1 Introduction

Aircraft encounter gust loads during flight, leading to critical requirements for structural design. Gusts can lead to augmented lift force as well as increased wing bending and torsion moments [1]. The objective of gust load alleviation is to reduce those demands to attain a lighter airframe structure. A more environmental and economic flight can be achieved that way. The purpose of this paper is to investigate a novel method oGust alleviation computationf load alleviation by spanwise-distributed load actuators. The advantage is a more precise load control along the wing span, resulting in much reduced structural loads. In this paper, a rigid aircraft wing is assumed. The goal of the derived load alleviation method is to keep loads rather close to 1 g flight conditions during gust encountering. In this case, structural tailoring is of rather limited value and aeroelastic effects of both the backward and forward configuration can neglected, to first-order approximation. Both configurations can be directly compared under these assumptions.

Gust load alleviation is a relevant topic since the early beginning of aviation. With increasing flight speed due to the introduction of jet engines, commercial airliners in the 1970s from Lockheed were the first to be equipped with gust load alleviation systems [2]. Accelerators at the wing tip delivered data for ailerons and stabilizers to counteract against gust. Detailed information of such systems are confidential and only superficial data are published by the aircraft manufacturers. Little detail of modern gust alleviation systems is publicly known. In case of the A320, introduced in 1987, a Load Alleviation function (LAF) was included. Nevertheless, it was removed in the following A321, A319 and A318. In recent time, the LAF has been reintroduced in modern A320s. An increase of 1.3% maximum take-off weight has been realized. The Load Alleviation system is based on an upgrade of the flight control system. Ailerons are deployed during gust encountering to counteract gust loads [3]. The A330/340 series, introduced in 1994/1993, were equipped with a Maneuver Load Alleviation (MLA) and a Comfort in Turbulence (CIT) system. An increase in the fuselage damping response from 2.0 to 4.0 Hz was achieved by actively controlling rudder and elevators [4]. The more recent A380, introduced in 2007, as well as the B787 feature MLA systems, that most likely include optional gust alleviation methods [5]. So far, mainly outboard located control surfaces have been used for load alleviation. Those actuation approaches might reach their limit in case of strong atmospheric gusts. The purpose of this paper is to use actuators along the complete wing, increasing the effectiveness of load alleviation by large factors.

Airbus introduced the concept of a moveable wing tip device for load alleviation in 2017 [6]. This concept is passive and robust, making it relatively easy to install in modern aircraft. The wing tip is connected to the wing via a hinge. During cruise condition, a brake is used to prevent unwanted motions of the wing tip. In release mode the wing tip can rotate around the hinge axis. The movement is damped by an actuator creating a counteracting torque to the aerodynamic force. The wing tip remains horizontal as long as aerodynamic forces and moment are less than the torque of the actuator. Hence, this wing tip offers span extension without the corresponding structural loads of the wing. Similar patent “Articulating Winglets” is published by McDonnell Douglas Corporation [7].

The patent “Active Winglet” was introduced by Tamarack Aerospace Group in 2014 [8]. The wing tip includes a movable wing tip flap. By deflecting the wing tip flap, the load distribution can be adjusted. In addition to wing bending and torsion adjustment, the maximum take of mass can be increased. Also, the active winglet can be used for outboard flow control in addition to aileron during maneuver flight, take-off, etc. While conventional wing tips are most effective at their specific design point, an active winglet can adapt to different flight conditions such as flight speed and altitude, so that a more effective configuration can be obtained.

Aeroelastic tailoring is another method to reduce gust loads. Aircraft wing structure by composite structures offer local tailoring of stiffness and strength, so that the nonlinear response to structural deformation reduces the load [9]. The outcome of this passive technology is reduced weight. Increased flexibility of the wing may result in upward directed movement of the wing during gust encountering so that gust loads are damped. By spanwise load alleviation as it is investigated in this paper, 1 g loads of cruise condition can be approximately maintained during gust encounter. In this case, active tailoring will not provide significant benefits. Consequently, the presented load alleviation method can be viewed as a potential alternative to sophisticated wings with tailored structures.

Most gust alleviation systems being implemented so far have used inertial accelerometers or angle of attack measurements to estimate the gust. At high flight velocity this concept comes to its limit. That is why a more complex and sophisticated gust alleviation system was introduced, the so-called light detection and ranging (LIDAR) system [10]. Different atmosphere conditions including clean air, rain, dense clouds and ice rain were considered. It turned out that the LIDAR system depends on a sufficient density of aerosols in local atmosphere. For high altitudes and areas of globe where the concentration of aerosols is low, direct-detection short-pulse ultraviolet Doppler LIDAR was developed and flight tested. LIDAR can measure disturbance in aerosol depleted regions by using molecular backscatter. Atmospheric disturbances of 50 m ahead of the aircraft can be measured, giving 30 ms of lead time which is regarded sufficient based on angular velocity and maximum deflection required by ailerons. The current LIDAR system is based on four line of sight measurements, enabling 3D airspeed detection [11]. In most cases the gust field ahead of the aircraft is highly nonlinear in space and time. This requires independent load actuators along span. The input from the LIDAR system could be directly used for feed-forward of spanwise-distributed actuators, hence supporting the load alleviation concept pursued in the present paper.

The recent demand for more economic aviation will lead to the design of aircraft with new wing planforms. One way to reduce friction drag and fuels costs might be the use of forward swept wings. Boundary layer transition can be delayed by forward swept wings, as reduced boundary-layer cross flow in spanwise direction comes from a reduced leading-edge sweep, compared to a backward swept wing. The main reason why the forward swept wing has not been used in the commercial aircraft sector yet appears to be due to its tendency of aeroelastic divergence. Forward swept wings tend to increase bending loads due to aeroelastic deformation as well as torsional loads whereas backward swept wings exhibit a natural decrease of these aeroelastic couplings. The specific need for aeroelastic tailoring in case of the forward swept wing increases wing weight. We expect that drastic load alleviation concepts are an important for the forward swept wing in transport aircraft.

