NASA Contractor Report 4465

A Computational Examination of

Directional Stability for Smooth

and Chined Forebodies at High-a

Ramakrishnan Ravi and William H. Mason

Virginia Polytechnic Institute and State University

Blacksburg, Virginia

Prepared for

Langley Research Center

under Grant NAGl-1037

National Aeronautics andSpace Administration

Office of Management

Scientific and TechnicalInformation Program

1992

TABLE OF CONTENTS

SUMMARY 1

INTRODUCTION 2

LIST OF SYMBOLS 4

F-5A FOREBODY 6

F-5A Grid Details 6

Results and Discussion of Computations on the F-5A Forebody 7

ERICKSON CHINE FOREBODY 11

Erickson Forebody Grid Details 11

Results and Discussion of the Computations on the Erickson Forebody 12

SOLUTION STRATEGY FOR PARAMETRIC GEOMETRY STUDY 15

ANALYTIC CHINE FOREBODY STUDY 16

Discussion of Results for the Generic Chine Forebodies 18

Effect of varying b/a 18

Effect of varying the chine angle 20

Effect of unsymmetrical b/a 21

Effect of unsymmetrical cross-sections to vary chine angles 22

Effect of varying the planform shape 22

CONCLUSIONS AND DESIGN GUIDELINES 23

ACKNOWLEDGEMENTS 25

REFERENCES 26

TABLES 27

FIGURES 29

iKBL.,.L.I._IN.I_INZION ALtJI Br.AN!

°°o

• r,,_ _ - _--r- t

A COMPUTATIONAL EXAMINATION OF

DIRECTIONAL STABILITY FOR SM(NTrH AND CHINED FOREBODIES AT HIGH-a

R. Ravi

William t-L Mason

Virginia Polytechnic Institute and State University

SUMMARY

Computational Fluid Dynamics (CFD) has been used to study aircraft forebody flowfields at

low-speed, high angle-of-attack conditions with sideslip. The purpose is to define forebody

geometries which provide good directional stability characteristics under these conditions. The

flows over the experimentally investigated F-5A forebody and Eriekson forebody, previously

computed by the authors, were recomputed with better grid topology and resolution. The results

were obtained using a modified version of cfi3d to solve either the Euler equations or the

Reynolds equations employing the Baldwin-Lomax turbulence model with the Degani-Schiff

modification to account for massive crosstlow separation. Based on the results, it is concluded that

current CFD methods can be used to investigate the aerodynamic characteristics of forebodies to

achieve desirable high angle-of-attack characteristics. An analytically defined generic forebody

model is described, and a parametric study of various forebody shapes was then conducted to

determine which shapes promote a positive contribution to directional stability at high angle-of-

attack. An unconventional approach for presenting the results is used to illustrate how the positive

contribution arises. Based on the results of this initial parametric study, some guidelines for

aerodynamic design to promote positive directional stability are presented.

INTRODUCTION

Current and future fighter aircraft are likely to be required to operate at high angles-of-attack

where they experience flowfields that are dominated by large regions of separated vortical flows.

Considerable research is being done both in the experimental and computational areas to

understand the physics of such complex flows. A good understanding of these flows would enable

engineers to design fighter aircraft to achieve better maneuverability at high angles-of-attack. At

high angies-of-attack the forebody aerodynamic characteristics make significant contributions to the

complete configuration aerodynamics. The surveys by Chambers (Ref. 1) and Chambers and

Grafton (Ref. 2) present the basis of the current understanding of high angle-of-attack

aerodynamics.

One of the specific aerodynamic characteristics of interest is directional stability. For the F-

5A, which has good high angle-of-attack characteristics, it has been shown experimentally (Ref. 3)

that the forcbody makes a significant positive contribution to directional stability at angles-of-attack

above which the vertical tail ceases to be effective. That forebody had a smooth cross section,

although it was not axisymmetric. The current authors recently demonstrated that the experimental

results could also be predicted using Computational Fluid Dynamics (CFD) methods (Refs. 4 and

5). The ability to reproduce previously obtained experimental results meant that it would be valid to

use CFD to try to design shapes for specific aerodynamic characteristics at high angle-of-attack,

where large regions of separated flow are present.

Future advanced fighters are likely to possess chine type forebodies, as evidenced by the YF-

22 and YF-23 configurations. For these aircraft, high levels of agility are demanded, and the

aerodynamic characteristics at high angle-of-attack play an important role in determining aircraft

handling qualities and agility.

Because of the interest in chine-shaped forebodies, a key issue in the application of

computational methods to forebody design is the ability to treat chine sectional shapes. Few general

chine-shaped forebody wind tunnel tests are available to use for comparison with computational

2

methods.Oneis the wind tunnel investigationconductedby Erickson and Brandon(Ref. 6, the

"Erickson Forebody"). In that studythe chine effects were investigatedfor a generic fighter

configuration, and pressuredistributions were measuredon the chine forebody. All forebody

resultswere acquiredin thepresenceof the wing. More recentlyKegelmanand Roos (Refs.7

and8) studiedexperimentallythe influenceof crosssectionalshapeon thevortexflowfield at high

alpha. They comparedthe surfacepressuresand the aerodynamic loads betweena circular,

elliptical anda chinedcrosssectionat high anglesof attack.Hall (Ref.9) studiedtheinfluenceof

the forebodycrosssectionalshapeon wing vortex-burst location.This studyalso involved the

comparisonof a two chine cross sections with a circular section.

The results were obtained using cfi3d (Ref. 10) to solve either the Euler equations or the

Reynolds equations employing the Baldwin-Lomax turbulence model with the Degani-Schiff

modification to account for massive crossflow separation. Version 1.1 of the code with the

modifications as described in Ref. 5 was used in all the computations.

In this report we first repeat the results obtained on the F-5A forebody (Ref. 5) using a grid

strategy better suited to the geometry to assess possible grid sensitivity on the previous results.

Secondly, we compare computed predictions with the experimental data for the chined class of

forebodies using the "Erickson Forebody" (Ref. 6) at t_ = 30 ° (5 ° and 10 ° sideslip)and at tx = 40 °

(10 ° sideslip). The above two cases were used to establish confidence in the methodology being

used for the analysis of various generic cross sectional forebodies.

An analytic model which can be used to systematically study forebody aerodynamics for

families of forebody shapes at high alpha is proposed. Using this model, a computational study is

carded out to determine which shapes lead to the best directional stability characteristics. The

reference parameters used in computing the forces and moments for the cases studied in this report

are presented in Table 1. The report concludes with some guidelines for high angle-of-attack

forebody design.

3

LIST OF SYMBOLS

a

b

b"

C

cL

Cn

Cn#

%%cyFS

l

m,n

M_

P

P_

q_

Re l

Sref

U

Vsep

x,y,z

XN

maximum half breadth of the generic forebody definition

maximum centerline of the generic forebody definition

wingspan

mean aerodynamic chord

lift-force coefficient, Yfft/qo.Sre f

yawing-moment coefficient, yawing momentlq.,,Srefb"

directional stability derivative, JC n / Jfl

pressure coefficient. (p-p.o)lq**

side-force coefficient, side force/q**Sre f

sectional side-force coefficient, sectional side forcelq**Sre f

fusehge station

model length

adjustable parametric coefficients

free-stream Mach number

pressure

fr_-str_m pressure

fr_os_ dynamic pressure

Reynolds number based on model length, l

reference area

wall friction velocity, _/cw / p

cross flow velocity magnitude at separation point ( chine edge)

body coordinate system :x positive aft along model axis,

y positive to right and z positive up

distance from the tip of the nose to the station where the planform span becomes

a constant.

inner law variable, yu*/v

angle of attack, deg

4

V

P

_w

angle of sideslip, dcg

kinematic viscosity

density

shear stress at the wall

difference between leeward and windward Cp across the vertical plane of

symmetry

5

F-5A FOREBODY

The wind tunnel experiment demonstrating the dominant contribution of the F-5A forebody

to directional stability at high angle-of-attack was simulated computationally in the first part of this

work (Ref. 5). This forebody had been tested by Sue Grafton, et.al, at NASA Langley Research

Center and the results are available in Ref. 3. The geometry math model and the comparison with

the wind tunnel model was described in detail in Ref. 5. In that study the grid was constructed

from two dimensional O-type cross flow grids which are longitudinally stacked, constituting a

single block H-O topology as shown in fig. 1. It is difficult to resolve the flow details near the

nose using an H-O topology. Hence, we investigated the same geometry using an alternate grid

system to assess possible grid effects on the results.

F-5A Grid Details

The inviscid calculations on the F-5A (Ref. 5) were repeated on the new grid shown in

fig. 2. This grid consists of two blocks, where the first block used a C-O topology to improve the

grid resolution at the nose. This grid was generated using a transfinite interpolation grid generator

provided by Ghaffari (Ref. 11). The ftrst block extends from the nose to the point where the fiat

sidewall starts i.e., 14.025 inches from the nose, as explained in Ref. 5. The inviscid calculations

were performed on a grid which used 32 axial, 93 circumferential and 45 radial points ( 32 x 93 x

45 ). The outer boundary extends 32.7 inches radially outward and is comparable to the length of

the forebody which was 31.02 inches. The second block used the previous H-O grid topology

with 13 axial, 93 circumferential and 45 radial points (13 x 93 x 45). The C-O grid generator used

for the first block requires a user specified normal distance to the first grid point and the distance of

the outer boundary as the input. The H-O grid generator used for the second block uses the

distance of outer boundary and a stretching parameter as the input. Care was taken to ensure that

6

thedistanceof thefirst grid normalto thesurfaceis thesamefor boththeblocksat the interface.

Figures 3 and 4 show the grid usedfor inviscid calculationsat different cross sections

downstreamfrom thenose.Figure3(a) showstheentirecrosssectionalgrid at FS 14.02and fig.

