Moving Body

The Moving Body statistics provide time-resolved kinematic and force-related quantities associated with each moving body in the simulation. These outputs describe the motion of the body (position, velocity, rotation), as well as the forces, torques, and stresses exerted on the body by the surrounding fluid. This output produces a tab-separated ASCII .txt file named MovingBody_{DynamicName}.txt, where the dynamic name corresponds to the name of the Moving Body in the Model Tree.

The data is written as a time series, where each row corresponds to a simulation time and each column corresponds to a statistic listed in the table below. Each row in the output file corresponds to a new statistics output time and is appended at the Statistics Output Write Interval.

The reported quantities fall into several categories:

• Kinematics: Position, velocity, angular position, angular velocity, and rotation axis describe how the body moves and rotates over time.

• Forces and Torques: Force and torque components (X, Y, Z, axial, radial, and orbit-based) quantify the fluid-induced loads acting on the body. Unless otherwise noted, these values exclude contributions from static pressure.

• Surface Quantities: Pressure, stress, and shear stress values represent spatial averages (or extrema) over the moving body surface, providing insight into fluid loading and boundary interactions.

• Interior Quantities: Interior forces and torques represent contributions from fluid contained within the moving body, when applicable.

• Geometric Properties: Area and wetted area describe the effective surface of the body interacting with the fluid.

• Derived Quantities: Metrics such as power number provide normalized measures of energy transfer and are useful for comparing operating conditions.

Statistics Table

The index table below shows the statistics that will appear in the Moving Body output file. Within this table, each statistic corresponds to a column in the output table that evolves with the time column.

