Fluid Exchange Definition

To define flow between a fluid cavity and its environment in Abaqus/Explicit, specify the single reference node associated with the fluid cavity. In the discussion that follows this fluid cavity is referred to as the primary cavity. When the flow is defined as a prescribed function, the flow can either be into or out of the primary cavity. If the flow is into the cavity, the properties of the material flowing in are assumed to be the instantaneous properties of the material in the cavity itself. When the flow behavior is based on analysis conditions, the mass flow can occur only out of the primary cavity but the heat energy flow can be either into or out of the primary cavity. For the case of mass flow Abaqus will use the fluid cavity pressure and the specified constant ambient pressure to calculate the pressure difference used to determine the mass flow rate. For the case of heat energy flow Abaqus/Explicit will use the fluid cavity temperature and the specified constant ambient temperature to calculate the temperature difference used to determine the heat energy flow rate.

To define flow between two fluid cavities, specify the reference nodes associated with the primary and secondary fluid cavities. When the flow is based on analysis conditions, the fluid will flow from the high pressure or upstream cavity to the low pressure or downstream cavity and the heat energy will flow from the high temperature to the low temperature.

The flow rate from the primary cavity for any fluid exchange property is proportional to the effective leakage area. The leakage area may represent the size of an exhaust orifice, the area of a porous fabric enclosing the cavity, or the size of a pipe between cavities.

In an Abaqus/Explicit analysis you can specify the value of the effective leakage area directly. Alternatively, you can define a surface that represents the leakage area by specifying the name of the surface on the boundary enclosing the primary fluid cavity. The effective area for fluid exchange is based on the area of the surface unless you specify the area directly or define the effective area with user subroutine VUFLUIDEXCHEFFAREA. If both the effective area and a surface are specified, the area of the surface is used only to determine blockage; see Accounting for Blockage due to Contacting Boundary Surfaces below. If neither area is specified, the effective area defaults to 1.0.

You can also define the effective leakage area with user subroutine VUFLUIDEXCHEFFAREA (see VUFLUIDEXCHEFFAREA) if leakage needs to be modeled as a function of the material state in the underlying elements of the specified surface. For example, this subroutine can be used to define the leakage area at an element level for modeling fabric permeability in uncoated airbags where the leakage can vary locally depending on the strains in the yarn directions and the angle between the fabric yarns. Only membrane elements are supported for use with VUFLUIDEXCHEFFAREA.

Elements enclosing fluid cavities may fail and create a ruptured leakage area allowing for fluid exchange. For example, two fluid cavities that share a common wall modeled by membrane elements will not exchange fluid as long as the membrane elements remain intact. When any of the shared membrane elements fail, fluid will be exchanged through an effective area determined by the sum of the area of the failed elements. In essence, the failed elements become holes in the membrane through which fluid can flow.

In an Abaqus/Explicit analysis you can define a surface set whose underlying elements may fail and allow fluid and/or heat energy to be exchanged through the surfaces of the failed elements. The effective area for the fluid exchange is computed from the surfaces of the failed elements.

For a high pressure fluid chamber, such as a balloon, rupture of a small portion of the enclosing surface can completely destroy the fluid chamber. In this case you can choose to deactivate the fluid cavity by setting a maximum rupture area ratio. The area ratio is defined as the area of the surfaces from the failed elements over the total area of the user-defined surface set for the fluid exchange. Once the current rupture area ratio exceeds the specified maximum, the cavity pressure is no longer applied to the fluid cavity surfaces.

In a fluid cavity computation only the failure of the elements used to define the fluid cavity can be detected. If a fluid cavity is physically enclosed by multiple layers of elements, the failure of the immediately adjacent elements creates a leakage path for fluid exchange even though no physical path exists. In such cases, fluid exchange based on the surfaces of failed elements should be used with caution.

