Dynamic Stall
Blade Element Momentum (BEM) codes rely on measured or computed lookup tables for steady-state lift, drag and moment coefficients as a function of angle of attack. These steady curves are generally not sufficient to model the dynamic response of a flexible rotor to variable inflow conditions. Therefore dynamic stall models are implemented in the Bladed code.
Note that the dynamic stall model refers here to the modelling of both the unsteady effects for attached flow as well as the dynamics of trailing-edge separation. The adopted dynamic stall models are not applied on cylindrical sections. The exclusion of the cylindrical parts is done automatically in Bladed without any required user inputs.
Dynamic Stall Modelling Options
Dynamic stall model:
Øye model: The Øye model is the most simple dynamic stall model offered, which only contains terms for modelling the dynamics of trailing edge separation.Incompressible Beddoes-Leishman model: The incompressible model is considered most appropriate for typical turbines with tip speeds of Mach number smaller than 0.25.IAG model: The IAG model is a first order Beddoes-Leishman type dynamic stall model with improved accuracy in deep stall conditions.Compressible Beddoes-Leishman model: The compressible model is suitable for high Mach numbers but is unstable for low Mach numbers.Pre-4.8 Beddoes-Leishman model: The pre-4.8 model is equivalent to the Beddoes-Leishman model as implemented in the aerodynamics module used up to Bladed 4.8. The pre-4.8 model article also explains the differences between this model and the incompressible and compressible Beddoes-Leishman models. This model typically provides the highest aerodynamic damping in parked/idling simulations where the blade experiences large angles of attack.No dynamic stall: Steady lift, drag and moment coefficient curves will be used.
Linear fit gradient method: When selected, the linear fit polar gradient is used to reconstruct the inviscid polar data. The fit is performed only within the linear polar regime that is searched automatically between the zero lift AoA to AoA = 7 deg. This approach is more suitable for polar data sets where the lift coefficient slope is not straight around 0 deg angle of attack. It is recommended to activate this option for more accurate computations. This option is turned on by default.Use Kirchoff equation for normal force coefficient: If selected, the normal force coefficient is computed using the dynamic separation position in Kirchoff's equation directly. If unselected, the dynamic separation position is used to linearly interpolate between fully separated and fully attached flow. The latter is the case by default. In normal operating conditions this setting will not lead to significant differences, it is however found that in parked/idling where the blade experiences high angles of attack this option will improve the aerodynamic damping of the blade.Dynamic pitching moment coefficient: This option is enabled by default. It is not recommended to disable this option for blades with a torsional degree of freedom because the so-called "pitch-rate damping" term of the moment coefficient is typically important to keep the blade torsional mode stable.Include impulsive lift and moment contributions: This option is used to activate the non-circulatory contributions in lift and moment coefficient. Note that some moment contribution terms are not controlled by this option; but are controlled by theDynamic pitching moment coefficientoption.Starting radius for dynamic stall: This is the radial position, given as a percentage, outboard of which the dynamic stall model will be used. 0% means that dynamic stall is applied from the blade root. Note that dynamic stall contribution for non lifting surfaces (for example cylinders) is automatically excluded in Bladed computations. Default = 0%.Ending radius for dynamic stall: This is the radial position, given as a percentage, outboard of which the dynamic stall model will be switched off.Adjust dynamic stall constants: A toggle to show the default constants applied in Bladed dynamic stall models. These values are valid for most cases but can be freely adjusted if desired by the usersSeparation position time constant: This is a dimensionless time constant, given in terms of the time taken to travel half a chord. It defines the lag in the movement of the separation point due to unsteady pressure and boundary layer response.Pressure lag time constant: This time constant describes the lag between the pressure and the lift.Vortex lift time constant: This time constant describes the rate of decay of the vortex induced lift that is generated when aerofoils undergo a rapid change in angle of attack towards positive or negative stall.Vortex travel time constant: This time constant controls the duration of the vortex induced lift that is generated when aerofoils undergo a rapid change in angle of attack towards positive or negative stall.Attached flow constant A1: Constant A1 for the Beddoes-Leishman type dynamic stall model to control the attached flow states.Attached flow constant A2: Constant A2 for the Beddoes-Leishman type dynamic stall model to control the attached flow states.Attached flow constant b1: Constant b1 for the Beddoes-Leishman type dynamic stall model to control the attached flow states.Attached flow constant b2: Constant b2 for the Beddoes-Leishman type dynamic stall model to control the attached flow states.