Statistics	Units	Details	When Appears
Time	s	simulation time
Angular Position	rad	angular position of rotation about moving body position
Angular Velocity	rad/s	angular velocity of rotation about moving body position
Angular Velocity X	rad/s	angular velocity
Angular Velocity Y	rad/s	angular velocity
Angular Velocity Z	rad/s	angular velocity
Area	m^2	total area of moving body surface
Direction X	Dimensionless	orientation direction of ball joint
Direction Y	Dimensionless	orientation direction of ball joint
Direction Z	Dimensionless	orientation direction of ball joint
Dynamic Pressure	Pa	spatial mean over moving body surface of dynamic pressure, does not include static pressure, positive indicates pressure in direction of triangle normal
Dynamic Stress	Pa	spatial mean over moving body surface of dynamic stress which is sum of dynamic pressure and shear stress, does not include static pressure
Force Axial	N	axial component of total force from fluid on moving body, does not include forces due to static pressure
Force Radial Magnitude	N	radial component of total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force X	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Y	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Force Z	N	total force from fluid on moving body, does not include forces due to static pressure
Interior Force X	N	total force from interior fluid on moving body
Interior Force Y	N	total force from interior fluid on moving body
Interior Force Z	N	total force from interior fluid on moving body
Interior Torque X	N-m	total torque from interior fluid on moving body
Interior Torque Y	N-m	total torque from interior fluid on moving body
Interior Torque Z	N-m	total torque from interior fluid on moving body
Max Dynamic Stress	Pa	spatial max over moving body surface of dynamic stress which is sum of dynamic pressure and shear stress, does not include static pressure
Max Stress	Pa	spatial max over moving body surface of total stress, includes static pressure
Orbit Position	rad	angular position of rotation about orbit point
Orbit Torque X	N-m	total torque from fluid on moving body taken about the orbit axis, does not include forces due to static pressure
Orbit Torque Y	N-m	total torque from fluid on moving body taken about the orbit axis, does not include forces due to static pressure
Orbit Torque Z	N-m	total torque from fluid on moving body taken about the orbit axis, does not include forces due to static pressure
Position	m	translation magnitude from initial location
Position X	m	translation from initial location
Position X	m	moving body position
Position X	m	translation of moving body from initial position
Position Y	m	translation from initial location
Position Y	m	moving body position
Position Y	m	translation of moving body from initial position
Position Z	m	translation from initial location
Position Z	m	moving body position
Position Z	m	translation of moving body from initial position
Power Number	Dimensionless	power number, power normalization is done using local density
Power Number Normalized by [dynamic] Density	Dimensionless	power number, power normalization is done using fluid 1 density
Rotation Angle	rad	angular position of rotation axis
Rotation Angle After	rad	angular position of rotation applied after translation
Rotation Angle Before	rad	angular position of rotation applied before translation
Rotation Axis X	Dimensionless	axis of rotation
Rotation Axis X After	Dimensionless	axis of rotation applied after translation
Rotation Axis X Before	Dimensionless	axis of rotation applied before translation
Rotation Axis Y	Dimensionless	axis of rotation
Rotation Axis Y After	Dimensionless	axis of rotation applied after translation
Rotation Axis Y Before	Dimensionless	axis of rotation applied before translation
Rotation Axis Z	Dimensionless	axis of rotation
Rotation Axis Z After	Dimensionless	axis of rotation applied after translation
Rotation Axis Z Before	Dimensionless	axis of rotation applied before translation
Rotational Velocity X After	rad/s	rotational velocity of rotation applied after translation
Rotational Velocity X Before	rad/s	rotational velocity of rotation applied before translation
Rotational Velocity Y After	rad/s	rotational velocity of rotation applied after translation
Rotational Velocity Y Before	rad/s	rotational velocity of rotation applied before translation
Rotational Velocity Z After	rad/s	rotational velocity of rotation applied after translation
Rotational Velocity Z Before	rad/s	rotational velocity of rotation applied before translation
Shear Stress	Pa	spatial mean over moving body surface of shear stress
Time-Avg Dynamic Pressure	Pa	spatial mean over time-averaged moving body surface of dynamic pressure, does not include static pressure, positive indicates pressure in direction of triangle normal
Time-Avg Total Pressure	Pa	spatial mean over time-averaged moving body surface of fluid pressure
Time-Avg Total Pressure	Pa	spatial mean over time-averaged moving body surface of pressure, includes static pressure
Torque X	N-m	total torque from fluid on moving body taken about the axis of rotation, does not include forces due to static pressure
Torque X	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque X	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque X	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque X	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Y	N-m	total torque from fluid on moving body taken about the axis of rotation, does not include forces due to static pressure
Torque Y	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Y	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Y	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Y	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Z	N-m	total torque from fluid on moving body taken about the axis of rotation, does not include forces due to static pressure
Torque Z	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Z	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Z	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Torque Z	N-m	total torque from fluid on moving body, does not include forces due to static pressure
Total Pressure	Pa	spatial mean over moving body surface of fluid pressure
Total Pressure	Pa	spatial mean over moving body surface of pressure, includes static pressure
Total Stress	Pa	spatial mean over moving body surface of total stress, includes static pressure
Velocity	m/s	velocity magnitude in direction of translation
Velocity X	m/s	velocity
Velocity X	m/s	velocity
Velocity X	m/s	velocity
Velocity Y	m/s	velocity
Velocity Y	m/s	velocity
Velocity Y	m/s	velocity
Velocity Z	m/s	velocity
Velocity Z	m/s	velocity
Velocity Z	m/s	velocity
Wetted Area	m^2	total wetted area of moving body surface

Usage and Interpretation

Kinematics

The kinematic quantities (e.g., Position, Velocity, Angular Position, Angular Velocity, Rotation Axis) define how the body translates and rotates over time. These are typically used to verify that the motion matches the intended operating conditions (e.g., impeller speed or orbital motion), and to interpret all force and torque quantities in the correct frame of reference.

Forces and Torques

The force and torque quantities (e.g., Force X/Y/Z, Force Axial, Force Radial Magnitude, Torque X/Y/Z) represent the total fluid-induced loading on the body. These are computed by summing the stress contributions over all mesh triangles belonging to the moving body family. At each triangle, the local pressure and viscous shear stresses act over the surface area, and these contributions are integrated to obtain the total force:

\[\mathbf{F} = \sum_k \left( -p_k \mathbf{n}_k + \boldsymbol{\tau}_k \right) A_k\]

where \(k\) indexes the surface triangles, \(p_k\) is the local pressure, \(\mathbf{n}_k\) is the outward normal, \(\boldsymbol{\tau}_k\) is the shear stress, and \(A_k\) is the triangle area.

Torque is computed from these same surface forces, but with an important distinction: it is evaluated about the moving body family mount point. The torque is given by:

\[\mathbf{T} = \sum_k \mathbf{r}_k \times \left( -p_k \mathbf{n}_k + \boldsymbol{\tau}_k \right) A_k\]

where \(\mathbf{r}_k=\mathbf{x}_k−\mathbf{x}_{mount}\) is the position vector from the family mount point to the triangle centroid. Because torque depends on this reference point, the choice of mount location directly affects the reported values.

