2005-01-1426

Crushing simulation of a partially filled Fuel Tank beyond failure

W.A. van der Veen MSC.Software Corporation

Copyright © 2005 SAE International

ABSTRACT

The crushing of a partially filled fuel tank is an important aspect of rear impact safety. A simulation will be presented of this event, where the fuel tank contains both fuel and air, and is crushed beyond failure. The simulation process starts with proper initialization of the fuel and air inside the tank under gravity loading, after which the fuel tank will be crushed between a wall and a moving rigid barrier. Once the fuel tank material fails, fuel leakage will be predicted.

Multiple, adaptive Euler domains are used to model the baffles inside the tank and the surrounding air. Since the model includes fuel and air, a multi-material Euler solver is required.

The simulation is performed with MSC.Dytran.

INTRODUCTION

This paper describes the simulation of crushing and subsequent leakage of fuel tanks. An example is the impact of a tank by another object such that it hits another obstacle and is partially crushed. In this paper we will describe the recent enhancements made to the algorithms in MSC.Dytran. This is a commercial software package for short-term transient analyses that involve structural parts and/or CFD parts. Important areas of applications are air bag deployment, tank fuel sloshing and impact events. For further information refer to [1] and for background on CFD in general see [2,3]. The purpose of the paper is demonstrating that MSC.Dytran is able to simulate fuel leakage. Since Euler elements are stationary, meshing of Euler elements requires no effort of the user and remeshing is avoided. The fuel tank is modeled with Lagrangian shell elements incorporating both a plasticity model as well as a failure model. Once a shell element meets a failure criterion it fails and flow can take place through this failed element. Whether flow really takes place depends on the presence of fuel at the failed segments and the velocity of the fuel. The inside of the tank is filled with a

combination of air and fuel and since displacements in the fluid can be quite large it is natural to model the inside with an Eulerian Finite volume domain. Only Euler elements that are completely or partially within the tank surface can contain mass. Therefore the shell elements of the tank provide the effective boundary of the Euler domain. The shell elements do not only serve as an effective boundary but can also function as a portal to move mass in the Euler domain to or from other regions. For example when shell elements fail flow can take place from inside this inner Eulerian domain to the surroundings of the fuel tank. As a first approximation one could model these surroundings as one large box that only permits uniform pressure and density, allowing no resolution of the flow pattern outside the tank and near the failed shells. To achieve a good resolution of the flow processes at these segments the surroundings of fuel tank will also be modeled by an Eulerian finite volume domain. The reason why the surrounding influences the flow pattern at the failed segments is that flow is subsonic and therefore outflow properties are determined by both sides of the outflow segment. To summarize, the leakage is modeled by two Euler domains that are separated by the tank surface. In this setting leakage to the surrounding is transport of material in the inner domain to the outer domain. From now on, the inner domain will be called the fuel domain and the domain that models the surroundings will be called the ambient domain. The paper describes a method to enable flow from one domain to another domain through failed shell elements. The ambient and the fuel domain can have meshes that do not coincide. By creating a so-called overlapping mesh, which is the union of the two meshes flow is enabled between the fuel and tank domain. The method operates automatically and requires no intervention by the user. Since baffles play an important role in fuel tanks a method is presented to simulate baffles. This is done by splitting the fuel domain inside the tank into two Euler domains, and block flow between the two domains at the location of the baffle. The paper concludes with presenting results for a real life example. For the application of the methods presented in this paper to multi compartment airbag simulations refer to [4].

FORMULATION OF THE PHYSICAL PROBLEM

In a typical crushing simulation there are air, fuel and the metal or plastic of the tank. The air is assumed to be an ideal gas and satisfies the equation of state:

( 1)p eγ ρ= −

Here p, ρ and e are respectively the pressure, density and specific internal energy and γ is the ratio of the heat capacities of the gas.

