Shock Waves (1997) 7:1–12

Hypersonic jet control effectiveness

D. Kumar 1,∗∗∗, J.L. Stollery1,∗, A.J. Smith2,∗∗

1 College of Aeronautics, Cranfield University, Cranfield, Bedfordshire, MK43 0AL, UK2 Fluid Gravity Engineering Ltd., Chiltee Manor, Haslemere Rd, Liphook, Hampshire GU30 7AZ, UK

Received 18 August 1995 / Accepted 27 June 1996

Abstract. The present study aims to identify some of the pa-rameters which determine the upstream extent and the lateralspreading of the separation front around an under-expandedtransverse jet on a slender blunted cone.

The tests were conducted in the Cranfield hypersonicfacility at M∞ = 8.2, Re∞/cm = 4.5 to 9.0× 104 and atM∞ = 12.3, Re∞/cm = 3.3 × 104. Air was used as theworking gas for both the freestream and the jet.

Schlieren pictures were used for the visualisation of thethree-dimensional structures around the jet. Pressure, normalforce and pitching moment measurements were conducted toquantitatively study the interaction region and its effects onthe vehicle. An analytical algorithm has been developed topredict the shape of the separation front around the body.

Key words: Hypersonic, Control jet, Transition, Force aug-mentation

Symbols

A AreaC ConstantCN Normal force coefficientCM Moment coefficientcp Specific heat coefficient (isobaric)d DiameterL Length of coneLsep Length of separated flow (alongθm = 0◦)M Mach numberM Pitching momentm Mass flow rateN Normal force (with respect to body axis)

Correspondence to: D. Kumar∗ Professor of Aerodynamics∗∗ Director of Aerothermodynamics∗∗∗ PhD student

An abridged version of this paper was presented at the AIAA Sixth Inter-national Aerospace Planes and Hypersonics Technologies Conference, 3–7April 1995 at Cattanooga, TN, USA (AIAAA-95-6066)

O Origin (nosetip of cone)R RadiusRs Shock radiusRe Reynolds numberP0 Reservior pressureT0 Reservior temperaturep Static pressureS Base areau Velocityx axial distance (from nosetip)

ρ Densityψ Jet bow shock stand-off distanceγ Ratio of specific heatsθm Meridian angle (measured from jet meridian)δc Cone semi-vertex angle

Subscripts

c Conei Interactionj JetN Noseo Stagnations Jet bow shocksep Separation front4 Tunnel driver∞ Freestream

1 Introduction

In hypersonic free-flight conditions, mechanically deflectedflaps are employed under continuum flow conditions pro-vided the freestream dynamic pressure is adequate. At highaltitudes, the low freestream dynamic pressure results inpoor control effectiveness from mechanical flaps. Underthese conditions, it becomes necessary to either augmentthe mechanical flap control system or to deploy an inde-pendent aerodynamic control using reaction jets. The pres-ence of an under-expanded transverse jet creates a highlythree-dimensional adverse pressure gradient. This generatesa three-dimensional separated interaction region. The result-ing viscous-inviscid interaction produces an increase in pres-sure in the separation region which augments the desiredcontrol force.

2

Fig. 1. General structure of the blunt cone model

2 Experimental set-up

2.1 Wind tunnel facility

The Cranfield hypersonic gun tunnel facility was used for thestudy. The tests were carried out with air as the working jetand freestream gas. Two axi-symmetric contoured nozzlesprovided a useful test jet diameter of 15.0 cm at freestreamMach numbers of 8.2 and 12.3. The tunnel is equipped witha single-pass schlieren system. This uses a high intensity mi-crosecond duration argon spark source to illuminate densitygradients in the flow. Pressure measurements were carriedout using Kulite XCS-190 series pressure transducers.

2.2 General structure of models

The general structure of the blunt cone configuration isshown in Fig. 1.

The models used for schlieren observations were equippedwith a single jet hole. Pressure models were equipped withtappings along the jet meridian and a number of jet holes(in the jet exit plane) at selected angular intervals. These jetsallowed the relative angle between the jet and the tappingmeridian to be altered.

