AbstractIn commercial vehicles which generally have large capacity fuel tank, sloshing of fuel and its effect on the tank structure is very important aspect during fuel tank design. Dynamic pressures exerted by the fuel on baffles, end plates and tank shell during sloshing can lead to structural failures and fuel leakage problems. Fluid structure interaction simulation of automotive fuel tank sloshing and its correlation with physical test is demonstrated in this study.

During physical sloshing test of 350 L fuel tank, cracks were observed on center baffle and spot weld failures developed on fuel tank shell. Same sloshing test was simulated for one sloshing cycle using fluid structure interaction approach in LS Dyna explicit FE solver. Water was used instead of fuel. Mesh free Smoothed Particle Hydrodynamics (SPH) method is used to represent water as it requires less computational time as compared to Eulerian or ALE method. Equation of State (EOS) was defined in LS Dyna using variable parameters of volumetric strain (EV1, EV2…etc) and constants (C1, C2…etc) in order to represent the nonlinear behavior of water accurately during sloshing event. High strain areas on baffle and end plates were studied. Locations of weld failures and cracks observed on the center baffle & shell during physical test correlated quite well with simulation results.

Post correlation, fuel tank with modified baffle design was re-simulated and found to have improved performance in terms of reduced strain values. Same modified fuel tank design tested physically for target number of durability cycles in the lab and found to be meeting the requirements.

This improved and proven CAE methodology thus became very important and reliable step in design and development of high capacity fuel tanks.

IntroductionHeavy commercial vehicles are used for long distance cargo movement as well as severe off road applications such as dump trucks, drilling rigs, cement mixtures etc. Since they need to travel for longer distances, such user environment and bigger engines demand high capacity fuel tanks of 350 to 500 L. Some of the tractors (used for pulling trailers) even have dual fuel tanks fitted on both the sides of the frame.

In field, heavy commercial vehicle which carry big fuel tank undergoes different kind of situations such as braking, cornering, pitching etc and these dynamic scenarios lead to sloshing of quantum of fuel moving inside the fuel tank. Complete fuel mass exerts the pressure on the fuel tank baffles and end plates in these kind of dynamic scenarios. In turn, they face different kinds of failures. Cracks on baffles, spot weld failure, severe deformation on end plates etc are quite common failure modes. To avoid these kinds of potential failures, it is very important to understand the dynamic behavior of fuel inside the tanks and its impact on the fuel tank structure.

Hence, durability testing of fuel tanks has become very challenging and early prediction of the potential durability failures using effective CAE technique has become very much essential.

During the development of one of the commercial vehicle program, square shaped fuel tank has been designed. Physical sloshing test of this tank is done to check the durability of the fuel tank for defined lifecycle requirements. This test is done with half filled fuel tank considering this as a worst case and carried out at ARAI (Automotive Research Association of India) as well as in-house validation lab. Typical approach to simulate this phenomenon in CAE is two ways, 1) calculate pressure profile on baffles & end plates using CFD solver 2) Using the pressure profile drawn from CFD solver, simulate the behavior of the fuel tank structure using any linear static FEA solver. This approach is time consuming and requires two completely different capabilities in order to solve the problem. Attempt has been made here to solve this complex fluid structure interaction problem

Fluid Structure Interaction Simulation of Automotive Fuel Tank Sloshing using Nonlinear Fluid Properties

2015-26-0240

Published 01/14/2015

Avinash Dhole and Chetan RavalMahindra & Mahindra Ltd.

Rishi ShrivastavaMahindra Engineering Services

CITATION: Dhole, A., Raval, C., and Shrivastava, R., "Fluid Structure Interaction Simulation of Automotive Fuel Tank Sloshing using Nonlinear Fluid Properties," SAE Technical Paper 2015-26-0240, 2015, doi:10.4271/2015-26-0240.

Copyright © 2015 SAE International and Copyright © SAEINDIA

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

using fluid structure interaction approach in LS Dyna explicit FE solver. Nonlinear water properties have been developed in-house and used in the simulation. Overall objective of this exercise was to establish the correlation between test and CAE high strain regions and suggest design modifications. This also helped to prove the accuracy of the non-linear water properties (developed in-house) used in simulation, increase confidence in CAE results and improve the prediction capability for future fuel tank simulations.

