VORTEX ASYMIETRY DEVELOPMENT ON A TANGENT …

7A-A123 924 VORTEX ASYMIETRY DEVELOPMENT ON A TANGENT OGIVE(U)NAVAL SURFACE WEAPONS CENTER SILVER SPRING NO

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REPORT DOCUMENTATION PAGE BEFOR CMPTING ORM1. REPORT NUMBER 2. GOVT ACCESSION NO. S. RECIPIENT'S CATALOG NUMBER

NSWC TR 82-394 / kl)-t el T

4. TITLE (and Subtitle) S. TYPE OF REPORT& PEIOD COVERED

VORTEX ASYMMETRY DEVELOPMENT ON A TANGENTOGIVE s. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(*) William J. Yanta S. CONTRACT OR GRANT NUMBER(&)

Andrew B. Wardlaw, Jr.Daniel Sternklar

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Naval Surface Weapons Center (Code K24) AREA N WORK UNIT NUMBERSWhit Oak61153N; WR02302; WR02302;

White OakR4A

Silver Spring, MD 20910 R44AA

I I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

October 198213. NUMBER OF PAGES

13714. MONITORING AGENCY NAME & ADDRESS(t different from Controlling Office) iS. SECURITY CLASS. (of this repot)

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Approved for public release, distribution unlimited.

17. DISTRIBUTION STATEMENT (of the ebstract entered in Block 20, if different Irom Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide it necessary aid identify by block numbar)

High Angle of AttackVortex SheddingSide ForceSeparated Flow

20. ABSTRACT (Continue on reveree aide if neceesary and Identify by block nunber)

A rigidly supported tangent ogive model has been tested in low turbulent,incompressible flow at an Incidence of 450 . A constant streamwise Reynoldsnumber of 1.5 (105) was maintained which produced laminar boundary layerseparation. The sharp nose tip was replaced in some tests with a 10%spherically blunted one. In the sharp nose experiments it was foundnecessary to stabilize the flow field by adding a small trip. Both unsteadysurface pressures and flow field velocities in the crossflow plane were

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measured, the latter with a two component Laser Doppler Velocimeter. The flowfield in the vicinity of the leeside of the model surface, including theprimary separation region was examined in detail. Results indicate that theflow field generally features two secondary structures on each side of themodel which contain vorticity of opposite sign. Asymmetry starts with thewindward crossflow plane streamline from the primary saddle point, whichdetaches from the body. It appears to be completed when the crossflow planefocus of the shed vortex combines with the primary saddle point. Theintroduction of nose bluntness is not found to fundamentally change theleeward flow field, although it does significantly reduce the level ofasymmetry and the side force magnitude.

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FOREWORD

A rigidly supported tangent ogive model has been tested in low turbulent,incompressible flow at an incidence of 450. A constant streamwise Reynoldsnumber of 1.5(105) was maintained which produced laminar boundary layerseparation. The sharp nose tip was replaced in some tests with a 10%spherically blunted one. In the sharp nose experiments it was found necessaryto stabilize the flow field by adding a small trip. Both unsteady surfacepressures and flow field velocities in the crossflow plane were measured, thelatter with a two component Laser Doppler Velocimeter. The flow field in thevicinity of the leeside of the model surface, including the primary separationregion was examined in detail. Results indicate that the flow field generallyfeatures two secondary structures on each side of the model which containvorticity of opposite sign. Asymmetry starts with the windward crossflow planestreamline from the primary saddle point, which detaches from the body. Itappears to be completed when the crossflow plane focus of the shed vortexcombines with the primary saddle point. The introduction of nose bluntnessis not found to fundamentally change the leeward flow field, although it doessignificantly reduce the level of asymmetry and the side force magnitude.

IRA M. BLATSTEINBy direction

Accession For

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CONTENTS

Chapter Page

1 INTRODUCTION ............. ........................ 7

2 NOMENCLATURE ............ ....................... 8

3 DESCRIPTION OF THE MODEL INSTRUMENTATION AND EXPERIMENT . 9

4 INFLUENCE OF THE NOSE TRIP ..... ................. . 11

5 PRESSURE AND FLOW FIELD MEASUREMENTS .............. ... 12

6 DISCUSSION OF RESULTS ...... ................... . 15

6.1 TOPOLOGICAL NOTIONS ...... .................. . 15

6.2 FLOW FIELD DEVELOPMENT ON THE SHARP TRIPPED MODEL. 16

6.3 FLOW FIELD DT.ZELOPMENT ON THE SHARP UNTRIPPED MODEL. 18

6.4 FLOW FIELD DEVELOPMENT ON THE BLUNTED MODEL ...... . 19

7 ASYMMETRY FORMATION ....... .................... . 20

8 SUMMARY AND CONCLUSIONS ...... .................. . 22

9 REFERENCES ......... ......................... . 68

Appendix A VELOCITY MEASUREMENTS ...... ................... . A-i

Appendix B SURFACE PRESSURE MEASUREMENTS .... ............... . B-i

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ILLUSTRATIONS

Figure Page

1 TANGENT OGIVE PRESSURE MODEL AND SUPPORT .... ............ . 242 SCHEMATIC OF THE LASER DOPPLER VELOCIMETER. ... ........... ... 253 PRESSURE MODEL MOUNTED IN THE WIND TUNNEL .... ............ . 264 NOSE TRIP MADE FROM .45mm GRIT ...... ................. . 275 C AS A FUNCTION OF MODEL ROLL ANGLE .... ............ . 28

Ypeak

6 AXIAL LOCATION OF C AND C = 0 AS A FUNCTION OF C . . . 29Ypeak Y Ypeak

7 CIRCUMFERENTIAL PRESSURE DISTRIBUTIONS ON THE SHARP, TRIPPEDMODEL ........... ............................ 30

8 CIRCUMFERENTIAL PRESSURE DISTRIBUTIONS ON THE BLUNT MODEL. ... 319 CIRCUMFERENTIAL PRESSURE DISTRIBUTION ON THE SHARP, UNTRIPPED

MODEL ..................................... 32

10 MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE SHARP, TRIPPEDMODEL ........... ............................ 34

11 MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE SHARP,UNTRIPPED MODEL ......... ........................ 41

12 MEASURED CROSSFLOW PLANE VELOCITY VECTORS ON THE BLUNT MODEL 4513 ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY

FLUCTUATIONS ON THE SHARP TRIPPED MODEL ... ........... . 49

14 ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY FLUCTUATIONSON THE SHARP, UNTRIPPED MODEL ...... ................ 53

15 ISOVORTICITY CONTOURS AND AREAS OF HIGH VELOCITY FLUCTUATIONSON THE SHARP, UNTRIPPED MODEL ...... ................ 54

16 STREAMLINES ON THE TRIPPED MODEL ...... ................ 56

17 STREAMLINES ON THE SHARP UNTRIPPED MODEL .... ............ . 6018 STREAMLINES ON THE BLUNT MODEL ..... ................. 61

19 TOPOLOGICAL SKETCH OF ASYMMETRIC FLOW DEVELOPMENT ....... 63

TABLES

Table Page

I WIND TUNNEL TESTS IN WHICH LDV DATA WAS TAKEN .. ......... .65

2 CIRCULATION CONTAINED IN REGIONS P, Sl AND S2 .... ......... 66

3 SIDE FORCE VARIATION ......... ...................... 67

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CHAPTER 1

INTRODUCTION

At incidences greater than a few degrees, the flow on the leeside of a slenderconfiguration separates and rolls up to form a pair of symmetric vortices. Withincreasing angle of attack, the pattern becomes asymmetric, even on axisymmetricbodies. In subsonic and transonic flow these vortices have a dominant andnonlinear influence on vehicle aerodynamics.

The asymmetric vortex pattern which develops on a circular body at high anglesof attack has been extensively studied.1- 1 2 In the subsonic flow regime this flowproduces a large side force which has been found difficult to repeat experimentally.Even on axisymmetric bodies, the side force varies with changes in the model rollorientation.1 3,14 The non-repeatability appears to be primarily due to theoccurence of a multiplicity of stable vortex patterns. Such patterns have beendocumented by the authors in Ref. 12. The different patterns are most likelytriggered by model irregularities on the order of the machining tolerance whichoccur in the vicinity of the nose tip. Unsteadiness can also contribute to thelack of repeatability problem. Free stream turbulence causes the vortex patternto jump from one stable configuration to another.1 3

In the present study, crossflow plane velocities and surface pressures havebeen measured on sharp and slightly blunted tangent ogive models at an incidenceof 450, under the condition of laminar separation. The sharp model was tested withand without a nose trip, which was designed to stabilize the flow field. Resultsobtained on all runs are presented in this report. This includes a listing of themeasured velocities and surface pressures which are tabulated in Appendices A and Brespectively, and an analysis of the data which is discussed in the main body ofthe report.

The data presented in this report differs from previously available informationin that it probes in detail the secondary flow regions near the model surface aswell as outer or primary areas of the crossflow plane. The resulting measurementsallow the presence of secondary vortices and shear layers to be determined. Furtheranalysis is carried out by integrating the crossflow plane velocities to determinethe crossflow plane streamlines. The resulting streamline patterns are interpretedin light of topological considerations. From this point of view it is possibleto gain an alternate perspective on the onset of asymmetry and the process ofvortex shedding.

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CHAPTER 2

NOMENCLATURE

Cp average value of (p-p.)/(qsin 2a)for 100 data points taken at eachvisit to a pressure tap

SF y/(Dqsin 2a)

Cypeak maximum Cy value.

D model diameter (5.715 cm)

Fy side force per unit length

q free stream dynamic pressure

Res Reynolds number based on freestreamproperties and D/sina

U0 freestream velocity

v,w velocity components in y, z directions

x, y, z cartesian coordinates (see Figure 1)

I angle of attack

r circulation (m2/sec)

Xr/(wDU 0sina) (sec- )

* circumferential angle (windward is * f 1800)aCp standard deviation of Cp

°Vc /Ov2+awl, where ov and aw are the standarddeviations of v and w respectively.

model roll orientation

[r/unit area] D/(7rUosin)

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CHAPTER 3

DESCRIPTION OF THE MODEL, INSTRUMENTATION AND EXPERIMENT

The experimental model shown in Figure 1 was a 5.715 cm in diameter tangent ogivewith a nose fineness of 3 and an afterbody length of 9.6 calibers. The sharpnuse tip could be unscrewed and replaced with a 10% blunted (spherical) nose tip.Six cross sectional stations were each instrumented with 24 pressure taps locatedcircumferentially at intervals of 150. Pressures were monitored using threeinternally mounted + .1 psi Setra differential pressure transducers. Each ofthese devices was connected to a 48 port internally mounted Scanivalve allowingall 144 pressure taps to be sampled. In order to maximize the response of thepressure measuring system the lengths of the tubes connecting pressure taps toScanivalves were minimized. Pretest calibrations indicated that pressurefluctuations on the order of 500 Hz could be measured.

The crossflow planes were surveyed using a two dimensional, two colorbackscatter LDV system shown schematically in Figure 2. In order to adequatelysurvey the entire leeward flow field, the model was mounted on the tunnel wallopposite the window through which the LDV measurements were made. The refractionresulting from the oblique passage of the laser beams through the glass wascompensated for by optically alligning the focal volumes of the two differentcomponents inside the tunnel. Off-axis collecting optics were used to minimize thefocal volume size which was estimated to have a diameter of .37mm and a lengthof 1.47mm. Directional ambiguity for both components were removed with the aidof Bragg cells. A coincident circuit was used to insure that both components ofvelocity were measured within a pre-selected time window. In general most of theoptical and electrical components for the LDV system were manufactured by TSI(Thermo-Systems Inc.). This included beam splitters, color separators,photomultiplier tubes, Bragg cells and counter type signal processors. Scatteringparticules consisted of olive oil atomized to a 1.5 micron diameter by a Laskinnozzle. The aerosol was injected upstream of the turbulence damping screens tominimize flow disturbance.

Experiments were conducted in the Naval Academy lm by 1.3m subsonic tunnelwhich has a nominal free-stream turbulence level of 0.1%. Tests were restrictedto an incidence of 450 and free-stream velocity of 24m/sec which produced an Resof 1.5(105). As discussed in Ref. 15, this resulted in a laminar boundary layerseparation. The wind tunnel model was mounted on the side of the wind tunnelwall illustrated in Figure 3. To increase the rigidness of the mounting, foursupport wires were attached to the model at a distance of 12.6 calibers from thenose tip.

Pressure alone tests were initally made on the sharp untripped model at thetwelve roll angles; 00, 300, 600... 3300 . Measurements were integrated todetermine the magnitude of the normal and side forces. The model was thenpositioned to a roll orientation featuring a maximum side force and detailed flow

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surveys were initiated. Unfortunately, the flow field exhibited a tendency tochange levels of asymmetry during a test and side force levels were also notrepeatable from test to test. Accordingly: a trip was added to the model nosetip to stabilize the flow field. The trip, shown in Figure 4 consisted of 0.45mmgrit glued to the model surface near the nose in a strip 5mm long and imm wide.Pressure alone tests were then repeated to determine a roll orientation whichproduced high side force levels and flow field surveys were than conducted atthis roll angle. A final series of tests were also made on the blunted modelusing a roll orientation which produced the highest observed blunt model sideforce. An outline of tests in which LDV data was taken is provided in Table 1.

