Investigations on the influence of control devices to the separation ...

Journal of Mechanical Science and Technology 32 (5) (2018) 2047~2057 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online)

DOI 10.1007/s12206-018-0414-3

Investigations on the influence of control devices to the separation characteristics of a missile from the internal weapons bay† Shiquan Zhu, Zhihua Chen*, Hui Zhang, Zhengui Huang and Huanhao Zhang Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China (Manuscript Received August 3, 2017; Revised January 17, 2018; Accepted February 10, 2018) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract To ensure the safe separation process of a missile from internal weapons bay, the control device is mounted in front of the internal weapons bay to control the separation process. Based on the coupling of Navier-Stokes (N-S) equations and six-degrees-of-freedom (6DOF) rigid-body motion equations, the separation process of missile under four different conditions (free separation, and rectangle, prism and wedge control) was numerically simulated. The separation process and flow fields were obtained, the aerodynamic parameters and trajectory parameters of four cases compared. Our results show that, the control device can improve the aerodynamic characteristics of the flow field, enhancing the safety of the missile separation. The wedge control device has the best control effect and makes the missile stable, the rectangular and prism control devices have strong bow shock wave and make the pitch angle of the missile large. Keywords: Compressible flow; Control device; Internal weapons bay; Missile separation; Six-degrees-of-freedom rigid-body motion ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction The use of an internal weapons bay in fighter aircraft can reduce the aerodynamic drag and radar signature of fighter aircraft [1, 2]; however, it also causes a large number of complex flow phenomena [3-5] and makes the missile separation from the weapons bay more dangerous. Therefore, it is of great significance to study the separation process and the flow control of a missile from the internal weapons bay. The flows surrounding an internal weapons bay is a typical cavity flow. Cavity flow has been studied since the implementation of internal weapons bay into aircraft in the 1950s [6, 7]. The control of cavity flow has attracted much academic interest over last several years [3, 4, 8-12]. The flow control is divided into two categories: Passive and active. For passive control, there is no external energy input into the flow, and the flow field is usually controlled by changing geometric shape, such as adding spoilers, ramps and others [4, 13]. Active control methods, however, involve external energy input, such as jets or oscillating flaps [3, 14]. The separation of a missile from the internal weapons bay is a very dangerous process, and much research work has been done. A store separation experiment under Mach 2.36 was conducted in the Langley Unitary Plan Wind Tunnel by Stallings [1], to determine the near-field separation character*

Corresponding author. Tel.: +86 25 84303929, Fax.: +86 25 84315644 E-mail address: [email protected] † Recommended by Associate Editor Hyoung-gwon Choi © KSME & Springer 2018

istics of a typical wing-control missile configuration from a cavity of various depths. The sensitivity of the trajectories to various store separation parameters was investigated by Davis et al. [15]. The investigation of high speed weapon delivery from internal weapons bay was conducted in a 0.6 m × 0.6 m sub-transonic and supersonic wind tunnel by Xue et al. [16]. When the store is released from an internal aircraft bay, it can return back under certain flight conditions [17-19]. To avoid this problem, some researchers have used some control methods to ensure the safety of missile during release. A low order model is derived, it captures the dominant mechanisms that govern the store trajectory with and without microjets, and conditions of safe and unsafe departure were delineated by Sahoo et al. [19]. Bower et al. [20] developed an active flow control approach for high-speed weapon dispensed from a bay. With the development of powerful computers and advanced numerical algorithms, computational fluid dynamics (CFD) has been widely used [21-23]. In this paper, based on the CFD and 6DOF rigid-body motion equations, and the application of dynamic mesh technique, we performed numerical studies of the separation process of a missile from the internal weapons bay under four different conditions (free separation and other three with rectangle, prism and wedge control, respectively). The influence of control device on the aerodynamic characteristics of flow field and the trajectory of missile was discussed. The control effects of the three different control devices were compared, which can provide references for the design of the

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relevant internal weapons bay, and the safe departure and accurate delivery of missile from internal weapons bay.

2. Numerical methods and validation 2.1 Numerical methods

Fig. 1. Computational model and surface meshes.

