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Detached eddy simulation of weapons bay ﬂows and store separation Duk Hyun Kim, Jae Hoon Choi, Oh Joon Kwon∗ Department of Aerospace Engineering, KAIST, Daejeon 305-701, Korea

a r t i c l e

i n f o

Article history: Received 12 October 2014 Revised 2 June 2015 Accepted 23 July 2015 Available online 6 August 2015 Keywords: Detached eddy simulation Cavity ﬂow Flow unsteadiness Pressure ﬂuctuation Store separation Steady blowing

a b s t r a c t When internal weapons bay is exposed to free-stream, highly unsteady ﬂow-ﬁeld is formed over and inside the bay. The pressure ﬂuctuation may cause damages on the surrounding structures, and increases noise. The complicated aerodynamic characteristics inside the weapons bay also affect the behavior of the stores released from the weapons bay. In the present study, numerical investigations of the unsteady ﬂow-ﬁelds inside a weapons bay were conducted by using a three-dimensional compressible ﬂow solver based on unstructured meshes. The effects of ﬂuctuating ﬂow inside the cavity on the aerodynamic loads of the store were also studied. Then simulations of the stores separating from the cavity were carried out, and the effect of ﬂow unsteadiness on the store trajectory was examined. Finally, steady blowing was applied to suppress the pressure ﬂuctuation and to help stabilizing the store separation. It was shown that ﬂow unsteadiness inside the cavity is mainly caused by the detaching and reattaching process of the shear layer. It was found that the results of the SST–DES simulation are in better agreement with experiment in predicting high frequency ﬂow contents than those of the k–ω SST turbulence model. When the store is located inside the cavity or at the shear layer, the pressure on the store oscillates in time. As a result, the trajectory of the store during the initial separation stage is signiﬁcantly affected depending on the release point in time. It was demonstrated that steady blowing is an effective mean for mitigating the pressure ﬂuctuation and stabilizing the store separation. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction Recently, internal weapons bay system is widely used in modern military aircrafts because of its advantages of reducing aerodynamic heating, drag, and radar cross-section. However, when the doors of weapons bay are open for releasing stores and the bay is exposed to free-stream, a highly-unsteady ﬂuctuating ﬂow-ﬁeld, so called cavity ﬂow, develops. The pressure ﬂuctuation inside the cavity may cause damages on surrounding structures, and may increase noise. The pressure ﬂuctuation can also inﬂuence the trajectory of released stores by changing the forces and moments acting on them. In this regard, detailed understanding of the ﬂow characteristics inside the internal weapons bay is essential for the design of advanced weapon systems in the future. A signiﬁcant number of studies about the ﬂow characteristics inside cavity were previously conducted with different cavity conﬁgurations for a broad range of Mach number and Reynolds number through wind-tunnel testing [1–4]. Numerical studies about the cavity ﬂows have also been performed using different levels of turbulence model. At the early stage of the study, Reynolds-averaged Navier–Stokes (RANS) equations were mostly used. However, it was ∗

Corresponding author. Tel.: +82 42 350 3720; fax: +82 42 350 3710. E-mail address: [email protected], [email protected] (O.J. Kwon).

http://dx.doi.org/10.1016/j.compﬂuid.2015.07.022 0045-7930/© 2015 Elsevier Ltd. All rights reserved.

found that RANS simulations are not capable of predicting high frequency contents of the ﬂow near the cavity corner by excessively over-estimating the eddy viscosity. Because of this reason, large eddy simulations (LES) and detached eddy simulations (DES) have been more widely used in the recent studies [5,6]. Nowadays, the stores are getting smaller and lighter, and therefore, when a store is released from the cavity, the trajectory of the store can be affected considerably by the surrounding unsteady aerodynamics. Studies about the effects of the ﬂow inside the cavity on the trajectory of separating stores have been previously performed. Johnson [7] and Westmoreland [8] showed the theoretical, computational and experimental evidences that the ﬂow unsteadiness inside the cavity can alter the trajectory of the stores depending on the time of release. Davis [9] carried out parametric studies to assess the sensitivity of the trajectory deviation due to the various store release parameters. To suppress the unsteady pressure ﬂuctuation and noise inside cavity by reducing the interaction between the aft wall and the shear layer, studies about adopting ﬂow control devices have also been carried out. The ﬂow control mechanism can be divided into either passive or active. Passive ﬂow control adopts devices such as rod or spoiler, or modiﬁes the conﬁguration of cavity to change the behavior of the ﬂow. Active ﬂow control can be classiﬁed into openand closed-loop approaches. The main difference between the two