The surface pressure data were acquired three ports at a time using theinternally mounted Scanivalves and transducer arrangement. At each pressure port100 samples were taken which allowed both pressure mean and standard deviationvalues to be determined. The LDV velocity data were measured by focusing thesystem on a specific point in the flow field. Velocity measurements were acquiredwhenever both v and w components were measured within a 100 p sec. window. Here100 samples were also taken at each point in the flow field allowing both themean and standard deviation values to be calculated. In the secondary flowregion near the leeside of the model surface, measurements were taken with ay, z spacing which varied from .76mm near the model nose tip to 1.27mm on theafterbody crossflow planes. This spacing was increased by a factor of 3 to 4 in theouter portions of the flow field. Pressure alone tests could be completed inabout 10 minutes while the LDV surveys which measured velocities at as many as 950points in a crossflow plane lasted up to three hours.

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CHAPTER 4

INFLUENCE OF THE NOSE TRIP

During the long experiments in which crossflow plane velocities were measured,the flow field occasionally changed level of asymmetry. This was determined bymonitoring the surface pressures throughout the tests. Measured variations inthe side force during the two sharp, untripped model tests are shown in Table 1.The level of variation was felt to be unacceptably large, hence the previouslydescribed trip was added to the model nose. Trips applied near the model nosehave been successfully used by other investigators to stabilize the flow eld1 6 .The magnitude of the peak local side force, Cypeak , with and without the ipin place is illustrated in Figure 5. The addition of the trip usually i easedCypeak, particularly at roll orientations which featured low side force __sin the untripped case. The grit trip also was found to produce a side f,which was repeatable throughout long experiments. In successive experimthe repeatability degraded somewhat as can be seen in Appendix B, howeve ._akwas still well reproduced. Application of a tape trip with a similar pla, .urmwas found to produce a more drastic effect which included reversal of the sideforce direction. This is more in keeping with the results of Ref. 16 where atape trip was found to control the side force direction except at roll orientationswhich placed the trip near the windward plane.

Although addition of the trip stabilizes the flow field, it is relevant to askwhether the presence of the trip alters the fundamental character of theflow field. It was noted in Ref. 12 that a side force characteristic which appearsrepeatable from test to test and facility to facility is the relation betweenthe axial location at which Cypeak or Cy = 0 occur and the magnitude of Cypeak.If the character of the flow field is unchanged by the addition of the trip, thetripped data should reproduce the previousl, observed relationship. As is shownin Figure 6, data taken on the untripped model from both this study and Ref. 12are in reasonable agreement with the tripped results. This suggests that thetrip locks the flow field into a pattern typical of the untripped model and doesnot fundamentally alter its character.

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CHAPTER 5

PRESSURE AND FLOW FIELD MEASUREMENTS

Pressure coefficient and standard deviation data taken on the sharp trippedand blunt models are illustrated in Figures 7 and 8 respectively. During theseexperiments, results repeated reasonably well during each test and from run torun. The data provided in these two figures is representative of the sharptripped and blunt model pressure measurements respectively. During the sharp,untripped model tests, the level of asymmetry was low and the measured side forcechanged during each run. In Figures 9a and 9b are illustrated the circumferentialCp distribution corresponding to the lowest and highest side force levelsencountered during runs I and 2.

The measured crossflow plane velocity vectors taken in the tests on the sharpuntripped, sharp tripped and blunt model are illustrated in Figures 10, 11 and 12respectively. Clearly visible in these figures are points located adjacent to themodel surface where the velocity component parallel to the surface reversesdirection. These locations are interpreted as attachment and separation pointsand are marked by an S and Ss respectively. Also marked by Ss are the windwardseparation points on each side of the body whose locations are estimated usingboth velocity and pressure data. Evident in Figures 7 and 9 are locations wheremaximum values of C0 occur. Such points are marked by P in Figures 10 to 12.Similarly, regions on the leeside of the body exhibiting large 1--essure gradientsin Figures 7 to 9 are marked in Figures 10 to 12 by a G.

As is evident in Figures 10, 11 and 12, the crossflow plane surveys consistedof closely spaced measurements taken near the model surface and measurements takenfarther from the model surface which are located a greater distance apart. Alongthe interface between the finely and coarsely spaced data occur points which havebeen probed twice; once as part of the finely spaced measurements and once aspart of the coarsely spaced measurements. In Figures 10, 11 and 12 both sets ofdata have been plotted which provides a measure of the repeatability of the results.Near the outer edges of the crossflow plane coincident velocity measurements aregenerally indistinguishable, but in the vicinity of vortices a difference canoften be seen (e.g. Figure lob).

The vorticity throughout each crossflow plane is calc lated by dividing thesurveyed area into quadrilateral elements with corners located at points whereflow field velocities are measured. The circulation associated with each elementis determined from:

r v.T = 1/2 [nl2.(Vl + v2) + n23"(v2 + V3)

+ n34"(V3 + v4) + n41"(v4 + Vl)] (1)

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Here nij is the vector connecting element corners i and j while vi is thevelocity at corner i. The computed circulation is assigned the location of theelement centroid. Isovorticity contours resulting from this calculation aredisplayed for the sharp tripped, sharp untripped and blunt models in Figures 13,14 and 15 respectively. Also indicated in these figures are regions of highvelocity fluctuations in which the standard deviation of the crossflow velocity,0Vc, exceeds .3Uw.

A convenient method of characterizing the crossflow plane is to divide it intothe regions shown in Table 2 which contain vorticity of the same sign. Thecirculation computed at each element in the crossflow plane is assigned to one ofthese regions allowing the total circulation in each region to be calculated. The fewelements which do not possess a symmetric counter part with respect to the pitchplane are excluded from the summation. The outer portion of the crossflow planeis divided into two primary regions, designated by a P, which contain circulationof opposite sign. Secondary flow structure often is visible near the modelsurface. On each side of the model the secondary crossflow plane areas aredivided into two regions, S and S2 which contain circulation of opposite sign.The boundaries between all three regions are somewhat subjective. Most easilydetermined is the dividing line between regions containing circulation ofopposite sign where the zero vorticity contour provides a convenient demarcationline. The boundary between the primary and secondary regions with circulation ofthe same sign is taken to be the contour with the minimum vorticity value. Thecalculated circulation of the primary and secondary regions are provided inTable 2.

In two of the cases listed in Table 2, the strength of one of the secondaryregion, )Sl, is marked with an asterisk. Here the surveyed portion of the flowfield clearly omits areas of high vorticity and the calculated strengths isunreasonably low. These tabulated values are estimated using the known ratio ofASl left to As1 right from nearby crossflow planes and the measured value ofXSl right-

It is important to note that the circulation contained in each region cannotnecessarily be associated with a vortex since not all regions contain vortices.Also, in region S1, there often exists both a strong shear layer which springsfrom the separation point and a vortex. Here the circulation attributable toeach structure cannot be determined.

Additional information concerning the structure of the flow field can beobtained by constructing the crossflow plane streamlines. A streamline can begenerated by integrating the equations:

dw (2)dt dt

from a starting point. The starting points are selected by trial and error tohighlight regions near the vortices and separation points. To evaluate Equations(2) a description of v and w throughout the surveyed portion of the crossflow olaneis necessary. Such a description is constructed using a bilinear interpolatingfunction of the form a + by + cz + dyz to specify each velocity component withinan element. Here a, b, c and d are constants evaluated using the measuredvelocities at the corners of the element. This provides a continuous description

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of the velocity throughout the crossflow plane. As is noted in Refs. 18 and 19the crossflow plane streamlines are not the projection of the three dimensionalstreamlines into the crossflow planes, but are instead the streamlines producedby the crossflow velocity vector field.

The streamlines determined by the above intcnation procedure are shown inFigures 17, 18-and 19, for the sharp tripped, sharp untripped and blunt modelsrespectively. These figures illustrate two notable characteristics. First,streamlines originating near the estimated primary separation points do not feedinto vortices but instead skirt the recirculation flow region. Second, streamlinesnear vortex cores often have a pronounced inwards or outwards spiral. Using thevelocity measurements of Figures 10 to 12 it is possible to resolve the directionof spiral. Pronounced inwards or outwards spirals tend to occur in flow fieldsfeaturing high asymmetry. In such cases primary vortices which are clearlyresolvable on adjacent crossflow planes usually retain the same direction ofspiral. The more symmetric flow patterns feature vortices with poorly defineddirections of spiral. Limit cycles are often observed with the direction of spiralchanging across the limit cycle. In these cases it is conceivable that thepresence of a spiral rather than a set of closed streamlines is a result ofexperimental error.

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CHAPTER 6

6.1 TOPOLOGICAL NOTIONS

It has recently been suggested that the crossflow plane structure can beconveniently characterized in terms of singularities, or points where thecrossflow velocity is zero. 17,18 Several types of singularities occur in theflow fields illustrated in Figures 10, 11 and 12. Saddle singularities occur onthe model surface as attachment or separation points. Also classed as saddlesingularities are crossflow plane stagnation points interior to the flow fieldwhich are formed by the intersection of four streamlines, two directed towards thesingularity and two directed away from it. Nodal singularities only occur off thebody surface as stagnation points about which the streamlines spiral or circle.This structure is reminiscent of a vortex and in this report, the term vortex andnodal singularity will be used interchangably. For a more complete discussion ofsingularities, the reader is referred to references 17 and 18.

These topological notions are useful in analyzing the structure of the crossflowplane for two reasons. First such notions provide a concrete definition of severaltypes of flow field structures. A vortex, for example, must contain a singularpoint. Thus the left secondary flow region depicted in Figures 10c and 16d isseen to contain a vortex and a shear layer rather than two vortices. Secondly,assuming that the crossflow plane is a continuous vector field and thatsingularities are limited to points, it can be proved that the following relationmust exist between the number of nodes and saddles: 18

Nv - Ns - (N;) = -1 (3)

Here Nv is the number of nodes or vortices while N' and s represent the numberof saddles on and off the body surface respectively. This rule does not definecrossflow plane structure but precludes certain structures. It may also point tothe existance of certain flow field features which are not resolvable with theavailable experimental data.

The streamline integration patterns shown in Figures 16, 17 and 18 illustratethe existence of both vortices and saddle singularities throughout the surveyedcrossflow planes. The primary region generally contains two vortices and a

saddle point. This saddle point, which is usually located in between thesevortices, is an important landmark and will be referred to as the primary saddlepoint. The secondary region on each side of the body often contains two vorticesand a saddle point. The saddle is not always clearly visible, howeversatisfaction of Equation (3) mandates its existence. In other instances, onlya single secondary vortex is present in this secondary region. A number of saddlepoints occur on the model surface. In all cases an attachment saddle is visiblenear the center of the model on the leeside. Also, on each side if the model aseparation saddle can be seen marking the windward extend of the separation region.These attachment and separation saddles will be referred to as the rear attachment and

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primary separation points respectively. When secondary vortices occur, anadditional separation and attachment saddle occur on each side of the model. Notvisible in the flow field surveys is a saddle of attachment which must occur onthe windward side of the body, often termed the crossflow plane stagnation point.

Using the results from the streamline integrations, it is possible to constructcrossflow plane topologies which contain the correct number of nodes and saddlesto satisfy Equation (3). As an example, sketches of the crossf low plane topologyfor the sharp, tripped model are exhibited in Figure 19. The left primary vortexand primary saddle are shown as combined in Figure 19c. Inclusion of these twostructures would also satisfy Equation (3).

6.2 FLOW FIELD DEVELOPMENT ON THE SHARP TRIPPED MODEL

The tabulated circulations on the surveyed crossflow planes are shown inTable 2. On each plane a net negative circulation occurs which increases inmagnitude with increasing distance from the model nose. The magnitude of the netcirculation increases in rough proportion to the size of the local side forcecoefficient. Also indicated in this table are the circulation strengths of theprimary and secondary regions P, S1 and S2 associated with each side of the model.As expected, the largest circulation occurs in P. The circulation contained inSl is about half as large as that in P while that in S2 is on the order of atenth of that in P.

At the forward most crossflow plane probed, which is at X/D = .75, the outeredges of two primary vortices can be seen. In this crossflow plane which isillustrated in Figure lOa, the primary saddle is not fully visible, but is likelyoffset to the left.

The crossflow plane velocity field at an axial station of X/D = 1.3 is shownin Figure lOb and features two primary vortices but no secondary vortex structure.The vortices and primary saddle point appear to be symmetrically located; however,the rear attachment point, marked by an SL is offset slightly to the right. Alsothe velocities between the two vortices, second row behind the model are allpointing to the left. As is shown in Figure 16a, the resulting streamline patternis highly skewed. The left and tLght vortices both spiral outwards and thewindward streamline from the primary saddle point does not attach to the modelsurface, but moves around the left vortex and then out the leeside of thevisible flow field. A topological sketch of this crossflow Plane which satisfiesEquation (3) is provided in Figure 19a.

