RCAIDE.Library.Methods.Powertrain.Converters.Rotor.Performance.Blade_Element_Momentum_Theory_Helmholtz_Wake.compute_wake_contraction_matrix
compute_wake_contraction_matrix#
- compute_wake_contraction_matrix(prop, Nr, m, nts, X_pts, prop_outputs)[source]#
Computes slipstream development factor for all points along the wake slipstream.
- Parameters:
prop (Data) –
- Propeller/rotor data structure with the following attributes:
- radius_distributionarray_like
Radial station positions [m]
- number_of_bladesint
Number of blades on the rotor
- hub_radiusfloat
Hub radius of the rotor [m]
- tip_radiusfloat
Tip radius of the rotor [m]
- originarray_like
Origin coordinates of the rotor [m]
Nr (int) – Number of radial stations on the propeller/rotor
m (int) – Number of control points in segment
nts (int) – Number of timesteps
X_pts (array_like) – Location of wake points [m], shape (m, B, Nr, nts, 3) where B is number of blades
prop_outputs (Data) –
- Propeller/rotor outputs with the following attributes:
- disc_axial_induced_velocityarray_like
Axial induced velocity on the disc [m/s]
- velocityarray_like
Velocity vector [m/s]
- Returns:
wake_contraction – Wake contraction matrix, shape (m, B, Nr, nts) Ratio of contracted radius to original radius at each wake point
- Return type:
array_like
Notes
This function calculates the wake contraction factor for all points along the slipstream of a propeller or rotor. The wake contraction is a key factor in determining the induced velocities in the wake and the overall performance of the rotor.
- The computation follows these steps:
Extract rotor geometry parameters (radius distribution, hub/tip radius)
Calculate the distance of wake points from the rotor plane
Compute the slipstream development factor based on distance
Calculate the velocity ratio factor
Compute the contracted radius at each wake point
Calculate the wake contraction ratio (contracted radius / original radius)
- Major Assumptions
Fixed wake with helical shape
Wake contraction is primarily influenced by the axial induced velocity
The wake contraction model is based on momentum conservation
Theory The wake contraction is modeled using a combination of distance-based and velocity-based factors. The slipstream development factor (s2) increases with distance from the rotor plane, while the velocity ratio factor (Kv) accounts for the effect of induced velocities on the wake contraction.
The contracted radius at each wake point is calculated as:
\[r'_{j+1} = \sqrt{{r'_j}^2 + ({r_{j+1}}^2 - {r_j}^2) \cdot K_v}\]- where:
\(r'_j\) is the contracted radius at station j
\(r_j\) is the original radius at station j
\(K_v\) is the velocity ratio factor
References
[1] Stone, R. Hugh. “Aerodynamic modeling of the wing-propeller interaction for a tail-sitter unmanned air vehicle.” Journal of Aircraft 45.1 (2008): 198-210.