The equation of state of the fuel is assumed to be of the form

2 3 2 31 2 3 0 1 2 3 0

0

( )

1

p a a a b b b b eµ µ µ µ µ µ ρρµρ

= + + + + + +

= −

Here p, ρ, 0ρ and e are respectively the pressure, density, reference density and specific internal energy. The variables ia and ib are constants that either follow from experiments or from theoretical considerations. The material flow is described by the conservation laws for mass, momentum and energy, that read:

Here V is a volume, A is the boundary of this volume, n is the normal vector along the surface A, u denotes the velocity vector and g denotes gravity. Using these equations for multi-material requires some care and will be discussed later on.

The usual strength and plasticity models describe the metal.

ANALYSES USING ONE EULER DOMAIN

INTRODUCTION

Before discussing the methods for analyses with several Euler domains, we briefly discuss the solution procedure used for analyses with one Euler domain enclosed by a deformable tank. Examples are sloshing and tank filling. These types of analyses have already been conducted many times with MSC.Dytran over the years. Euler

domains are allowed to contain several materials. Typically, the tank domain contains air and fuel, however, more are allowed.

It is expected that for the intended applications first-order space and time accurate methods are adequate.

The inside of a tank is filled with a combination of air and fuel. Euler Elements that are outside the tank surface cannot hold material and only elements that are partially or completely inside the surface have the capacity to contain mass. This surface defines the effective boundary of the Euler domain and will be called the coupling surface.

The mass of air and fuel is not separated by any kind of material interface but the mass transport logic limits mixing as much as possible. Only when mixing is really physical mixing does occur. So in most simulations there is an interface visible between regions filled with fuel and regions filled with air. Nevertheless after extensive sloshing it might happen that only a mixture of air and fuel is left and that there is only a fragmented interface.

The tank surface consists of shell elements that deform under pressure and support failure models. An explicit finite element solver solves the shell dynamics, and an explicit Euler solver solves the fluid dynamics inside the fuel tank. The interaction between these two solvers takes place in two ways

• The mass in the Euler elements exerts a pressure load on the tank surface. These loads constitute an additional set of boundary conditions for the finite element solver, resulting in new gridpoint accelerations and velocities for the tank. From the updated plastic strain or updated stresses of the shell elements it is determined which elements are failing. Finally the tank grid points are moved with the new velocities

• The tank grid points move and so the Euler mesh has a new boundary. Consequently, the volume of mass in each element may change. Since density is mass divided by the volume of the mass, densities will also change, and so will the pressures.

THE EULERIAN SOLVER

Within an Euler element the state variables are assumed to be constant, and are defined in the element center. The grid points of the Euler elements will remain stationary throughout the simulation.

The Euler elements are integrated in time by applying a finite volume method directly to the physical domain, avoiding the use of coordinate transformations. Therefore the finite volume method is applied to the 3D object that consists of that part of the Euler element that is inside the tank. This is in general not a cube but a

3

( · ) 0

( · )

( · )

V A

i i iV A A

i iV A A

d dV u n dAdt

d u dV u u n dA pn dA ge Vdt

d edV e u n dA u pn dAdt

ρ ρ

ρ ρ ρ

ρ ρ

+ =

+ = − −

+ = −

∫ ∫

∫ ∫ ∫

∫ ∫ ∫

multi-faceted object. For the 2D case this is sketched in Figure 1.

Figure 1: The boundary of an Euler element

In this figure the square represents the Euler element. It is intersected by the tank surface. The area bounded by the square and the tank surface is the effective volume of the gas and fuel in the element. The boundary of this portion consists of two types of surfaces:

1. Euler element boundaries that connect two neighboring elements called ‘Euler faces’.

2. Parts of the tank surface that are within the Euler element. They will be called ‘polpacks’, which is short for “polyhedron packets”.

Therefore the effective boundary of an Euler element consists of Euler faces and polpacks.

A polpack is the intersection of a tank shell element with an Euler element and is completely inside an Euler element and completely inside a tank shell element. In MSC.Dytran an algorithm is available that computes these polpacks for any given, closed 3D faceted surface, and any 3D Euler domain.

Faces refer to two Euler elements, whereas polpacks refer to only one Euler element. For both faces and polpacks, areas and normals are computed.

