(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

AIAA:99-4107 . A99-36&j --------____

AFFORDABLEHYBRIDSIMULATlION FORPREDICTING STORE SEPARATION

Jaakko Hoffren* and Esa Salminent Helsinki University of Technology

P.O. Box 4400, FIN-02015 HUT, FINLAND

A new method for predicting store separations is described. It combines aerodynamic data from low-speed wind tunnel tests for the store only, panel-method calculations and steady-state Navier-Stokes flow simulations in a way that facilitates a realistic study of even blunt stores and mildly transonic conditions. The unnecessity of sophisticated test equipment makes the method practical for organizations having limited resources. An example involving an awkward store geometry is presented with comparisons to a flight test to demonstrate the potential of the affordable simulation.

1 Introduction As technical progress goes on, the air forces often want to combine new, separable external stores with their air- craft. Before approving a new aircraft-store combination for operational use, it must be verified that the store sep- aration is safe. Within an approved operational envelope, the separating store may not hit the aircraft.

The ultimate verification of the safety of the separa- tions is obtained by flight tests. However, to reduce the potential hazards of the flight test program, it is neces- sary to predict the separations beforehand. There are several ways of making these predictions, reviewed for example in Ref. 1. Wind tunnel tests could be arranged, where store models are actually dropped from aircraft models. Because of the scaling problems involved in the direct tests, wind tunnels are often used to gather just aerodynamic data for subsequent trajectory calcula- tions by systematically moving a store model attached to a sting balance beneath an aircraft model. In any case, the wind tunnel tests are complex, requiring relatively large models to be representative and transonic facilities if the drops are to be conducted in that speed range. To avoid the cost and complexity of the wind tunnel tests, purely computational schemes for the prediction of store separation have been developed. Schemes based on the panel methods2 are simple and fast, but their reliabil-

*Research Scientist, member AIAA, Lab. of Aerodynamics e-mail Jnnkko.Hoffren@hut.fi

tReseurch Engineer, Lab. of Applied Thermodynamics e-mail Esa.Salminen@hut.fi. Copyright @I999 by J. Hoffren and E. Salminen. Published by the American Institute of Aeronautics and Astronautics, Inc. with permis- sion.

ity is questionable and their applicability is necessarily limited. More recently, methods based on flow simu- lations employing the Euler or Navier-Stokes equations have been developed’p3, but the inviscid simulations ap- pear not to be reliable enough, and the viscous simula- tions are very costly, particularly if applied in a time- accurate mode for the separating store.

From the discussion above, it is concluded that the store separation predictions based on wind tunnel exper- iments with an aircraft-store combination are costly and require complex facilities. In small countries, suitable wind tunnels may not even exist. On the other hand, the purely theoretical methods are noted to be unreliable and of limited applicability or impractical. Therefore, there is a need to develop affordable but still useful prediction methods for store separation. Although such engineer- ing methods exist’, there is room for new concepts in this field.

In this paper, an affordable hybrid scheme for predict- ing store separations is described. The method combines the aerodynamic data from low-speed wind tunnel tests, CFD calculations and a panel code to enable six-degree- of-freedom path simulations. The method is applicable to blunt, complex store geometries and mildly transonic conditions. As an example of its application, a study of the separation of a blunt store from a BAe Hawk is dis- cussed and the results are compared with flight tests.

319

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

2 Simulation Method

2.1 Integration of the Flight Path In the calculation of the relative geometry between the store and the aircraft, the flight path of the aircraft is pre- scribed, and no structural responses are taken into ac- count. The path of the store is integrated in time apply- ing full six-degree-of-freedom equations of motion. The integration is based on an explicit Runge-Kutta scheme, which predicts the motion for a time-step when the iner- tial properties and the external forces and moments are known at the beginning of the step. The external forces and moments in turn result from the gravity and the aero- dynamic properties of the store. While the aerodynamic forces and moments depend strongly on the store loca- tion and motion state, they must be determined interact- ively as the simulation proceeds. Typically, the aerody- namic forces and moments are updated at an interval of 0.01 seconds although the Runge-Kutta integration actu- ally applies shorter steps.

