Application of CEL method for simulation of multiphysics events in automobiles

Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 2011-01-0793 Application of CEL Method for Simulation of Multiphysics Events in Automobiles Published 04/12/2011 Ranjit Tanaji Babar, Varma Pakalapati and Vidyadhar Katkar Tata Technologies Ltd Copyright © 2011 SAE International doi:10.4271/2011-01-0793 ABSTRACT In automobiles, there are various multiphysics (specifically fluid structure interaction) events taking place which are very important from vehicle operations Examples are - oil splashing in engine, water spraying on the windscreen, fuel sloshing in a tank etc The simulation of such events becomes important in the design stage in order to study their proper functioning before the prototypes are made This paper enlightens the systematic procedures developed for the simulation of such events using coupled EulerLagrangian method available in commercial finite element explicit codes These simulations are very time consuming because of very small time steps and very large cycle time To overcome this problem an attempt is made to use rigid bodies and a low bulk modulus fluid to speed up the simulation exponentially These quick simulations can be used for early design iterations and final designs can be revalidated with flexible bodies and correct bulk modulus Based on this simulation method, following case studies are presented • Oil splashing in an engine • Fuel sloshing in fuel tank sequentially i.e the fluid domain was solved differently and after the completion of fluid simulation, its response on the structure was evaluated Recently such problems are solved using coupled simulation capability (referred to as co-simulation) available in various commercial softwares There are various methods available for simulation of such problems namely, coupled Eulerian Lagrangian (CEL) approach; Arbitrary Lagrangian - Eulerian (ALE) approach, Smooth Particle Hydrodynamics approach (SPH) and co-simulation of general purpose CFD code and FEA code [1] Each method has its advantages and disadvantages Engineers have tried solving multiphysics problem using various methods and have presented differences between them [1, 5, 6, 8] It is found from the literature that suitability of a particular method varies from application to application In this paper, CEL method is used for the simulation of FSI problems in automotive domain It is observed that, this method is well suited for the presented applications The authors have used Abaqus software for simulation of these events BASICS OF LAGRANGIAN AND EULERIAN METHOD • Fluid Motion Study LAGRANGIAN METHOD • Low fuel level management in a vehicle In the Lagrangian method the spatial part of the domain is discretized by 1-D, 2-D, 3-D or discrete elements Lagrangian elements are constant mass elements and a finite element mesh is attached to the material and these elements deform as the material starts to deform These finite elements are connected by the common grid points The material mass and velocity is defined at the grid points Forces such as inertia, INTRODUCTION The study of Fluid-structure interaction (FSI) events in an automobile is an interesting topic but difficult from simulation point of view In past, such problems were solved SAE Int J Mater Manuf | Volume | Issue 969 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Table comparison of Lagrangian and Eulerian methods stiffness, interaction and external forces act on the grid points Stresses are defined at the integration points or the element centroid Fig Lagrangian Method In this method as the boundary nodes remain on the boundary itself; boundary conditions and interface conditions can be easily defined Since the mesh deforms with the material, severe mesh deformations can occur deteriorating mesh quality Due to all these peculiarities, this method is suited for problems in which the mesh deformations are less, particularly in case of metal structures [9] EULERIAN METHOD In the Eulerian method the spatial part of the domain is discretized by volume elements In this method only brick elements (8-noded hexahedral elements) are available Eulerian mesh is fixed in time and space Eulerian elements are constant volume elements and the grids have no degrees of freedom In the Eulerian method, the material moves from element to element and allows severe deformations of the mesh since the material can freely flow inside the Eulerian mesh The material state at each point of the Eulerian domain is defined by velocity, density, specific internal energy and 970 SAE Int J Mater Manuf | Volume | Issue stress tensor at any point of time These variables relate to each other by conservation of mass, momentum, energy equations and equation of state The solution in this method is computed in space using control volume method Fig Eulerian Method Mesh boundary nodes and material boundary may not coincide in this method hence boundary conditions on the Eulerian elements are difficult to apply