Technological progress in numerical flow prediction and flow disturbance sensors opens the path towards more drastic load alleviation approaches by which gust loads and maneuver loads are reduced to rather small augmentations of steady-state cruise flight. Such approaches may be seen as enabler for wings with high aspect ratio to reduce induced drag. A critical first step is to evaluate the potential of active aerodynamic flow control to remove most of the additional loads due to atmospheric gusts. Fundamental preliminary work into this direction have included investigations of active flaps mounted at the fuselage [12] as well as active bumps mounted on the upper airfoil surface [13], as alternatives to the use of hinged flaps mounted on the trailing edge and the leading edge [14,15,16]. It turned out that control of the wing bending moment can be achieved most effectively by trailing-edge flap deflection while the torsion moment may be controlled by leading-edge flaps. Furthermore, to achieve even more control authority over the wing bending moment and wing torsional moment as induced by a critical vertical gust scenario, pre-deflected steady trailing- and leading-edge flaps could be overlayed with dynamic flap deflections Gust-induced flow separation need special attention, specifically during transonic flight conditions.

The objective of the present paper is to investigate actuation authority and sound kinematics of well-designed trailing-edge and leading-edge flaps on a forward swept wing to control both, wing bending loads and torsional loads during transonic gust encounter. Representative gust strength is derived from certification requirements of large transport aircraft. The present work compares RANS simulations of a mid-range research configuration with a forward swept wing to published results of the same configuration with backward swept wing [17]. The simulations assume a rigid wing, since the target is to eliminate aerodynamic gust loads with carefully tailored flap actuation as far as possible. For that purpose, a novel method for gust load alleviation, using the aerodynamic strip theory, is defined as described in [17]. This method is extended and applied to the configuration with the forward swept wing, and the results are carefully analyzed. As the present study considers the feasibility of transonic wing load alleviation to first order, the effects of engine integration and tail plane are neglected.

2 Simulation

2.1 Flow solver

Numerical gust URANS computations are performed with the TAU code, developed by the “German Aerospace Center—DLR” [18]. This code features a 1-cos gust computation module. The Navier Stokes equations are solved by the finite volume method (FVM). A steady-state computation converged after 15,000 iteration is used as an initial solution for the unsteady URANS gust computations. The 3v multigrid method is used to speed up the numerical convergence of the inner iterations performed to converge the flow solution of the individual time step. A CFL number of 1 is defined for both the steady and unsteady computations. Only symmetrical flow conditions are considered in the present paper. A standard second-order central scheme with artificial dissipation added for numerical stability is used for spatial discretization. The unsteady URANS computations are computed over a total time period of Δt = 0.5 s. Previous investigations have shown that within this time period the complete gust encounter process takes place at the considered transonic flow conditions. Time step convergence studies haven proven that an unsteady time step of Δtunsteady = 0.0025 s used with a maximum of 400 inner iterations is suitable.

The numerical grids used for the present wing-body configurations consist of around 30 × 106 unstructured cells. Figure 1 shows the outer dimensions of the farfield. Additionally, a close-up view of the surface grid of the forward swept wing configuration is displayed. Meshing was performed by CENTAUR version 13.0. 40 Prism layers are used to resolve the boundary layer. A y+ value of around 1 is assured by appropriate height of the first cell. Turbulent boundary layers are simulated by employing the one-equation model of Spalart and Allmaras [19]. The farfield consists of a rectangular box of 200 × 250 × 100 m.

Fig. 1
figure 1

Farfield box and surface grid

Local grid refinements are used at the leading edge and other locations of relatively high surface curvature as well as in the region of transonic shocks.

A steady-state RANS computation is used as an initial solution for the unsteady gust computation, as noted before. It is made sure that the steady-state solution is fully converged before the unsteady URANS computation is started. The gust is initially located in front of the aircraft and moves with free stream velocity through the flow field. The numerical simulation of the flow with gust yields the following coefficients of overall lift and drag:

$${{C}_{L}=\frac{{\varvec{L}}}{{q}_{\infty }S}}_{ref},$$
$${{C}_{D}=\frac{\mathbf{D}}{{q}_{\infty }S}}_{ref}.$$

Here, reference wing area \({S}_{ref}\) includes both the projected wing area as well as the wing extension in the fuselage from wing root toward the symmetry line, and \({q}_{\infty }\) denotes the freestream dynamic pressure. The coefficients of wing bending moment CWBM wing and the wing torsion moment CWTM wing include load contributions from the wing only, and refer to the wing root. Both coefficients are calculated by following integration rule.

$${C}_{\mathrm{WBM \,wing}}= \frac{{M}_{WBM \,wing}}{{q}_{\infty } {S}_{ref} {c}_{ref}}.$$

The integration is performed along the 45% chord line of the wing. This line is called “geometric”, in short “geo” in the following equations. Along “geo” structural loads are integrated. The line “geo” is swept relative to the x–z plane instead of the line “y” being normal to the x–z plane. The reason why the integration of the loads is performed along an inclined line is that structural loads of a real aircraft are transmitted via this swept line. The geometric line is shown in Fig. 15.

$${C}_{WBM\, wing} = \frac{{\int }_{y \,root}^{y \,tip}{f}_{L }{y}_{geo} d{y}_{geo}}{{q}_{\infty } {S}_{ref} {c}_{ref}},$$
$${C}_{WTM\, wing}={\int }_{{y}_{root}}^{{y}_{tip}}\frac{{c}_{M}\left(y\right)c{(y)}^{2}}{{S}_{ref}{c}_{ref}}dy=\frac{1}{{S}_{ref}{c}_{ref}}\sum_{n=1}^{200}{c}_{M,n}{{c}_{n}}^{2}\Delta y.$$