In MSC.Dytran the finite volume method amounts to applying the conservation laws for mass, momentum, and energy to these 3D objects. In applying these laws, we encounter volume and surface integrals. The volume Integrals are straightforward to compute and the surface integrals are computed by summing over the faces and polpacks. In the three conservation laws the surface integral on the left-hand side signifies transport of either, mass, momentum or energy through polpacks and

faces. A contribution of a polpack or a face to these integrals is called a flux.

When there is more than one material present in the simulation the mass conservation law applies to each material separately. This means that for each material inside an Euler element the density has to be monitored. In applying the momentum law it does not matter whether there are several materials since all materials inside an Element are assumed to have the same velocity. The energy equation will also be applied to each material separately.

First consider simulations with only one material present. In the mass conservation law, the mass flux across a face gives:

Here M is the mass in the Euler element, V is the velocity vector, A denotes the area vector of the face, ∆t is the timestep, DONOR denotes the element supplying mass and ACCEPTOR denotes the element receiving mass. In most cases the tank surface is not permeable, and there will be no transport across the polpacks. However, in case fuel tank shell elements have a porosity model assigned, the flux equations will take that into account.

The momentum in an element can increase by either transport of momentum, or by a pressure load working on the polpacks and faces. The pressure load contribution to this momentum increase is the surface integral i

A

pn dA t− ∆∫ . The force contribution of a face to

the momentum increase of the element left to the face and right to the face reads:

Here P is the momentum of an element, A is the area vector pointing from the left element to the right element and pface is a weighted average of the pressure in the two elements that are on the left and right of the face. These momentum updates clearly conserve the combined momentum of the left and right element.

For polpacks the contribution is likewise, but now the pressure at the polpack is given by the pressure in the Euler element that contains the polpack. To conserve momentum the negative of this momentum contribution is put as a force on the tank shell element that hosts the

| · |

| · |DONOR DONOR

ACCEPTOR DONOR

M V A t

M V A t

ρ

ρ

∆ = − ∆

∆ = + ∆

uuruur

ur ur

FaceLeft

FaceRight

P p A t

P p A t

∆ = − ∆

∆ = ∆

ur ur

ur ur

polpack. This is the way boundary conditions are imposed on the tank surface. In a similar way the energy equation is applied.

The procedure for advancing the Euler domain with one timestep is as follows:

1. Update stresses and plastic strain of the tank shell elements and determine which elements are failing. Move the grid points of the tank using their velocities. Determine contact between tank, impacting objects and other structural parts.

2. Using the new position of the tank compute new polpacks. Using polpacks and faces compute for all Euler elements the volume of the portion that is inside the tank.

3. Transport mass, momentum, and energy across all faces and permeable polpacks using the conservation laws. The flux velocity is the average of the left and right Euler element velocity. In case no right Euler element is available the flux velocity is determined from an inflow condition and in some cases the velocity of the Euler element. Examples are holes and parts of surfaces that enable flow into the tank as a means of filling the tank.

4. For each Euler element compute density from the new mass and volume and compute pressure from the equation of state using the new density.

5. Compute the force contribution to the momentum increase for all faces and polpacks. The transport contribution to the momentum increase has already been computed in step 3.

6. Advance the tank surface with one timestep using the internal shell element forces, contact forces and external forces from the Euler domain and compute new velocities on the grid points.

7. Compute a new stable timestep based on the mesh size, speed of sound and velocity. The stability criterion used is the CFL condition and applies to both the structural tank surface as well as to the Euler elements.

For simulations involving multi-material, some modifications to the transport logic and pressure computation are necessary. This modified transport logic is known as preferential transport and tries to maintain interfaces between materials. Consider for example the case of a blast wave of air in water. It is important that the interface between water and air during the expansion of the blast wave is maintained and does not deteriorate by the unphysical mixing of water and air.