At an axial station of X/D = 2.6, both primary and secondary vortices arevisible in Figures 10c and 16b. The left primary vortex has moved away from themodel surface while the right primary vortex ha; rotated towards the leeside.The primary saddle point has moved away from the model and to the left. Thewindward streamline from the primary saddle point feeds into the left vortexwhich has reversed its direction of spiral when compared to the axial station atX/D = 1.3 and now spirals inwards. The right primary vortex retains the outwardsspiral visible at X/D = 1.3. Streamlines originating in the vicinity of the rightprimary separation point pass between the two primary vortices and leave thevisible flow field from the left side. The streamlines originating near theleft primary separation point also leave the visible flow field from the left side.

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As can be seen in Figures lOd and 16c, the same flow field structure whichexists at X/D = 2.6, persists at X/D = 3.6. The left primary vortex has movedfarther from the model surface, but it still spirals inward and is fed by astreamline from the primary saddle point. The right vortex continues to spiraloutwards, except very near to the vortex core where a limit cycle occurs. Thetopology sketched in Figure 19b which satisfies Equation (3) is representativeof the crossflow plane structure at X/D = 2.6 and 3.6.

The maximum measured side force coefficient occurs at X/D = 4.7 and theaccompanying flow field structure differs from that at X/D = 2.6 and 3.6. InFigure 10e only the right primary vortex is clearly visible. The distancebetween the left primary vortex and primary saddle point has decreased suggestingthat these two structures have combined. The term combined is applied sinceboth structures must disappear simultaneously in order to satisfy Equation (3).A careful construction of streamlines in the vicinity of the left primary vortexand adjacent saddle which is shown in Figure 16d indicates that the process ofcombination is not complete. The right primary vortex retains the outwards spiralvisible at upstream stations and has moved leeward to a position nearly behindthe model. The secondary region has become highly skewed with the rear attachmentpoints and secondary separation points rotated in a counter-clock-wise direction.On the right side of the model, two counter-rotating secondary vortices arepresent while on the left side only one secondary vortex which rotates in a counterclock-wise manner can be seen. The clockwise rotating vortex and adjacent saddlepoint visible on this side of the model at X/D = 2.6 and 3.6 have combined toleave a strong shear region. An examination of the flow field adjacent to theleft primary separation point indicates the formation of a region of counter-clockwise rotation. Although this is not particularly evident in Fig. lOe, thecirculation of a number of adjacent elements in this region is positive suggestingthe formation of a new secondary vortex. The calculated strength of this newvortex is given in Table 1. A plausible topology for this crossflow plane whichsatisfies Equation (3) is shown in Figure 19c. Here the left primary vortex andsaddle are taken to be combined and are therefore not shown. Inclusion of thesetwo structures would also satisfy Equation (3).

Circumferential pressure profiles measured at the axial stations ofX/D = 2.6, 3.6 and 4.7 are shown in Figure 7. It can be seen that flow fieldasymmetry produces differing levels of pressure on each side of the model.Lowest pressures occur on the side of the model with the closest primaryvortex. The differing pressure levels occuring on each side of the model arebridged by sharp pressure gradients on the leeside of the model. These gradientsextend from below each primary vortex core to the rear attachment point and areindicated by a G in Figure lOe. At an X/D of 2.6, both primary vortices arelocated fairly close to the model surface and two pressure gradients of oppositesign occur. A single sharp pressure gradient exists beneath the right primaryvortex at X/D = 3.6 and 4.7. Also indicated by a P in Figure 10 are points onthe model surface where the pressure standard deviation reaches peak value.These peak values are located in the vicinity of the large pressure gradients andare likely caused by an unsteady circumferential motion of the vortex pattern.Such unsteadiness moves the position of the surface pressure gradients andproduces large pressure fluctuations at fixed points on the model which arelocated nearby.

17

NSWC TR 82-394

A comparison of Figures 7 and 10 indicates that secondary vortices have littlediscernable effect on the measured surface pressures. This is probablyattributable to the small circulation strengths of these structures. Table 2indicates that the circulation contained in the S2 region is typically small.The strength of the vortices in the S1 region cannot be determined since thisregion contains both a strong shear layer and a vortex.

6.3 FLOW FIELD DEVELOPMENT ON THE SHARP UNTRIPPED MODEL

On the sharp untripped model, surveys were carried out at X/D values of2.6 and 5.7 with the latter survey covering only the secondary region. FromAppendix B it is evident that the side force levels on the untripped model aremuch lower than those measured on the tripped model. As was previously mentioned,fluctuations in the surface pressures were noted in tests involving the untrippedsharp model. The level of variation is indicated in Table 3 where samples ofside force data spanning runs 1 and 2 are shown. The crossflow planes at X/D of2.6 and 5.7 were probed in runs 1 and 2 respectively. It can be seen from Table 2that side force levels in both of these runs were fairly steady at the axiallocations where the velocity measurements were made.

At the axial station of X/D = 2.6 little asymmetry is visible in the crossflowvelocity vector plots and streamline contours of Figures lla and 17 respectively.As is shown in Table 2, the net circulation is nearly zero and the side forcecoefficient, although fluctuating slightly, is also small. The crossflow planeclearly contains two primary vortices and on each side of the model two secondaryvortices. The streamlines originating near the estimated primary separation

points do not roll up into the primary vortices but skirt the recirculatory regionand pass out of the surveyed portion of the flow field on the side of the modelfrom which they originated. This is in contrast to the asymmetric case shown inFigure 16b where the streamlines originating near the right primary separationpoint pass between the two primary vortices and out of the visible portion ofthe flow field from the left side. Another notable aspect of the streamlinepattern is the windward streamline from the primary saddle point. As in theasymmetric case this streamline does not attach to the body but circles aroundthe left vortex. Neither of the primary vortices has a well defined directionof spiral and limit cycles occur near each vortex.

At an axial station of 5.7, only the secondary portion of the flow field wassurveyed. The primary vortices appear to have moved to the right since the rearattachment point is on the right side of the model. On the left side of the modeltwo counter rotating vortices are visible in the secondary region shown inFigures llb while on the right hand side only one vortex appears to exist.The second vortex has presumably combined with the adjacent saddle in a similarmanner to that observed on the rfrht hand of the sharp, tripped model atX/D = 4.7 (see Figure 16e).

The pressure distributions on the sharp untripped model are presented inFigure 9 and display the same general features which occur in the asymmetric case.In low side force cases where the flow field is relatively symmetric, a sharppressure gradient occurs beneath each primary vortex. A single pressure gradientoccurs when a larger side force is present (e.g. Figure 9b) and is likelylocated below the closer of the two primary vortices. As in the case of thetripped model, the secondary vortices do not induce a discernable effect on thecircumferential pressure distribution.

18

NSWC TR 82-394

6.4 FLOW FIELD DEVELOPMENT ON THE BLUNTED MODEL

The blunt model was tested at a roll orientation producing a Cypeak of .95,which is one of the highest values observed for this model. The velocity datawas measured at axial stations with X/D values of 2.6 and 5.7.

Crossflow plane velocities and streamlines at X/D = 2.6 are shown in Figures12a and 18a respectively. This crossflow plane contains two primary vorticesand two secondary vortices of opposite rotation on the left side of the model.On the right side of the model only a secondary vortex of clockwise rotation ispartially visible. The primary vortex pattern is slightly offset to the left sideof the model. As is shown in Table 2, the net circulation is positive as is thelocal side force. This is in contrast to the sharp tripped model case where anet negative circulation is associated with a positive side force. The streamlinesin the vicinity of the right primary vortices show a pronounced outwards spiralwhile those near the left primary vortex feature a limit cycle with an outwardsspiral inside of the cycle and an inwards spiral outside of it. Streamlinesoriginating near the primary separation points skirt the recirculatory flowregion and leave the flow field from the same side on which they started. Thewindward streamline from the primary stagnation point does not attach to thebody surface, but instead circles around the right vortex. When compared to thesharp untripped model streamline pattern, a strong similarity is evident. In theblunt model case, though, the primary vortices appear to have a more defineddirection of spiral.

The blunt model achieves its maximum side force at X/D = 5.7. The measuredflow field at this axial station is displayed in Figures 12b, 18b and showssignificant asymmetry. The primary vortex pattern is offset to the left. Unlikethe tripped, sharp model flow field, the left hand vortex has not moved awayfrom the model. The secondary flow field region has two counter rotatingvortices and a saddle on each side of the model but these areas are clearly notsymmetric in structure or location. The attachment and separation points notedin Figure 12b are offset in a counter-clockwise direction. On the left side ofthe body the secondary vortex of clockwise rotation has moved away from the bodysurface. The net circulation over the surveyed portion of the flow field isslightly positive as indicated in Table 1. The streamline pattern which is shownin Figure 18b features primary vortices which have a well defined outwards spiral.This structure is reminiscent of that visible on the sharp tripped model atX/D = 1.3 (see Figure 16a). As in the sharp, tripped model case, streamlinesoriginating near the right primary separation point appear to pass between thetwo primary vortices and then out of the surveyed portion of the flow field fromthe left side. An unusual aspect of the blunt model flow field can be seen byconsidering Figures 8 and 15b which indicate that both the velocity and surfacepressures show very high levels of fluctuation.

The pressure profiles on the blunted model are very similar to those on thesharp model. The different pressure levels which form on each side of the modelwhen a side force occurs are bridged by sharp pressure gradients which occurbeneath the vortex nearest to the model surface. The symmetric primary vortexpattern, which occurs at X/D = 2.6 features pressure gradients beneath eachprimary vortex.

19

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CHAPTER 7

DEVELOPMENT OF FLOW FIELD ASYMMETRIES

It has been suggested that flow field asymmetry is a manifestation of ahydrodynamic instability which develops when primary vortices are crowded together.

19

Peake, et al. 1 1 form the hypothesis, based on Nishioka and Sato's20 incompressiblecylinder data, that amplification of perturbations in the flow field near theprimary saddle point results in the development of the asymmetric flow field.Irregularities in the model geometry serve only to determine the extent anddirection of the flow field asymmetries. The results from the current studysupport the hypothesis that the flow field near the primary saddle point plays aprincipal role in the formation of the asymmetric flow field. Many of thecrossflow planes surveyed appear to be symmetric both with respect to vortexlocation and strength. However, in all cases the windward streamline from theprimary saddle point does not attach to the body surface but insteady circles aboutone of the primary vortices as is indicated in Figures 16 to 18. It thus seemsto be this streamline which first reflects flow field asymmetry and presumablyonly small perturbations in the vicinity of the saddle point are sufficient tocause this streamline to detach from the model surface.

Using the streamline traces of Figures 16 to 18 it is possible to constructa description of vortex shedding in terms of saddle and nodal singularities.Small perturbations near the primary saddle point leads to a detachment of thewindward primary saddle streamline from the body surface, as is shown in Figures17 and 18a. This streamline initially appears to roll up into one of the twoprimary vortices, neither of which have a well defined spiral direction.Figures 16a and 18b suggest that as the asymmetry in the crossflow plane grows,both vortices tend to develop a well defined outwards spiral. The windwardstreamline form the primary saddle now circles one of the vortices and thenpasses out the leeward side of the surveyed flow field. This topology isillustrated in Figure 19a and still features primary vortices which are relativelysymmetrically located. As the crossflow plane asymmetry increases, one of thevortices moves away from the model and reverses its direction of spiral to inwardsas illustrated in Figures 16b and 16c. The windward streamline from the primarysaddle now feeds into this vortex and the resulting crossflow plane topology isillustrated in Figure 19b. Further asymmetry development leads to a combinationof a primary vortex and the primary saddle. Figure 16d suggests that such acombination occurs while Figure 19c illustrates the resulting topology. Clearly,in order to satisfy Equation (3), the vortex and primary saddle must simultaneouslydissappear from the flow field.

It is of interest to compare the topological description of asymmetrydevelopment with the more conventional view of this process. Traditionally thecrossflow plane has been visualized as containing both shed and attached primaryvortices. Each attached vortex is connected to a primary separation point by afeeding sheet. As asymmetry develops and a vortex starts to move away from thebody surface, the feeding sheet is torn and the vortex is shed. In the current

20

NSWC TR 82-394

study the calculated crossflow plane streamlines which originate near theprimary separation points do not feed into vortices. Hence the current data doesnot define a feeding sheet and an analog to the tearing of the feeding sheet isnot evident. The clearest topological landmark visible in the asymmetrydevelopment process is the combining of the primary saddle and a primary vortex.This occurance provides a convenient definition of vortex shedding in the currentstudy. However, the present study is limited in scope and it is not clear whethersuch a combination process takes place as subsequent vortices are shed or underdifferent test conditions. Thus, the general applicability of this definition ofvortex shedding remains to be demonstrated.

The blunt model experiences,in general,a much lower level of side force thandoes the sharp model. Not only are maximum side loads lower, but average valuestaken over many different roll angles are significantly less. The maximum localside force occurs on the blunt model at X/D = 5.7. The resulting velocity andstreamline data at this axial station are shown in Figures 12b and 18b respectively,and represent a roll orientation with the highest observed side force. From thesefigures it is evident that the maximum degree of flow field asymmetry whichoccurs on the blunt model is much less than that observed on the sharp model (seeFigures 10 and 16). In fact, the degree of asymmetry is sufficiently low on theblunt model to suggest that vortex shedding does not take place. The reasonfor the difference in asymmetry levels observed on the sharp and blunt modelsremains unclear. A comparison of the blunt measurements taken at X/D = 2.6 withthose at the same axial station on the sharp and sharp, tripped models indicatesthat the general flow field structure is qualitatively the same. Quantitativelysome differences are detectable which include a 10% to 15% reduction in primaryvortex strength in the case of the blunt model. An interpolation of the measuredvelocities along the pitch plane indicates that the primary saddle point isclose: to the body surface on the blunt model than on the sharp model. Also, onthe blunt model asymmetries in vortex strengths are principally confined tosecondary vortices. However, it is difficult to construct an explanation for theapparent increased stability of the blunt flow field from any of these observeddifferences and the best hypothesis appears to concern the absence of a sharp nosetip. Near the tip of a sharp nose the local diameter is small and localirregularities may amount to extremely large local perturbations. A similarperturbing mechanism does not exist on the blunt model.