2.2.1 Force model

The air feed system for the force model plenum chamberused dual injection ports located in the horizontal axis plane

Fig. 2. Coiled pipe structure used to feed the plenum chamber of the forcemodel

of the model. This set-up imposed yaw moments due to dif-ferences in feed pipe pressure. For the balance, the couplingbetween the normal force and the pitching moment compo-nents to yaw moments was negligible.

The pressure feed employed coiled tubes, as shown inFig. 2.

These coils allowed movement similar to a spring andthus reduced the coupling forces between the jet feed systemand the model.

2.3 Data filtering for force measurements

During the running of the tunnel, the working section issubjected to severe mechanical oscillations. Due to its massinertia, these oscillations produce damped harmonic oscilla-tions of the model.

The natural frequency of these oscillations was deter-mined by a tare calibration. In this, the tunnel was run withthe flow blocked off by means of a 5 cm thick brass discplaced immediately upstream of the nozzle entry plane. Dig-ital filters were used to remove the natural frequency com-ponent from test signals.

3 Results and discussion

3.1 General structure of the interaction region

The flow structure created by the interaction of an underex-panded sonic jet with the cone freestream is shown in Fig. 3.This test was conducted atM∞ = 12.3,Re∞/cm = 3.3×104

with a jet reservior pressure ofPoj = 29.7 psia.Due to the relatively high Mach number and the low

Reynolds number, the interaction region is fully laminar.The blunt leading edge of the body generates a highly

curved bow shock. The curvature of this shock generates anentropy layer. Density gradients in the entropy layer maskthe density gradients in the boundary layer and hence makeit is difficult to identify the edge of the cone boundary layer.

The presence of a transverse underexpanded jet is some-what analogous to a finite circular cylinder projecting fromthe cone surface. This generates a bow shock around the jet(called the jet bow shock).

3

Fig. 3a–c. General structure of the interaction region. (M∞ = 12.3,Re∞/cm = 3.3× 104, Poj = 29.7 psia)

The interaction of the jet bow shock with the coneboundary layer produces a complex three-dimensional ad-verse pressure gradient. This feeds out radially through thesubsonic portion of the cone boundary layer (sublayer), caus-ing a loss of momentum and a subsequent separation of theboundary layer some distance upstream of the jet.

In the vicinity of the separation point, the thickening ofthe sublayer rapidly increases the local thickness of the dis-placement body. This results in the formation of a separationshockwave. The separated flow region is characterised by theseparation vortex whilst immediately upstream of the jet, ahorseshoe vortex is formed. Downstream of the jet, a wakeregion consisting of a recompression vortex / shock systemis formed. The general flow structure in the interaction re-gion of the blunt cone is shown in Figs. 3b and 3c.

If the strength of the adverse pressure gradient due tothe jet bow shock structure is sufficient, the primary sepa-ration region extends right round to the 180◦ meridian. Theresulting thickening of the boundary layer along this merid-

ian generates a separation shockwave. This is evident in theschlieren photograph of Fig. 3a.

3.2 3-D studies of the interaction region

3.2.1 Schlieren studies

The curvature of the jet bow shock and the separation frontwas studied using schlieren techniques. For this, selectedmeridians were placed normal to the schlieren beam by arotation of the model. The results are shown in Fig. 4.

The photographs show a separation shock well ahead ofthe jet. The separation front shows a small movement fromx/d = −12 along the jet meridian (θm = 0◦) to x/d = −9along theθm = 75◦ meridian.

For meridiansθm ≤ 30◦, the jet bow shock shows negli-gible sweep. However forθm > 30◦, it is rapidly swept andalong the 75◦ meridian, it lies downstream of the trailingedge. The sweep of the jet bow shock and of the separationfronts are further discussed in Sect. 3.5.

3.2.2 Pressure measurements

Pressure measurements along selected meridians are shownin Fig. 5. The tests were conducted at the same conditionsas those shown in Fig. 4.

Along the jet meridianθm = 0◦, the flow separates atx/d = −12.5. The separation shock increases the pres-sure level. This attains a plateau as the separation stream-line becomes straight. A second increase in pressure fromx/d = −3.82 is due to the jet bow shock.

