(c)l999 American Institute of-Aeronautids & Astronautics

A994 6063

AIAA 99-0126 Prediction of JDAM Separation’ Characteristics from the F/A-18C Aircraft Bruce D. Fait-lie and Regina H. Caldeira Aeronautical and Maritime Research Laboratory, Melbourne, AUSTRALIA

37th AIAA Aerospace ‘Sciences Meeting and Exhibit

January 1 l-l 4, 1999/Rena, NV For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive, Suite 500, Reston, VA 22191-4344

(c)l999 American Institute of Aeronautics & Astro,nautics

1

t ---I Prediction of JDAM Separation Characteristics

from the F/A-ISC Aircraft

Bruce D. Fairlie*and Regina H. Caldeirat Aeronautical and Maritime Research Laboratory,

Melbourne, AUSTRALIA

As the authority responsible for supporting store carriage and release inveetigations for all aircraft in the Australian Defence Force, the Air Op- erations Division of the Aeronautical and Maritime Research Laboratory is continually seeking more efficient methods for predicting the effect of the presence of the parent aircraft on the aerodynamics of the store. Tra- ditionally this data has been obtained from extensive ‘wind tunnel testing, but recently Computational Fluid Dynamics (CFD) tools have gained ac- ceptance as accurate and timely methods, at least in the subsonic regime. This paper presents the results of CFD analyses using the RAMPANT solver designed to test the applicability of such CFD ‘methods to the pre- diction of the trajectories of stores released at transonic speeds. Flight data for the release of a JDAM store from the F/A-1!8C aircraft are used to validate the computational predictions.

Nomenclature Store axial force coefficient (positive to rear) Store side force coefficient (positive outboard) Store normal force coefficient (posi- tive down) Store rolling moment coefficient (positive outboard fin down) Store pitching moment coefficient (positive nose up) Store yawing moment coefficient (positive nose outboard) Store reference diameter (m) Mach number Roll, pitch and yaw rates (deg/s) Non-dimensional roll, pitch and yaw rates ($ etc.) Local velocity (m/s) Free-stream velocity (m/s) Spatial coordinate (m) Angle of attack (deg) Angle of side slip (deg) Vorticity vector Angular velocity vector Roll, pitch and yaw angles (deg)

*Head Flight Mechanics Applications, Air Operations Division, Senior Member AIAA.

tProfessional Officer, Air Operations Division. Copyright @ 1999 by the Commonwealth of Australia.

Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

Introduction

T HE Air Operations Division (AOD) of the Aeronautical and Maritime Research Labo-

ratory is responsible for providing aerodynamic data and trajectory predictions for store carriage and release investigations for all aircraft in the Australian Defence Force. In common with all practitioners in this field, our major problem is to deal with the complex variations in aerodynamic characteristics experienced by a store while it re- mains within the influence of the parent aircraft. In this region, mutual interference effects between the store and the parent aircraft, its pylons and other stores lead to a highly complex flow field. At transonic Mach numbers, the situation is ex- acerbated by the appearance, development and motion of shock waves.

Traditionally, store aerodynamics have been determined from wind tunnel testing, using ei- ther the Captive Trajectory System (CTS) or the “grid” method to measure aerodynamic forces and moments on sub-scale models. The development of Computational Fluid Dynamics (CFD) as a vi- able tool for aerodynamic prediction, especially in the last few years, has led to proposals for the integration of CFD into the store trajectory pre- diction process.

For some time, AOD has been using the po- tential flow “panel” method VSAEROl to predict the aerodynamics characteristics of stores within the flow field of the parent aircraft. Solutions for quite complex geometries may be generated quite quickly (in the order of ten minutes CPU

1 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPERER-0126

(c)l999 American Institute of Aeronautics & Astronautics

time) on currently available processors. This has allowed the code to be used to generate aerody- namic data equivalent to wind tunnel “grid” data in an acceptable time (one to two days). We now have sufficient confidence in trajectories based on aerodynamic data produced by VSAERO used in this manner to accept clearance of stores from several configurations based solely on the CFD re- sults, without conducting any wind tunnel testing. However, all these cases have involved releases at low Mach numbers, where the flow field is entirely sub-sonic. With the appearance of shock waves, potential flow codes such as VSAERO become un- usable. Unfortunately, this transonic regime is where most practical store separation problems occur.

