Variable cant angle winglets for improvement of aircraft flight performance

Regulatory civil aviation agencies are pushing aircraft manufacturers and operators to improve aircraft efficiency by reducing fuel consumption, cutting carbon dioxide \(CO_2\) and nitrogen oxide NOx emissions, and lowering the perceived external noise. One way to help achieve this goal is by using improved and innovative technologies targeting drag reduction, specifically, lift-induced drag reduction. The drag breakdown of a typical transport aircraft shows that the lift-induced drag can amount to as much as 40% of the total drag at cruise conditions and 80–90% of the total drag during take-off and climb conditions [1‐9]. Reducing lift-induced drag is therefore of paramount importance to improve aircraft efficiency.

One way to reduce the lift-induced drag is by increasing the wingspan. However, increased wingspan requires strengthening the wing structure so that it can withstand the increased bending moments. Increasing the wingspan can also pose limitations in airport ground operations and gate clearance requirements. Another way of reducing lift-induced drag is by using wingtip devices, such as winglets (as illustrated in Fig. 1). Winglets do not all look the same; nevertheless, their ultimate goal is always lift-induced drag reduction by artificially increasing the span of the wings. But as for the case of wingspan increment, winglets increase bending moments; therefore, it might be necessary to reinforce the wings. From an aerodynamic point of view winglets are desirable; whereas, from a structural standpoint they are detrimental.

Many studies have found that winglets addition can achieve a fuel burn reduction of about 4–6%, reduce take-off distance and increase climb rate [1‐8, 10‐13]. Also, as less fuel is burned, emissions are reduced. Winglets can provide up to a 6% reduction in \(CO_2\) emissions and an 8% reduction in NOx emissions [14‐16]. They also increase the aftermarket value of the aircraft and add more aesthetic to the airplane design. Winglets are among the most used fuel saving and performance improvement technologies in today’s aviation. The drag reduction gained by adding winglets can be seen as the equivalent decrease in aircraft weight required to carry a payload over a specific distance. A reduction of one drag count in cruise conditions on a subsonic civil transport airplane means about 200 lbs more in payload [17‐19] (where one drag count is equal to the drag coefficient \(C_D\) multiplied by 10000 or \(\varDelta C_D = 10000 \times C_D\)). As fuel has a large direct operating cost impact in the air transport industry, fuel consumption reduction is translated in more savings, fewer emissions as less fuel is burn, extended operating range and increased payload.

The increment of wing root bending moment is among the few negative effects of winglets. They also increase parasite drag, which is the contribution of skin friction, interference drag, and pressure drag due to separation. Recall that the total drag of an aircraft or a wing is equal to the sum of parasite drag, lift-induced drag and wave drag. Winglets are aerodynamically viable only when the reduction of lift-induced drag is larger than the increment in parasite drag, and this situation is illustrated in Fig. 2, where we show the drag polars of two hypothetical wings, one wing with no winglets and one wing with winglets installed.

In Fig. 2, we can evidence that when operating above the crossover line or the line that passes through the crossover point (which is the point where the two polars intersect), the total drag of the wing with winglets is lower than the total drag of the wing with no winglets. Conversely, when operating below the crossover line, the total drag of the wing with no winglets is lower than the total drag of the wing with winglets. Therefore, in order to justify the use of winglets in the hypothetical situation illustrated in this figure, we should look at the performance of the wing at a given flight condition. Thus, if the wing were to operate in cruise conditions most of the time (the dark grey region in Fig. 2), the use of winglets is not justified from a point of view of total drag reduction. On the other hand, if the wing were to operate in climb conditions (the light grey region in Fig. 2), the use of winglets is justified from an aerodynamic point of view, as the wing generates less drag for a given lift.

From the hypothetical scenario discussed previously, the justification of the use of winglets can be based on total drag reduction arguments. So for example and by looking at Fig. 2, if the crossover point for a given winglet design is located in the cruise region, the use of winglets is justified for that flight condition. The crossover point gives a simple way to measure the total drag reduction trade-off when using winglets. Although this criterion might be a little bit simplistic as a performance metric for a complex system such as a wing-winglet configuration, as a design metric, it can deliver clear trends. The reader should be aware that more sophisticated aerodynamic performance criteria exist for winglet design [20‐25].

