The static aeroelastic effect of aircraft ailerons with high aspect ratio at transonic velocity is investigated in this paper by the CFD/CSD fluid-structure coupling numerical simulation. The influences of wing static aeroelasticity and the ‘scissor opening’ gap width between aileron control surface and the main wing surface on aileron efficiency are mainly explored. The main purpose of this paper is to provide technical support for the wind tunnel experimental model of aileron static aeroelasticity. The results indicate that the flight dynamic pressure has a great influence on the static aeroelastic effect of ailerons, and the greater the dynamic pressure, the lower the aileron efficiency. Aileron deflection causes asymmetric elastic deformation of the main wing surfaces of the left and right wings. The torque difference caused by the load distribution on the main wing surface offsets the rolling torque generated by the aileron. This results in a significant reduction in aileron efficiency, and it is noticeable that it is not the elastic deformation of the aileron itself or the reduction in effective deflection that leads to the reduction in rolling control efficiency. Under typical transonic conditions, the rolling control torque of the aileron can be reduced by more than 25%, in the range of 2.5–10 mm, and the ‘scissor opening’ gap width of the aileron has almost no influence on its static aeroelastic effect.

For a large aircraft, the heaviest load-bearing component is the wing. Technical indexes, such as aircraft carrying capacity, cruise speed, operation cost and the performance of takeoff and landing, are closely related to the design of wings. Generally, the stiffness of high aspect ratio wings is small, and the aeroelastic phenomenon caused by the interaction between aerodynamic force and wing elastic structure has a significantly influence on the aerodynamic performance and structural safety of the aircraft. Therefore, aeroelasticity is an important problem that must be considered in aircraft design (especially for these aircrafts with high aspect ratio) [

The structural deformation of the wing has a great impact on the rudder surface efficiency. When the deformation is small, it may reduce the efficiency, while for a large deformation, it may lead to the failure of rudder surface, or even reverse the effect. For example, the “Concorde” aircraft changed by 2° during cruise due to the effect of static aeroelasticity [

Considering the time and cost, the industry mostly utilizes the methods of engineering estimation or numerical simulation to analyze static aeroelasticity of aircrafts in the preliminary design stage. Due to the limitations of calculation methods and calculation conditions, aircraft designers mainly estimate the static aeroelastic characteristics of aircraft based on linear aerodynamic theory. For example, NASTRAN and other calculation software widely used in engineering are based on linear small disturbance theory. They can only be applied to subsonic, low supersonic, non-viscous flow conditions and the calculation of static aeroelasticity with simple surface geometry [

In this paper, aiming at the problem of aileron efficiency reduction caused by static aeroelasticity of large aircrafts under transonic and complex aerodynamic conditions, the CFD/CSD fluid-structure coupling numerical simulation method is used to predict the relationship between structural deformation and aerodynamics. The characteristics and mechanism of the effect of wing static aeroelasticity on the efficiency of the aileron are explored. Moreover, the effect of the ‘scissor opening’ gap width between aileron control surface and the main wing surface on aileron efficiency is also discussed.

The main purpose of this paper is to provide technical references for aerodynamic/structural design and wind tunnel experimental model development of large aircrafts.

The time-dependent three-dimensional conservative compressible RANS equation was adopted to the governing equation. In the general curvilinear coordinate system (_{v}_{v}_{v}

This paper adopted the finite volume method based on grid cell center. The convection term was discretized by the Upwind Flux-Difference-Splitting method based on the three-dimensional Roe scheme. During the reconstruction and interpolation, a minimo limiter was introduced to suppress the nonphysical oscillation near the shock wave based on the MUSCL condition proposed by Van Leer. The viscous term was discretized by the second-order central difference scheme. Implicit LU-SGS method was used for time advance, and SA model was selected as the turbulence model. The material's surface was in an adiabatic no-slip boundary condition, and the far field was in a pressure far-field non-reflecting boundary condition.

For linear elastic problems, the flexibility influence coefficient method can be used to solve the structural static equations, which can avoid solving the complex structural modal equations. In practice, only a finite number of matrix operations can be performed to obtain the structural elastic deformation. With the advantages of short calculation time and simple processing, it is especially suitable for the study of static aeroelastic problems [

For general static aeroelastic calculation, CFD is described based on Euler coordinate system, while CSD is described based on Lagrange coordinate system. Therefore, the generation of CFD grids and the establishment of structural models are carried out independently. Thus, it is necessary to introduce data exchange technology between flow field and structure. One is to convert the displacement of structural points into the deformation displacement of grid points in flow field calculation, and the other is to convert the aerodynamic force of CFD grid points into an equivalent force acting on the structural points. The static aeroelastic calculation of large aircraft wings belongs to the small deformation in three-dimensional space. Considering the memory occupancy, calculation efficiency and interpolation accuracy, it is more suitable to use the three-dimensional TPSI method. For the specific calculation formula, please refer to [

