RCAIDE.Library.Methods.Powertrain.Converters.Rotor.Performance.Blade_Element_Momentum_Theory_Helmholtz_Wake.compute_wake_induced_velocity

compute_wake_induced_velocity#

compute_wake_induced_velocity(rotor, rotor_conditions, evaluation_points, ctrl_pts, identical_flag=False)[source]#

Computes the velocity induced by a rotor wake on specified evaluation points.

Parameters:

  • rotor (RCAIDE.Library.Components.Powertrain.Converters.Rotor) –

    Rotor component with the following attributes:
    • tip_radiusfloat

      Tip radius of the rotor [m]

    • originarray_like

      Origin coordinates of the rotor [m, m, m]

    • rotationint

      Rotation direction (1 for CCW, -1 for CW)

  • rotor_conditions (Data) –

    Rotor operating conditions with:
    • disc_radial_distributionarray_like

      Radial distribution on the disc [m]

    • blade_axial_induced_velocityarray_like

      Axial induced velocity at the blade [m/s]

    • blade_tangential_induced_velocityarray_like

      Tangential induced velocity at the blade [m/s]

  • evaluation_points (Data) –

    Points where induced velocities are to be evaluated:
    • XCarray_like

      X-coordinates of evaluation points (vehicle frame) [m]

    • YCarray_like

      Y-coordinates of evaluation points (vehicle frame) [m]

    • ZCarray_like

      Z-coordinates of evaluation points (vehicle frame) [m]

  • ctrl_pts (int) – Number of control points in segment

  • identical_flag (bool, optional) – Flag indicating if evaluation points are identical to rotor points, default False

Returns:

rotor_V_wake_ind – Induced velocities at evaluation points, shape (ctrl_pts, n_cp, 3) where n_cp is the number of evaluation points

Return type:

array_like

Notes

This function calculates the velocity induced by a rotor wake at specified evaluation points using a simplified wake contraction model. It is particularly useful for analyzing rotor-rotor interactions and rotor-airframe interactions.

The computation follows these steps:

  1. Extract rotor parameters and induced velocities at the blade

  2. Identify evaluation points within the rotor’s influence range

  3. Calculate the distance of evaluation points from the rotor plane

  4. Apply wake contraction model based on McCormick’s formulation

  5. Interpolate axial and tangential induced velocities at evaluation points

  6. Apply contraction factor to scale induced velocities

  7. Adjust sign of tangential velocities based on position relative to hub

Major Assumptions

  • The wake contracts following McCormick’s formulation

  • Induced velocities are only calculated for points within the rotor’s radial range

  • Inboard and outboard regions of the rotor are treated separately

  • Tangential induced velocities change sign across the hub center

Theory The wake contraction factor (kd) is calculated as:

\[k_d = 1 + \frac{s}{\sqrt{s^2 + R^2}}\]
where:

  • s is the distance from the rotor plane

  • R is the rotor tip radius

The induced velocities at evaluation points are then scaled by this contraction factor:

\[v_{a,new} = k_d \cdot v_a(y)\]
\[v_{t,new} = k_d \cdot v_t(y)\]
where:

  • v_a is the axial induced velocity

  • v_t is the tangential induced velocity

  • y is the radial position

References

[1] McCormick, B.W., “Aerodynamics of V/STOL Flight”, Academic Press, 1969

See also

RCAIDE.Library.Methods.Powertrain.Converters.Rotor.Performance.Blade_Element_Momentum_Theory_Helmholtz_Wake.wake_model