-1.0

-0.5

0.0

Cp

The numerical simulation of the missile release from an internal weapons bay is similar to the multi-body separation problem. All involve the accurate solution of the flow field and the calculation of the 6DOF motion of the moving body. In this study, the FLUENT software is combined with user defined function (UDF) to simulate the separation process. In each time step, there are three main steps [24, 25]: (i) Solving the governing equations of unsteady flow field; (ii) solving the 6DOF trajectory of missile; (iii) dynamic updating of flow field grid. The three-dimensional, unsteady N-S equations were solved by using a higher precision detached eddy simulation (DES) method. In the computational domain close to the wall region, the realizable k-ε turbulence model was adopted, and the large eddy simulation (LES) method was adopted to calculate the fluid fields which are far away from the wall. The finite volume scheme was used for spatial discretization. The advection upstream splitting method (AUSM) term was used for the convection term and the central difference scheme for the viscosity term. To solve the 6DOF trajectory of missile, the mass and moment of inertia of missile are given using UDF. UDF is a function written by the user that is dynamically linked with the FLUENT solver at run time. Using the same 6DOF trajectory calculation method with Refs. [24-26], and combined with the aerodynamic parameters of the flow field, the whole missile separation process is calculated. Two dynamic mesh methods, smoothing and remeshing method, are used for the missile move. When the missile displacement is smaller than the mesh size, the mesh does not have a serious skewness problem, the smoothing method is used to move the nodes of the mesh and adapt the mesh to the changes of the computational domain. With this method, the mesh topology is always stable, and the computational accuracy can be guaranteed. When the missile displacement is large, the remeshing method regenerates the distorted meshes; the interpolation method is also applied to regenerate a better quality mesh in the computational region where the mesh quality does not meet the requirement.

t=0.00s t=0.16s t=0.37s t=0.00s t=0.16s t=0.37s

0.5

1.0

1.5

0.0

0.2

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0.6

Numerical results Numerical results Numerical results Experimental Experimental Experimental 0.8

1.0

x/L Fig. 2. Pressure coefficient at φ = 5°.

termined by the right hand rule. The origin of the coordinate system is located at the center of store. The store mass is 907 kg, and the altitude of the calculation condition is 11600 m, The computational Mach number of main flow is Ma = 1.2 and the angle of attack α = 0°. The initial velocity and initial angular velocity of the store are zero. The ejector characteristics, other parameters and calculation conditions can be found in Refs. [24, 27, 28]. The typical numerical simulation results are shown in Figs. 2 and 3, which agree well with the experimental data [24, 27, 28]. Fig. 2 shows the pressure profiles at φ = 5° for three times t = 0.0, 0.16 and 0.37 s. The pressure coefficient calculated is in good agreement with the experimental data. Fig. 3(a) shows the variation of center of gravity (CG) of the store in the global coordinate system versus time. The calculated Euler angles at different times which are shown in Fig. 3(b) also agree well with the experimental results. Therefore, the numerical method in this paper can be applied to the numerical simulation of the missile separation process.

3. Missile separating from internal weapons bay 2.2 Verification example

3.1 Physical model

A classical store separation case [24, 27, 28] was used to verify the numerical method in this paper. The computational model and the meshes of store and wing are shown in Fig. 1. The global coordinate system is based on the store, and the store body coordinate system coincides with it at the initial time of calculation. The centerline of the store lies along the x axis with the positive direction toward the store tip. The z axis is along the positive direction of gravity, and the y axis is de-

Fig. 4 shows the typical model of an air-to-air missile embedded in the internal weapons bay simulated in this paper. The internal weapons bay was rectangular with dimensions of L×D×W = 4.2 m×0.525 m×0.8 m. The missile is similar to the American AIM-120C air-to-air missile, with a length of 3.65 m and a diameter of d = 0.178 m. The CG location of the missile is 1.816 m from the missile tip. The distance between the CG location of the missile and the front, bottom of internal

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25

-2

Euler angle (deg)

Distance (m)

15

0

y

1 2 3

Numerical results Experimental

4

z

5 6

Roll

20

x

-1

Yaw

10 5 0 -5

Pitch Numerical results Experimental

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t/s

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t/s

(a) Center of gravity location

(b) Angular orientation

Fig. 3. The trajectory parameters of the store.