For transonic conditions, the ideal CFD ap- proach would be to solve the time-dependent Navier-Stokes equations. For configurations of the complexity typically involved in the release of a store from a modern jet aircraft, such solu- tions, while certainly not beyond the state of the art, currently require CPU times orders of mag- nitude too large to to be practicalable. Solutions of the Euler equation are, however, now feasible. While execution times remain much too long to suggest that such methods can replace the wind tunnel, AOD has been investigating their use to support and extend wind tunnel testing. It has become clear that such methods can be of signifi- cant benefit in at least three areas: in generating trajectory predictions prior to wind tunnel test- ing, thus allowing wind tunnel test programs to be concentrated in the most productive areas; in providing details of the flow field and hence ex- planations for unexpected values measured in the wind tunnel; and in quantifying the effects of sup- port and wind tunnel wall interference on wind tunnel measured data.

Before any CFD-based method may be used with confidence, its predictions must be vali- dated, preferably against flight measured data. The F/A-18C JDAM CFD Challenge, sponsored jointly by the AIAA and the Joint Weapons Mod- ification and Simulation Capability (WSMAC) Applied Computational Aerodynamics (ACFD) of the US DOD, provides an opportunity to carry out such a validation. This paper presents the results of an investigation to evaluate the perfor- mance of a commercial Euler Flow solver mar- keted by Fluent Inc. against the data supplied by the JDAM Challenge. Predictions of both car- riage loads and store trajectory data are compared with the experimental database. Issues concern- ing grid generation, the time and effort required to generate the grid and create solutions, compu- tational efficiency and general ease of use are also

considered.

Background Over the past few years there have been several

attempts organized to validate CFD-based store trajectory prediction with a view to hastening their introduction into the store certification pro- cess. Two notable attempts have used a Generic Wing/Pylon/Finned Store database,3 and an F- 16/Generic Finned Store database (see for exam- ple Kern3). While each of these attempts have created useful comparisons and generated much important information, both suffered from being wind tunnel generated test cases, without many of the ‘%eal” effects experienced in flight. In an at- tempt to overcome this limitation, the Naval Air Systems Command has made available an exten- sive database of correlated wind tunnel and flight test measurements4 of the release of a JDAM from an F/A-18C. The F/A-18C JDAM CFD Chal- lenge is based on this database.

Two particular release conditions have been se- lected from the F/A-18C JDAM database for the Challenge. These consisted of a high subsonic and a low supersonic release. Details of the release conditions for each case are given in Table 1.

TEST CASE PARAMETERS Case1 Case2

Mach Number 0.962 1.055 Altitude (ft) 6332 10832 a: 0.46’ -0.65” Dive Angle $30 440

Table 1 Release conditions for the F/A- lSC/JDAM CFD Challenge.

For each case, the aircraft/store configuration utilised is as follows: an F/A-18C with a 330 gal- lon fuel tank on the inboard pylon, the JDAM under consideration on the outboard pylon and an AIM-9 air-to-air missile mounted on the wing tip station. This configuration differs from that used in the flight tests (which had no tip missiles) and that used in the wind tunnel tests (which had AIM-9 missiles on the wing tip and AIM- 7 missiles on the armpit station). The US Navy has conducted4 an investigation into the sensitiv- ity of the JDAM trajectories to these differences. The results showed that the differences in con- figuration had negligible effects on trajectories computed from-both wind tunnel and flight test results.