21

NSWC TR 82-394

CHAPTER 8

SUMMARY AND CONCLUSIONS

A tangent ogive model with nose fineness of three has been tested in incompres-sible flow at an incidence of 450 and with a Reynolds number producing laminarseparation. The model was rigidly supported in the wind tunnel which had astreamwise turbulence level of .1%. The model's sharp nose tip was interchangedin some tests with a 10% spherically blunted one. In tests on the sharp model,a strip of grit placed near the nose was often used to stabilize the flow field.Both surface pressures and crossflow velocities were measured on several crossflowplanes. A two component LDV system was used to probe the flow field near theprimary separation points as well as further out from the model. Axial stationsupstream of the location at which the maximum side force occured were investigated.Based on the data taken in this study the following conclusions can be drawn:

1. Use of a grit trip near the model nose stabilizes the flow field withoutchanging its basic side force characteristics.

2. In addition to two primary vortices and a primary saddle, the flow fieldgenerally contains two counter-rotating secondary vortices and a saddlepoint on each side of the model.

3. The development of the asymmetric flow field on the sharn tripped modelup to the point of maximum side force can be characterized by the followingthree steps:

a. Flow field asymmetries seem to originate with instabilities at theprimary saddle point. The windward streamline leaving this pointdetaches itself from the body surface, circles about one of thevortices and then moves out into the leeward flow field.

b. The vortex circled by this primary saddle point streamline movesaway from the model.

c. The primary sAddle and a primarv vortex appear to combine on the

crossflow plane at which the peak side Force occurs. The point ofcombination appears to offer a convenient definitionof vortex shedding.

4. Blunting the model nose by 10% drastically reduces side force and thedegree of flow field asymmetry. The windward primary saddle point stream-line detaches from the model and circles a primary vortex as in the sharpmodel case. However, at the axial station featuring maximum Cy, neitherprimary vortex appears to be in the process of shedding. The increasedstability of the blunted model flow field is hypothesized to be related tothe absence of a slender nose tip on which model irregularities becomelarge perturbations.

22

--- - ----

NSWC TR 82-394

ACKNOWLEDGMENTS

This project was supported by William C. Volz of the Naval Air Systems Command.The authors wish to thank Commander Paul Schlein and his staff at the U. S. NavalAcademy for making the wind tunnel testing facilities available.

23

NSWC TR 82-39h

z

Y

X/D =2.6X 3.6

4.7 GYWR

5,O.7 5. SUPPORT

". 3 /

D 66D

Figure 1. Tangent ogive pressure model arid vupport

24

NSWC TR 8--) 1

2-D BACKSCATTER LDV

a 450

I=> 3FT x 4Ff

FLOW TEST SECTION

22 COLOR

COLLECTING OPTICS

Fii~lire 2. 2c'homat-i e of the l,*uver i o 1-- meter

25

NSWC TR 82-39),

".~~emodel mounted in the wind tunnel

26

cm1Fir-ure h. Nose trip wrvi e !poit

27

NSWC TR 82-394

SHARP MODEL3 a = 4503-

0 NO TRIP

Cypeak 2t •TRIPPED

I TRIP ONTRPOLEEWARD WINDWARD

PLANE PLANE

030 6901201501 210 240270300330

0-1

-2

-3 L

Figure 5. C as a function of model roll anglepeak

28

NSWC TR 82-39h

9-

C y " 0 o 0 0 0 0 0elocation 0 0

X'/D 0 00-eoA A 0 0AA U0 0

A6A A

5

7

00 A6 -°°e o o0

Cypeak OA Alocation A- 8

X'/D 5 A

0 NO TRIP o& TRIPPED

A ,L

4 o NO TRIP, REF 17A NO TRIP, HIGH

TURBULENCE3

2(i I a I I 1_1 I I

0 .5. 1.0 1.5 2.0 2.5

Cypk

Firure 6. Axial location of' !Itr 1 a' , faunctionl of C.Yjl-ak ypeak

29

r7NSWC TR 82-394

.3

0 i,,C

1.2 2.L

I II

-180 150 -90 -60 -30 0 150

--0 30 60 90 120 180

-1.0

o X/D = 2.6. Cy = .77A X/D = 3.6, Cy = 1.48.13 X/D = 4.7, Cy = 2.11

--- 3.0

Fiure 7. 2 ircumferential pressure distriutions on the sharp, trippedno(,el. (pen Symbols are anr sol i ones are o

c p

30

NSWC TR 82-394

0 X/D 2.6, Cy = .33 Cp ,A X/D=5.7, Cy = .93 1

.452

/.2 P )or

1504

r--T- \

-180 -150 120 -90 -60 -30 30 60 90 120 180

- 1.0

-2.. 1

Figure 8. Circumferential pressure distributions on the blunt model.

Open symbols are C and solid ones are a

p p

31

NSWC TR 82-39h

A) Highest side force case.

-.6 -3.

acp Cp

-.44-2.\

~1 "'- W --

0C

-180 -150 -120 -90 -60 -30 30 60 90 120 150 180

a A -1.

0 X/D = 2.6, Cy = .27

O X/D = 5.7, Cy = 1.205

Figure 9. Circumferential pressure distribution on the sharp,untrippedmodel. Open symbols are C and solid symbols are a

p p

32

NSWC TR 82-394

B)Lowest side force case

GCp .6--

4

/ 40 -0, ir Air 1.

-~ * 150

-180-150 -120 -90 -60 -30 0 30 60 90 120 180

I0 X/D= 2.6, Cy = .08603 X/D =5.7, Cy =-.022

Figure 9. (Continued)

33

NSWC TR 82-394

A) X/D = .75

Figure 10. Measured crossflow plane velocity vectors on the sharp, trippedmodel. S' and S' are attachment and separation points respec-

a stively. The P represents peak aC locations while the G indicates

regions of sharp pressure gradients

34

NSWC TR 82-394

B) X/D =1.3

7//iZi~


35

NSWC TR 82-394

C) X/D =2.6

,)/D2 / , Tt \ \ \\ \ ,

it

/7c

1G ,


36

NSCTE 82-394

D) X/D 3.6

/X7 t

Mir~

Figurle 1. (Cnt; ud

-~~I -A---

NSWC TR 82-394

E) X/D = .7


38

4 -

NSWC TR 82-394

E) (Continued) Enlargement of left secondary region.

4/4

4--


39

NSWC TR 82-394

E) (Continued) Enlargment of right secondary region.


40

1 7 A X/ D 2 .6N S W C TI R 8 2 -3 9 4

A) X/ = 2.

* It t '

Figure ]1. Measuzred crossflow plane velocity vectors on the sharp,untri pped model. S' and S' are the attachment and separation

points respectively. The P represents peak a locationls while

the Gl indicates regions of sharp pressure gradients.

41

NSWC TR 82-394k

B) XID 5.7

\ 4

%.4 '.r


42

NSWC TR 82-39h

B) (Continued) Enlargement of left secondary region.

k-

ii

3 +

Figure 11. (Conti.nued)

43

NSWC TR 82-39h

B) (Continued) Enlargement of right secondary region.

A


44

NSWC TR 82-394

A) X/D = 2.6

Figure 12. Measured Crossflow plane velocity vectors on the blunt model.S' and S' are attachment and separation points respectively.a s

The P represents peak aC locations while the G indicates

regions of sharp pressuA gradients.

45

NSWC TR 82-394

B) X/D 57

ZIP p

4 Z~

,*P p >3zv kk

Fiur 12.Cniud46

NSWC TR 82-394~

B) (Continued) Enlargement of the left secondary region.

_____ 71


47

NSWC TR 82-394

B)(Coltiflued) Enlargement of righat secondary region.

484

NSWC TR 82-394

A) X/D =1.3

SHARP, TRIPPED MODEL

X/D =1.3

>0ISOVORTICITY CONTOURS

49.

8.0W . . . . .

NSWC TR 82-394

B) X/D = 2.6* C = 7

/ - - ~-2.0

"-4.0

+2 +4.0

8.00

NSWC TR 82-394

C) xID =3.6, Cy= 1.52

-2.

/ -4.

/ ~ I2.

-2.1 ~-2.

22

Figur 134Cotnud

0451

NSWC TR 82-394

D) X/D 4.7 C -2.11

IX- +2.0

+4.0

......... +880

-88.0

Figre13+(onnud

+Z52

NSWC TR 82-394

X/D =2.6 , = .09

-4.0+4.

I i.U +80~+8+20

80.

onteshrun.p0dmdl - w.0 ; w

j7~~lO~ /U 4..

2.0 50

NSWC TR 82-394

A) XID =2.6 ;C = .33

-2.0 1

-4.

/'.; '~ (

Figure 15. Isovorticity contours and areas of' high velocity fluctuationson the sharp, untripped model. > 0; --- w < 0

0v /U > .3iC

54

NSWC TR 82-394~

B) X/D 5.7, C - .93

-2.0- t.0 :*~ 1 +2.0

N -. 0....... ......-40- j) X

.. 20.. ...

............ +8.0

2.0 +2.0

2.0 -- +4.0

+8.0


55

NSWC TR 82-394

A) X/D =1.3

Figure 16. Streamlines on the tripped model.

56

NSWC 'FR 82-394

B) X/D =2.6


Nswc TB 82-394

C) X/D =3.6/


58

NSWC 'PB 82-394

D) X/D 4.


59

Nswc TE 82-394

X/D =2.6

Figure 17. ',trewnlines on the ,harI, untrij'ped model.

60

NSWC TR 82-394~

A) X/D =2.6

Figure 18. Streamlines on the blunt model.

61

NSWC TR 82-394

B) X/D =5.7


62

NSWC TR 82-394

a) X/D = 1.3 b) X/D 2.6

SS

N N

S, S,

s' s ,/ N

Figure 19. Topological sketch of asymmetric flow development.

63

.... ... I - -IN II .. ... I '' I I=

I t'I=

- II I

NSWC T1R 82-394

0) XiD 4.7

fN

4N


64

NSWC TR 82-394

TABLE 1

WIND TUNNEL TESTS IN WHICH LDV DATA WAS TAKEN

CrossectionalPlane Surveyed

Run No. Model (X/D) Comments Test No.

1 Sharp, no trip 2.6 Flow field unsteadiness 81061602occured

2 Sharp, no trip 5.7 Only secondary region 81061701surveyed

3 Sharp, tripped .75 Vortices not clearly 81070702

resolved.

4 Sharp, tripped 1.3 81070701




8 Blunt 2.6 81071515

9 Blunt 5.7 81071601

65

- --- ----- ----

NSWC TR 82-394

TABLE -2

CIRCULATION CONTAINED IN REGIONS P, S1 and S2

X/D Left Hand Side Right Hand Side C

Secondary Primary Secondary Primary_ Xs-_ ASs 2 Ip X__X?_X

SHARP_ TIPPED ,ODEL.75 -.019 .010 -0

1.30 -. 218 .198 -.0202.60 -.218 .053 -.403 .209 -.046 .360 -.044 .77

3.60 -.265 .048 -.581 .245 -.070 .578 -.095 1.475

4.70+ -.332* .031 -.755 .297 -.064 .665 -.158 2.1

SHARP, UNTRIPPED MODEL

2.60 -.203 .068 -.412 .204 -.047 .388 -.003 0 ".2

5.70 .037 -.039 -.6b -8

BLUNT, TRIPPED MODEL

2.60 -.203 .048 -.346 .216 -.030 .340 .026 .33

5.70 -.188* .046 -.837 .201 -.048 .869 .043 .93

* Estimated

+ Second vortex with a X = .0023 starts to form on left hand side ofmodel.

P

sI Sl

66

NSWC TR 82-394

TABLE 3

SIDE FORCE VARIATION

Run 1Samp le

X/D 1 2 3 4

2.6 .093 -.018 0.86 .270

3.6 .038 -..18 059 .520

4.7 .013 -.47 .013 .909

5.7 -.075 -.723 -.022 1.205

Run 2

Sample

X/D 1 2 3 4

2.6 -.005 -.019 -.043 -.058

3.6 -.161 -.137 -.205 -.231

4.7 -.442 -.412 -.523 -.578

5.7 -.656 -.620 -.779 -.845

67

NSWC TR 82-394

CHAPTER 9

REFERENCES

1. Gowens, F. E. and Perkins, E. W., "Study of the Effects of Body Shape on theVortex Wakes of Inclined Bodies at M = 2.," NACA, 1953, RM A53117.

2. Fiechter, M., "Uber Wirbelsysteme an Schlanken Rotationskorpern undIhren Einfluss auf die Aerodynamischen Beiwerte," Deutsch-FranzosischesForschungsinstitut, Saint-Louis, 1966, Bericht 10/66.