Fuel Tank Design DetailsA standard heavy commercial vehicle fuel tank consists of tank shell, baffles, end plates and fastening mechanism with chassis. Design under consideration is 350 L square shaped fuel tank with 3 baffles and 2 end plates. Baffles are welded to tank shell by spot welds. Baffle design have holes incorporated along the face in order to allow fuel flow through them during sloshing and reduce the impact intensity. End plates are welded (continuous weld) to tank shell in order to avoid fuel leakage. This complete fuel tank assembly is attached to frame long members via brackets and straps (see Figure 1).

Figure 1. Fuel Tank Assembly

1. Fuel tank shell

2. End Plate

3. Fuel tank mounting bracket

4. Holding Straps

5. Chassis long member

Physical Test Setup DetailsFor durability testing of the square shaped fuel tank with 350 L capacity, tank was mounted on slip table in the same orientation axis, as it is fitted on the vehicle using brackets and fixture arrangement. Servo hydraulic actuator was connected to the slip table so as to excite the fuel tank in the longitudinal direction. Unidirectional accelerometer was used to measure acceleration and mounted at the top of fuel tank, see Figure 3. Figure 2 shows the test setup for fuel tank. Test specifications for durability testing of fuel tank were

finalized after number of trial runs to achieve acceleration of ±3g on the top of the fuel tank. After number of iterations, we have finalized peak displacement input of 80 mm in 0.05 sec in fore and aft direction with hold period of 0.5 sec in longitudinal direction. Figure 4 shows the durability cycle used for testing. Output acceleration at top of the fuel tank is shown in Figure 5 which ensures the target acceleration of 3g is achieved. Durability for square shaped fuel tank was carried out with above mentioned specification in longitudinal direction for certain specified number of hours.

Figure 2. Test Rig Setup

6. 350 L Fuel tank

7. Test bed with stationary base and oscillating mounting

8. Pneumatic actuator

9. PLC (Control System)

Figure 3. Accelerometer Location

Figure 4. Ramp and Hold Input for Fuel Tank Testing

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

Figure 5. Output Acceleration Measured at the top of the fuel tank

Finite Element Model DetailsThe finite element program used in the analysis was LS DYNA [1]. This program is developed by Livermore Software Tech Corporation (LSTC). FE modeling and setup was done in accordance to LS Dyna requirements. Mesh model of square shaped fuel tank was prepared using hypermesh 12.0. Shell elements were used in order to model the tank shell, baffles & end plates (see Figure 7) A fine mesh of 10 mm average size was used for the tank to ensure accurate geometry representation. Materials were modeled using *MAT_PIECEWISE_LINEAR_PLASTICITY (MATL24) and stress strain curves used for respective materials. Beams were used to model spotwelds between baffles & tank shell and end plates & tank shell. *MAT_SPOTWELD card was used for spotweld beams.

A homogeneous material, not undergoing any chemical reactions or phase change, may be defined by two state variables. This relation is called as Equation of state (EOS). Different forms of the EOS describe different form of materials and how their volumetric compression or expansion behavior. Here we have modeled Water with SPH (smoothed particles hydrodynamic) element for which *EOS_TABULATED card (see Figure 6) has been used to define non linear behavior of water. In Figure 6 GAMA (γ) is ratio of CP and CV, E0 and V0 are Initial internal energy and Initial relative volume respectively, EV1, EV2, EV3… are Volumetric strain, ln(V), where V is relative volume. The first abscissa point, EV1, must be 0.0 or positive if the curve extends into the tensile regime with subsequent points decreasing monotonically. C1, C2, C3…are tabulated points for function C. *EOS_TABULATED card uses below relation between EV1, EV2, EV3…. and C1, C2, C3… to define pressure,

Non linear relationship between pressure and volumetric strain was obtained by defining values of EV and C in EOS card of water SPH, see Figure 6. These values were obtained by doing iterations. Density of water was considered 1000 kg/m3. 15-20 mm pitch was taken while creating SPH element for reducing the calculation time. Node to surface contact was defined between water and fuel tank parts. In model total number of elements was 94400, in which SPH count was 45743. [1] [7] [3] [5]