The F/A-18 JDAM data is a particularly good test case due to the presence of non-linearities in the variation of carriage load data with Mach number. While these results were first noticed in

2 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

the wind tunnel data, they were subsequently con- firmed by an examination of the flight test results. The non-linearities are particularly notable in the variation of pitching and yawing moments, both exhibiting a strong increase between M = 0.90 and M = 0.95 following a gentle decrease from M = 0.80 to M = 0.90. If CFD is to be accepted as a legitimate tool for store clearance, it must be able to predict this type of behaviour.

Computational Method All the CFD analyses reported here have been

conducted with one of the flow solvers supplied by Fluent Inc. The majority of the solutions pre- sented make use of the RAMPANT code, but a few results are presented from the recently re- leased Fluent Version 5 family of solvers.

RAMPANT is designed for the efficient solu- tion of high-speed compressible flows. It solves the governing equations on an unstructured hy- brid grid which may contain mixtures of tetra- hedra, prisms and hexahedra. For the solutions presented here, all grids consist of tetrahedra alone. While RAMPANT is capable of solving the Navier-Stokes equations for either laminar or tur- bulent flow, in all cases presented here, the code has been used in its inviscid mode. In this mode, the code solves the Euler equations. Integration in time is handled via a multi-stage Runge-Kutta scheme with full-approximation storage multigrid (with a user specified number of levels) conver- gence acceleration. Generally all equations are solved using second-order discretization. A first order scheme is available for use in cases in which initial convergence is difficult to obtain. More de- tails on the solution algorithms may be obtained from Fluent I~c.~

The release of Fluent 5 has added an implicit compressible flow solver option in addition to the original (explicit) RAMPANT solver. This new option makes use of an algebraic multigrid method in conjunction with a point Gauss-Seidel solution process. The new implicit solver allows the use of a much larger time step (CFL number) for steady flow calculations, leading to faster convergence and shorter execution times.

Both solvers incorporate a solution-adaptive mesh refinement scheme that allows the grid to be refined and/or coarsened on the basis of ei- ther geometric or numerical solution data. Cells may therefore be added where they are needed to better resolve features of the flow. In all of the solutions include in this paper, adaption has been performed on the basis of gradients in static pres- sure in order to better resolve shock waves.

Extensive validation studies have been con- ducted on the Fluent solvers both within and out-

(c)l999 American Institute of Aeronautics & Astronautics

side AOD. Fluent Inc. provides an extensive suite of code validation cases covering a wide range of flow geometries and flow conditions. Within AOD, the results of RAMPANT analyses have been compared with a wide range of wind tun- nel and flight test results for the F-111C and F/A-18 aircraft, together with the free-stream characteristics of a wide range of stores. In all cases, the comparisons show good agreement for those conditions in which an Euler code can be expected to produce reasonable solutions. For those cases where strong shocks and subsequent extensive boundary layer separation are present, RAMPANT results diverge from the experimental values, as would be expected of a code solving the inviscid equations of motion.

Computational Geometry and Grid Generation

While the Fluent suite of codes includes an un- structured grid generator, we have chosen to make use of a grid generator marketed by ICEM CFD Engineering. This code, known as ICEM CFD Tetra, creates unstructured tetrahedral grids. We also use an optional add-on module to ICEM CFD Tetra known as ICEM CFD Prism. This module is used to create a hybrid grid with high aspect ra- tio prism layers located near solid surfaces to allow efficient modelling of the high gradients associated with boundary layers. However, this module has not been used in the current investigation.

Fig. 1 Computkional mesh for JDAM in car- riage position.

ICEM CFD Tetra is highly automated, not re- quiring a triangular surface mesh as a starting point, but generating the entire volume mesh di- rectly using an &tree approach. Its input con- sists of a set of defined surfaces, curves and pre- scribed points. The triangular surface mesh is

3 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

(c)l999 American Institute of Aeronautics & Astronautics

Fig. 2 Detail of computational mesh around JDAM

unity as possible. required to be tangential to the specified sur- faces. The specified curves are used to ensure that the mesher t&es note of surface discontinu- ities by aligning triangle edges along these curves. Similarly, a prescribed point is used to allow the mesher to recognise sharp corners by placing tri- angle vertices at such points. Mesh sizes may be specified by the user on all specified surfaces and curves. The rate of change of cell size from ar- eas of smaller to larger size may also be specified. In addition, non-physical entities (surfaces, curves and points) may be added to the geometry, either on the surface or inside the flow field, to allow local control of mesh size and growth rates.

