aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities#

Module Contents#

Functions#

_calculate_induced_velocity_line_singularity_panel_coordinates(...)

Calculates the induced velocity at a point (xp_field, yp_field) in a 2D potential-flow flowfield.

_calculate_induced_velocity_line_singularity(x_field, ...)

Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield.

calculate_induced_velocity_line_singularities(x_field, ...)

Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield.

Attributes#

X

aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities._calculate_induced_velocity_line_singularity_panel_coordinates(xp_field, yp_field, gamma_start=0.0, gamma_end=0.0, sigma_start=0.0, sigma_end=0.0, xp_panel_end=1.0)[source]#

Calculates the induced velocity at a point (xp_field, yp_field) in a 2D potential-flow flowfield.

The p suffix in xp… and yp… denotes the use of the panel coordinate system, where:

  • xp_hat is along the length of the panel

  • yp_hat is orthogonal (90 deg. counterclockwise) to it.

In this flowfield, there is only one singularity element: A line vortex going from (0, 0) to (xp_panel_end, 0). The strength of this vortex varies linearly from:

  • gamma_start at (0, 0), to:

  • gamma_end at (xp_panel_end, 0). # TODO update paragraph

By convention here, positive gamma induces clockwise swirl in the flow field.

Function returns the 2D velocity u, v in the local coordinate system of the panel.

Inputs x and y can be 1D ndarrays representing various field points, in which case the resulting velocities u and v have corresponding dimensionality.

Equations from the seminal textbook “Low Speed Aerodynamics” by Katz and Plotkin. Vortex equations are Eq. 11.99 and Eq. 11.100.

  • Note: there is an error in equation 11.100 in Katz and Plotkin, at least in the 2nd ed:

The last term of equation 11.100, which is given as:

(x_{j+1} - x_j) / z + (theta_{j+1} - theta_j)

has a sign error and should instead be written as:

(x_{j+1} - x_j) / z - (theta_{j+1} - theta_j)

Source equations are Eq. 11.89 and Eq. 11.90.

Parameters:

  • xp_field (Union[float, aerosandbox.numpy.ndarray]) –

  • yp_field (Union[float, aerosandbox.numpy.ndarray]) –

  • gamma_start (float) –

  • gamma_end (float) –

  • sigma_start (float) –

  • sigma_end (float) –

  • xp_panel_end (float) –

Return type:

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

aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities._calculate_induced_velocity_line_singularity(x_field, y_field, x_panel_start, y_panel_start, x_panel_end, y_panel_end, gamma_start=0.0, gamma_end=0.0, sigma_start=0.0, sigma_end=0.0)[source]#

Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield.

In this flowfield, there is only one singularity element: # TODO update paragraph A line vortex going from (x_panel_start, y_panel_start) to (x_panel_end, y_panel_end). The strength of this vortex varies linearly from:

  • gamma_start at (x_panel_start, y_panel_start), to:

  • gamma_end at (x_panel_end, y_panel_end).

By convention here, positive gamma induces clockwise swirl in the flow field.

Function returns the 2D velocity u, v in the global coordinate system (x, y).

Inputs x and y can be 1D ndarrays representing various field points, in which case the resulting velocities u and v have the corresponding dimensionality.

Parameters:

  • x_field (Union[float, aerosandbox.numpy.ndarray]) –

  • y_field (Union[float, aerosandbox.numpy.ndarray]) –

  • x_panel_start (float) –

  • y_panel_start (float) –

  • x_panel_end (float) –

  • y_panel_end (float) –

  • gamma_start (float) –

  • gamma_end (float) –

  • sigma_start (float) –

  • sigma_end (float) –

Return type:

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

aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities.calculate_induced_velocity_line_singularities(x_field, y_field, x_panels, y_panels, gamma, sigma)[source]#

Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield.

In this flowfield, the following singularity elements are assumed: # TODO update paragraph

  • A line vortex that passes through the coordinates specified in (x_panel, y_panel). Each of these vertices is

called a “node”. * The vorticity of this line vortex per unit length varies linearly between subsequent nodes. * The vorticity at each node is specified by the parameter gamma.

By convention here, positive gamma induces clockwise swirl in the flow field.

Function returns the 2D velocity u, v in the global coordinate system (x, y).

Inputs x_field and y_field can be 1D ndarrays representing various field points, in which case the resulting velocities u and v have the corresponding dimensionality.

Parameters:

  • x_field (Union[float, aerosandbox.numpy.ndarray]) –

  • y_field (Union[float, aerosandbox.numpy.ndarray]) –

  • x_panels (aerosandbox.numpy.ndarray) –

  • y_panels (aerosandbox.numpy.ndarray) –

  • gamma (aerosandbox.numpy.ndarray) –

  • sigma (aerosandbox.numpy.ndarray) –

Return type:

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

aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities.X[source]#