About Surface-Based Fluid Cavities

In certain applications it may be necessary to predict the mechanical response of a liquid-filled or a gas-filled structure. Examples include pressure vessels, hydraulic or pneumatic driving mechanisms, and automotive airbags. A primary difficulty in addressing such applications is the coupling between the deformation of the structure and the pressure exerted by the contained fluid on the structure. Figure 1 illustrates a simple example of a fluid-filled structure subjected to a system of external loads. The response of the structure depends not only on the external loads but also on the pressure exerted by the fluid, which, in turn, is affected by the deformation of the structure. The surface-based fluid cavity capability provides the coupling needed to analyze situations in which the cavity can be assumed completely filled by fluid with uniform properties and state. Applications with significant spatial variation within cavities cannot be modeled with this feature. For example, consider the fluid-structure interaction and coupled Eulerian-Lagrangian capabilities for applications involving sloshing and wave propagation through a fluid (see Eulerian Analysis and Fluid-Structure Interaction).

Figure 1. Fluid-filled structure.

The boundary of the fluid cavity is defined by an element-based surface with normals pointing to the inside of the cavity. The underlying elements can be standard solid or structural elements as well as surface elements. Surface elements can be used to model holes in the structure or to fill in rigid regions where rigid or other load-carrying elements do not exist (see Surface Elements). Care must be taken when using surface elements such that nodes completely surrounded by only surface elements have proper boundary conditions.

Consider the example presented in Figure 1. Solid elements are defined on the top and side of the cavity as indicated in Figure 2. A surface element is defined on the bottom rigid boundary of the cavity where no standard elements exist. The node located at the intersection of the axis of symmetry and the lower rigid boundary of the cavity must be restrained in the r- and z-directions because it is connected only to a surface element. The surface defining the cavity is based on the underlying solid and surface elements.

Figure 2. Axisymmetric model of fluid-filled structure.

An additional user-defined volume can be added to the actual or geometric volume of the cavity. If the boundary of the cavity is not defined by an element-based surface, the fluid cavity is assumed to have a fixed volume that is equal to the added volume.

The behavior of the fluid within the fluid-filled cavity can be based either on a hydraulic or a pneumatic model. The hydraulic model can simulate nearly incompressible fluid behavior and fully incompressible behavior in Abaqus/Standard. The compressibility is introduced by defining a bulk modulus. The pneumatic model is based on an ideal gas. The gas can be defined by multiple species in Abaqus/Explicit, and you can specify the temperature of the gas or have it calculated based on the assumption of adiabatic behavior. A multi-species ideal gas with an adiabatic temperature update is an appropriate model for automotive airbags.

There are many ways in Abaqus to model the transfer of fluid into or out of a cavity. The flow can be specified as a prescribed mass or volume flux history or can model physical mechanisms due to a pressure differential such as venting through an exhaust orifice or leakage through a porous fabric. Fluid exchange definitions are used for this purpose and can model flow between a fluid cavity and its environment or between two fluid cavities (see Fluid Exchange Definition for details). In addition, Abaqus/Explicit has the capability to model inflators used for the deployment of automotive airbags. Conditions at the inflator can be specified directly, or tank test data can be used (see Inflator Definition for details).

Many fluid-filled systems such as airbags have multiple chambers with fluid flowing between chambers through holes or fabric leakage. In other cases it is advantageous to divide a single physical chamber into multiple chambers with fictitious walls to model a gradient in pressure across the physical chamber. Some fictitious leakage mechanisms through inter-chamber walls can be defined to obtain reasonable behavior. This can be a useful modeling technique when simulating the complex unfolding of an airbag. To model multiple chambers, define a fluid cavity for each chamber and link the fluid cavities together with the appropriate fluid exchange definitions. Averaged properties for the multi-chambered model can be output if requested (see Fluid Cavity Definition for details).

The inertia of the fluid inside a fluid cavity or fluid exchanged between cavities is not automatically taken into account. To add the effect of inertia, use MASS elements on the boundary of the cavity. You should make sure that the total added mass corresponds to the mass of the fluid in the cavity and that the distribution of the MASS elements is a reasonable representation of the distributed fluid mass for the type of loading to which the structure is subjected. Only the overall effect of the fluid inertia can be modeled; the uniform pressure assumption in the cavity makes it impossible to model any pressure gradient-driven fluid motions. Thus, the approach assumes that the time scale of the excitation is very long compared to typical response times for the fluid.

If a large amount of fluid is removed from a cavity or the material surrounding the cavity is very flexible, the cavity may partially collapse and portions of the cavity walls may contact each other. Self-contact of the cavity walls and contact with surrounding structures can be handled effectively by using the standard techniques available in Abaqus for modeling contact. Abaqus/Explicit can also account for the blockage of flow out of a cavity due to contacting surfaces (see Accounting for Blockage due to Contacting Boundary Surfaces).

In some applications in Abaqus/Standard, negative eigenvalues may be encountered during the solution. These negative eigenvalues do not necessarily indicate that a bifurcation or buckling load has been exceeded. If the predicted response otherwise appears to be reasonable, these messages can be ignored. A detailed description of how negative eigenvalues can develop during the solution of hydrostatic fluid element problems is presented in Hydrostatic fluid calculations.