Following its expansion around the jet, the flow separatesdue to the adverse pressure gradient generated by an obliquelip shock. The location of this shock is shown schematicallyin Fig. 3.

The separation generates a jet wake with a pair of contra-rotating recompression vortices (see Figs. 3b and 3c). Sincethe lip shock is weak, the centreline pressure immediatelybehind the jet is similar to the pressure at the separationpoint. The centreline pressure behind the jet is lower thanthe cone pressure. The recovery of static pressure is due tothe contraction of the jet wake (see Fig. 3c).

The pressure distributions of Fig. 5 show little movementin the location of the separation point along theθm = 0◦,θm = 15◦ andθm = 30◦ meridians. This is confirmed by theschlieren photographs of Fig. 4.

In Sect. 3.5, it is shown that the shape of the separationfront reflects that of the jet bow shock. Along meridiansclose to the jet meridian (θm = 0◦), the jet bow shock is “rel-atively two-dimensional”. Thus the separation front alongmeridians close to the jet meridian is also two-dimensional(i.e. varies little in axial position).

In Fig. 5, the absence of a pressure rise along the 180◦meridian means that the flow remains attached. This is alsoevidenced from the absence of shockwaves in the corre-sponding schlieren photographs along this meridian (seeFig. 6).

4

Fig. 4. Three-dimensionality of the interaction region (M∞ = 8.2,Re∞/cm = 9.0× 104, Poj = 74.7 psia)

3.3 Parametric studies of the interaction region

3.3.1 Jet pressurePoj

The effect of jet reservior pressure on the extent of the sep-arated flow atM∞ = 8.2, Re∞/cm = 9.0× 104 is shown inFig. 6.

Under given freestream conditions, an increase in jet re-servior pressure promotes separation along the jet meridian(θm = 0◦). This agrees with the observations of Zoukowskiet al. (1964) and of Hefner et al. (1972). The mass flow ratethrough a choked jet nozzle (forγ = 1.4) is given by

Fig. 5. Pressure distributions in the interaction region (M∞ = 8.2,Re∞/cm = 9.0× 104, Poj = 74.7 psia)

m√cpToj/(AjPoj) = 0.393 (1)

For a given jet geometry and reservior temperature, the jetmass flow rate increases with reservoir pressure. As is evi-dent in Fig. 6, an increase in jet reservior pressure increasesthe diameter and the penetration of the jet. This is due tothe increase in the jet mass flow.

Using the circular cylinder analogy of the jet and a blastwave type approach to model the shock around the bluntcylinder, Karamcheti and Hsia (1963) found that, for an in-viscid flowfield on a flat plate, the shape of the trace of thejet bow shock is given by

Rs

dj= C

(Poj

p∞

)1/4 [ψ

dj

]1/2

(2)

C is a constant based on the freestream Mach number andspecific heat ratio. This is given by Karamcheti and Hsia(1963) as

C =1.14γM∞

(2

γ + 1

) γ+12(γ−1)

(1 +

γ − 12

M2∞

)( γ−1γ

)+(

γ+12(γ−1)

)1/4

(3)

Equation 2 shows that an increase in jet reservior pressureincreases the lateral spreading of the jet bow shock. This,

5

Fig. 6. The effect ofPoj on the interaction region (M∞ = 8.2,Re∞/cm =9.0× 104)

together with the increased penetration of the jet promotesseparation.

3.3.2 Gun tunnel driver pressureP4

The schlieren photographs of Fig. 7 show the effect of guntunnel driver pressure on the extent of the interaction region.The tests were conducted atM∞ = 8.2 with a fixed jetreservoir pressure.

At a given Mach number, a change in driver pressure isaccompanied by a change in the freestream unit Reynoldsnumber. In the tests shown in Fig. 7, freestream Reynoldsnumber changes are small and have little effect on the devel-opment of the laminar boundary layer. Thus, these Reynoldsnumber changes do not affect the location of the separationfront. The effect of Reynolds number on separation is furtherdiscussed in Sect. 3.5.

