RCAIDE.Library.Methods.Powertrain.Converters.Rotor.Performance.Blade_Element_Momentum_Theory_Helmholtz_Wake.wake_model.evaluate_wake#
- evaluate_wake(rotor, wake_inputs, conditions)[source]#
Evaluates the rotor wake using Helmholtz vortex theory.
- Parameters:
rotor (RCAIDE.Library.Components.Powertrain.Converters.Rotor) –
- Rotor component with the following attributes:
- number_of_bladesint
Number of blades on the rotor
- tip_radiusfloat
Tip radius of the rotor [m]
- hub_radiusfloat
Hub radius of the rotor [m]
- sol_tolerancefloat
Solution tolerance for wake convergence
wake_inputs (Data) –
- Wake input parameters with:
- ctrl_ptsint
Number of control points
- Nrint
Number of radial stations
- Naint
Number of azimuthal stations
- use_2d_analysisbool
Flag for 2D (azimuthal) analysis
- velocity_totalarray_like
Total velocity magnitude [m/s]
- velocity_axialarray_like
Axial velocity component [m/s]
- velocity_tangentialarray_like
Tangential velocity component [m/s]
- twist_distributionarray_like
Blade twist distribution [rad]
- chord_distributionarray_like
Blade chord distribution [m]
- radius_distributionarray_like
Radial station positions [m]
- speed_of_soundsarray_like
Speed of sound [m/s]
- dynamic_viscositiesarray_like
Dynamic viscosity [kg/(m·s)]
conditions (Data) – Flight conditions
- Returns:
va (array_like) – Axially-induced velocity from rotor wake [m/s]
vt (array_like) – Tangentially-induced velocity from rotor wake [m/s]
Notes
This function evaluates the rotor wake using Helmholtz vortex theory to calculate the induced velocities. It solves for the inflow angle (PSI) that satisfies the circulation equation, then computes the axial and tangential induced velocities.
- The computation follows these steps:
Initialize the inflow angle (PSI) array
Solve for the inflow angle using a nonlinear equation solver
Calculate the axial and tangential induced velocities from the converged solution
- Major Assumptions
The wake is modeled using Helmholtz vortex theory
The solution converges to a steady state
The inflow angle (PSI) is the primary variable being solved for
Theory The wake model is based on Helmholtz vortex theory, which relates the circulation around the blade to the induced velocities in the wake. The key equation being solved is:
\[R = \Gamma - \frac{1}{2}W \cdot c \cdot C_l = 0\]- where:
Γ is the circulation
W is the relative velocity
c is the chord
Cl is the lift coefficient
The circulation is related to the tangential induced velocity by:
\[\Gamma = v_t \cdot \frac{4\pi r}{B} \cdot F \cdot \sqrt{1 + \left(\frac{4\lambda_w R}{\pi B r}\right)^2}\]- where:
vt is the tangential induced velocity
r is the radial position
B is the number of blades
F is the tip loss factor
λw is the inflow ratio
References
[1] Drela, M. “Qprop Formulation”, MIT AeroAstro, June 2006 http://web.mit.edu/drela/Public/web/qprop/qprop_theory.pdf