To enable a multi-material simulation a certain amount of bookkeeping is needed. For every Euler element the following information needs to be available

• The number of materials inside the Euler elements

• For each material the volume fraction, the material ID, the density, the mass, the specific energy, the total energy and volume strain rates

are stored. The volume fraction of a material is defined as the fraction of Element volume that is filled with that material.

The transport logic for multi-material amounts to:

1. Compute the volume that will be transported. This is | · |V A t∆

ur urand this volume flux gives rise

to a mass flux. Had there been only one material the mass flux would have been the density times the volume flux, but now the donor element has several materials and each material has a distinct density and therefore the mass flux will be split into several mass fluxes. Each material in the donor element has a distinct mass flux and this material specific mass flux can be easily converted into a volume flux by using the material density. Using this conversion the mass fluxes should give rise to volume fluxes that add up to a total volume flux that equals | · |V A t∆

ur ur.

Materials will be transported out of the element until the prescribed total volume flux is reached. The only remaining issue is which materials should be transported first.

2. Determine for both donor element as well as acceptor element which materials are present in the element.

3. Look which materials are common to both elements.

4. First transport any material that is common to both elements. Transport these common materials in proportion to their acceptor material fraction. A material is transported with the material density of the donor element and this material density translates a volume flux into a mass flux and vice versa. Subtract any mass that is transported from the flux volume. If there is sufficient mass of the common materials in the donor element the whole flux volume will be used to transport the common materials.

5. If after transport of the common materials the flux volume is not fully used yet, transport materials in ratio to their donor material fraction.

To illustrate how this procedure tries to preserve material interfaces, consider two adjacent Euler Elements and assume that flow is from the left element to the right element. The left element is filled with fuel and air and the right one is filed with only air. Since air is the only material common to both elements first air will be transported. If there is sufficient air only air will be transported. If during transport there is no air left transport of this common material is not able to use the full flux volume and also fuel will have to be transported. In both cases the interface between fuel and air is maintained.

The pressure computation for Euler elements with only one material is straightforward: the pressure readily follows from the equation of state and the density. For elements with more than one material each material has a distinct equation of state and a distinct density and this results in a distinct pressure for each material. The pressure computation for these elements will be based on the thermodynamic principle of pressure equilibrium. Since masses of materials in Euler elements are only changed by the transport computation these masses are fixed during the pressure computation. The volume taken up by each material in an Euler element is not known but determines the pressure inside the material. By adjusting the volumes of the materials simultaneously pressure equilibrium is achieved. Therefore the pressure computation amounts to an iterative process that iterates on the volumes of the materials inside the Euler element.

To understand the influence of the material volumes consider an element with fuel and air. Suppose that at the start of a cycle there is pressure equilibrium and that during transport air enters the element. Because of the surplus of air there is no longer pressure equilibrium. Physically it is expected that the air will very slightly compress the fuel until pressure equilibrium is achieved. The compression of the air is just the adjustment of the material volumes of fuel and air. The material volume of air increases while the material volume of fuel decreases.

ANALYSES USING MULTIPLE EULER DOMAINS

Until recently analyses with MSC.Dytran were limited to one Euler domain. With the method described here it has become possible to analyze several Euler domains enclosed by structures. Furthermore, flow and other communication from one Euler domain to another takes place through failed shell elements. These failed elements will be called holes and any polpack that represents a hole will be called a flow polpack.

To model the crushing of a fuel tank two Euler domains will be used. The contents of the tank are modeled by the fuel domain and this domain is enclosed by the tank surface. All material of this Euler domain is inside the tank surface. The ambient domain also has the tank surface as part of the boundary, but now material is outside the tank surface and there is no material inside the tank surface. The outer boundary of the ambient domain is given by a sufficiently large fixed box. Therefore both Euler domains use the tank surface as part of their enclosure.

The fuel domain will be initialized by a combination of air and fuel while the ambient domain will be initialized by conditions that resemble an ambient surrounding.

