Numerical simulation of the effect of elastic deformation on the fairing separation process

In view of the potential impact of structural deformation on the separation safety of elastic fairing at low altitude and high speed, the aerodynamic/deformation/motion coupling analysis method is established. The numerical simulation of the separation process of the fairing considering elastic deformation after disengaging is carried out. The motion characteristics and structural response characteristics of the elastic fairing in the separation process are obtained. Moreover, the impact of elastic deformation on the attitude and trajectory of the fairing is studied. The results indicate that the elastic deformation has an impact on the attitude and trajectory of the fairing after hinge decoupling. However, for the calculation conditions in this paper, elastic deformation has no subversive effect on the separation safety.


Introduction
The fairing is an important part of the aircraft, which can maintain the aerodynamic shape of the rocket/missile and protect the internal payload during flight.When a rocket or missile reaches a certain altitude, the fairing must be separated and discarded in time to make the internal payload work properly.Whether the fairing can be successfully separated becomes a key link to determine the success or failure of the flight mission.Therefore, it is necessary to develop accurate simulation methods to provide support for the rocket/missile design and ensure reliable separation of the fairing.
With the demand of improving the carrying capacity of the aircraft and the special trajectory requirements, the research on the separation of elastic fairings under low-altitude high-speed condition is urgently needed.The biggest difference between the low-altitude high-speed separation and the highaltitude high-speed separation or low-altitude low-speed separation is that the flow dynamic pressure is larger.The motion of the fairing during the low-altitude high-speed separation is mainly dominated by aerodynamic force.Meanwhile the fairing will produce large elastic deformation and structural vibration [1], which will have an impact on the separation process.It is necessary to consider both structural rigidflexible coupling and fluid-solid coupling.
In early research, the multi-rigid body assumption was adopted for the fairing separation problem [2], and even the influence of aerodynamic force was ignored.With the deepening of research, the simulation methods of the fairing separation process can be roughly divided into two categories.One is to ignore the influence of aerodynamic force and consider the coupling of rigid body motion and elastic deformation of the elastic fairing [3][4][5].This method is suitable for elastic fairing separations under high altitude condition.The other is to use the computational fluid dynamics (CFD) method coupled the rigid body motion equation to study the separation process [6][7].This method is suitable for the separation of the fairing with small deformation.Some scholars have also carried out one-way coupling by calculating aerodynamic load or structural deformation in advance [8][9][10][11][12], in order to consider the influence of fluid-solid coupling and rigid-flexible coupling on the separation of the fairing.But the simulation accuracy of the one-way coupling method is insufficient, due to the failure to realize synchronous dynamic coupling.
In order to more accurately study the influence of faring elastic deformation on the safety of fairing separation process, based on the unsteady flow simulation method of multi-body relative motion, this paper fully considering the coupling effect between fluid/structure deformation/structure motion, and establishes a fluid-solid coupling simulation method through the direct coupling of computational fluid dynamics and elastic aircraft dynamic model.This method is used to numerically simulate the separation process of the fairing considering elastic deformation after hinge decoupling, and the motion characteristics and structural response characteristics of the elastic fairing during the separation process are obtained.

Fluid-solid coupling simulation method
Based on the inhouse CFD code [13][14], this paper realizes the aerodynamic/deformation/motion coupling simulation by constructing the elastic aircraft dynamics solution module, grid deformation module and fluid-solid interaction module.The numerical simulation flow is shown in Figure 1.

Dynamic model of elastic aircraft
According to the separation characteristics, the Tisserand frame [15][16] is selected to establish the elastic body dynamic model of the fairing.The origin of the coordinate system is located on the instantaneous center of mass of the aircraft, which changes with the structural deformation of the aircraft.The direction of the coordinate axis satisfies that the linear momentum and angular momentum caused by the elastic deformation are zero.
In this paper, the elastic body dynamic model, shown in Equation ( 1), which was established by Waszak [17] under the Tisserand frame is used.The model assumes that elastic deformation of the structure is suitable for the small deformation assumption.Thus, the influence of elastic deformation on the centroid position and inertia tensor of the fairing is ignored.The model is similar to the traditional rigid body dynamics equation and structural dynamics equation.Equation ( 1) can be solved by following the existing computational structure dynamics (CSD) and rigid body six-degree-of-freedom (Six DOF) motion solving modules and using the Runge-Kutta method in time domain in the coupling calculation process with CFD.At this time, the coupling of the fairing deformation and the rigid body motion is realized by the aerodynamic force.

Flow field solution
In this paper, the governing equations of the flow field are Reynolds Averaged Navier-Stokes (RANS) equations in curve coordinates, which are discretized by the finite volume method.The inviscid terms are discretized by the second-order Roe upwind scheme, and the viscous terms are discretized by the second-order central scheme.The turbulence model adopts the Menter's SST k-omega model.In the CFD code, LU-SGS method is used to solve the discrete equations of steady problems while dual-timestep method is used to solve the discrete equations of unsteady problems.The multi-grid method and parallel calculation method based on MPI are used to accelerate the flow field solution.According to the characteristics of fairing separation, the dynamic overlapping grid method is used to simulate the free motion of moving parts in the separation process.

