Dytran Simulations for Fluid-Structure Interaction Problems Associated with
Airbag Deployments
Kwen Hsu, TRW
W.A. van der Veen, Vijay Tunga, MSC Software Corporation
Abstract
This paper discusses simulation models developed for the Fluid-Structure Interaction (FSI) phenomena
encountered in the internal flow region of airbag related engineering problems. The goal is to show the
effectiveness of using the commercial code Dytran to perform advanced FSI simulations to more accurately
reproduce the physical processes and predict the performances of the products.
The cases presented in this paper are for highly compressible, highly transient internal flows interacting with
deformable structures. The first case is related to the study of the airbag deployment noise. In this case multiple
flow domains, which are separated by the airbag surface, are simulated in one model. The second case is for the
study of an airbag module-can design with air-entrainment capability, while in the third case an inflator retainer
under sudden gas flow impact is simulated. At this point only the commercial code Dytran has this capability to
handle the FSI problems involving multiple coupling domains.
Some of the details of the models are TRW proprietary information. Therefore, the discussion will emphasize on
the capabilities of the code without going into too much detail in the models. Also discussed are the insights into
the physics behind the observable trends of the test results, which are revealed by the simulations.
Introduction
Transient, internal flow related to airbag deployment
Airbag deployment process is one of the most dynamic and non-linear internal flow problems. When deployment
starts, the inflation gas exits the inflator quickly and forces the airbag to expand within a very short period of time,
usually in the order of 20 to 50 milliseconds. During this process the shape of the bag changes dramatically, and
the fabric of the airbag experiences significant stress and strain. The motion of the bag is driven by the gas flow,
but the bag and other related structures (for example the bag-cover and module can) define the moving boundary of
the flow and have a profound impact on the developing flow. Therefore this is a Fluid-Structure Interaction (FSI)
problem. This FSI problem is characterized by the supersonic, highly compressible and highly transient internal
flow, together with the highly deformable confining structures. To meet the challenge of accurately reproducing
this physical process, a simulation code must have robust and accurate solvers for both the flow part and the
structure part. Dytran is specifically designed for this challenge. The reasons are enumerated in the following
sections.
Dytran’s gas flow and fluid-structure interaction simulation methodology
The gas is modeled as ideal gas without assuming that the flow is isentropic. The ideal gas equation is called the γlaw equation of state in Dytran. Dytran uses the Eulerian approach to simulate the gas flow. Mass is not attached to
the elements but moves from one element to the other. The respective conservation laws are directly applied to the
Euler elements to update mass, momentum and internal energy of the elements. This ensures global conservation
of mass. In addition to transport of mass, the total forces on all flow boundaries cutting through Euler elements
have to be computed. The resulting net force increases the momentum inside the cut elements. The transport
algorithm and the Eulerian load computation are all first-order. This is sufficient for airbag simulations.
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Airbag or other structure entities functioning as flow boundaries are represented by Lagrangian surface (shell or
membrane) elements. They intersect some of the Euler elements. For an accurate and robust Fluid-structure
interaction each surface element is subdivided such that any sub element is in only one Euler element. This
treatment enables smooth communication between the airbag segments and the Euler elements. In addition these
sub surface elements allow the computations of the volumes of the portions of the Euler elements that are within
the airbag. Only this part of the Euler element can contain fluid mass. And only to this part the conservation laws
are applied.
Dytran adopts a tightly-coupled approach to tie the motion of the structure with the evolution of the gas flow.
When the airbag moves into the Euler element the effective volume of an intersected element is reduced. To
prevent a pressure rise mass has to leave the intersected element and go to it’s neighboring elements. At the same
time the pressures in the Euler elements, through the sub segments of the Lagrangian surface elements, exert forces
on the airbag grid points. These forces cause the grid points to move. The subsequent movements of those grid
points are determined by those loading forces as well as the stresses and strains in the Lagrangian surface elements.