3(b) showsthedetailsnearthe bodyat the samestation.Figures4(a)and4(b) containthe same

informationat FS29.61.Becauseof thepresenceof theflat sidewallat sectionsdownstream,the

grid pointswereclusterednearthemaximumhalf breadthpointsforwardof theflat sidewall.This

providedadequatedefinitionof thefiat wall portionof theforebody.

A grid refinement study was done for both inviscid and turbulent solutions for an angle-of-

attack of 40 °. The grids used in this study were the same H-O grids used in the first part of this

work (Ref. 5). The baseline inviscid grid had 33 (axial), 93 (circumferential) and 45 points in the

radial direction. The baseline viscous grid had 33 (axial), 93 (circumferential) and 65 points in the

radial direction. During the grid refinement study, the number of points in the radial direction were

increased with improved radial stretching, so that at least four fine grid points were present in the

first grid point of the crude grid. The circumferential and axial densities were kept the same. The

inviscid refined grid had 90 points in the radial direction while the refined viscous grid had 100

points radially.

Results and Discussion of Computations on the F-5A Forebody

Inviscid calculations were performed for tt = 30 ° and fl = 5 ° to compare the results of this

new grid system with those obtained using a H-O grid earlier in Ref. 5. The boundary conditions

were the same in both the cases except on the axis that runs from the nose to the upstream farfield

boundary where a singularity type boundary condition was imposed for the new grid. In the earlier

computations this boundary was a part of the surface and so an inviscid boundary condition was

imposed.

Figures 5 and 6 show the comparison of the inviscid surface pressures between the two grid

systems at FS 6.58 and FS 26.77 respectively. It is very difficult to identify a difference between

the two results at these stations. For the two-block grid system, FS 6.58 is in the first block where

the surface grid was different from that of the H-O grid used earlier in Ref. 5. FS 26.77 is in the

second block, where the surface grid was same as that used earlier. A comparison of the

longitudinal variation of Cp on the leeward plane is shown in fig. 7. This figure shows the

improved resolution of the solution near the nose with the new C-O grid. There was negligible

change in the value of the directional stability Cn_ After demonstrating that the two grid systems

produced similar results, a grid resolution study, as well as a detailed study of the solutions, was

done on the single block H-O grid used in Ref. 5.

Figure 8 shows the sign convention used in computing the side force and yawing moment.

The F-SA forebody experimental directional stability data from Ref. 3 are shown along with the

computed inviscid and viscous results in fig. 9. The computed results revealed the same trend

found in the wind tunnel data and were already presented in Refs. 4 and 5. Additionally, we show

the results obtained with the refined grid for both inviscid and turbulent cases at o_-- 40 °.

Although the results changed slightly with grid resolution, the trends were the same in both the

cases.

Figure 10 shows the axial distribution of side force contributing to the yawing moment

presented in fig. 9 at o_ ---40 °. The importance of the viscosity in producing the positive stability is

clearly demonstrated. The viscous solution develops a significant restoring force, with a positive

side force over most of the forebody and generally increasing with downstream distance. This is a

consequence of the increasing asymmetry of the forebody vortices with distance from the nose.

The inviscid solution shows essentially no side force over the majority of the forebody. Figures 11

and 12 provide the circumferential pressure distributions at two stations for both inviscid and

turbulent cases. The corresponding cross sectional shape, the direction of incoming flow and the

origin of reference for the angular measure are shown below each of these figures. The negative

8

peak pressures are due to the vortices on the upper surface of the cross section and are shown more

clearly in the following flow visualization pictures to be presented in fig. 14. The asymmetry in the

pressure distribution due to the sideslip can be seen in fig. 11, and is much more noticeable in

fig. 12. At FS 14.02 the viscous solution results clearly show the effect of the vortices, with two

low pressure regions, denoted B and C, underneath the vortices. The low pressure peaks A and D

are due to the attached flow accelerating around the highly curved sides of the body. At station FS

29.61 the inviscid results contain four distinct low pressure peaks corresponding to the high

curvature regions at the cross section corners. Considering viscous effects, the turbulent flow is

separated and the primary vortices are moving away from the body, as shown later in fig. 14. The

small low pressure peak at C in fig. 12 is due to the primary windward vortex. The primary

leeward vortex is sufficiently far off from the surface and hence the suction created by it is

insignificant.

Figure 13 contains the pressure differences, ACp, between the leeward and windward sides

of the body at the same stations at which the pressures were plotted in figs. 11 and 12. These

provide insight into the distribution of side force at a particular station to help explain the effect of

viscosity in creating the restoring force. Although the viscous effects are primarily associated with

the vortex and separated flowfield on the top side of the forebody, the effects of viscosity are seen

to alter the balance of pressures between the sides of the body over most of the side projection. It is

particularly interesting to notice that the near zero side force associated with the inviscid flow arises

as a delicate balance between a side force in one direction on the lower portion of the body, and a

side force in the opposite direction on the upper part. The effects of viscosity are to reduce the

magnitudes of the vortex suction peak levels as well as producing a shift in the location of the

ZlCp curve which results in a distribution which has a much larger net side force.

Figures 14(a) and 14(b) show the cross sectional stagnation pressure contours at axial

stations x = 14.02 inches and x = 29.61 inches from the nose for the viscous calculation at the

same flow conditions shown in figs. 11 and 12. The incoming flow is the same as shown in

9

figs. ll(b) and 12(b). The leeward (LHS) vortex is farther away from the surface than the

windward (RHS) vortex. The asymmetry of the low pressures on the body under the vortices is

generally considered to be pulling the body to smaller sideslip, and thus provides a stabilizing

moment. However, we have shown in fig. 13 that the side force is affected by the separated flow

indirectly through its effect on the pressure distribution over virtually the entire surface. These local

effects of the vortices actually act primarily on the essentially flat top-surface and don't directly

contribute to the side force. At FS 29.61 we can also see the secondary vortices under the primary

vortices.

Figures 15 and 16 show the inviscid and turbulent calculation pressures at FS 14.02 and FS

29.61 plotted as vectors perpendicular to the surface. In these diagrams, the surface is u'eated as a

line of zero pressure and the vectors going outward from the surface represent negative pressure

coefficients. These diagrams should be studied in conjunction with pressure plots of fig. 11 and

12. At FS 14.02 the viscous diagrams show clearly the effect of the vortices resulting in two low

pressure peaks on the upper surface. At FS 29.61, the inviscid results show two peaks as the flow

accelerates around the sides to the upper surface. The viscous results shown in fig. 16(b) can be

explained by looking at the flow structure in fig. 14(b). The leeward vortex is sufficiently far off

from the surface and hence the leeward vortex suction peak is almost insignificant. On the

windward side, as expected, the windward vortex is closer to the surface and the low pressure

peak is therefore still visible.

Figure 17 shows the vortex path development along the body. The leeward vortex (here on

the RI-IS of the body) is seen to be rising above the body much faster than the windward vortex

(LHS). The windward vortex is actually "blown back" over the forebody, and is moving along the

top surface near the center. This is also evident from fig. 14.

10

ERICKSON CHINE FOREBODY

Erickson and Brandon experimentally investigated the chine effects on a generic fighter

configuration and have published the detailed pressure data over a large range of angles of attack

and sideslip (Ref. 6). This flowfield on such a model was computationally investigated in the

earlier part of this work and the details were presented in Ref. 5. The geometry math model and the

comparison with the wind tunnel model are also described in detail there. In that study, the grid

was constructed from two dimensional O-type cross flow grids which are longitudinally stacked,

constituting a single block H-O topology as was done earlier in the case of F-5A. Here we

investigate the same geometry using an alternate grid system and also study the grid resolution

requirements for a chined forebody.

Erickson Forebody Grid Details

The inviscid calculations on the Erickson forebody were repeated on the alternate C-O grid

shown in fig. 18. The baseline inviscid calculation grid had 45 points in the radial direction and

101 points in the full circumferential direction. Longitudinally, the grid was clustered near the nose

with 25 stations on the forebody as shown in fig. 18. The axial grid planes were defined at

stations corresponding to the experimental measured stations. These were at a distance of 7.19,

13.56 and 19.94 inches from the nose along the length of the body. The smoothing of the surface

unit normals introduced some grid skewness near the chine nose as well as around the chine edge.

This was done to avoid large cell volume discontinuities.

As compared to the inviscid solution grid, the viscous calculation used a grid with 65 points

in the radial direction, and with longitudinal and circumferential grid points remaining identical

with the grid used for the inviscid calculations. The baseline grid was established with sufficient

normal clustering near the surface to adequately resolve the laminar sublayer in the turbulent

11

boundarylayer flow. This grid produced an average normal cell size of approximately 10-4l. At

the frecstream conditions used in the computations for the Erickson forebody (M., = 0.2,* Re/=

1.02 x 106 based on model length, and ct = 20 ° ) the baseline grid typically resulted in a value of

y+ -- 2 at the first mesh point above the surface.

Figure 19 shows the grid used for inviscid calculations at the last section downs_'eam from

the nose. Figure 19(a) shows the entire cross sectional grid at FS 14.02 and figs. 19(b) and 19(c)

provide the details near the surface and chine edge respectively.

A grid refinement study was done with both the inviscid and turbulent grids. In each of these

cases the number of grid points were doubled in the normal direction with increased clustering in

the normal direction. The circumferentialand axialdensitieswere kept the same. Approximately

fourfinegridpointswere packed in thefirstcellof the baselinegridforboth thefineinviscidand

the fineturbulentgrids.The fineNavier-Stokcsgridprovided ay+ valueof approximatcly 0.5.

Results and Discussion of Computations on the Erickson Forebody

Inviscid calculations were performed for a = 30 ° and jfl = 0 ° to compare the results of this

new gridsystem with thoseobtainedearlierusingan H-O gridinRef. 5.The H-O gridused earlier

had 33 axialstationswith 25 on the surfaceand 8 ahead of the nose.With the new C-O topology

gridstrategy,the radialand circumferentialgriddensitieswere kept the same. As in the case of

F-SA, the boundary condition on the axis that runs from the nose to the upstream farfield boundary

was altered to a singularity type boundary condition. In the earlier computations this boundary was

a part of the surfaceand so an inviscidboundary conditionwas imposed.