3. Thomson, K. D. and Morrison, D. F., "The Spacing, Position and Strength ofVortices in the Wake of Slender Cylindrical Bodies at Large Incidence,"Journal of Fluid Mechanics, 50, 4, 1971, pp. 751-783.

4. Clark, W. H. and Nelson, R. D., "Body Vortex Formation on Missiles at HighAngles of Attack," AIAA Paper 76-65, 1976.

5. Clark, W. H., "Body Vortex Formation on Missiles in Incompressible Flows,"AIAA Paper No. 77-1154, 1977.

6. Fidler, J. E., Schwind, R. G. and Nielsen, J. N., "Investigation of Slender-Body Vortices," AIAA Journal, 15, 12, Dec 1977, pp. 1736-1741.

7. Yanta, W. J. and Wardlaw, A. B., "Laser Doppler Velocimeter Measurements of

Leeward Flowfields on Slender Bodies at Large Angle-of-Attack," AIAA Paper77-660, 1977.

8. Schwind, R. G. and Mullen, J., "Laser Velocimeter Measurements of Slender

Body Wake Vortices," AIAA Paper 79-0302, 1979.

9. Owen, F. K. and Johnson, D. A., "Wake Vortex Measurements of an OgiveCylinder at a = 36 Degrees," Journal of Aircraft, Sep 1979, pp. 577-583.

10. Wardlaw, A. B. and Yanta, W. J., "Flow Field About and Forces on SlenderBodies at High Incidence," AIAA Journal, 19, 3, Mar 1981, pp. 296-302.

11. Peake, D. J., Owen, F. K., and Johnson, D. A., "Control of Forebody VortexOrientation to Alleviate Side Forces," AIAA Paper 80-0183, 1980.

12. Yanta, W. J. and Wardlaw, A. B., "Multi-Stable Vortex Patterns on Slender,Circular Bodies at High Incidence," AIAA Journal, 20, 4 Apr 1982, pp 509-515.

13. Lamont, P. J. and Hunt, B. L., "Pressure and Force Distributions on a Sharp-Nosed Circular Cylinder at Large Angles of Inclination to a Uniform SubsonicStream," Journal of Fluid Mechanics, 76, 3, 1976, pp. 519-559.

68

NSWC TR 82-394

14. Wardlaw, A. B. and Morrison, A. M., "Induced Side Forces at High Angles ofAttack," Journal of Space Craft and Rockets, 13, 10, 1976, pp. 589-593.

15. Wardlaw, A. B. and Yanta, W. J., "The Flow Field About and Forces on SlenderBodies at High Incidence," AIAA Paper 80-0184, 1980.

16. Canning, T. N. and Nielson, J. N., "Experimental Study of the Influence ofSupports on the Aerodynamic Loads of an Ogive Cylinder at High Angles ofAttack," AIAA Paper 81-0007, 1981.

17. Hunt, J. C. R., Abell, C. J., Peterka, J. A., and Woo, H., "Kinematical Studiesof the Flows Around Free or Surface-Mounted Obstacles; Applying Topology toFlow Visualization," Journal of Fluid Mechanics, 86, 1, 1978, pp. 179-200.

18. Tobak, M. and Peake, D. J., "Topology of Two-Dimensional and Three DimensionalSeparated Flows," AIAA Paper 79-1480.

19. Keener, E. R. and Chapman, G. T., "Similarities in Vortex Asymmetries OverSlender Bodies and Wings," AIAA Journal, 15, 9, 1977, pp. 1370-1372.

20. Nishioka, M. and Sato, H., "Mechanism of the Determination of the SheddingFrequency of Vortices Behind a Cylinder at Low Reynolds Number," Journal ofFluid Mechanics, 89, 1, 1978, pp. 49-60.

69

NSWC TR 82-394

APPENDIX A

This appendix provides a listing of the measured crossflow plane velocitiesand standard deviations. The symbols using in the listing are defined as follows:

X,Y,Y - x,y,z coordinate (see Figure 1)

V,W - v and w velocity components

VS,WS - standard deviation of the v and w velocity components.

In some cases the standard deviation values are not available. In these instancesthe listed value is 0.0000. A tape containing the information provided in thisappendix is available on request.

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I N-..-.... P.M- - - -P.M-------- -4 - - P - - M N..4

NSWC TR 82-394~

*e p. 4*=0 * ~ e 4Omer M- mn.4.-0 O~. .~ omo.

o o 0 4 N040 . U0.4 a0.

~ *N~. :1 ........... :0 1 1 . . . . .

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CD 0

omee 0 Mx Z~

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N

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fu N N-.-N N nMmt o0# tM

cMNNNNN i'N ~~ M ~ M p~ O * E E * 4 * 4 Z N o ryMM

A-1-5

NSWC TR 8a-394

lot: m@N m44Nt@4NN-4 0 0,0* 41, @ 0N I5 0N P 40dy*5A0N~4P-4m 00N045 40N00N~-~0~FIN aA~4.Wa0 44P~al0a0- a~0fl 4ON 4O00l.U fl05 N00 p.*..N@ ... 0 S~4 N@. @0a

34 4NN~ 4NN0 44400 0 ;";e 40 00 N Nowa 0@ pa e

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a,~ None Om r:-a. M* I.

N- to tm0 @O N@ NN -mm NmN aNN @0.. ft .. oNN o.oeN-ftoN .ooo.P

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00 00ID Zzz

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3 04 N 0 M A 0 0 PS' v 0 M S0 0P 0 0P S4P l .. 0 N N A @ 4 0al4 0N4N44 44444 404N 44044 NNNN 4 411 00 N4 4 4NN*p.0 1

0t

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a mm N m N mn a m

@ NN NN N-N NN NN @ O- 0.--0 @0O -0 -..A-..16.

INSWC m 82-394

.m .0 . .em . .e 40 1 . .m*. N.A4*0 . .. .. .. . .. .0...* *me00I'n# *n Oi Mol a & IV n P@-0 4M m0'"nef ec4t,..me.....e...

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0 ,V N004 N0 N .. N N . N 4 N N a 0 N4.4 0 .e0a4. N eN .. 04gi0IA 44P-4 *O44AsNNP-0f-io - - - -N00a00 4N .....- 44N00 ...- 0 N .. N-

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-a.-0N-4m-NN~f14N4Naa. -17eO.0N-NN04NO4AaN.m

NSWC TR 82-394

4-4w,*in* * *on 0# ino- 14It n o o0 0 0 0 0 0

4vie**-4ivi4 @v4,*44O9 f P vi. p...4V @ @* * @ @ O O

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z

in

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5 .U05.44iv44SPivv444viv44ivv4e444viA-18PS~i

NSWC TB 82-394

.o .......... .... .. ... ... o 1 1 11 tI t tiC t .I tI000Oa00 00080000 0000000000 00 0 aOaOOOOOOOOOOOOOO OO 00000

It It Ct I 000 0 0 8 0 0 8 0 0 t0 0 8 0 8c 0 0 0 0 0 8 @g00 0o00 8 8 8 0 8 0 0 80 0.t0 tI P ... .. It ... .. It .. .. .. :I i C ItC .°. o o o .ooo ... .. .. ... .. Ct0 POP-pet. M0 YF000080000 0000000a080 0000000#N00a00000 00000

00 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0000 40408000000000000-..................................

-04M0"0 -F-0@ ",,,,M0 4. .. .. N 4 ....4 M .. .4 ..... .0 MO NFoo o4ooooooooooooo-ooo4oNo-0ooooooOoo 0o44oo

0oM

* F N - 0 N 4 0 0 0 0 N . .- 4 N 4 0 0 - ~ - P1 0 N 4 0 0n fu A' . ,AF 0 N 0... 0 - M 0 0 P1 0

30 M-..F-0-..O4ONOO 400-F000M0000o00N0M0000040 04mflN-F --- - -0 . - - -.0 4 0 - - - -F- M 000 - - F- 0 - .. - - -F 00 .. -0 -0 N. ..0 -N.. 84 - -

10o0 ooooo oooooooa oo .oo o o o o o o o o o o . .

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800 0000 88 00 0 @0 0 0 0 0 0 8 0 00080 00 800 00 000 00 00

2 *-00 NM40F-00.NM40F-08.M400F000.m 40F00-N 40-00-0

A-19

NSWC TR 82-394

1 V .. .. .. MA O N N 0e 4 4- 0 0 .. ... .. . ..04t o~~ .1

36NN0N@ 1200NN @*0 44O0 NN I* 1 0 00.p-N 19 S A 00

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

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P;.190 OO N .S . l ti a.t .. .. .. t i a I 0 N. .1A1

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Iq I lo l to is$@ $ISO*$ 0 01N N N AO01tA N 00O - 1 00

N N 0 0-----...O.. ----0 -..O .- -- ----

a,

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m; ,.Nm m N90

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0N - N-- -. 6000 4 a em1:1o, NNoN.'-.'NNN M A

M 0 N no0 As 14 N. 00N N MN N 0(9 cu NOM N N M0.- A 0 0y N 0 A N N u; Nv t;0 -40 Nz z Z N010N

lot t0 O l ,1 sA10 0 o m1 IA N 0. I'N,: c 00, 1000 0 00-- N 0 r- 0 900 Fin P- 0 1 1 : N 00 a 0 0 mNgo "M0 00 0 0 I9 9 NN 1 .

A-2

NSWC TR 82-394

9*** *** * .. . . .. .. ... . . . . . . . . . .

Eq~~og~ 04..Eq4 00 4 Eq9 N .-- 4 a 0010, or- 00

.* . . . . . . . . .. .. 1 V 111.4 1 ......

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0- *Mom lSTlI MNt4tt........ C! .111 1 ! V!d tV

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00om

MO N 00 : 4VtV , ...... ...

inM4 N y. 4I 00.ooo o e 0 MM-MI MN0ooM mo-o- -eo .....-.- o-oomoo oo oooNMo

0 ~ ~ ~ o 00 00~ 0:;00z 00 0 4 00 4 00 0 N~fmlmOOo

W~~~N '.44 00 04 00 09 99 99 9 00 00 00 - - - - -

00N NN N NCI NN NN 0 MNN N

34-. ~ P N 00a.. 94 N0 4ENEqNq 0 Eq -. N- 4 -9 q o 0 N 9 0 N44 4N 40 4.9N 44 q9 09 94 N99 90..44 0N 4Eq q4 4E 0E 4E 09N N0 04 9..4

Ny1 I0 ~ ~~~~~~~~~~~~ 4qq44N444q-E44q...4qq. .- E N-... .. . . . .. t

0 yI1 4 -D 0172 :!

~~~~~ 00 Eq P. t- P. a 0 4 0 a 0 00 0 0 0 0 in0409044E N.. MN404004.-.04N ~ ~ ~ ~ . . .N. .N4 . ..4O .N . . .. 0 ; 0 4E 4.* - 64 0 N

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Nmo0eoN m m

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44N 9 4. E 4N90 4 44NN N4 06E 4N 0 N4 E 0 4 4 N q0Aq 4EqNEqE

Nswc TR 82-394

a f.: V240 * m* 440ii Otu 0 InN@ EM 44

00, to0M 4N O 4. * 1. m.n. e gemPop-kAN OcoONANN400I -04 Aon 4 P 0U .. 0 00q:4 ellO NN M* A IME ** ff ea *44

JA A A A 4 j jENN.

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m * m .0 go 4 EO N O P- m V : VN 4 N A 0 QN 0 EN .- 4-4WN4 4- E E em .NE 41, P W EO N * * 4M - M O~~S000P10n m0N00N440'44 NO M W 0 -40.4 44 M NN"WM o

P. & a m c 4In ma n 0r-a aI-- I 441NMN - -. NNNomf, Itself#es *i m*i t aI II,

00

------------------------ ---------

Cmes M 4 0 02CUM4 ao !9= 404p

U O N N N N N NM MNM MN wIn Z

z

Ps0 N C n0 0 400 0 - o 0 m &4 P- 0 - 0, N NO 00 *q F40 MN N. 04 M0*. . . . . . . . .. . . . . . . . .. . . . . . at c

.0 n Itm mIn m40 400N4"0 oC)M cc* M rNm i . ME ENc 0 am 4M3N .-t-0 *30 n ym a - d

ND01l o; ,oP OWE N M 4 W M M W 33N * mN 00m ME m4W4 M M N N

0'

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z NO AIN NO O O - ON M O E - N . E O N * 0 . . M 0 M M O 0 3 ~ 4 M

IA N- N0 EN 0E 0~Iq W4 0* 0N o0M .. N4 o0 0e 00*A-22M N3

NSWC TR 82-394

.* .7tv v . . .. . ..N 4%4 *4 N CU ~ A % M onN N v MM f C 0 N9449. i eyIV 4..

tNNO 0 - - N - 4 4 W1 0 @ 0 9 0 94440 99ON9.0901

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ew.. 4 M 410. In9 *0&9In.0NN-m4 4 M ty - 04- n40 4N 4 900 cu9N 000

NNN. . . . N ..- .. . . a a -* .. t iV , I .% 1... 0.V i 1

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, w It 121.. .* .--N :N1 !0 I. .l .m .lamliIt I

4 yNN------WNNNl N N ----- N N N------N N N------N

N 0 0 N4a-0= 0-.N.. . N op..N14J..:0.. 00 *4 4To .N----otmmom o o o o om o o a e .m o o o o o o m o m o o o o e . m................

N40N 49~ O9-N40 N49m O9.~N40 N49 4O9N049 4O9..N~ N M4M409.... . . . . . . . . . . ... . . . . . . . . .

* 0 xNfl- - - -"nNNN- - - - -JNNN- - -NINNN- - -* 10-NNAIEmma- - - -MNmm

U ~ m s ms i ,, alg l 4m aml, m0. cmc,, sva a a llnamasMo 1 otinr 4 z

a 4 O eN 90 N 9 N4 m4. e.N 90 N 9 N444 090.MM a 4 m4FNPi:0 ~ 9 9 9 . 9 o o oo ~ - - - - - - ~ 4~

~~~~~~~~~ O 9 4 e 4 4 4 4 4 4 4 4 4 0 n . N M 0 0.... 4P. ZM!