Note that to simulate a multi-compartment airbag with Dytran, each compartment has to be modeled with a distinct
Euler mesh. By specifying the shell elements that make up the hole between two compartments, transport of mass,
energy and momentum between two compartments can take place. There is no limit on the number of distinct
Euler domains. Dytran contains algorithms that will create special interface elements that connect an Euler element
of one compartment to an Euler element of another compartment. It is also possible to model the ambient as an
Euler domain.
In the initial phases of the deployment, the airbag only takes up a small volume and therefore only a small number
of Elements are within the airbag. It would be waste of CPU time and memory to have a complete Euler domain at
this stage. To avoid this, Dytran allows creating Euler elements automatically and dynamically during the
simulation process. Initially only a small number of Euler elements are created. As the airbag expands, new layers
of Euler elements are created. This algorithm increases the efficiency of the analysis dramatically. Also note that as
the airbag deploys the gas pressure distribution in the air bag becomes more and more uniform, allowing reduction
of the simulation resolution. Dytran also provides a coarsening capability to reduce the total number of Euler
elements if so desired. This capability increases the computational efficiency even more.
The flow solver in Dytran is based on the so-called density-based CFD schemes [1,2], rather than the so-called
pressure-based schemes [3,4]. It is well known that instabilities and divergence are much less likely to occur when
the density-based schemes are adopted to handle the highly compressible and highly transient flows with complex
geometries [5]. All these aforementioned traits make Dytran particularly suited for airbag related FSI problem
simulations. Other applications of Dytran include blast wave analysis and sloshing.
Although, from the system-performance point of view, the airbag deployment process can sometimes be simulated
using the so-called uniform-pressure method, very often it is necessary to reproduce the evolution of the gas flow
inside the deploying bag by employing a CFD solver. For example in the OOP (Out-Of-Position) situation, the
airbag contacts the passenger while it is still deploying, or when certain aspects of the deployment have to be
studied in more detail and higher levels of fidelity. The simulation examples discussed in the following section are
all cases of true FSI simulations, in other words the flow parts are all modeled with CFD, not uniform pressure
method. Nevertheless, Dytran provides both the uniform-pressure and CFD options for the airbag deployment
simulations.
Simulation Examples
Case 1: Airbag Deployment Noise
The first simulation case focuses on the leading pressure wave, which is the major component of the impulse sound
generated by a deploying airbag and experienced by the occupant. The airbag deployment sound is short in
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duration and high in intensity, and is therefore characterized as impulsive. This set of simulations is conducted to
better understand the role the bag plays in this physical phenomenon. The airbag deployment sound mechanism
and the simulations of expanding-structure generated sound are reported in more detail by Hsu[6].
The simulation of bag inflation generated sound requires the flow modeling software capable of modeling the
compressible flows inside and outside the bag at the same time with the FEA modeling of the bag fabric included.
Currently only Dytran is able to do that, therefore it is used for this study. Viscosity of air is ignored (inviscid flow
assumption) and the 2nd-order solver is employed. Quarter model is sufficient for the current case of a generic
DAB (Driver-Air-Bag). See Figures 1.a to 1.c for the descriptions of the bag model before inflation. Dummy
elements are used at the plane of symmetry to form a closed volume for the airbag. The shell elements representing
the car-cabin structure enclose the entire airbag and define the remaining part of the boundary of the flow domain.
The simulation setup contains two adaptive fluid domains. The first domain models the inside region of the airbag
and is used to capture the flow of gas from the inflator into the airbag, while the second flow domain models the
air outside the airbag.
The Euler elements discretizing the domain outside the bag must be small enough to resolve the sound wave
generated by the deploying bag. In the current efforts two element sizes are tried. For the course mesh case :
dx=dz=15 mm, dy=5.5 mm. Fine mesh case : dx=dz=7 mm, dy = 3 mm. According to Lockard et al[7], the fine
mesh is, arguably, capable of resolving the sound wave of frequency up to 17 KHz.