By decreasing the gun tunnel driver pressure, the effec-tive freestream reservior pressure and hence the freestreamstatic pressure is decreased. The decrease in the ambientpressure into which the jet exhausts increases the expansionof the jet. This increases the diameter and the penetrationof the jet, as evidenced from the schlieren photographs inFig. 7. The combination of these effects increases the ad-verse pressure gradient associated with the jet bow shockand thus promotes separation.

3.3.3 Jet-to-freestream pressure ratioPoj/p∞

Schlieren photographs of the interaction region for two con-ditions with similar jet to freestream pressure ratioPoj/p∞

Fig. 7. The effect ofP4 on the interaction region (M∞ = 8.2, Poj =134.7 psia)

are shown in Fig. 8. The similar pressure ratios were sim-ulated by varying the jet and freestream reservior pressure.The latter was achieved through changes in the gun tunneldriver pressure.

The test Mach number was maintained atM∞ = 8.2whilst the test Reynolds number varied fromRe∞/cm =4.5× 104 for the P4 = 500 psig test toRe∞/cm = 7.0×104 for theP4 = 1000 psig test. The small difference in thefreestream unit Reynolds number between these tests doesnot affect separation. In both tests, the cone boundary layerwas laminar upto separation.

The similar locations of the separation shockwave alongtheθm = 0◦ and theθm = 180◦ meridian indicates the lateralspreading of the separation front between these meridiansto be similar and suggests that the extent of the jet inter-action region is determined by neitherPoj (see Sect. 3.3.1)nor P4 (see Sect. 3.3.2) but by the non-dimensional parame-ter Poj/p∞. The influence of this parameter arises primarilythrough its effect on the diameter and penetration of the jet.

6

Fig. 8. The effect ofPoj/p∗ on the interaction region (M∞ = 8.2)

3.4 Separation length correlation

A correlation of the length of separated flow along thejet meridian for various freestream conditions is shown inFig. 9a.

The tests at Mach 8.2 encompass data from tests con-ducted in the freestream unit Reynolds number rangeRe∞/cm = 4.5× 104 to 9.0× 104. The correlation of thedata in the absence of any Reynolds number factors suggeststhat small (factor of 2) changes in unit Reynolds number donot affect length of the separated flow.

For a given jet to freestream pressure ratio, the lengthof separated flow atM∞ = 12.3, Re∞/cm = 3.3 × 104

is considerably reduced as compared to tests at Mach 8.2.The decrease in the lateral extent of the separation regionwith Mach number has also been observed by Zukowskiand Spaid (1964). The latter authors showed that the penetra-tion distance of the jet was reduced by increasing freestreamMach number. This may be responsible for the reduction inthe lateral spreading of the separation region by increrasingMach number.

Our scaling of the separation length based on the free-stream Mach number, jet diameter and the jet to freestreampressure ratio is shown in Fig. 9b. The data correlates as

LsepM5/2∞

dj= 21

[Poj

p∞

]3/4

(4)

The correlation suggests that the length of the separated flowregion increases with an increase in the jet to freestreampressure ratio. This agrees with the observations of thepresent study as described in Sect. 3.3. The absence of aReynolds number parameter from the scaling is supportedby the observations described in Sect. 3.3.3. However, it is

Fig. 9. Correlation of the separated flow length along the jet meridian

important to note that the range of variables was limited andmore data is required.

3.5 Lateral spreading of the separation front

As was described in Sect. 3.1, the interaction region aroundthe underexpanded jet is characterised by a highly three-dimensional bow shock. The variable adverse pressure gradi-ent associated with this shock produces a three-dimensionalseparation front upstream of the jet.

In order to maximise the augmentation of the jet reactionforce by the interaction force, the upstream extent of theseparation front along theθm = 0◦ jet meridian must bemaximised whilst the flow alongθm ≥ 90◦ meridian shouldbe maintained as attached.

In Sect. 3.3, it was shown that the upstream extent of theseparation interaction region on the jet meridian (θm = 0◦)and its lateral spreading is affected by the jet reservoir pres-sure, freestream pressure and the freestream Mach number.During the flight of a vehicle, these parameters vary due tochanges in altitude and velocity. This will produce changesin the extent of the separation interaction region and hencein the effectiveness of the control jet.

