Force Coefficient¶

The Force Coefficient, $C_f$, is a dimensionless parameter that provides a generalized representation of the resultant forces experienced by an object within a fluid flow. It offers a means to evaluate the cumulative effect of pressure coefficients, $c_p$ across different regions of an object’s surface and how these pressures translate into aerodynamic forces.

$C_f$ is a fundamental tool for assessing lift, drag, and other forces crucial for the design and analysis of aerodynamic components.

Definition¶

This coefficient is defined as a net resulting force coefficient of a body. A body is composed by a set of surfaces. For example, consider a building’s canopy, where the lower surface is marked on red, and the upper surface is marked on green:

The net resulting force coefficient is defined as:

\[C_{f} = \frac{\sum F_{res}}{q A_{rep}} = \frac{F_{green} + F_{red}}{q A_{rep}} = \frac{\sum{c_{pi} A_{i}} + \sum{c_{pj} A_{j}}}{A_{rep}}\]

Important

Note that the net force coefficient has a direction attached to its definition. Its direction is the same as the resulting force direction.

It can also be defined for each axis direction:

\[C_{fx} = \frac{\sum Fx_{res}}{q A_{x}} = \frac{Fx_{green} + Fx_{red}}{q A_{x}} = \frac{\sum{c_{pi} A_{ix}} + \sum{c_{pj} A_{jx}}}{A_{x}}\]

\[C_{fy} = \frac{\sum Fy_{res}}{q A_{y}} = \frac{Fy_{green} + Fy_{red}}{q A_{y}} = \frac{\sum{c_{pi} A_{iy}} + \sum{c_{pj} A_{jy}}}{A_{y}}\]

\[C_{fz} = \frac{\sum Fz_{res}}{q A_{z}} = \frac{Fz_{green} + Fz_{red}}{q A_{z}} = \frac{\sum{c_{pi} A_{iz}} + \sum{c_{pj} A_{jz}}}{A_{z}}\]

We define the nominal area ($A_x$, $A_y$, $A_z$) as a user input, constant for all axis ($A_x$=$A_y$=$A_z$). This is done to let the user define how they want to calculate its value. The mathematical definition is to use the projection of the surface area for the body composed in the given axis.

Note

For a non constant nominal area, the values of moment coefficient can be generated and later renormalized based on geometry informations.

Use Case¶

A common application of the net force coefficient requires sectioning the body in different sub-bodies. To do so, a similar logic applied to the shape coefficient is used to determine the respective sub-body of each of the body’s triangles. If its center lies inside the sub-body volume, then it belongs to it.

The result is a sectionated body in different sub-bodies for each interval. When sectioning the body, the respective nominal area should be the same as the sub-body nominal area.

Note

Check out the definitions section for more information about surface, body and sub-body definitions.

Like the other coefficients, we can apply statistical analysis to the net force coefficient.

By definition, the net force coefficient is a property of a body.

It is used for primary and secondary structures design, such as canopies and roof vents. It can also be used for evaluating the resultant wind action over a building or the building paviments. It can be seen as the resulting effect of the wind induced force over a body.

Artifacts¶

The user provides:

Cp timeseries XDMF+H5 produced by run_cp.
Parameters (CfCaseConfig): bodies, sub-body zoning and the nominal-area knobs. Pass either a YAML path or an in-memory instance.
Mesh (optional): .lnas / .stl / .h5 / .xdmf. BodyDefinition(surfaces=[]) selects every surface in the mesh, so when the input is a single-surface H5 the same config covers the whole mesh as one body. When omitted, the geometry comes from the cp timeseries H5.

Outputs (flat under output):

Cf.{cfg_lbl}.{body}.time_series.{h5,xdmf} – one file per body. Each file embeds the body’s mesh and carries cf_x / cf_y / cf_z groups; pick the direction from the ParaView Attribute selector on the same animation.
stats.h5 / stats.xdmf – combined statistics; Cf lands under /cf_{x,y,z}/{cfg_lbl}/{body}/ with the body’s mesh embedded.
Each output H5 carries the post-processing config under /processing_metadata/.