(a) Internal weapons bay and missile model without control device

(b) Rectangular control device

(c) Prism control device

(d) Wedge control device

Fig. 4. Geometric model.

weapons bay is 2 m and 0.2625 m, respectively. The coordinate system is the same as the verification example of Sec. 2.2, and the origin of the missile body coordinate system is located at the CG of the missile. It is assumed that the internal weapons bay is stationary, and the tail fins and missile wings are "X" inside the internal weapons bay. Three different kinds of passive flow control devices were employed (Fig. 4): Rectangular control device (RCD), prism control device (PCD) and wedge control device (WCD). The size of the control devices was ∆x = ∆z = 0.15 m, W = 0.8 m, and the maximum length of the three control devices in the x, y and z directions is the same. The volume of the prism control

device is half of the rectangular control device, and the volume of the wedge control device is one-sixth of the rectangular control device. 3.2 Computational conditions and mesh The chosen computational domain and the corresponding boundary conditions are shown in Fig. 5. The surface of missile, passive control device, internal weapons bay and nearby aircraft structures are subjected to no-slip wall conditions. The air is considered to be ideal and the pressure far-field boundary condition is applied to other boundaries. Pressure far-field

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Table 1. Computational conditions. Altitude (km)

10

Mach number

2

Angle of attack (º)

0

Mass of missile (kg)

156.8

Moment of inertia Ixx (kg·m2)

1.0708

Moment of inertia Iyy (kg·m2)

199.59

Moment of inertia Izz (kg·m2)

199.59

Ejector force Ft (kN)

20

Initial velocity (m/s)

0, 0, 0

Initial angular velocity (rad/s)

0, 0, 0

(a) t = 0.0 s

(b) t = 0.2 s

(c) t = 0.4 s Fig. 7. Variation of flow field mesh in wedge control device case.

Fig. 5. Computational domain and boundary conditions.

Fig. 6. Mesh distribution of missile.

conditions are used in ANSYS Fluent to model a free-stream condition at infinity, with free-stream Mach number and static conditions being specified. It cannot be applied to flows that employ constant density, the real gas model, and the wet steam model [29]. The initial calculating conditions are shown in Table 1. The ejection separation method was adopted in this paper. The ejection configuration was neglected in the calculation, but the restraint of ejection device on the missile was considered. The ejector force is about Ft = 20 kN, and acts on the center of gravity of the missile along z positive direction. When the missile moves more than 0.15 m in the direction of z, the ejector force disappears. During the acting time of the ejector force, the missile is constrained and moves only along z direction. The initial velocity and initial angular velocity of the missile are zero. Fig. 6 shows the mesh distribution of missile, and the unstructured mesh was adopted in the computational fluid domain. Fig. 7 shows the mesh distribution in the symmetry plane (xoz plane) at three different times during the separation process of missile from the internal weapons bay for wedge

Fig. 8. Computational domain size.

control device. As can be seen from Fig. 7, the mesh maintains high quality in the process of calculation. 3.3 CFD domain independent study To keep a balance between the numerical accuracy and calculation efficiency, the independence of CFD domain was tested first. Three different sizes of computational domain without control device were calculated, the computational domain sizes are shown in Fig. 8 and Table 2. All dimensions of the computational domain are nondimensionalized using the diameter of missile d. Fig. 9 shows the CG location of missile in the z direction in the global coordinate system as a function of time. Fig. 10 shows the variation of the pitch angle versus time. Case 2 has both high numerical accuracy and less computing resources; therefore, the case 2 size was adopted for the simulation.

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Table 2. Computational domain sizes (nondimensionalized using the diameter of missile d). h

w

l1

l2

Case 1

29 d

13 d

22 d

8d

Case 2

34 d

17 d

27 d

11 d

Case 3

39 d

21 d

32 d

14 d

(a) NCD

(b) RCD

(c) PCD

(d) WCD

-0.5 0.0

z (m)

0.5

Fig. 11. Vorticity distribution.

case 1 case 2 case 3

1.0 1.5 2.0 2.5 0.0

0.1

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0.4

0.5

t (s) Fig. 9. CG trajectory of missile in the z direction. (a) NCD

(b) RCD

(c) PCD

(d) WCD

Fig. 12. Mach number distribution.