According to the TPSI method, the structural displacement interpolation matrix _{s} and _{a} be the deformation displacement vector of the structural point and the deformation displacement vector of the aerodynamic grid point, respectively. Then, the relationship between the vectors can be expressed as

According to the principle of virtual work, the force interpolation matrix from aerodynamic loads to structural loads and the displacement interpolation matrix from structural points to aerodynamic grid points are transposed to each other. Let

Therefore, if the load of the aerodynamic grid point _{a} of the aerodynamic grid point on the object surface can be obtained according to

After the surface deformation, the original flow field computational grid will no longer be applicable. Therefore, it is necessary to generate a new computational grid. There are two methods for this. One is to regenerate the mesh directly, but this method has low computational efficiency, and usually leads to variation in mesh topology and the number of mesh elements. Its failure to inherit the flow field calculation results of the previous deformation step would result in an excessively long iteration process of static aeroelastic calculation, so this method is not conducive to solving practical engineering problems. The other is to add a certain amount of correction on the original grid. In terms of local areas, the structural deformation of aircrafts is not severe, so this correction method is feasible and has high calculation efficiency. Therefore, this method has been popular in aeroelastic calculation.

In this paper, the unstructured mesh deformation method based on radial basis function was adopted. Wendland's C2 function was selected as the radial basis function, and the greedy algorithm and subspace step-by-step approximation method were used to simplify the object surface interpolation nodes. The grid points near the wall moved with the model wall, and the displacement of grid points far away from the wall was obtained by regional interpolation. This method has high computational efficiency and perfect adaptability to large-scale deformation problems. The quality of the deformed computational grid can be effectively guaranteed.

RBF method is a kind of volume spline function interpolation method, which can be regarded as a three-dimensional extension of surface spline function interpolation method (such as two-dimensional infinite plate spline method) [

The matrix form of the equations can be expressed as

After calculating the coefficients of the interpolation function, for any interpolation point

Theoretically, the displacement of the object surface grid is known, and the displacement of the far-field grid point is set to zero. The displacement of the whole spatial grid can be directly interpolated by using the radial basis function method. However, when the geometric shape of the object surface is complex and the number of the object surface grid is large, the dimension of the matrix in ^{(N)}, which was determined by known displacement nodes (including the object surface and the far field). Considering only the object surface grid points and based on

Assume that there are

Object surface grid nodes were selected by the greedy method again, and an L-dimensional radial basis function interpolation pair was constructed in the N-dimensional radial basis function space ^{(N)}, which was determined by the object surface displacement nodes. Without losing generality, assuming that there are

The above steps were repeated, with a certain number of nodes selected according to the greedy method each time to interpolate the radial basis function of the residual in the previous step, until the residual met the mesh deformation requirements. Then, by superimposing the weight coefficients obtained in this

The above-mentioned method has obvious advantages over the simple greedy method in terms of computational efficiency. If the dimension of function subspace at all levels is uniformly specified as

After obtaining the displacement of each point in each grid block edge by interpolation based on the RBF method, the displacement of each point in the grid block surface could be obtained by the TFI method based on the displacement of the corresponding grid block edge. Similarly, the displacement of the internal points of each grid block could also be obtained by the TFI interpolation based on the displacement of the grid block surface [

In this paper, the static aeroelastic numerical calculation based on CFD/CSD coupling method was carried out by using a wing-body configuration semi-model, and the simulation results were compared with the wind tunnel experimental results. The geometric outline of the model is shown in

The initial computational grid of CFD used multi-partition docking structure grid, and the grid unit size was about 5 million. During grid generation, a layer of boundary layer grid was wrapped around the fuselage and the wing respectively, and the thickness of the first layer of grid was 0.002 ∼ 0.005 mm. In order to apply multigrid technology to accelerate computational convergence, the number of grid points of each structure was strictly controlled according to the rule of 4

The verification calculation state was: ^{6}, and the angle of attack α was −4° ∼ 8°.

_{L}_{L}

The wing-body configuration full model could be obtained by adding the other symmetrical half to the semi-model in

Gap width/(mm) | ||||
---|---|---|---|---|

2.5 | 0.6 | 35 | 2 | 0, 5, 10, 20 |

0.75 | 35, 45, 55, 65 | −2, 0, 2, 4 | 0, 5, 10, 20 | |

0.85 | 35 | 2 | 0, 5, 10, 20 | |

5 | 0.6 | 35 | 2 | 0, 5, 10, 20 |

0.75 | 35, 45, 55, 65 | −2, 0, 2, 4 | 0, 5, 10, 20 | |

0.85 | 35 | 2 | 0, 5, 10, 20 | |

10 | 0.6 | 35 | 2 | 0, 5, 10, 20 |

0.75 | 35, 45, 55, 65 | −2, 0, 2, 4 | 0, 5, 10, 20 | |

0.85 | 35 | 2 | 0, 5, 10, 20 |

_{l}_{l}

_{l} δa |
||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Δ/(%) | Δ/(%) | Δ/(%) | Δ/(%) | |||||||||