Winglets use can also be justified in the base of other factors, such as wing (or aircraft) performance at a different altitude. For example, if we climb to a higher altitude where the air is lighter, the wing in discussion would have to fly at a higher angle-of-attack (AOA) that might fall in the light grey region illustrated in Fig. 2; therefore, the use of winglets is justified based on total drag reduction arguments. As it can be guessed, there might exist different winglet configurations that might shift the crossover point below (or above) what is illustrated in Fig. 2.

During the 1970s oil crisis, commercial airlines and aircraft manufacturers explored many ways to reduce fuel consumption as a consequence of the high cost of jet fuel. It was not until the late 1970s that R.T. Whitcomb, an engineer at NASA Langley Research Center, pioneered the concept of the modern winglet we see in today’s aircraft, as a mean to reduce cruise drag and improve aircraft performance [11, 12]. Whitcomb’s work [12], marks the first time a winglet was seriously considered for large and heavy aircraft. Since Whitcomb breakthrough work on winglets, many variations have been designed (as depicted in Fig. 1), but all of them have been designed as passive or fixed devices attached at the wingtips. That is, the angle between the wing plane and the winglet plane (or cant angle) does not change; therefore, they are designed to deliver lift-induced drag reduction at a single design configuration, which might not be the best winglet configuration to generate the largest lift-induced drag reduction during different flight phases.

Hereafter, we propose the use of variable cant angle winglets that can be actuated by a mechanism (which is not described in this study). In the proposed arrangement, the winglet cant angle can be changed from a planar configuration up to a vertical layout (including intermediate cant angles) and vice-versa. Therefore, the winglet can be adjusted at different flight conditions to get the best lift-induced drag reduction for the given flight phase; or it can be kept in the vertical position while in ground so that it reduces wingspan while meeting gate and runaway clearance; or it can act as a load alleviation mechanism where in the case of gusts or strong sideslip velocities, the winglet can adjust itself, so it reduces the bending moment on the wing and the device itself. This study is an extension of a previous work conducted by the authors [26]; however, hereafter it is extended to cover Mach numbers values of 0.3 and 0.8395. In addition, a more detailed wave drag quantitative and qualitative analysis is presented, together with a discussion of the effect of compressibility on the aerodynamic performance. Also, based on the outcome of the numerical study it is proposed how the winglet cant angle could be set to obtain the best aerodynamic performance at a given flight phase.

It is worth mentioning that similar solutions have been already proposed, but most of them focused on the use of shape memory alloy materials [27‐32], foldable wings during ground operations [33‐37], load alleviation mechanisms [38‐42], complaint surfaces [32, 43‐49], and rotating systems for mitigating wingtip vortices [50‐54]; but just a few of them have addressed variable cant angle winglets for drag reduction while flying [55‐59].

The wing used in this study is the Onera M6 wing [60, 61] with a winglet installed. To study the effect of the variable cant angle winglet on the aerodynamic performance, different winglets with different cant angles were simulated. We conduct the study at two Mach numbers (\(Ma = 0.3\) and \(Ma = 0.8395\)) and different angle-of-attack values. Thus, we aim at covering take-off, climb, approach, descent, and cruise conditions. The concept presented hereafter represents an innovative approach that the authors’ hope holds potential to realize the goal of drag reduction to directly address the global challenge of improving aircraft fuel efficiency and reduce pollutant emissions, as highlighted in the reports ACARE—European aeronautics: A vision for 2020 [62] and ACARE—Flightpath 2050: Europe’s vision for aviation [63].

Before describing the numerical experiment and discussing the results, let us give a brief explanation of what is lift-induced drag and the role of winglets on lift-induced drag reduction. We would like to highlight that similar explanations can be found in references [2‐4, 9, 13, 26, 64], among many.