Figure 6. EOS card for water SPH

Figure 7. FEA Model for Fuel Tank Sloshing

SPH TheoryOne of the recent advances in LS DYNA is the addition of SPH algorithm which allows the efficient and accurate modeling of fluid structure problems. Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating fluid flows. It was developed by Gingold and Monaghan (1977) and Lucy (1977) initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcano logy and oceanography. It is a mesh-free Lagrangian method (where the coordinates move with the fluid) and the resolution of the method can easily be adjusted with respect to variables such as the density.

The smoothed-particle hydrodynamics (SPH) method works by dividing the fluid into a set of discrete elements, referred to as particles. These particles have a spatial distance (known as the “smoothing length”), over which their properties are “smoothed” by a kernel function. This means that the physical quantity of any particle can be obtained by summing the relevant properties of all the particles which lie within the range of the kernel.[6]

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

In LS Dyna, different formulations are available to describe the motion of fluid and these can be used for fluid structure interaction.

1. Lagrangian formulation 2. Eulerian formulation 3. Arbitrary Langrangian-Eulerian formulation (ALE) 4. Smoothed Particle Hydrodynamic (SPH)

In a comparative study [2] of all above methods, where a box was modeled as shown in Figure 8, it has been found that measured pressure at the center of the end plate (Point 1(sensor) in Figure 8) are almost same. But in SPH and Lagrangian models, water retained the form of container (see Figure 9) which would not happen in reality. In case of fuel tank sloshing where only impact on one wall at a time is needed, the deformation pattern (as in SPH and Lagrangian methods) on the other side can be neglected. Also computational time taken by SPH method was significantly lower than other approaches (see Table 1), so SPH method has been taken up here for fuel tank sloshing. [2] [4]

Figure 8. Box dimensions and measurement point

Figure 9. SPH Elements Retain the Shape of Fuel tank

Table 1. CPU-time comparison of different methods

Load and Boundary ConditionIn finite element model, fuel tank was constrained at straps regions in all direction except longitudinal translation direction. This was done by assigning MATL20 to elements of tank shell which were coming in strap region and kept only X direction free in MATL20 card (see Figure 10). Displacement was applied to straps using *BOUNDARY_PRESCRIBED_MOTION_RIGID card. Gravity was also active during the calculation and applied by *LOAD_BODY_Z card. Ramp and hold inputs were used same as in the test (see Figure 4) and simulation was run for 1000 ms (one fore and aft motion). LS dyna explicit version R 6.1.2 code was used for calculation.

Figure 10. Strap region for constraining DOF and for displacement application

Result Review: TEST v/s CAETwo designs were tested at ARAI for fuel tank durability. During testing of first design-01, water leakage observed from the bottom spot welds. When fuel tank was cut open, it was found that center baffle had cracked at multiple locations and got disconnected at weld spots (see Figure 11). Second design-02 with extra slots (triangular shaped) on baffles completed target number of hours without failure (see Figure 12).

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

Figure 11. Tank design-01 - Cracks at center baffle during Physical Test

Figure 12. Tank design-02 (with modified baffles) - Snap showing no failures during Physical Test

In the fuel tank design-01, CAE results have shown high strain levels (strains > rupture strain of respective material) exactly at the same cracked areas around the holes of center baffle (lower half) as observed during the physical test (see Figure 13). Strain levels were almost similar in upper area too.

Figure 13. Correlation Results - Tank design-01

Overall results look severe than the physical testing which might be due to absence of air in the upper portion of fuel tank. In absence of air, water moves much freely in fuel tank and rises higher against the baffles which results in higher strain at the upper portion.

In the fuel tank design-02 with modified baffles shows improvement in strain levels (see Figure 14). Strain levels at center baffle reduced significantly.

Figure 14. Correlation Results - Tank design-02 with modified baffles

Pictorial representation of sequence of simulation is given below. See Figure 15 and Figure 16 for forward and backward animation. Forward movement from 0 to 50 ms and back ward from 550 to 600 ms, see Figure 4.

