Pressure Coefficient

The Pressure Coefficient, \(c_p\), is a dimensionless quantity that provides a generalized representation of the pressure distribution on a surface, or body, exposed to a fluid flow. It allows us to assess how the local pressure at a specific point differs from the surrounding free-stream pressure, accounting for the dynamic pressure of the fluid flow.

Definition

The pressure coefficient is a dimensionless form of the pressure signal. It is obtained by the following expression:

\[ c_{p}(t) = \frac{p(t) - p_{\infty}(t)}{q} \]

By definition, the pressure coefficient is a local property for each triangle of the mesh.

Use Case

It is used primarily for analysis and interpretation of the measured data.

It should always be generated, since it is the first analysis step. It is a fundamental property of the pressure normalization, and it is used to calculate the other coefficients. However, it is not the final result to be delivered to clients.

Artifacts

The Cp template declares:

  1. Body pressure (kind: surface): per-timestep pressure on every mesh triangle.

  2. Reference probe (kind: points, optional): atmospheric reference pressure signal. If omitted, the reference pressure is taken as 0.

and a pipeline that subtracts the reference (sub), divides by the dynamic pressure (scale by 1 / q), and reduces to per-element statistics. The outputs are a cp time series and a cp statistics data source, each writable to an XDMF+H5 pair (ParaView-readable).

Usage

Run the shipped template from the command line:

cfdmod run fixtures/tests/pressure/templates/cp.yaml

or drive it from Python over any storage backend:

from cfdmod import load_template, run_template, XdmfH5Storage

template = load_template("cp.yaml")
bindings = run_template(template, storage=XdmfH5Storage(root="."))
cp_t = bindings["cp_t"]          # SurfaceDataSource, one row per triangle

The calculate_cp.ipynb notebook walks through this template step by step; a fuller end-to-end version (Cp / Cf / Cm / Ce over a container pack) lives at examples/container_pack/process_container_pack.ipynb in the repository.

Data format

Note

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

\(c_p(t)\)

time_idx/point_idx

Normalized time (\(t^*\))

0

1

2

0

0.0

1.25

1.15

1.32

0

1.0

1.1

1.5

1.13
\(c_p (stats)\)

scalar

0

1

2

3

min

-1.25

-0.9

-1.1

-0.2

max

1.15

0.95

1.13

0.19

mean

0.83

0.9

0.5

0.13

rms

0.26

0.25

0.13

0.19

skewness

1.15

-0.95

1.13

0.19