Finite span wings generate lift due to the pressure imbalance between the bottom surface (high pressure) and the top surface (low pressure), as illustrated in Fig. 3. However, as a byproduct of this pressure differential, cross flow components of the velocity are generated (which are unavoidable but can be mitigated). The higher pressure air under the wing flows around the wingtips and tries to displace the lower pressure air on the top of the wing. This motion generates a trailing edge vortex, and at the wingtips, where the flow curls, large vortices are formed. This flow around the wingtips is sketched in Fig. 3. These structures are referred to as wingtip vortices, and high velocities and low pressure exist at their cores. These vortices (trailing edge vortices and wingtip vortices), produce a downward flow in the neighborhood of the wing, known as the downwash and is denoted with the letter w in Fig. 4. The downwash interacts with the free-stream velocity to induce a local relative wind deflected downward in the vicinity of each airfoil section of the wing, as sketched in Fig. 4. The presence of the downwash reduces the angle-of-attack that each section of the wing effectively sees, and it creates a component of drag, the lift-induced drag. This drag component is an unavoidable consequence of lift generation in finite span wings.

One way of reducing lift-induced drag is by using wingtip devices, such as winglets. Well-designed winglets will reduce the trailing vortex strength (hence the wingtip vortex) and the average wing downwash by modifying the pressure distribution (which is related to the spanwise lift distribution), and shifting the shed vorticity away from the wing plane. They can also counteract the skin friction and interference drag of the winglets by generating a thrust force induced by the sidewash [2, 12, 64]. All this translate into less total drag due to the reduction of lift-induced drag and the parasite drag generated by the winglet.

The wing model used in this study is the Onera M6, as described in references [60, 61]. To model the variable cant angle winglet, an extension to the baseline Onera M6 wing was added (as shown in Fig. 5). Then, the cant angle is modeled by adding a small curvature radius at the wingtip join with the winglet, in such a way as to guarantee a smooth transition between the wing and the winglet (as illustrated in Fig. 6). The winglet span used in this study corresponds to a 20% of the wingspan of the baseline wing. This value was chosen on the basis of previous studies [1, 6, 12, 65‐68], where the authors suggest the use of winglet span values between 10% to 20% of the wingspan. Additionally, we also studied the influence of the winglet sweep angle on the aerodynamic performance of the wing, where the sweep angle is defined as illustrated in Fig. 7. In Table 1, we report the cant angles, sweep angles, and angle-of-attack values used in this study. As a guideline, in Table 2 we report the wetted area of each wing used. Lastly, in Table 3, we report the values of the relative wingspan reduction in reference to the wing with winglet at cant angle \(0^{\circ }\).

In Fig. 8, a sketch of the computational domain, dimensions, and the boundary conditions layout is depicted. The far-field boundary in this figure corresponds to a Dirichlet type boundary condition and the outflow to a Neumann type boundary condition. The boundaries were placed far enough of the wing surface so there are no significant gradients normal to the surface boundaries. The wing was modeled as a no-slip wall, where we used continuous wall function boundary conditions for the turbulence variables. In all cases, the average distance from the wing surface to the first cell center off the surface is approximately \(y^+ \approx 2.4\) viscous wall units, and the maximum value is approximately \(y^+ \approx 4\) viscous wall units.

A hybrid mesh was used for all the simulations, with prismatic cells close to the wing surface and tetrahedral cells for the rest of the domain. In the wing surface we placed enough prismatic layers so the boundary layer profile could be resolved (20 prismatic layers). Also, in the vicinity of the wing and wake region, we added a refinement region with uniform cell size (as illustrated in Fig. 9) so the integral length scales could be properly modeled. A typical mesh is made up of approximately 3.8 to 4.5 million cells, depending on the cant and sweep angle.

The lift force L and drag force D are calculated by integrating the pressure and wall-shear stresses over the wing surface; then, the lift coefficient \(C_L\) and drag coefficient \(C_D\) are computed as follows:where \(\rho\) is the air density, \(V_{\infty }\) the free-stream velocity, and \(S_{ref}\) is the wing reference area.

Finally, the AOA was changed by adjusting the incidence angle value of the inlet velocity, and all forces were computed in the reference system aligned with the inlet velocity. All the computations were initialized using free-stream values and the incoming flow is characterized by a turbulence intensity value equal to 5.0%. All the turbulence variables were initialized following the guidelines given in references [69‐71].