Figures 20 and 21 show the comparison of the inviscidsurfacepressuresbetween the two

grid systems at FS 7.19 and FS 13,56 respectively.The surfacegridfor the C-O gridtopology

was changed toaccommodate more pointsnear thechine edge while keeping the circumferential

"The experimental Mach number of .08 was not used because of previous problems using otherNavier-Stokes codes. An examination of the results showed that the largest Mach number in the

flowfield was well removed from the compressibility range.

12

grid density same as that of the H-O grid. The difference is almost insignificant as was seen in the

case of F-5A. The advantage of using this grid system is that you can maintain the same grid

density on the surface while eliminating the upstream grid extension.

Figures 22 - 24 present the computed upper surface pressure distributions at three stations

obtained on the isolated forebody along with experimental data on the forebody-wing model for

various angles of attack and sideslip. The details of the experimental investigation are available in

Ref. 6. Some of the results arising from earlier computations are reproduced from Ref. 5 in these

figures. The surface grid used in later computations were stretched to accommodate more points

near the chine edge. Figure 22 shows the upper surface pressures for the ct = 30 ° and fl = 5 °

case. At the section closest to the nose (FS 7.19) the inviscid computations predict the pressures

very close to the experimental values. At stations further downstream the agreement deteriorates.

At FS 19.94 the wind tunnel data appears to reflect the higher local incidence induced by the wing

flowfield. The inviscid refined grid results show a suction peak in better agreement than the

baseline grid at the fit-st station, but produce little change further downstream. Turbulent viscous

effects do not change the pressure levels at the mid section of the forebody, but do have some

effect on the peak suction pressure level. The peak suction pressures were reduced, as expected,

resulting in poorer agreement with the experimental data. In the turbulent flow case the refined grid

solution resulted in only minor changes in the pressure distribution. The trend remains the same

when the sideslip is increased to 10 ° as shown in fig. 23. The fine grid Navier-Stokes calculation

was not done for this case. Figure 24 shows the pressures for o_ = 40 ° and fl = 10 °. Erickson

and Brandon ( Ref. 6 ) suggest that the extent of upstream influence of vortex breakdown

occurring downstream was found to differ at different combinations of angles of attack and

sideslip. For example, vortex core bursting had occurred on the windward side at t_ = 40 °

whenever the sideslip angle exceeded 5 °. The computations do not include a model of the wing

effects. We did not observe any vortex bursting in the solution.

13

Figure25 shows the side force computed for the Erickson forebody. Both the inviscid and

the viscous solutions show similar trends, and the minor grid effects indicate that the solutions are

grid resolved. Here, in contrast to the smooth forebody cross section results for the F-5A, both

inviscid as well as the turbulent results develop restoring forces, with a positive side force over

most of the forebody and generally increasing with downstream distance. This is expected because

of the f'Lxed separation lines along the edge of the chine, regardless of viscosity, and is in marked

contrast to the smooth cross section results obtained on the F-5A forebody (Ref. 4). There the

inviscid and viscous solutions were completely different, with the inviscid solution providing

essentially no side force. The vortical flow in this case is being governed essentially by inviscid

phenomena. The directional stability characteristics in fig. 26 show the stabilizing effect of the

chined forebody over the entire range from 20 ° to 40 ° angle-of-attack. Qualitatively, the trend

shown by both Euler and Navier-Stokes grids are very similar. This observation is important, and

provides a basis for deciding on the solution strategy to be used for the parametric computations on

a generic forebody to be discussed later.The directional stability computed for this forebody is

similar using either Euler or Navier-Stokes solutions at 30 ° angle of attack. At o_= 40 °, the refined

Navier-Stokes grid calculation resulted in improved correlation with Euler results.

Figures 27 and 28 show the inviscid and turbulent calculation pressures at FS 7.19 and FS

19.94 plotted as vectors perpendicular to the surface. As before, the surface is treated as a line of

zero pressure and the vectors going outward from the surface are proportional to the negative

pressures. These diagrams should be studied in conjunction with pressure plots of fig. 23. Unlike

the case of F-5A, the inviscid and turbulent cases are very similar at both the stations because of

the f'LXed separation line as discussed earlier. The flow decelerates as it approaches the chine edge

because of the change of the body cross sectional shape, and separates at the chine edge.

Figures 29 and 30 show inviscid and turbulent stagnation pressure contours respectively at

two different stations. These clearly show the chine-edge generated vortices. The position and

magnitude of the primary vortices are nearly identical in both the inviscid and turbulent cases. The

turbulent solution also shows the formation of secondary vortices near the chine edge due to

14

boundarylayer separation. For chine shapes the effects of viscosity are a secondary effect on

vortex size, position and strength. Strong vortex formation can be seen all along the forebody in

fig. 31 with the leeward vortices rising above the surface much faster than the windward vortices.

Such strong vortex formation on bodies with sharp chines is responsible for positive directional

stability even at 20 ° angle of attack which was not found in the F5-A case.

SOLUTION STRATEGY FOR PARAMETRIC FOREBODY GEOMETRY STUDY

Based on the analysis of the computational solutions obtained on the Erickson chine

forebody, a solution strategy for forebody shaping study was chosen. When fl was fixed at 5 ° it

was shown in the case of the Erickson chine forebody that the inviscid pressures were very close

to the experimental data and the side force and Cn_ trends were qualitatively similar and nearly the

same for the Euler and turbulent flow computations. Though refining the grid made a slight

improvement in the Euler results, it was very expensive considering the minor change in the

results. Hence, it was decided that to assess aerodynamic trends arising from forebody geometry

variations on chine-shaped forebodies, the computations could be done with an Euler analysis and

the baseline grid.

To study the advantage of using multigrid and multisequencing, the inviscid flow over a

generic analytical forebody was computed at ot = 30 ° and fl = 5 °. Three levels of sequencing

were used with multigridding on each level. The surface pressures as shown in fig. 32 were

identical when the residual went down to the same order of magnitude in both cases. However,

there was a 33% reduction in CPU time. After this approach was established, the remaining Euler

calculations were performed with three levels of sequencing and multigridding on each level of

sequencing.

15

ANALYTIC CHINE FOREBODY STUDY

To study geometric shaping effects on forebody aerodynamic characteristics, an analytical

forebody model with the ability to produce a wide variation of shapes of interest was defined in

Ref. 5. This generic forebody model makes use of the equation of a super-ellipse to obtain the

cross sectional geometry. The super ellipse, used previously to control flow expansion around

wing leading edges (ReL 12), can recover a circular cross section, produce elliptical cross sections

and can also produce chined-shaped forebodies. Thus it can be used to define a variety of different

cross sectional shapes.

The super-ellipse equation for the forebody cross section was defined in Ref. 5 as:

z_2+n +(y_2+m = 1bJ k.a)

where n and m are adjustable coefficients that control the surface slopes at the top and bottom

plane of symmetry and chine leading edge. The constants a and b correspond to the maximum

half-breadth and upper or lower centerlines respectively. Depending on the value of n and m, the

equation can be made to meet all the requirements specified above. The case n = m = 0

corresponds to the standard ellipse. The body is circular when a = b.

When n = -1 the sidewall is linear at the maximum half breadth line, forming a distinct crease

line. When n < -1 the body cross section takes on the cusped or chine-like shape. The derivative

of z / b with respect to y / a is:

2+m_

dy ( i+n'_

[1_ y--(2+')_2-_nJ

where _ = z / b and y = y / a. As y --_ 1, the slope becomes:

16

n>-I

n<-I

n=-I

Different cross sections can be used above and below the maximum half-breadth line. Even

more generality can be provided by allowing n and m to be functions of the axial distance x,

although in this study the parameters n and m were taken to be constants with respect to x. The

parameters a and b are functions of the planform shape and can be varied to study planform

effects. Notice that when n = - 1 the value of m can be used to control the slope of the sidewall at

the crease line.

Using the generic forebody parametric model deirmed above, and the computational strategy

developed based on the Erickson forebody results, an investigation of directional stability

characteristics of various chine-shaped forebody geometries was made. It was decided to analyse

the effect of changing b/a, chine angle and combinations thereof. This range of cross sectional

shapes provides an extremely broad design space to investigate aerodynamic tailoring of forebody

characteristics through geometric design.

For the present study the following cases were initially selected :

(a) Geometrical parameters:

m=0

-1.5 < n < -1.0, An = -0.25

0.5 _<b/a < 1.5, Ab/a = 0.5

(b) Flow conditions:

20 ° < _z < 40 °, Aa = 10°

0o t <_5o, o

The resulting cross sectional shapes are shown in fig. 33. The computational study was

carried out to determine the shape which leads to the largest increase in directional stability. This

17

test case matrix, shown in Table 2, resulted in 54 different configurations with symmetrical upper

and lower surfaces, showing how large the possible set of cases could be without careful selection.

The _ = 0 ° cases were initially included to compare the flow physics with and without sideslip.

However, with C a = 0 at _ = 0 ° and the number of cases being excessive, the _ = 0 ° cases were

eliminated. Further combinations were eliminated as the study progressed and the results

examined. Some asymmetric upper/lower cross section geometries were also analysed. These

geometries were defined using different b/a or different n for upper and lower surfaces.

It was also decided that the planform shape would initially be defined to be similar to the

Erickson chine case and to study the effects of varying cross section geometry. In this calculation

the momem center for the computation of the directional stability was kept fixed at the value used in

the Erickson forebody test (Table 1). Based on the best cross sectional shape, limited planform

effects were studied. The total CPU time used for the Euler study is given in Table 3.