Nunn (1970) suggests that the shape of the separationfront around a circular jet on a flat plate is a function ofthe shape of the bow shock. The latter is given by Eq. 2.

7

Fig. 10. Co-ordinate transformation for the separation front on a curvedbody (Nunn, 1966)

Using this, the shape of the associated separation front canbe written as

Rsep

dj= C

(Poj

p∞

)1/4 [ (x− xsep)dj

]1/2

(5)

For interactions on axisymmetric bodies with lateral curva-ture, Karamcheti and Hsia suggest that the flat plate sep-aration front generated around a circular sonic jet can bewrapped around the curved surface using the transformation

θm,sep = k1C

(Poj

p∞

)1/4 [x

dj− xsep

dj

]1/2dj

dBx(6)

wherek1 is a constant anddBx is the local body diameterat x. The coordinates of the transformation are shown inFig. 10.

For the present tests, the separation length directly up-stream of a jet was correlated in Sect. 3.3 in the

Mach number range 8.2 ≤ M∞ ≤ 12.3. Eq. 4 gave theaxial location of separation along the jet meridian as

xsep

dj=Lj

dj− 21

M5/2∞

(Poj

p∞

)3/4

(7)

Substituting forxsep/dj and the local diameter on thecone gives the angular location of separation on a blunt con-ical configuration as

θm,sep = k1CQ

(Poj

p∞

)1/4

×[x

dj−(Lj

dj− 21

M5/2∞

(Poj

p∞

)3/4)]1/2

(8)

where from the cone geometry

Q =dj

dN(1− tanδc) + 2x tanδc(9)

In Fig. 11, the predictions from the algorithm of Eq. 8 arecompared with experimental observations of the location ofthe separation front. The latter was obtained from schlierenphotographs.

The predictions were made fork1 = 6.0 whilst Nunn(1970) found agreement withk1 = 2.0. The difference inthis parameter is probably due to the lower freestream Machnumber of the latter tests which were conducted in the su-personic Mach number regime.

The agreement between the experimental and predictedlocations of the separation front (see Fig. 11) is within±5%.

Fig. 11. Comparison of the predicted and measured separation fronts

The difference between the two results for theP4 = 500 psigtest is conjectured to be the result of transition, generatedpossibly due to local surface imperfections. The energisationof the boundary layer by transition along selected meridiansresults in a local delay in separation. Heat transfer measure-ments using either thin-film gauges or liquid crystals arerequired to substantiate the conjecture.

The predictions of Eq. 8 are independent of Reynoldsnumber effects. The agreement of the predictions with theexperimental measurements (conducted over a small Reynoldsnumber range) suggests that the location of a laminar sepa-ration front around the body is insensitive to small Reynoldsnumber changes.

3.6 The effects of incidence on the flow structure over ablunt cone

Circumferential heat transfer distributions on a blunt cone atincidence are shown in Fig. 12.

At low incidence (α = 5◦), the heat transfer attains itsminimum along the leeward meridian. This is due to a localthickening of the boundary layer along this meridian.

At high incidence (α = 10◦), the heat transfer along theleeward meridian is greater than along surrounding meridi-

8

Fig. 12. Circumferential heat transfer distributions on a blunt cone at inci-dence (Wrisdale, 1992)

ans. This is due to the reattachment of separated crossflowvortices along the leeward meridian.

Liquid crystal tests for the present study (Kumar, 1995)showed an initial minumum in heat transfer along the lee-ward meridian atα = 3◦. However atα = 6.0 andα = 9.5,a high temperature streak was present along the leewardmeridian. This was attributed to the reattachment of cross-flow vortices.

3.7 The effect of incidence on jet interaction

3.7.1α < δc

Schlieren photographs (see Fig. 13) show that an increase inincidence fromα = 0◦ to α = 3◦ increases the diameter andpenetration of the jet.

