Simulation of a Compartmented Airbag Deployment Using an Explicit, Coupled Euler/lagrange Method with Adaptive Euler Domains

The paper presents a new simulation method for airbags with multiple compartments. In recent years many accidents happened with passengers that were out of position (OOP) when their airbag deployed. Therefore new safety regulations have come into effect in the USA and an airbag now has to meet several requirements that concern out of positioning. In meeting these requirements simulations of deploying airbags are very useful and are widely used. In OOP the airbag hits the passenger when it is still deploying and the pressure field is far from uniform and so there is a complicated interaction between gas flow and the deploying membrane. This calls for an analysis in which the dynamics of the airbag membrane is coupled with a CFD (Computational Fluid Dynamics) solver. MSC.Dytran is capable of handling these interactions. To weaken the frontal blow, an airbag with multiple compartments is sometimes used. The idea is to divert the gas stream in the airbag away from the frontal direction into sideways directions. Since these airbags especially need to operate well in OOP setting the CFD approach is required. The paper presents a new method to simulate a multi-compartment airbag in which each compartment is modeled by the CFD approach and each with a separate Euler domain. Before discussing multi-compartment simulations, we present background on simulations for one airbag using one Euler mesh. In these simulations the gas flow is described by the conservation laws of mass, momentum and energy. Also modeling of the interaction between CFD solver and airbag membrane solver is discussed. The conservation laws are applied to the 3D objects that are formed by taking an Euler element and cutting away everything that is outside the airbag surface. The boundary of this 3D object is in general a multi-faceted surface that consists of: (1) Polygons that connect an Euler element to another Euler element and that are called faces. (2) Polygons that connect Euler elements to the airbag surface, and are called polpacks. In MSC.Dytran a procedure is available that creates these polpacks given the Euler elements and the airbags. In the conservation laws several surface integrals occur. Many of these integrals have to do with transport and are computed by running over faces and polpacks. This gives rise to mass being transported across faces. In most cases there is no transport across polpacks since they are part of the airbag surface. For multi-compartment simulations we have to consider multiple Euler domains. Each Euler domain models one airbag. Communication between the airbags proceeds via the holes that connect one airbag with the other. Holes are modeled as a piece of airbag surface that is fully porous. Given that the largest possible timestep depends on the mesh size, each Euler domain could be advanced with a specific timestep. This would require subcycling. For the multi-compartment application mesh sizes are expected to be of comparable magnitude and all Euler meshes are advanced with the same timestep. Applying conservation laws is straightforward except at a polpack that connects an Euler element to the surface that models the hole. This polpack refers to only one Euler element in one domain and cannot provide the communication between the domains. It has to be replaced by a polpack that can refer to one Euler element in the first domain and one Euler element in the second domain. These new polpacks will be called flow polpacks. In the vicinity of each hole two Euler domains overlap. Each flow polpack is located inside this overlap and should be completely in an element in the first mesh and completely in an element in the second mesh. Clearly flow polpacks cannot be created by the polpack creation procedure mentioned that only considers one Euler domain. A good solution to this problem is to create an auxiliary mesh, that we shall call the hole mesh. This mesh is obtained by putting the two meshes on top of each other. So each mesh is a subset of this hole mesh. To make flow polpacks the airbag surface and the hole mesh are passed to the polpack creation routine. This gives polpacks that refer to elements in the hole mesh. Since each hole mesh element lies in exactly one element of the first and in exactly one element of the second mesh we can easily form flow polpacks. The flow polpacks are used to transport mass, energy, and momentum from one domain to the other. Also through, these flow polpacks, the Euler elements in one domain exert pressure forces on the boundary of Euler elements in another domain. For this new method three test problems are presented. The first two are theoretical, but the last one is a real life airbag simulation. The results show that the method presented is a promising method for multicompartment airbag simulations.