There are no mesh distortions in this method as the mesh is fixed in space However the domain that needs to be modeled is larger since the material should not leave the body Because of all these peculiarities, this method is best suitable in the problems where the severe material deformations are possible particularly in case of fluids [9] COMPARISON OF EULERIAN AND LAGRANGIAN METHODS The following table summarizes the difference between these two methods with respect to different features Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 COUPLED EULERIAN-LAGRANGIAN (CEL) METHOD FOR FLUID STRUCTURE INTERACTION Fluid-structure interaction events can be effectively modeled using CEL formulation available in various commercial FE codes In CEL formulation, Lagrangian domain deals with the deformations of the structure part and Eulerian domain deals with the fluid part of the problem These two domains interact with each other with contact definition between two General contact algorithms in explicit codes, enforce contact between Eulerian materials and Lagrangian surfaces All or individual Eulerian surfaces can be specified in the contact domain with Lagrangian surfaces Contact interactions between Eulerian materials and interactions due to Eulerian material self-contact, are handled by the Eulerian formulations [2] As explained earlier; the fundamental equations governing the motion of rigid and deformable bodies are those of motion, continuity and energy Finite element explicit codes solve these equations in an explicit dynamics analysis procedure These equations are listed below: CONTINUITY EQUATION (CONSERVATION OF MASS) (1) denotes the total derivative and denotes the Where, partial derivative ‘del’ ( ) is the gradient / differential operator and ‘del dot’ ( ) is the divergence operator which results in Finite element solver solves the continuity, motion and energy equations The notion of a material (solid or fluid) is introduced when specific constitutive assumptions are made The choice of a constitutive law for a solid or a fluid will reduce the equation of motion appropriately The various constitutive choices for fluids are : - i) Navier- Stokes equations for compressible and incompressible fluids with and without Bulk viscosity ii) Euler equations in case of inviscid fluids, ideal gases [4] TIPS FOR SOLVING CEL PROBLEMS In the present study, Simulia - Abaqus is used as a finite element solver for CEL method in explicit domain Following tips and techniques make the CEL simulations more accurate and fast MATERIAL MODELING IN EULERIAN DOMAIN As the material strains in the Eulerian domain tends to increase far beyond, the material data needs to be defined over the extended strain range to avoid simulation termination due to severe mesh distortions and mesh tangling (negative volumes) In case of fluid flow problems such as fluid sloshing and hydroplaning problems (applications in automotive domain); equation of state material models is recommended to use Fluid viscosity should be accounted by introducing shear properties [2] The compressibility of the fluid shall be used close to the actual physical value by choosing the correct bulk modulus value CONTACT BETWEEN LAGRANGIAN AND EULERIAN DOMAINS EQUATION OF MOTION (2) ENERGY EQUATION (3) Where is the strain rate (commonly referred to as rate of deformation tensor) For incompressible SAE Int J Mater Manuf | Volume | Issue flows, variations of density within the flow are negligible Eulerian mesh needs to be modeled in all areas where the possible fluid flow will occur during the course of the simulation event Also it is recommended that the Eulerian domain has to be extended beyond the Lagrangian domain by at least 1-2 elements General contact formulation allows the contact between all the Eulerian and Lagrangian elements along with self contacts In order to reduce the simulation time non-essential Lagrangian surfaces can be excluded from the general contact domain In case of fluid problems, the refinement of Eulerian elements helps to reduce the penetrations and leakage of fluid beyond the Lagrangian domain Typically Eulerian mesh size up to times less than minimum element size of the Lagrangian meshes works well in most of the problems discussed in this paper 971 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Initial volume fractions of the Eulerian domain elements need to be defined for representing initial volume of fluid at the start of simulation In case of complex geometries, this becomes a difficult task and use of appropriate preprocessors such as ABAQUS-CAE becomes necessary HOURGLASS CONTROLS OF EULERIAN DOMAIN As the Eulerian elements are reduced integration solid elements, hourglass control is required for solution In most of the solvers, the default hourglass settings (viscous hourglass control in case of reduced integration Eulerian elements) work well For flow-type problems using the EOS models, viscous hourglass control causes the fluid to behave more like a sponge or foam In such