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.

49 N NO u N mu 0 N N4 N 9 494 N .4 N N -00 44 moo NN N 04 N m C9 cu N4 Y cy mm 0u N N 0 mm N N

N 4 O NN 00N 44444440MN m m-OD m * m N P. L0O N = 244 404 Ng0N In4.-...

M WI ON N .000 t. N N0 N 49 I~ 9 u u O N 4 i 049 n N 0D , F-. N M N a,0 N 4 N. 0 14 N M40 90

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.4 N ~N0p N 0N 0 4 N49.0 444 N V- SO,04044 % NM 00 4 0 Nlo N NO-N 4#0 . 0* 9-.-O4N -. 400 4 400 4 0 4.4 .0 mo M409N N 4 N0 00N.4

N M MM 490 M994 0 0 4 0N94 4 49.40N0 .09N4 0 .

00.-09409 9 94NN 9.iN 04940N *0N 4N 494N -4AON0-20304

49440044NNNN49NN-...~~~-mom Uuw l.-N N-1404444940014.N0-.b

NSWC TB 82-394

*....*.....................

ti* . . . .

4! lo 09Nn: tl'tI t k1 %..

v- MA----- ---- NAMM ------ Nmmf -- -- MN N -- -- MAI

N9000l-ONOE~n~n E I00: 0:003-0:099.0 ... N...l NM

#4N NO O0N E #0010O ~n In LO n inNO0 in 00ENO n 0Inx I N111j l. g . gii ... 1 1 6 6 6 6

o zm la alaIn

N ~ ~~~~~~ .N. N . N - N - N N N N '~ .N -~ . -....

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in i

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fuE Al aft-Oft O PE a NN PN Innn E NnN9nnE EE~ M .nnn ~ 0In eIn 0n~

li:.0!: l .I....1 ...... -I!E.. .N. .

-~ 00,00000N0MN90n0I 0:2-N . . .SMInnNna. . . .N ...o ~~~~~~ ; 1;N 1; 1N;0N . nM N N n~E I~n O 0 E9 O N 9N O N 04 O~

-03O~~N6N0Itn9oIrE-nnM~~CnnIMIENN.I0 ~ N 0 NE n n N .o n * E M I n N N 0 E E E - I O n E E E E O I 0 N * E M E M n M N I 1

C,4 4 0

A-2

NVWC TR 82-394

ly Pool- MMMV * ~ M

-O .-4 1, G. 0 4 41 4 4 4 in 04In444:44444N0M

me .a 5ea

O M O E N E N M00:4E0E=NE.

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0000000 0000000 000000 0000000 0000 M0 0.000 0 0 00 00 0N0 .NM E 0O 4 N0 "a0t N M 0~. NMM2100 44 NO000 M..-.NMM

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x 0000000000000000 000I 00v000000000 0000 O0 0 000000'D00 0000-

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Te7 77 17

004-. ONMOM .-. MM ... 00 00004 0000N N In401 a W, OM NM OMt Vi iNO 0M . . . . E .0 Vi040 :4. . . . .. . -. 04 - -. -

3N40N.0.....N.O.4.E.N.N.O.E.O.O.N.O.O.O.O.O.O.O.N.O.0 0 40 E 0 N .0 N E N 00 N N - EM-0 00EE 000 E OEMN MN 0 M 400 E 47 N N N 00

enfMn0I

0 . .-. .NN MNM MM MMM NN -. N MM MMM MEM MMM NM

NSWC TR 82-394

*94 ~ ~~aimm9o.449mma - -- - -- --- ---------------

. .. .l . . . . .V

I1i i ii ' . 1 . . ..e4el % .N. It .444l .N*44 N .-. 4 N. . . ..-

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M 0or MO ;:M 4A OOifilfi .00 0 NB9 M 0 V1I0 a-0 .0,0 0 0 a, .O.oe e

00=. NOO. 0.0* OO0NN0-04 4 N . 0 N 0 9 * 0 4 0 O o

O a.i .iS .'! ., ,, 'ir ia am 1 1 . 1 . %. I

N 00000-0 N N N M f" M0 0 NM M N *0 00 - .N 900-. N N M 9 M 0 M 0 N N - 9 00-..

00 m -40,P M M AL4

1G1tV Va tC ! l 1

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o ~ 1 We o NJtNN NNtNNN0NOa oaoz'

got* 11 1i

A-2

NSWC TR 82-394

- - -- -0.l p. -0 p0 NO 400 p0m0 m04 Nu 404 NO' 404 m4 P14 p. eu m 04 N Num mm

P10 p. 1 0 0 0 0 .O 1 1 N 0 N 0.. P1 o 4 - 1 P 4 1 4 . . 0 P 0 0 P 0 1 PmA, - 1 10 .Pp 44 N PN 140 p 400.o4~o PO- 4P.U-0

0000100N0 ma mol0N0 p .. pNom 4p.04p 04-0 MN 4P4-POof.P1NP-.... ..... ..... ..... ..... ....

000 P10 m 1 N I I N - P1PN 1 N-aOO NO 04,, N! 401'. P1 100 N !U* 00- ON 00 Z!! zNI O U cu0NP40pN4014.N... 4P0N04PN10p4. 4.NP

NO 04 P1 .1 0 04 4 .- 4 . . I. %4 ON 00 . . 0 .0 40 P10 . p. .0 . 0 P1 . ..

if ------------------------------------ NN.N.N N.N...N N--

mmm

~ 000 0000 0000 0000 0000 00000 0000 0000 0000 0000 0000

at 600 00 00000Cc0 004 0 0 00a0 00 0 0 0 00 0 0 0 000-000000000----NNNNNP1P11P1zPNP1M4444444V40000

I Q Ic cy m N InoNoma

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F0. ..0PP. a 0 0 . 1- . .... P. .P.P.PI-.. f . P.PI..0.0a.1..0P...0oft4t.0s.P..-pa

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NSWC TB 82-394~

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A-39

NSWC Tm 82-394

t 9: 3 eo;4=; 020 4 P 0 NM,- 0 0: N. 2 mlA4N~i-MOO-0 40440-0044- N000M0.A,00 4owiiO~ P.O...NO.~0.- m 0 N 0 N 4.-.N 0 N 04000in0 ToM O N0 U O

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- NSWC TR 82-394

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A-41

NSWC TR 82-394

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Nswc TR 82-394

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NSWC TB 82-394

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A-4

Nswc TR 82-394-,

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NSWC TR 82-394

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A-5

NSWC TR 82-394

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0A 5

NSWC TE 82-394

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A-5

NSWC TB 82-394

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NSWC TR 82-394

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A-5

NSWC TR 82-394

in in: M9N0404*40 M-4 4N -4 4*

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NSWC TR 82-394

APPENDIX B

The measured surface pressures are provided in this appendix at pressurestations 1 to 4 (see Figure 1). Due to equipment problems, data at pressurestations 5 and 6 were not acquired in all tests and this information has beenomitted from the listed results for all runs. The symbols appearing in thedata list are defined as follows:

PHI - Circumferential angle measured from the leeward plane.

X/D - x/D (see Figure 1)

CP - Average pressure coefficient based on a sample of 100 measurements.

Here CP is defined as (p - p,)/qsin 2.

SCP - Standard deviation of the pressure coefficient using a sample of

100 measurements.

CN - Local normal force coefficient: normal force/(Dqsin 2)

CY - Local side force coefficient: side force/(Dqsin 2)

In runs 1 and 2, two sets of data are .listed. During these tests, substantialfluctuation in the measured pressure was seen and the listed data sets producedthe highest and lowest side force values. In the remaining- tests, pressureswere fairly stable throughout each experiment and the presented data represents atypical set of measurements. A tape containing this information is available onrequest.

B-i

NSWC TR 82-39h

TEST NUMBEt k1061602 RUN NUMHER 1

PORT PHI X/D/2.6 x/D3.6 A/Da4.1 X/D*S.7CP SCP CP SCP CP SCP CP SCP

1 -180.00 1.079 .028 .991 .028 .9b6 .032 .976 .0302 -16S.00 *968 .OjO .908 .034 .965 .034 .986 .0323 -150.00 .399 .040 .386 .046 .525 .OS4 .606 .0O4 -135.00 -.461 .050 -.434 .062 -. 161 .090 -. 003 .0985 -120.00 -1.316 .044 -1.187 .074 -.827 .114 -.Sys .1746 -10S.00 -10o26 osa -I.S26 .08 -.94a .188 -. 556 .1967 -90.00 -1.758 .060 -1.257 .082 -.767 .150 -.474 *144a -S.O0 -1.647 .058 -1.248 .104 -. T63 .164 -.472 .1869 -60.00 -1.684 .078 -1.309 .088 -. 776 .160 -.546 .146

10 -45.00 -1.701 .076 -1.33S .094 -.86S .138 -.630 .17211 -30.00 -1.9T1 .09? -1.406 .112 -.932 .80 -.604 .16012 -IS.00 -2.079 .118 -1.k64 .11u -. 953 .214 -.599 .20613 0.00 -. 927 .046 -. 626 .050 -. 506 .148 -.939 .45814 16.00 -1.572 .074 -1.b09 .136 -1.641 .356 -2.0S6 .480IS 30.00 -1.969 10b -1.841 .136 -1.833 .186 -1.903 .29616 45.00 -1.887 .114 -1.95O .le* -1.796 .190 -1.7S9 .26617 60.00 -1.961 .078 -1.814 .108 -1.776 .186 -1.759 .242I8 75.00 -1.878 .058 -1.711 .112 -1.677 .202 -1.797 .26619 90.00 -1.881 .068 -1.677 .104 -1.652 .170 -1.708 .ZS20 IOS.00 -2.212 .054 -1.907 .144 -1.646 .224 -1.813 .37021 120.00 -1.899 .OSO -1.882 .090 -1.896 .140 -1.990 .22622 135.00 -1.042 .052 -1.126 .070 -1.190 .140 -1.255 .IS223 150.00 -. 067 .042 -.200 b060 -. 274 .078 -. 292 .11224 165.00 .737 .040 .584 .036 .563 .054 .S11 .OS8

cN 1.760 1.455 1.286 1.191CY .270 .502 .909 1.209

TEST NUMbEH 81061602 RUN NUMOER 1

PORT PHI X/D*2.6 X/D3.b X/0-4.7 X/DS.?CP SCP CP SCP CP SCP CP Sc

1 -180.00 1.090 .028 1.000 .02 1.019 .026 1.104 .0342 -16S.00 .961 .036 .873 .034 .932 .036 .930 .0483 -150.00 .355 .040 .298 .046 .379 .076 .424 .0984 -13S.00 -. 508 .040 -.564 .080 -. 349 .106 -.306 .1945 -120.00 -1.400 .058 -1.3b3 .060 -1.165 .176 -.904 .2466 -105.00 -2.007 .048 -1.723 .112 -1.325 .196 -1.097 .3667 -90.00 -1.842 .062 -1.446 .092 -1.135 .188 -. 961 .2668 -TS.O0 -1.734 .058 -1.437 .068 -1.127 .174 -. 991 .2529 -60.00 -1.786 .066 -1.471 .10* -1.132 .184 -.949 .286

10 -45.00 -1.771 .090 -1.474 .104 -1.209 .164 -. 951 .31011 -30.00 -1.951 .122 -1.582 .130 -1.236 .226 -1.130 .35612 -15.00 -2.067 .132 -1.0Y7 .132 -1.378 .202 -1.304 .42613 0.00 -.860 .052 -.730 .08 -. s2t .156 -.543 .24614 15.00 -1.543 .074 -1.397 .11 -1.153 .322 -1.151 .SS615 30.00 -1.860 .120 -1.482 .09b -1.132 .164 -1.007 .28816 45.00 -1.806 .122 -1.524 .11e -1.176 .228 -.8ss .260I7 60.00 -1.627 .074 -1.488 .09/ -. 961 .190 -. 842 .2S6i1 75.00 -1.719 .066 -1.391 .08d -1.028 .182 -. 761 .24019 90.00 -1,725 .060 -1.383 ,084 -.q99 .162 -. 789 .26220 10.00 -2.063 .068 -1.5 7 .120 -1.130 .234 -. 809 .30221 120.00 -1.70 .056 -1.613 .11b -1.327 .210 -1.1b .35622 13S.00 -.957 .056 -.941 .080 -.886 .168 -.7,6 .21623 IS0.00 .003 .046 -.107 .0be -. 035 .106 -. 053 .13824 16S.00 .761 .034 .64Y .042 .657 .060 .661 .076

