BEM algorithm

The Blade Element Momentum (BEM) theory is used to compute the aerodynamic loads on the rotor. For that, each blade is divided into a number of Blade aerodynamical station, and the force exerted by the air on each station is computed.

The BEM theory uses the concept of induced velocity to calculate the aerodynamic loads on the blade elements: as a result of extracting kinetic energy from the flow, the velocity of the air is modified. This variation is represented by the so-called induced velocity. Estimating the induced velocity is key in determining the aerodynamic loads on the blade element.

The Induced Velocity is a mathematical representation of the action of the blade on the air: when air particles hit the blade, they will produce an aerodynamic load on the element that will move the blade. As a consequence of Newton's third law, the element produces an equal and opposite force that modifies the velocity of the air particles. The difference between the air particle velocity upstream and downstream the blade is represented by the induced velocity

Two different BEM algorithms have been implemented in Ashes.
  • The  Steady BEM  can be used to compute loads in steady conditions, and is used as the initial condition for the  Unsteady BEM . The steady BEM will calculate the aerodynamic loads on the rotor assuming quasi-static conditions, therefore it is not recommended to use it in situations where the incoming wind velocity on a blade element varies (i.e. any realistic situation)
  • The  Unsteady BEM accounts for the time variations within the simulation and calculates the aerodynamic loads on the rotor at a time step based on the characteristics of the system at that time step and the loads at the previous time step. The Unsteady BEM uses the loads calculated by the  Steady BEM for the first time step of the simulation.
It is possible to swicth between these two implementations in the Advanced section of the  Aerodynamics tab in the  Analysis parameters dialog.

1 Aerodynamic-Structural Coupling in ASHES: Explicit Time Integration

1.1 Overview of the Simulation Workflow

ASHES uses an explicit coupling scheme to simulate the interaction between aerodynamic forces and structural dynamics. This means that at each time step, the aerodynamic loads are calculated based on the structural configuration from the previous time step, and then these loads are applied to advance the structure forward in time.

1.2 Step-by-Step Process

At each time step, the simulation proceeds as follows:

1.2.1 Aerodynamic Load Calculation

The aerodynamic forces on the blades are computed using the BEM. These calculations use the current wind conditions and the blade positions, velocities, and orientations from the previous time step. This includes:
  • Wind velocity at each blade station
  • Blade pitch angles
  • Rotor azimuth position
  • Structural deflections and velocities

1.2.2 Structural Dynamics Solution

The computed aerodynamic loads are applied to the structural model, and the finite element solver advances the structure forward in time. This updates:
  • Blade deflections and deformations
  • Tower motions
  • Rotor rotation and azimuth angle
  • All nodal displacements, velocities, and accelerations

1.2.3 State Update

The simulation time advances, and the new structural configuration becomes the basis for the next aerodynamic calculation.

1.3 What the Live Visualization Shows

When viewing a simulation in real-time with the live visualization feature:
  • Structural Elements (blades, tower, nacelle) are displayed at their current positions after the structural solve for each time step
  • Aerodynamic Load Vectors are displayed at the blade positions corresponding to the current structural state
The magnitude and direction of the aerodynamic load vectors represent the forces that were calculated based on the flow conditions and blade kinematics at the previous time step, and these forces are what drive the structural motion you see in the current time step.

While the aerodynamic loads are computed from the previous structural state (explicit coupling), this introduces only a minimal lag that is negligible for practical purposes when appropriate time steps are used.