cases for getting realistic fluid behavior, it is better to set the displacement hourglass scaling factor to instead of 1.0 In the present study it is observed that there is no significant difference in the results of Lagrangian domain elements by changing these settings but becomes useful in the cases where the fluid flow pattern is of interest Standard checks on hourglass energy are required to be done TECHNIQUES TO REDUCE THE SOLUTION TIME In case of quasi-static problems and involving strain-rate independent material properties, loads can be ramped to the actual value in artificially shorter time to reduce the total event time Higher material density for elements can be used to increase the stable time increments In both of these cases the kinetic energy has to be low in comparison to the internal energy In some models, such as low frequency tank sloshing, fluid compressibility condition can be relaxed It is observed that results did not affect significantly This is achieved by reducing the ‘bulk modulus’ which reduces the speed of sound and correspondingly increase the stable time increments In such cases the solution must be verified carefully It is recommended to check that the volume of fluid doest not change significantly The energy due to the change of volume of all Eulerian elements has to be much lower than internal energy in the model Eulerian Element Size Selection Total simulation time depends on the stable time increment which is a direct function of element length, density and elastic modulus of material Also the significant simulation time is consumed in resolving the Eulerian-Lagrangian contact This time is directly dependent on the number of elements in the general contact domain This cost can be 972 SAE Int J Mater Manuf | Volume | Issue reduced by excluding non-essential Lagrangian surfaces from the contact domain Choosing correct Eulerian element size helps to reduce the solution time It is recommended to use the Eulerian element size equal to the smallest Lagrangian element size to start with In case the penetrations or fluid leakages occur, reduce the element size by ∼20 % and check for the penetrations again These iterations can be done in a model with rigid Lagrangian mesh which requires less simulation time as compared to flexible Lagrangian mesh Use of rigid Lagrangian mesh is explained below in one of the case studies After the verification of the contact penetrations, final solution with flexible Lagrangian elements can be given SIMULATION OF OIL SPLASHING IN AN ENGINE There are various situations in the vehicle operation conditions when the oil in the engine is splashed These situations include Vehicle is going on a gradient and the crankshaft dips in the oil in the oil sump During the braking or the acceleration of the vehicle Balancer shaft used in the engine to reduce vibrations caused by the rotation of the crankshaft; is submerged in the oil in the sump and rotation of the balancer shaft causes splashing of oil In all of the above situations, as the crankshaft and balancer shaft rotates; oil is stirred in the oil pan causing bubbles in the oil, formation of foam and oil is splashed on the walls of the crankcase This causes to reduce the lubricity of the oil Hence excessive splashing of oil in the engine crankcase is not desired The simulation of these events helps to identify the probable problems during design stage To simulate such multi-physics event, coupled Eulerian-Lagrangian method is suited where oil is modeled in Eulerian domain while all other engine aggregates are modeled in Lagrangian domain SIMULATION MODEL To simulate this event entire engine assembly consisting of following components is modeled • Cylinder block, crankshaft assembly consisting of crankshaft, flywheel, damper pulley • Balancer shaft assembly consisting of balancer shafts, gears and housing • Piston, piston pin, conrod assembly consisting of connecting rod, cap and sleeves Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig Model used for the oil splashing analysis • Rear crankcase cover, front oil pump assembly, oil sump and oil pan Refer fig for the model used in the analysis this case Engine assembly is constrained at the engine mounting brackets locations The simulation performed for revolutions of the crankshaft Revolute joints are defined at the following joint locations It was observed that there is excessive splashing of oil due the balancer shaft rotation, which may cause bubble or foam formation of oil, leading to reduction in the lubricity of oil Covering balancer shaft with separate enclosure will help to reduce splashing and churning of oil As discussed above there will also be possibility of oil splashing in case of vehicle traveling on gradients This also needs to be evaluated and these studies can be easily done with this method Conrod small end -Piston Pin, Conrod big end -Crankpin, Journal-Main bearings, Balancer shaft-bearings Oil is modeled in Eulerian domain with mm element size Eulerian domain needs to be defined