In the explicit solvers the stable timestep depends on the mesh size. Multiple Euler domains may have different mesh sizes and therefore different stable timesteps. It is possible to update each Euler domain with a timestep

that is specific for the domain, but this would require subcycling. For the analyses under consideration it is expected that the mesh sizes of the various Euler domains are of the same order of magnitude. Therefore, it seems appropriate to evolve all Euler domains with the same timestep.

To advance the Euler domains with one timestep the conservation laws are applied to all elements in the Euler domains using faces and polpacks. This is straightforward, except where the boundary of an Euler element is connected to failed shell elements. This connection takes place via the polpacks of the Euler element and these polpack should provide the communication between the two domains. The problem is that these polpacks still refer to only one Euler element in one domain and cannot refer to another element in a second domain. For enabling the communication between two Euler domains through a hole, polpacks are needed that refer to two Euler elements that are each in a different Euler domain. How this new type of polpack is constructed, will be described below. For now we assume that it can be done and we will call them flow polpacks. At these flow polpacks the flow between the Euler domains takes place.

The procedure to advance the Euler domains with one timestep consists of the following steps:

1. Move the gridpoints of the tank using the velocity on the grid points.

2. For all Euler domains check whether the Euler mesh is still sufficiently large to contain the tank. If not, extend the Euler mesh. If possible, delete empty Euler elements that have become too far away from the tank surface.

3. Using the new position of the tank surface, compute polpacks for all domains. Using polpacks and faces, compute for all elements the volume of that part of the element that is inside the tank.

4. For all Euler Domains do transport across all faces and porous polpacks using the mass conservation law. The flux velocity is the average of the left and right Euler element velocity. Here, an Euler mesh is processed independently of the other meshes. Communication between the domains is postponed until step 5.

5. For all flow polpacks do transport. Here mass is going from an element in one domain to an element in the other domain.

6. For all Euler elements compute density from the new mass and compute pressure from the equation of state using the new density.

7. Compute the force contribution from the regular polpacks and faces to the momentum increase in the elements. The pressure at the face is a weighted average of the left and right Euler element. Pressures in the Euler elements that have polpacks give rise to forces on the tank.

8. For all flow polpacks calculate the force contribution to the momentum increase. Here contributions from the flow polpacks are going into two Euler domains.

The procedure is exactly the same as for faces. At regular polpacks the mass in the Euler element exerts a force on the tank shell element, but at fully porous flow polpacks no forces are exerted on the tank.

9. Advance the tank grid points with one timestep using internal shell element forces, contact forces and external forces from the Euler domain. Compute new velocities for the grid points.

10. Based on the CFL condition, compute a new timestep using the mesh size, speed of sound and material velocity. Every element in every domain yields a largest stable time step. Also the time step restriction of the FE structural part has to be taken into account. The time step that will be used to advance all the domains to the next step is the smallest of these timesteps.

Now we describe the construction of flow polpacks and step 5 in more detail.

CONSTRUCTION OF FLOW POLPACKS

The current procedure for creating polpacks in MSC.Dytran takes as input a closed surface and an Euler mesh. The surface is defined by means of triangular and quadrilateral shell elements. The output consists of polpacks that refer to the Euler mesh that was passed as input. For every polpack we know the surface element from which it was derived and we know the Euler element it is located in.

In the vicinity of the hole there are two Euler meshes that have a partial overlap and polpacks should refer to both one element in the first mesh as well as to one element in the second mesh. Furthermore, each flow polpack should fit completely in an element of the first mesh and completely in an element of the second mesh.

Here the problem arises that the polpack creation procedure can only handle one Euler domain. A good way to solve this problem is to create a third auxiliary mesh that is called the hole mesh. First we determine the largest box that is inside both Euler domains. This box represents the overlap of the two meshes. Putting the two meshes on top of each other, and ignoring all elements that are outside the overlap box, gives the hole mesh. This procedure is illustrated in Figure 2. By construction, every element in the hole mesh is completely in an element of the first mesh, and completely in a element of the second mesh. Also the surface of the hole is completely in this hole mesh, because the surface of the hole is in both Euler domains, and therefore in their overlap.

