Spanwise Load Distribution Research Articles

Two Aerodynamic Mid-Fidelity Approaches on a Distributed Propulsion Wing

A comparison of two potential-theory based mid-fidelity approaches on the aerodynamics of a distributed propeller–wing tractor configuration is presented. The design space for aircraft configurations is enlarged by using distributed electric propulsion so a demand for investigating different variants, especially regarding the number of propellers, is present. While many lower fidelity tools are available in the literature, they are often only documented with integral results. This paper presents two different, independently implemented numerical approaches and provides a comparison of spanwise load distributions on a distributed propeller configuration under cruise conditions with existing Reynolds-averaged Navier–Stokes (RANS) results. The isolated propeller and wing calculations using both methods are verified a priori with respect to their agreement. In addition, a discretization study of both methods is presented. The detailed results of the spanwise lift and drag distributions are compared between the two methods. Two different angles of attack and two different propeller pitch settings are calculated, and the differences in the spanwise distributions and the governing integral results between both methods and the RANS results are highlighted. Finally, a comparison of the individually required computational effort is presented.

Modelling the effects of boundary proximity on a tidal rotor using the actuator line method

For a turbine in unconstrained flow, the maximum power coefficient (CP ) is limited to 16/27 of the undisturbedkinetic energy flux through the rotor area according to work attributed to Betz, Lanchester, and Joukowsky [1].This maximum, often referred to as the Betz limit, occurs when the rotor presents the optimum resistance tothe incoming flow, imparting enough force to generate power without overly choking the flow through the rotor.However, in the context of tidal stream energy, the flow is often constrained by the seabed and the free surfacechanging the balance of optimal rotor resistance. Thus, the limit for maximum power extraction is modifiedto the form first presented by Garrett and Cummins, CP = (16/27)(1 − B)−2 [2]. The factor B, known as theblockage ratio, represents the fraction of the channel cross-section occupied by the rotor swept area, and allowsrotors operating in confined conditions to theoretically exceed the Betz limit. Subsequent theoretical work byNishino and Willden extended this model to demonstrate that constructive interference effects between closelyspaced turbines in a co-planar fence can allow efficiency increases above the Betz limit, even in an infinitely widechannel where the global blockage ratio is negligible [3]. This phenomenon, attributed to the concept of localblockage, defined as the ratio of rotor swept area to the surrounding flow passage area, has been observed byseveral studies both experimentally, and numerically using actuator disk and blade element momentum methods[4, 5, 6]. However, neither the experimental nor the numerical studies provided detail on unsteady loading effectsstemming from azimuthal variations in the flow field caused by anisotropy in the local blockage, such as whenthe rotor is not centred in the flow passage. In this study, a single tidal rotor is simulated using the actuatorline model embedded in a Reynolds-Averaged Navier-Stokes solver with varying degrees of anisotropic blockageimposed by proximity to a non-deformable upper boundary. The investigation is carried out in the contextof the Supergen ORE Unsteady Tidal Turbine Benchmarking Project using a 1.6 m rotor in a computationaldomain equivalent to the towing tank dimensions at the Qinetiq Haslar facility in which the turbine was testedexperimentally [7]. The discrete blade representation and unsteady nature of the actuator line method allowsinvestigation of variations in loads and the importance of boundary proximity by extracting the spanwise loaddistributions and local flow parameters at different positions around the azimuth. The effects of two differenttip-loss correction models on the spanwise force distributions and overall loads are investigated. Analysis of theintegrated rotor loads shows potential for an increase in the maximum CP of ∼1% with changing proximity tothe upper boundary without any detriment to the power-to-thrust ratio. However, anisotropy in the local flowpassage can result in azimuthally varying blade forces, introducing an additional source of fatigue loading tothe rotor and drive train.

Effect of the Radial Velocity Distribution on the Loss Generation of a Contra-Rotating Fan in a Ventilation System.

Quantification of the loss generation of ducted contra-rotating fan (CRF) blades is difficult to achieve, since there are no guide vanes between rotors. A blade design program was established to investigate the relationship between radial velocity distribution and incurred loss. Numerical and experimental techniques were used to confirm the optimal configuration's overall performance. The relationship between loss and velocity distribution under the impact of spanwise load distribution was confirmed by the entropy contour from various perspectives. The appropriate radial velocity distribution can improve the operating efficiency of a CRF by reducing the entropy around the annulus under design and near-stall conditions. This regularity could provide some strategies in the design of contra-rotating blades.