ICEM CFD Tetra incorporates sophisticated mesh editing and diagnostic tools to quickly lo- cate and correct any meshing errors, and a mesh smoother. The smoother works by moving nodes, merging nodes, swapping edges and in some cases

deleting bad elements altogether, with the aim of producing a volume grid of the highest quality i.e. with aspect ratios of all tetrahedra as close to

The PLOT3D format geometry file of the F/A- 18C JDAM configuration provided by USN was read directly into ICEM CFD DDN, the CAD system associated with the mesher. This mod- ule was used to generate the surfaces, curves end points defining the features of the geometry re- quired as input by Tetra. Only the port semi-span of the configuration was modelled, with a sym- metry boundary condition imposed on the lateral plane of symmetry. A far-field boundary was provided in the form of a semi-sphere centred on the aircraft’s centre of gravity, with a radius of approximately five fuselage lengths. The fi- nal tetrahedral mesh is shown in Figures 1 and 2. Note the use of a significantly smaller sur- face mesh size on the JDAM store. This was motivated by the need to produce high quality estimates of JDAM carriage loads. In general, ICEM CFD Tetra produced surface and volume meshes quickly and efficiently. However, the very thin AIM-9 canards proved to be a meshing chal-

4 OF 10 .i

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

-- -1s- (c)l999 Americ% Institute of Aeronautics & Astronautics

.

lenge, as did the very detailed JDAM strakes and the JDAM/pylon interface. These areas required some manual intervention to correct minor ehors generated during the meshing process.

Carriage Load Predictions Computations were carried out on the tetrahe-

dral grid generated by ICEM CFD Tetra using the RAMPANT solver. Carriage loads on the JDAM were extracted from solutions conducted at a range of Mach numbers between 0.8 and 1.2 at an aircraft angle of attack of zero. Results for JDAM pitching and yawing moments are shown in Figures 3 and 4. The agreement between com-

putation and wind tunnel is generally quite good.

-3.0 ’ I 0.8 0.9 1.0 1.1 1.2

M

Fig. 3 Variation of JDAM pitching moment at carriage with Mach number.

o.o’.. “““I”,... ,,’ 0.8 0.9 1.0 1.1 1.2

M

Fig. 4 Variation of JDAM yawing moment at carriage with Mach number.

The reason for the unusual variation in both pitching and yawing moments is clarified by an examination of Figures 5 and 6 which show con- tours of Mach number on the aft end of the JDAM and the 330 gallon fuel tank mounted on the in- board pylon. Clearly, at a Mach number of 0.8, a shock has formed on the lower surface of the wing. This shock is stronger in the “passage” formed between fuel tank and the JDAM, but is

clearly still well upstream of the JDAM fins. As the Mach number is increased, this shock moves quickly aft, reaching the JDAM fins at a Mach number of approximately 0.9 (see Figure 6). As the shock strengthens further and moves further aft, it generates increasing values of nose-down pitching moment and nose-out yawing moment.

While the overall agreement between CFD pre- dicted carriage loads and the experimental values is generally good, we were disappointed with the marked disagreement in yawing moment at super- sonic velocities. In many respects, this region of the Mach number envelope should be the easier to predict, shock waves generally being fixed at trailing edges and boundary layers being gener- ally thin and attached. Several possible sources for this discrepancy were investigated, but none showed any significant effects. This ultimately led to a x-examination of the engine inlet face modelling. Initially, the possibility that the state of the flow into the engine inlet face could have an effect on the carriage loads experienced by the JDAM mounted on the outer pylon had been dis- counted. The boundary condition at the inlet face was specified as a constant value of static pressure. The particular value of static pressure was chosen so that the engine ‘Lswallowed” the approaching stream tube with little or no spillage, equivalent to a moderate engine power setting. In the absence of any knowledge of the state of flow through the engine inlet face in the wind tunnel tests, several solutions were generated in which there was no flow through the engine face. This proved to have the effect of increasing the supersonic values of yawing moment into close agreement with the ex- perimental data, while having little or no effect at lower Mach numbers or on other coefficients. The results for pitching and yawing moments obtained with no flow through the inlet face axe included in Figures 3 and 4.

