Application of CEL method for simulation of multiphysics events in automobiles

• Oil splashing in an engine • Fuel sloshing in fuel tank • Fluid Motion Study • Low fuel level management in a vehicle INTRODUCTION The study of Fluid-structure interaction FSI events i

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

Euler-Lagrangian 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

• Fluid Motion Study

• Low fuel level management in a vehicle

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

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

LAGRANGIAN METHOD

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,

Application of CEL Method for Simulation of

Multiphysics Events in Automobiles

2011-01-0793 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

stiffness, interaction and external forces act on the grid

points Stresses are defined at the integration points or the

element centroid

Fig 1 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

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 2 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

Table 1 comparison of Lagrangian and Eulerian methods

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)

Where, denotes the total derivative and denotes the

partial derivative ‘del’ ( ) is the gradient / differential

operator and ‘del dot’ ( ) is the divergence operator

EQUATION OF MOTION

(2)

ENERGY EQUATION

(3)

Where is the strain rate (commonly

referred to as rate of deformation tensor) For incompressible

flows, variations of density within the flow are negligible 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

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 2 times less than minimum element size of the Lagrangian meshes works well in most of the problems discussed in this paper

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 0 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

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

1 Vehicle is going on a gradient and the crankshaft dips in

the oil in the oil sump

2 During the braking or the acceleration of the vehicle.

3 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

• Rear crankcase cover, front oil pump assembly, oil sump

and oil pan

Refer fig 3 for the model used in the analysis

Revolute joints are defined at the following joint locations

Conrod small end -Piston Pin, Conrod big end -Crankpin,

Journal-Main bearings, Balancer shaft-bearings

Oil is modeled in Eulerian domain with 4 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 4 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

this case Engine assembly is constrained at the engine mounting brackets locations The simulation performed for 5 revolutions of the crankshaft

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 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

Fig 3 Model used for the oil splashing analysis

• 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

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

Fig 4 Eulerian domain and initial oil level at the start of the simulation (balancer shaft is submerged in the oil)

Fig 5 Results of the oil splashing simulation

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

6 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

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

7 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

Fig 6 Displacement, velocity and acceleration of the vibration table used in slosh testing

Fig 7 Model used for the analysis and initial water fraction

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 9 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

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

Fig 8 Water sloshing states inside the tank at the end of simulation

Fig 9 Contour plot of fatigue life cycles of the fuel tank structure during the slosh test

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 3 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

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

to fuel cut off Simulation results show that there is no fuel at

the pump inlet location while the vehicle is taking left turn

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]

Thus this study enables designers to choose correct locations

of fuel pump inlets through simulation at various vehicle

operation conditions

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

techniques are given for the effective use of this method particularly for FSI events in the automobile domain

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

REFERENCES

1 Ma, Jean, Usman, Mohammad “Modeling of fuel sloshing

phenomenon considering solid structure interaction” 8th International LS-Dyna user conference paper

2 ABAQUS 6.9EF User Documentation

3 Tata Motors technical specifications on fuel tank testing

4 Ibrahim, Raouf A “Linear sloshing dynamics: Theory and

Applications”

5 Legay, J Chessa and Belytschko, T “An

Eulerian-Lagrangian Method for Fluid-Structure Interaction Based on Level Sets.” Computer Methods in Applied Mechanics and Engineering, in press, 2005

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