5 | −0.0127 | −0.0104 | 18.5% | −0.0128 | −0.0096 | 25.4% | −0.0127 | −0.0098 | 22.7% | −0.0125 | −0.0103 | 17.9% |

10 | −0.0234 | −0.0167 | 28.3% | −0.0230 | −0.0167 | 27.5% | −0.0229 | −0.0167 | 26.9% | −0.0229 | −0.0162 | 29.0% |

20 | −0.0397 | −0.0333 | 16.2% | −0.0402 | −0.0330 | 18.1% | −0.0401 | −0.0343 | 14.6% | −0.0404 | −0.0349 | 13.7% |

In order to better reflect the difference in the influence of static aeroelasticity on aileron efficiency at different angles of attack, _{l}

Effect of dynamic pressure on aileron efficiency of elastic model

_{l}

Influence of Mach number on the static aeroelastic effect of aileron

_{l}

It can be found from

According to the previous analysis and discussion, for the swept wing with high aspect ratio, the rolling control force is weakened and the aileron efficiency is significantly reduced by the effect of static aeroelasticity. In this section, the reasons for the reduction of aileron efficiency will be analyzed based on the numerical simulation results of aileron geometric deformation, surface pressure coefficient and flow characteristic data, and the mechanism of the aileron static aeroelastic effect will be explained.

_{left} _{right}

At these two sections, pressure distributions of the rigid model and the elastic model were obviously different along the chord length of the wing. Specifically, the pressure load of the rigid model was significantly greater than that of the elastic model, and this difference was particularly obvious at the right wing (observed along the course) near the leading edge of the wing tip (torsional deformation caused the weakening of the shock wave and downward deflection of right aileron, which in turn led to greater torsional deformation). It is worth noting that the largest difference in pressure distribution between rigid model and elastic model did not appear in the chord position of the corresponding aileron control surface, but mainly existed before 50% of the wing chord length. When it was close to the aileron control surface, the difference in pressure distribution was rather small. After careful analysis, there are two reasons for this phenomenon. First, when the aileron control surface deflected and bore aerodynamic load, it was equivalent to a large concentrated load at the aileron position for the whole wing. Since this concentrated load was farther from the elastic axis of the wing than that of the aileron, the elastic deformation of the wing caused by the aileron control torque would be greater than that of the aileron control surface itself. In other words, the aileron control surface acted as a “lever” (the elastic deformation of the main wing occurred after “prying” under aerodynamic load). The inconsistent elastic deformation of the main wing surfaces of the left and right wings caused by its differential deflection, rather than the large elastic deformation of the aileron control surface, was the main reason for the reduction in the rolling control efficiency. With the increase in the elastic deformation, the local angle of attack changed greatly, which led to a larger difference in the pressure distribution. Therefore, it is not difficult to understand the pressure distribution difference in the main wing surface shown in

According to the comparative analysis of

Whether for real aircraft or wind tunnel experimental model, to realize the differential deflection of aileron control surface, a certain gap must be left between control surface and main wing surface to avoid interference during control surface deflection. Reference [

This paper mainly studied the influence of three kinds of “scissor opening” gaps with different widths, namely 2.5, 5, and 10 mm. _{l}_{ }=_{l}_{ }=_{l}_{ }=

It can be seen from the figures that under different angles of attack, dynamic pressure and Mach numbers, the gap width of “scissor opening” had no obvious effect on the static aeroelastic effect of aileron. In other words, although the gap width of the control surface would affect the aileron control characteristics of the rigid model or the elastic model, it had no effect on the difference between the two models. Therefore, in order to study the static aeroelastic effect or influence degree of the aileron, the simulation requirements for the “scissor opening” gap of the aileron control surface can be relaxed when designing the static aeroelastic model of the aileron.

This paper has investigated the static aeroelastic effect of large aircraft ailerons based on the high-precision CFD/CSD coupling numerical simulation method. The results have shown that the influence of static aeroelasticity on the rolling control of high aspect ratio swept wings cannot be ignored, because it can significantly change the aileron efficiency. The findings are summarized as follows:

Decreasing the rolling control torque leads to the reduction in aileron efficiency. Near the design cruise point, the rolling control torque of the elastic model decreases by 26.9% compared with that of the rigid model when

In the range of medium and small angles of attack, the flight attack angle and Mach number have little influence on the static aeroelastic effect of ailerons. The flight dynamic pressure is an important parameter affecting the static aeroelastic effect of ailerons. And the higher the dynamic pressure, the lower the aileron efficiency.

Through the comprehensive analysis of the geometric deformation, surface pressure distribution, and surface flow characteristics of the swept wings, it is found that the differential deflection of the aileron control surface will lead to the corresponding geometric deformation of the wing. The aerodynamic load generated after the deformation will offset the load difference between the left and right ailerons, thereby resulting in a significant reduction in the aileron efficiency.

For the typical high-speed static aeroelastic model studied in this paper, the “scissor opening” gap width of the aileron has little effect on its static aeroelastic effect in the range of 2.5–10 mm.