Analytic design methodology for flexible wing parametrization and spanwise load estimation

Presented is an analytic study of aerodynamic loading along a high aspect ratio wing, typical for airliners, under passive aeroelastic deformation. Such a highly non-planar, curved wing is feasible using the latest composite material technology, and is expected to enhance airliners aerodynamic performance at transonic cruise conditions, given it allows lower induced drag, similar to a wingletted wing. Also, gust and manoeuvring loads can be partially alleviated by the structure elasticity, hence the concept is of great interest for the airliner industry. A major problem to designing highly flexible wings is their constantly shifting shape and, as a result, their hardly predictable, non-constant lift force generated. This paper provides an attempt to precisely estimate load distribution along the statically inflected wing at different stages of its deformation, using mathematical parametrization of the curved wing shape to relate its geometry to aerodynamic loading and structural stiffness in a closed form function. This is achieved using the geometric dependency of local angles of attack on local wing curvatures, therefore load distribution is a function of the parametrized deformed wing shape. Spanwise load distributions in turn can be coupled with structural stiffness distributions using cantilever beam theory.

Design of an Axial Transonic Rotor by Modified Spanwise Loading Distribution

Improving the aerodynamic performance of the transonic fan in a turbofan engine can be beneficial for both the fuel consumption and maneuverability of an airplane. Deep insight into the supersonic aerodynamics is needed for the simultaneous improvement of all operating parameters of a transonic rotor, including the pressure ratio, efficiency, and surge margin. A design method was developed for an axial transonic rotor by using a combination of radial equilibrium theory, the free vortex method, and a distributed span-wise diffusion factor. The loading distribution obtained by this method was the highest in the hub section and gradually decreased in the tip section. To evaluate the method, a transonic rotor was designed using the geometric parameters and operating conditions of NASA rotor 67. A code was developed to determine a geometry for the new rotor and to modify it. The code was coupled with a RANS flow solver for 3D modification of the new designed rotor. Only standard multi- and double-circular arc airfoils were applied in different radial sections of the new rotor with no blade profile optimization. The results of the RANS equations solution for the new designed rotor showed 1.5% higher efficiency, 3% higher pressure ratio, and more than 1.5 times larger operating range in comparison to NASA rotor 67. The new designed method seems to be an efficient approach that not only improved the efficiency and pressure ratio but also increased the operating range of an axial transonic rotor.

Influence of Spanwise Load Distribution on Blended-Wing–Body Performance at Transonic Speed

The influence of spanwise load distributions on the overall performance of a blended-wing–body (BWB) model at transonic speed is investigated to understand the tradeoffs between aerodynamic efficiency and wing structure weight. The overall performance improvement is measured by the net weight saving relative to the maximum takeoff weight (). A BWB model based on the reference shape of the Boeing second-generation BWB model is taken as the baseline model. Taking the elliptic and triangular spanwise loading as the two extreme distributions, models with varying spanwise loadings have been designed. High-fidelity Reynolds-averaged Navier–Stokes solutions coupled with an inverse design optimization code considering static aeroelasticity is used in the inverse design process. For the BWB models, shifting the spanwise load from the elliptic design toward the triangular design shows a significant reduction in wing root bending moment compared with the traditional civil transports, thus resulting in significant structural weight savings. A wing root bending moment relief of 19% is obtained for the averaged elliptic–triangular design relative to the elliptic design, whereas the loss in aerodynamic efficiency is only 4.4%. The combined effects result in a net weight saving between 0.63 and 1.86% of .

Prediction of Crosswind Separation Velocity for Fan and Nacelle Systems Using Body Force Models: Part 2: Comparison of Crosswind Separation Velocity with and without Detailed Fan Stage Geometry

Modern aircraft engines must accommodate inflow distortions entering the engines as a consequence of modifying the size, shape, and placement of the engines and/or nacelle to increase propulsive efficiency and reduce aircraft weight and drag. It is important to be able to predict the interactions between the external flow and the fan early in the design process. This is challenging due to computational cost and limited access to detailed fan/engine geometry. In this, the second part of a two part paper, we apply the fan gas path and body force model design process from Part 1 to the problem of predicting flow separation over an engine nacelle lip caused by crosswind. The inputs to the design process are based on NASA Stage 67. A body force model using the detailed Stage 67 geometry is also used to enable assessment of the accuracy of the design process based approach. In uniform flow, the model produced by the design process recreates the spanwise loading distribution of Rotor 67 with a 7% RMS error. Both models are then employed to predict crosswind separation velocity. The two approaches are found to agree in their prediction of the crosswind separation velocity to within 5%.

