Abstract
This reports presents comparison of the steady state HAWC2 [1, 2, 3] simulation results and the HAWCStab2 computations of the DTU 10 MW reference turbine [4], as well as a comparison of structural blade-only frequencies and damping ratios. It serves as a simple verification study of the HAWCStab2 [5, 6, 7] computations.
The steady state comparison is shown in Section 2. For a fair comparison, the following simplifications of the DTU 10 MW reference turbine are made:
• no gravity;
• shaft tilt angle is set to zero, since HAWCStab2 assumes the inflow is perpendicular to the rotor plane;
• uniform aligned inflow conditions (no turbulence, shear, veer or yaw);
• tower and shaft flexibility are not considered to assure the shaft remains perfectly aligned with the wind inflow vector (horizontal).
Furthermore, each main-body in the HAWC2 model must contain as many bodies as elements, to be equivalent to the co-rotational formulation used by HAWCStab2.
There are four test cases considered in the steady state comparison:
• Case 1: no blade flexibility, and the aerodynamic modelling reduced to strip theory: no induction and no tip correction, labelled as “no induction” or “without induction”.
• Case 2: no blade flexibility in conjunction with BEM induction model and Prandtl tip correction (labelled as “induction+tip”).
• Case 3: flexible blades in conjunction with “induction+tip”. Includes power and thrust curve comparison with HAWCStab2 2.15.
• Case 4: flexible blades in conjunction with “induction+tip”, 15 degrees coning. Includes power and thrust curve comparison with HAWCStab2 2.15.
Both HAWC2 and HAWCStab2 have the ability to use different aerodynamic models. For the “induction+tip” model, the rotor induced velocities are calculated with Blade Element Momentum theory, and the presence of the tip vortex is accounted for by the Prandtl tip loss model. For not completely planar rotors, for example due to cone or blade deflection, a component of the rotor rotation is a rotation of the aerodynamic cross sections about the local blade axis (often referred to as a pitch rate or torsion rate). Furthermore, there will be a centripetal acceleration of the airfoil cross sections due to the rotor rotation, that causes added mass lift and drag components. These effects and their modelling are described in [8]. The corresponding terms are included in the HAWCStab2 steady state computations since version 2.16. Because the terms are part of the unified dynamic stall model in HAWC2, dynamic stall in HAWC2 is active in all comparisons to ensure the correct steady state results.
Section 3 contains a comparison of the structural blade-only frequencies and damping ratios. The comparisons are performed using the classical beam model and the FPM model, as well as the damping_posdef and damping_aniso_v2 commands.
This investigation has been carried out with HAWC2 version 13.1 and HAWCStab2 version 2.16. Previous iterations of this report compared HAWC2 version 12.2 with HAWCStab2 2.12 [9] and HAWC2 version 12.5 vs HAWCStab2 2.14 [10].
The steady state comparison is shown in Section 2. For a fair comparison, the following simplifications of the DTU 10 MW reference turbine are made:
• no gravity;
• shaft tilt angle is set to zero, since HAWCStab2 assumes the inflow is perpendicular to the rotor plane;
• uniform aligned inflow conditions (no turbulence, shear, veer or yaw);
• tower and shaft flexibility are not considered to assure the shaft remains perfectly aligned with the wind inflow vector (horizontal).
Furthermore, each main-body in the HAWC2 model must contain as many bodies as elements, to be equivalent to the co-rotational formulation used by HAWCStab2.
There are four test cases considered in the steady state comparison:
• Case 1: no blade flexibility, and the aerodynamic modelling reduced to strip theory: no induction and no tip correction, labelled as “no induction” or “without induction”.
• Case 2: no blade flexibility in conjunction with BEM induction model and Prandtl tip correction (labelled as “induction+tip”).
• Case 3: flexible blades in conjunction with “induction+tip”. Includes power and thrust curve comparison with HAWCStab2 2.15.
• Case 4: flexible blades in conjunction with “induction+tip”, 15 degrees coning. Includes power and thrust curve comparison with HAWCStab2 2.15.
Both HAWC2 and HAWCStab2 have the ability to use different aerodynamic models. For the “induction+tip” model, the rotor induced velocities are calculated with Blade Element Momentum theory, and the presence of the tip vortex is accounted for by the Prandtl tip loss model. For not completely planar rotors, for example due to cone or blade deflection, a component of the rotor rotation is a rotation of the aerodynamic cross sections about the local blade axis (often referred to as a pitch rate or torsion rate). Furthermore, there will be a centripetal acceleration of the airfoil cross sections due to the rotor rotation, that causes added mass lift and drag components. These effects and their modelling are described in [8]. The corresponding terms are included in the HAWCStab2 steady state computations since version 2.16. Because the terms are part of the unified dynamic stall model in HAWC2, dynamic stall in HAWC2 is active in all comparisons to ensure the correct steady state results.
Section 3 contains a comparison of the structural blade-only frequencies and damping ratios. The comparisons are performed using the classical beam model and the FPM model, as well as the damping_posdef and damping_aniso_v2 commands.
This investigation has been carried out with HAWC2 version 13.1 and HAWCStab2 version 2.16. Previous iterations of this report compared HAWC2 version 12.2 with HAWCStab2 2.12 [9] and HAWC2 version 12.5 vs HAWCStab2 2.14 [10].
| Original language | English |
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| Place of Publication | Risø, Roskilde, Denmark |
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| Publisher | DTU Wind and Energy Systems |
| Number of pages | 36 |
| DOIs | |
| Publication status | Published - 2024 |