CN 1.748 1.430 1.234 1.042CY .086 .054 .013 -. 022

B -2

NSWC TR 82-394

TEST NUMbEh 81061701 RUN NUMeULW

PORT PHI X/0aZ.6 X/0*3.6 A/DX0.7 X/D0.7CP SCP CP sCP Ce SCP cP SCP

1 -160.00 1.081 .030 .987 .06 1001 .030 1.022 .0242 -165.00 .917 .034 .806 .030 .643 ,U38 .813 .0443 -150.00 .300 .038 .212 .0#4 .231 .070 .223 .0S24 -135.00 -.590 .044 -. 704 .066 -. 64? .086 -.647 .1345 -120.00 -1.44? .052 -1.513 .07b -1.4d6 .154 -1.445 2146 -105.00 -2.068 .054 -1.939 .088 -1.13 .00 -1.07 .2727 -90.00 -1.096 .062 -1.641 .1e -j.513 .190 -1.581 *2708 -75.00 -1.779 .058 -1.633 .096 -1.516 .216 -1,569 .2129 -60.00 -1.85 .054 -1.679 .10e -1.579 .170 -10.55 .224

10 -45.00 -1.789 .068 -1.713 .098 -3.553 .166 -1,S99 .224It -30.00 -2.345 .128 -1.748 .112 -1.758 .168 -1.06 .26412 -15.00 -2.508 .338 -1.803 .144 -1.853 .184 -Z.117 .20613 0.00 -.619 .050 -. 76Y .060 -946 .202 -1.53 *01414 15.00 -1.476 .00 _-10238 .108 -. 715 .168 -. S#S .194lb 30:00 08 -1:414 :116 -.965 *140 -. Is8 .28416 45.00 -1.731 :132 -1.483 *124 -. 97 ,168 -. 0 .Iya17 60.00 -1.790 .072 -1.386 .114 -.N20 .152 -. 66i .226in 75.00 -1.674 .060 -1.297 .096 -.012 .126 -.56 .20219 90.00 -1.667 .054 -1.260 .086 -.815 .126 -.521 .17620 105.00 -2.011 .050 -1.446 .082 -.911 .172 -.527 .17021 120.00 -1.701 052 -1.4o0 .082 -1.066 .136 -. 716 .17622 135.00 -.873 .052 -.803 .068 -.561 .112 -. 395 .14623 150.00 .044 .044 .022 .056 .152 .074 .276 .08624 165.00 .778 .032 .692 .038 .770 .038 .796 .052

Ch 1.811 3.465 1.373 1.310CY -. 058 -.231 -.570 -.045

TEST NUMBEK 81061701 HUN NUMBER 2

PORT PHI X/Du2.6 X/Om3,6 A/DM4.7 X/OwS.7

CP SCP CP SCP CP SCP CP SCP1 -180.00 1.074 .026 .994 .026 .994 .026 .997 .0242 -165.00 .927 .030 .623 .032 .825 .032 .613 .0443 -150.00 .320 .038 .215 .044 .235 .068 .207 .0464 -135.00 -.578 .044 -.687 .064 -.653 .102 -.032 .1305 -120.00 -1.427 .046 -1.510 .082 -1.450 .136 -1.478 .2026 -105.00 -2.059 .052 -1.904 .106 -1.789 .224 -1.441 .1127 -90.00 -1.868 .058 -1.607 .104 -1.385 .094 -1.476 .320o -75.00 -1.749 .054 -1.616 .086 -1.476 .190 -1.505 .2529 -60.00 -1.794 .064 -1.645 .098 -1.527 .186 -1.498 .27610 -45.00 -1.779 .084 -10683 z120 -1.509 .160 -1.578 .25411 -30.00 -2.288 .106 -1.72? .132 -1.688 .172 -1.654 .24412 -15.00 -2.459 .lob -1.729 .122 -1, 7pg .198 -1.939 .45613 0.00 -.623 .056 -.738 .068 -.900 .252 -1.285 .SI114 15.00 -1.761 .024 -1.433 .032 -. 790 .182 -0590 .19615 30.00 -1.768 .122 -1.477 .108 "1.D 7 .162 -.8#0 .25016. 45.00 -1.733 .124 -1.531 .106 -1.028 .164 -.676 .17017 60.00 -1.796 .074 -1.428 .098 -. 920 .178 -.697 .21418 75.00 -1.714 .056 -1.339 .088 -.939 .15O -. 706 .20619 90.00 -1.704 .058 -1.323 .09d -. 936 .164 -. 683 .19820 105.00 -2.021 .052 -1.472 .102 -. 968 .166 -. 628 .22421 120.00 -1.728 .048 -1.498 .076 -1.167 .174 -. 865 .23022 135.00 -.691 .044 -.829 .070 -. 612 .120 -. 468 .16223 lbO0. .031 .034 -.013 .044 .099 .0806 174 .11024 165.00 .782 .026 .693 .032 .792 .046 .755 .054

Ch 1.635 1.481 1.344 1.249CY -.005 -. 161 -.441 -.659

B-3

NSWC TR 82-394

TEST NUMbFN 81070702 NUN NUMBER 3

PORT PHI XID*2.• A/0-3.6 A/O-4.7 1/0.5.7CP SCP CP blcl. CP SCP CP SCP

1 -160.00 1.074 .036 .956 .034 .92J .034 .929 *0342 -165.00 1.035 :036 .989 .034 .997 .034 .955 .0363 -150.00 .552 .036 .%9 4 .036 .676 .034 .569 .0404 -135.00 -.211 .052 -. 042 .#J36 job .03• -. 078 *0525 -120.00 -1.007 .05& -.671 .048 -. 375 .050 -. 697 .0046 -105.00 -1.489 .052 -.816 .066 -. 410 .062 -.684 .1387 -90.00 -1.280 .054 -.6lo .06b -. 318 O252 -. 762 .138a -75.00 -1.231 .062 -.647 .06e -.346 .054 -.825 .1409 -60.00 -1.278 .070 -. 690 .074 -.391 .072 -.941 .144

10 -45.00 -1.247 O07b -. 6b .060 -.446 .054 -1.027 *10211 -30.00 -1.466 .080 -. 687 .064 -.Sv6 .080 -1.152 .12412 -15.00 -1.507 .078 -. 758 .05O -1.344 .188 -2.098 .10613 0.00 -.947 .062 -1.109 .15b -2.M19 .242 -2.572 .19614 15.00 -1.900 .128 -2.837 .190 -2.541 .218 -2.031 .140is 30.00 -2.519 .172 -2.7u .182 -2.636 .218 -1.098 .12216 45.00 -2.287 .116 -2.656 .140 -2.8W7 .170 -1.947 .11617 60.00 -2.369 .084 -2.625 .084 -2.745 .094 -2.034 .1501e 75.00 -2.295 .066 -2.49% .094 -2.68 .070 -2.062 .12819 90.00 -2.341 .064 -2.549 .090 -2.697 .082 -2.042 .10020 105.00 -2.6s6 .056 -2.975 .098 -3.095 .060 -2.340 .16821 120.00 -2.2S3 .052 -e.544 ,0t0 -2.671 .050 -2.212 .06222 135.00 -1.304 .048 -1.568 .052 -1.713 .048 -1.435 .06623 150.00 -.264 .040 -.477 .046 -.S95 .038 -.436 .04624 165.00 .601 0040 .449 .040 .360 .038 .430 .040

Ch 1.577 1.448 1.678 1.644CY 1.038 1.807 2.147 1.144

TEST NUMBER 81070701 RUN NUMHLR 4

PORT PHI X/0-2.6 X/0=3.6 X1/04.7 X/05.7CP SCP CP SCP CP SCP CP SCP

1 -180.00 1.092 .034 .977 032 .924 .032 .905 0342 -165.00 1.042 .032 1.000 .032 1.004 .030 977 .0323 -1O50 .537 040 .50 .040 .694 .034 .636 .0404 -135.00 -.245 .038 -.084 044 .129 034 .068 .046S -120.00 -1.070 .050 -.767 ,Obb -. 356 .044 -.440 .0666 -105.00 -1.612 .052 -.979 .064 -. 372 .054 -.519 .0947 -90.00 -1.414 .060 -.745 .060 -. 284 .054 -.428 .098a -75.00 -1.344 .068 -.774 ,072 -.307 .050 -.499 .0929 -60.00 -1.390 .068 -.787 .07o -.351 .068 ".5s$ .110

10 -45.00 -1:397 :006 -.764 :0 -.393 .074 -.S99 .122il -30.00 -1.606 .000 -.S07 .078 -444 062 -.92b .12612 -15.00 -1.636 .096 -.832 .068 -.847 .160 -2.053 .19613 0.00 -.970 .064 -.779 .102 -2.381 .326 -2.020 .24014 1500 -1.609 .130 -2.528 .190 -2.569 .220 -2.314 .19015 30.00 -2.214 .126 -2.480 .13e -2.639 .216 -2.291 .16816 45.00 -2.121 .13d -2.352 .130 -2.664 .170 -2.294 .14217 60.00 -2.250 .090 -2.410 .09o -2.676 .106 -2.227 .11616 75.00 -2.131 .068 -2.249 .084 -2.598 .090 -2.286 .10819 90.00 -2.129 .070 -2.216 .078 -2.606 .098 -2.309 .00820 105.00 -2.475 .062 -2.621 .106 -2.969 .000 -2.630 .09421 120.00 -2.110 .048 -2.3t0 .074 -2.621 .062 -2.445 .05822 135.00 -1.226 .044 -1.427 .052 -1.717 .048 -1.570 .05223 350.00 -. 189 .040 -.381 .048 -. 505 .042 -.512 .04624 165.00 .647 .034 .478 034 .360 036 .366 =034CN 1.566 1.372 1.522 1.698Cy .776 1.477 2.129 1.658

B-4i

NSWC TR 82-394

TEST NUMBER 81070802 RUN NUMBER 5

PORT PHI X/0-2.6 X/0-3.6 A/D)84.7 A/057CP SCP CP SCP CP SCP CP SCP

1 -160.00 1.064 .036 .956 .038 .919 .038 .931 .0342 -165.00 1.041 .036 .992 .030 1.011 .036 .964 .0343 -150.00 .546 .040 .609 .034 .691 .036 .596 .0464 -135.00 -.201 .044 -. 029 .042 .140 .038 -. 004 .0585 -120.00 -.901 .046 -.662 .050 -. 331 .040 -.565 .0746 -IOS.00 -1.494 .048 -.813 .066 -. 358 .056 t-.0803 .1427 -90.00 -1.265 .058 -.611 .062 -.272 *060 -.695 .1328 -75.00 -1.225 .066 -.638 .060 -.297 .050 -. 726 .1289 -60.00 -1.237 .072 -.66A .072 -. 339 .068 -. 014 .156

10 -45.00 -1.228 .082 -.634 .068 -.402 .062 -.925 .18811 -30.00 -1.449 .078 -.688 .064 -.510 .084 -1.043 .13012 -IS.00 -1.499 .092 -.742 .064 -1.169 .188 -2.050 .14613 0.00 -.931 .052 -1.015 .140 -2.651 .232 -2.522 .18014 15.00 -1.771 .140 -2.75A .188 -2.458 .190 -2.027 .15215 30.00 -2.386 .152 -2.626 .164 -2.602 .200 -1.917 .14216 45.00 -2.172 .130 -2.520 .132 -2.779 .156 -1.089S .10817 60.00 -2.323 .070 -2.539 .082 -2.682 .086 -1.996 .13618 75.00 -2.200 .064 -2.433 .098 -2.614 .084 -2.077 .12619 90.00 -2.253 .070 -2.420 .096 -2.596 .082 -2.050 .11020 10.S00 -2.604 .060 -2.829 .090 -2.994 .066 -2.319 .11821 120.00 -2.163 .054 -2.447 .064 -2.586 .048 -2.213 .06422 135.00 -1.271 .052 -1.506 .058 -1.669 .044 -1.390 .05823 150.00 -.225 .044 -.430 .046 -. 550 .042 -. 405 .04824 165.00 .622 .040 .461 .042 .390 .042 .431 .042

CN 1.678 1.543 1.730 1.745CY .972 1.726 2.122 1.218


PORT PHI X/0.2.6 X/0-3.6 X/D4.7 X/ST.7CP SCP CP SCP CP SCP CP SCP

1 -100.00 1.055 .034 .947 .038 .906 .032 .900 .0342 -165.00 1.013 .038 .973 .036 .994 .036 .960 .0363 -150.00 .509 .038 .574 .038 .676 .034 .624 .0424 -13S.00 -.237 .040 -.086 .038 .140 .036 .052 .OSO5 -120.00 -1.059 .048 -. 738 .052 -.334 .048 -.481 .0746 -1OS.00 -1.582 .046 -. 938 .068 -.354 .052 -.574 .1027 -90.00 -1.372 .062 -. 727 .072 -.259 .050 -.454 .1068 -75.00 -1.295 .070 -. 739 .066 -.276 .058 -.484 .0929 -60.00 -1.331 .072 -. 754 .072 -.300 .072 -.572 .106