Sweep and anisotropy effects on the viscous hydroelastic response of composite hydrofoils

Composite materials have become prevalent in hydrofoil design due to their favorable characteristics. Both material anisotropy and planform sweep are factors that affect hydrofoil performance. However, the interplay between these two factors has not been studied systematically. This paper investigates this interplay in the viscous hydroelastic response of linearly tapered composite hydrofoils with a modified NACA 0009 cross-section using high-fidelity hydrostructural simulations. The simulations are based on a Reynolds-averaged Navier-Stokes solver coupled to a structural finite-element model. Both sweep and off-axial fiber layup reduce the bending-mode natural frequencies due to the decrease in bending rigidity. Sweep reduces the form drag by suppressing trailing edge separation, but it can increase the lift-induced drag by causing the spanwise load distribution to deviate away from the ideal elliptical distribution. The spanwise load distribution can be tailored to reduce the induced drag and delay cavitation inception using sweep-induced geometric, material-induced bend-twist coupling, or both. Nevertheless, a poor combination of sweep and material configurations can accelerate static divergence, early separation, cavitation, noise, and material failures. Besides changing the structural response and resultant fluid-structure interaction, the material failure inception load and failure location depend directly on the fiber orientation due to the anisotropic characteristic of composites.

Stall Inception in Low-Pressure Ratio Fans

A combined experimental and computational test program, with two low-pressure ratio aero-engine fans, has been used to identify the flow mechanisms at stall inception and the subsequent stall cell growth. The two fans have the same rotor tip clearance, annulus design, and downstream stators, but different levels of tip loading. The measurement data show that both the fans stall via spike-type inception, but that the growth of the stall cell and the final cell size is different in each fan. The computations, reproducing both the qualitative and quantitative behavior of the steady-state and transient measurements, are used to identify the flow mechanisms at the origin of stall inception. In one fan, spillage of tip leakage flow upstream of the leading edge plane is responsible. In the other, sudden growth of casing corner separation blockage leads to stall. These two mechanisms are in accord with the findings from core compressors. However, the transonic aerodynamics and the low hub-to-tip radius ratio of the fans lead to the following two findings: first, the casing corner separation is driven by shock-boundary layer interaction and second, the spanwise loading distribution of the fan determines whether the spike develops into full-span or part-span stall and both types of behavior are represented in the present work. Finally, the axial momentum flux of the tip clearance flow is shown to be a useful indicator of the leakage jet spillage mechanism. A simple model is provided that links the tip loading, stagger, and solidity with the tip clearance axial momentum flux, thereby allowing the aerodynamicist to connect, qualitatively, design parameters with the stall behavior of the fan.

Static Structural Analysis of a Variable Span Morphing Wing for Unmanned Aerial Vehicle

While the primary reason to develop an adaptive wing is the aerodynamic benefits, the primary hindrance is the structural and vibrational considerations due to the unsteady nature of the airflow during the flight. Hence this study forms an important part of the morphable wing technology. In this paper, the design of a moderate aspect ratio variable span wing will be performed. The morphing wing is modeled structurally to observe the effect of spanwise load distribution on the wing structure. For the structural design and analysis of the unmanned aerial vehicle (UAV) under this study, commercial software Solidworks and Ansys/Static Structural/Modal are used. The static structural analyses of the wing are performed under different load conditions. The results of these analyses show that the designed structure is safe within the flight envelope. It is observed that the wing-root bending moment increases drastically due to an increase in the wingspan. Thus, the bending moment along the wingspan of the morphing wing is much larger than that of the conventional wing which results in an increase in the deflection of the free-end. The maximum stress for the un-extended wing configuration increases for the extended wing configuration.

A vortex model for forces and moments on low-aspect-ratio wings in side-slip with experimental validation.

This paper studies low-aspect-ratio ([Formula: see text]) rectangular wings at high incidence and in side-slip. The main objective is to incorporate the effects of high angle of attack and side-slip into a simplified vortex model for the forces and moments. Experiments are also performed and are used to validate assumptions made in the model. The model asymptotes to the potential flow result of classical aerodynamics for an infinite aspect ratio. The [Formula: see text] → 0 limit of a rectangular wing is considered with slender body theory, where the side-edge vortices merge into a vortex doublet. Hence, the velocity fields transition from being dominated by a spanwise vorticity monopole ([Formula: see text] ≫ 1) to a streamwise vorticity dipole ([Formula: see text] ∼ 1). We theoretically derive a spanwise loading distribution that is parabolic instead of elliptic, and this physically represents the additional circulation around the wing that is associated with reattached flow. This is a fundamental feature of wings with a broad-facing leading edge. The experimental measurements of the spanwise circulation closely approximate a parabolic distribution. The vortex model yields very agreeable comparison with direct measurement of the lift and drag, and the roll moment prediction is acceptable for [Formula: see text] ≤ 1 prior to the roll stall angle and up to side-slip angles of 20°.