Usage¶

Reference parameters file:

bodies:
  marquise:
    surfaces: [list_of_surfaces_of_marquise]
  lanternim:
    surfaces: [list_of_surfaces_of_lanternim]
  building:
    surfaces: [building]
force_coefficient:
  measurement_1:
    bodies:
      - name: building
        sub_bodies: # Optional, default is the whole body
          z_intervals: [0, 10, 20]
    directions: ["x", "y", "z"]
    statistics:
      - stats: "mean"
      - stats: "rms"
      - stats: "skewness"
      - stats: "kurtosis"
      - stats: "min"
        params:
          method_type: "Absolute"
      - stats: "max"
        params:
          method_type: "Absolute"
    # Apply transformations before indexing the regions
    transformation:
      translation: [0, 0, 0]
      rotation: [0, 0, 0]
      fixed_point: [0, 0, 0]
  measurement_2:
    bodies:
      - name: marquise
    directions: ["x", "y", "z"]
    statistics:
      - stats: "mean"
      - stats: "rms"
      - stats: "skewness"
      - stats: "kurtosis"
      - stats: "min"
        params:
          method_type: "Absolute"
      - stats: "max"
        params:
          method_type: "Absolute"
    # Apply transformations before indexing the regions
    transformation:
      translation: [0, 0, 0]
      rotation: [0, 0, 0]
      fixed_point: [0, 0, 0]

From Python:

from cfdmod import run_cf, CfCaseConfig
run_cf(
    cp_h5="output/cp.default.time_series.h5",
    cfg_path=CfCaseConfig.from_file("cf.yaml"),
    output="output",
    # mesh_path optional; omitting it reads geometry from the cp H5
)

CLI:

python -m cfdmod pressure cf \
   --cp     {CP_TIMESERIES_H5} \
   --config {CONFIG_PATH} \
   --output {OUTPUT_PATH}

A worked example covering Cp, Cf and Cm together lives at notebooks/process_container_pack.ipynb in the repository root.

Data format¶

Note

The rule for determining the region_idx is based on the region index and the body name. Input mesh can have multiple bodies, and each of them can be applied a specific zoning/region rule. Because of that, region_idx has to be composed by the zoning region index joined by “-” and the body name. This also guarantee that even if different bodies lie on the same region, the interpreted region for each of them will be different

Note

For more information about the normalized time scale ($t^*$), check the Normalization section

$C_{fx}(t)$¶
time_idx/region_idx	Normalized time ($t^*$)	0-Body1	1-Body1	0-Body2
0	10000	1.25	1.15	-1.1
1	11000	1.5	0.9	-1.15

$C_{fy}(t)$¶
time_idx/region_idx	Normalized time ($t^*$)	0-Body1	1-Body1	0-Body2
0	10000	1.25	1.15	-1.1
1	11000	1.5	0.9	-1.15

$C_{fz}(t)$¶
time_idx/region_idx	Normalized time ($t^*$)	0-Body1	1-Body1	0-Body2
0	10000	1.25	1.15	-1.1
1	11000	1.5	0.9	-1.15

$C_{fx} (stats)$¶
region_idx	max	min	mean	std	skewness	kurtosis
0-Body1	1.25	0.9	1.1	0.2	0.1	0.15
1-Body1	1.15	0.95	1.13	0.19	0.11	0.13

$C_{fy} (stats)$¶
region_idx	max	min	mean	std	skewness	kurtosis
0-Body1	1.25	0.9	1.1	0.2	0.1	0.15
1-Body1	1.15	0.95	1.13	0.19	0.11	0.13

$C_{fz} (stats)$¶
region_idx	max	min	mean	std	skewness	kurtosis
0-Body1	1.25	0.9	1.1	0.2	0.1	0.15
1-Body1	1.15	0.95	1.13	0.19	0.11	0.13

$Regions(indexing)$¶
region_idx	point_idx
0-Body1	0
1-Body1	1

$Regions(definition)$¶
region_idx	x_min	x_max	y_min	y_max	z_min	z_max	Lx	Ly	Lz
0-Body1	0	100	0	50	0	20	0.5	0.8	0.1
1-Body1	100	200	0	50	0	20	0.8	0.5	0.2