10 -4S.00 -1.366 .076 -. 735 .066 -.364 .062 -.640 .12411 -30.00 -1.556 .082 -. 816 .082 -. 430 .062 -.929 .14012 -15.00 -1.588 .084 -.833 .066 -. 843 .172 -1.99S .20213 0.00 -.931 .058 -. 769 .114 -2.337 .256 -2.629 1TS14 15.00 -1.723 .126 -2.585 .196 -2.431 .188 -2.195 .17415 30.00 -2.328 .146 -2.492 .144 -2.591 .186 -2.148 .12816 45.00 -2.136 .116 -2.355 .128 -2.624 .164 -2.142 .14017 60.00 -?.23S .074 -2.426 .084 -2.621 .106 -2.154 .10416 7S.00 -2.114 .068 -2.277 .090 -2.545 .084 -2.221 .10219 90.00 -2.144 .058 -2.295 .084 -2.582 .092 -2.214 .08620 105.00 -2.499 .056 -2.665 .098 -2.960 .076 -2.542 .11021 120.00 -2.113 .048 -?.347 .060 -2.572 .058 -2.345 .06222 135.00 -1.220 .054 -1.452 .O0S2 -1.651 .054 -1.512 .0SO23 150.00 -. 215 .044 -. 392 .052 -.562 .046 -.478 .04824 165.00 .6?1 .042 .4S3 .042 .370 .044 .378 .036

CM 1.689 1.490 1.607 1.746CY .821 1.516 2.109 1.552

B-5

NSWC TR 82-394

TEST NUMREH 81062SO2 RUN NUMNER I

PORT PHI X/02.6 X/0-3.6 1/o04.7 X/0.5.7CR SCP CP SCP CP SCP CP SCP

1 -100.00 1.094 *032 .991 .020 *937 .028 .925 .0302 -165.00 1.041 .030 .999 .032 1.021 .032 .992 0323 -150.00 .532 o038 .578 .034 .706 032 .b70 .0364 -135.00 -.240 .044 -. 094 .048 .152 .040 .122 .0505 -120.00 -1.061 .050 -. ?63 .052 -. 325 .044 -. 359 .0666 -105.00 -1.604 .052 -1.011 .078 -. 349 .066 -.399 .0767 -90.00 -1.401 .060 -.768 .062 -. 249 b056 -. 315 .0788 -75.00 -1.332 .062 -.798 .070 -.266 .050 -. 354 .0649 -60.00 -1.368 .074 -.7R .072 -. 287 .066 -. 429 .108

10 -45.00 -1.391 0072 -.756 .076 -. 348 .068 -o486 .09411 -30.00 -1.608 .094 -.809 .076 -. 391 .062 -. 799 .14412 -15.00 -1.648 *084 -.872 .076 -.667 .152 -1.742 .2513 0.00 -.906 0054 -. 695 .082 -2.021 .300 -2.682 .23214 IS.00 -1.581 o04 -2.306 .174 -2.445 .200 -2.342 .166IS 30.00 -2.117 .132 -2.404 .124 -2.504 .194 -2.224 .SO16 45.00 -2.027 .124 -2.238 .122 -2.4684 .162 -2.303 .152I7 60.00 -2.170 .076 -2.25a .096 -2.525 .106 -2.233 .09618 75.00 -2.032 .060 -2.159 .096 -2.442 .084 -2.266 .09619 90.00 -2.057 .036 -2.151 .116 -2.489 .034 -2.248 .08020 10.S00 -2.370 o054 -2.0S? .110 -2.768 .102 -2.594 .06621 120.00 -2.038 .050 -2.246 .074 -2.489 .072 -2.362 05422 135.00 -1.161 .046 -1.385 ,056 -1.603 .046 -1.SS .05023 1SO.00 -.1SS .042 -. 345 .054 -.521 .044 -. 495 .04424 165.00 .640 .032 .529 .036 .388 .034 .394 .036

C¢ 1.679 1.4s9 1.544 1.639CY .704 1.363 2.036 1.736


PONT PHI X/D2.6 X/0.3.6 X/034.7 X/D-S.?CP SCP CP SCP CP SCP CP SCP

1 -180.00 1.091 .026 1.000 .030 .979 .030 .974 0342 -165.00 1.066 .026 1.002 .02v 1.014 .030 1.020 .0283 -150.00 .628 .038 .582 .040 .650 .050 .693 .0564 -135.00 -. 117 .036 -. 139 .052 .044 .072 .130 .096S -120.00 -3.023 .046 -.921 .060 -.663 .122 -.463 .1266 -10S.00 -1.690 .042 -1.403 .004 -.985 .140 -. 713 .1967 -90.00 -I.715 .054 -3.157 .090 -. 767 .124 -. 475 .1760 -TS.00 -1.491 056 -1.122 .090 -.753 .130 -.507 .1749 -60.00 -1.526 .068 -1.180 .084 -. 786 .140 -.563 .18230 -45.00 -1.587 .086 -1.207 .090 -. 807 .134 -. 565 .1703 --30.00 -1.030 .124 -1.302 .106 -.878 .154 -.616 .1722 -3S.006 -3.826 .13* -1.331 .100 -.942 .102 -.680 .25613 0.00 -.903 .058 -.687 .070 -. 444 .354 -. 4V4 .26614 15.00 -1.066 .066 -.99? .082 -1.118 .302 -1.469 .460Is 30.00 -1*933 .130 -3.559 ,lio -1.466 .146 -1.634 .24816 4S.00 -2.001 .122 -1.62T .116 -I.533 .182 -1.405 .2401? 60.00 -1.741 .06? -1.478 .090 -1.365 .166 -1.325 .2241 79.0* -1.614 .018 -1.48? ."84 -1.352 .134 -1.371 .228I9 90.00 -1.62s .06? -1.431 .094 -1.325 .148 -1.321 .218210 30. -1.903 .na. -).3 .106 -10371 .189 -1.373 .26421 12000 -. 067 A*%v -1.6s .0012 -1.%84 .152 -1.559 .2182 13%.00 -1.064 .0* -. 0?.% .070 -1.090 .104 -3.008 .14023 ISO.#$ -. 123 .034 -. ?0 .04 -. p43 .084 -.245 .30824 365.00 .6%2 .02 ,s70 0038 .sll .044 S06 .070

co 1.564 1.223 1.059 1.050CT .308 A4bl .661 .867

B-6

-!

NSWC TR 82-394

TEST NUMBEN 61071601 RUN NUMBER 9

PORT PHI X/ID2.6 4/D=3.6 X/0-4.7 X/OrS.7CP SCP CP SCP CP SCP CP SCP

1 -180.00 1.010 .030 .912 .032 .903 .032 .890 .0362 -165.00 .996 .028 .920 .028 .953 .030 .950 .0303 -150.00 .545 .038 .488 .038 .b84 .046 .627 .0524 -135.00 -.244 .040 -.272 o056 -. 058 .082 .018 .0985 -120.00 -1.162 .036 -1.054 .060 -.774 .114 -.578 .1246 -105.00 -1.827 .046 -1.526 .074 -1.107 .150 -. 767 .1787 -90.00 -1.846 .058 -1.298 .084 -.878 .154 -.609 .158a -75.00 -1.622 .052 -1.2bb .100 -. kbO .124 -.629 .2129 -60.00 -1.659 .072 -1.2b3 .086 -.870 .146 -.602 .16410 -45.00 -1.736 .070 -1.339 .092 -.928 .134 -.647 .17011 -30.00 -1.958 .116 -1.430 .090 -.964 .130 -. 718 .17812 -15.00 -1.937 .120 -1.418 .114 -1.082 .17? -. 787 .27013 0.00 -1.037 .060 -. 816 .062 -. 565 .150 -. 581 .23814 15.00 -1.175 .064 -1.144 .108 -1.20 .290 -1.762 .5321S 30.00 -2.064 .136 -1.729 .106 -1.620 .148 -1.870 .24416 45.00 -2.142 .124 -1.776 .120 -1.717 .188 -1.595 .23217 60.00 -1.885 .072 -1.668 .106 -1.541 .160 -1.570 .2361 75.00 -1.790 .060 -1.640 .092 -1.527 .146 -1.559 .21219 90.00 -1.782 .064 -1.562 .086 -1.517 *166 -1.469 .21620 105.00 -2.046 .064 -1.673 .100 -1.553 .184 -1.526 .16421 120.00 -1.933 .044 -1.816 .084 -1.767 .140 -1.771 .21622 135.00 -1.178 .042 -1.217 .066 -1.204 .110 -1.138 .14423 150.00 -. 259 .044 -.350 .048 -. 369 .090 -. 383 .10224 165.00 .563 .034 .459 .042 .437 %046 .409 .070

CN 1.723 1.363 1.212 1.096CY .327 .440 .723 .959

B-7

NSWC TR 82-394

DISTRIBUTION LISTCopies

Hughes Aircraft Co. 1Missile Systems GroupCanoga Park, CA 91304Attn: Mr. Henry August

Calspan Field Services, Inc. 1PWT-4T, MS 600AEDC (AFSC)Arnold Air Force Station, TN 37389Attn: Dr. W. B. Baker

AEDC/DOFAA 1Arnold Air Force Station, TN 37389Attn: Mr. Thomas Best

AFATL/DLMAEglin AFB, FL 32542Attn: Mr. Carroll B. Butler

Naval Weapons CenterCode 3246China Lake, CA 93555Attn: Dr. William H. Clark

Department of Engineering SciencesUniversity of FloridaGainesville, FL 32611Attn: Dr. Mark H. Clarkson

AEDCArnold Air Force Station, TN 37389Attn: Mr. Stuart Coulter

AFATL-DLBEglin Air Force Base, FL 32542Attn: Dr. Donald C. Daniel

CommanderUS Army Missile CommandRedstone Arsenal, AL 35898Attn: Mr. Ray Deep, DRSMI-RDK

(1)

NSWC TR 82-394

DISTRIBUTION LIST (Cont.)

Copies

Department of Aeronautical Engineering IUniversity of BristolBristol B58 ITRUnited KingdomAttn: Mr. Paul Dexter

Lockheed Missiles and Space Co. Inc.Dept. 81-10, Bldg. 154, Fac. 1P.O. Box 504Sunnyvale, CA 94086Attn: Dr. Lars E. Ericsson

Vought CorporationAdvanced Technology CenterP. 0. Box 226144Dallas, TX 75266Attn: Dr. C. H. Haight

Nielsen Engineering and Research, Inc.510 Clyde AvenueMountain View, CA 94043Attn: Dr. Michael J. Hemsch

Rockwell InternationalMissile System Division4300 East 5th AvenueColumbus, OH 43216Attn: Mr. Fred Hessman, D-165

Northrup Corporation. Aircraft DivisionOrgn 3813, Zone 82One Northrop AvenueHawthorne, CA 90250Attn: Dr. Brian L. Hunt

Department of Mechanics of FluidsUniversity of ManchesterManchester M13 9PLENGLANDAttn: Dr. Peter Lamont

AFWAL/FIGCDepartment of the Air ForceWright Patterson Air Force Base, OH 45433Attn: Dr. William H. Lane

AFATL/DLJCAEglin AFB, FL 32542Attn: Dr. Lawrence E. Lijewski

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'V ____

NSWC TR 82-394

DISTRIBUTION LIST (Cont.)

Copies

FIMGAir Force Wright Aeronautical Laboratories (AFSC)Wright-Patterson AFB, Ohio 45433Attn: Capt. Alex J. Malanowski

NASA-Ames Research CenterMail Stop 227-8Moffett Field, CA 94035Attn: Mr. Gerald N. Malcomn

CommanderUS Army Research OfficeP. 0. Box 12211Research Triangle Park, NC 27709Attn: Colonel Duff G. Manges

Department of Aerospace and MechanicalEngineeringUniversity if Notre DameNotre Dame, IN 46556Attn: Dr. Robert C. Nelson

Nielsen Engineering and Research510 Clyde AvenueMountain View, CA 94043Attn: Dr. Jack N. Nielsen

AEDC/DOFAA, DOTArnold Air Force Station, TN 37389Attn: Captain Alvin R. Obal

Complere, Inc.P. 0. Bcx 1697Palo Alto, CA 94302

Attn: Dr. F. K. Owen

CommanderNaval Sea Systems CommandSEA 62R41Washington, DC 20362Attn: Mr. Lionel Pasiuk

Mechanical Engineering DepartmentClemson UniversityClemson, SC 29631Attn: Dr. C. E. G. Prizirembel

(3)

NSWC TR 82-394

DISTRIBUTION LIST (Cont.)Copies

Director 1Engineering Sciences DivisionUS Army Research OfficeP. 0. Box 12211Research Triangle Park, NC 27709Attn: Dr. Robert E. Singleton

Commander 1U.S. Army Missile CommandRedstone Arsenal, AL 35898Attn: David Washington, DRSMI-RDK

USAFA/DFAN 1USAF Academy, CO 80840Attn: Captain G. J. Zollars

Defense Technical Information Center

Cameron StationAlexandria, VA 22314 12

Library of CongressAttn: Gift and Exchange DivisionWashington, DC 20540 4

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VORTEX ASYMIETRY DEVELOPMENT ON A TANGENT …

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