2.2 Combination of the Aerodynamic Forces and Moments

When a store is being carried on an aircraft, the aerody- namic interference between them is strong. Therefore, the aerodynamic properties of the combination must be considered in an integral manner. In the present method, the captive store loads are determined purely by numer- ical flow simulations around the store-aircraft configura- tion based on the Navier-Stokes equations. The method is applicable to complex geometries and separated flow, and transonic conditions pose no problem. Although the viscous simulations around a complex geometry are computationally time-consuming, they are manageable, being just steady-state calculations. Simpler inviscid cal- culations are not realistic enough for the purpose3.

The captive loads give the initial aerodynamic im- pulse to the store and are of decisive importance to the store separation behavior. However, after release, the loads start to change gradually, and they should be re- evaluated. If Navier-Stokes flow simulations were ap- plied in this phase, extremely heavy time-accurate cal- culations would be required. Since they are considered to be impractical, a hybrid modeling is employed. As the store drifts apart from the aircraft, their mutual in- terference becomes weaker. Thus, it appears feasible to model the interference effects in a simpler manner after a while from the release. This is done by calculating the flowfield around the aircraft by a panel method without the store, which gives local corrections to the effective angles of attack and sideslip for the store. These correc- tions and the additional effects coming from the motion

of the store are applied to the aerodynamic store proper- ties determined in a steady free stream beforehand to ob- tain the relevant aerodynamic loads. Overall, the captive loads from the CID simulations and the loads for a store in a free stream at flow angles resulting from its attitude, aircraft flowfield and falling dynamics are combined as

where the pitching moment coefficient C,,, is used as an example. The subscript act refers to the actual value to be applied in the drop path simulations, N - S means. the Navier-Stokes calculations, and free, pan refers to the free-stream data corrected by the panel calculations around the aircraft. The time-dependent mixing function fmiz blends the result smoothly from the captive loads used initially to the corrected free-stream data. After some tests, the mixing function was given the form

fmis(t) = min[l, max(0, 1.5 - t/0.1)] (2)

which means that during the first 0.05 seconds when the store is still almost in its initial location, just the captive loads are applied, and after 0.15 seconds the CID results are not used at all. However, it must be stressed that this specific function is aimed at situations where a store ejector is not applied.

The corrected free-stream aerodynamic loads for the store, like Cmf,.ee,pan, result from a combination of low- speed wind tunnel data, steady free-stream CFD calcu- lations and panel method. In a mathematical form, the moment coefficient can be expressed as

C mfree,pan = him blef f 7 Pef f )Gnpan,dyn +(Veff/Voo)2[C,,,p,corr((YeffrPeff)

-fzim(~eff,Peff)Cmpan,stat(~efftPeff)l (3)

Here Cmpan,dyn is a moment coefficient computed by a panel method interactively during the drop simula- tion using the local normal velocities as the bound- ary conditions at each panel. In the bracketed term, C mezp,corr(aef f, ,&f f) is the moment coefficient meas- ured for the store alone in a wind tunnel and correc- ted for Mach effects at the angles of attack and sideslip (wf , AffL and Cmpan,stat(~eff, Aff) is the mo- ment coefficient computed by the panel method in the corresponding conditions. These values are determined beforehand and stored as tables. The effective flow angles aeff and ,&ff are computed using the relative velocity components at the store center of gravity, which result from the store attitude and translation as well as the local down- and sidewash from the aircraft flowfield. The ratio of the squares of the local effective flow ve- locity Veff and the free-stream velocity V, scales the free-stream coefficients appropriately for the situation.