Fig. 10. Time-varying angular orientation of y axis.

4. Results and discussion 4.1 Influence of control device on the flow field For convenience, the computational case without control device is referred to as NCD, and the case with rectangular, prism and wedge control device is denoted as RCD, PCD and WCD, respectively. Figs. 11 and 12 show the vorticity distribution and Mach number contours in the symmetry plane (xoz plane) of the missile separation process at the initial time (t = 0 s). The results at t = 0 s are obtained from the steady flow field using the realizable k-ε turbulence model. As shown, for the NCD case there is a strong shear layer under the internal weapons bay. When the missile passes through the shear layer, it suffers a strong aerodynamic force modification; under the condition of high angles of attack, it may return back to the weapons bay. For the controlled cases, the shear layer under the internal weapons bay becomes wider, which makes the missile pass

smoothly through the shear layer. The control device delays the modification of velocity of the shear layer, which reduces the aerodynamic forces (pitch moments) of the missile during the separation process and improves the attitude of the missile. Fig. 13 denotes the pressure contours on the surface of three control devices and the symmetry plane (xoz plane) at t = 0 s. There is a bow shock wave at the front of the control device, and the pressure behind the shock wave is high. The pressure on the surface of the rectangular control device is the highest; therefore, its drag is also the largest, then the prism control device, and the pressure of the wedge control device is the lowest. Therefore, the drag acting on the wedge control device is the minimum, and it is beneficial for its structural strength. 4.2 Influence of control device on the flow field and aerodynamic force (moment) coefficients of a missile Fig. 14 shows the pressure distribution contours in the symmetry plane (xoz plane) at six different times during the missile separation process. For NCD case, the pressure at the rear of the internal weapons bay is higher than the pressure at the front, which makes the missile head rise during the separa-

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(a) RCD

(b) PCD

(c) WCD Fig. 13. Pressure distribution of control devices and the symmetry plane (xoz plane).

tion process; it increases the lift of the missile and under the condition of large angle of attack, it is very dangerous since the missile may move up and hit the bottom of the aircraft. The flow field characteristics of the three controlled cases are similar (Figs. 14(b)-(d)). The bow shock wave of the three control devices is strong and has influence on the separation of the missile. At t = 0.1 s, the head of missile passes the shock wave, and the bow shock wave makes the missile head go nose-down. At the same time, the force of the missile in the z direction increases, so that the missile accelerates away from the internal weapons bay. During the whole missile separation process, the shock wave at the front of the control devices first acts on the missile head. With its continuing separation, the acting area of the shock wave moves to the tail (t = 0.4 s), until the missile is completely removed from the influence of internal weapons bay (t = 0.5 s). Since the DES is adopted for the unsteady simulation, usually, the small vortical structure should be found in the shear layer around the cavity. However, since the 6DOF motion of the missile during the separation needs to be discussed, we have to use unstructured dynamic meshes, and the application