Extracting lift and drag polars from blade-resolved computational fluid dynamics for use in actuator line modelling of horizontal axis turbines

Low order rotor models such as the actuator line method are desirable as an efficient method of computing the large range of operating and environmental conditions, required to design wind and tidal rotors and arrays. However, the integrated thrust and torque predictions for each rotor are dominated by the blade loading on the outboard sections, where three-dimensional (3D) effects become increasingly significant, and the accuracy of the reduced order methods remains uncertain. To investigate the accuracy of the spanwise blade loading on an individual rotor, actuator line and blade boundary layer resolved computations of the Model Rotor Experiments in Controlled Conditions (MEXICO) rotor are presented. The high fidelity blade-resolved simulations give good agreement with measured pressure coefficient and particle image velocimetry data. Alternative lift and drag polars are extracted from the 3D simulated flow fields as a function of radial position. These are then used as replacement inputs for the actuator line method. Significant improvement in the accuracy of the actuator line predictions is found when using these 3D extracted polars, compared with using simulated two-dimensional lift and drag polars with empirical correction applied to the spanwise loading distribution. Additionally, the 3D flow field data is used to derive different axial and tangential spanwise loading corrections for use with the two-dimensional blade polars. Copyright © 2016 John Wiley & Sons, Ltd.

CFD study on the impact of yawed inflow on loads, power and near wake of a generic wind turbine

AbstractThis article deals with the influence of yawed inflow conditions on the performance of a single generic 2.4MW wind turbine. It presents the results of studies performed at the Institute of Aerodynamics and Gas Dynamics by means of computational fluid dynamics, using a fully meshed wind turbine with all boundary layers being resolved. The block‐structured flow solver FLOWer is used; a dual‐time stepping method for temporal discretization and a second‐order Jameson–Schmidt–Turkel method for the calculation of the convective fluxes are applied. All simulations are carried out using a detached eddy simulation approach. In detail, two different wind speeds and a yaw angle range between −50° and +50° are evaluated in the paper. Based on these data, it is shown that the reduction of power output follows a cosine to the power of X function of the yaw angle. Furthermore, the growing azimuthal non‐uniformity of the load distributions with increasing yaw angle magnitude is analysed by spanwise load distributions. As a central influence on the load distributions, the advancing and retreating blade effect is identified. Moreover, the deflection of the wake as a result of the inflow is investigated, and the deflection angles are compared with a modelling approach. A connection line between wake deflection and load asymmetry is drawn. The results are of particular importance for wind park situations with downstream turbines facing the distorted inflow created from upstream ones. Copyright © 2016 John Wiley & Sons, Ltd.

Experimental and numerical studies of low aspect ratio wing at critical Reynolds number

In this study, the three-dimensional flow behaviors and aerodynamics characteristics of a NACA0003 wing with an aspect ratio (AR) of 1 at Reynolds numbers of 1.0×105 has been investigated both experimentally and numerically. The force measurement and flow visualization (oil flow visualization) through the wind tunnel experiment were applied to verify the reliability of the simulation. The investigation with different angles of attack reveals that flow structure contained three dimensional laminar separation bubble (LSB) and wing-tip vortex. As increasing angle of attack, the area occupied by LSB expands both streamwise and spanwise. The wing-tip vortex has strong impact on the formation of LSB. In addition, the spanwise load distribution has shown that both three dimensional LSB and wing-tip vortex provide additional vortex force.

Measurements of Loading and Tip Vortex Due to High-Reynolds Number Flow Over a Rigid Lifting Surface

An experimental study of high-Reynolds number flow over a rigid hydrofoil (David Taylor model basin (DTMB) modified NACA66-009, rectangular planform, aspect ratio (AR = 4, square tip) is presented. The measurements were performed in the Garfield Thomas Water Tunnel at Applied Research Laboratory (ARL) Penn State. Load measurements were performed at ReC = 1.5 × 106 and 2.4 × 106, for angles of attack between −8 deg and +8 deg. Measurements of three components of velocity were performed using stereo particle image velocimetry (SPIV) on a cross-flow plane to resolve the tip vortex flow 0.42 chord lengths downstream of the trailing edge, for four angles of attack ranging from 0.5 deg to 3.5 deg. Nondimensional tip vortex circulation varied weakly with angle of attack. Vortex location in the plane of measurement, relative to the trailing edge, was unchanged for the ranges studied, though the vortex core grew in size with angle of attack. These results are consistent with the finding that the net lift force acts between 45% and 46% span, measured from the root, in that any angle of attack variations in tip vortex strength or radius result in minimal changes in spanwise loading distribution.