Default Constants and Options Used in Bladed Dynamic Stall Models
The following constants in Table 1 and options in Table 2 are applied as default in the available Bladed dynamic stall models. The number of constants vary depending on the model being used. These constants are valid for most cases but can be freely adjusted if desired by the users.
| Model/Constant | \(A_1\) | \(A_2\) | \(b_1\) | \(b_2\) | \(T_p\) | \(T_f\) | \(T_v\) | \(T_vl\) |
|---|---|---|---|---|---|---|---|---|
| Øye Model | N/A | N/A | N/A | N/A | N/A | 3.0 | N/A | N/A |
| Incompressible Beddoes-Leishman Model | 0.165 | 0.335 | 0.0455 | 0.3 | 1.7 | 3.0 | 6.0 | 7.5 |
| IAG Model | 0.3 | 0.7 | 0.7 | 0.53 | 1.7 | 3.0 | 6.0 | 6.0 |
| Compressible Beddoes-Leishman Model | 0.165 | 0.335 | 0.0455 | 0.3 | 1.7 | 3.0 | 6.0 | 7.5 |
| Pre-4.8 Beddoes-Leishman Model | 0.165 | 0.335 | 0.0455 | 0.3 | 1.7 | 3.0 | 6.0 | 7.5 |
| Linear fit gradient method | |
|---|---|
| Øye Model | Enabled |
| Incompressible Beddoes-Leishman Model | Enabled |
| IAG Model | Enabled |
| Compressible Beddoes-Leishman Model | Enabled |
| Pre-4.8 Beddoes-Leishman Model | Enabled |
| Use Kirchhoff equation for normal force coefficient | |
|---|---|
| Øye Model | Disabled1 |
| Incompressible Beddoes-Leishman Model | Disabled |
| IAG Model | Enabled1 |
| Compressible Beddoes-Leishman Model | Disabled |
| Pre-4.8 Beddoes-Leishman Model | Enabled1 |
| Dynamic pitching moment coefficient | |
|---|---|
| Øye Model | Enabled |
| Incompressible Beddoes-Leishman Model | Enabled |
| IAG Model | Enabled |
| Compressible Beddoes-Leishman Model | Enabled |
| Pre-4.8 Beddoes-Leishman Model | Enabled |
| Include impulsive lift and moment contributions | |
|---|---|
| Øye Model | Disabled1 |
| Incompressible Beddoes-Leishman Model | Disabled |
| IAG Model | Enabled |
| Compressible Beddoes-Leishman Model | Disabled |
| Pre-4.8 Beddoes-Leishman Model | Disabled |
| Starting radius for dynamic stall | |
|---|---|
| Øye Model | 0% |
| Incompressible Beddoes-Leishman Model | 0% |
| IAG Model | 0% |
| Compressible Beddoes-Leishman Model | 0% |
| Pre-4.8 Beddoes-Leishman Model | 0% |
| Ending radius for dynamic stall | |
|---|---|
| Øye Model | 95% |
| Incompressible Beddoes-Leishman Model | 95% |
| IAG Model | 95% |
| Compressible Beddoes-Leishman Model | 95% |
| Pre-4.8 Beddoes-Leishman Model | 95% |
Computational cost of different options
There is no significant difference in computational cost anticipated when switching between different options, with the following exceptions:
Dynamic stall model:Øye model: Typically, this model runs faster but captures less flow physics compared to the Beddoes-Leishman type dynamic stall models.Incompressible Beddoes-Leishman model: With this model, the simulation will run slower when the impulsive lift and moment contributions are activated but this effect is less significant compared to the compressible model.IAG model: With this model, the simulation will run slower when the impulsive lift and moment contributions are activated but this effect is less significant compared to the compressible model. The accuracy of this model is improved when the impulsive contribution is activated.Compressible Beddoes-Leishman model: With this model, enabling impulsive lift and moment contributions can significantly reduce the integrator step, thereby slowing the simulation.No dynamic stall: The fastest of the models.
Ending radius for dynamic stall: Near the tip many blades have very small chord lengths. In combination with the high effective inflow speed, this can lead to small time constants in the dynamic stall models requiring small integrator time steps. For example, the non-dimensional time constant for pressure lift defaults to 1.7. In dimensional form this time constant would be:
Where:
\(c\) is local chord length
\(T_p\) the non-dimensional pressure lift time constant
\(W_{xy}\) the effective wind speed which can be approximated by \(\Omega r\).
If the chord length is for example 0.2 m and the tip speed 75 m/s then this would result in a time constant of 2.3ms or 441Hz causing the integrator to take steps of less than 2 ms. A rule of thumb is to avoid time constants less than 10ms in the simulations.
Last updated 25-09-2024