aerosandbox.aerodynamics.aero_3D.singularities.uniform_strength_horseshoe_singularities#

Module Contents#

Functions#

calculate_induced_velocity_horseshoe(x_field, y_field, ...)

Calculates the induced velocity at a point:

Attributes#

args

aerosandbox.aerodynamics.aero_3D.singularities.uniform_strength_horseshoe_singularities.calculate_induced_velocity_horseshoe(x_field, y_field, z_field, x_left, y_left, z_left, x_right, y_right, z_right, gamma=1, trailing_vortex_direction=None, vortex_core_radius=0)[source]#
Calculates the induced velocity at a point:

[x_field, y_field, z_field]

in a 3D potential-flow flowfield.

In this flowfield, the following singularity elements are assumed:

  • A single horseshoe vortex consisting of a bound leg and two trailing legs

This function consists entirely of scalar, elementwise NumPy ufunc operations - so it can be vectorized as desired assuming input dimensions/broadcasting are compatible.

Parameters:

  • x_field (Union[float, aerosandbox.numpy.ndarray]) – x-coordinate of the field point

  • y_field (Union[float, aerosandbox.numpy.ndarray]) – y-coordinate of the field point

  • z_field (Union[float, aerosandbox.numpy.ndarray]) – z-coordinate of the field point

  • x_left (Union[float, aerosandbox.numpy.ndarray]) – x-coordinate of the left vertex of the bound vortex

  • y_left (Union[float, aerosandbox.numpy.ndarray]) – y-coordinate of the left vertex of the bound vortex

  • z_left (Union[float, aerosandbox.numpy.ndarray]) – z-coordinate of the left vertex of the bound vortex

  • x_right (Union[float, aerosandbox.numpy.ndarray]) – x-coordinate of the right vertex of the bound vortex

  • y_right (Union[float, aerosandbox.numpy.ndarray]) – y-coordinate of the right vertex of the bound vortex

  • z_right (Union[float, aerosandbox.numpy.ndarray]) – z-coordinate of the right vertex of the bound vortex

  • gamma (Union[float, aerosandbox.numpy.ndarray]) – The strength of the horseshoe vortex filament.

  • trailing_vortex_direction (aerosandbox.numpy.ndarray) – The direction that the trailing legs of the horseshoe vortex extend. Usually,

  • freestream. (this is modeled as the direction of the) –

  • vortex_core_radius (float) – To prevent a vortex singularity, here we use a Kaufmann vortex model. This parameter

  • (e.g. (governs the radius of this vortex model. It should be significantly smaller) –

  • of (at least an order) –

  • question. (magnitude smaller) than the smallest bound leg in the analysis in) –

Return type:

[Union[float, aerosandbox.numpy.ndarray], Union[float, aerosandbox.numpy.ndarray], Union[float, aerosandbox.numpy.ndarray]]

Returns: u, v, and w:

The x-, y-, and z-direction induced velocities.

aerosandbox.aerodynamics.aero_3D.singularities.uniform_strength_horseshoe_singularities.args = ()[source]#