To create the flow polpacks we take the following steps:

1. Create all polpacks for the individual Euler domains as explained in the section “Analyses using only one Euler domain”.

2. Assemble the hole mesh from the Euler meshes. For every Euler element in the hole mesh we compute in

which element of the first domain and in which element of second domain it is located.

3. Put the hole mesh plus the tank surface into the polpacks creation procedure. Only that part of the tank that is inside the hole mesh is processed. The resulting polpacks are called hole polpacks. They are not flow polpacks yet, because they still refer to one mesh, that is the hole mesh.

4. This new set op polpacks also contains polpacks that are not part of a hole. Therefore it is determined which ones are part of a hole surface.

5. In the list of polpacks created in step 1 for the individual Euler domains, delete all polpacks that are part of the hole and that still refer to one Euler domain.

6. We have obtained hole polpacks that refer to elements in the hole mesh. Now we can make flow polpacks that refer to two elements in the two domains using the information obtained in step 2.

Note: It is not needed to make a new hole mesh every cycle. Only when tank shell grid points move outside the hole mesh, a new hole mesh is created. Also a new mesh is created when the adaptive Euler mesher changes one of the Euler domains. Of course the flow polpacks need to be updated every cycle due to the changing tank surface geometry.

Figure 2: Assembling the hole mesh

FLUXING ACROSS THE HOLE POLPACKS

Given a flow polpack the transport of mass across the hole is given by:

1 21 ( )2

·

TRANS ELT ELT TANK

TRANS ppDONOR pp

V V V V

M V n Area tρ

= + −

∆ = ∆

ur ur ur ur

ur r

in the case of a single material simulation. Here, VELT1 and VELT2 are the velocity vectors in respectively the element in the first Euler domain and the element in the second domain, pp stands for polpack and ρDONOR is the density of the Euler element that is supplying mass. In the same way momentum and energy are transported.

When there are multiple materials inside the two elements then the modification is followed that was described in section ANALYSES USING ONLY ONE EULER DOMAIN. This means that materials common to the element in the fuel domain and the element in the ambient domain are transported first.

Figure 3: a baffle

MODELING BAFFLES

To counteract sloshing baffles are commonplace and need to be taken into account in any accurate simulation. Baffles can be much thinner than an Euler element and this complicates the simulation. Using ALE will avoid these complications but requires detailed meshing by the user and is time consuming. Any other finite volume approach has to use overlapping Euler elements

In principle one could simulate flow around a baffle by taking an Euler mesh, making a cut in the mesh along the baffle and extending the mesh across the cut on both sides of he cut. However, this approach is not generally applicable and this paper presents a general approach using multiple finite volume domains.

Consider the setup shown in figure 4. To model the flow around the baffle the fuel domain is split into two fuel domains each having a separate coupling surface. A coupling surface provides an enclosure for the material in an Euler domain and has to be a closed surface. To create a closed coupling surface for each domain a fully porous surface that connects the baffle to the nearest walls is added to the coupling surfaces. This porous surface is meshed with regular shell elements, which have no strength but have a porosity model assigned. This porous property triggers the creation of flow

polpacks for these shell elements and flow can take place across this porous surface in the same way as transport can take place across failed surface elements.

Figure 4: Modeling a baffle

ADAPTIVE EULER DOMAINS

An Euler domain is associated with a coupling surface. This surface indicates the region inside the Euler domain that may contain mass. If parts of the inside region of the coupling surface are not completely covered by Euler elements then these parts cannot hold mass. To prevent this modeling error Euler elements must always cover the whole inside of the coupling surface. A straightforward way do this is to create an Euler domain that is sufficiently large. This is inefficient especially when the coupling surface is moving through the Euler domain. In MSC.Dytran the efficient method of adaptive finite volume meshing is available. This method deletes Euler elements that are completely outside the coupling surface and creates Euler elements to ensure that the coupling surface is fully covered.