Trajectory Simulation Method The trajectories followed by the JDAM after its

release have been simulated using the Defence Sci- ence and Technology Organisation Release Eval- uation Suite (DSTORES). DSTORES has been developed within ‘AOD over the past few years to replace a series of old, poorly documented (and hence difficult or impossible to maintain) FOR- TRAN codes that had been created in an ad hoc fashion over the years by their individual authors. DSTORES has been designed to be a fully inte- grated stores release analysis package which, when complete, will consists of:

l a module which integrates the six degree-of- freedom equations of the store, taking into

5 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

----_- ---

(c)l999 American Institute of Aeronautics & Astronautics

1.4

1.3

1.2

':

0.6

Fig. 5 Contours of Mach number: A4 = 0.8, (Y = 0.0.

1.6

Fig. 6 Contours of Mach number: M = 0.9, a = 0.0.

6 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-%126

account external forces generated by the ejec- tor system as well as aerodynamic forces,

a module which generates store aerody- namic characteristics using wind tunnel data, CFD data or a locally developed empiri- cal method, the Flow Field Decomposition (FFD) method,

a module which generates values of miss dis- tance throughout a trajectory and identifies minimum miss distances, paying particular attention to regions in which the miss dis- tance is decreasing,

a module which runs the trajectory predic- tion module for a range of values of its in- put parameters determined on the basis of a Monte Carlo statistical analysis, in order to investigate the effects of such statistical vari- ations on the minimum miss distances, and

a module which displays data in several for- mats for presentation and discussions.

These modules are all to be linked by a common Graphical User Interface (GUI). In addition, the suite produces output files in a format suitable for input to the AOD Graphics Replay System (GRS). This is a fully three-dimensional animated display system featuring extensive interactive user controls on viewpoint selection and animation speed.

For the present configuration, all trajectory pre- dictions have been made using the empirical FFD method. Given a database of store free-stream aerodynamic characteristics, this method requires just two further CFD analyses to predict a trajec- tory: a set of CFD generated carriage loads and a computation of the flow field beneath the par- ent aircraft without the presence of the released store. This allows the prediction of release trajec- tories for a wide range of release conditions to be calculated quickly and cheaply. While the accu- racy of the resulting trajectories may suffer when compared with other more complex methods, it is adequate for directing wind tunnel test programs towards the most %fficult” release conditions, the purpose for which it was created.

Full details of the FFD method may be found in Bulbeck et al.,6 but for completeness a short description will be included here. To begin, the velocity field (ui(x), i = 1,2,3) beneath the par- ent aircraft without the released store is expanded in a Taylor series about the geometric centre (xo) of the current location of the store, thus

(c)l999 American Institute of Aeronautics & Astronautics ----f*:

ui(xo + Ax) = ui(xo) + h( )Azj+ 82 xo 3

*(xo)AzjAxk + . . . (1)

#8Xjt3Xk

An approximation to the flow field in the vicin- ity of the store is then obtained by discarding terms of order Ax2 and higher in the expansion. The two remaining terms are the average velocity vector ‘~ci(xn), which defines the average angles of incidence and side slip over the store, and the ve- locity gradient tensor $$ = Aij. The velocity gradient tensor ‘may be split into symmetric and anti-symmetric components

Aij = Sij + Wij (2)

where

is the symmetric component, which de6nes the average shear velocity along the store. Experience has shown that contributions to the overall values of the store’s aerodynamic coefficients from this source may be safely ignored.

