aerosandbox.aerodynamics.aero_2D.singularities.linear_strength_line_singularities
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Module Contents#
Functions#
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Calculates the induced velocity at a point (xp_field, yp_field) in a 2D potential-flow flowfield. |
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Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield. |
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Calculates the induced velocity at a point (x_field, y_field) in a 2D potential-flow flowfield. |
Attributes#
- 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]]