320

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

The limiting function fiirn (cy,ff , ,&ff) multiplying the panel method values is unity at low flow angles and goes to zero at high angles, because the method is not applic- able for high angles due to flow separation. The follow- ing form for the limiter is applied:

fZim(Qeff , Peff) = maz[O, minp, 1+ 0.1(30° - lc&J~l)]] x maz[O, min[l,, 1-t 0.1(30” - l/3&1)]] (4)

The combination given by Eq. (3) reduces to the correc- ted experimental value far from the aircraft if no angular velocities are present. Thus, in the final separation sim- ulations, just the aerodynamical effects coming from the non-uniform flowfield caused by the aircraft and from the angular velocities are modeled applying the panel method.

The experimental results in turn are basically ob- tained in a low-speed wind tunnel. However, Mach and Reynolds number corrections are done by making steady Navier-Stokes simulations around the store alone according to the conditions corresponding to the experi- ments and to the actual drop conditions. From the com- puted differences caused by the variation of the Mach and Reynolds numbers, suitable corrections for the ex- perimental results can be devised.

The hybrid scheme described above aims to combine the limited aerodynamical methods of study efficiently. The NavierStokes simulations give reasonable captive loads for difficult geometries and all speed ranges. The store-only wind tunnel data applied subsequently is rel- evant for complex, possibly blunt geometries, and low- speed data can be adapted to higher Mach numbers by CFD-based corrections. The simple panel method is used just to partially model the flowfield nonuniformity and the dynamic effects in a quasi-steady manner. Thus, it is envisaged that the system is reasonably applicable to dif- ficult store geometries and mildly transonic conditions.

In the following sections, each of the components em- ployed in this work are described, but they could natur- ally be substituted by any other corresponding method.

2.3 Application of Panel Method In this work, a simple low-order panel code originating from MBB” was applied. The code models the effects of thickness on the velocity potential by sources and sinks located on the surface of the object, and lift is generated by separate, user-defined vortex lattices placed inside the lifting surfaces. Although somewhat dated, the subsonic code is robust and quite flexible in the definition of geo- metry. In the Laboratory of Aerodynamics at HUT, the code has been utilized routinely after extensive modern- ization of its input and output routines. Another modi- fication enables throughflow boundary conditions to be

defined to model actual inlets and outlets, or to model separated wakes in an approximate manners.

When used in the drop simulations, the aircraft flow- field at each Mach number and angle of attack and side@ can be straightforwardly computed beforehand by the basic code. Similarly, the data matrix for the store alone,representedbyC,,,,,,tat(a,ff,PefP)inEq. (31, can be run without new code modifications. However, this stage benefits from the existence of the related wind tunnel results since the definition of the panel model for a store may not be unique and obvious. Often, the stores have blunt bases with separated flow, and there may be small fins relative to the body. Traditionally, these kinds of geometries are not suitable for panel methods at all, but here, only certain effects on the stores are sought. To improve the important aspects of the panel predictions, it is desirable to build the panel model in such a way that it gives a behavior of the moment coefficients with respect to flow angles, which is similar to the wind tunnel tests. This tuning is best done by adjusting the model for the lifting vortex lattice.

For adaptation of the panel code to the interact- ive calculations during the drop simulations, producing C mpan,dyn in Eq. (3), slight modifications had to be made. In addition to the coupling of the code to the over- all simulation, it had to be made to read the aircraft flow- field in the beginning and to automatically move the store panel model into a new location in the aircraft-fixed co- ordinate system at each time-step. The most fundamental modification makes the code calculate local normal ve- locities for each panel boundary condition based on the store attitude, translational and angular velocities and the nonuniformity of the surrounding flowfield.

2.4 Wind ‘Ibnel Tests

In this work, the low-speed wind tunnel of the Labor- atory of Aerodynamics at HUT is considered. The di- mensions of the test section are 2 x 2 m2, the maximum speed attainable is 65 m/s, and there is an external six- component balance. The dimensions of the tunnel enable real stores to be employed as models, which further re- duces the cost of the study. However, the attachment of real stores may be a problem if standard lugs are to be used since the necessary rig may form an unrealistic ad- ditional fin on the store. Better, more consistent data are obtained if a dummy store can be converted to a model or if a purpose-built model can be used.

