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J O U R N A L A R T I C L E S B Y F L U E N T S O F T W A R E U S E R S

Working closely with the U.S. Air Force MunitionsDirectorate, Jacobs Sverdrup engineers havedeveloped a method to accurately simulate thebehavior of stores (such as munitions) as they arereleased from transonic aircraft. The separation ofstores is a challenging problem that cost manyaircraft during the period when flight testing was theonly way to evaluate alternative designs.Computational fluid dynamics (CFD) simulations ofmunitions separation are challenging because therapid movement requires continual modification ofthe mesh, which drives the demand forcomputational resources. Jacobs Sverdrup engineershave overcome this problem by using an unstructureddynamic mesh technique. The ability to dynamicallychange an unstructured mesh greatly increases thespeed of grid generation at each time step of thecalculation. Comparing the CFD results with windtunnel testing for one case studied showed that thismethod was able to accurately predict the locationand velocity of the center of gravity, the angularorientation and its rate of change, and surfacepressure profiles after release. The ability to simulateseparation events willsubstantially reduce designtime and cost and will allowengineers to evaluate manymore potential designs,presenting the opportunity forsubstantial performanceimprovements.

The aerodynamic behavior of munitions or otherobjects as they are released from aircraft is critical

both to the accurate arrival of the munitions at thetarget and the safety of the releasing aircraft. Thechallenge is especially great for objects that aredynamically unstable, such as fuel tanks and somemodern, agile munitions in the event of controlfailure. In the distant past, separation testing wasaccomplished solely using flight tests. This approachwas very time-consuming, often requiring years tocertify a weapon. It was also expensive andoccasionally led to the loss of an aircraft due tounexpected behavior of the store being tested. In the1960s, methods of predicting store separation in windtunnel tests were developed. These tests have provenso valuable that they are now the primary design toolused. However, wind tunnel tests are still expensive,have long lead times, and suffer from limitedaccuracy in certain situations, such as wheninvestigating stores released from within weaponsbays or the ripple release of multiple moving objects.In addition, because very small-scale models mustoften be used, scaling problems can reduce accuracy.

Dynamic Meshing Models StoreSeparation from Transonic Aircraft

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Figure 1: Perspective view of the wing/pylon/store geometry

By Deryl O. SnyderAerospace Engineer,Jacobs Sverdrup, Inc.Eglin Air Force Base, Florida

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The advent of simulation

In recent years, engineers have begun using modelingand simulation to reduce certification cost andevaluate additional designs in order to increase themargin of safety for flight-testing. A CFD simulationprovides fluid velocity, pressure, temperature, and

other variables, as appropriate, throughout thesolution domain for problems with complexgeometries and boundary conditions. As part of theanalysis, an engineer may change the geometry of thesystem or the boundary conditions, and observe theeffect of the changes on fluid flow patterns ordistributions of other variables.

The use of CFD for modeling store separation beganby combining traditional steady-state solutions withempirical or semi-empirical approaches. Themethodology became more useful with the innovationof Chimera overset (overlapping) grid approachesthatmade it possible to perform unsteady, full fieldsimulations with or without viscous effects. Until

recently, CFD has not reached its full potential formodeling transonic separation events because of thelarge amount of time required to perform simulations.The grid must be generated, assembled andrecalculated at each time step of the simulation. Finegrids and small time steps are often required foraccuracy and stability, which increases computationaltime. The most time-consuming aspect of the

Figure 2: Surface meshes for coarse, nominal, and fine grids

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simulation is usually the grid generation andassembly. This is especially true for complex storegeometries, and in particular, for the case of storesreleased from weapons bays. These bays oftencontain intricate geometric features that affect theflow field.

Unstructured dynamic meshing approach

To improve on these methods, Sverdrup engineers setout to develop an unstructured dynamic mesh

approach for store separation simulations. Gridgeneration time with unstructured meshes is reducedbecause the user's input is largely limited to thegeneration of a surface mesh. Also, because there areno overlapping grid regions, fewer grid points arerequired.