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approaches is in the fact whether the control includes a feedback loop or not. Smith [10] conducted experiments by installing rods with various sizes at different locations. Nayyar [11] showed that the ﬂow characteristics can be changed depending on the locations of spoiler and jet blowing. In the present study, numerical simulations of the unsteady ﬂow features inside a cavity were conducted using an unstructured mesh ﬂow solver. Then, the effect of store presence on the ﬂow characteristics was studied by its location. Also, variation of the store trajectories depending on the point of release time was investigated. Next, the effects of steady blowing as a mean of ﬂow control to affect the trajectory of separating stores were also examined. For this purpose, the weapons internal carriage and separation (WICS) cavity bay with a length-to-depth ratio of 4.5 was chosen as the baseline geometry. The free-stream Mach number was set to 0.95, and the Reynolds number was 3.75 × 106 . The unsteady turbulent ﬂow over the rectangular cavity was simulated by using the k–ω shear stress transport (SST) turbulence model [12] and also with the detached eddy simulation (DES) based on the k–ω SST [13] to test the effect of turbulence model. The results were compared with available experimental data [3] for validation. 2. Methodology 2.1. Numerical method The numerical simulations were performed by using a threedimensional compressible ﬂow solver based on an unstructured mesh technique [14]. The governing equations were discretized using a vertex-centered ﬁnite-volume method. The convective terms were discretized using Roe’s ﬂux-difference splitting scheme, while the viscous ﬂux terms were computed by adopting a central-difference method. An implicit time integration algorithm based on the linearized second-order Euler backward differencing was used to advance the solution in time. Dual-time stepping was also adopted to minimize the error involved in the linearization. The linear system of equations was solved at each time step by using a point Gauss– Seidel method. The k–ω SST turbulence model and the DES based on the k–ω SST turbulence model were used to estimate the turbulent eddy viscosity. The ﬂow solver was parallelized by partitioning the computational domain into several subdomains using the MeTis library [15]. Communication of the data between the processors was achieved using the message passing interface (MPI) library.

Fig. 1. Conﬁguration of weapons bay and stores.

Table 1 Mesh topology for the calculations. Cavity

# of nodes

Surface cell size

Store

# of nodes

Coarse Medium Fine

576, 552 1, 903, 550 3, 871, 460

0.022L 0.011L 0.0055L

GMPM AIM-9L

266, 522 861, 721

In the present study, the constant CDES was set to 0.95. The ﬁlter size was determined by doubling the maximum distance from the center of each cell to the faces of the cell of the unstructured mesh.

2.2. Turbulence models 2.3. Conﬁguration and mesh To include the effect of turbulence, the k–ω SST turbulence model and the DES based on the k–ω SST turbulence model were applied. The k–ω SST turbulence model is constructed with blended functions of k–ω and k–ε models as follows:

∂k ∂ ρk ∂ ρu jk ∂ (μl + σk μt ) ∂ x j + − ∂ t ρω ∂ x j ρu jω ∂ x j (μl + σω μt ) ∂ω ∂xj τi j Si j − β ρ kω =

(1)

ρσω2 ∂ k ∂ω α 2 νt τi j Si j − βρω + 2(1 − F1 ) ω ∂ x j ∂ x j

The turbulent length scale Lt is deﬁned by transforming the destruction term in the k -equation:

β ρ kω = ρ √

k3/2 k/(β ω)

=ρ

k3/2 Lt

(2)

In the SST–DES, the length scale is replaced by the DES length scale:

β ρ kω • max

L t

CDES

,1

(3)

The WICS wind-tunnel experiment [3] conducted in the Arnold Engineering Development Center (AEDC) was used as the baseline data for comparison. The weapons bay with a length-to-depth ratio of 4.5 was chosen for the cavity geometry in the present study. As the store conﬁguration, the Generic Missile Pressure Model (GMPM) was chosen to test the effect of the presence of store by its location. For the store separation simulations, the AIM-9 L store conﬁguration was used. Fig. 1 shows the geometry of the WICS cavity, GMPM store, and AIM-9 L store. Fig. 2 and Table 1 show the computational mesh and the boundary conditions applied. The mesh is presented for the case when the store is installed inside the cavity. It is shown that small cells are distributed mostly inside and over the cavity such that the detailed cavity ﬂow behavior and its inﬂuence on the store can be captured more accurately. Inside the boundary layer, 25 layers of prism cells are packed on the cavity and store surfaces. The initial thickness of the prism cell is 7.99 × 10−6 , which is normalized by the reference length, L, of the cavity length. The y+ value at the ﬁrst prism layer is approximately one.