Discussion of Results for the Generic Chine Forebodies

Effect of varying b/a

This study was conducted for cross sectional shapes with m = 0 and n = -1.5 and bla = 0.5,

1.0 and 1.5 (see fig. 33d). Figure 34 shows Cn_ vs angle of attack with bla as the varying

parameter. It is interesting to note that the contribution to positive directional stability increases as

b/a decreases at a fixed angle-of-attack, b/a = 0.5 is the best cross section in promoting positive

directional stability. An understanding of these results requires an examination of the flowfield

details presented below.

Figure 35 shows the variation of the side force with the axial distance at each angle-of-attack.

Near the nose the force is initially destabilizing, being negative for all cases computed. Moving aft

from the immediate vicinity of the nose, the trend is reversed and the side force starts to increase

18

towardpositivevalues.The sideforcebecomesmorepositivewith increasingangle-of-attack.In

general,the sideforce becomesincreasinglynegativeasthe valueof b/a increases, making the

body more unstable. However, some crossover occurs at the aft end of the body at the higher a,

where the b/a - 0.5 case is not as positive as the b/a = 1 case.

Figures 36 to 38 show the ACp vs z plots at a typical cross section ( x = 18.35 ). The

integration of this pressure difference produces the side force values presented in the fig. 35. The

cross section below the chine edge always makes a negative contribution to the side force. Above

the chine edge there is an abrupt large positive spike in the side force. This arises because of the

asymmetry in strength and position of the vortices. At 0_= 20 ° the shallow b/a = .5 case produces

a much larger spike than the b/a = 1.5 case. At higher tt the b/a = 1 case has nearly the same size

spike.

The asymmetry in the position and strength of the windward and leeward vortices which is

responsible for the positive side force on the forebody is shown in fig. 39 for a = 30 ° and b/a =

0.5 and 1.5. Figure 39(a) shows the minimum static pressure found in the vortex over the length

of the body. In this case the lower pressure for the b/a = 0.5 geometry is much stronger compared

to the b/a = 1.5 case. Also, the windward vortex for this geometry is much stronger than the

leeward vortex resulting in a larger asymmetry. This corresponds to the large difference in

directional stability shown in fig. 34. In the sideview shown in fig. 39(b), for b/a = 0.5 both the

vortices are further away from the chine line than in the b/a = 1.5 case, and they are above the top

eenterline, allowing communication between the windward and leeward vortices. In the planform

view, fig. 39(c), the b/a = 0.5 case shows more lateral movement particularly in the aft region than

the b/a = 1.5 case. Here the windward and leeward vortices are separated by the large hump on the

upper surface all along the length of the forebody, and thus restricts the influence of one vortex on

the other, as well as the vortex movement. This is illustrated in fig. 40, which presents stagnation

pressure contours to show the increase in vortex movement as b/a decreases

Using these results the physics of chined forebody aerodynamics emerges. A shallow upper

surface (bla = 0.5) results in a stronger, more asymanetric vortex system compared to a deep

19

surface(b/a = 1.5).A deeplower surfaceresultsin a largernegativecontribution to directional

stability.Hence,higherb/a for the upper or the lower surface is undesirable.

Effect of varying chine angle

In this study b/a was held constant at 0.5 (corresponding to the best result obtained above)

and n was varied over -1.5,- 1.25 and -1.0, which increases the edge angle from a sharp chine to a

sharp edge ( Fig. 33a ). Recall that theoretically the chine edge has a zero angle when n = -1.5 and

n = -1.25 and therefore has a 180 ° slope discontinuity. When n = -1.0 the included edge angle is

finite (127 °) and the slope discontinuity is smaller.

The effect of changing the shape parameter n on the directional stability is shown in fig. 41.

Essentially, all the results are similar at ct = 20 ° and 30 ° but show differences at ot = 40 °. The

sudden decrease in Cn_ for n = -1.0 at tt = 40 ° was further investigated by looking at the side

force variation in fig. 42. Based on the results shown in this figure for the n = -1 case over the

axial distance from about 3 to 23, the source of the decrease of Cn_ at a = 400 for n = -1.0 can

be identified. This result provides an indication of how to keep Cn, 6 from becoming too positive

at high angles-of-attack. Figures 43 to 45 show the ACp vs z plots at a typical cross section

( x = 18.35 ). At t_ = 20°and 30 ° the effect of the chine angle is predominant on the upper surface.

Though the behavior changes on the upper surface, the area under the curves remains nearly the

same. At a = 40 ° the area under the curve suddenly decreases for the n = -1.0 case and this leads

to a decrease in side force at this cross section. Figure 46 shows the vortex strength and position

for the case of n = - 1.0. This shows that the side force could arise from the asymmetry in both the

relative strengths and relative positions of the windward and leeward vortices.

The vorticity being generated due to flow separation has been shown to be proportional to the

square of the velocity at the separation point in Ref. 14. When n < -1 the slope discontinuity is

maximum at the chine edge, and results in large velocities approaching the separation point. This

20

resultsin largervorticity beinggeneratedat thechineedgefor thesecases.Figure 47 showsthe

squareof velocity at the separationpoint plotted for different chine angles at ct = 40". The

n = -1.0 case is distinctly different than the other cases. When n < -1 the edge angle is zero and

hence the strengths of the corresponding leeward and windward vortices are comparable. Also,

very close to the nose the leeward vortex is stronger than the windward vortex leading to a negative

side force. As the axial distance increases the vorticity shed on the windward side increases and

hence the side force is positive. Such observations were also made by Kegelman and Roos based

on experimental results in Ref. 7. When n = -1, as expected, the vorticity shed is much less and of

an entirely different character because of reduced slope discontinuity. Moving downstream from

the nose, the edge with the largest separation velocity switches sides several times. This is reflected

in the side force plot of fig. 42(c). In this case, very close to the nose the windward vorticity shed

is larger than leeward vorticity leading to a positive side force. As we move aft, the side force

changes sign as the relative shed vorticity strength changes.

Effect of unsymmetrical b/a

Unsymmetrical cross sections were generated using different values of b/a for the upper and

lower surfaces while keeping the same functional form with m = 0 and n = -1.5. This maintains the

zero chine edge angle for all the cases. Two cases were tested. The first one had b/a = 0.5 for top

and b/a = 1.5 for bottom. The second one had b/a = 1.5 for top and b/a = 0.5 for bottom. Figure

48 shows the cross sectional shapes together with the computed Cn_ for these bodies alongside

the results already presented for symmetrical b/a. The Erickson forebody result is also included,

which is geometrically similar with symmetrical b/a lying between 0.5 and 1.0. The shallow upper

surface is seen to provide higher Cn_ than the shallow lower surface geometry. This is because

the shallow upper surface results in a stronger vortex and provides a bigger contribution to stability

than the use of a shallow lower surface to reduce the negative contribution to stability.

21

Using the b/a = .5 case as the baseline in fig. 48, it is interesting to contrast the effects of

increasing the body height above and below the chine line. The rate of Cn/3 reduction at a fixed

angle of attack due to additional body height above the chine line is less than the rate of Cn 8

reduction when the height is added below the chine line. In addition, the change of Ca O with

angle of attack differs depending on whether the height is added above or below the chine

line.Here too, the loss in rate of change with angle of attack is less when thickness is added above

the chine line instead of below it.

Effect of unsymmetrical cross sections to vary chine angle

Unsymmetrical cross sections were generated using different values of shape parameter n for

the upper and lower surfaces while keeping the same b/a = 0.5 which was found to be the best

ratio earlier. Such a variation of n would vary the chine angle. The effect of varying this parameter

on the directional stability is shown in fig. 49. The chine angles were zero for symmetrical cross

sections with n < -1 and were trmite for all other cases shown in that figure. Only the symmetrical

case with n = -1.0 which had the highest chine angle shows a sudden decrease in Cn_ at o_ =

40 °. This difference in behavior with the different chine angles suggests the existence of a critical

angle which controls the rate of feeding of the vortex as the angle-of-attack changes.

Effect of varying the planform shape

The planform shape for the forebodies studied thus far was same as that of the Erickson

forebody. This planform is shown in fig. 50. The parameter XN shown for the tangent ogive

forebodies is the distance from the tip of the nose to the station where the planform span becomes a

constant. The side force variation in figs. 35 and 42 showed that most of the positive side force

22

camefrom the aft portion of the forebody where the chine line was swept nearly 90 °. Hence it was

postulated that expanding to a constant cross section faster would give greater positive side force.

Because the Erickson planform approximates a tangent ogive with XN = 18, the alternative

planform was chosen to expand faster with XN =7, as shown in fig. 50.

The effect of the planform variation on the directional stability is shown in fig. 51. There is a

small increase in Cn_ for a fixed cross sectional shape with b/a = 0.5, m = 0 and n = -1.0. One

other cross section, with a flat lower surface, was computed with this planform, and resulted in a

Cn_ increase. This supported our previous assertion that a smaller b/a on the lower surface

reduces the adverse contribution to Cn_ at a = 20 ° and also at a = 40 °. Here, note that the chine

included angle is much less than the symmetrical case. The directional stability continues to

increase at oc = 40 °, rather than remain nearly constant, reinforcing the idea that a critical chine

angle might exist which reduces extreme contributions to stability at high angle-of-attack.

Figures 52 and 53 show the effect of planform shape on side force variation at oc = 20 ° and

= 400 respectively. As expected, after the initial negative side force, the rate of increase of side

force is greater in the aft portion of the forebody for the blunt nosed planform. Also note that at

a = 400, the double hump is eliminated with a blunt-nosed planform and with a flat bottom

surface the configuration is even better. However very close to the nose the side force is more

negative. A look at the slopes and curvatures of the different planforms in fig. 54 shows that the

tangent ogive planform has a large negative cm'vature close to the tip of the forebody.

CONCLUSIONS AND DESIGN GUIDELINES

A number of conclusions arise based on the results obtained here. For chined-shaped

forebodies, where the separation position is not influenced by viscosity, the Euler solutions were

23

found to be in reasonably good agreement with the results of Navier-Stokes calculations using the

Baldwin-Lomax turbulence model as modified by Degani and Schiff. Thus Euler solutions could

be used to carry out the parametric study. CFD has been used to explicitly identify the method in

which the pressure distribution on the chine contributes to the directional stability. An

unconventional approach to presentation and evaluation of forebody aerodynamics has been

introduced.

