Application of CEL method for simulation of multiphysics events in automobiles

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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
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Table 1. 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 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
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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.


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

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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

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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


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Fig 3. Model used for the oil splashing analysis
• Rear crankcase cover, front oil pump assembly, oil sump
and oil pan
Refer fig. 3 for the model used in the analysis.

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

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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

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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
• 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
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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


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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
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.

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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

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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
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.

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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


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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 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

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


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6. 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
7. Babar, Ranjit, Katkar, V “Simulation of fuel tank slosh
test-coupled Eulerian Lagrangian Approach” Abaqus RUM
09 India
8. 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
9. 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

Mr. Vidyadhar Katkar

Mr. Pakalapati Varma


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

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