REAL LIFE EXAMPLE: CRUSH OF A PARTIALLY FILLED TANK BEYOND FAILURE

PROBLEM SETUP

This problem demonstrates the multi-domain modelling technique for simulating sloshing of fuel and fuel leakage when shell elements of the fuel tank fail and rupture. The fuel tank is partially filled with fuel and the remaining volume with air. The tank is impacted by a sled moving at a velocity of 20 m/s and is subsequently crushed by the presence of a wall. During the impact both violent sloshing as well as fuel leakage will take place. To counteract sloshing of fuel a baffle is inserted in the tank. Moreover, the tank surface is locally deforming to the extend that it produces a second baffle. This occurs at the location were the cross-sectional is minimal. To model these two baffles three Euler domains will be used for the inside region of the tank. A fourth Euler

model models leakage to the ambient. Gravitational force is applied in the negative z-direction.

Figure 5: problem setup

The fuel tank surface is modeled with quadrilateral and triangular elements. The material of the fuel tank surface is modeled using an elasto-plastic material model where an effective stress-plastic strain curve and plastic strain failure limit are specified. The sled is modeled as a rigid body and can only move in the X-direction. The initial velocity of the sled in X-direction is 20 m/sec. The wall and the floor are rigid and fixed in position and are modeled with quad elements.

Contact is defined between the fuel tank and other structural components in the model: sled, wall and floor. A single surface adaptive contact is defined for the elements of the fuel tank. This will allow self-contacting elements after buckling of the tank surface.

The tank is shown in more detail in Figure 6. For modeling flow around the baffles the approach described in section “MODELING BAFFLES” is used. The baffles will be modeled by rigid shell elements. On each side of the baffle separate Euler domains are created. Consider the baffle shown in Figure 6. To create closed coupling surfaces that contain this baffle a fully porous surface is added that extends the baffle to the nearest walls. This fully porous surface consists of membrane shell elements that have no resistance to deformation. These elements only serve to close coupling surfaces and to enable transport of mass between the Euler domains by means of flow polpacks. Therefore these elements will be called dummy elements. The fully porous surface and the baffle divides the tank into two sections as shown in figure 7.

The first Euler domain models the fluid between the surface consisting of the baffle shell elements, the dummy elements and the rear part of the tank and its effective boundary is formed by a coupling surface. This first coupling surface consists of:

• The part of the tank surface that extends from the baffle to the rear

• The baffle surface and the surface of dummy shell elements

Figure 6: location of the baffle

This first coupling surface and the first Euler domain are shown in figure 7. For this coupling surface and the second and third coupling surfaces material is inside each coupling surface.

Figure 7: The first coupling surface

In view of large deformations it is possible that at the tank cross-section where area is minimal the coupling surface deforms so much that geometry resembles a baffle. The approach for baffles will be used at this cross-section to maintain accuracy and therefore the

remainder of the tank is split into two parts. This splitting is provided by a second dummy shell surface that is fully porous and is located at the section with minimal area. We shall call this surface the porous bulkhead.

This fully porous surface also divides the tank into two parts and requires an Euler domain to the left of the surface and one Euler domain to the right.

The coupling surface of the second domain will consist of:

• The part of the tank surface that extends from the baffle to the porous bulkhead

• The porous bulkhead

• The baffle surface and the surface of dummy shell elements that were needed for the baffle approach.

and is shown in Figure 8.

Figure 8: The second coupling surface

The third one will be:

• The part of the tank surface that extends from the porous bulkhead to the front

• The porous bulkhead.

The third coupling surface is shown in figure 9.

For the outside of the tank we need a fourth Euler domain, which gives a total of four Euler domains. The coupling surface of this last Euler domain is the whole tank surface and is shown in figure 10. The baffle and dummy shell surfaces are not included in this coupling surface.

Since the fourth Euler domain models the ambient, the material is outside of the fourth coupling surface material. Material in this Euler domain has two boundaries. The first boundary is the fourth coupling surface and the second boundary is the end of the Euler domain. This last boundary consists of the faces of the boundary Euler Elements. A transmitting boundary condition will be applied at these faces, which allows fuel to leave the ambient domain.