For aerodynamic design consideration the following guidelines were obtained:

The best ratio of maximum half-breadth to the maximum centerline width proves to be

b/a = 0.5 among the cases analysed for positive directional stability. In general, lower b/a

for both the upper and lower surfaces improves directional stability. In cases where higher

b/a is a requirement, it is better to increase the lower surface b/a which results in a smaller

penalty than if we were to increase upper surface b/a. The rate of change of Cn_ is also a

function of the surface to which the thickness is added.

The effect of chine angle on the directional stability characteristics was found to be

insignificant except when the chine angle was large. There could be a critical chine angle

beyond which it becomes an important factor (we did not attempt to find one in this study).

If such a critical angle exists, it provides an indication of how to keep Cn fl from becoming

too positive at .high angles of attack.

The positive contribution to the stability is seen to come from the aft portion of the

forebody where the chine line is swept nearly 90 °. Changing the planform shape by

allowing it to expand faster to a constant value increases the CnB only by a small amount.

However, the behavior of the side force plots vary significantly for different planform

shapes.

24

ACKNOWLEDGEMENTS

Theresultspresentedwereobtained under the support of NASA Langley Research Center

through Grant NAG-1-1037. At NASA Langley the technical monitor, Farhad Ghaffari, helped us

technically and provided numerous constructive comments. At VPI & SU, Robert Waiters

consulted with us regularly on the use of cfl3d, and Tom Arledge provided assistance with the

figure preparation. Each of these contributions is gratefully acknowledged.

Virginia Polytechnic Institute and State University

Blacksburg, Virginia 24061

October 22, 1991

(rev., June 10, 1992)

25

REFERENCES

1. Chambers,J.R.,"High-Angle-of-AttackAerodynamics:LessonsLearned,"AIAA Paper86-1774, June 1986.

2. Chambers, J.R. and CJrafton, S.B., "Aerodynamic Characteristics of Airplanes at High Angleof Attack," NASA TM 74097, Dec. 1977.

3. Grafton, S.B., Chambers, J.R., and Coe, P.L., Jr., "Wind-Tunnel Free-Flight Investigation

of a Model of a Spin Resistant Fighter Configuration," NASA TN D-7716, June 1974.

4. Mason, W.H., and Ravi, R., "A Computational Study of the F-5A Forebody EmphasizingDirectional Stability," AIAA-91-3289, September 1991.

5. Mason, W.H., and Ravi, R.,'TIi-Alpha Forebody Design : Part I - Methodology Base andInitial Paramettics," Vial- Aero-176, October 1990.

4 Erickson, G.E., and Brandon, J.M., "Low-Speed Experimental Study of the Vortex Flow

Effects of a Fighter Forebody Having Unconventional Cross Section," AIAA Paper No. 85-1798.

7. Kegelman, J.T., and Roos, F.W.,"lnfluence of Forebody Cross Section Shape on VortexFlowfield Structure at High Alpha," AIAA Paper 91-3250, September 1991.

8. Roos, F.W., and Kegelman, J.T.,"Aerodynanfics Characteristics of Three GeneticForebodies at High Angles of Attack," AIAA Paper 91-0275, Jan 1991.

9. Hall, R.M., "Influence of Forebody Cross Sectional Shape on Wing Vortex-Burst Location,"

Journal of Aircraft, Vol. 24, No. 9, September 1987.

10. Thomas, J.L., van Leer, B., and Waiters, R.W., "Implicit Flux-Split Schemes for the Euler

Equations," AIAA Paper 85-1680, July 1985.

11. Ghaffari, F., personal communication, 1990.

12. Mason, W.H., and Miller, D.S., "Controlled Superctitical Crossflow on Supersonic Wings -An Experimental Verification," AIAA Paper 80-1421, July 1980.

13. Mendenhall, M.R., and Lesieutre, D.J., "Prediction of Subsonic Vortex Shedding FromForebodies With Chines," NASA Contractor Report 4323, September 1990.

14. Mendenhall, M.R., Spangler, S.B., and Perkins, S.C.,"Vortex Shedding from Circular andNoncircular Bodies at High Angles of Attack," AIAA Paper 79-0026, Jan 1979.

26

Reference Par_lmeters F-5A Erick.s.on Genetic

Mean Aerodynamic Chord c

Wing Span b'

Model Length l

Reynolds Number Re l

Reference Area Sre f

Moment Reference Center from Nose

16.08 in 32.04 in 32.04 in

52.68 in 46.80 in 46.80 in

31.025 in 30.00 in 30.00 in

1.25 x 106 1.02 x 106 1.02 x 106

754.56 in 2 1264.32 in 2 1264.32 in 2

57.72 in 12.816 in 12.816 in

Table 1. Reference Data Used in Computing Forces and Moments

27

Matrix of Cases for "Svmmemlc" Chine Forebtxty Directional Stability.

n = - 1.50

fi= 0° 13= 55

a=20 ° _z=30 ° _=40 ° a=20 ° a=30 ° a=40 °

x x x ¢" ¢" ¢"

b/a = 0.5 n = - 1.25 x x X ¢" ¢" ¢"

n = -1.00 x x × ¢" ¢" ¢

n = -1.50 x x x ¢ ¢" ¢

b/a= 1.0 n=-1.25 × x × x x x

n = -1.00 × x × x × x

n = -I.50 x x × ¢" ¢" t ¢_

I I ,p Ib/a = 1.5 n = -1.25 x x I × I × i × x'

n = -I.00 × , X X _ X _ x X

Table 2. Total Cases for Parametric Study

Each inviscid "crude grid" run = 3400 CPU seconds + 200 sec = 3600 sec

effect planforms b/a's a's ,/_ n'___fis total

b/a 1 3 3 1 1 9

sideslip (/3 = 10 °) 1 1 3 1 1 3

chine angle (extra) 1 1 3 1 2 6

split b/a 1 2 3 1 1 6

split chine angles 1 1 3 1 2 6

plan form 2 1 2 1 1 4

flat bottom 1 1 2 1 1 2

36

Total CPU time for Euler design: 36 hours

Table 3. CPU Time for Parametric Study

28

t I IlltlllIlllllll[

i llllllJllll!!!!!

111 11 11 1

ail|i-N

i i ii-4-i ; it4-i iH-4-

i i _4-4.--

; ; ;;;

I

i iiiii

Figure 1. F-5A grid with H-O grid topology used in earlier computations

Figure 2. F-5A grid with C-O grid topology for front block and H-O grid for rear block

29

a) entire crossplane grid at FS 14.02

b) near body details at FS 14.02

Figure 3. F-5A forebody grid details in crossflow plane

30

a) entire erossplane grid at FS 29.61

b) near body details at FS 29.61

Figure 4. F-5A forebody grid details in crossflow plane

31

-20

Cp

-1.5

-1.0

-0.5

0.0

0.5

------0--- H-O grid

_,,x-- 2-block grid_X=30 °

=5 °x = 6.58

1.0 l I I I f I i

0 IO0 2O0 500

0

Figure 5. Comparison of inviscid surface pressures between the two grid systems

at FS 6.58

32

-20

Cp

I 1 I I I I I

100 200 500

@

Figure 6. Comparison of inviscid surface pressures between the two grid systems

at FS 26.77

33

%

0.20

0.10

0.00

-0.10

-0.20

-0.30

-0.40

-0.50

-0.60

''''1''''1''''1''''1''''1''''1''''1''''

=30 °

=

-- I

(

i

_ , I, + 2-block grid

Iri l n I n I I o | i m m I | I i l I | t m , I I I i n t I i o i a i m m n !

-5 0 5 10 15 20 25 30 35

axial coordinate, x

Figure 7. Comparison of F-5A inviscid surface pressures on the leeward plane

34

IxPlan view

/cY

ref

positive

(

C positiveY

__'_- ,,.._Y

_(Co)wind_,ard

Looking from behind

Afp --(Cp )leeward--(f p )windward

C_-fAC.d_

Xbase

f (X -- Xref)Cydx

Xle

Figure 8. Sign convention for forces and moments used in the present study

35

c_

0.0080

0.0060

0.0040

0.0020

0.0000

Cnl3 - isolated forebody W.T. data

Cn_- turbulent solution(H-Ogrid)

Cnl3 - inviscid solution (H-O grid)

Cnl5 - turb. sol'n (refined H-O grid)

inviscid sorn (refined H-O grid)

/

-0.002010o 20 ° 30 ° 40 ° 50 °

6¢

Fig. 9 F-5A directional stability: Comparison of calculation with experiment.

36

0.20 t I t I I I

Cy

0.15

0.10

0.05

0.00

-0.05

-0.10

,x Inviscid

[] Turbulent

I I ! I I I-0.15

0 5 10 15 20 25 30 35

Axial coordinate, x

Figure 10. Computed distribution of side force along the F-5A forebody.

