How should the lift and drag forces be calculated from 2-D airfoil data for dihedral or coned wind turbine blades?

In the present work, a consistent method for calculating the lift and drag forces from the 2-D airfoil data for the dihedral or coned horizontal-axis wind turbines when using generalized lifting-line methods is described. The generalized lifting-line methods include, for example, lifting-line (LL), actuator line (AL), blade element momentum (BEM) and blade element vortex cylinder (BEVC) methods. A consistent interpretation of classic unsteady 2-D thin airfoil theory results for use in a generally moving frame of reference within a linearly varying onset velocity field reveals that it is necessary to use not only the relative flow magnitude and direction at one point along the chord line (for instance three-quarter-chord), but also the gradient of the flow direction in the chordwise direction (or, equivalently, the flow direction at the quarter-chord) to correctly determine the magnitude and direction of the resulting 2-D aerodynamic forces and moment. However, this aspect is generally overlooked and most implementations in generalized lifting-line methods use only the flow information at one calculation point per section for simplicity. This simplification will not change the performance prediction of planar rotors, but will cause an error when applied to non-planar rotors. The present work proposes a generalized method to correct the error introduced by this simplified single-point calculation method. In this work this effect is investigated using the special case, where the wind turbine blade has only dihedral and no sweep, operating at steady-state conditions with uniform inflow applied perpendicular to the rotor plane. We investigate the impact of the effect by comparing the predictions of the steady-state performance of non-planar rotors from the consistent approach with the simplified one-point approach of the LL method. The results are verified using blade geometry resolving Reynolds-averaged Navier-Stokes (RANS) simulations. The numerical investigations confirmed that the correction derived from thin airfoil theory is needed for the calculations to correctly determine the magnitude and direction of the sectional aerodynamic forces for non-planar rotors. The aerodynamic loads of upwind and downwind coned blades that are calculated using the LL method, the BEM method, the BEVC method and the AL method are compared for the simplified and the full method. Results using the full method, including different specific implementation schemes, are shown to agree significantly better with fully-resolved RANS than the often used simplified one-point approaches.

A Modified Van Der Pol Oscillator Model for the Unsteady Lift Produced by a Flapping Flat Plate for Different Positions of the Rotation Axis

To understand the nonlinear interaction between unsteady aerodynamic forces and the kinematics of structures, we theoretically and numerically investigated the characteristics of lift coefficients produced by a flapping thin flat plate controlled by the rotation axis position. The flat plate was placed in a 2-D incompressible flow at a very low Reynolds number (Re = 300). We showed that the behavior of the unsteady aerodynamic forces suggests the existence of a limit cycle. In this context, we developed a Reduced Order Model (ROM) by resolving the modified van der Pol oscillator using the Taylor development method and computational fluid dynamics (CFD) solutions. A numerical solution was obtained by integrating the differential equation of the modified van der Pol oscillator using the fourth-order Runge–Kutta method (RK4). The model was validated by comparing this solution with the reformulated equation of the added mass lift coefficient. Using CFD and ROM solutions, we analyzed the dependency of the unsteady lift coefficient generation on the kinematics of the flapping flat plate. We showed that the evolution of the lift coefficient is influenced by the importance of the rotation motion of the Leading Edge (LE) or Trailing Edge (TE), according to the position of the rotation axis. Indeed, when the rotation axis is moved towards the LE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the TE and the rotation axis. However, when the rotation axis is moved towards the TE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the LE and the rotation axis.

Study on Aerodynamic Nonlinear Characteristics of Semiclosed Box Deck Based on Variation of Motion Parameters