Wij = i (Aij - Aji)

is the anti-symmetric component. Wij defines the average flow curvature along the store, and is re- lated to the components of the vorticity vector w, of the fluid by

The angular velocity of the fluid (F) relative to the store (S) is

(6)

The angular velocity of the store relative to the fluid is defined as

P i-&F= q =-n$‘S [I T

(7)

and may be used to relate the flow curvature to pseudo store rotation rates.

In practice, to ,ensure that the effects of just the velocity field in the immediate vicinity of the store are taken into account, the evaluation of the flow field in equation (1) is restricted to a small

7 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

(c)l999 American Institute of Aeronautics & Astronautics

volume in the vicinity of the store known BS the “surrounding volume”. The aerodynamic forces and moments may then be estimated based on the values of the mean angles of incidence and side slip ((II and p) and the mean angular rates (p, Q and T) calculated from the decomposition of the flow field, using equations such as

where the values of CZ,, CZ, and CZ, axe ob- tained from a database of store free-stream aero- dynamics.

Since the FFD method does not take into ac- count the mutual interference between the store and the parent aircraft, the method becomes in- accurate close to the carriage position. Hence, within one store diameter of carriage, estimates of interference coefficients are obtained by linear interpolation between the carriage loads and the coefficients estimated by the FFD method one store diameter below carriage.

Trajectory Predictions Predictions of the trajectory followed by the

JDAM store have been computed using the FFD method together with estimates of carriage loads obtained from CFD analyses using the RAM- PANT solver in its Euler mode. Store mass

and inertia properties, ejector force-displacement histories, and wind tunnel measurements of free- stream static aerodynamics and damping derive tives, were obtained from data made available by the US Navy.

1w I

so -

60 - PredIctad 0 --- PredIcted 6

401 I 0.0 0.2 0.4 0.6 0.8 1.0

Time (eacond6)

Fig. 7 Comparison of flight and predicted tra- jectory data: M = 0.962

Comparisons between the predicted variation of store Euler angles and those measured in flight are presented in Figures 7 and 8 for the M = 0.962 and M = 1.055 test cases respectively. As may

100

60 - Pmdkid 0 --- Predkted 6

0.2 0.4 0.6 0.6 Time (seconds)

Fig. 8 Comparison of flight and predicted tra- jectory data: M = 1.065

be seen, in both cases, the predicted angles follow the general trends of the flight data quite well, at least for the first 400 ms after release. After that time, the predicted and flight measured an- gles begin to diverge. In general, this will reflect the integrated effect of small errors in the pre- dicted angles at earlier times. However, there is a complete failure to predict the rapid increase in roll angle from approximately 450 ms for both re- lease Mach numbers. At present, the reasons for this disagreement are not known.

Predictions of the motion of the store cen- tre of gravity (not shown here) exhibit a simi- lar degree of agreement with flight data in the early part of the trajectory, with subsequent di- vergence. In general, the x- and z-components are predicted well throughout, with a consistent under-estimation of the y-component later in the trajectory.

It is notable that the predicted values of roll an- gle, particularly for the M = 0.962 release, appear to lag the flight values by approximately 100 ms. The lag is also present in the M = 1.055 data, but only for the early part of the release trajectory. The reason for this discrepancy has been traced to the behaviour of yaw angle during the ejection phase of the trajectory. DSTORES predicts that the friction between the ejector feet and the store remains significantly greater than the total side force on the store throughout the ejection phase. Thus, with no sliding motion possible between the ejector feet and the store, the store is constrained to remain at zero yaw angle until one of the ejec- tors reaches the end of its stroke. The flight data, on the other hand, shows yaw angle growing from the beginning of the ejection phase.

