A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

A SPH simulation of the sloshing phenomenoninside fuel tanks of the aircraft wings.

J. Calderon-Sanchez, L.M. Gonzalez, S. Marrone, A. Colagrossi

CNR-INM, INstitute of Marine engineering, Rome, Italy

Universidad Politecnica de Madrid (UPM), Spain.

13th SLOWD presentation

June, 8th May 2019,

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

FSI model for the aircraft wing tanks.

Inspiration: beam test campaign performed by Airbus UK.Three main elements: the fluid, the tank and the beam.The wing is represented by a 2.35m cantilever with a liquidtank attached at its tip.The system is studied once the beam is deformed and released.

SLOSHING WING DYNAMICS PROTOTYPE TEST DESCRIPTION

Technical Report

ORIGIN EGLCX REFERENCE X010RP1824050 ISSUE 1.0 DATE 21 Sep 2018

© Airbus Operations LTD 2018. ALL RIGHTS RESERVED. CONFIDENTIAL AND PROPRIETARY DOCUMENT.

Page 25 of 52

There were two main light sources, which were 2 LED lamps that emit light at such a high frequen-cy that the camera is not affected by fluctuations in the signal. These lights were located in front of the tank.

One light at the rear of the tank and one light on the floor pointing at the tank were also used to improve the quality of the video. The light behind the tank had to be covered by a white, translu-cent panel to avoid image saturation.

This setup is shown in Figure 22. Note that only one of the two LED lamps is displayed since the other was removed for this picture to show clearly the tank.

Figure 22: Overall view of the test rig

3.2 Test procedure

This section describes the procedure that was followed for each test. This procedure was separat-ed in 3 parts. The first one consisted in setting up the variables for the test. Then, pulling down the beam to the required position. Finally, releasing the beam and ensuring recordings are saved.

Pre-strain checks:

1. Set required fill level if differing from before. Fill level was calculated using the density of the fluid and measuring weight on a scale.

2. Clean tank lid if necessary (usually first test of each configuration).

3. Set required mass ballast level if differing from before. This was done using the threaded bars below the tank and the blocks of material as shown in Figure 23. Each block has a mass of 462 g, representing a 10% of the volume of the tank filled with water.

Electronically validated - Released on 09 Oct 2018

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Computational model

Confined liquid: density and viscosity. WCSPHSolid rigid tank. Newtonian description.Two tank-beam models:

Simplified model: one vertical degree of freedom.Elastic Euler-Bernoulli beam and 3 degrees of freedom for thetank.

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

δ-LES-SPH for the liquid.

Weakly compressible SPH.Mass conservation and momentum conservation.Large Eddy Simulation description. Low parameterdependance.Boundary integrals methodology.AQUA GPU software.Energy conservation

A SPH simulation of the sloshing phenomenon inside fuel tanks ofthe aircraft wings.

J. Calderon-Sanchez, L.M. Gonzalez ∗Universidad Politecnica de Madrid (UPM). Madrid, Spain.

S. Marrone, A. ColagrossiCNR-INM, INstitute of Marine engineering, Via di Vallerano 139, 00128 Rome, Italy

Abstract

The wings of large civil passenger aircrafts, which are designed to withstand the loads occurring from atmosphericgusts and turbulence to landing impacts, still demand further research. This goal will be achieved through investi-gating the damping effect of sloshing on the dynamics of flexible wing-like structures carrying liquid (fuel) via thedevelopment of experimental set-ups complemented by numerical models. The aim of this work is to analyze the useof fuel slosh to reduce the design loads on aircraft structures using SPH as the main numerical tool. The first step ofthis research was performed inside the Airbus facilities, where a scaled model of the problem was tested. The wing isrepresented by a 2.35m cantilever with a liquid tank attached at its tip. The behaviour of the system once deformedand 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 tounderstand and analyse the damping mechanisms, the structure is modelled through the Euler-Bernouilli beamtheory and solved by modal analysis [2]. For the fluid, the δ-LES-SPH model is used [3], which has been implementedfor the boundary integrals methodology that was developed in [1]. Figure 1 illustrates the tank-beam configuration,and the model used in the simulations, where the constraints considered to bind the two solids are shown.

The main conclusions of this work are: first, that SPH as numerical tool is able to confirm that the presence ofliquid in the tanks attached to flexible structures introduces a damping effect that can be numerically measured interms of energy and compared to the experiments. Second, that SPH is able to model complex baffled geometriesinvolving several phenomena at the same time through the boundary integrals approach, and finally, that the coupledsystem is able to capture the energy mechanisms and transfers involved in the phenomenon.

Fig. 1. Coupled system during the simulation. Figure top left shows the set-up for the experiments. Figures top right and

bottom show the simplified model considered for the simulations. Non-dimensional turbulent kinetic intensity is represented at

the fluid particles inside the tank. The beam is coloured according to its vertical displacement.

References

[1] J. Calderon-Sanchez, Cercos-Pita J.L., and Duque D. A new shepard renormalization factor formulationfor boundary integrals. In Proceedings of ERCOFTAC SPHERIC 13th International Workshop, 2018.

[2] Merlin L James, Gerald M Smith, JC Wolford, and PW Whaley. Vibration of mechanical and structuralsystems: with microcomputer applications. Harper Collins, 1994.

[3] Domenico D Meringolo, Salvatore Marrone, Andrea Colagrossi, and Yong Liu. A dynamic δ-sph model:How to get rid of diffusive parameter tuning. Computers & Fluids, 179:334–355, 2019.

∗ Corresponding author.Email address: leo.gonzalez@upm.es (L.M. Gonzalez ).

Preprint submitted to SPHERIC 2019 17 February 2019

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

The tank.

The tank is a 3 degrees of freedom rigid solid governed by theNewton laws.

The fluid forces Fx , Fy and torque M reduced to the center ofmass G of the tank.The beam forces: 3 reactions coming from the beam V1,V2,H

where

Fx =∫T · nds · −→i Fy =

∫T · nds · −→j

M =∫r × T · nds being T = −pI + τ .

mtank xG = V1 +

∫T · nds · −→i

mtank yG = V2 +

∫T · nds · −→j

Itank θ = M +

∫r × T · nds

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

The Euler-Bernoulli beam.

The equation for a beam is given by the Euler-Bernoulli beamtheory as:

m(x)∂2w(x , t)

∂t2+ c

∂w(x , t)

∂t+ EI

∂4w(x , t)

∂x4= f (x , t)

Solution: w(x , t), w , w

3 reactions coming from the tank f (x , t) = V1 + H.

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Simplified model.

The beam is concentrated as a point mass with 1 degree offreedom y .

my + cy + ky = f (t)

Where: k = 3EI/L3 Solution: y(t), y , y

Vertical reaction coming from the tank f (t) = V1.

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Coupling scheme

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Results static case 1.

An initial load is used for a un-deformed beam at (t=0).The beam deforms dynamically → final stationary position.The final position is compared to the experiments.

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Results static case 2.

An initial solid mass is used for a deformed beam at (t=0).

The beam deforms dynamically → final stationary position.

The final position and the dynamic evolution is compared tothe experiments.

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A SPH simulation of the sloshing phenomenon inside fuel tanks of the aircraft wings.

Results fluid cases.

Presence and absence of baffles.

Constant damping rate and one filling level 50%.

Results are compared to the Airbus experimental campaign.

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