The compressible Reynolds-Averaged Navier–Stokes (RANS) equations are solved by using the finite volume solver Ansys Fluent [72]. The cell-centered values of the variables are interpolated at the face locations using a second-order centered difference scheme for the diffusive terms. The convective terms are discretized by means of the second-order upwind scheme [73]. For computing the gradients at cell-centers, the least squares cell-based reconstruction method is used. In order to prevent spurious oscillations, a multi-dimensional gradient limiter is used [74]. The pressure-velocity coupling is achieved by means of the SIMPLE algorithm [75, 76], where we used the default (or industry standard) under-relaxation factors. As the solution takes place in collocated meshes, the Rhie-Chow interpolation scheme is used to prevent the pressure checkerboard instability. For turbulence modeling, the \(k-\omega\) SST model is used [69‐71]. The turbulence quantities, namely, turbulent kinetic energy k and specific dissipation rate \(\omega\), are discretized using the same scheme as for the convective terms.

Before proceeding with the parametric study, we assessed the accuracy of the numerical scheme and mesh resolution used. In this validation study, we compare the numerical solution outcome against the data of the physical experiments at the same operating conditions described by Schmitt and Charpin [60], that is, Reynolds number \(Re = 11.72 \times 10^6\), Mach number \(Ma = 0.8395\), and angle-of-attack equal to \(3.06^{\circ }\).

During this validation study, we used five different meshes, as listed in Table 4. As our main interest was the accurate prediction of the aerodynamic forces, we focused our attention on the mesh refinement of the surface mesh, prismatic layers, and the growth rate of the volume cells from the wing surface. For meshes 4 and 5, we used a non-uniform surface mesh in such a way to guarantee a proper resolution towards the leading edge and trailing edge sections. For meshes 1–3, we used uniform surface meshes, with aspect ratios smaller to those used in meshes 4 and 5. Also, in meshes 1–3, we used a smaller cell size in the wake region of the domain than that used on meshes 4–5 (refer to Fig. 9).

In Fig. 10, we plot the mesh convergence of the lift and drag coefficients. In the same figure, the Richardson extrapolation values for both coefficients are also depicted. The Richardson extrapolation values were computed using the finer meshes (mesh 1 and mesh 2). To compute these values, we used Eq. 1, where we assumed an order of convergence p equal to 2, and a mesh refinement ratio r equal to 1.6 (in reference to the average \(y^+\) value). In Eq. 1, \(f_1\) represents the finer mesh (mesh 1 in our case). The value obtained using this equation represents the continuum value at zero grid spacing [79]. The results shown in this figure, appear to be approaching nearly the same results as the mesh is refined. Notice that the convergence of the lift coefficient shows an oscillatory behavior.In Table 5, we show the values of the Richardson extrapolation and the outcome of the QoI of mesh 1. In Table 6, the percentage change between the meshes 1–5 and the Richardson extrapolation, and the percentage change between the meshes 2–5 and mesh 1, are listed. From these results, we can see how the error in reference to the Richardson extrapolation and the outcome of mesh 1 are reduced as the mesh is refined.

In base of the results presented in Fig. 10 and Table 6, we decided to use the reference values of mesh 3 (refer to Table 4) to conduct the parametrical study. It is worth mentioning that we also conducted a quantitative study related to the shock wave resolution, where the growth rate and surface refinement used in mesh 3 gave acceptable results compared to meshes 1 and 2. In conclusion, mesh 3 gave a good compromise between solution accuracy and computing speed.

In Fig. 11, we plot the pressure coefficient \(Cp = (p - p_{\infty }) / (0.5 \rho V_{\infty }^2)\) values obtained from the numerical simulations against the experimental values at different wingspan locations (using mesh 3). As it can be seen, the numerical solution shows a similar trend to the Cp distribution obtained in the wind tunnel experiments. Additionally, in Table 7 we compare the \(C_L\) and \(C_D\) values against the values obtained using different CFD solvers [61]. In this table, we can evidence a fairly good match among all solvers, even if the meshes and solution methods are different. In this validation study, the reference area used for \(C_L\) and \(C_D\) computations is equal to 0.7532 \(\mathrm{m}^2\), as described in reference [60].