The wing torsion moment is calculated by integration of local moments along a swept reference axis, starting at 0.45c at wing root and ending at 0.45c at wing tip. Aerodynamic and structural loads at given wing sections are normalized by the local reference chord \({c}_{local}\), e.g.,

$${c}_{L\, local}=\frac{2 {f}_{\mathrm{L}}}{\rho {{|\mathbf{U}}_{\mathbf{\infty }}|}^{2} {c}_{local}}.$$

2.2 Gust computation

The so-called gust disturbance velocity approach (DVA) is used for the gust computation [20,21,22]. Vertical velocities components \({\mathbf{v}}_{\mathbf{i}}\), representing the gust, are superimposed on the numerical cells within the flowfield. Grid movements due to flap deflections are considered by a boundary velocity \({{\varvec{v}}}_{b}\). The continuity equation of grid cells at the surface, for example, adapts to following expression:

$$\frac{d}{dt}{\int }_{V}\rho dV+{\oint }_{S}\rho \left({\varvec{v}}-{{\varvec{v}}}_{b}-{v}_{i}\right)dV=0.$$

Following figure illustrates the gust computation in a schematic way. The vertical gust velocity is illustrated by black arrows. An exemplary grid cell at the lower surface of the wing is represented by a black box. At soon as the gust reaches this grid cell the gust velocity is superimposed on the grid cell (Fig. 2).

Fig. 2
figure 2

Schematic illustration of gust computation [23]

In case of a rigid wing with no moving flaps, the velocity of the computational cell surface can be neglected.


The gust-induced velocity \({{\varvec{v}}}_{i}\) can be considered by, e.g., a \(1-cos\) function.

The (1 − cos) gust is defined by two parameters, the wave length and the amplitude. The parameters are described in the EASA CS 25 norm. The critical gust amplitude, leading to most severe aerodynamic forces, was defined in previous work [24]. Hence a gust with a vertical of amplitude of 14.48 m/s and wave length of λ = 50 m is chosen in the present study. The gust velocity can be described by the following relation:

$${{\varvec{v}}}_{i}={v}_{g}\left(x\right)={\widehat{v}}_{g}\left(1-cos\frac{2\pi x}{\lambda }\right),$$

constrained by

$$0\le x\le \lambda .$$

\(\lambda\) represents the wave length of the gust. The gust travels with freestream velocity, resulting in

$${{\varvec{u}}}_{g }= {{\varvec{U}}}_{\infty }.$$

For each of the 5 wing sections used for load alleviation, the temporal distribution of the vertical velocity can be described by following approach. A reference point \({x}_{ref gust}=-2.5m\) ahead of the nose of the fuselage serves as the initial location of the gust for \(t=0s\). The index \(i\) used in the following represents the wing section I–V as shown in Fig. 15. \({\Delta x}_{i}\) is the distance in x from the initial gust position to the leading edge of the wing section i. The gust kinematics follows then for each wing section:

$$t< {t}_{1,i}= \frac{\Delta {x}_{i}}{{|{\varvec{U}}}_{\mathbf{\infty }}|}: {v}_{g}=0,$$
$${t}_{1,i}\le t\le {t}_{2,i}={t}_{1,i}+\Delta {T}_{f}={t}_{1,i}+\frac{\lambda }{\left|{\mathbf{U}}_{\mathbf{\infty }}\right|}: {v}_{g,i}={\widehat{v}}_{g,i}\left(1-\mathrm{cos}\frac{2\pi }{\Delta {T}_{f}}t\right),$$
$${t>t}_{2,i}: {v}_{g}=0.$$

The parameter \(\Delta {T}_{f}\) refers to the flap deflection period, explained in Sect. 4. This parameter takes into account the gust wave length \(\lambda\) as well as the freestream velocity \({\mathbf{U}}_{\mathbf{\infty }}\).

2.3 Grid deformation

Dynamic flap actuation is applied at both the leading and the trailing edge at different positions along span. The grid deformation needed for dynamic flap actuation is performed by radial basis functions [25]. The grid is deformed within a user-defined distance normal to the surface. The flap deflection angle is computed around a rotation axis being limited by inner and outer points that define the spanwise extent of the flap. To do so, non-deformed and deformed surface patches are controlled by separate boundary markers, exemplary illustrated in Fig. 3 for the deflection of the trailing-edge flap of a wing segment. Cell clustering at the interface between non-deformed and deformed surfaces is required to maintain grid quality during deformation. Four boundary points \({\mathbf{r}}_{1\mathbf{l}\mathbf{r}},{\mathbf{r}}_{2\mathbf{l}\mathbf{r}},{\mathbf{r}}_{3\mathbf{l}\mathbf{r}},{\mathbf{r}}_{4\mathbf{l}\mathbf{r}}\) are defined at the left and right sides of the flap.

Fig. 3
figure 3

RBF—Grid deformation technique

$$\left(\begin{array}{c}{{\varvec{r}}}_{1l}\\ {{\varvec{r}}}_{2l}\\ {{\varvec{r}}}_{3l}\\ {{\varvec{r}}}_{4l}\end{array}\right)=\left[\begin{array}{c}{x}_{1l}{y}_{1l}{z}_{1l}\\ {x}_{2l}{y}_{2l}{z}_{2l}\\ {x}_{3l}{y}_{3l}{z}_{3l}\\ {x}_{4l}{y}_{4l}{z}_{4l}\end{array}\right],$$
$$\left(\begin{array}{c}{{\varvec{r}}}_{1r}\\ {{\varvec{r}}}_{2r}\\ {{\varvec{r}}}_{3r}\\ {{\varvec{r}}}_{4r}\end{array}\right)=\left[\begin{array}{c}{x}_{1r}{y}_{1r}{z}_{1r}\\ {x}_{2r}{y}_{2r}{z}_{2r}\\ {x}_{3r}{y}_{3r}{z}_{3r}\\ {x}_{4r}{y}_{4r}{z}_{4r}\end{array}\right].$$