You can control how the effect of the cavity pressure on a fluid exchange surface is accounted for in Abaqus/Explicit. By default, the cavity pressure generates forces at all of the fluid exchange surface nodes, using the same method as for other portions of the fluid cavity. Optionally, the resultant force of the cavity pressure on the fluid exchange surface can be distributed among only the nodes that lie on the perimeter of the fluid exchange surface (for example, of the nodes shown on the fluid exchange surface in Figure 1, only the nodes at locations A and B lie on the perimeter). This option can be used to avoid local bulging of a vent surface that will cause inaccurate computation of the leakage area. Figure 2 shows an example of bulging when cavity pressure forces are distributed among all nodes of a vent surface.

In an Abaqus/Explicit analysis, when elements enclosing a fluid cavity fail, the fluid cavity pressure is not applied on the surfaces of those failed elements, which may help prevent potential numerical issues associated with free-flying nodes of failed elements enclosing the fluid cavity.

Initial configuration of a fluid exchange surface.

Deformed configuration of a fluid exchange surface.

Fluid flux into or out of the primary fluid cavity can be defined directly by prescribing the mass flow rate per unit area, $\dot{\overline{m}}$. The mass flow rate is

where A is the effective area.

Fluid flux can also be defined by prescribing a volumetric flow rate per unit area, $\dot{\overline{V}}$. The mass flow rate is

where $\rho$ is the density.

A negative value for $\dot{\overline{m}}$ or $\dot{\overline{V}}$ will generate flux into the primary fluid cavity. When a second fluid cavity is not defined, the state of the fluid flowing into the primary cavity is assumed to be that of the fluid already present in the primary cavity.

The mass flow rate, $\dot{m}$, can be related to pressure difference by both viscous and hydrodynamic resistance coefficients such as

where $\mathrm{\Delta }p$ is the pressure difference, A is the effective area, $C_V$ is the viscous resistance coefficient, and $C_H$ is the hydrodynamic resistance coefficient. The resistance coefficients can be functions of the average absolute pressure, average temperature, and average of any user-defined field variables. A positive value of $\dot{m}$ corresponds to flow out of the first cavity.

The mass flow rate through a vent or exhaust orifice that can be approximated by one-dimensional, quasi-steady, and isentropic flow is given (Bird, Stewart and Lightfoot, 2002) by

where C is the dimensionless discharge coefficient, A is the vent or exhaust orifice area, $\theta$ is the temperature in the upstream fluid cavity, ${\theta }^Z$ is the absolute zero on the temperature scale being used, and ${\tilde{p}}_e$ is the absolute pressure in the upstream fluid cavity. The pressure ratio, q, is defined as

where $\tilde{p}$ is the absolute pressure in the orifice. The critical pressure, $p_c$, at which choked or sonic flow occurs is defined as

where $\gamma$ is the ratio of the constant pressure heat capacity, $c_p$, and the constant volume heat capacity, $c_v$:

The orifice pressure, $\tilde{p}$, is then given by

where $p_a$ is equal to the ambient pressure for flow out of a single fluid cavity or the downstream cavity pressure for flow between two fluid cavities.

The value of the discharge coefficient can be a function of the absolute upstream pressure, upstream temperature, and any user-defined field variables. Fluid exchange through a vent or exhaust orifice is valid only for pneumatic fluids and is available only in Abaqus/Explicit.

The mass flow rate due to leakage through fabric can be expressed as

where C is the dimensionless fabric leakage or discharge coefficient and A is the effective fabric leakage area.

The value of the discharge coefficient can be a function of absolute upstream pressure, upstream temperature, and any user-defined field variables.

The overall mass flow rate can be calculated from a specified mass flow rate per unit area, $\dot{\overline{m}}$, by

where A is the effective area.

In this case you can define the mass flow rate per unit area in a table depending on the absolute value of pressure difference and, optionally, on the average absolute pressure, average temperature, and average value of any user-defined field variables. Values for $\dot{\overline{m}}$ and $\left|\mathrm{\Delta }p\right|$ must be positive and start from zero.