From the wind tunnel tests, the uncorrected values of the experimental load coefficients, represented by c mezp,corr(~eff, ,Qf) in Eq. (3), are obtained in a tab- ular form.

321

2.5 Navier-Stokes Simulations The Navier-Stokes simulations applied for the captive loads and for the corrections of the store-only wind tunnel data are performed using a code called FIN- FLO. FINFLO has been developed in the Laboratories of Aerodynamics and Applied Thermodynamics at HUT since 1987, and the code is capable of simulating three- dimensional flow around complex geometries. There are numerous publications documenting the codeG9, and therefore, only the most prominent features are briefly described here.

FINFLO is a finite-volume code working with struc- tured multi-block grids. A recent, useful addition is the Chimera technique involving overlapping grids, which enables a store grid to be generated separately from the aircraft grid. The inviscid fluxes are computed applying Roe’s upwind-type scheme with second or third-order spatial differences, and the viscous and heat fluxes ap- ply conventional central differences. In steady-state cal- culations, the flow equations are solved by an implicit pseudo-time integration utilizing a multigrid accelera- tion of convergence. There are several turbulence models available, but in this study, the algebraic Baldwin-Lomax model and the lc - E model of Chien were employed.

The calculations required for the corrections of the

Fig. 1: Surface grid of the store used in the Navier-Stokes sbnula- ti0n.S.

Table 1: Drop case definitions

Case number Altitude TAS Ma CL [ml [m/s1 deg.

1 10000 239.6 0.80 1.35

wind tunnel data are straightforward. A grid is gener- ated around the store, and the flow solutions represent- ing the tunnel conditions and the actual conditions are sought to enable the final values of the load coefficients, like Cmezp,corr (aeff, &p) in Eq. (3), to be determ-

2 10 000 170.7 0.57 5.0 3 12 000 191.8 0.65 5.0 4 0 85.1 0.25 8.1 5 2 500 205.0 0.62 0.68

ined. The effort required to obtain the captive loads, like C&N-S in Eq. (l), is much greater. The genera- tion of a grid around the aircraft, or at least around its wing and pylon, may take several weeks, but the same grid may be used for several different separation stud- ies. For the store, a special grid for the captive case must be currently generated since the flow solver cannot ac- cept overlaid Chimera grids which penetrate the aircraft surfaces. Therefore, the store grid must be tightly com- pressed between the store surface and the pylon, which causes some numerical problems. An improvement re- moving this difficulty is planned.

to pure panel calculations. The store is carried on the inner wing pylon of the Hawk applying a special adapter block, as seen in Fig. 2. The separation of the store is conducted just by releasing the locks without using any ejection.

3.2 Drop Cases

3 Application Example

3.1 Aircraft and Store

In operational use, the store is to be dropped at a relat- ively high altitude. For the basic calculations, the altitude of 10 000 m was selected, and the flight Mach number was given a mildly transonic value of 0.8. Additional cases were defined at a lower speed and at a higher alti- tude, and emergency jettisons were to be studied at low altitudes. The exact altitudes, true airspeeds, Mach num- bers and angles of attack are given in Table 1, and a straight and level flight was always assumed. The separation study described in this paper involves a

British Aerospace Hawk Mk. 51 as the carrier aircraft. The store is a parachute flare used for peace-time training of missile attacks. The length of the cylindrical store is

3.3 Aerodynamic Modeling about 1.1 m, its diameter is 0.28 m, and it weighs 93 kg. Panel Models. As seen in Fig. 1, the shape is very blunt and not suitable The model of the Hawk contains the inner wing pylons

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

322

. I

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

Fig. 2: Store adapter as added to the right inner wing pylon of the Hawk panel model.

and store adapters as well as an empty fuselage centerline pylon. There are throughflow boundary conditions at the engine inlets and at the jet pipe exit. On each half of the symmetrical model, there are altogether 2 063 surface panels. The panel model can be seen in the subsequent drop animations-of F igs. 6 and 7.