The Sverdrup computational approach consists ofthree distinct components: a flow solver, a six-degree-of-freedom (6DOF) trajectory calculator, anda dynamic mesh algorithm. The FLUENT flow solverfrom Fluent Incorpor, Lebanon, New Hampshire, isused to solve the governing fluid dynamic equationsat each time step. From this solution, theaerodynamic forces and moments acting on the storeare computed by integrating the pressure over thesurface. The forces and moments are used to computethe movement of the store by the 6DOF trajectorycode. This code integrates the Newton-Eulerequations of motion within FLUENT as a user-defined function (UDF) that is dynamically linkedwith the FLUENT solver at run time. A localremeshing algorithm is used to accommodate themoving body in the discretized computationaldomain. Finally, the unstructured mesh is modified toaccount for store movement via the dynamic meshalgorithm. When the motion of the body is small, alocalized smoothing method is used. When themotion of the moving body is large, poor qualitycells, based on volume or skewness criteria, areagglomerated and locally remeshed.

Validating the new method

This approach was demonstrated on a genericwing/pylon/store geometry for which benchmarkexperimental data was available. The wing is a 45-degree clipped delta with a 25-foot root chord length.The ogive-flat pylon extends 2 feet below the wingleading edge. The store consists of a tangent-ogiveforebody, a clipped tangent-ogive afterbody, and acylindrical centerbody. Fluent' preprocessor, Gambit,was used to generate triangle surface meshes fromCAD geometry files. The meshes were imported intoFluent's meshing preprocessor, TGrid, for generationof the tetrahedral volume mesh. The automatedmeshing tools in GAMBIT and TGrid made itpossible to create all three meshes in just a fewhours. Nonpermeable wall boundary conditions wereused for the wing, pylon, and store surfaces. Apressure far field condition was used at the upstreamand downstream domain extents, a symmetry planewas used at the wing root, and the downstreamboundary was assigned a pressure outlet condition.The initial condition used for the separation analysis

Figure 3: Comparison ofnumerical (blue) andexperimental (shadow)separation events

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was a fully converged steady-state solution. Timesteps of three sizes, 0.01 sec., 0.002 sec and 0.0004sec., were evaluated for each of three gridrefinements used.

The results showed that CFD performed very well inmodeling a separation event at Mach 1.2 at analtitude of 38,000 feet. The center of gravity locationmatched very closely with the experimental data forall three grid refinements The store moved rearwardand slightly inboard as it fell. The CFD resultsslightly underpredicted the rearward acceleration.The pitch and yaw angles of the store calculated bythe simulation also agreed well with the experimentalresults. The roll angle is especially difficult to modelbecause the moment of inertia about the roll axis ismuch smaller than that of the pitch and yaw axes.Consequently the roll is very sensitive to errors inaerodynamic force prediction. In this case, the storeinitially pitched nose-up in response to the momentproduced by the ejectors. Once free of the ejectors,the nose-down aerodynamic pitching momentreversed the trend. The store yawed initially outboarduntil about 0.55 seconds, after which it began turninginboard. The store rolled continuously outboardthroughout the first 0.8 seconds of the separation.This trend was underpredicted by the simulation andthe curve tended to diverge from the experimentsafter approximately 0.3 seconds.

Experimental surface pressure data was also availablefrom the wind tunnel tests. The data was comparedwith the simulation along axial lines of the store bodyat four circumferential locations and three instants intime. The agreement between the simulation andexperiments was exceptional. Of particular interestedwas the 5 degree circumferential location line at t=0.0because it is located in the small gap between thepylon and store. The simulation did a good job ofcapturing the deceleration near the leading edge ofthe pylon.

All in all, this study showed that CFD withunstructured dynamic meshing can be a powerful toolfor modeling transonic store separation. Thesimulation captured the experimental location,velocity, orientation and angular rate trends. Surfacepressure distributions were also in excellentagreement with the experiments at the three times at

which they were compared during the separationevent. This new approach offers the ability to obtainaccurate store separation predictions with quick turn-around times. Grid generation can be accomplishedin a matter of hours, and runs such as the nominalgrid case examined in this study can be completedovernight on a desktop workstation. The use ofunstructured tetrahedral meshes and a fullyparallelized, accurate and stable solver allows forsmall grids and relatively large time steps without anexcessive computational burden.

Figure 4: Rigid boundary layer mesh attached to the store