The complete airbag module includes a folded airbag placed inside a plastic cover. Upon activation, the inflator is
triggered to release gas into the bag. When the pressure inside the bag is high enough, the cover breaks open and
then the bag unfolds to protect the occupant. It was found that the bag folding introduces even smaller physical
length scale into the model and the cover creates another level of geometry complexity. Due to limitations in
current simulation technology, only highly simplified cases can be simulated. The current simulations are therefore
limited to a generic flat-bag model without plastic cover. Some of the structural components, especially those noncritical to the flow pattern, are simplified in geometry. The simulated deployment process is compared with the
real deployment process in Figure 2. Figures 3.a and 3.b are the pressure contours showing the pressure waves
generated by the deploying airbag. Figures 4.a and 4.b are the velocity vector plots showing the flow field inside
the airbag. CMARKN1 marker elements are used to capture the sound pressure at the monitoring points 1 and 2.
The pressure signals recorded in the simulation results are compared with the test results in Figure 5.
Fig. 1a the flat-bag model. Dummy symmetric
elements are included.
Fig. 1b Local close-up of the flat-bag model. Dummy symmetric
elements are removed to show the inflator inside the bag.
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Fig. 1c Global views of the whole airbag deployment sound simulation model. Dummy symmetric elements
are removed to show the flat-bag inside the car-cabin.
Fig. 2 Comparison of the tested parts with
the simulation model. (a) t = 3 ms, (b) t =
5 ms, (c) t = 7 ms.
(a)
(b)
(c)
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Fig. 3.b Simulated pressure waves
generated by the deploying bag. T = 2 ms.
Fig. 3.a Simulated pressure waves
generated by the deploying bag. T = 1 ms.
Fig. 4.a Velocity vector plot of the simulated flow
field inside the deploying bag. T = 1.5 ms.
Fig. 4.b Velocity vector plot of the simulated flow field
inside the bag. T = 1.5 ms. Same as Fig. 1a except from a
different viewing angle.
Sound Pressure (Pa)
600
500
Test_Chan_1
Test_Chan_2
400
ac5 _Chan_1
ac5_Chan_2
300
Fig. 5 Simulated sound pressure histories at two
monitoring points. Compared to data obtained from tests.
200
100
0
-100
-200
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Time(s)
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Case 2: PAB Module with Air-Entrainment
In this Passenger-Air-Bag (PAB) module-can design, the aim is to entrain air from the vehicle compartment into
the airbag module during the inflation process. This method is proposed to reduce the power of the inflator and at
the same time to reduce the over-pressure (major component of the airbag deployment sound) the occupant
experiences. The airbag and module-can together form a coupling surface which encompasses a closed volume.
Non-uniformly distributed Euler mesh is used to capture the details of the flow inside the module-can. The suction
ports on the module-can are defined using PORHOLE definitions which allows air flow to occur due to the
difference in atmospheric pressure and pressure inside the module-can, as shown in Figures 6a and 6b. The design
of this module aims at generating highly supersonic flow near the suction ports so that the pressure can be lower
than the surrounding atmospheric pressure, yielding maximal air entrainment. Figures 7a to 7d reveal the
deploying process of the folded airbag as viewed from the outside of the bag.
Fig. 6.a : FSI model predicted
gas flow inside the module
during the deployment process.
Global view of the model.
A
A
Fig. 6.b : FSI model predicted
pressure-contours on a cut-plane
inside the module. Local closeup to show the low-pressure
near the suction ports at t = 17
ms.
Suction ports
View A-A
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(a)
(b)
Fig. 7 (a)-(dc) : The
deployment process
predicted by the foldedbag FSI model.
(c)
t = 30 ms
(d)
This model shows how a complex model can be constructed within Dytran and used to guide the design of an
advanced airbag module design.
Case 3: Inflator Retainer Deformation During Deployment
This retainer holds the inflator inside the airbag module and provides the heat-shielding and gas flow regulation
effects. A dynamic pressure load on the retainer is generated by the gas being rapidly discharged from the inflator.
