김경종
384 lines
21 KiB
Markdown
384 lines
21 KiB
Markdown
<!-- source-page: 1031 -->
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$$
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| \dot {m} | = C A \frac {\tilde {p} _ {e}}{\sqrt {R (\theta - \theta^ {Z})}} \sqrt {\frac {2 \gamma}{\gamma - 1} (q ^ {\frac {2}{\gamma}} - q ^ {\frac {\gamma + 1}{\gamma}})},
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$$
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where $c$ is the dimensionless discharge coefficient, A is the vent or exhaust orifice area, 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, ${ \pmb q } ,$ is defined as
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$$
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q = \frac {\tilde {p}}{\tilde {p} _ {e}},
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$$
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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
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$$
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p _ {c} = \tilde {p} _ {e} \left(\frac {2}{\gamma + 1}\right) ^ {\frac {\gamma}{\gamma - 1}},
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$$
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where $\gamma$ is the ratio of the constant pressure heat capacity, $c _ { p } { } _ { : }$ , and the constant volume heat capacity, $c _ { v } .$
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$$
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\gamma = \frac {c _ {p}}{c _ {v}}.
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$$
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The orifice pressure, $\tilde { p } ,$ is then given by
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$$
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\tilde {p} = p _ {a} \quad \text { if } p _ {a} \geq p _ {c},
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$$
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$$
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\tilde {p} = p _ {c} \quad \mathrm{if} p _ {a} < p _ {c},
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$$
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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.
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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.
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=ORIFICE, DEPENDENCIES=n discharge coefficient
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Abaqus/CAE Usage: Fluid exchange through vents or orifices is not supported in Abaqus/CAE.
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# Specifying the flow rate due to fabric leakage
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The mass flow rate due to leakage through fabric can be expressed as
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$$
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| \dot {m} | = C A \sqrt {2 \rho | \Delta p |},
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$$
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where C is the dimensionless fabric leakage or discharge coefficient and A is the effective fabric leakage area.
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The value of the discharge coefficient can be a function of absolute upstream pressure, upstream temperature, and any user-defined field variables.
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<!-- source-page: 1032 -->
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=FABRIC LEAKAGE, DEPENDENCIES=n discharge coefficient
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Abaqus/CAE Usage: Defining fluid exchange due to fabric leakage is not supported in Abaqus/CAE.
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# Specifying a table of mass flow rate versus pressure difference
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The overall mass flow rate can be calculated from a specified mass flow rate per unit area, $\dot { \bar { m } } ,$ b y
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$$
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| \dot {m} | = \dot {\bar {m}} (| \Delta p |, \tilde {p}, \theta) A,
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$$
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where A is the effective area.
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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 $\dot { \bar { m } }$ and $| \Delta p |$ must be positive and start from zero.
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=MASS RATE LEAKAGE,DEPENDENCIES=n0, 0m1,|△pl1
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Abaqus/CAE Usage: Interaction module: Create Interaction Property: Fluid exchange: Definition: Mass rate leakage: Mass Flow Rate: $\dot { \bar { m } } ,$ Pressure Difference: $| \Delta p |$
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Use the following options to include pressure, temperature, and field variable dependence:
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Toggle on Use pressure-dependent data, toggle on Use temperature-dependent data, Number of field variables: n
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# Specifying a table of volumetric flow rate versus pressure difference
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The overall mass flow rate can be calculated from a specified volumetric flow rate per unit area, $\dot { \bar { V } }$ , by
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$$
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| \dot {m} | = \rho \dot {\bar {V}} (| \Delta p |, \tilde {p}, \theta) A,
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$$
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where A is the effective area and $\rho$ is the density.
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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 and $\dot { \bar { V } }$ $| \Delta p |$ must be positive and start from zero.
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=VOLUME RATE LEAKAGE,DEPENDENCIES=n
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<!-- source-page: 1033 -->
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$$
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\begin{array}{l} 0, 0 \\ \dot {\bar {V}} _ {1}, | \Delta p | _ {1} \\ \dots \end{array}
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$$
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Abaqus/CAE Usage: Interaction module: Create Interaction Property: Fluid exchange:
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Definition: Volume rate leakage: Volumetric Flow Rate:
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$\dot { \bar { V } } _ { \cdot }$ , Pressure Difference: $| \Delta p | _ { 1 }$
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Use the following options to include pressure, temperature, and field variable dependence:
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Toggle on Use pressure-dependent data, toggle on Use temperature-dependent data, Number of field variables: n
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# Specifying a heat energy flux
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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, ${ \bar { Q } } .$ The heat energy flow rate is
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$$
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\dot {Q} = \dot {\bar {Q}} A,
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$$
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where A is the effective area. A positive value for $\dot { \bar { Q } }$ generates heat flux out of the primary fluid cavity.