Separation along the leeward meridian is promoted fromx/d = −12 atα = 0◦ to x/d = −34.03 atα = 3◦. Stetson(1972) measured a progressive decrease in cone pressurealong the leeward meridian with incidence.

The decrease in the local cone pressure along the lee-ward meridian with incidence effectively increases the lo-cal jet pressure ratioPoj/pe. The increased jet pressure ra-tio increases the diameter and penetration of the jet. Thisstrengthens the interaction and promotes separation alongthe leeward meridian.

3.7.2α > δc

As was described in Sect. 3.6, an increase in incidence be-yond theδc causes crossflow separation. At these incidences,the leeward jet exhausts into a separated crossflow structure.The crossflow on the present configuration was separated atincidences ofα = 6◦ andα = 9.5◦.

Schlieren photographs of the jet interaction region atα = 6◦ and α = 9.5◦ are shown in Fig. 13. The densitygradients associated with the crossflow vortices mask thegradients associated with the jet interaction region and thusmake it difficult to observe the effects of the jet on the lo-cal flowfield. The interaction structures at these incidences

Fig. 13.The effect of incidence on jet interaction (M∞ = 8.2,Re∞/cm =9.0× 104, Poj = 74.7 psia)

are discussed by Kumar (1995). Using liquid crystal thermo-graphs of the interaction region, it is conjectured that a jetinduced separation interaction region forms within the cross-flow induced separation interaction region. Further studiesusing laser sheet visualisation techniques are required forconfirmation.

4 Force measurements

The sign convention used for the normal force and momentmeasurements are shown in Fig. 14. An upward force (nor-

9

Fig. 14. Sign convention used for normal force and pitching moment

mal to the axis of the model) and a nose up pitching momentwere taken as positive.

The normal force measurements were non-dimensional-ised using the freestream dynamic head and the base area ofthe blunt cone.

CN = N/ 12ρ∞U

2∞S (10)

The pitching moments were non-dimensionalised using thefreestream dynamic head, base area and the length of thecone.

CM = M/ 12ρ∞U

2∞SL (11)

The pitching moments were measured at the moment refer-ence point located atx/d = −10.18 along the body axis.

4.1 Jet only force measurements

The jet only normal force and moment coefficients, measuredunder evacuated tunnel conditions withPoj/pam = 700, wereCN(j) = −25× 10−3 andCM(j) = 3.4× 10−3 respectively.The negative reaction force was generated due to the upwardexhaust of the jet. The pitching moment generated by the jetwas nose-up due to the jet axis being aft of the momentreference centre.

4.2 Jet interaction force measurements

4.2.1 Force history (α = 0◦)

The tests to study the effects of the jet/crossflow interactionon the total reaction force generated by the jet were con-ducted by first establishing a steady jet and then firing thetunnel. The normal force history resulting from this process(Poj/p∞ = 570) is shown in Fig. 15.

The presence of the jet att = 0 produces a negativeforce. The magnitude of this force is constant after 100 msdue to the jet plenum chamber becoming choked.

The firing of the tunnel and the increase in pressure inthe interaction region atα = 0◦ augments the jet force.The completion of the tunnel run and the removal of theaugmentation force results in the mean force returning tothe jet force level. The increase in noise during and after therun is due to the mechanical oscillations.

4.3 Force augmentation (α = 0◦)

The normal force and moment measured on a cone (in theabsence and in the presence of the jet) is shown in Fig. 16.

4.3.1 Cone only

At α = 0◦, a small normal forceCN(c) = −13× 10−3 anda pitching momentCM(c) = −0.87× 10−3 was measured onthe blunt cone (in the absence of the jet). The forces andmoments observed are due to the centreline focusing effectassociated with imperfections in the surface of the Mach 8.2nozzle. The forces and moments were absent in similar testsconducted with the Mach 12.3 nozzle.

4.3.2 Normal force

The method used and the assumptions made in the derivationof the interaction force is given in the appendix.