of unstructured dynamic meshes decreases the accuracy of the results and the small vortical structures disappear. On the other hand, since the aerodynamic force and missile motion during separation agree well with previous results (Figs. 2 and 3), we keep discussing the data calculated by the numerical method described in Sec. 2.1. Fig. 15 illustrates the force coefficient history of the missile during the separation process. It contains the aerodynamic force, ejector force and the gravity of the missile. Fig. 16 illustrates the pitch moment coefficients history of the missile during separation. Generally speaking, the force (moment) coefficients of NCD case are quite different from the other three cases. The force (moment) coefficients of RCD and PCD are almost similar to each other, but there are also some differences. The force (moment) coefficients in WCD case have the same trend with RCD and PCD cases, but differ in values. Fig. 17 shows the pressure contours in the symmetry plane (xoz plane) of NCD case at t = 0.10 s to 0.175 s. Fig. 18 is the pressure distribution of the upper side of the missile for WCD. As shown in Fig. 15(a), the force of the missile in the x direction is negative for all four cases due to aerodynamic drag. For NCD and WCD cases, the magnitude of the force coefficients Cx-NCD and Cx-WCD varies little, compared with the other two cases, there is a big difference at the later stage of separation process. Fig. 15(b) shows the force coefficients Cz; it is decreased greatly at 0.0465 s due to the disappearance of ejector force. Without the control device, the force coefficient CzNCD is negative after t = 0.14 s. This means that the direction of the missile lift is upward; the missile may move upward if the lift is large enough, and this should be avoided during the separation process. However, for all of the three control devices, the force coefficients Cz is positive; it indicates that the missile moves accelerated downward which is beneficial to the separation. As shown in Figs. 14(b)-(d), the shock wave at the front of the control devices act on the upside of missile, which makes the head pressure of the missile be large and its move direction downwards, and Cz is positive. After the disappearance of the ejector force, Cz-RCD, Cz-PCD and Cz-WCD increase first and then decrease. Before t £ 0.45 s, the pressure on the upper side of missile increases under the action of bow shock wave, and it becomes small and vanishes due to the weak interaction of shock wave after t > 0.45 s. As shown in Fig. 17, for no control case, the region of higher pressure on the upper side of the missile increases at t = 0.10 s ~ 0.12 s, and the pressure also increases with time, and leads to the increase of aerodynamic force in the z direction. When t = 0.13 s and 0.14 s, the higher pressure area on the upper side of the missile begins to shrink and the pressure decreases; therefore, the Cz-NCD begins to decrease until to zero. When t > 0.14 s, the higher pressure area on the upper side of missile continues to decrease, and the lower pressure area on the upper side of missile increases; it makes Cz-NCD negative, and is harmful to separation.


(a) NCD

(b) RCD

(c) PCD

(d) WCD Fig. 14. Pressure distribution contours in the symmetry plane (xoz plane).

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Cx-NCD

Cx

0.5

Cx-RCD

0.0

Cx-PCD

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Cx-WCD

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t (s) (a) Cx 15

Cz-NCD Cz-RCD

10

Fig. 17. Pressure distribution contours in the symmetry plane (xoz plane) of NCD case.

Cz-PCD

Cz

Cz-WCD 5

0

-5 0.0

0.1

0.2

0.3

0.4

0.5

t (s) (b) Cz Fig. 15. Force coefficients. 1.5

CMy-NCD

Fig. 18. Pressure distribution of the upper side of missile in the WCD case.

CMy-RCD

1.0

CMy-PCD CMy-WCD

CMy

0.5

interacts with the front, middle and rear of missile during the separation process (Fig. 14, t = 0.2 ~ 0.4 s).

0.0

4.3 Influence of control device on the trajectory of missile

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t (s) Fig. 16. Pitching moment coefficients.

According to the pitch moment coefficients curve (Fig. 16), the variation trend of the moment coefficients CMy-NCD is similar to the force coefficients Cz-NCD. The maximum value is at t = 0.12 s, which corresponds to the change of the pressure before and after the CG of the missile. As shown in Fig. 14, when t ≤ 0.12 s, the pressure at the back of missile upside gradually increases with time, and the CMy-NCD is increased gradually. When t > 0.12 s, the pressure at the back of missile upside decreases and the pressure at the upside of missile head increases, so the CMy-NCD begins to decrease. The pitch moment coefficient CMy appears to increase first and then decrease in the NCD, PCD and WCD cases. From Figs. 14(b)(d) this is because the bow shock wave of control devices

Fig. 19 shows the CG location of the missile in the global coordinate system as a function of time. During the action time of ejector force, the missile is restricted and moves only in the z direction. Its displacements and angular motion in other directions are zero. When the ejector force disappears, the missile is subjected to aerodynamic forces. For all of the four cases of this paper, the missile has almost the same displacements in the x direction, but there are also some small differences. When t < 0.33 s, the displacement of the missile in the x direction is close for all three cases with the control device, and it is smaller than the no control case. However, when t > 0.33 s, the displacement of the missile in the x direction increases rapidly for the RCD and PCD cases, and greater than the values of NCD case at t = 0.5 s. This is because the absolute values of the force coefficient Cx for RCD and PCD cases is greater than the other two cases, at this time (Fig. 15(a)). The CG location of missile in the z direction is shown in Fig.