37

-1.50

-0.90

-0.30

c,0.30

0.90

1.50

(Y

o Inviscid [ a = 40 ° _

I

• Turbulent ] fl = 5°x = 14.02

I I I

_3 o 180 ° 270 °

0

a) inviscid and turbulent surface pressure distribution

360 °

4

3

2

I

0

-I

-2

-3

-4

I I I I I

I I

-4 -3 -2 4

I I

X = 14.02

)o ___flow direction -

I I I I I

-1 0 1 2 3

b) cross-section at FS 14.02

Figure 11. Comparison of F-5A inviseid and turbulent surface pressures at FS 14.02

38

rO Inviscid

-2 00 I-1 l J• ]L • Turbulent ct-40 °

-1.50 _- fl=5°[ o_o x = 29.61i

I o_ ,o oo _r.Cp I cs, ,,_ ,_ o.=.° Ill

-0.50t- o, _ o ; 'Vla_/ o' _ o o•D/ o,' a_o C__ Q

o.0ok "i ,.,o• _ ,_.,Lo

___o.5@= i l i gggl0_ 90_ 180° 270_ 360°

8

a) inviscid and turbulent surface pressure distribution

0

-3

I i i

D

B

x = 29.61

flow/_ di_:tionI

2 4

I I

-2 0

b) cross-section at FS 29.61

Figure 12. Comparison of F-5A inviscid and turbulentsurface pressures at FS 29.61

39

4 I I I I I !

a =40o

3 /_ =5°

. f I I i I I-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

(a)F$ = 14.02

6

5

4

3

2

1

0

-1

-2

-0.6

I

a : #O°

=5 °x : 29.61

I I I

I I I I I I

-0.4 -0.2 0.0 0.2 0.4 0.6

,%Co)FS 29.61

Figure 13. Variation of ACp vertically along the cross section at FS 14.02 and FS 29.61

40

NORMAL 17[ 13 STAGNA1 ION PRESSUR[

primary leeward vortex

CONTOUR LEVELS _.

0. 96001]0,96 101]11 qh?nfl t_

flPl17 rl r..qll _-I h[] !i_ 41|(I

Bt,[J{]tl

, L

_; =E}t]ItU _:: ,'UU09_R9_O._UYUU0,9_110[I9.gqlOg0,992000.993D09,9q40fl0,99501]n.99601]U.g_,'UU[1,gqHlJll

primary windward vortex

//

#

:7- _'l"I"

/leeward \. : windward

a) FS 14.02

NORBRL IZEn STRGNR110N PRESSIIRE

primary windward vortex

secondary windward vortex

leeward windward

b) FS 29.61

Figure 14. F-5A forebody turbulent stagnation pressure contours for o_= 40 ° and ]_= 5 °

61

ORIGINr_L PP.GE IS

OF POOR QUALITY

5

4

3

2

1

0

-1

-2

-3

- Cp outward

+Cp inward f

\

t

-8 -6 -4 -2 0 2 4 6 8

a) Inviscid

5

4

3

2

1

0

-1

-2

-3

-Cp outward

+Cp inward

\

-8 -6 -4 -2 0 2 4 6

b) Turbulent

8

Figure 15. F-5A forebody pressure vectors at FS 14.02 for oc = 40 ° and fl = 5 °

42

i

- Cp outward

4

2

0

-2

-4

+Cp inward / \

j

/

\ /

-8 -6 -4 -2 0 2 4 6 8

a) Inviscid

6

2

0

-2

-4

- Cp outward

+Cp inward

suction effect from

primary windward vortex

:,¢--

t

I!

Lr.

-8 -6 -4 -2 0 2 4 6 8

b) Turbulent

Figure 16. F-5A forebody pressure vectors at FS 29.61 for a = 40 ° and fl = 5 °

43

_'i_;' '!iI_

if!!,

leeward

windward

Figure 17. F-5A vortex path along forebody for a = 40 ° and ]3= 5 ° ,

(turbulent stagnation pressure contours)

44

-I

m

(a) Full plane

(b) closeup at the nose

Figure 18. Erickson chine forebody longitudinal baseline grid details

45

(a) Cross secfionaJ grid

Co)Closcup at the surface

(¢) Closcup at the chine edge

Figure 19. Erickson chine forebody cross sectional baseline grid detailsx = 30 in. (i= 25 )

46

-5

-4

-3

-1

0

Experiment

--O ct= 30°fl=O°,H'O g rid

_ . ot = 30° [J = 0 °, C-O grid

x = 7.19

: X ..¢'

1 I I I I L I I

--0.8 --0.4 0.0 0.4 0.8

y/ymGx

Figure 20. Comparison of Erickson forebody inviscid surface pressuresfor H-O and C-O grid topologies at FS 7.19

-5

I _ Experiment--C> " a f 3OO _l = OO , H-O gric

--D " a = 300 fl = 0 °, C-O grid

-- 4 [ x -- 13.56I

-3

-1

0

/ Xk.._ // "\

1 I I I I I ! _ I I

-0.8 -0.4 0.0 0.4 0.8

y/ymox

Figure 21. Comparison of Erickson forebody inviscid surface pressuresfor H-O and C-O grid topologies at FS 13.56

47

--4.0 } 0 Euter (crude grid)

--5.5 ] z_ Euler (fine gqd)x=19.94 _ * Novier-Stokes (crude grid)--5.0 0 Novier-Stokes (fine grid)

o Experiment

_ 2 m _

s c(=30

o-2.0 , _ , /• _" _ /

_1.0 / , ,_ _- _, /

-0.5_0.0

-0.6 0.0 @.6

y/ymax

c) FS 19.94

-4.0

--5.5

-5.0

--2.5

--2.0

-1.5

--i .0

--0.5

0.0

x=7,!9

I I i i i

-0.6 0.0 0.6

I ,.allk,.[_,

II I I J

-4.0

-5.5

-5.0

-25

-20

-15

-10

-05

O0

x= 1,.3.56

,9_Q,

_ ,e ,q ,,_ o,_,

J ' I I I I I I I I I

-0.6 0.0 0.6

y/ymax y/ymax

a) FS 7.19 b) FS 13.56

Figure 22. Erickson chine forebody surface pressures at a = 30 ° and fl = 5 °

48

-4.0-3.5 _=_9.94

-3.0

-_.s t %%t- 1.0 __-o 29 -_-0.

-0.6 0.0 0.6

y/ymax

Ealer (cruae 9 ric)

z_ Euler (fine grid)

Nav]er-Stokes (crsae

0 Experiment

c_:30

_=10

9_id}

c) FS 19.94

C

-4.0

-3.5

-3.0

-2.5

-2,0

-1.5

-1,0

-0.5

0.0

x=7.19 i__l

, _

-0.6 0.0 0.6 yly_o,

y,/ymox

a) FS 7.19

-4.O

-2.o _- :, ".£,

0.0 -0,6 0.0 0.6

b) FS 13.56

Figure 23. Erickson chine forebody surface pressures at _z = 30 ° and _ = 10 °

49

Q

-4.0

-5.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

z_

x= 19.94 D_ z_

0 z_

a_. o[]

,, , _,,_Z , ,Tn ]Z' e _ -"'._tj,,

_,_e.'- E i I t I I I 1

-0.6 0.0 0.6

y,/ymax

[] Euler (cruae grid)

z_ Euler (fine griC)-*- Navier-S_okes (cruae gria)

0 Navier-StoKes (fine grid)

o Fxper]ment

0_=40

8=10

c) FS 19.94

-5

-4

-5

-2

-1

0

O

1 I t I I I [ I I

-0.6 0.0 0.6

-5

-4,-

-5

-2

-1

0

z_ z_

A

x=13.56 _ ,-,El3

E_D zx

_ OOrq

-0.6 0.0 0.6

y/ymax y/ymax

a) FS 7.19 b) FS 13.56

Figure 24. Erickson chine forebody surface pressures at ez = 40 ° and/3 = 10°

50

0.4' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' " I ' ' ' ' I ' ' ' '

+ Inviscid + TurbulentInviscid ref'med + Turbulent refined

0.3

0.2

0.1

0.0

.... fl =5°-0.1_

0 5 10 15 20 25 30

axial coordinate, x

Figure 25. Erickson chine forebody side force variation along the forebody

51

0.005

0.004

Inviscid

Inviscid refined

Turbulent

Turbulent refined

0.003

Cn¢

0.002

0.001 I

0.000

15° 2O°

tI,,,,I,,,,I,,,,I,,,,I ....

25° 30° 35° 40° 45° 50° 55°

O_

Figure 26. Erickson chine forebody directional stability characteristics

52

-2

leewar windward

InviscidFS 7.19

ot = 30 °

p = 10 °

-4 -2 0 2 4 66

leeward_5 windward

4

3

2

1

0

-1

-2

TurbulentFS 7.19or=30 °

= 10 °

-4 -2 0 2 4 6

- Cp outward

+Cp inward

a) Inviscid

b) Turbulent

Figure 27. Erickson forebody inviscid and turbulent pressure diagrams at FS 7.19

53

-1

-2

-3

5

-I

-2

leeward-'_---windward

TurbulentFS 19.94o_=30 °

fl = 10 °

-3

-6 -4 -2 0 2 4 6

-4 -2 0 2 4 6

leewar_ _ windward

iscid

__ 1 _ rs 19.94a =30 °

- _ _ # = 10°

- Cp outward

+Cp inward

a) Turbulent

b) Inviscid

Figure 28. Erickson forebody inviscid and turbulent pressure diagrams at FS 19.94

54

CONTOUR t LULL Stl. LJI)lJ|lljIJ. _ I [IllI1. Ill __'1111

IJ. _tG:llJ[III. ql, Illllli ,1_-,' Ill]

lecward_-_ windward

D, 9C;{,III JLI, _1:¢,'U[]

O. qRflnOO. 9KI StltlU. 9_Oll[1O..qfl I flOLl. tJ_'_ Ij|l[1. 993t10Ij. _q 411110.9_500

li. (ll_Jfil Illfl. _q 7 Clllfl. _q98 O[I

i!¸;_;ii;!i_.'_:.

......... _ ps.7:_9I I

windward

b) FS 13.56

Figure 29. Erickson forebody inviscid stagnation pressure contours for a = 30 ° and fl = 5 °

55Ol}ff_le#_::F'.jt2E IS

.... ,_._LITY

III II

leeward-_----_ windward

a) FS 7.19

leeward - windward

b) FS 13.56

Figure 30. Erickson forebody turbulent stagnation pressure contours for o_= 30 ° and/_ = 5 °

56

OF POOR _-::_':_I:TY

NORMALIZED STAGNATION PALSSURE

windward

leeward

Figure 31. Erickson forebody vortex path along forebody for a = 30 ° and fl = 5 °

57

-5.0

-2.5

-2.0

-1.5

Q -1.0

-0.5

0.0

0.5

1.0

[] no multigrid

_ A with multigrid

x=3.542

-f"..__./

I I I I I I I I

-0.6 0.0 0.6

y/ymox

-5.0

-2.5

-2_0

-1.5

o.

