PASSIVE_RIGID_BODY

It is possible to define a rigid body motion in nanoFluidXwhen the body is freely interacting with the fluid (exchanging momentum and heat with the fluid).

In order to define such motion as generally as possible, a number of parameters have to be set in Imposed motions.

PASSIVE_RIGID_BODY motion defines the standard 6-DOF motion and constrains motion in a number of ways, and also includes linear and torsional spring forces that act on the body. PASSIVE_RIGID_BODY offers parameters that can be set for this type of motion. Some of the commands are simple and can be considered self-explanatory, for example, body_mass, init_CoM, init_vel, but others require clarification.

Depending on the complexity of the case and the data you have available, you may need to specify 0, 1, or 2 additional coordinate systems.

The Cartesian coordinate system, which is commonly referred to as a global coordinate system or global reference frame, is the default coordinate system in which the code is operating and does not need a definition. It is assumed that it coincides with the inertial frame of reference.

The first additional coordinate system that may be needed (optional) is the principal axes coordinate system. Depending on the complexity of the geometry and the data you have available, it may be easier to specify only the diagonal elements of the moment of inertia matrix, assuming that initially the principal axes do not align with the global coordinate system. In this case, you can specify the principal axes coordinate system in which this is the case. For defining a new coordinate system (reference frame) it is necessary to specify any two axes of the new system in unit vector form. The third axis will be automatically calculated from that. For defining the principal axes coordinate system you can use any two of the three possible axes:
  • mom_principal_ax_x_i "x y z"
  • mom_principal_ax_y_i "x y z"
  • mom_principal_ax_z_i "x y z"

Where, the “x y z” coordinates represent the unit vectors expressed in global coordinates. The suffix “i” at the end of the command stands for “inertial”, to indicate which coordinates to use when defining the unit vector components.

The second coordinate system is the constraint coordinate system or constraint reference frame. This coordinate system is also optional and is needed in cases where the linear (translational) or angular motion constraints are happening along the axes which are not aligned with the global coordinate system. In such situations you need to define the constraint reference frame and all the subsequent parameters for constraining the motion will happen with respect to this constraint coordinate system. If this coordinate system is not defined, the code assumes that the constraint axes are aligned with the coordinate system and the constraint commands keep their function. The definition of the constraint coordinate system is done in the same manner as for the principal axes:
  • prbcon_ax_x_i "x y z"
  • prbcon_ax_y_i "x y z"
  • prbcon_ax_z_i "x y z"
The three coordinate systems and their respective commands are shown in Figure 1.


Figure 1. Coordinate Systems used for PASSIVE_RIGID_BODY and the Respective Definition Commands. In general, it is not necessary for the three coordinate systems to align.
An example of a hexagonal body that is rotated by 45 degrees around the z axis in Figure 2. Since it is easier in this case to specify the moment of inertia with only diagonal terms, you will define a principal axes coordinate system.


Figure 2. Hexagonal Body Rotated by 45 Degrees around the Z-Axis. Appropriate commands are used to define the principal axes coordinate system.

The exact same principle can be applied to the constraint coordinate system if you, for example, want to constrain the motion of the body in the direction that is under 45 degrees with respect to the global x or y axes.

By default the origin of the constraint coordinate system is located at the center of mass of the body. That is to say that if the body is to rotate, it will rotate around its center of mass. However, there are a number of situations where this behavior is not suitable. One example is a simulation of a hinge. In a situation like that, where you want the rigid body to rotate around a specific point, you need to shift the coordinate center of the constraint coordinate systems. For this purpose you can use the prbcon_pt_i command. Along with the new coordinate center you need to set the rotational constraints for the new “hinge point”. This is done using prbcon_ax_hinge_c command, where it is a vector that says which rotational motions are locked (x, y or z axis in constraint coordinate system). By setting all three values to 0 you will essentially define a ball-joint. The simplified 2D setup of a hinge is shown in Figure 3.


Figure 3. 2D Hinge. This example shows how to define a new coordinate center for the constraint coordinate system using prbcon_pt_i command.

Linear or torsional springs can also be defined. To illustrate the basic concept of such a setup, refer to Figure 4. The example shows the setup of a body which is hanging on a spring. The initial location of the body does not correspond to the equilibrium point of the spring, that is to say that you have a pre-deformation of the spring (prbcon_linspr_p_c) when starting the simulation. Along with this you of need to set the stiffness coefficient of the spring (prbcon_angspr_k_c). Between these two parameters you can define a force that is initially acting on the spring. Same principles apply for torsional springs, except that the deformation is expressed in [rad], and the stiffness of the spring in [Nm/rad].

There is also an option to set upper and lower coordinate (angle) bounds for the body. In order to do so you must use prbcon_linlim_pls_candprbcon_linlim_mns_c (or prbcon_anglim_pls_candprbcon_anglim_mns_c for angular limits) to define positive and negative displacement, respectively. These commands are always defined with respect to the init_CoM.


Figure 4. Linear Spring Setup with Annotated Commands
The linear commands for the above options all have their rotational counterparts which can be found in the Motions section.
Note:

Rigid-rigid body or wall-rigid body interactions are not supported. It is possible to simulate more than one rigid body in the domain, but their interactions are not modeled.

Also, a rigid body cannot cross a PERIODIC boundary.

With passive rigid body motion it is also possible to prescribe constant force or torque acting on a body by using prbcon_cnstfrc_c or prbcon_cnsttrq_c.

Alternatively, you can prescribe either constant or varying linear or angular velocities to each of the bodies by using prbcon_linvel_* and prbcon_angvel_* sets of commands.