In order to study the nonlinear characteristics of self-excited aerodynamic forces of bluff body bridge section with the change of motion parameters, a numerical wind tunnel is established by the dynamic mesh technique of computational fluid dynamics (CFD). A state-by-state forced vibration method is used to identify the self-excited aerodynamic forces of single degree-of-freedom (DOF) heaving and pitching motion. Fast Fourier transform (FFT) is adopted to obtain frequency-domain data for analysis. The reliability of the obtained aerodynamic results is verified by wind tunnel tests. The results show that the high-order harmonic components are found in the self-excited aerodynamic forces of semiclosed box deck section, which are more significant in aerodynamic lift than in aerodynamic moment. The proportion of aerodynamic nonlinear components increases with amplitude. The effect of amplitude on the nonlinear components of heaving motion is generally higher than that of pitching motion, and aerodynamic moment is highly sensitive to the increase of vertical amplitude. The variation of the nonlinear components of the deck section with frequency is not a simple monotonic relationship, and there is a stationary point at 10 Hz frequency. The existence of wind attack angle makes the proportion of nonlinear components reach more than 30% and greatly increases the proportion of second harmonic. In addition, the high-order harmonic components, which are not integer multiples, are found at large amplitude and positive angle of attack.

Aerodynamics of a Train and Flat Closed-Box Bridge System with Train Model Mounted on the Upstream Track

The aerodynamic features of a train and flat closed-box bridge system may be highly sensitive to train-bridge aero interactions. For the generally utilized railway bridge-deck with two tracks (the upstream and downstream ones), the aero interactions above are occupied-track-dependent. The present paper thus aims to reveal the aero interactions stated above via a series of wind tunnel tests. The results showed that the aero interactions of the present train-bridge system display four typical behaviors, namely, the underbody flow restraining effect, bridge deck shielding effect, flow transition promoting effect, and the flow separation intensifying effect. The above four aero interactions result in obvious reductions in the aerodynamic forces of the train in wind angle of attack α of [−4°, 12°] and in the static stall angle of the bridge-deck, and leads to sensible increases in the absolute values of the bridge aerodynamic forces in α of [−4°, 12°]. Upon comparing the results with the same train and bridge system but with the train model mounted on the downstream track, the quasi-Reynolds number effect was non-detectable when the train model was moved to the upstream track. Thus, no drag crisis and other saltatory aerodynamic behaviors were observed in the present study in α of [0°, 12°].

Resonant passive energy balancing of morphing helicopter blades with bend–twist coupling

With increasing demand for rotor blades in engineering applications, improving the performance of such structures using morphing blades has received considerable attention. Resonant passive energy balancing (RPEB) is a relatively new concept introduced to minimize the required actuation energy. This study investigates RPEB in morphing helicopter blades with lag–twist coupling. The structure of a rotating blade with a moving mass at the tip is considered under aerodynamic loading. To this end, a three-degree-of-freedom (3DOF) reduced-order model is used to analyse and understand the complicated nonlinear aeroelastic behaviour of the structure. This model includes the pitch angle and lagging of the blade, along with the motion of the moving mass. First, the 3DOF model is simplified to a single-degree-of-freedom model for the pitch angle dynamics of the blade to examine the effect of important parameters on the pitch response. The results demonstrate that the coefficient of lag–twist coupling and the direction of aerodynamic moment on the blade are two parameters that play important roles in controlling the pitch angle, particularly the phase. Then, neglecting the aerodynamic forces, the 3DOF system is studied to investigate the sensitivity of its dynamics to changes in the parameters of the system. The results of the structural analysis can be used to tune the parameters of the blade in order to use the resonant energy of the structure and to reduce the required actuation force. A sensitivity analysis is then performed on the dynamics of the 3DOF model in the presence of aerodynamic forces to investigate the controllability of the amplitude and phase of the pitch angle. The results show that the bend–twist coupling and the distance between the aerodynamic centre and the rotation centre (representing the direction and magnitude of aerodynamic moments) play significant roles in determining the pitch dynamics.

Experimental techniques in the wind tunnel of naval architecture faculty

The implementation of innovative solutions in the field of shipbuilding requires the continuous development of research infrastructure. The hydro-aerodynamic problems of fluid flow around the hulls can be solved with numerical and/or experimental techniques. In any case, the validation of the numerical solutions is performed in specialized hydro-aerodynamic laboratories by means of the experimental model tests. In this context, a wind tunnel was developed at the Naval Architecture Faculty of “Dunarea de Jos” University of Galati, in order to measure the aerodynamic forces and moments or the speed and pressure distribution on the hull, generated by the wind action. This paper presents the most important types of problems that can be experimentally approached in the aerodynamic tunnel and the specific experimental equipments. The wind tunnel development was financed from the university funds.