Interpolated points between those four boundary points are added, forming an interpolated deformation area, shown in Fig. 4. The number of interpolated points depend on the number of slices in x- and y-direction, used for the interpolation. The deflection angle of the flap is measured around a rotation axis placed between points \({{\varvec{r}}}_{1l}{,{\varvec{r}}}_{3l}\) and \({{\varvec{r}}}_{1r}{,{\varvec{r}}}_{3r}\). Grid cells close to the interface between non-deformed and deformed surfaces are extremely squeezed and stretched, and even negative cell volumes may result from the flap deflection process. Therefore, a blended region is introduced to smooth the interface region. The blending area extends over 9.29% of the local chord length.

Fig. 4
figure 4

Schematic visualization of interpolation for flap deflection

The grid deformation itself is controlled by radial basis functions. The radial basis functions are applied to interpolate the deformation for surface points which are between two neighbored nodes. The deformation for those points is then approximated by following general known volume spline.

$$\Delta x\left(x,y,z\right)={\alpha }_{1}+{\alpha }_{2}x+{\alpha }_{3}y+{\alpha }_{4}z+{\sum }_{i}^{N}{\beta }_{i}\sqrt{{(x-{x}_{i})}^{2}+{ (y-{y}_{i })}^{2}+{ (z-{z}_{i })}^{2}}.$$

In this case, the blending region is chosen to 9% of the chord length.

3 Backward and forward swept configurations

The generic reference aircraft of the present work is the DLR LEISA configuration [26]. This geometry represents a medium-range aircraft. The backward swept wing (BSW) of LEISA uses the DLR-F15 airfoil as a reference. The inner wing planform of the BSW displayed in Fig. 5 exhibits a local wing segment with high taper, commonly used to make room for integrating the aircraft undercarriage. Towards the wing root and tip, wing section geometries are adjusted to cope with the aerodynamic mid-effect and to delay wave drag onset. The fuselage has circular cross sections, and exhibits generic nose and afterbody geometries. A simple fairing with a functional side surface parallel to the symmetry plane serves to reduce flow losses in the wing-body junction. The present work does not take the propulsive engine and the empennage of the LEISA configuration into account. Therefore, these components of the configuration are omitted. The cruise reference design condition of LEISA is H = 35 000 ft, M = 0.8, and CL = 0.5.

Fig. 5
figure 5

Planform of BSW and FSW configurations used in the present work

The DLR LEISA configuration has been used as a reference configuration to design a comparable forward wing configuration. Wing area and aspect ratio, fuselage, and the wing sweep angle at mid-chord position were kept the same when defining the forward swept wing (FSW) configuration. The wing root and its fairing were shifted backward, relative to the backward swept wing, so that the wing reference points of both wings relative to the fuselage are the same. The resulting planform of the forward swept configuration is also shown in Fig. 5. The initial FSW wing used the DLR-F15 airfoil section, as taken from the kink position of the BSW, along the whole wing span.

In the first step of the design of the forward swept configuration, wing twisting defined at five sections along the span was employed to attain a low induced drag, as seen in Fig. 6a (left). Nevertheless, analysis of drag of the configuration still revealed large wave drag towards the wing root. A new FSW wing denoted RCUS (Reduced Curvature Upper Surface) was then designed in the second step to improve the flow in the inner wing region of the FSW. This modification involved a change of the root airfoil geometry and an optimization of inner planform by locally reducing the leading-edge sweep towards the root. The latter approach introduced an inner kink section into the planform. Figure 6a (right) shows the pressure distribution for the kink position study using the RCUS wing profile. Despite these changes, a region of separated flow could not be eliminated at the inner wing, as Fig. 6b shows.

Fig. 6
figure 6

a Adjustment of twist and wing kink position of forwards swept wing. b Friction lines for kink positions regarding Fig. 6a

The pressure distribution of the RCUS geometry reveals particular shortcomings, as seen in Fig. 7. In mid-chord position, upper and lower pressure are on similar levels, so that little or even negative lift is locally contributed. Shock strength is relatively large, especially in the inner wing region, resulting in significant wave drag, and finally, the shock is located at a rather upstream position, at less than 50% local chord. An upstream position of the shock position is particular disadvantage for a FSW configuration, for which wing taper increases the local sweep from the leading to the trailing edge.

Fig. 7
figure 7

Root airfoil pressure distribution

To improve this situation a third design step was made using the DLR transonic 3D inverse method [27]. This allowed to consider the complicated 3D flow of the FSW inner wing. In the inverse design process a new wing geometry is computed changing the pressure distribution according to a target pressure distributions. The target pressure distributions were specified with desired properties, as to remove the adverse features of the RCUS geometry, whereas the spanwise circulation distribution and the thickness distribution of the RCUS wing for span position larger than the kink position were kept approximately the same. A noteworthy outcome of the design work was the new root geometry as shown in Fig. 7. The newly designed root airfoil is thicker, and has a quite distinct curvature distribution on its upper side. Similar geometry changes as performed for the root section were also applied in a reduced and blended form to the rest of the wing, up to a section located at η = 0.89, shown in Fig. 8.

Fig. 8
figure 8

FSW pressure distributions for RCUS geometry and 3D design, red line indicates local critical pressure coefficient

As shown in Fig. 8, the pressure distribution results for the FSW final design has a reduced shock strength, increased lift in the middle chord region and a downstream displacement of the shock position. The right side of Fig. 9 shows that the flow separation was eliminated for the final design denoted as FSW 3D design. Total drag was reduced by 41 drag counts (d.c.). Total drag values for the cruise design point with CL = 0.5 are: CD = 283 d.c. for the FSW RCUS geometry, CD = 242 d.c. for the FSW 3D design and CD = 232 d.c. for the BSW geometry. It turned out that the 3D inverse design approach was necessary to obtain a comparable forward swept configuration relative to the existing backward swept configuration.