In general, the quality of the trajectories pre- dicted using the FFD method are quite good, certainly good enough for directing a wind-tunnel

8 OF 10

AMEFUCAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

.

test program towards “difficult” releases, the pur- 7 pose for which the method was created. The pre-

dictions are certainly not of sufficient accuracy to allow them to be used as the basis for certification. This is not surprising, given that these particular releases are most certainly not free of mutual in- terference between the aircraft and store, one of the basic assumptions on which the FFD method is based. It may be possible to increase the ac- curacy of the method by incorporating data from CFD analyses for store positions below carriage, only relying on the FFD method when the store is further away from carriage, and hence less subject to interference effects. This will be investigated as part of our ongoing work in this area.

Solution Metrics All unstructured tetrahedral grids were gener-

ated using ICEM CFD Tetra as described above. Experience with this code has shown that the time required to develop a grid for a new store, inte- grate that grid into a preexisting aircraft grid and refine the combined grid to a state suitable for input to the RAMPANT solver is approximately two weeks. In the present case, the time required to produce a final grid was considerably longer, in the order of ten weeks. The increase was due to the need to produce a grid for the parent aircraft as well as the JDAM, the use of staif with little experience with the Tetra code and some difficul- ties experienced with gridding the JDAM strakes and the wing tip missile canards.

The initial grid as input to the RAMPANT solver consisted of just over 1.05 million tetrahe- dra. A typical RAMPANT run consisted of about 200 iterations with the value of the CFL number set to 0.5, followed by about 300 iterations with CFL set to 1.0. This was generally sufficient to re- duce the normalised residuals of continuity, x-, y- and z-momentum and energy by between two and one half and three orders of magnitude compared with their initial values. At this stage, the grid was adapted in regions in which the static pres- sure gradient exceeded a particular value (initially set to 10% of its maximum value, but varied de- pending on the number of tetrahedra generated in the new grid) in an attempt to better define shock waves. After adaption, the grid generally contained somewhat more than 1.25 million tetra- hedra. The solution was then iterated for up to a further 500 iterations. After an initial transient created by the adaption of the grid, the residu- als once again fell to their previous, or even lower values. The variation of residuals with iteration number for the solution at M = 0.9,a = 0 is shown in Figure 9. Note that at this Mach number the passage shock is just moving onto the JDAM

(c)l999 American Institute of Aeronautics & Astronautics

fins. Thus this ‘is a “difficult” solution. Residual histories for other solutions generally show better convergence. The variation of the carriage loads on the JDAM were also monitored throughout the process to ensure convergence. Their variation with iteration number for the same case is shown in Figure 10. Note that despite the less than opti- mum behaviour of the residuals, the aerodynamic coe%icients show satisfactory stability. I Fmldld. I

Fig. 0 Variation of solution residuals with it- eration number.

4.0 ~ 3.0

2.0

lh ’

_/-------___--__--_---~----~~-. 0.0 ill---

1 1.0 \ 1 - CL - cm

u 1 --- c, 3.0’ 8 8 ’

0 200 400 800 1000 1200 Iteration Number

Fig. 10 Variation of JDAM aerodynamic char- acteristics with iteration number.

All computations have been carried out on a Silicon Graphics Origin 2000 server. This ma- chine has sixteen RlOOOO processors running at 250 MHz and is equipped with 4 GB of mem- ory. Typically, the initial 500 iterations on the m-r-adapted grid required a little less than 40 hours of CPU time on a single processor, and occupied approximately 460 MB of memory. After adap- tion, the additional 500 iterations used somewhat more resources, the exact amount depending on the number of ‘tetrahedra in the adapted grid. While the vast majority of the calculations pre- sented here were carried out on a single CPU, the RAMPANT code may be run in parallel. Thus far, no more than four parallel processors have

9 OF 10

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126

been used, yielding a speed-up of just over 3.8 compared with a single processor.