Grid deformation and fluid-solid interaction
The flow field grid update is carried out by combining rigid moving grid and dynamic grid deformation method.The rigid moving grid method is used for large-scale rigid body motion and dynamic grid deformation method is used for structural elastic deformation grid update.Dynamic grid deformation employs RBF_TFI [18] method, which is a hybrid dynamic grid deformation method based on Radial Basis Functions(RBF) and Transfinite Interpolation(TFI) method.Infinite Plate Spline (IPS) method or Thin Plate Spline (TPS) method are used for data transfer between fluid-solid coupled interface by construct the transfer matrix of aerodynamics load and structural deformation between CFD module and CSD module.

Computing Model and Grid
In this paper, the influence of structural deformation on the separation of elastic fairing is studied by numerical simulation.The missile and the split-half fairing are selected as calculation models, and the model shape is shown in Figure 2. The length of the fairing is 3m and the diameter is 0.63m.The upper and lower half of the fairing are symmetrical.The structural parameters of the fairing are shown in Table 1.When the fairing is separated, the upper and lower half fairing are opened at a certain angle under the action of the actuator, and then rotate around the fairing shaft under aerodynamic force.When the fairing rotates to the decoupling angle, the fairing is separated from the missile, and begins to move freely under aerodynamic force.It should be noted that this paper only focuses on the influence of elastic deformation on the motion of the fairing after decoupling.The decoupling angle is 25 degrees, and the opening angle of the model in Fig. 2 is the angle when the fairing is decoupled.The flow field calculation uses structural overlapping grids, which are divided into 508 blocks.The number of grid elements is about 25.91 million.It is divided into three sub-grids, the first group is the background grid containing the missile body, the second group is the upper fairing, and the third group is the lower fairing.
According to the calculation model, the finite element model of the elastic fairing is established for modal analysis.Figure 3 shows the first six structural modes of the upper half fairing.Based on the small deformation assumption described in Section 2.1, this paper assumes that the structural modal characteristics will not change during the fairing movement.In the calculation, the reference length is 7.28m, the reference area is 0.3848m 2 .The coordinate system of the aerodynamic data and motion is defined as follows: the X-axis is pointing from the warhead to the tail along the airflow direction, the Y-axis is vertically upward, and the Z-axis is perpendicular to the X-axis and Y-axis to the right side of the aircraft.

Calculation results and discussion
The separation process is simulated with the calculation state of Mach number 7, 0 angle of attack and dynamic pressure of 381.8kPa.The influence of elastic deformation on the separation process is obtained by the comparison of elastic fairing and rigid fairing.Because the shape and structural parameters of the upper and lower half fairing are symmetrical, the motion law is basically the same.In order to facilitate the description of the results, the results in this section are displayed and discussed for the upper half fairing.

Comparison of separation motion characteristics between elastic fairing and rigid fairing
Figure 4 shows the comparison of the time-varying curves of the attitude and position of the elastic fairing and the rigid fairing.From the beginning of decoupling, the opening angle of the fairing increases first under the action of initial velocity.And then the angle decreases under the aerodynamic force.The difference gradually appears at 0.01s.The difference reaches the maximum at about 0.05s, and the maximum difference is about 4 º.The axial displacement of elastic fairing is smaller than that of rigid fairing, and the maximum difference is about 0.3m at 0.1s.The normal displacement of the elastic fairing is smaller than that of the rigid fairing, and the maximum difference is about 0.6m at 0.1s. Figure 5 intuitively compares the differences in attitude and position between the elastic fairing and the rigid fairing during the separation process.

Structure elastic deformation
Figure 7 shows the generalized displacement of elastic fairing with time.It can be seen that the main modes of the vibration of the elastic fairing structure are mode1 and mode2.There is no coupling phenomenon between the structural modes, and the generalized displacement of each order shows a convergence trend with time.In order to more intuitively show the structural deformation of the elastic fairing, the structural deformation monitoring points are set at the position shown in Figure 8(a).It can be seen that the maximum displacement monitoring point is the corner point of the fairing, and the maximum deformation is about 0.1 m.

Conclusion
In order to study the influence of the elastic deformation of the fairing on the safety of the separation process more accurately.In this paper, an aerodynamic/deformation/motion coupling analysis method is established through the direct coupling of CFD and elastic aircraft dynamic model.The separation motion of rigid and elastic fairing under large dynamic pressure is numerically simulated.The motion characteristics and structural deformation characteristics of the elastic fairing after hinge decoupling are obtained.The results show that the elastic deformation of the fairing causes the pitch angular velocity to increase and the axial and normal displacements to decrease.However, for the calculation conditions in this paper, elastic deformation has no subversive effect on the separation safety.

Figure 4 .
Figure 4. Motion characteristics of elastic fairing and rigid fairing.