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=ENERGY FLUX
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Abaqus/CAE Usage: Defining fluid exchange by specifying the heat energy flow rate explicitly is not supported in Abaqus/CAE.
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# Specifying a table of heat energy flow rate versus temperature difference
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The overall heat energy flow rate can be calculated from a specified heat energy flow rate per unit area, $\dot { \bar { Q } } ,$ , by
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$$
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\dot {Q} = \dot {\bar {Q}} (| \Delta \theta |, \tilde {p}, \theta) A,
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$$
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where A is the effective area.
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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 $\dot { \bar { Q } }$ and $| \Delta \theta |$ must be positive and start from zero.
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=ENERGY RATE LEAKAGE,DEPENDENCIES=n
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$$
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\begin{array}{l} 0, 0 \\ \dot {\bar {Q}} _ {1}, | \Delta \theta | _ {1} \\ \dots \end{array}
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$$
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Abaqus/CAE Usage: Defining fluid exchange by specifying the heat energy flow rate as a function of temperature difference and pressure is not supported in Abaqus/CAE.
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<!-- source-page: 1034 -->
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# Specifying mass flow rate and/or heat energy flow rate with a user subroutine
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The mass flow rate, , or the overall heat energy flow rate, , can be defined in Abaqus/Explicit using user subroutine VUFLUIDEXCH (see “VUFLUIDEXCHEFFAREA,” Section 1.2.18 of the Abaqus User Subroutines Reference Guide).
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Input File Usage: \*FLUID EXCHANGE PROPERTY, TYPE=USER
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Abaqus/CAE Usage: User subroutine VUFLUIDEXCH is not supported in Abaqus/CAE.
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# Activating the fluid exchange definition in Abaqus/Explicit
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Fluid exchange will not occur in Abaqus/Explicit unless the fluid exchange definition is activated in an analysis step.
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<table><tr><td>Input File Usage:</td><td>Use the following options to activate a fluid exchange for a given analysis step:*FLUID EXCHANGE, NAME=fluid_exchange_name*FLUID EXCHANGE ACTIVATIONfluid_exchange_name</td></tr></table>
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Abaqus/CAE Usage: Fluid exchange is activated automatically for Abaqus/Explicit steps in Abaqus/CAE.
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# Varying the magnitude of the flow
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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.
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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.
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<table><tr><td>Input File Usage:</td><td>Use the following options:*AMPLITUDE, NAME=amplitude_name*FLUID EXCHANGE ACTIVATION, AMPLITUDE=amplitude_name</td></tr></table>
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Abaqus/CAE Usage: The use of an amplitude to activate a fluid exchange is not supported in Abaqus/CAE.
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# Accounting for blockage due to contacting boundary surfaces
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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.
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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
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<!-- source-page: 1035 -->
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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,” Section 37.1.4).
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Input File Usage: \*FLUID EXCHANGE ACTIVATION, BLOCKAGE=YES
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Abaqus/CAE Usage: Accounting for blockage due to contacting boundary surfaces is not supported in Abaqus/CAE.
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# Limiting the flow direction
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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.
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Input File Usage: \*FLUID EXCHANGE ACTIVATION, OUTFLOW ONLY
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Abaqus/CAE Usage: Limiting the flow direction is not supported by Abaqus/CAE.
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# Activating the fluid exchange based on the change in the leakage area
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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.
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Input File Usage: Use the following options:
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\*FLUID EXCHANGE, SURFACE=surface\_name
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\*FLUID EXCHANGE ACTIVATION, DELTA LEAKAGE
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AREA=surface\_ratio
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Abaqus/CAE Usage: Activating the fluid exchange based on the change in the leakage area is not supported by Abaqus/CAE.
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# Activation in multiple steps
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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.
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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.
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<!-- source-page: 1036 -->
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<table><tr><td>Input File Usage:</td><td>Use the following option to modify an existing fluid exchange activation or to specify an additional fluid exchange activation (default):*FLUID EXCHANGE ACTIVATION, OP=MODUse the following option to deactivate all fluid exchange definitions in the model and optionally reactivate new ones:*FLUID EXCHANGE ACTIVATION, OP=NEW</td></tr><tr><td>Abaqus/CAE Usage:</td><td>Fluid exchange activation is automatic for all fluid exchange interactions in all steps in Abaqus/CAE. No modifications or additions are allowed.</td></tr></table>
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Specifying mass flux in Abaqus/Standard
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<table><tr><td colspan="2">In Abaqus/Standard the amount of fluid in a cavity can be varied in a step. An amplitude curve can be used to define the mass flow rate during the particular step.</td></tr><tr><td>Input File Usage:</td><td>Use the following options:*AMPLITUDE, NAME=amplitude_name*FLUID FLUX, AMPLITUDE=amplitude_nameUse the following option to modify an existing fluid flux or to specify an additional fluid flux to a cavity (default):*FLUID FLUX, OP=MODUse the following option to deactivate all fluid flux definitions in the model and optionally reactivate new ones:*FLUID FLUX, OP=NEW</td></tr><tr><td>Abaqus/CAE Usage:</td><td>The use of fluid flux to modify mass flow rates is not supported in Abaqus/CAE.</td></tr></table>
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# Additional reference
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• Bird, R. B., W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 2002.
