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11.7.7 Using the Six DOF Solver

FLUENT's Six Degree of Freedom (6DOF) solver computes external forces and moments such as aerodynamic and gravitational forces and moments on an object. These forces are computed by numerical integration of pressure and shear stress over the object's surfaces. Additional load forces can be added (e.g., injector forces, thrust (propulsive) forces, moments produced by a coil spring, etc.). This technique, along with the FLUENT solver and the use of dynamic meshes, can be readily applied to many useful applications, such as store separation [ 328, 346].

Overview of the Six DOF (6DOF) Solver

The 6DOF solver in FLUENT uses the object's forces and moments in order to compute the translational and angular motion of the center of gravity of an object. The governing equation for the translational motion of the center of gravity is solved for in the inertial coordinate system (Equation  11.7-11).

 \dot{\overrightarrow{\nu_G}} = \frac{1}{m} \sum {\overrightarrow{f}_G} (11.7-11)

where $\dot{\overrightarrow{\nu_G}}$ is the translational motion of the center of gravity, $m$ is the mass, and $\overrightarrow{f}_G$ is the force vector due to gravity.

The angular motion of the object, $\dot{\overrightarrow{\omega_B}}$, is more easily computed using body coordinates (Equation  11.7-12).

 \dot{\overrightarrow{\omega_B}} = \bf {L}^{-1} \left ( \sum ... ...\rm B}} \times \bf {L}\overrightarrow{\omega_{\rm B}} \right ) (11.7-12)

where $ \bf {L}$ is the inertia tensor, $\overrightarrow{M_{\rm B}}$ is the moment vector of the body, and $\overrightarrow{\omega_{\rm B}}$ is the rigid body angular velocity vector.

The moments are transformed from inertial to body coordinates using

 \overrightarrow{M_{\rm B}} = \bf {R} \overrightarrow{M_{\rm G}} (11.7-13)

where $\bf {R}$ is the following transformation matrix:

$C_\theta C_\psi$ $C_\theta S_\psi$ - $S_\theta$
$S_\phi S_\theta C_\psi - C_\phi S_\psi$ $S_\phi S_\theta S_\psi + C_\phi C_\psi$ $S_\phi C_\theta$
$C_\phi S_\theta C_\psi + S_\phi S_\psi$ $C_\phi S_\theta S_\psi - S_\phi C_\psi$ $C_\phi C_\theta$

where, in generic terms, $C_\chi = cos(\chi)$ and $S_\chi = sin(\chi)$. The angles $\phi$, $\theta$, and $\psi$ are Euler angles that represent the following sequence of rotations:

Once the angular and the translational accelerations are computed from Equation  11.7-11 and Equation  11.7-12, the rates are derived by numerical integration [ 346]. The angular and translational velocities are used in the dynamic mesh calculations to update the rigid body position.

Setting Rigid Body Motion Attributes for the Six DOF Solver

When the Six DOF Solver is enabled, you need to provide additional information for rigid body dynamic zones. For instance, you must use a user-defined function to define the six degrees of freedom parameters, and you must set the velocity and angular velocity for the center of gravity. For each moving object, exactly one user-defined function has to be defined, no matter how many zones there are for each object. For more information about the Six DOF Solver settings in the Dynamic Mesh Zones panel for rigid body motion, see Section  11.7.2.

Note that you can also keep track of an object's motion history using the text user interface and by entering yes for the motion-history? text interface command.

define $\rightarrow$ models $\rightarrow$ dynamic-mesh-controls $\rightarrow$ six-dof-parameter $\rightarrow$ motion-history?

This command generates a single motion history file for each moving object which can be used to display zone motion for postprocessing your results. For more information on zone motion, see Section  11.7.3.

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