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Fig. 2. Computational mesh and boundary conditions.

Fig. 3. Location of transducers. Table 2 Coordinates of transducers.

K9 K12 K16 K18

X(in.)

Y(in.)

Z(in.)

4.675 9.175 17.725 18.000

0.0 0.0 0.0 0.0

4.0 4.0 4.0 0.725

Table 3 Frequency of Rossiter mode. Mode

1

2

3

4

Frequency(Hz)

201.5

470.0

738.6

1007.2

Fig. 4. Instantaneous velocity vectors colored with Mach number at the symmetric plane of cavity.

3. Results and discussion In the WICS experiment, the pressure was measured along the centerline of the cavity wall and the power spectral density (PSD) was calculated by using the fast Fourier transform. Then the sound pressure level (SPL) can be obtained from the following equation:

SPL(f ) = 10log

PSD( f ) fre f

Pre2 f

(4)

where Pref is the international standard for the minimum audible sound with a value of 2 × 10−5 Pa. fref represents the reference frequency. Fig. 3 and Table 2 show the location of the transducers inside the cavity and the coordinates. 3.1. Pressure ﬂuctuation inside cavity The most signiﬁcant feature of cavity ﬂow is characterized by pressure ﬂuctuation. The semi-empirical formula proposed by Rossiter [16] is available for the estimation of the pressure ﬂuctuation frequency. Table 3 shows the ﬂuctuation frequency estimated for the cavity ﬂow depending on the mode number. It is shown that the WICS experimental results are in good agreement with the frequency of the Rossiter Mode, indicating that the ﬂow in the experiment well represents the physical characteristics of typical cavity ﬂows. To capture the unsteady ﬂow characteristics accurately, the time step size was set to 1.0 × 10−5 s for all calculations. Fig. 4 shows the velocity vectors colored by Mach number at the symmetric plane of the cavity. When the weapons bay doors are open, one large main vortex is initially generated as the ﬂow enters into the weapons bay. As time goes on, small secondary vortices

are repeatedly generated at the corners of the cavity and then they merge with the main vortex. In the meantime, a shear layer is formed along the edge of the cavity. The oscillation and instability of the free shear layer leads to generation of repetitive compression and expansion waves, impacting the rear wall. The synching of the timing of those upstream and downstream traveling waves causes strong cavity resonance. Fig. 5 shows the pressure history at the K16 transducer location and the velocity vectors colored by Mach number at two selected time instances with high and low pressure during the pressure ﬂuctuation. As shown in the ﬁgure, the shear layer is highly oscillatory, and high pressure occurs when the shear layer is reattached to the aft wall, while low pressure appears as the shear layer is detached from it. To examine the frequency of the pressure ﬂuctuation, a spectrum analysis was performed. Fig. 6 shows the results of the sound pressure level (SPL) for the two turbulence models with three different sizes of computational mesh presented in Table 1. As shown in the ﬁgure, the results obtained by using the SST–DES are in better agreement with the experiment [3] than those of the k–ω SST model, particularly at high frequencies. This is because the turbulence eddies are better captured using the SST–DES. It is also shown that the high frequency contents are better captured as the mesh becomes ﬁner. Fig. 7 shows the effect of the two different turbulence models on the instantaneous vorticity structure inside the cavity. In this test, the medium-size mesh was used for both calculations. In the ﬁgure, the vorticity is represented by the iso-surface contours colored by pressure. Since numerical dissipation is decreased when the SST–DES is performed, the turbulence eddies are better captured than using the k–ω SST model. As a result, the high frequency contents of the ﬂow are also better captured by using the SST–DES, as shown in Fig. 6.

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Fig. 7. Effect of turbulence model on instantaneous vorticity distribution inside cavity.

Fig. 5. Pressure history at K16 transducer and instantaneous velocity vectors at the symmetric plane of cavity.