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x (m)

0.0

NCD RCD PCD

-0.5

WCD

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-1.5 0.0

0.1

0.2

0.3

0.4

0.5

(a) NCD

(b) RCD

(c) PCD

(d) WCD

t (s) (a) x -1 0 1

z (m)

2

NCD RCD PCD

3 4

WCD 5 6 0.0

Fig. 21. The missile separation process. 0.1

0.2

0.3

0.4

0.5

t (s) (b) z Fig. 19. Evolution of center of gravity of the missile.

Fig. 20. Time-varying angular orientation of y axis.

19(b). When t < 0.25 s, the displacements are close to each other for all four cases. When t > 0.25 s, the displacement of the missile in the z direction increases rapidly for all the controlled cases, but increases slowly for NCD case. On the other hand, since the Cz-WCD is smaller than the Cz of other two control cases (RCD, PCD) (Fig. 15(b)), its displacement in the z direction is also slightly smaller than the displacement of RCD and PCD at t = 0.5 s. At t = 0.5 s, the displacement of missile in the direction of z under the cases with control device is more than twice that of without control device case. This means that the flow control device makes the missile quickly separate from the internal weapons bay. Fig. 20 shows the variation of the pitch angle of the global coordinate system. There is almost no change of the pitch

angle of missile for all four cases before t = 0.1 s. However, when t > 0.1 s, the pitch angles of all four cases show different trends. For the missile without control device, its head moves nose-up, and the other cases with control device move nosedown. In the separation process, the range of the pitch angle of the WCD case is the smallest, which means that the separation process of WCD case is the most stable of three control cases. The variations of pitch angle for both RCD and PCD cases are similar; they are negative during the whole process and become the largest (-16º) at about t = 0.43 s. This also indicates that the rectangular and prism control devices have almost the same control potential and the missile head is down. Fig. 21 shows separated locations of the missile at six different times (t = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5 s). The figures show almost the whole separating movement of missile from the internal weapons bay. From these figures, we can clearly see the missile movement and attitude during the separation process.

5. Conclusions With the coupling of N-S equations and 6DOF rigid-body equations, and the employ of dynamic mesh technology, the separation process of a missile from the internal weapons bay was numerically simulated under four different conditions: Free separation and other three with rectangle, prism and wedge control, respectively. The numerical method used in this paper has been validated and can be applied to calculate the missile separation. The flow fields of separation process, the missile trajectory, and the force (moment) coefficients were obtained. The numerical results of four different cases were compared.

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Our numerical results show that, the mount of control devices in front of internal weapons bay makes the shear layer under the internal weapons bay widen, which is beneficial for the missile to pass through the shear layer smoothly. At the front of the control device, the bow shock wave appears. When the missile leaves the bay, high pressure acts on the upper side of the missile and accelerates the separation process. The shock wave makes the missile head nose-down after the missile leaves the bay. The above three kinds of applied control devices can accelerate the missile separating away from the internal weapons bay. At t = 0.5 s, the separation distance between the missile and the bay is larger, and it is more than two-times that of without control case. For all of the three cases with control devices, the displacement of the missile is similar; however, different control devices have some influence on the attitude variation of the missile. For the wedge case, the variation of Euler angles is the smallest, and the same with the missile drag; therefore, its separation process is the best. The variations of pitch angles of the missile for other two control devices (rectangle and prism) are similar; they turn into negative and large later, and they have almost the same control effects on the separation, except that the rectangle causes a little larger drag.

Acknowledgment This work was supported by the Key Laboratory Fund (61426040303162604004) and the Fundamental Research Funds for the Central Universities (30917012101), China.

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Zhu, Shi-quan is currently pursuing his Ph.D. in the Key Laboratory of Transient Physics, Nanjing University of Science & Technology. His research interests include computational fluid dynamics of supersonic flow, multibody separation problem and fluidstructure interaction. Chen, Zhi-hua received two Ph.D. degrees: One is from the New Jersey Institute of Technology, USA in 2001, and the other from Nanjing University of Science & Technology, China, in 1997. Dr. Chen is currently a Professor at the Key Laboratory of Transient Physics at Nanjing University of Science & Technology, Nanjing, China. His research interests include supersonic and hypersonic flow, detonation, and flow control.