at all locations where the oil is supposed to splash during the entire event In this case the Eulerian domain is defined from the bottom of the oil pan up to the bottom of the pistons covering the entire width and breadth of the cylinder crankcase allowing the oil to be splashed over entire available space Initial volume fraction of oil domain is defined based on the initial oil level in the oil sump Refer fig Oil properties at the operating temperature are used for the analysis Hydrodynamic material model in the form of equation of state along with viscous shear behavior is used for modeling oil Other components are modeled with Lagrangian shell and solid elements Automatic general contact is defined to allow interactions between all Eulerian and Lagrangian elements in the model Use of rigid Lagrangian bodies has shown the drastic reduction in the simulation time without largely affecting the simulated fluid motion Angular velocity corresponding to engine rpm is given to crankshaft Balancer shaft rotates with double the speed of the crankshaft Maximum continuous rpm of engine is considered in this study as the oil splashing will be highest in SAE Int J Mater Manuf | Volume | Issue These simulations enable designers to study oil splashing phenomenon in detail when balancer shafts are used in engines and the importance of enclosing balancer shaft to reduce the splashing FUEL TANK SLOSH ENDURANCE TEST The study of behavior of fluid in a fuel tank (fuel sloshing) is an important aspect for ensuring minimum fluid turbulence inside the tank The sloshing phenomenon in a partially filled tank is observed when the vehicle experiences sudden acceleration and deceleration During the sloshing fluid impacts the tank walls which results in sloshing induced vibrations of the tank structure which causes undesirable noise Additionally, these fuel sloshing waves generate impact forces on tank structure In view of this sloshing dynamics, following are critical fuel tank design objectives • Design of baffles to control the sloshing of the fuel 973 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig Eulerian domain and initial oil level at the start of the simulation (balancer shaft is submerged in the oil) Fig Results of the oil splashing simulation • Adequate structural integrity along with optimum weight and cost • Design of tank shell and baffles for low sloshing noise levels • Design of baffles to aid low fuel level management These design parameters are validated through the fuel tank slosh test [3] The slosh test parameters are designed in such 974 SAE Int J Mater Manuf | Volume | Issue way that the system simulates real world sloshing phenomenon These physical tests are specifically designed for ensuring the durability of the fuel tank But physical validation of slosh test is very tedious and expensive Also, visual inspection of fuel sloshing inside the tank during physical testing is not possible which is required for the baffle design Due to all these complexities associated with Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig Displacement, velocity and acceleration of the vibration table used in slosh testing Fig Model used for the analysis and initial water fraction sloshing phenomenon, CAE simulation becomes desirable to study design parameters related to sloshing dynamics This shortens the development time, cost and leads to optimized fuel tank design for NVH and durability SIMULATION MODEL This slosh endurance test was simulated using CEL method The tank was simulated for the half volume slosh endurance test During test one half of tank volume was filled with water and it was subjected to a sinusoidal movement of the vibration table actuated by a slider crank mechanism [3] Fig shows the displacement, velocity and acceleration of the vibration table These values were derived from the dimensions of the slider crank mechanism used in the test Fuel tank assembly was modeled with Lagrangian shell elements and water was discretized by solid brick Eulerian mesh Automatic general contact was defined to allow interactions between all Eulerian and Lagrangian elements in the model Hydrodynamic material model in the form of equation of state along with viscous shear behavior was used for modeling water SAE Int J Mater Manuf | Volume | Issue The Eulerian mesh was modeled in all the possible areas where the fluid is expected to flow during the entire simulation This includes the entire stroke of the slider crank mechanism Initial state of water at the start of simulation was defined by the volume fraction of Eulerian material Fig shows the simulation model Reciprocating motion in horizontal plane was imposed on tank structure as per fig.6 This was imposed by a sinusoidal motion given to base platform which is actuated by a slider crank mechanism in the test set up Entire model was subjected to gravity load The simulation was run for one cycle event of the slosh test Fig.8 shows the results of the simulation at the end of the simulation The baffles in the