(Z/D = 0.75) and at the shear layer (Z/D = 0.0), the pressure significantly changes along the longitudinal direction of the store. Meanwhile, the pressure remains mostly unchanged when the store is located outside of the shear layer (Z/D = –0.3). Thus, it is presumed that the trajectory and the attitude of the store in free-ﬂight separation are affected by the changing aerodynamic loads in time. Fig. 9 shows the variations of integrated force and moment coefﬁcients on the store at the three store locations. When the store is at the shear layer, the amplitude variations of the lift and moment coefﬁcients are much higher than at the other two locations. As the store moves outside of the cavity and is exposed to free-stream, the drag is progressively increased. Fig. 10 shows the SPL results at the two different transducers when the store is inside the cavity. The calculations were made using the SST–DES model. Overall, the SPLs are in good agreement with the experimental data [3], even though the amplitude of the third mode is slightly over-predicted. It is known that when the store is located near the leading edge of the cavity, it behaves as a suppression device [3]. In Fig. 11, the SPL results obtained at the K12 transducer are compared between without and with the store inside the cavity (Z/D = 0.75). It is shown that the presence of the store reduces the amplitude of the primary mode, but increases the amplitude of the secondary mode.

3.3. Cavity ﬂow with separating store

Fig. 6. Effects of turbulence model and mesh size on sound pressure level at K16 transducer.

3.2. Cavity ﬂow including ﬁxed store Next, simulation about the cavity ﬂow including a store inside was carried out for three locations of the GMPM store [3]. Fig. 8 shows the instantaneous velocity vectors colored by Mach number at the symmetric plane of the cavity. The pressure coeﬃcient distributions on the store surface are also presented in the ﬁgure at three selected store locations. When the store is located inside the cavity

Next, investigation about the stores separating from the cavity was conducted using six-degree-of-freedom (DOF) simulations fully coupled with the ﬂow solver. As the store in the present study, the AIM-9 L conﬁguration was taken, and the results were compared with those of the experiment [3]. In the experiment, the store trajectory and the attitude were estimated by applying the measured quasisteady aerodynamic loads on the store in the six-DOF simulations. The initial ejecting condition of the store was assumed, in full-scale units, to be a downward translational velocity of 30 ft/s and a pitch angular velocity of 1 rad/s (nose down) as in the experiment. Fig. 12 shows the sequence of the separating store in several time frames. It was well demonstrated that the present six-DOF simulation, coupled with the ﬂow solver, works well for predicting the behavior of the store separating from the cavity. The store was exposed to free-stream at approximately 0.04 s after it was released from the cavity.

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Fig. 8. Velocity vectors and pressure coeﬃcient distribution on store at three selected store locations.

Since the ﬂow and the pressure ﬁeld around the store change signiﬁcantly in time, the trajectories of the store are also affected by them depending on the release time. In Fig. 13, variation of the moment coeﬃcients on the store initially set inside the cavity before the release is presented in time. It is shown that due to the highly unsteady nature of the ﬂow inside the cavity, the aerodynamic moments on the store are also ﬂuctuating signiﬁcantly, particularly in the pitch and yawing directions. These values are the results of the ﬂow characteristics inside the cavity, and thus determine the initial directivity of separating stores. In Table 4, the time-averaged force and moment coeﬃcients for the ﬁxed store is presented. The results show that there exist relatively strong sideward force and dominant yawing and pitching moments acting on the store. To test the effect of the release time of the store, out of the continuously ﬂuctuating ﬂow conditions, four release points were se-

Table 4 Time-averaged force and moment coeﬃcients on ﬁxed store.

Mean Value

CFX

CFY

CFZ

CMX

CMY

CMZ

0.2800

–1.1723

–0.1526

–0.5841

–2.5937

–8.20536

lected as indicated in the ﬁgure. Case 1 was selected at time of 0.072 s, where the ﬂuctuating amplitudes of the pitching and yawing moments are relatively small. Cases 2 and 3 were chosen for the critical values of the pitching and yawing moments in which the amplitudes of oscillation reach their maximum in each direction, respectively. Case 4 was selected at a point where the magnitudes of the pitching and yawing moments diminish momentarily near zero during the oscillation.

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Fig. 10. Sound pressure levels at K9 and K12 transducers with store inside cavity.

Fig. 11. Comparison of sound pressure levels at K12 transducer between with and without store.

The trajectories and the attitudes of the separating stores for the four different release points are presented in Fig. 14. As shown in the ﬁgure, the store is generally moved in the lateral (y) direction, which is consistent with the strong averaged y-direction force presented in Table 4. Similarly, the yaw angles are generally in negative values because of the high yawing moment. However, the yaw angle of Case 1 shows a slightly different behavior, since the store is released before the pressure ﬂuctuation increases signiﬁcantly. Other trajectories in the x- and z-directions and the pitch angle are not signiﬁcantly affected by the release time. Comparison of the results with the experimental data, which was obtained in a quasi-steady manner based on the captive trajectory support (CTS) system, also shows that the predicted store trajectory and attitude of Case 1 are in better agreement. Fig. 9. Variation of force and moment coeﬃcients on store at three selected store locations.

