`RotatingFlow`#

class acoular.environments.RotatingFlow

Bases: FlowField

Analytical approximation of a rotating flow field with velocity component in z-direction.

This class provides an analytical model for a fluid flow field with a rigid-body-like rotation about the z-axis. The flow combines rotational motion in the x-y plane and a constant velocity component in the z-direction.

Notes

The rotation is assumed to be about the z-axis. The velocity components in the x-y plane are determined by the angular velocity omega, while the z-component is constant and set by v0.
The angular velocity omega is computed as: omega = 2 * np.pi * rps, with the rps given in revolutions per second (i.e. Hz).

Examples

>>> import acoular as ac
>>> import numpy as np
>>>
>>> flow = RotatingFlow(rps=1, v0=1.0)
>>> velocity, jacobian = flow.v(np.array((1.0, 1.0, 0.0)))
>>> velocity
array([-6.28318531,  6.28318531,  1.        ])
>>> jacobian
array([[ 0.        , -6.28318531,  0.        ],
       [ 6.28318531,  0.        ,  0.        ],
       [ 0.        ,  0.        ,  0.        ]])

rps: Rotational speed in revolutions per second. Negative values indicate clockwise rigid-body-like rotation of the flow. Default is 0.0.

v0: Constant flow velocity in the z-direction. Default is 0.0.

origin: The location of the center of rotation. Default is (0.0, 0.0, 0.0).

digest: A unique identifier based on the field properties. (read-only)

omega: Angular velocity (in radians per second) of the rotation. This is a derived property based on rps.

v(xx)

Compute the rotating flow field and its Jacobian matrix at a given location.

This method calculates the velocity vector and its Jacobian matrix at the specified location xx in the fluid domain. The flow field consists of rotational components in the x-y plane and a constant velocity component in the z-direction.

Parameters:

xxnumpy.ndarray of floats: The 3D Cartesian coordinates of the location in the fluid where the velocity field is to be computed, shape (3,).

Returns:

velocity_vectornumpy.ndarray of floats

The velocity vector at the specified location xx, shape (3,). The components are:

U: Velocity in the x-direction (dependent on y-coordinate and omega).
V: Velocity in the y-direction (dependent on x-coordinate and omega).
W: Constant velocity in the z-direction (set by v0).

jacobian_matrixnumpy.ndarray of floats

The Jacobian matrix of the velocity vector field at the specified location xx. The matrix contains partial derivatives of each velocity component with respect to the spatial coordinates \((x, y, z)\), shape (3, 3).

Notes

The Jacobian matrix is constant for this flow field and represents the linear relationship between the velocity components and spatial coordinates in the x-y plane.

RotatingFlow#

`RotatingFlow`#