Fig. 9
figure 9

Skin friction lines for inner wing region. Left side RCUS wing geometry, right side FSW 3D design

The comparison of pressure distributions between the BSW and final FSW geometry is given in Fig. 10. Note that at the outer wing, the BSW geometry still produces more lift around mid-chord, mainly because the FSW exhibits lower pressures on the lower side. This is due to the fact that the FSW geometry of the outer wing has a 1.5% larger thickness relative to the chord.

Fig. 10
figure 10

Comparison pressure distributions for FSW and BSW at the design point M = 0.8, CL = 0.5

As a consequence, the FSW configuration has higher drag in comparison to the BSW for higher lift values above the design point, as shown in Fig. 11. This is due to higher wave drag and the onset of separated flow. Improving the FSW configuration at off-design conditions would require a further design step, as there is still potential in adapting the pressure and thickness distribution of the lower surface in the outer wing (η > 0.35) to the one of the BSW cases. Furthermore, by moving the shock position further downstream, shock strength could be further reduced. Note, that the forward swept configuration tends to stall earlier in terms of angle of attack, compared to the backward swept configuration, as shown in the figure below. Further improvement is possible, especially if the distance to the buffet boundary of the forward swept configuration is of interest.

Fig. 11
figure 11

Lift and drag polars for FSW and BSW configurations at M = 0.8

However, such detailed design work of the FSW was deemed outside the scope of the present research on fundamentals of load alleviation. Instead the here designed FSW configuration is used to analyze gust simulations at different lift coefficients close to its design point, for which gust-induced flow separations vary. Therefore, in this work, for both, BSW and the FSW geometries, two gust simulation were performed, one with design flight condition CL = 0.50, another at CL = 0.35. In the first case, the FSW geometry without load alleviation measures exhibits massively separated flow, whereas in the second both geometries show attached flow. At CL = 0.35 (FSW) and CL = 0.50 (BSW) a useful comparison of both configurations is given.

4 Gust alleviation computation

Gust alleviation is performed by employing five flap segments along span, see Fig. 12. At each wing section a moveable leading edge and a moveable trailing edge is implemented. Leading-edge deflections are used to control wing torsion moments along span during gust encounter. The gust-induced wing bending moment is compensated by trailing-edge flap deflections. The dimensions of the control surfaces represent current practice of real aircraft design. The trailing-edge devices are an integrated part of high-lift devices and the ailerons designed for the LEISA configuration. Ten–fifteen percent of local wing chord were defined as trailing-edge flap chord, following considerations of retaining enough space for a suitable structure of the respective movables. The ailerons also serve the purpose of gust alleviation and have a length of 25% local wing chord. The number of five flap segments along span was chosen to allow for sufficient spanwise variation of load alleviation. In case of leading-edge devices, a hinged droop nose is employed. The dimensions of the droop noses are based on real aircraft data as well. Servo-hydraulic or servo-electric actuation of the control surfaces would be likely employed. However, sizing of the actuators is not considered in the present work.

Fig. 12
figure 12

Sketch of flaps for load alleviation and chord lengths

An overview of the flap dimensions and sweep angles of each wing section is summarized in Tables 1 and 2.

Table 1 Dimension of flaps for load alleviation
Table 2 Sweep angles of backward and forward swept configuration

A suited approach for deflecting the individual flaps is based on the aerodynamic strip theory. This theory assumes that effective angles of attack of the flow along the span are large relative to the induced angles, thereby allowing to estimate flap deflection angles to compensate gust loads by approximating flap effectiveness by swept airfoil data. For the application of strip theory, we assume that a simulation of gust flow delivers the augmentations of lift coefficient and pitching moment for each flap section.

$$\Delta {{\varvec{C}}}_{{\varvec{m}}}= \left[\begin{array}{c}\Delta {C}_{WTM\mathrm{sec}I}\\ \Delta {C}_{WTM\mathrm{sec}II}\\ \Delta {C}_{WTM\mathrm{sec}III}\\ \Delta {C}_{WTM sec IV}\\ \Delta {C}_{WTM secIV}\end{array}\right] \quad\Delta {{\varvec{C}}}_{{\varvec{L}}}=\left[\begin{array}{c}\Delta {C}_{L\mathrm{sec}I}\\ \Delta {C}_{L\mathrm{sec}II}\\ \Delta {C}_{L\mathrm{sec}III}\\ \Delta {C}_{L sec IV}\\ \Delta {C}_{L sec IV}\end{array}\right].$$

Then, representative 2D airfoils are extracted at the spanwise center of each flap section for estimating the required trailing-edge flap (TEF) and leadings edge flap (LEF) deflections according to Fig. 13.

Fig. 13
figure 13

Sketch of deflected leading and trailing-edge flaps at exemplary wing section

In the first step of the load alleviation computation, the trailing-edge devices are deflected alone to remove gust-induced lift. As mentioned previously, an additional pitching moment occurs due to trailing-edge deflection. In the second step, the leading edges are additionally deflected.

The movement of both control surfaces can be mathematically described by the following 1 − cos function:

$${\delta }_{i}\left({t}_{i},{\Delta T}_{f},{{\delta }_{i}}_{amplitude}\right)= {{\delta }_{i}}_{amplitude}\left[1 -\mathrm{cos}\left(\frac{{t}_{i}}{\Delta {T}_{f}}2\pi \right)\right]\frac{1}{2}.$$

The purpose of the present load alleviation kinematics is to control (1 − cos) gust loads. Previous investigations have shown that a (1 − cos) gust leads to an almost (1 − cos) aerodynamic response of the wing, with a phase lag that is similar to the phase lag of a hinged flap. That is why a (1 − cos) deflection routine is chosen for the actuators. Future research on suitable load alleviation systems should include more sophisticated laws to control gust loads other than originated by (1 − cos) gusts.

