploiting the dissipation inherent to the fluid structure interaction process for dynamic load alleviation.
Fuel sloshing is seen as a potential mechanism to reduce the loads in aircraft due to atmospheric turbulence and gusts via an increase in the effective damping. A series of step-release experiments have been performed on a cantilever beam structure with a tank at its end filled with different levels of liquid in order to provide experimental data to characterise the amount of damping caused by the sloshing motion and to validate future numerical models. This paper presents an analysis of some of the acceleration data sets acquired during the experiments and shows how the frequency and damping behaviour varies during the time decay resulting from the step-release. Correlation is made between the amount of effective damping and the different fluid motions in the tank. The analysis is repeated for the dry beam configurations as well as different test conditions including tank level filling and number of compartments in the tank.