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<!-- source-page: 1037 -->
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# 11.5.4 INFLATOR DEFINITION
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Product: Abaqus/Explicit
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# References
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• “Surface-based fluid cavities: overview,” Section 11.5.1
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• “Fluid cavity definition,” Section 11.5.2
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• “Fluid exchange definition,” Section 11.5.3
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• \*FLUID INFLATOR
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• \*FLUID INFLATOR PROPERTY
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• \*FLUID INFLATOR ACTIVATION
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# Overview
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An inflator definition:
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• can be used to inflate a fluid cavity to simulate actual inflators used for airbag supplemental restraint systems;
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• can inflate a fluid cavity with an ideal gas mixture different from that present in the fluid cavity;
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• can be specified directly or by defining data from a tank test;
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• has a name that can be used to identify history output of mass flow rates; and
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• can be activated at any time during the analysis.
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# Defining an inflator
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The inflator capability in Abaqus/Explicit is suited for modeling the flow characteristics of inflators used for airbag systems. You must associate the inflator definition with a name. You specify the reference node of the fluid cavity that the inflator will fill with gas. A single fluid cavity can have any number of inflators.
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Input File Usage: \*FLUID INFLATOR, NAME=name fluid\_cavity\_reference\_node
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# Defining the inflator property
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The inflator property defines the mass flow rate and temperature as a function of inflation time either directly or by entering tank test data. It also defines the mixture of gases entering the fluid cavity. You must associate the inflator property with a name. This name can then be used to associate a certain property with an inflator definition.
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<!-- source-page: 1038 -->
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Input File Usage: Use the following options:
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*FLUID INFLATOR, NAME=fluid_inflator_name,
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PROPERTY=property_name
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*FLUID INFLATOR PROPERTY, NAME=property_name
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# Specifying the gas temperature and mass flow rate directly
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The temperature and the mass flow rate of the gas entering the fluid cavity can be given directly as functions of inflation time. Enter a table of mass flow rate and temperature versus inflation time.
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Input File Usage: *FLUID INFLATOR PROPERTY, TYPE=TEMPERATURE AND MASS inflation time, inflator gas temperature, inflator mass flow rate ...
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# Using tank test data
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The mass flow rate and the temperature of the gas entering the fluid cavity can be determined by the results of a tank test. In the test the inflator is discharged into a closed, fixed volume tank, and the time history of pressure in the tank is measured. The inflator mass flow rate can then be calculated from the pressure history using the equations of gas dynamics. For an ideal gas, conservation of energy for an adiabatic process is given by
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$$
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\dot {m} _ {t a n k} c _ {v} \theta_ {t a n k} + m _ {t a n k} c _ {v} \dot {\theta} _ {t a n k} = \dot {m} _ {i n} c _ {p} (\theta_ {i n} - \theta^ {Z}),
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$$
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where is the temperature, $\theta ^ { Z }$ is the absolute zero on the temperature scale being used, and the subscripts and refer to quantities in the inflator and the rigid tank, respectively. Using mass balance
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$$
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\dot {m} _ {t a n k} = \dot {m} _ {i n},
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$$
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and the equation of state for an ideal gas with constant volume gives
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$$
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\dot {p} _ {t a n k} V _ {t a n k} = R (\dot {m} _ {t a n k} \theta_ {t a n k} + m _ {t a n k} \dot {\theta} _ {t a n k}).
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$$
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The mass flow rate can be found by combining the above equations
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$$
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\dot {m} _ {i n} = \frac {\dot {p} _ {t a n k} V _ {t a n k}}{\gamma R (\theta_ {i n} - \theta^ {Z})},
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$$
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where $\gamma$ is the ratio of the constant pressure heat capacity, $c _ { p }$ , and the constant volume heat capacity, $c _ { v }$
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$$
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\gamma = \frac {c _ {p}}{c _ {v}}.
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$$
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To calculate the mass flow rate using the results of a tank test, enter a table of tank pressure and inflator temperature versus inflation time, and specify the volume of the tank.