At α = 0◦, the absolute normal force measured in thepresence of the jet wasCN(j+i+c) = −55×10−3 (including thenormal force on the cone). The combined jet and interactionnormal force was therefore

CN(j+i) = CN(j+i+c) − CN(c) = −42× 10−3 (12)

This compares with the jet only force (see Sect. 4.1) ofCN(j) = −25×10−3. Thus, the interaction augments the totalforce generated by the jet by 70%.

4.3.3 Pitching moment

As is shown in Fig. 15, the jet increases the moment onthe cone (atα = 0◦) from CM(c) = −0.87× 10−3 (in theabsence of the jet) toCM(j+i+c) = 2.98×10−3. Therefore, thecombined jet and interaction pitching moment was

CM(j+i) = CM(j+i+c) − CM(c) = 3.85× 10−3 (13)

This compares with a jet only moment ofCM(j) = 3.4×10−3. Thus, the interaction augments the pitching momentgenerated by the jet by 13%.

4.3.4 Centre of pressure

The relative locations of the centre of pressure of the jetalone and of the interaction force (alone) are shown inFig. 17.

The centre of pressure of the jet alone force was locatedat x/d = 0.16. This is within 1% (with respect toL) ofthe location of the jet exit plane. The centre of pressureof the jet interaction force is located within the separationinteraction region. The latter is mapped by the separationfront calculated using the algorithm given in Sect. 3.5.

The increase in pressure upstream of the jet on meridiansin the regionθm < 90◦ favourably assists the normal forceand pitching moment of the jet. The over-expansion behindthe jet and the increase in pressure along meridians in theregion θm > 90◦ adversely affect the forces and momentsgenerated by the jet. The centre of pressure of the interac-tion is effectively an integration of the elemental forces andmoments generated in the interaction region.

10

Fig. 15. The effects of the jet and the jet/crossflow interaction on normal force

Fig. 16. Force and moment augmentation by the jet (M∞ = 8.2,Re∞/cm = 9.0× 104, Poj = 74.7 psia)

4.4 Small incidenceαδc

The effect of incidence on the normal force and pitchingmoment generated by the interaction was studied for thePoj = 60 psig jet. The tests were conducted atM∞ = 8.2,Re∞/cm = 9.0× 104 and p* = 0.13 psia.

Fig. 17. The relative locations of the centre of pressures of the jet andthe interaction force (M∞ = 8.2, Re∞/cm = 9.0× 104, Poj = 60 psig,α = 0◦)

In order to prevent the effects of crossflow separationon the jet interaction region (see Sect. 3.7), the study of theeffects of incidence on the force and moment augmentationwas limited toα = 3◦. The forces and moments measuredare shown in Fig. 16.

On a cone at incidence, the pressure along windwardmeridians increases whilst the pressure along leeward merid-ians decreases. The pressure difference between the leewardand windward meridians generates a positive normal forceon the cone. For the present tests, a normal force on the coneof CN(c) = 83× 10−3 was measured atα = 3◦.

Stetson (1972) has shown that incidence generates axialpressure gradients along the windward and leeward merid-ians of a cone at incidence. These axial pressure gradientstogether with the pressure differences between the leewardand windward meridians creates a positive pitching moment.For the present tests, this was found to beCM(c) = 10×10−3

(see Fig. 16).

At α = 3◦, the jet (and its associated interaction region)reduce the normal force fromCN(c) = 83×10−3 toCN(j+i+c) =29× 10−3. Thus, the normal force generated by the jet andinteraction is

CN(j+i) = CN(j+i+c) − CN(c) = −54× 10−3 (14)

11

Fig. 18. The effect of incidence on the shape of the separation front

This compares with the jet only normal force (see Sect. 6.1)of CN(j) = −25× 10−3. Hence, atα = 3◦, the interactionaugments the jet force by 112%.

As was shown by the schlieren photographs of Fig. 13,increasing incidence fromα = 0◦ to α = 3◦ promotes sep-aration along the leeward meridian. This is due to the de-crease in cone pressure along leeward meridians effectivelyincreasing the local jet to cone pressure ratio.

Along with decreasing the cone pressure along leewardmeridians, incidence increases the pressure along windwardmeridians. This effectively reduces the local jet to cone pres-sure ratio along windward meridians and thus limits the lat-eral extent of the separation region. The conjectured shapesof the separation front on the cone atα = 0◦ andα = 3◦ areshown in Fig. 18.

