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 Study on Aerodynamics and Stability Characteristics of a Bell-Shaped Span-Load Wing

The existence of the new bell-shaped span-load wing is said to has the best lift distribution especially comparing to the elliptical wing. Bell-shaped span-load wing is designed by configuring the twist of the wing. However, the information on the aerodynamic and stability characteristics of the bell-shaped span-load wing is limited. Thus, the main purpose of the research is to evaluate the aerodynamic and stability characteristic to strengthen the claim of the capability of bell-shaped span-load wing in producing minimum induced drag. As the research is expected to be beneficial to the aviation design team, detailed information regarding the lift distribution as well as the induced drag produced is analysed at the optimum angle of attack and the results is further explained in this research. The numerical method for the analysis is done by using Lifting Line Theory (LLT) in the XFLR5 software which can analyse the wings of aircraft in terms of its aerodynamic and stability characteristic. Then, the comparison of the aerodynamic characteristics for bell-shaped span-load, elliptical span-load and tapered wing done in this research is to strengthen the appeal made stating that the bell-shaped span-load wing is the best type of wing ever existed and may replace the elliptical wing as the best wing shape with aerodynamically most efficient. The research has proven that along the wingspan, the bell-shaped span-load wing produced the lowest and minimum induced drag when being compared. At the optimum angle of attack of bell-shaped span-load wing, though the lift produced is slightly lower than the elliptical and tapered wing, the difference in the induced drag is obvious as bell-shaped span-load wing produces induced drag that is lower than 0. In other words, starting from the semi span of the wing to the wingtip, the bell-shaped span-load wing managed to be the most aerodynamically efficient wing.

COUPLED RANSE AND LIFTING LINE THEORY FOR ESTIMATION OF SHIP PROPULSION FACTORS

Advances in Computational Fluid Dynamics (CFD) techniques through the development of the Reynolds-Averaged Navier-Stokes Equations (RANSE) have assisted in estimation of resistance and propulsion characteristics of ships to a reasonable level of accuracy. The aim of this paper is to test and demonstrate the capabilities of the coupled RANSE and Lifting Line theory for undertaking ship resistance, propeller open-water and self-propulsion simulations. Further, parametric studies for generation of numerical propeller design sheets and optimisation of propulsive efficiency using the coupled simulation approach has been discussed. Commercial CFD solver “M/s Flowtech - Shipflow” has been used for the study. Initially, some benchmark experimental/numerical model results are validated with the results of the CFD simulations and then, further parametric analyses have been undertaken with the KRISO Container Ship and the KP505 Propeller. The numerical propeller series and the preliminary study methodology for optimization of location of propeller disc behind the ship’s hull are being proposed as an effective concept/feasibility design stage tool for estimation of ship propulsion characteristics.

A comprehensive comparative investigation of the Lifting Line Theory and Blade Element Momentum Theory applied to small wind turbines

Small wind turbines are adequate for electricity generation in isolated areas to promote local expansion of commercial activities and social inclusion. Blade element momentum (BEM) method is usually used for performance prediction, but generally produces overestimated predictions since the wake effects are not precisely accounted for. Lifting line theory (LLT) can represent the blade and wake effects more precisely. In the present investigation the two methods are analyzed and their predictions of the aerodynamic performance of small wind turbines are compared. Conducted simulations showed a computational time of about 149.32 s for the Gottingen GO 398 based rotor simulated by the BEM and 1007.7 s for simulation by the LLT. The analysis of the power coefficient showed a maximum difference between the predictions of the two methods of about 4.4% in the case of Gottingen GO 398 airfoil based rotor and 6.3% for simulations of the Joukowski J 0021 airfoil. In the case of the annual energy production a difference of 2.35% is found between the predictions of the two methods. The effects of the blade geometrical variants such as twist angle and chord distributions increase the numerical deviations between the two methods due to the big number of iterations in the case of LLT. The cases analyzed showed deviations between 3.4% and 4.1%. As a whole, the results showed good performance of both methods; however the lifting line theory provides more precise results and more information on the local flow over the rotor blades.

Experimental Validation and Evaluation of a Coupled Twist-Camber Morphing Wing Concept

A morphing wing concept allowing for coupled twist-camber shape adaptation is proposed. The design is based on an optimized thickness distribution both spanwise and chordwise to be able to morph the wing sections into targeted airfoil shapes. Simultaneously, the spanwise twist is affected by the actuation. The concept provides a higher degree of control on the lift distribution which can be used for roll control, drag minimization, and active load alleviation. Static deformation and flight tests have been performed to evaluate and quantify the performance of the proposed mechanism. The ground tests include mapped actuated wing shapes, and wing mass and actuation power requirements. Roll authority, load alleviation, and aerodynamic efficiency estimates for different configurations were calculated using a lifting line theory coupled with viscous 2D airfoil data. Roll authority was estimated to be low when compared to a general aviation aircraft while the load alleviation capability was found to be high. Differences between the lift to drag ratio between the reference and morphing wing configurations are considerable. Mass and actuation energy present challenges that can be mitigated. The flight tests were used to qualitatively assess the roll control capability of the prototype, which was found to be adequate.

AN ALTERNATIVE APPROACH TO INDUCED DRAG REDUCTION

Induced drag constitutes approximately 40% of the total drag of subsonic civil transport aircraft at cruise conditions. Various types of winglets and several non-planar concepts, such as the C-wing, the joined wings, and the box plane, have been proposed for its reduction. Here, a new approach to induced drag reduction in the form of a combination of an elliptical and an astroid hypocycloid lift distribution is put forward. Lift is mainly generated from high circulation in the center part of the wing and fades away along the semi-span towards the wing tip. Using lifting line theory, the analysis shows that for fixed lift and wingspan the combined lift distribution results in an induced drag reduction of 50% with respect to the elliptical distribution. Due to its wing planform the combined lift distribution leads to a 51.5% higher aspect ratio. If structural constraints are placed, then the higher aspect ratio may affect wing weight. Although any substantial increase of wing weight is not envisaged, further study of the matter is required. Zero-lift drag and lift-dependent drag due to skin friction and viscosity-related pressure remain unaffected. The proposed lift distribution is particularly useful in a blended wing-body design.