tank clearly show the separation of fluid and hence the reduction in the turbulence inside the tank which in turn, reduces noise as well as stresses induced on the tank structure Impact of the water on the fuel tank structure induces stresses These transient stress results obtained through one complete simulation cycle were used for the fatigue life evaluation of the tank The fatigue life calculated from the 975 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig Water sloshing states inside the tank at the end of simulation Fig Contour plot of fatigue life cycles of the fuel tank structure during the slosh test fatigue analysis gives the number of events that the tank would be able to complete Based on the acceptance criterion of the slosh test the design of the fuel tank was passed or further modified Refer Fig for the fatigue life contours of the fuel tank structure These simulations are found to be very useful in the design stage and help to reduce number of prototypes required for the design validation CEL method used for the simulation is found to be well suited for this application However, it requires huge computational time because of small time steps and higher total cycle time when run on single processor Simulations on multiple processors give very good simulation time reduction and all the available commercial softwares have the capability to parallelize the problem without compromising the solution accuracy 976 SAE Int J Mater Manuf | Volume | Issue FLUID MOTION STUDY SIMULATION BY RIGID FUEL TANK BACKGROUND As discussed, the slosh test simulation is time consuming These simulations become necessary only when the tank structure stress response is required for the fatigue evaluation or the pressure fluctuations on the tank shell are required for the NVH study of sloshing noise In these cases the fuel tank structure needs to be discretized by flexible finite elements CONCEPT AND FINITE ELEMENT MODELING In the cases where only fluid motion is required to be studied in order to decide the correct position of baffles; the fuel tank structure need not be discretized by flexible finite elements In order to reduce the simulation times, Lagrangian tank is considered as a rigid body and the bulk modulus of water is reduced (reduction by ∼100 times) In the available Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig 10 Contour Difference in sloshing results with the flexible and rigid tank approach Fig 11 Fuel sloshing results at the end of the simulation in different baffle designs commercial software codes, it is possible to model the fuel tank structure as rigid body and interactions between rigid fuel tank structure with other fluid elements In this study it is observed that there is very little difference in the results of the fluid motion inside the tank with the use of this approach as compared to the simulation with a flexible tank and actual bulk modulus of water Fig.10 shows the fluid sloshing results with the rigid tank simulation approach and the flexible tank simulation approach This approach speeds up the simulation exponentially and it is possible to evaluate different designs quickly [7] CONCEPT EVALUATION: - CASE STUDY FOR BAFFLES DESIGN In order to prove the concept, study was done to evaluate two different baffle designs against the one without any baffles for the fluid motion [7] Fig 11 below shows the results of sloshing of fuel at the end of slosh test simulation It is observed that in design1 with full height baffles, there is complete separation of water within different compartments formed by two baffles which will reduce the sloshing noise significantly In design 2, with half height baffles there is partial separation of water within the tank These two designs will reduce the fluid turbulence and in turn sloshing noise as compared to the tank design without baffles by separation of the fuel, but the strength of the baffles needs to be evaluated afterwards for slosh endurance test These simulations were completed vary fast with the above approach and different design iterations were possible before finalization of the best design particularly for deciding the appropriate baffle positions in order to create minimum fluid turbulence inside the tank during vehicle operation LOW FUEL LEVEL MANAGEMENT IN A VEHICLE USE OF FLUID MOTION STUDY One of the important design aspects of the fuel system in an automobile is low fuel management While designing the fuel systems, the location of fuel pump inlet in the fuel tank needs to be chosen in such a way that enough fuel exists at any vehicle operation condition (e.g turning at high speeds, cruising on high gradients during very low fuel levels in the tank Such studies can be performed with the use of this CEL method during the design stage without the need of physical testing SIMULATION MODEL To simulate this phenomenon, fuel tank assembly is modeled with Lagrangian shell elements and fuel is modeled in Euler domain Refer fig 12 for the model details In this study, minimum possible