The panel model of the store is somewhat problem- atic because of the bluntness of the true geometry. Based on the general knowledge of aerodynamics, it is obvious that the flow always separates at the corner between the front plate and the cy lindrical shell. Because the panel method models just attached flows, the front part of the model was s lightly bulged to approximate the stream sur- face, as seen in F ig. 3. Although the sharp s lope dis- continuity was avoided with this trick, the body model cannot be very good for vary ing angles of attack, be- ing unrealistically unstable. Another problematic area of the store is its blunt base with massive flow separation. This feature was approximated by bleeding air through the base at the free-stream velocity.

The span of the lifting vortex lattices at the store tail was iteratively changed to obtain s imilar static stability as observed in the corresponding wind tunnel tests. It turned out that the span had to be increased much larger than the actual span of the fins to obtain a reasonable be- haviour. Even with a vortex lattice of 30 % larger than the geometric span, the predicted neutral point was 0.17 m too far forward. This result confirms the unsuitability of the store for panel calculations, but in the present hy- brid separation s imulation method, this difficulty is not

Fig. 3: Panel model of the store.

too cr itical. W ind ‘Ihnel Tests. An actual store could be modified as a wind tunnel

model. A bracket was welded on top of the store near the center of gravity, and an additional support strut, at- tached at the base, was used to adjust the pitch angle. By turning the whole balance platform to which the store was attached, a redundant s ideslip sweep for the axisym- metric store could be performed.

In the measurements, the flow velocity was set to 45 m/s, and the angles of attack and s ideslip were var ied 30” from zero at 5” intervals. As the aerodynamic loads behaved smoothly in these conditions, a representative data matrix for all the force and moment coefficients to be used in the drop s imulations after Mach number cor- rections was obtained.

Navier-Stokes Simulations. For the calibration of the wind tunnel data, calcu-

lations for the store alone in a free stream were per- formed. The five-block grid, extending about 20 store lengths around the body, was generated using a commer- c ial IGG-packagelO . The total number of cells in the grid modeling one half of the store was 425 984.

,In the calculations, Chien’s k - E turbulence model was applied, assuming the boundary layer to be fully tur- bulent. F irstly, the wind tunnel conditions were emu- lated by setting the appropriate Reynolds number and the Mach number to 0.2 to ensure good convergence of the compressible computation. The angles of attack studied were 0, 5” and 10”. Secondly, the computations were repeated for the flight conditions at Ma = 0.8. A com- parison of the measured and calculated drag and pitch- ing moment coefficients is shown in F ig. 4 to illustrate the level of accuracy achieved for the awkward-shaped store. The reasonable agreement between the corres- ponding data sets supports the feasibility of using CFD in these k inds of cases. The figures also contain the res- ults for the flight conditions, enabling the evaluation of

323 .

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

a>

simulation Id tunnel

so.21 ._____ FO.8) . . . . . . . . . . . . #

-2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0

b)

-2.0 010 2:o 410 610 810 10.0 12.0

a

Fig. 4: a) Drag coefficient b) pitching moment coefficient for the store alone as a function of angle of attack determined experhnent- ally and computationally in different conditions.

the appreciable Mach number effects. Based on the free-stream calculations at the two Mach

numbers, corrections were applied only to the measured drag and pitching moment since the lift slope did not ap- pear to be sensitive to the conditions. The drag correction was formulated as an additional drag coefficient ACD, given by

ACD = -0.3160 + 0.3096/d/1 - Ma2 (5)

The pitching moment coefficient in turn was corrected by a ratio

Cm(Ma)/Cm(Ma = 0.2) = -0.1060 + 1.084/d- (6)

These corrections match the points studied and give qual- itatively reasonable behaviors with the Mach number. For the directional moment, the same correction as for the pitching moment was applied due to the axisym- metry.

Fig. 5: Surface grids for the wing-pylon and the store in the captive position. The rear upper fin of the store was removed to facilitate the Chimera grid block generation, and the attachment lugs and sway braces were omitted.