-1.0

D no multigrid

_ zs with multigridx=7.771

j"

Lj f---

I I I I I I I I

-0.6 0.0 0.6

y/ymox

a) Upper Surface

-3.0

-2.5

-2.0

-t .5

-1.0

-0.5

0.0

0.5

1.0

[] no multigrid

- " with multigridx=3.542

I I I I I I I I

-0.6 0.0 0.6

y/ymax

-3.0

-2.5

-2.0

-1.5

0 -1.0

[] no multigrid

_ A with multigrid

x=7.771

0.0 ..

0.5

1.0 I I I i

-0.6 0.0 0.6

y/ymox

b) Lower Surface

Figure 32. Surface Pressures on a generic forebody showing effect of multigridding and

multisequencing

58

2.0 I I I i -

1.5

1.0

0.5

z/a

0.0

-0.5

-1.0

-1.5 I

-2.0

b/a ---0.5a= 1.0

I [ I f

0 0.2 0.4 0.6 0.8

Y_

a) b/a = 0.5

2.0

1.5 f

0.5n

-1.50z/a -1.25

0.0 -1.oo

b) b/a = 1.0

0.5

z/a

0.0

-1.0 -1.0

-1.: -1.5 I

-2.q -2.0

y/a

c) b/a = 1.5

0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

y/a y/a y/a

d) n = -1.5 e) n = -1.25 f) n = -1.00

2.0. I t I I

1.5 1.5

0.5 "_z/a

0.0

-0.5

n = -1.00a= 1.0

I I I I

0 0.2 0.4 0.6 0.8

Figure 33. Cross-sections used in the present forebody design study

59

0.005b/a= 0.5b/a= 1.0b/a= 1.5

%

0.004

0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

15°20 ° 25° 30 ° 35° _3 o 45°

Figure 34. Effect of varying b/a on the directional stability characteristics

60

0.I0 .... _ ........ i .... i .... i ....

t_ = 20 ° i : •ooo :: _!

_0.1o . i.......................i...............iiii!iiiiiiii;iiiii

-0.30

-0.40 ................................................................................................

-0.50 .... ' .... ' .... J .... ' .... ' ....0 5 10 15 20 25 30

axial coordinate, x

a) cz= 20 °

(}.20

0.10

0.00

-0.10

CYo.20

-0.30

-0.40

-0.50

,__-)_0' i .... i .... !.... _

i!iiiiiiiiiiiiiii!.... l .... I .... I .... I .... I ....

5 10 15 20 25 30

axial coordinate, x

b) a = 30 °

0.40

0.30

0.20

0.10

Cy 0.00

-0.10

-0.20

-0.30

-0.400

b/a -- 0.5, m = O, n = -1.50---m- b/a = 1.5, rn = O, n = -1.50

b/a = 1.0, m = O, n = -1.50

Ot = 40 °

5 10 15 20 25 30axial coordinate, x

c) c_= 40 °

Figure 35. Effect of varying b / a on side force at various angles of attack

61

8.0

6.0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0-0.4

..........-::'...........f t......_

-0.2 0 0.2 0.4 0.6 0.8

a) ACp distribudon

N 0.0

b)geomen'yvariation

Figure 36. Effect of varying blaon the variadon of zlCpat a = 20 °

62

8.0

6.'0

4.0

2.0

0.0

-2.0

-4.0

-6.0

-8.0

-0.5

| i | i r i w i _ | 1 i ] | i 1 w

a= 30°

_-......................................i......................i....................

im

.... m ............. t ................................................................ .._

t i i | _ ! | i | i I ! I I I I I

0 0.5 I 1.5

_cp

bla = 0.5

b/a= 1.0

b/a= 1.5

a) ACp distribution

N 0.0

b) geometry variation

80

-5 -3 -1 1 3 5

Y

Figure 37. Effect of varying b/a on the variation of ACpat a = 30 °

63

80

60

'4.0

20

O0

-2.0

-4.0

-6.0

-8.0-0.5

n f i , ,,,,I '1'' ' ' ' I I ' ' ' '

a = 40 °

.............. ................................x=_0:35 ......

I

........... -II l ................. 4-................. ( .................. ) ..............

: I

m

m

m

-8.0

-2.0

0.0

2.0

60

o|ll I,,, , , ,,, I , ,,,I,,,,

0 0.5 1 1.5 2

zcp

a) AC.p distribution

b) geomen3, variadon

Figure 38. Effect of varying b/a on the variation of ACpat a = 40 °

64

0.98

0.96

c 0.94h-"_ 0.92G_

c 0.90

0.88

0.86

_SHARP CHINE CASE,q,

,',,

_'-._ ...o.--- .

q_

i,i

m

,[_"

"_- t9- -13,

I L 1 _ I I

5 10 15 20 25 30

6

4

2

0

-2

-4

-6

SIDE VIEW _/ &- i

L :_::_---

I

0

_ J

5 10 15 20 25 30

x

:>.,

4

2

0

-2

4

-6

PLAN VIEW _ --- _ ......... --4_:_:_-_-_e_--a--_a--_-- I

i !

I I I P ' I i

0 5 10 15 20 25 30

-_ D_,a=l.5,wiqavvara= i .5,1eewcra

. b///cO=O.5,windwarcP, =0.5,1eewcra

a) minimum pressure

b) side view

c) plan view

Figure 39. Vortex position and strength variation with bla at a = 30 ° and fl = 5 ° (n = -1.5)

65

i m

NU_IZID ITIMTIIll i_lltllt

..................a)b_a= z.s .................

NO_IZ[O STIIGN_IIUI_ PmFSSUR!

CON'IOtS LEI/_L S. _I_IUUU,_100• 11_2OO

, _J3UU• gE,4UU

IlL '_%111

i_ _

t'J, _ P,_,1111n 9_GOIB

O. _FIRO0O. _dgO0

. 99000• _100

O. 9'_ _ OIL10.99300

O. _500

: _,1)'I <<_-_,_.." .. r_._:_-__._- -",

b)bla=0.5

Figure 40. Stagnation pressure contours for ct = 40 ° and/3 = 5 ° at x = 27.99 in.

66

OF POOR _Uf, I TTY

0.0045

0.0040

0.0035

0.0030

Cnfl 0.0025

0.0020

0.0015

0.0010

0.0005

15°

b/a = 0.5, m = 0, n = -1.25

b/a = 0.5, m = 0, n = -1.0

20 ° 25° 30° 35 ° 40 ° 45 °

Figure 41. Effect of varying chine angle on the directional stability characteristics for b/a = 0.5.

67

0.08

0.06

0.04

0.02

Cy0.00

-0.02

-0.04

-0.06

.... I .... _ .... ! .... I ........

,_--2o° i

iiiiiiiiilj ................................i................ t i , i . v i • i . , . , I . . J t I i i . . I . • , .

0 5 10 15 20 25 30

axial coordinate, x

a) tx = 20 °

Cy0.05

0.20 .... , .... , .... I .... , .... , ....

Ololo..............................

0.00

.... i o . . , I J , J . I .... I .... ! ....

0 5 10 15 20 25 30-0.05

axial coordinate, x

b) cz = 30 °

0.40

0.30

0.20

Cy

0.10

0.00

-0.10

--a-- b/a = 0.5, m =0, n = -1.50b/a = 0.5, m = O, n = -1.25b/a = 0.5, m = O, n = -1.0

Ot=40 °

0 5 10 15 20 25 30

axial coordinate, x

c) a = 40 °

Figure 42. Effect of varying chine angle on side force at various angles of attack

forb/a =0.5

68

3.0

2.0

1.0

0.0

-1.0

-2.0

• II

, IJ

, | i | , , i , | w , =

..................i.................i................................

O__ 20 °x = ":..28.35

,, , I,,, I,,, I,, , I , , ,

0 0.2 0.4 0.6 0.8

'%

a) ACp distribution

.-3 DLa = ,11=o/a m = ,11 = '

-2

-I

z 0

1

2

3 ''' ,I,,,i, .....-5 _ -1 I 3

Y

b) geometry variation

Figure 43. Effect of varying chine angle on the variation of zlCp at a = 20 .0

69

2.0

1.0

0.0

-1.0

- III

. I

-2.0

-3.0

-0.5

o_ .=30 °x =i 18.35

0 0.5 1 1.5

,%

a) ACp distribution

----=--- /a-- ,m= ,n---l.-3 ------4F---- /. ---- ,m= ,n--- .

-2

-I

z 0

I

2

3-5 -3 -1 1 3 5

Y

b) geometry variation

Figure 44. Effect of varying chine angle on the variation of ACp at a = 30 °

70

3.0

2,0

1.0

0.0

-1.0

-2.0

i

. II

J ....... t

. II

" I. I

I- I

.... I .... I ........ I ....

I

i O_ = 40ox = 8.35

0 0.5 1 1.5 2

a) ACp distribution

-3 + Din:Dla :

-2

-1

Z 0

1

2

3 'IAlllll'''l'''l'''-5 _ -1 1 3 5

y

b) geometry variation

Figure 45. Effect of varying chine angle on the variation of ACp at tz = 40 °

71

°

O.

O.

"E 0

n 0.

n O.v

c__.0.:s

O.

O.

O.

8

6

4N

2

0

-2

4

2

0

>..,-2

-4

-6

98

96

94

92

90

88

86

84

82

8O

0

0

m

_. ",_-o_ _ _d_.o._.o._.o.._.e -

/D" /i

\ d .,

I t I

5 10 15

x

..o._-_---_-_- _,O "_ A-'"

I I I

20 25 50

SIDE VIEW4:Y

f

•'Or .4t:" -o" - - _u

" =_ _1-- .