The increase in the area of the interaction region togetherwith the limitation of its effect to the leeward meridiansresults in an increased augmentation of the normal forcewith incidence.

At α = 3◦ (see Fig. 16), the jet increases the nose upmoment fromCM(c) = 10× 10−3 (in the absence of the jet)to CM(c+j+i) = 13.1×10−3. The moment generated by the jet& interaction is

CM(j+i) = CM(c+j+i) − CM(c) = 3.1× 10−3 (15)

This compares with the jet alone pitching moment ofCM(j) =3.4× 10−3. Therefore, atα = 3◦, the total nose up momentassociated with the jet & interaction is lower than that of thejet alone.

For α = 3◦, the schlieren photographs of Fig. 13 showthe upstream limit of the separation front to be located wellupstream of the moment reference point. The conjecturedseparation front atα = 3◦ is mapped in Fig. 18.

The relative locations of the centre of pressure atα =0◦ and atα = 3◦ are shown in Fig. 19. The promotion ofseparation along leeward meridians atα = 3◦ causes thecentre of pressure of the interaction force to move upstreamof the moment reference point.

The promotion of separation along leeward meridiansmoves the centre of pressure of the interaction from down-stream of the moment reference point atα = 0◦ to upstreamof the reference point atα = 3◦. This increases the nosedown pitching moment associated with the interaction re-gion and causes the jet moment to be reduced.

Fig. 19.Schematic diagram of the effect of incidence on the location of thecentre of pressure

5 Conclusions

1. The upstream length (along the jet meridian) and the lat-eral spreading of the separation interaction region increaseswith jet to freestream pressure ratio.2. The upstream length of the interaction region (along the jetmeridian) increases with incidence but its lateral spreadingdecreases with incidence.3. The extent of the separation interaction region is reducedby increasing Mach number.4. Small (factor of 2) changes in the freestream unit Reynoldsnumber do not affect the shape of the separation interac-tion region. Further work is required to extend the Reynoldsnumber range of the jet interaction database.5. At zero incidence, the shape of the separation interactionregion is a direct function of the shape of the jet bow shock.6. In the freestream Mach no. range 8.2≤M∞ ≤ 12.3 andin the freestream unit Reynolds number range 3.3× 104 ≤Re∞/cm ≤ 9.0◦104, the shape of the separation front iswell predicted by the model described in Sect. 3.5. Furthertests are required to extend the Mach and Reynolds numberenvelope of this model.7. The interaction region significantly augments the normalforce of the jet. The augmentation of the normal force in-creases with incidence.8. At zero incidence, the interaction favourably augments thepitching moment of the jet. However, at small incidence, theinteraction adversely affects the pitching moment of the jet.

Appendix

Derivation of the interaction force and momentThe following normal force and moment coefficients

were derived by non-dimensionalising force and momentmeasurements made from the gun tunnel force balance:CN(c), CM(c) – Force and moment coefficients generated onthe cone only in freestream flow atM∞ = 8.2CN(j) , CM(j) – Force and moment coefficients generated bythe jet in the absence of freestream flowCN(c+i+j),CM(c+i+j) – Force and moment coefficients generatedby the combined cone and jet in freestream flow atM∞ =8.2.

12

Using these measurements, the jet + interaction forceCN(i+j) was derived from

CN(j+i) = CN(c+j+i) − CN(c)

Since the individual forces generated by the cone, the jetand their combination are measured, the force generated bythe interaction can be derived from

CN(i) = CN(j+i) − CN(j)

This method for deriving the individual forces generated bythe cone, jet and the interaction fundamentally asssumes thatthe force generated by the cone in the presence of the jetis equal to the sum of the individual components i.e. thealgebraic sum of the forces generated by the cone, the jetand their interaction

CN(c+j+i) =∑

[CN(c) +CN(j) +CN(i) ]

This assumption is valid since the force generated by themutual interaction between the cone and the jet flowfields istaken into account by the interaction force.

References

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