For the calculation of the captive loads, the wing with the pylon and the store adapter had to be modeled in ad- dition to the store, as shown in Fig. 5. The grid around the wing-pylon combination consisted of four blocks, and the Chimera grid of the store overlaid on the back- ground grid had five blocks. Altogether, the grids con- tained 1441792 cells, but most of the runs were per- formed applying the second multigrid level having l/8 of the cells to save computational effort. In these simu- lations, the algebraic Baldwin-Lomax turbulence model was applied. The steady-state calculations did not reach a fully converged state, but after some 1500 pseudo-time- steps, a cyclic oscillatory behavior emerged, enabling the store loads to be taken as average values over an integra- tion period. The oscillations in the solution were found to be caused by an unsteady wake behind the store, which is certainly a real physical feature of the case.

After these preparations, actual drop simulations could be performed, as described next.

3.4 Drop Simulations In the drop simulations, the situation was assumed to be symmetrical about the aircraft symmetry plane, although in practice, only one store is dropped at a time. This simplification saves some computing time, and it is as- sumed to have a negligible effect on the simulation ac- curacy since the lateral separation of the inner pylons is about 5 meters. The time-step between the updating of the aerodynamic loads was 0.01 s, which had turned out to be sufficient in earlier tests. As a special feature of the calculations, the Mach number in the panel calculations was limited from above to 0.6 to remain within the range of applicability of the scheme. This should not be too serious, bearing in mind the relatively small role of the panel method in the overall simulation. In all cases, the situation was followed for 0.7 s. The CPU time for each

324

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

2 -2.0 -3.0 -4.0 -5.0 -6.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 t

Fig. 8: Comparison of the store pitch attitude histories obtained Fig. 9: Comparison of the store axial distance histories obtained from the simulations and a flight test at HP = 10 000 m and Ma = from the simulations and a flight test at HP = 10 000 m and Ma = 0.80. 0.80.

simulation, including 70 panel solutions for the store and as many Hermite interpolations from the two predeter- mined data sets, was of the order of two hours using a Silicon Graphics Indy workstation.

In Figs. 6 and 7, the simulated drop paths in cases 1 and 2 are illustrated using the panel models. The store appears to oscillate both in pitch and yaw, but the general behavior is benign. Based on all the computations, it is noted that, as the angle of attack at the release increases, the pitch-down of the store becomes stronger, which is a natural consequence of its basic static stability. The equivalent airspeed at the release also has a marked effect on the relative flight path of the extremely draggy store with the maximum axial deceleration of 1.3 G in case 5.

3.5 Comparison with Flight Tests To evaluate the realism of the simulation method, the res- ults were compared to actual flight test data obtained for case I. The separation, taking pIace closeIy in the nom- inal conditions, was recorded by video for subsequent analysis from a chase plane flying alongside the Hawk. The store attitude and location extracted from the tape provide a reference for the computations although a dir- ect comparison is somewhat difficult. One factor redu- cing the validity of the comparison is the relatively poor quality of the video, leading to inaccuracies in its ana- lysis. Another factor is the unavoidable sudden 10 - 15” roll of the aircraft at the release, as noted in the flight test report. This makes a reasonable comparison of ver- tical distances impossible since aircraft dynamics was not modelled in the simulations. However, the most im- portant quantity, the pitch attitude can be studied, and the comparison for it is given in Fig. 8. Another sensible comparison can be made to the axial distance, as shown in Fig. 9.

0.0-t --j- I I I I I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Of7

t

From the comparisons, it is seen that the computed and the measured behavior are qualitatively similar although there are some discrepancies. However, from only one flight test result available one cannot draw any strong conclusions. At least the simulation method appears to have potential to produce realistic results that can be used in preliminary planning of flight tests and in evaluating the hazards of store separations.

4 Conclusions

An affordable hybrid simulation method for the study of store separations has been developed. It combines low- speed wind tunnel data, panel calculations and Navier- Stokes flow simulations in such a manner that realistic studies of blunt stores at mildly transonic speeds can be conducted. Thus, the method has a much wider range of applicability than pure panel-calculation-based schemes while no sophisticated experimental facilities are needed. Real hardware may be used as a wind tunnel model in the required store-only tests. With current computers, the run-times of the steady Navier-Stokes and interact- ive panel calculations are reasonable, and the modeling effort remains within practical constraints.