The deflection period, ΔTf, for each of the flaps is calculated from the gust wave length, λ, by

$$\Delta {T}_{f}=\frac{{|\mathbf{U}}_{\mathbf{\infty }}|}{\lambda }=constant.$$

For swept wings, the effect of the gust reveals a phase lag for each flap segment shown in Fig. 14. For example, the most outer wing section of the forward swept wing gets in touch with the gust at first, followed by the inner wing sections. Consequently, individual lag of flap deflection, t1,i, can be defined. The index \(i\) represents the individual wing sections I–V

$${{t}_{1,i}=\frac{{\Delta x}_{i}}{{U}_{\infty }},}$$

where \({\Delta x}_{i}\) is the leading-edge \(x\)-coordinate of the wing section i, relative to the x-location where the gust begins at t = 0 s. Figure 14 illustrates the strip theory graphically.

Fig. 14
figure 14

Schematic visualization of lag of flap deflection in spanwise direction and moving gust simulation

Hence, the kinematics of the flap deflection follows the kinematics of the gust velocity, by assuming that time lag due to unsteady flow response is similar for the gust and the flow actuation. This assumption was asserted in previous works [14].

The effectiveness of the flap actuators are determined by 2D airfoil computations. Airfoil wing slices of the 3D configuration are extracted at the center of each of the five wing sections, I–V. The extraction is performed in flight direction, followed by a transformation of the resulting airfoil to represent the geometry normal to the swept line of mid-chord wing positions. We note that the geometry of the flaps as well as the Reynolds number differ from wing section to wing section. The freestream Mach number for the 2D slice computations is adjusted according to the wing sweep theory:

$${M}_{2D}=M cos\left(\varphi \right).$$

The required lift value for the 2D slice steady computation is also adjusted according to the local sweep angle of the 3D wing.

$${C}_{L2D} = \frac{{C}_{L }}{\mathrm{cos}({\varphi )}^{2}}.$$

This alignment of 2D and 3D lift coefficients aims at generating comparable transonic flow conditions for 2D and 3D results [26]. Unsteady 2D computations of different deflection amplitudes are performed for both the leading and trailing-edge actuators so that deflections for a required change of the aerodynamic coefficient can be interpolated.

Upward deflected TEF generate a significant nose-up wing pitching moment which increases the nose-up effect of the gust. Therefor LEF deflections are required to compensate the nose-up moment. Thus, the above-mentioned sectional \(\Delta {C}_{m}\) need to be evaluated for the simulation of the reference gust with dynamic TEF deflections. This allows to extract the overall increase in \(\Delta {C}_{m}\).

Figure 15 shows exemplarily the lift reduction with deflection angles for the trailing edge and the response to flap deflections at leading edge at wing Sect. 4. The numerical 2D results exhibit a rather linear increase of lift reduction with increasing upward deflection. This holds also for leading-edge deflections up to about 20 deg; beyond this deflection, the recovery part of the aerodynamic response changes drastically, which indicates flow separation onset.

Fig. 15
figure 15

Instationary lift response yielded by trailing-edge flap 4 (left) and pitching moment yielded by leading-edge flap 4 (right) of the FSW with φ = 25.1 deg for M = 0.8, CL = 0.5

The obtained 2D alleviation data of each wing section are used as an input for defining flap deflections on the 3D wing by following the wing sweep theory:

$${\Delta C}_{L}=\Delta {c}_{L \,2D}\mathrm{cos}({\varphi )}^{2},$$
$${\Delta C}_{m}=\Delta {c}_{m\, 2D}\mathrm{cos}({\varphi )}^{2}.$$

Hence, 3D simulations are performed in three steps as described in [15, 16]: (1) gust-only simulations to extract the sectional \(\Delta {C}_{L}\) and, thus, the required TEF deflection angles, (2) dynamic TEF deflections at gust inflow condition to determine the sectional \(\Delta {C}_{m}\) needed for determining the LEF deflections. (3) the final simulation includes dynamic TEF and LEF deflections on the 3D configuration which aim of controlling both, \(\Delta {C}_{L}\) and \(\Delta {C}_{m}\). In the third step, the rather small effect of the LEF deflection on the sectional ΔCL is considered by an appropriate adjustment of the TEF deflection amplitudes. A more detailed description of the 2D–3D transformations and the utilized approach for kinematically defining flap schedules as functions of the gust passing by the wing together with its validation can be found in [26].

It is well known that the effectiveness of movables at the trailing edge is affected by the displacement effect of the cross flow of the boundary layers which can become significant towards the trailing edge. The trailing edge of a forward swept wing is characterized by a relatively high sweep at the trailing edge as given in Table 2. 3D simulations of the deflected flaps with cross flow were, therefore, performed to evaluate to what extent the flap effectiveness at the trailing edge of the forward swept wing is affected by boundary-layer cross-flow and if a correction of the estimated flap deflections due to the adverse effect of boundary-layer cross flow is needed. Figure 16 presents the computed flap effectiveness using swept wing theory and 2D viscous simulations (left) as well as the results of providing a 3D simulation for a flap segment that includes viscous cross flow.

Fig. 16
figure 16

Analysis of the effects of unsteady flap actuation (left) and boundary-layer cross flow on the lift decrease by TEF for various sweep angles of flap Sect. 2 with a flap deflection amplitude of 4 deg, M = 0.8, CL = 0.5

It turns out that lift reduction due to unsteady flap actuation is about 40% less, compared to a steady flap simulation, for the present case of a 50 m gust. The 3D simulations with boundary-layer cross flow reveal significant reduced lift decreases compared to swept wing theory with 2D simulations. This effect grows with trailing-edge sweep angle. As an important outcome, much higher trailing-edge deflection angles are needed compared to the backward swept configuration to alleviate gust loads.