Drag Minimization Based on the Navier–Stokes Equations Using a Newton–Krylov Approach

A methodology is presented for performing numerical aerodynamic shape optimization based on the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations. An initial multiblock structured mesh is first fit with B-spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on B-spline surfaces. The RANS equations and the one-equation Spalart–Allmaras turbulence model are solved in a fully coupled manner using an efficient parallel Newton–Krylov algorithm with approximate-Schur preconditioning. Gradient evaluations are performed using the discrete-adjoint approach with analytical differentiation of the discrete flow and mesh movement equations. The overall methodology remains robust even in the presence of large shape changes. Several examples of lift-constrained drag minimization are provided, including a study of the common research model wing geometry, a wing–body–tail geometry with a prescribed spanwise load distribution, and a blended-wing–body configuration. An example is provided that demonstrates that a wing optimized based on the Euler equations exhibits substantially inferior performance when subsequently analyzed based on the RANS equations relative to a wing optimized based on the RANS equations.

Winglet multi-objective shape optimization

A series of multi-objective winglet shape optimizations are performed to find the Pareto front between the wing aerodynamic drag and the wing structural weight for a wing equipped with a winglet. The paper discusses the addition of winglets to existing aircraft designs. The outer shape of the wing is therefore fixed but the internal structure and associated weight are adjusted based on the change of spanwise loading (magnitude and distribution) due to the addition of the winglet. In order to estimate the aerodynamic and structural characteristics of a non-planar wing, a quasi-three-dimensional aerodynamic solver is integrated with a quasi-analytical weight estimation method inside an optimization framework. Using those tools, the aerodynamic drag and the structural weight of a wing equipped with various winglets are estimated with a high level of accuracy. A multi-objective genetic algorithm is used to determine the Pareto front for two objective functions: minimum wing drag and minimum wing weight. In order to find the best winglet shape among the winglets on the Pareto front, three figures of merit are used: the aircraft Maximum Takeoff Weight (MTOW), the aircraft fuel weight and the aircraft Direct Operating Cost (DOC). The optimization results showed that about 3.8% reduction in fuel weight and about 29M$ reduction in 15 years DOC of a Boeing 747 type aircraft can be achieved by using winglets.

Aerodynamic shape optimisation, wind tunnel measurements and CFD analysis of a MAV wing

AbstractThe aerodynamic shape optimisation of a micro air vehicle (MAV) wing is performed to obtain the basic wing geometrical characteristics which produce the maximum range and endurance requirements. Multhopp’s method based on Prandtl’s classical lifting line theory is used for the determination of the spanwise load distribution required during the optimisation process. The obtained lift and drag characteristics are used for the derivation of the range and endurance equations of an electrically driven micro air vehicle. The optimisation process is based on the modified feasible directions gradient based optimisation algorithm. Results are validated using wind tunnel measurements showing very good agreement. Results are also compared with solutions to the Navier-Stokes equations obtained with ANSYS-CFX finite elements using different turbulence models. These include the k-ε and the shear stress transport (SST) models as well as the Reynolds stress model.

Optimal wing twist distribution for roll control of MAVs

AbstractThe aerodynamic design optimisation of a Micro Air Vehicle (MAV) wing is performed to obtain the optimal anti-symmetric wing twist distribution for the roll control of the MAV’s wing instead of using conventional ailerons. This twist distribution should produce minimum induced drag and achieve a better roll response. The implementation of several anti-symmetric load distributions such as the half lemniscates and the Horten distributions is studied leading to an initial solution for the optimal distribution that could achieve better roll requirements. Multhopp’s method based on Prandtl’s classical lifting line theory is used for the determination of the spanwise load distribution required during the optimisation process. The optimisation process is based on the modified feasible directions gradient based optimisation algorithm implemented in the optimisation system, VisualDOC, given by Dr. Garret Vanderplaats. The proposed optimisation process is applied to the ‘BARQ’developed MAV which has successful flight in July 2009.

Aerodynamic optimization of wind turbine rotors using a blade element momentum method with corrections for wake rotation and expansion

ABSTRACTThe blade element momentum (BEM) method is widely used for calculating the quasi‐steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now be obtained in the blade root and tip sections. It is expected that this will lead to small changes in optimum blade designs. In this work, has been implemented, and the spanwise load distribution has been optimized to find the highest possible power production. For comparison, optimizations have been carried out using BEM as well. Validation of shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using , and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM. In short, allows fast aerodynamic calculations and optimizations with a much higher degree of accuracy than the traditional BEM model. Copyright © 2011 John Wiley & Sons, Ltd.