As a side note, the turbulence model used in reference [61] was the Spalart–Allmaras whereas in this study we used the \(k-\omega\) SST. Additionally, we did not model the rounded wingtip as described in references [60, 61], so these two factors might represent a source of uncertainty, which however we deem to be negligible for the purposes of this study. Based on the results presented, we can state that the selected numerical scheme, turbulence model, and mesh resolution are adequate to resolve the physics involved.

Finally, during this study air was modeled using the equation of state for ideal gases, and the dynamic viscosity was computed using the Sutherland model. It is worth mentioning that the original Onera M6 wing report [60], does not give specific details about the working conditions; therefore, we assumed air at sea-level and at \(300^{\circ }\) K. The temperature was determined by using an iterative procedure so that Re and Ma conditions are matched, together with the equation of state \(p=\rho R T\), the speed of sound relationship \(a=\sqrt{\gamma R T}\), and the Sutherland dynamic viscosity equation \(\mu = (C_1 T^{3/2}) / (T + C_2)\) (where T is the temperature given in degrees Kelvin, and \(C_1\) and \(C_2\) are the coefficients of the Sutherland model). While it is difficult to determine if the operating conditions used in the simulations correspond to the same conditions of the wind tunnel experiments, the assumptions taken in this study appear to be justified given the good agreement between the physical experiments and the numerical simulations.

In this section, we discuss the results of the aerodynamic performance of the wing with variable cant angle winglet in reference to the baseline wing (original Onera M6 wing). An extensive campaign of simulations was carried out, as per the design space listed in Table 1. For all cases, the reference area used for \(C_L\) and \(C_D\) computations is equal to 1.0 \(\mathrm{m}^2\). The computations were carried out in parallel using 16 cores, and each simulation took approximately 4–6 h to convergence to a level where the forces showed either a non-oscillatory behavior or a periodic behavior. All the details regarding the computational domain, boundary conditions, initial conditions, and numerical method, are given in Sects. 3 and 4.

In this manuscript, we have studied the use of variable cant angle winglets which could potentially allow aircraft to get the best all-around performance in terms of drag reduction over different flight phases. While the wing studied does not correspond to an actual wing used in civil transport aircraft, the insight gathered can be used to set the guidelines for the design of variable cant angle winglets and the adjustment of their cant angle during flight.

During this work, we considered high and low Mach number values (0.8395 and 0.3, respectively) and different angle-of-attack values. Thus, we aimed at covering take-off, climb, descent, and cruise conditions. All the quantitative results suggest that by carefully controlling the winglet cant angle, noticeable drag reductions for the same lift value can be obtained at high and low Mach numbers. It was also observed that the variable cant angle winglets do not have adverse effects on the stall behavior and the AOA at which \(C_{L_{max}}\) and \(C_{D_{min}}\) occurs. It also worth noting that at high cant angle values (\(80^{\circ }\)), the maximum lift coefficient and the slope of the lift curve is reduced (but their values are still larger than the values of the baseline wing); therefore, the proposed winglet could potentially be used as a load alleviation system.

Furthermore, it was also found that large winglet sweep angle values have a positive impact on the aerodynamic performance improvements gained by using the proposed winglet. The improvement due to sweep angle is mainly due to a combination of reduced parasite drag, decreased wave drag at high Mach number, and the effect of the inboard lift force generated by the winglet.

In summary, the following benefits have been found:On the other side, the following shortcomings have been found:It is clear that to obtain the best trade-off between benefits and shortcomings, a multi-disciplinary design optimization study should be conducted, together with the use of more realistic wing geometries and additional winglet design variables, such as toe-angle, taper ratio, and span. Nevertheless, the concept studied in this manuscript represents an innovative approach that might help in addressing the challenge of improving aircraft fuel efficiency, reduce pollutant emissions, and lowering the perceived external noise.

We envisage conducting a flight performance study and estimating fuel savings for typical flight scenarios using more realistic wing-winglet configurations. Also, as the main focus of this work was the study of the aerodynamic performance of variable cant angle winglets, we did not give details about the mechanical design of the device and its performance (such as estimation of actuation power, weight, and so on); however, these topics are object of ongoing research.