The separation of an awkward-shaped store at tran- sonic speeds has been studied with the method described. No particular difficulties in the application were en- countered. The results were compared with available limited flight test data for verification. Although there appear to be some discrepancies between the simulated and measured paths of the store, it is concluded that the method is useful for predicting store separation beha- viour.

In the future, the method could be refined as new cases emerge. The Chimera technique of the Navier-Stokes

325

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

solver should be made more flexible to allow the store 8 grid to penetrate the aircraft structure. More general and sophisticated methods for the correction of the wind tunnel data could be devised. Furthermore, the mixing function that combines the results of the captive Navier- Stokes simulations with the corrected wind tunnel data s should be made more general to suit different cases in the best possible way. Although the scheme presented is cer- tainly not perfect, it should offer a practical framework for store separation studies within organizations having limited resources. 10

5 Acknowledgement This work was funded by the Finnish Air Force via Patria Finavitec company.

References i Bore, C., “Integrated design of fighters with stores for

best airforce value,” Progress in Aerospace Sciences, Vol. 33, 1997, pp. 709-730.

2 Bulbeck, C., McKenzie, G., and Fairlie, B., “An En- gineering Methodology for Subsonic Store Trajectory Prediction,” in Proceedings of ICAS98, (Melbourne, Australia), ICAS-98-2.10.3, September 1998.

3 Cenko, A., “ACFD Applications to Store Separation,” in Proceedings of ZCAS98, (Melbourne, Australia), ICAS-98-2.10.4, September 1998.

4 Kraus, W., “Das MBB-UFE Unterschall-Panel- Verfahren. Teil 3: Flugel-Rumpf-Kombination in kompressibler Stromung. MBB-Bericht Nr. UFE 634-70 (o),” Messerschmitt-Bolkow-Blohm, Otto- brunn, Germany, 197 1.

a Salminen, E., “Modernized MBB Panel Code - User’s Guide Including Background Theory. Report B-33,” Helsinki University of Technology, Laborat- ory of Aerodynamics, Espoo, Finland, 1991.

6 Siikonen, T., Hoffren, J., and Lame., S., “A Mul- tigrid LU Factorization Scheme for the Thin-Layer Navier-Stokes Equations,” in Proceedings of ICAS90, (Stockholm, Sweden), ICAS-90-6.10.3, September 1990.

7 Siikonen, T., Kaurinkoski, P., and Lame, S., “Tran- sonic Flow over a Delta Wing Using a k - E Tur- bulence Model,” in Proceedings of ICAS94, (Ana- heim,CA), ICAS-94-2.3.2, September 1994.

326

Kaurinkoski, P., Salminen, E., and Siikonen, T., “Computation of Turbulent Flow over Finned Pro- jectiles,” in Proceedings of AIAA Atmospheric Flight Mechanics Conference, (Scottsdale,AZ), AIAA Pa- per 94-3502-CP, August 1994.

Lehtimaki, R., Laine, S., Siikonen, T., and Salminen, E., “Navier-Stokes Calculations for a Complete Air- craft,” in Proceedings of ICAS96, (Sorrento, Italy), ICAS-96-1 .ll.l, September 1996.

“IGG - An Interactive Geometry Modeller & Grid Generator System.” User Manual, Version 3.5, Nu- meca International s.a., Brussels, 1997.

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

Fig. 6: Simulated flight path of the store in relation to the aircraft in case 1 with HP = 10 000 m, V = 239.6 m/s, Ma = 0.80 and ac = 1.35’. The store is drawn at an interval of 0.1 seconds.

327

(c)l999 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization.

Fig. 7: Simulated flight path of the store in relation to the aircraft in case 2 with HP = 10 000 m, V = 170.7 m/s, Ma = 0.57 and Q = 5.0“. The store is drawn at an interval of 0.1 seconds.

328