- -CY --.r2 - -r_ -

I I I I 1 I L

0 5 10 15 20 25 30

x

PLAN VIEW _----__.,__..e.__.e-.._ e -e--

"0-_#

__-_--_.__

- ",_- 2 ::GL._- A

I I t t I "_

5 10 15 20 25 30

x

_=30 WlNDWAR__=30 LEEWARD_=40 WINDWARS

O _=40 LEEWARD

a) minimum pressure

b) side view

c) plan view

Figure 46. Vortex position and strength comparison between ¢z = 30 ° and o_= 40 ° (n = -1.0)

72

A m=0,n=- 1.5,windwardO m=0,n=- 1.5,ieewara

m=0,n=- 1.25,winawardx m=0,n=-l.25,[eeward+ m--0,n=- 1.0,wlnciwardO m=0,n=-l.0,1eeward

V2sep

4.00E-04

5.50E-04

5.00E-04

2.50E-04

2.00E-04

1.50E-04

1.00E-04

5.00E-05

°

1 , I I I l I I

0 5 10 15 20 25 30

axial coordinate, x

Figure 47. Comparison of square of velocity at separation for a-- 40 `>for various chine angles

73

O.004

0.005

0.002

0.001

0.000

-0.001

-0.002

_: Erickson Chine ('computed)[] b/a (top)= 0.5,bZa (bo_) =0-5

b/a(top)= 1.0 b/.a(bot) = 1.0A bXa(top)= 1.5'bXa(bot) =1.50 bXa(top) = 1.5'by, a( b°t)=0-5X b/ai, top)=O.5',b'/a(,bot) = 1.5m=O, n=-1.5/_=5

, I I I I I

2O 25 3O 35 40

Angle of Attack

2r-- 1O_

-2L

-4i/ --6 111] J

0 2 4

2

0

-2

0 2 4

6

4

2

0

-2

-4

-6 i0 2 4

2 \

O- >

-2- /

-4- ,_,, ,I

0 2 4

0

-2

0

[]

Figure 48. Effect of unsymmetrical b/a on the direcdonal stability characteristics

74

0.0045

0.0040

0.0035

0.0030

='*<3.0O25

0.0020

0.0015

O.O010

0.0005

2O

X Erickson Chine (computedrn m,n(top)=O,-1.5 ; m,n(bc* m,n(top)=O,-1.25 ; m,n(_A m,n(:top)=O,-1.0 ; m,n(bc0 m,n(top)=O,-1.5 ; m,n_bo

m,n(top):O,--1 0 • m.n(bo

; bTa('bot)=O.

I I

25 30 55 40

Angle of Attack

_=0,- 1 5t)=0,-i.25=0,-1.0=0,-1.0=0,-t.5

0

-2

0 2 4

0

-2

0 2 4

0

-2

0 2 4

0

-2

0 2 4

,b,,10

-2

0 2 4

0

z&

[]

Figure 49. Effect of unsymmetrical shape factor n on the directional stability characteristics

75

30

x ERICKSON FOREBODYEQUIVALENT TANGENT OGIVE

o NEW PLANFORM XN =7

XN =18

25

2O

15

I0

5

0

-4 0 4

Figure 50. Planform shapes used in this study

76

0.0035

0.0030

O.O025

_0.0020

0.0015

O.O010

0.0005

X Erickson Chine (compute, d),, Plon=Erickson ; b/oUop__=.5; ,b/a(bot)=.50 Plan=Tangent Ogive xn=7; b/a(,top)=.5 ; b/,o(bot)=.5X Plan=Tangent Ogive xn=7; b/a(,top)=.5 ; b/o(,bot)=Om=O . n=-l.0/3=5

I ,, I I l,

2O 25 5O .35 4O

Angle of Attack

2

0 2 4

2

0 2 4

0

-2

0 2 4

K PLAN - TANG OGrVE (XN=7)

O PLAN - TANG OG)VE (XN=7)

PLAN = ERICKSON

Figure 51. Effect of planform shape variation on the directional stability characteristics

77

0.08

0.06

0.04

d 0.020

0- 0.00

"0

•_ -0.02

-0.04

-0.06

-0.08

n Plan=Erickson " b/o(top) =-5; ,b/°.(b°t)='5 • - "0 Plan=Tangent Ogive xn=7; b/,a(top) =.5 ; b/,a(bot)x Plan=Tangent Ogive xn=7; b/o(top)=.5 ; b/o(bot)m=O , n=-l.0

a=20/3=5

I I I I 1 _ J

0 10 20 50

axial coordinate, x

0 2 4

0

-2

0 2 4

0

-2

0 2 4

=.5=0

_t PLAN - TANG OGIvE (XN_7)

O PLAN - TANG OGIV[ (XN-7)

PLAN = ERICKSON

Figure 52. Effect of planform shape variation on the side force at tz = 20 °

78

0.30

0.25

0.20

_ 0.15.

0"-- 0.10QJ

0.05

0.00

-0.05

-0.10

z_ Plan=Erickson ; b/a(top)_=.5 .; ,b/a.(bot)=.5 , . .

0 Plan=Tangent Ogive xn=7; b/a_top)=.5 ; b/,a(,bot)=_)5x Plan=Tangent Ogive xn=7; b/a(,top)=.5 ; b/a(,bot)m=O , n=-1.0

I I I l 1 J

0 10 20 30

axial coordinate, x

0 2 4

0

-2

0 2 4

0

-2

0 2 4

x PLAN - TANG OGIVE (XN-7)

0 PLAN - TANG OGIVE (XN=?)

_, PLAN = ERJCKSON

Figure 53. Effect of planform shape variation on the side force at c_ = 40 °

79

10

0

-10

-20

-30

-40

-50 i0

. - =_ _- = .m _- = = _ _- _-

[] Erickson chinez, slope0 curvoture

I I ,| I I I

5 10 15 2O 25 30

X

a) Erickson chine

I0

0

-10

-20

-30

-40

-50

[] Tong Ogive Xn=7" slope0 curvoture

I ,1 I , I I I |

0 5 10 15 20 25 30

b) Tangent Ogive

Figure 54. Variation of planform shapes with their slopes and curvatures

80

qk

Form Approved

REPORT DOCUMENTATION PAGE oMa No.o7odoz88

Public reportln| burclen'for'thit collection of Inlocmotlen Is eltlmated to everale I hour par relpanse, lncludln I the time for reviewinl[ _lnstructions, search_n| exlstin| data sourcal.

r setherin_and malntofnln| the data needed, and completinl end rsviewinll the eMlection of information. Send comments re|ardln| this burden estimate or any other aspect of this

I collection of |nformofion.|ncludin| =UllleStions Ior rsducin| this burden, to Weshinlton Headquarters Services, Directorate for Information Oporetlens and Rsportl, 121S Jefferson

Davis Hilihway. Suite 1204, Arlin|ton, VA 22202-4302, and te the Office of Mena|sment sndBudliet. Paperwork Reduction Project (0T0$-0Zlig). Washinl;ton , DC 20S03i i i

t. AGENCY USE ONLY(Leave blank) 2. REPORT DATE

August 1992

4. TITLE AND SUBTITLE

A Computational Examination of Directional Stability

for Smooth and Chined Forebodies at High-c=

i i

6. AUTHOR(S)

Ramakrishnan Ravi and William H, Mason

7. PERFORMING ORGANIZATION NAME(S) AND ADDRES$(ES)

Virginia Polytechnic Institute and State University

Blacksburg, VA 24061

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDR_:SS(ES)

National Aeronautics and Space Administration

Langley Research Center

Hampton, VA 23665-5225

11. SUPPLEMENTARY NOTES

Technical Monitor: Mr. Farhad Ghaffari

NASA Langley Research Center

Hampton VA 23665-5225

t2a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited

Subject Category 02

3. REPORT TYPE AND DATES COVERED

Contractor Report (8/15/90 to 8/15/91)i i

S. FUNDING NUMBERS

G NAG-t-1037

WU 505-68-30-03i i

8. PERFORMING ORGANIZATION

REPORT NUMBER

VPI-Aero-182(rev. June 1992)

" tO. SP(INSORING/MONITORING '

AGENCY REPORT NUMBER

NASA CR-4465

12b. DISTRIBUTION C(}DE

i i i

13/ABSTRACT (Maxlmum 200 woods)

Computational Fluid Dynamics (CFD) has been used to study aircraft forebody flowfieldsat low-speed, high angle-

of-attack conditions with sideslip. The purpose is to define forebody geometries which provide good directional

stability characteristics under these conditions. The flows oyez the experimentally investigated F-SA forebody and

chine type configuration, previously computed by the authors, were recomputed with better grid topology and

resolution. The results were obtained using a modified version of CFL3D (developed at NASA Langley) to solve

either the Euler equations or the Reynolds equations employing the Bnldwin-Lomax turbulence model with the

Degani-Schiff modification to account for massive crossflow separation. Based on the results, it is concluded that

current CFD methods can be used to investigate the aerodynamic characteristics of forebodies to achieve desirable

high angle-of-attack characteristics. An analytically defined generic forebody model is described, and a parametric

study of various forebody shapes was then conducted to determine which shapes promote a positive contribution

to directional stability at high angle-of-attack. An unconventional approach for presenting the results is used to

illustratehow the positive contribution arises. Based on the results of this initialparametric study, some guidelines

for aerodynamic design to promote positive directional stability are presented.

14. SUBJI_CT TERMS

Computational Fluid Dynamics, Fighter aircraft, Forebody geometry design, Vortex

flow, High-angles-of-attack, Directiozlal stability, Eulet/Navier-Stokes analysis

i

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATIOr_ 19. SECURITY CLASSIFICATION

OF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

_SN ZSdO-OZ-_80-sSO0

IS. NUMBER OF PAGES

84

16. PRICE CO[_Ei i

Ao,520. LIMITATION

OF ABSTRACT

itandard Form 29StRaY. 2-89)Prelcribedby ANSIStd. Z39-14129e-t02

NASA -Langl,'y, 1992