Future Work There remain several lines of investigation rel-

evant to the configuration studied here that have not been thoroughly investigated. First, and most important, is the question of the relevance of the inviscid Euler code solver used here to this type of configuration. Typical of releases at transonic Mach numbers and angles of attack close to zero, a strong shock is present on the lower surface of the wing, particularly within the passage formed between the fuel tank and the JDAM. The devel- opment and movement of this shock with Mach number have a marked influence on the carriage loads experienced by the JDAM. We have seen, however, that the RAMPANT solutions match the measured loads quite closely. Is this a coinci- dence, or can we expect this type of agreement for a wide range of, similar configurations? There is no easy answer to this question, but much could be learnt from a viscous Navier-Stokes solution for the same configuration. RAMPANT (and the new Fluent 5 version) may be operated in a viscous mode, providing a choice of a wide range of tur- bulence models. It is our intention to follow this path, making use of the ICEM CFD Prism module to generate prismatic cells (rather than tetrahe- dra) close to the surface to better resolve the gradients within the boundary layer. However, the total number of grid cells required for a vis- cous solution is still expected to be almost twice that for the inviscid solution, leading to commen- surate increases in execution time and memory requirements. Clearly, such solutions will not be- come commonplace in the near future.

One possible solution to the increased resource requirements for viscous solutions is to model the boundary layer only on those parts of the configu- ration where it is essential. This would obviously include the store and its pylon, other stores and pylons (such as the fuel tank in the present case) and the lower wing surface. But do we also need to model the viscous flow over the upper surface of the wing in order to correctly model the circu- lation? What-about the fuselage? Such questions can only be answered by numerical experiments.

The use of a very quick and simple method (the FFD method) to generate store trajectories using a minimum number of CFD evaluations has been shown here to produce quite reasonable agreement with measurement. Can the quality of these pre- dictions be increased significantly by the addition of the results from one or two more CFD solu- tions? We intend to investigate this proposal, beginning by integrating the results from a CFD

(c)l999 American Institute of Aeronautics & Astronautics

solution for the store positioned one store diam- eter below the carriage position into the FFD method.

Finally, there are two areas of investigation which we fully intended to complete during the current study, but we were defeated by a lack of available time. These are a study of the sensitivity of the CFD solutions to grid density, especially on the JDAM, and to the particular value and distri- bution of mass flow through the engine face. Both these areas will be included in our future work.

Conclusions The carriage loads acting on a JDAM store

mounted on the outboard wing pylon of an F/A- 18C aircraft have been successfully computed us- ing RAMPANT, a commercial CFD package solv- ing the Euler equations. The non-linear variation of the predicted carriage loads with Mach number, particularly pitching and yawing moments, shows good agreement with wind tunnel measured val- ues. The utility of CFD analyses for illustrating the physics behind such variations has been well demonstrated. The computed carriage loads, to- gether with CFD predictions of the non-uniform flow field beneath the aircraft, have been com- bined with a simple empirical method to generate estimates of the aerodynamic loads acting on the store throughout its release. Predicted release trajectories based on these aerodynamic load es- timates demonstrate quite good agreement with flight measured data. While the quality of these predictions are sufficient to direct a wind-tunnel test program towards “difficult” release condi- tions, they are not accurate enough to be used as the basis for certification.

Acknowledgements The authors wish to thank our colleagues, espe-

cially Dr. Jaime-Bulbeck, Mr. Phillip Postle and Mr. Greg McKenzie, for their support and assis- tance throughout this project.

References lAnalytical Methods Inc., “VSAERO User’s Manual,”

1997. 2Heim, E., “CFD Wing/Pylon/Finned-Store Mutual

Interference Wind Tunnel Experiment,” Tech. Rep. AEDC-TR-91-84, AEDC, 1991.

3Kern, S. and Bruner, C., “Extended Carriage Analysis of a Generic Finned Store on the F-16 Using USMBD,” AIAA Paper 96-2456, June 1996.

4Cenko, A. and Lutton, M., L‘ACFD Applications to Store Separation,” ICAS Paper A98-31529, 1998.

5Fluent Inc., “Fluent 5 User’s Guide,” July 1998. OBulbeck, C. J., McKenzie, G. J., and Fairlie, B. D.,

“An Engineering Methodology for Subsonic Store Trajec- tory Prediction,” ICAS Paper A98-31528, 1998.

10 OF I6

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 99-0126