fuel level in the tank is considered Centrifugal acceleration experienced by vehicle during turning is calculated by minimum turning radius and vehicle speed These acceleration magnitudes are applied at the mounting locations of the fuel tank in negative and positive lateral-directions simulating the vehicle taking left turn or right turn Other degrees of freedom are constrained The simulation was run for 0.2 seconds in which the acceleration was ramped up to desired level initially and kept constant till the end of the simulation Following fig 13 shows this case of the vehicle turning at low fuel levels present the possibility of engine shut off due SAE Int J Mater Manuf | Volume | Issue 977 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Fig 12 Model used in the analysis of low fuel motion study Fig 13 Low fuel management study using sloshing simulation - Results at the end of simulation to fuel cut off Simulation results show that there is no fuel at the pump inlet location while the vehicle is taking left turn techniques are given for the effective use of this method particularly for FSI events in the automobile domain This particular vehicle was tested and the phenomenon of fuel cut-off was observed in the physical testing as predicted by the simulation results [7] These simulations have been found very useful in the design stage and minimizes the testing of physical prototypes and helps to reduce the overall design cycle time and cost Thus this study enables designers to choose correct locations of fuel pump inlets through simulation at various vehicle operation conditions REFERENCES SUMMARY/CONCLUSIONS Out of the various available methods for fluid-structure interaction problems, coupled Eulerian-Lagrangian method can be used for the various automotive FSI applications It is found that this method is well suited for the problems involving severe contact changes between fluid and structure and found to be the better option for solving problems with complex and changing contact states [5, 6, 8] Applications described in this paper have shown fair correlation with the physical tests Based on the work done on this topic, tips and 978 SAE Int J Mater Manuf | Volume | Issue 1 Ma, Jean, Usman, Mohammad “Modeling of fuel sloshing phenomenon considering solid structure interaction” 8th International LS-Dyna user conference paper ABAQUS 6.9EF User Documentation Tata Motors technical specifications on fuel tank testing Ibrahim, Raouf A “Linear sloshing dynamics: Theory and Applications” Legay, J Chessa and Belytschko, T “An EulerianLagrangian Method for Fluid-Structure Interaction Based on Level Sets.” Computer Methods in Applied Mechanics and Engineering, in press, 2005 Downloaded from SAE International by Hacettepe Univ, Sunday, July 24, 2016 Abdalla, Basel, Pike, Kenton, Eltaher, Ayman, Jukes, Paul “A Coupled Eulerian Lagrangian Finite Element Model of Ice-Soil-Pipe Interaction” Advanced Engineering Group, J P Kenny Houston, TX, USA Babar, Ranjit, Katkar, V “Simulation of fuel tank slosh test-coupled Eulerian Lagrangian Approach” Abaqus RUM 09 India Brown, Kevin H., Burns, Shawn P., Christon, Mark A “Coupled Eulerian Lagrangian Methods for Earth Penetrating Weapon Applications” Sand Report SAND2002-1014, Sandia National Laboratories Belytschko, T., Liu, W.K., and Moran, B “Nonlinear Finite Elements of Continua and Structures” John Wiley and Sons, Ltd., New York CONTACT INFORMATION Mr Ranjit Babar Ranjit.Babar@tatatechnologies.com Mr Vidyadhar Katkar v.katkar@tatatechnologies.com Mr Pakalapati Varma Varma.Pakalapati@tatatechnologies.com ALE Arbitrary Lagrangian-Eulerian method SPH Smooth Particle Hydrodynamics CFD Computational Fluid Dynamics FEA Finite Element Analysis FSI Fluid Structure Interaction CAE Computer Aided Engineering NVH Noise Vibration and Harshness EOS Equation of state ACKNOWLEDGMENTS We would like to thank Mr Ashok Joshi (Head - Vehicle Performance Group - ERC Tata Motors) for giving us the opportunity to work on these projects The author would also like to thank co-workers involved in the vehicle testing group and vehicle design group for giving us the desired technical inputs at the appropriate time of the project Also the authors would like to thank Simulia-India local technical support team for their software technical inputs ABBREVIATIONS CEL Coupled Eulerian-Lagrangian method SAE Int J Mater Manuf | Volume | Issue 979 ... finite element solver for CEL method in explicit domain Following tips and techniques make the CEL simulations more accurate and fast MATERIAL MODELING IN EULERIAN DOMAIN As the material strains... Fluid-structure interaction events can be effectively modeled using CEL formulation available in various commercial FE codes In CEL formulation, Lagrangian domain deals with the deformations of the structure... SAE International by Hacettepe Univ, Sunday, July 24, 2016 Initial volume fractions of the Eulerian domain elements need to be defined for representing initial volume of fluid at the start of simulation