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<!-- source-page: 1039 -->
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Input File Usage: \*FLUID INFLATOR PROPERTY, TYPE=TANK TEST, TANK VOLUME= inflation time, inflator gas temperature, tank pressure
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# Using the dual pressure method
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If both the inflator pressure, $\tilde { p } _ { i n } ,$ and tank pressure, $p _ { t a n k }$ , time history curves can be measured during a tank test, the inflator mass flow rate and temperature can then be calculated using the assumption of isentropic flow (Wang and Nefske, 1988). The mass flow rate through the inflator orifice can be described by
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$$
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\dot {m} _ {i n} = C A \frac {\tilde {p} _ {i n} ,}{\sqrt {R (\theta_ {i n} - \theta^ {Z})}} C _ {t a n k},
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$$
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where C is the discharge coefficient, A is the effective area, and the coefficient $C _ { t a n k }$ is determined by assuming choked or sonic flow as
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$$
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C _ {t a n k} = (\frac {2}{\gamma + 1}) ^ {\frac {1}{\gamma - 1}} \sqrt {\frac {2 \gamma}{\gamma + 1}}.
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$$
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Comparing the expression for inflator mass flow rate obtained in a rigid tank with that given above, the inflator temperature is given by
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$$
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\theta_ {i n} - \theta^ {Z} = \frac {1}{R} \left(\frac {\dot {p} _ {t a n k} V _ {t a n k}}{\gamma C A C _ {t a n k} \tilde {p} _ {i n}}\right) ^ {2},
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$$
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and the inflator mass flow rate is
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$$
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\dot {m} _ {i n} = \frac {\gamma (C A C _ {t a n k} \tilde {p} _ {i n}) ^ {2}}{V _ {t a n k} \dot {p} _ {t a n k}}.
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$$
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To calculate the inflator mass flow rate and temperature using the dual pressure method, enter a table of tank pressure and inflator pressure versus inflation time; and specify the volume of the tank, the effective area, and the discharge coefficient. The tank volume and effective area must be specified. The discharge coefficient has a default value of 0.4.
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Input File Usage: \*FLUID INFLATOR PROPERTY, TYPE=DUAL PRESSURE, $\mathrm { T A N K } \mathrm { V O L U M E } { = } V _ { t a n k } , \mathrm { E F F E C T I V E ~ A R E A } { = } A ,$ DISCHARGE COEFFICIENT=C inflation time, inflator pressure, tank pressure
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# Specifying the inflator pressure and mass flow rate directly
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You can enter a table of the mass flow rate and inflator pressure versus inflation time and specify the effective area and discharge coefficient. The gas temperature in the inflator will be calculated by using
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<!-- source-page: 1040 -->
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the assumption of isentropic flow. The effective area must be specified. The discharge coefficient has a default value of 0.4.
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Input File Usage: *FLUID INFLATOR PROPERTY, TYPE=PRESSURE AND MASS, EFFECTIVE AREA=A, DISCHARGE COEFFICIENT=C inflation time, inflator pressure, inflator mass flow rate ...
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# Specifying the gas mixture
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To define the inflator gas mixture, specify the number of gas species used for the inflator, and enter a list of names of fluid behaviors and a table of the mass fraction or molar fraction of the species. The mass fraction or molar fraction of the species may be a function of inflation time. The sum of the mass fractions or molar fractions for the species should be equal to one at any given time.
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Input File Usage: Use the following options to specify the gas mixture in terms of the mass fractions:
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*FLUID INFLATOR PROPERTY
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*FLUID INFLATOR MIXTURE, NUMBER SPECIES=k,
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TYPE=MASS FRACTION
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fluid_behavior_name_1, fluid_behavior_name_2, etc.
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inflation time, mass fraction 1, mass fraction 2, etc.
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...
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Use the following options to specify the gas mixture in terms of the molar fractions:
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*FLUID INFLATOR PROPERTY
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*FLUID INFLATOR MIXTURE, NUMBER SPECIES=k,
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TYPE=MOLAR FRACTION
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fluid_behavior_name_1, fluid_behavior_name_2, etc.
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inflation time, molar fraction 1, molar fraction 2, etc.
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...
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# Activating the inflator definition
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Inflation will not occur unless the inflation definition is activated in an analysis step.
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Input File Usage: Use the following options to activate a fluid inflator for a given analysis step:
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*FLUID INFLATOR, NAME=fluid_inflator_name
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*FLUID INFLATOR ACTIVATION
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fluid_inflator_name
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# Relating inflation time to analysis time
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Inflator property definition consists of specifying tables of gas variables versus inflation time. In Abaqus/Explicit the inflation time, $t _ { i n }$ , is related to the value of an amplitude curve by
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