3.4. Suppression of pressure ﬂuctuation by steady blowing To reduce the severe unsteadiness in the ﬂow, steady blowing was adopted as an active ﬂow control technique. Nayyar [11] carried out numerical simulations of steady blowing for a two-dimensional

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Fig. 12. Sequence of separating store in several time frames using coupled six-DOF simulation.

Fig. 14. Effect of release time on trajectory and attitude of separating stores.

Fig. 13. Variation of moment coeﬃcients on ﬁxed store inside cavity before separation. Fig. 15. Location and strength for steady blowing.

conﬁguration. The results based on the k–ω SST turbulence model showed that steady blowing is most effective for reducing the pressure ﬂuctuation when the blowing slot is installed on the front wall near the edge of the cavity. In the present study, the location and the height of the slot were chosen identically as suggested by Nayyar [11]. The width of the slot in the lateral direction for the three-dimensional simulations was same to the width of the cavity. In Fig. 15, the geometry of the cavity and the slot location for blowing are presented. The ﬂow velocity of blowing was set to be 50% of the free-stream Mach number. In Figs. 16 and 17, comparisons of the instantaneous velocity vectors colored by Mach number and the pressure distributions at the symmetric plane of the cavity are presented between with and with-

out steady blowing. The results show that in comparison with the case without blowing, ﬂuctuation of the shear layer was much reduced and the pressure distribution also become more benign. Fig. 18 shows the pressure histories in time predicted at the K12 and K16 transducer locations. It is shown that the amplitude of pressure ﬂuctuation is decreased signiﬁcantly and the high-frequency contents are also much reduced, demonstrating the effectiveness of steady blowing as a mean of ﬂow control for the cavity ﬂow. In Fig. 19, comparison of the SPL results between with and without blowing is presented at three different transducer locations. Overall, the SPL was decreased after applying steady blowing, except for the second mode.

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D.H. Kim et al. / Computers and Fluids 121 (2015) 1–10

Fig. 18. Comparison of pressure histories in time at two transducer locations between with and without blowing.

Table 5 Time-averaged force and moment coeﬃcients on ﬁxed store under steady blowing.

Mean Value

CFX

CFY

CFZ

CMX

CMY

CMZ

0.0981

–0.1314

0.2785

–0.0526

–1.9164

–0.6982

3.5. Effect of steady blowing on store separation

Fig. 16. Comparison of instantaneous ﬂow ﬁelds between with and without blowing.

Finally, numerical simulations were conducted to investigate the effect of steady blowing on the separating store. The effects of unsteady forces and moments can possibly be overwhelmed/overcome by increasing the store ejection force. However, there exist adverse effects, such as damaging the electronic equipment inside the store due to the high impulsive force. In Fig. 20, variations of the moment coeﬃcients on the store, which is set inside the cavity before release, are presented in time. It is shown that steady blowing signiﬁcantly reduces the magnitude of oscillation of the aerodynamic moment in all directions compared to those without blowing in Fig. 13. In Table 5, the time-averaged force and moment coeﬃcients on the ﬁxed store inside the cavity are presented. In comparison with those without blowing, the lateral force and moment are decreased signiﬁcantly, which increases the relative inﬂuence of the ejector forces compared to the unsteady cavity-induced forces and moments. Next, unsteady store separation simulations were performed. Out of the continuously ﬂuctuating ﬂow, four store release points were selected by adopting the same criteria for the previous store separation simulations without blowing in Fig. 13. Fig. 21 shows the trajectories and attitudes of the released store in time. It was observed that variation of the trajectories and attitudes depending on the time of release is much reduced compared to that without blowing in Fig. 14. The results conﬁrm that steady blowing as a mean of ﬂow control inside the cavity also works well for stabilizing separating stores. It is also shown that the predicted trajectories and attitudes of the store are generally in good agreement with experimental results obtained in a quasi-steady manner.

4. Conclusions

Fig. 17. Comparison of instantaneous pressure distributions between with and without blowing.

Unsteady ﬂow simulations inside a cavity were conducted by using a three-dimensional compressible ﬂow solver based on unstructured meshes with both the k–ω SST and SST–DES turbulence models. It was shown that the ﬂow unsteadiness is caused by the oscillation of the shear layer at the edge of the cavity, and the compression and expansion waves repetitively generated by the oscillating shear layer

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Fig. 19. Comparison of sound pressure levels between with and without blowing.