Since the lift response due to TEF deflection varies proportional with deflection up to about 15 deg the results of 2D and 3D calculations for wing segments are well displayed as derivatives. The results of our RANS-computations of TEF flap data of the FSW indicate thee major detrimental effects on flap efficiency: (1) the effect of unsteady flap actuation, (2) the effect of trailing-edge sweep, and (3) the effect of cross flow in the boundary layer. These relative effects are displayed in Fig. 17. The effect of unsteady flap actuation depends on the chosen gust wave length, relative to the chord length of the wing section, while the other two depend on the shape of the wing planform. Since all three effects are of the same order of magnitude, it is obvious that all three must be considered in order to capture the flow physics of the TEF correctly. Note that effects (2) and (3) compensate each other for the BSW, since a tapered BSW has a trailing-edge sweep that is smaller compared to the mid-chord sweep. For the FSW, on the other hand, trailing-edge sweep is always larger than sweep at mid-chord, and hence both detrimental sweep effects add up in this case.

Fig. 17
figure 17

Flap effectiveness for local sweep angles of 25.1 deg (left) and 32 deg (right) for TEF no. 2 of FSW

Sensitivities of droop-nose effectiveness were investigated in a similar way as flap effectiveness at the trailing edge. Note that the aerodynamic effect of a droop nose to boundary-layer cross flow is very small, hence systematic analyses of cross flow are omitted here. Figure 18 displays the effects of flap chord lengths, leading-edge sweep angle, and flap deflection angles. The data for both flap lengths indicate that a linear dependency of airfoil pitching moment is obtained up to deflection angles of 20 deg, before flow separation takes place. For reasonable flap lengths of around 15% wing chord flap effectiveness at lower sweep angles is larger, whereas flap efficiency for the higher sweep angle increases strongly with flap length.

Fig. 18
figure 18

Droop-nose moment sensitivities from 2D computations at φ = 25.11 deg (left) and 3D droop-nose derivatives derived from 2D computations for use on 3D wing as functions of chord length and nose sweep angle

The effect of the droop-nose deflection on lift is comparably small until a deflection of roughly 10 deg. Figure 19 indicates that larger flap chords lead to nonlinear flow response for deflection angles higher than 10 deg that result in shock-induced flow separation on the upper surface of the airfoil.

Fig. 19
figure 19

Droop-nose lift sensitivity for φ = 18.8 deg and CL = 0.35

5 Assessment of results for gust alleviation

This section presents the results of numerical flow simulations following the methodology, as presented above. The aerodynamic response of backward and forward swept wing configurations to a critical vertical gust and to means of load alleviation are first compared at the nominal design point of cruise condition with a lift coefficient of CL = 0.5. An additional flow case is discussed for the forward swept configuration with CL = 0.35, as CL = 0.5 is much closer to drag rise and flow separation for FSW than the BSW. Aerodynamic as well as structural loads at the wing root and along the wing in spanwise direction are tracked for both configurations.

For CL = 0.5 both configurations show a similar response to the gust for the coefficients of lift, wing bending moment, and wing torsion moment, according to Fig. 20, but also distinctive differences are apparent. I.e., the negative sweep of the FSW results in a slightly earlier increase of wing bending moment and wing torsion moment, and earlier occurrence of the corresponding peak values. Response of lift and wing bending are almost in phase, meaning that the highest wing bending at the root occurs when the lift reaches its maximum. Wing torsion, however, reaches its maximum somewhat earlier. The forward swept configuration stalls during gust encounter which can be noticed by the lower maximum lift coefficient, and flow recovery after the gust interaction, during which lift drops below the initial value, as the flow recovers from stall.

Fig. 20
figure 20

3D load alleviation computation at CL = 0.5—global lift, wing root loads and lift distributions over span

The (1 − cos) gust with λ = 50 m leads to actuation times of 0.2 s, for each of the flaps involved for load alleviation. By applying the described gust load alleviation technique, extra wing bending moment due to the gust can be reduced by about 85%, by employing the TEF. Note that much higher residual bending moments were observed if TEF deflections were determined without considering the cross-flow boundary-layer effects and the trailing-edge sweep angle on flap effectiveness, as described in Chapter 5 for the FSW (results not shown here). The effectiveness to control wing loads over span is also displayed in Fig. 20 by the comparison of the local lift distribution over span for the different simulations obtained at the time of maximum bending load. The lift distribution of the FSW at maximum load closely follows the respective cruise distribution over the whole span, while the BSW shows more variations over the span, presumably as a result of its planform with the relatively large increase of chord length towards wing root. Deflecting the TEF results in an additional torsion moment, as displayed in Fig. 20. Relatively high deflection angles of the LEF up to 25° are required, if both, the additional wing torsion from the gust as well as from the TEF need to be compensated. This results in flow separation and lift decrease below the initial lift value during flow recovery. If one seeks compensation of augmented wing torsion moment by the deflected TEF only, control of torsion moment is feasible without significant flow separation (index WTM TEF). Note that for the simulations with deflected TEF and LEF, the deflection angle of the TEF was adapted to account for the lift change due to the LEF. Figure 21 shows a sample of the employed flap settings at about the maximum deflection on the FSW, including surface friction lines. The Figure indicates the large flow separation of the upper wing surface as a result of deflecting the leading edge for compensating augmented wing torsion from gust loads and TEF deflections.