Unless otherwise noted, these quantities exclude contributions from static pressure and therefore represent dynamic fluid loading.

Surface Quantities

The surface quantities (e.g., Dynamic Pressure, Shear Stress, Total Stress, Max Stress) represent spatial averages or extrema over the moving body surface. They are computed by integrating local values over all surface triangles in the moving body family.

The surface-averaged quantity \(⟨ϕ⟩\) is computed as an area-weighted average:

\[\langle \phi \rangle = \frac{1}{A_{\text{tot}}} \sum_k \phi_k \, A_k\]

where: \(\phi_k\) is the local value on triangle \(k\) (e.g., pressure, shear stress), \(A_k\) is the triangle area, and \({A_{\text{tot}}}=\sum_k, A_k\) is the total surface area of the moving body family.

The dynamic pressure excludes static pressure and is defined as

\[p_{\text{dyn},k} = p_k - p_{\text{static}}\]

And the reported Dynamic Pressure is the surface average

\[\langle p_{\text{dyn}} \rangle = \frac{1}{A_{\text{tot}}} \sum_k \left( p_k - p_{\text{static}} \right) \, A_k\]

The shear stress represents the tangential viscous stress at the surface

\[\langle \boldsymbol{\tau} \rangle = \frac{1}{A_{\text{tot}}} \sum_k \boldsymbol{\tau}_k \, A_k\]

And the total stress combines pressure and shear contributions

\[\langle \sigma \rangle = \frac{1}{A_{\text{tot}}} \sum_k \left( -p_k \mathbf{n}_k + \boldsymbol{\tau}_k \right) \cdot \mathbf{n}_k \, A_k\]

where this represents the normal component of total stress on the surface.

The maximum stress is computed as the maximum value over all surface triangles:

\[\sigma_{\text{max}} = \max_k \left( \sigma_k \right)\]

Interior Quantities

The interior quantities (e.g., Interior Force, Interior Torque) represent contributions from fluid contained within the moving body, when applicable. These terms are important for geometries where fluid exists inside the body volume (e.g., partially filled or porous bodies), and allows separation of external fluid loading from internal fluid contributions.

Geometric Properties

The geometric quantities (e.g., Area, Wetted Area) describe the effective surface of the body interacting with the fluid. These are computed by summing the contributions from all surface triangles belonging to the moving body family.

The total surface area is given by:

\[A_{\text{total}} = \sum_k A_k\]

where \(A_k\) is the area of triangle \(k\).

The wetted area represents the portion of the surface in contact with the fluid and is computed as

\[A_{\text{wetted}} = \sum_k \phi_k A_k\]

where \(ϕk\) is the fluid volume fraction adjacent to the surface triangles.

Derived Quantities

The power and power number provide a direct link between fluid loading and energy input. The instantaneous power is computed from torque and angular velocity:

\[P = \mathbf{T} \cdot \boldsymbol{\omega}\]

The power number is then defined as

\[N_p = \frac{P}{\rho N^3 D^5}\]

where \(ρ\) is the fluid density, \(N\) is the rotational speed (rev/s) derived from the instantaneous angular velocity, and \(D\) is the characteristic diameter defined for the moving body family.

In multiphase systems, the choice of density is not unique. M-Star reports two power number definitions: Local Density-based Power Number uses the instantaneous, local fluid density field. Fluid 1 Density-based Power Number uses the reference density of Fluid 1.

This distinction reflects a modeling choice. Using the local density accounts for spatial and temporal variations in density due to phase distribution, while using Fluid 1 density provides a consistent reference for comparison to single-phase correlations and experimental data.

Both quantities are computed on a total family basis, using the fully integrated torque over all surface triangles. Because the calculation uses instantaneous values, the reported power numbers reflect the current operating condition at each output time.

Important

All Moving Body statistics are computed at the family level, including forces, torques, power, and all derived quantities. Each reported value represents the total or average obtained by integrating all surface triangles associated with the moving body family.

If a family contains multiple child geometries, the reported quantities reflect the combined contribution of all child surfaces within that family. To obtain statistics for individual geometries, each must be assigned to its own moving body family.