Fig. 20. Variation of moment coeﬃcients in time for ﬁxed store inside cavity under steady blowing.

impact the rear wall and thus produce the high frequency contents. The results obtained by using the SST–DES were in better agreement with experiment than those of the k–ω SST model, particularly at high frequencies. When the store is located inside the cavity and at the shear layer, the pressure on the surface of the store signiﬁcantly changes in time. The unsteady ﬂuctuating nature of the ﬂow inside the cavity determines the initial directivity of the trajectory and the attitude of separating stores. The ﬂow unsteadiness and varying forces and moments on the store also signiﬁcantly affects the subsequent trajectory and the attitude of the separating stores in free ﬂight depending on the release point, particularly for the sideward displacement and the pitch and yaw angles. It was found that steady blowing from the front wall of the cavity mitigates the ﬂow unsteadiness and the pressure ﬂuctuation. Steady blowing as a mean of ﬂow control also works well at suppressing the amount of spread or uncertainty in the trajectory and the attitude of separating stores by reducing the dependency on the release time.

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government (MEST) through Multi-phenomena CFD Engineering Research Center.

References

Fig. 21. Trajectories and attitudes of released store under steady blowing.

Acknowledgment The authors would like to acknowledge the ﬁnancial support from the Space Core Technology Development Program (no. 2011–0020808) by the Ministry of Education, Science and Technology. This work was also supported by the National Research Foundation of Korea (NRF) grant no. 20090083510 funded by the Korean

[1] Tracy M, Plentovich E, Chu J. Measurements of ﬂuctuating pressure in a rectangular cavity in transonic ﬂow at high reynolds numbers. NASA 1992;TM:4363. [2] Ross J, Peto J. Internal stores carriage research at RAE, Royal Aircraft Establishment TR 2233 (1992). [3] Dix RE, Bauer RCS. Experimental and theoretical study of cavity acoustics, TR-994, AEDC (2000). [4] Nightingale D, Ross J, Foster G. Cavity unsteady pressure measurements-examples from wind-tunnel tests, Ver.3, QinetiQ, Aerodynamics & Aeromechanics Systems Group, Farnborough, England, U.K (2005). [5] Rizzetta DP, Visbal MR. Large-Eddy simulation of supersonic cavity ﬂow-ﬁelds including ﬂow control. AIAA J 2003;41(8):1452–62. [6] Viswanathan AK, Squires KD, Forsythe JR. Detached Eddy simulation of the ﬂow over an axisymmetric cavity. In: Proceeding of 41th AIAA Aerospace Sciences Meeting, Reno, Nevada; 2003 AIAA2003-0265. [7] Johnson RA, Stanek MJ, Grove JE. Store separation trajectory deviations due to unsteady weapons bay aerodynamics. In: Proceeding of 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada; 2008 AIAA2008-0188. [8] Westmoreland WS. Trajectory variation due to an unsteady ﬂow-ﬁeld. In: Proceeding of 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida; 2009 AIAA 2009-0550. [9] Davis MB, Yagle P, Smith BR, Chankaya KM, Johnson RA. Store trajectory response to unsteady weapons bay ﬂowﬁelds. In: Proceeding of 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, Florida; 2009 AIAA2009-0547. [10] Smith BR, Welterlen TJ, Maines BH, Shaw LL, Stanek MJ, Grove LE. Weapons bay acoustic suppression from rod spoilers. In: Proceeding of 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada; 2002 AIAA 2002-0662. [11] Nayyar P, Barakos GN, Badcock KJ. Analysis and control of transonic cavity ﬂow using DES and LES. In: Proceeding of 35th AIAA Fluid Dynamics Conference and Exhibit, Toronto, Ontario; 2005 AIAA 2005-5267. [12] Strelets M. Detached Eddy simulation of massively separated ﬂows. In: Proceeding of 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada; 2001 AIAA 2001-0879. [13] Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J 1994;32(8):1598–605. [14] Jung MS. Development of a conservative overset mesh scheme via intergrid boundary reconnection on unstructured meshes. Ph.D. Thesis. Daejeon, Republic of Korea: Korea Advanced Institute of Science and Technology; 2004. [15] Karypis G, Kumar V. Multilevel k-way partitioning scheme for irregular graphs. J Parallel Distributed Comput 1998;48(1):96–129. [16] Rossiter J. Wind tunnel experiments on the ﬂow over rectangular cavities at subsonic and transonic speeds. Royal Aircraft Establishment 1964.TR 64037

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