Fig. 21
figure 21

Flow visualization of FSW surface during 3D load alleviation computation at CL = 0.5 with strong flow separation due to control by LEF

Load alleviation of the forward swept configuration was also simulated for a reduced lift coefficient, CL = 0.35. This value was chosen, so that the FSW had approximately the same margin to transonic wing stall as BSW, as displayed in Fig. 11. The comparison of BSW and FSW with the adjusted flow condition is displayed in Fig. 22. The gust responses for both the FSW and the BSW configurations are now very similar, especially for the lift coefficient. Lift drop below its initial value during flow recovery after gust interaction is no longer observed for the FSW. The temporal variations of wing bending moment as a result of TEF actuation are now very similar for BSW and FSW. The main noticeable difference between the two configuration is seen in the response of root bending and torsion moments as a result of LEF actuation to compensate gust loads and additional loads from the TEF. Load alleviation by the trailing edge of the FSW is now around 90%. The somewhat larger data variations of BSW indicate that the superposition of flow changes from the variation of the effective angle of attack by the gust, from deflecting the TEF, and from deflecting the LEF do not lead to precise cancelation of loads, most likely due to nonlinear flow interactions of the 3D transonic flow field.

Fig. 22
figure 22

3D Load alleviation computation at CL = 0.5 for BSW and CL = 0.35 for FSW—global lift and wing root loads

More insight into the flow physics of the two configurations is offered by inspection of the spanwise distributions of lift, lift coefficient and pitching moment at the instant of maximum wing loads. Figure 23 displays spanwise distributions for two flow control cases: TEF deflection only and synchronous deflection of TEF and LEF to compensate wing torsion moment due to TEF deflection. The simulations reveal significant qualitative differences of flow control along the span for the two wings. Flow control of wing bending for the FSW by using the aerodynamic strip theory works very well on the inboard wing, whereas strip theory appears to somewhat over-estimate 3D flap effectiveness on the outer wing. This leads to residual loads on the outer wing and hence, residual wing bending. Flow control of wing bending on the BSW, on the other hand, appears to be less effective on the inner wing, as the lift distribution is above the target set by the undisturbed cruise distribution at the inboard wing. These results indicate that the induced downwash of the 3D wing, that is neglected in the aerodynamic strip theory, are the origin of these qualitative differences. We note that induced downwash of the FSW is small on the inner wing and larger on the outer wing, whereas the downwash of the BSW behaves just in the opposite manner. Analysis of flow control of the wing pitching moment is more challenging. Here, the control target was to achieve the distribution of the simulation with gust, as denoted by dashed lines in Fig. 23. For the FSW, this target is over-achieved along most of the span, except the outermost part of the wing, where the target is rather well achieved. This explains why the overall wing torsion moment is below the value of the gust-only computation, according to Fig. 23. For the BSW, on the other hand, the control target is over-achieved along most of the span except for the inner wing part. Again, this explains why the overall wing torsion moment is below the target. The reasons for the observed discrepancies of the pitching moment could be a combination of nonlinear transonic flow interactions on the upper wing surface and the neglection of induced downwash in the definition of the amplitudes of the movables.

Fig. 23
figure 23

Spanwise distribution of local lift, lift coefficient, and pitching moment at instant of maximum aerodynamic load

6 Conclusions and outlook

The present paper investigates the feasibility of transonic gust load alleviation on backward and forward swept wing configurations by spanwise-distributed trailing-edge and leading-edge control surfaces to alleviate wing bending and wing torsion moments. For this purpose, a novel scheme to determine flap actuation amplitudes and temporal schedules is devised that builds on the aerodynamic strip theory. The flap actuation scheme needs knowledge about flap effectiveness which is obtained by a data base of assuming an infinite swept wing. This data base can be computed from purely 2D flow computations or, alternatively, from yawed computations that take the effects of boundary-layer cross-flow into account. We find that the viscous effects of boundary-layer cross-flow and the effect of local wing sweep are significant and must be considered for a realistic estimate of control efficiency on a swept wing. This is particular important for forward swept wings, for which the wing taper causes high sweep angles of the trailing edge. The results for the backward swept wing geometry are based on the existing wing-body DLR LEISA configuration. For the forward swept wing an equivalent transonic cruise geometry has been designed within the present work.

The three-dimensional flow simulations for two generic wing-body configurations with a backward swept wing and a forward swept wing indicate that gust response strongly depends on gust amplitude, flight condition, and the aircraft configuration. Gust-induced flow separation was observed for some cases, leading to a relatively long recovery time. The adoption of load alleviation with flap scheduling based on the strip theory indicates that effective control of wing bending moments and wing torsion moments is feasible. The simulations reveal reductions of wing bending caused by vertical gusts of large strength by 85–90%. The comparison of forward and backward swept configurations indicates that one main limitation of our current control approach is caused by the neglect of the lift-induced downwash. Effective control of wing torsion moments is more difficult to obtain since nonlinear interactions appear to play a stronger role for the pitching moment. The yet open question related to the role that nonlinear transonic interactions play should be resolved in the future by investigating purely subsonic gust interaction flow cases as well as by varying the flow parameters of transonic cases. At this point, our numerical data indicate that about 60% of wing torsion loads due to gusts can be removed by careful application of droop-nose control laws.

Next research steps should consider optimized kinematics, e.g., an iterative application of aerodynamic strip theory. There is also the need to demonstrate control effectiveness for nonhomogeneous gust velocities in spanwise direction, alternative gust shapes, and gusts in horizontal directions. Pre-deflection of flap setting along the span for static redistributions of loads may be particularly helpful to cope with limited actuator authority. An important future research question relates to the feasibility of providing sufficiently fast and strong flap actuators that can be integrated at the hinge positions of trailing-edge and leading-edge flaps. We note that particularly high rotational speeds of up to around 150 deg/s are needed to cope with the present, critical gust loads. Finally, realistic aircraft control simulations that include estimates of the uncertainty in measuring the gust amplitude ahead of the aircraft should be performed to evaluate how much of the above described load reduction potentials can retained in practical applications of a complete load alleviation system.