The overall mass flow rate can be calculated from a specified volumetric flow rate per unit area, $\dot{\overline{V}}$, by

where A is the effective area and $\rho$ is the density.

In this case you can define the volumetric flow rate per unit area in a table depending on the absolute value of pressure difference and, optionally, on the average absolute pressure, average temperature, and average value of any user-defined field variables. Values for $\dot{\overline{V}}$ and $\left|\mathrm{\Delta }p\right|$ must be positive and start from zero.

In Abaqus/Explicit heat energy flux into or out of the primary fluid cavity can be defined directly by prescribing the heat energy flow rate per unit area, $\dot{\overline{Q}}$. The heat energy flow rate is

where A is the effective area. A positive value for $\dot{\overline{Q}}$ generates heat flux out of the primary fluid cavity.

The overall heat energy flow rate can be calculated from a specified heat energy flow rate per unit area, $\dot{\overline{Q}}$, by

where A is the effective area.

In this case in Abaqus/Explicit you can define the heat energy flow rate per unit area in a table depending on the absolute value of temperature difference and, optionally, on the average absolute pressure, average temperature, and average value of any user-defined field variables. Values for $\dot{\overline{Q}}$ and $\left|\mathrm{\Delta }\theta \right|$ must be positive and start from zero.

The mass flow rate, $\dot{m}$, or the overall heat energy flow rate, $\dot{Q}$, can be defined in Abaqus/Explicit using user subroutine VUFLUIDEXCH (see VUFLUIDEXCHEFFAREA).

By default, the magnitude of the flow is based on the specified flow behavior. A time variation of flow magnitude during a step can be introduced by an amplitude curve. The magnitude based on the specified flow behavior is multiplied by the amplitude value to obtain the actual mass or heat energy flow rate. For example, a time variation of prescribed mass or volumetric flux can be defined.

An amplitude curve may be used to trigger an event for fluid exchange in the middle of a step. For example, an airbag may deploy at some predetermined time during a step, and it may be desirable to close off all exhaust orifices until the actual deployment. A step amplitude curve that starts at zero and steps up at deployment time could be used for this purpose.

Abaqus/Explicit can account for the blockage of flow out of a cavity due to an obstruction caused by contacting surfaces. For example, flow out of an exhaust orifice may be fully or partially blocked because it is covered by another contacting surface.

Blockage can be considered for any fluid exchange property. However, a surface must be defined on the boundary of the fluid cavity to be checked for contact obstruction. Abaqus/Explicit will calculate the area fraction of the surface not blocked by contacting surfaces and apply this fraction to the mass or energy flow rate out of the cavity. You can control the combination of surfaces that can cause blockage. Abaqus/Explicit will not consider contacting surfaces to cause blockage unless you specify that they can potentially cause blockage (see Contact Blockage).

By default, flow can occur both in and out of the primary fluid cavity when a second node is included in the fluid exchange definition. In addition, heat energy flow can occur in both directions when flow is defined between a single cavity and its environment. You can limit the flow direction in Abaqus/Explicit in these cases such that fluid or heat energy flows only out of the primary fluid cavity. This method is relevant only for a fluid exchange definition based on analysis conditions and not on prescribed mass, volume, or heat energy flux.

The flow between cavities can be activated in Abaqus/Explicit based on a change in the area of the surface defining the effective area. You need to specify the ratio of the actual surface area to the initial effective area, which represents the threshold value for triggering the fluid exchange. The effective area used for the fluid exchange between the cavities (or between the cavity and the ambient) is the area difference between the actual area and the initial area.

By default, when you modify the activation of a fluid exchange definition or activate a new fluid exchange definition, all existing fluid exchange activations in the step remain. When modifying an existing activation, all applicable data must be respecified.

Activated fluid exchange definitions remain active in subsequent steps unless deactivated. You can choose to deactivate all fluid exchange definitions in the model and optionally reactivate new ones. If you deactivate any fluid exchange definition in a step, all fluid exchange definitions must be respecified.