Force and Moment Coefficients

Besides the non-dimensional output fields, there are also many coefficients commonly used in the computational fluid dynamics community, e.g. pressure coefficient (\(C_p\)), skin friction coefficient (\(C_f\)), lift coefficient (\(C_L\)), drag coefficient (\(C_D\)), etc. Flow360 also exports the above coefficients found in VolumeOutput, SurfaceOutput, SliceOutput.

Attention

It should be noted that the reference velocity \(U_\text{ref}\) used to calculate the \(C_p, C_f, C_D, C_L\) can be set via AerospaceCondition.velocity_magnitude or AerospaceCondition.reference_velocity_magnitude by users. It is not the same as the reference velocity (\(C_\infty\)) used for the non-dimensional outputs in Table 8.1.4.

In particular, we want to emphasize that the non-dimensionalization of force and moment for BET Disk and Actuator Disk are different from the coefficients shown in this page.

The force coefficients and moment coefficients exported by Flow360 are listed in Table 8.1.5. These coefficients can be obtained from total_forces_v2.csv, surface_forces_v2.csv files on WebUI. They can also be fetched by the case.results.total_forces and case.results.surface_forces Python API calls.

Table 8.1.5 Force coefficients and moment coefficients exported by Flow360

Property	Definition
CL	\(\text{Lift}/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}\)
CD	\(\text{Drag}/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}\)
CFx	\(\text{Force}_x/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}\)
CFy	\(\text{Force}_y/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}\)
CFz	\(\text{Force}_z/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref}\)
CMx	\(\text{Moment}_x/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[0\right]\)
CMy	\(\text{Moment}_y/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[1\right]\)
CMz	\(\text{Moment}_z/\frac{1}{2}\rho_\infty U_\text{ref}^2 A_\text{ref} L_\text{ref}\left[2\right]\)

Note

In the above table, all reference values can be accessed through Python API as shown in the Reference Variable Table.

The typical output options in the WebUI and various csv files are outlined in Table 8.1.6. The conventions assume z-axis upwards, y-axis spanwise (+ towards starboard side) and x-axis in the axial direction (+ in the freestream direction) for the global axes, as shown in Fig. 8.1.10.

Fig. 8.1.10 Axis conventions demonstrated using the CRM geometry

Table 8.1.6 Force and Moment output conventions.

Output
\(CFx, CFy, CFz\)	Force coefficients (global axes)
\(CMx, CMy, CMz\)	Moment coefficients (global axes)
\(CL = CFz\cdot cos(\alpha) - CFx\cdot sin(\alpha)\)	Lift coefficient (wind axes)
\(CD = CFx\cdot cos(\alpha) cos(\beta) +\) \(CFz\cdot sin(\alpha) cos(\beta)\)	Drag coefficient (wind axes)
\(CFxPressure, CFyPressure, CFzPressure\)	Pressure contributions to force coefficients (global axes)
\(CMxPressure, CMyPressure, CMzPressure\)	Pressure contributions to moment coefficients (global axes)
\(CFxSkinFriction, CFySkinFriction,\) \(CFzSkinFriction\)	Skin friction contributions to force coefficients (global axes)
\(CMxSkinFriction, CMySkinFriction,\) \(CMzSkinFriction\)	Skin friction contributions to moment coefficients (global axes)
\(CLPressure, CDPressure\)	Pressure contributions to the lift and drag coefficients
\(CLSkinFriction, CDSkinFriction\)	Skin friction contributions to the lift and drag coefficients
\(CS = CFy\cdot cos(\beta) + CFx\cdot cos(\alpha) sin(\beta) -\) \(CFz\cdot sin(\alpha) sin(\beta)\)	Side force coefficient (wind axes). Not available in the csv file and can be calculated from body forces.

Example: Lift Force and Pitching Moment

# The output values are averaged over the last 10% steps
total_forces = case.results.total_forces.averages

length_unit = project.length_unit
density = case.params.operating_condition.thermal_state.density
A_ref = case.params.reference_geometry.area

# If reference_velocity_magnitude is provided
# when defining operating_condition, use
# U_ref = case.params.operating_condition.reference_velocity_magnitude
U_ref = case.params.operating_condition.velocity_magnitude

# Compute Lift Force
CL = total_forces["CL"]
Lift = CL * 0.5 * density * U_ref**2 * A_ref

# Compute Pitching Moment
CMy = total_forces["CMy"]
Pitching_Moment = CMy * 0.5 * density * U_ref**2 * A_ref * length_unit