Figure 9: The third coupling surface

The first three Euler domains have material only inside the coupling surface and for efficiency adaptive meshing will be used. The fourth Euler domain has material outside the coupling surface and for that case there is no adaptive meshing. Consequently this Euler mesh does not change during the run.

Figure 10: The fourth coupling surface

RESULTS

The simulation time is 0.1 sec and runs for 25.5 hours on a 1.5 Ghz windows 2000 system.

Figures 11-15 show the sloshing of the fuel. Also seen is the fuel leakage outside the tank when the elements of the fuel tank have ruptured due to plastic strain failure.

These figures show the material interface between air and fuel as an iso surface of the material fraction of fuel.

To compare the influence of the baffle an additional simulation without baffles has been carried out. The top and bottom picture in Figure 11 respectively show the simulation without and with baffles. When the tank begins to crush a fuel crest starts to move towards the front of the tank. Figure 11 shows the effect of the baffle on the propagation of this crest. The fuel crest is partially blocked by the baffle. Figure 13 and 14 indicate that the leakage for the case with baffle is significantly smaller than for the case without baffles.

Figure 11:The effect of the baffle on sloshing

Validation of the tank crush model is not available yet. A validation of MSC.Dytran for simulations involving colliding and failing structures was done using a ship collision experiment described in [6]. An MSC.Dytran model was created that modeled the two colliding ships as shell structures. In [7] it was shown that the match with experimental results and results obtained by MSC.Dytran was better than expected. In [8] experimental results and simulation results are

compared for a partially filled tank that is placed on an oscillating table. In [8] MSC.Dytran was also compared with the established LR.FLUIDS code. Agreement was shown to be good.

Figure 12: Results at t=0 sec

Figure 13: Results at t=50ms

Of special interest is the location and size of the ruptured tank surface parts. To visualize these holes the failure results of the Langrangiain shell elements are used. Where an element has failed there is a hole. In Figure 16 and 17 the elements that have failed are shown in red.

CONCLUSION

It is now possible to accurately simulate fuel tank crushing, using the Multi-material Euler Solver of MSC.Dytran. The unique “Adaptive Multiple Euler Domains” technology makes it possible to model efficiently. Although experimental data is not yet available, the simulation results confirm expectations. MSC.Dytran can be a practical tool to reduce costs and time to the design and testing of a tank system.

Figure 14: Results at t=100ms

ACKNOWLEDGMENTS

Figures 11-17 are made with CEI-Ensight. The Author wants to gratefully recognize the contributions by Mr. Vijay Tunga for creating and running the tank crush model, as well as for visualizing its results with the help of the CEI/Ensight code.

REFERENCES

1. A link to the website of MSC.Dytran can be found at the following URL: http://www.mscsoftware.com 2. C.Hirsch, Numerical Computation of Internal and External Flows, Vol 1 and 2,John Wiley&Sons, 1990 3. R.J. Leveque, Finite Volume Methods for Hyperbolic Problems, Cambrigde University Press, 2002 4. W.A. van der Veen, Simulation of a compartmented airbag deployment using an explicit, coupled Euler/Lagrange method with adaptive Euler domains, NAFEMS, Florida, March 2003 5. H. Lenselink, K.G. Thung, H.L. Stipdonk, P.J. van der Weijde, Numerical simulations of ship collisions, Proceedings of the Second International Offshore and

Polar engineering Conference, San Francisco, June 1992 6. Full scale ship collision tests results, version 3,TNO-report, 1992 7. H. Lenselink and K.G. Thung, Numerical simulations of the Dutch-Japanese full scale ship collision tests, Internal report, MacNeal-Schwendler Company B.V. 8.S.H. Lee, J.Y. Kim, K.J. Lee, S. Rashed, A. Kawahra, Sloshing and structural response in ship’s tanks, 13th MSC Japan user’s conference, Tokyo, 1995

Figure 15: Side view

Figure 16: Holes

Figure 17: Holes

CONTACT

The author can be contacted by e-mail at:

wolter.vanderveen@mscsoftware.com