It is desired to use thinner steel-sheet for this retainer to reduce the weight; therefore the design of the vent-hole
locations and patterns becomes critical to the success of this airbag module. Without proper design, the retainer
may exhibit excessive deformation which is sometimes called fish-mouthing. Note that this is a FSI problem
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because, while the gas flow deforms the structure, the deformed structure also affects the flow significantly. Here
accurate FSI models were developed to evaluate many similar designs.
The model consists of the inflator body, the retainer, gas inlets and outlets. The retainer encloses the inflator body
with outlets modeled using PORFLOW entries at the desired location as shown in Figure 8.a. The retainer wall and
inflator forms a closed coupling surface. The full stress-strain curve is used to accurately describe the behavior of
the retainer wall material in the elastic and plastic strain range.
Note that in all three cases presented above, the so-called fast-coupling method (see Dytran user’s Guide), which is
nothing but the Cartesian Method discussed by Hsu[8], is adopted. This coupling method not only makes the
generation of the Euler mesh a very easy task, because it requires that all the edges of the Euler elements are
aligned with the basic coordinate system axes, but also saves the computational time significantly. It is therefore
recommended.
Fig. 8.a: Retainer Model Setup
Figure 8.b shows the retainer stress contours and the deformation. It was found that the simulation predicted
deformation match very well with the test results. In addition, one saves the manual works of transferring the
pressure load predicted by CFD into the FEA model. In the FSI model, this is automatically done by the code
without user intervening.
Fig. 8.b: Retainer Deformation and
Stress Results
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Conclusion
The simulation cases presented in this paper show that Dytran can accurately simulate various types of fluid
structure interaction problems. Ability to model multiple airbag compartments with adaptive fluid element
domains for each compartment in Dytran makes the simulation of airbag deployment sound possible. In addition,
Dytran’s fast coupling methodology reduces significantly the time spent in creating elements in a pre-processor as
well as the computational time required by the solver, hence makes the simulation of complex physical processes a
much more computationally affordable task. Future work in the area of parallel processing will reduce significantly
the simulation run time, and makes this code more convenient for scientific research and advanced product
development.
References
[1] B. Ven Leer, “Towards the Ultimate Conservative Difference Scheme II. Monotonicity and Conservation
Combined in a Second Order Scheme,” J. of Computational Physics, Vol. 14, 1974, pp. 361-370.
[2] P.L. Roe, “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes.” J. of Computational
Physics Vol. 43,357, 1981.
[3] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corp.,1980.
[4] C. L. Merkle, P.E.O. Buelow and S. Venkateswaran, “Comparison between the PISO algorithm and
preconditioning methods for compressible flow”, Tenth Workshop for Computational Fluid Dynamic Applications
in Rocket Propulsion, Part 1 p 123-146 (SEE N92-32278 23-34), 1992.
[5] H.Q. Yang, M.Z. Pindera, A.J. Przekwas and K. Tucker, “A Study of Pressure-Based Methodology for
Resonant Flows in Non-linear Combustion Instabilities”, AIAA-1992-779
Aerospace Sciences Meeting and Exhibit, 30th, Reno, NV, Jan 6-9, 1992. 25 p. Research supported by NASA.
[6] K. Hsu, “Airbag Deployment Sound Mechanism”, Noise Control Engineering Journal, Vol. 55, No. 3, pp. 311
to 321. 2007.
[7] D.P. Lockard, K.S. Brentner and H.L. Atkins, “High-Accuracy Algorithms for Computational Aeroacoustics,”
AIAA journal, Vol. 33, No. 2, pp.246 - 251,1995.
[8] K. Hsu, “Numerical Performances of Explicit Cartesian Methods for Compressible Moving-Boundary
Problems”, FEDSM2006-98086, 2006 ASME Joint U.S.-European Fluids Engineering Summer Meeting, July
2006, Miami FL.
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