Forces and Moments

Simcenter STAR-CCM+ computes the resultant force and moment from the contributions of the individual forces and moments defined for the 6-DOF body.

The resultant force and moment acting on the body can be written as:

Figure 1. EQUATION_DISPLAY

F = f_{r} \sum f + \sum f_{c}

(4879)

Figure 2. EQUATION_DISPLAY

N = f_{r} \sum n + \sum n_{c}

(4880)

where:

$f_{c}$ represents external forces that are generated by multi-body constraints or joints, and $f$ represents all other forces such as flow, gravity, and user-defined forces (see External Forces and Moments).
$n_{c}$ represents external moments that result from multi-body constraints or joints, and $n$ represents all other moments (see External Forces and Moments).
$f_{r}$ is a time-ramping function that is defined as:
Figure 3. EQUATION_DISPLAY

$f_{r} = {\begin{matrix} 0 & : & t < t_{s} \\ \frac{t - t_{s}}{t_{r}} & : & t_{s} \leq t < t_{s} + t_{r} \\ 1 & : & t \geq t_{s} + t_{r} \end{matrix}$

(4881)

where $t_{s}$ is the user-specified release time and $t_{r}$ is the specified ramp time.

External Forces and Moments

User-defined Forces and Moments

Simcenter STAR-CCM+ allows you to define external forces and moments directly. You can define:

Forces acting on the 6-DOF body at its center of mass:
Forces acting on the 6-DOF body at a specified location:
Moments acting on the 6-DOF body with respect to the body position:

In addition to user-defined forces and moments, Simcenter STAR-CCM+ provides the following predefined types:

Gravity Force

The gravity force is defined as:

Figure 4. EQUATION_DISPLAY

f_{g} = m g

(4882)

where

m

is the mass of the rigid body.

Fluid Force and Moment

The force and moment exerted by the surrounding fluid can be written as:

Figure 5. EQUATION_DISPLAY

f_{f l u i d} = \sum_{f}^{} p_{f} a_{f} - \sum_{f}^{} τ_{f} a_{f}

(4883)

and

Figure 6. EQUATION_DISPLAY

n_{f l u i d} = \sum_{f}^{} [r_{f} \times (p_{f} a_{f})] - \sum_{f}^{} [r_{f} \times (τ_{f} a_{f})]

(4884)

where:

$p_{f}$ and $τ_{f}$ are, respectively, the pressure and shear stress acting on face $f$
$a_{f}$ is the area vector of face $f$
$r_{f}$ is the distance vector from the body center of mass to the center of face $f$

Torsional Spring Moment

The torsional spring moment mimics the effect of a torsional spring on a rotating body. This moment acts to rotate the body into the angular position that is given by the relaxation angle.

The magnitude of the moment is proportional to the difference between the current angular position of the body and the relaxation angle:

Figure 7. EQUATION_DISPLAY

M = - k (α - α_{r})

(4885)

where $k$ is the spring constant, $α$ is the rotation angle, and $α_{r}$ is the relaxation angle at which the moment vanishes.

The axis of rotation depends on the motion type.

Damping Moment

The damping moment acts with respect to the position of the body in opposition to the angular velocity vector.

The damping moment is defined using a linear damping function:

Figure 8. EQUATION_DISPLAY

n_{d} = {- a}_{d, n} ω

(4886)

where $a_{d, n}$ is the angular damping constant.

Damping Force

The damping force acts on the body at the body position and in the opposite direction to the body’s velocity vector.

The damping force is defined using a linear damping function:

Figure 9. EQUATION_DISPLAY

f_{d} = {- a}_{d, f} v

(4887)

where $a_{d, f}$ is the linear damping constant.

DEM Force and Moment

The DEM force and moment is calculated by the DEM Boundary Forces model. It computes the DEM contact force acting on the DFBI body resulting from an explicit coupling between DEM particles and the DFBI body. See Contact Force. The total force acting on the DFBI body is the sum of the forces on the individual faces:

Figure 10. EQUATION_DISPLAY

f_{DEM} = \sum_{f}^{} f_{DEM, f}

(4888)

The total moment is:

Figure 11. EQUATION_DISPLAY

n_{DEM} = \sum_{f}^{} r_{f} \times f_{DEM, f}

(4889)

where $r_{f}$ is the distance vector from the body position to the center of face $f$ .

Electromagnetic Force and Moment

The electromagnetic force and moment represent the magnetic force (Eqn. (4350)) and torque (Eqn. (4352)) that act on a 6-DOF body in presence of electromagnetic fields. For more information, see Electromagnetic Force.

Virtual Disk Force and Moment

The virtual disk force and moment represent the forces and moments that act on a 6-DOF body when a virtual disk is used to move the body.

Forces and moments of a virtual disk can be calculated in different ways depending on the virtual disk method active on a virtual disk. See different methods in Virtual Disk Model. The forces and moments are defined with respect to the virtual disk local coordinate system. See also Local Coordinate System.

To apply the values from disk to DFBI body, forces and moments must be transformed to the laboratory coordinate system as follows:

Figure 12. EQUATION_DISPLAY

f_{V D} = M f_{V D}^{D i s k S y s t e m}

(4890)

Figure 13. EQUATION_DISPLAY

n_{V D} = \vec{r} \times f_{V D} + M n_{V D}^{D i s k S y s t e m}

(4891)

where

$n_{V D}^{D i s k S y s t e m}$ is the moment in the virtual disk local coordinate system.
$f_{V D}^{D i s k S y s t e m}$ is the force in the virtual disk local coordinate system.
$M$ is the transformation matrix from the virtual disk local coordinate system to the laboratory coordinate system.
$f_{V D}^{}$ and $n_{V D}^{}$ are the force and moment in the laboratory coordinate system.
$\vec{r}$ is the distance vector between the body position and the virtual disk's origin.

The transformation for a vessel impulsed with a Body Force Propeller is illustrated below:

Figure 14. EQUATION_DISPLAY

\vec{r} = {\vec{r}}_{D i s k O r i g i n} - {\vec{r}}_{B o d y P o s i t i o n}

(4892)

Both body position and disk origin are specified in the laboratory coordinate system. Forces and moments from the virtual disk model are calculated first in the disk local coordinate system.