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

Figure 15. Sequence of Simulation - Forward Movement

Figure 16. Sequence of Simulation - Backward Movement

Acceleration v/s time plot from virtual simulation taken at the same location as like test shown in Figure 17. This correlates well with test acceleration as shown in Figure 5.

Figure 17. Acceleration v/s Time Plot (Virtual Model)

Conclusion & SummaryA finite element model utilizing the smoothed particle hydrodynamics (SPH) algorithm in LS dyna was developed to simulate the behavior of automotive fuel tanks in sloshing tests. The methodology developed for fuel tank simulation in CAE proved to be very much reliable and achieved good correlation with test. Also the water non linear behavior properties developed in-house were validated and proved to be accurate.

Future WorkAir should be modeled in upper portion of fuel tank by SPH elements using a SPH coupling between Water SPH and Air SPH. Also spotweld modeling should be modified in order to simulate spotweld failure.

Current FEA simulation is capable to predict potential cracks location. But it is possible for only one cycle. To predict number of cycles before crack generation is another challenge which will be addressed in further studies of fatigue failure. Output strain levels can be used to predict total number of cycles before fatigue failure.

References1. LS-DYNA, “KEYWORD USER'S MANUAL”, VOLUME I

AND VOLUME II, Livemore Software Technology Corporation (LSTC), version 971 R6.1.0, August 2012.

2. Vesenjak Matej1, Mullerschon Heiner2, Hummel Alexander3 and Ren Zoran1, “Simulation of Fuel Sloshing - Comparative Study”,1 University of Maribor, Maribor, Slovenia,2 DYNAmore GmbH, Stuttgart, Germany,3 DaimlerChrysler AG, Stuttgart, Germany, User Forum, Bamberg 2004.

3. Bedewi, N. and Omar, T., “Modeling of Automotive Fuel Tanks Using Smoothed Particle Hydrodynamics,” SAE Technical Paper 2007-01-0682, 2007, doi:10.4271/2007-01-0682.

4. Vesenjak M. and Ren Z., “Application Aspects of the Meshless SPH Method”, University of Maribor, Maribor, Slovenia, Journal of the Serbian Society for Computational Mechanics / Vol. 1 / No. 1, 2007.

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015

5. Shyue Keh-Ming, A Fluid-Mixture Type Algorithm for Compressible Multicomponent Flow with Mie-Gruneisen Equation of State”, Department of Mathematics, National Taiwan University, Taipei, Taiwan 106, Republic of China, Journal of Computational Physics 171, 678-707 (2001)

6. Smoothed-particle hydrodynamics http://en.wikipedia.org/wiki/Smoothed_particle_hydrodynamics, Wikipedia, the free encyclopedia.

7. LS-DYNA Examples, http://www.dynaexamples.com/sph, LS-DYNA example library.

Contact InformationMr. Avinash DholeMahindra & Mahindra Ltd.Trucks & Bus Divisiondhole.avinash@mahindra.comPhone No - +91 20 30694541

Mr. Rishi ShrivastavaMahindra Engineering Services Ltd.Shrivastava.rishi@mahindraengg.comPhone No - + 91-20 27501106

Mr. Chetan RavalMahindra & Mahindra Ltd.Trucks & Bus Divisionraval.chetan@mahindra.comPhone No - +91 20 30617242

AcknowledgmentsThe authors would like to thank Mahindra & Mahindra for providing an opportunity to present this work.

Definitions/AbbreviationsALE - Arbitrary Lagrangian Eulerian

CFD - Computational Fluid Dynamics

ARAI - Automotive Research Association of India

CAE - Computer Aided Engineering

FEA - Finite Element Analysis

SPH - Smoothed Particle Hydrodynamics

The Engineering Meetings Board has approved this paper for publication. It has successfully completed SAE’s peer review process under the supervision of the session organizer. The process requires a minimum of three (3) reviews by industry experts.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE International.

Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE International. The author is solely responsible for the content of the paper.

ISSN 0148-7191

http://papers.sae.org/2015-26-0240

Downloaded from SAE International by Daimler AG - Germany, Tuesday, July 07, 2015