Supersonic Rectangular Over-Expanded Jets of Single and Two-Phase Flows

ISABE 2003-1119A. Mohamed* and A. Hamed†

Department of Aerospace Engineering & Engineering MechanicsUniversity of Cincinnati, Cincinnati, Ohio

T. Lehnig‡Vice President and Director of Engineering and Operations

Coldjet Inc., Cincinnati, Ohio

AbstractAn experimental investigation wasconducted to study supersonic jets fromconvergent divergent nozzles withrectangular cross section. The flowregimes and shock structure in the plumewas characterized for jets in quiescentatmosphere at over-expanded conditions.Schlieren pictures of the jets are presentedto show the shock structure and jet spreadrate at different nozzle pressure ratios.LDV measurements are presented for thejet flow field and the centerline velocitydecay. The results indicate that therectangular supersonic jet spread rate isgreater along the minor axis and increaseswith the nozzle pressure ratio. Theindividual shock cell length, as well a, thetotal number of shock cells within the jetplume were found to increase with nozzlepressure ratio. In two-phase rectangularjets of gas and dispersed solid particles theshock strength was found to attenuate withincreased particle loading.

IntroductionRecent interest in rectangular supersonicjets is motivated by the need to reduceplume length and acoustically excitedstructural loads in the exhaust systems ofhigh performance aircrafts. Semi-periodic_____*Doctoral student†Professor, Fellow AIAA‡Member AIAA

shock structures form in the jet plumes ofthese vehicles during low speed flight whenthe convergent divergent nozzles operate atoff design conditions. These shock cellsaffect the jet velocity and temperature decayas well as the jet spread rate and its acousticfield.

A number of studies presented experimentalresults for the centerline jet velocity decayand spread rate of subsonic rectangular jets.Sfier [1] studied air jets issuing fromrectangular channels and slots in quiescentatmosphere. The results demonstrated thatthe jet growth rate in terms of the 50%velocity spread was greater in the directionof the minor axis. Sfier also presentedexperimental results for the axial variationof the mean velocity, longitudinal and lateralturbulence intensity and turbulence shearstress profiles and compared them to two-dimensional jets. Lazanova and Shanov [2]conducted an experimental investigation tostudy the effect of rectangular jet aspectratio on subsonic jet velocity and turbulenceintensity. Experimental data obtained from50 m/sec jets for aspect ratios between threeand ten indicated that jet spreading rate inhigher in the direction of the minor axis andthat the crossover point of the jet half widthmoved downstream with increased aspectratio. They also presented the axialvariations in jet entrainment, axial jetmomentum, and centerline turbulenceintensity. By computing separately the mass

flow in four triangular sections from thecenter to each of the four rectangular jetsides, Lazanova and Shanov determinedthat the entrainment in the quadrantscontaining the long sides were double thatin the quadrant containing the short sidewhich confirms the more intensive spreadof the jet in the minor plane. They alsoinvestigated the turbulence intensitypatterns and the establishment of similarityvelocity after distances greater than fortytimes the hydraulic diameter from thenozzle exit plane.

Krothapalli et al. [3] studied the mixing ofincompressible rectangular jets for aspectratios between 5.5 and 16.7 up to axialdistances 115 times the jet exit width(small nozzle dimension). Their resultsdemonstrated similarity in both the meanvelocity and shear stress profile in theplane along the minor axis beyond 30times the width.

Experimental investigations of rectangularhigh-speed jets also indicated higher jetspread rate in the plane of the minor axis.Von Glahn’s experimental studies [4,5,6,7]of rectangular and circular high-speedsubsonic jets in quiescent surroundingsconfirmed that the spread rate ofrectangular jets in the direction of theminor axis is greater than in circular jetswith the same area equivalent diameter.Von Glahn [6] developed correlations forthe plume centerline velocity decay and50% velocity spread variation with theaxial distance in terms of the jet aspectratio (AR), jet Mach number, and jet toambient temperature ratio. The correlationswere compared to the data for AR 6rectangular jets at 0.784 Mach number andfor a heated Mach 1.045 jet. He gave adifferent set of correlations in each of thethree jet regions, namely, the initial mixingregion, the transitional region, and the fully

mixed region. He also included flight effectsin the correlations based on velocitymeasurements of jets from rectangularnozzles in secondary streams. Seiner [8]compared the measured centerline velocitydecay and acoustic efficiency of unheatedjets for circular and rectangular nozzles withthe same area equivalent diameter. Theresults for these Mach 0.857 shock free jetsdemonstrated the high mixing capability andbeneficial noise reduction of rectangularnozzle exit geometry. A drastic reduction inthe potential core length of the rectangularjet was reported compared to the equivalentcircular jet. Seiner [8] reported a less drasticreduction in the core length of a Mach 1.52fully expanded elliptic jet to 5.2 equivalentdiameters, as compared to a 7.8 round jet[9]. Seiner [8] also presented phase-averaged Schlieren photos of supersonicelliptic jets at fully expanded and over-expanded conditions. While the Mach 1.52fully expanded elliptic jet mixing layersexperienced similar growth rate along themajor and minor axes, the shock structure inthe jet plume greatly enhanced the jetspreading rate along the minor axis in thecase of the over-expanded elliptic jet.

Several experimental and analytical studiesof under-expanded jets have been reportedin the literature. Adamson and Nicholls [10]proposed a simple one-dimensional model tocalculate the boundaries and distance of thefirst shock disk from the nozzle exit. Theyreported good agreement between thecomputed results and existing experimentaldata [11,12]. Pao and Abdolhamid [13]computed the flow fields of supersonicunder-expanded circular and elliptic jetsusing different turbulence models andcompared the computed first shock celllength with the experimental results forMach 2 circular jet [14]. Grenville et al. [15]used a laser-based imaging method in awall-adaptive wind tunnel to define the outer

edges of supersonic jets. They alsopresented computed results that predictedreductions in the jet core length in under-expanded and over-expanded jets withincreased and decreased nozzle exit staticpressure respectively.

Krothapalli et al. [16], Gutmark et al. [17]and Zaman [18] conducted experimentalstudies of under expanded jets ofsymmetric and asymmetric cross sections.Their results indicate that the presence ofshocks in the jet core further increased thespread rate along the minor axis comparedto subsonic jets. Zaman [18] instantaneousschlieren pictures demonstrated that tabsspanning the narrow edges of the AR 3rectangular nozzle weakened theshock/expansion structure, increased jetspreading along the minor axis, andreduced it along the major axis. Gutmark etal. [17] demonstrated transition to flappingmode at the minor axis plane for circular,elliptic, and AR 3 rectangular jets. Thepresented jet spread rate in the Mach 1-2.4range demonstrated that the transition tothe flapping mode with increased Machnumber is abrupt in rectangular jets andmore gradual in elliptic and circular jets.

Tam [19] developed a linear shock cellmodel in which the mixing layer wasapproximated by a vortex sheet. Tamdemonstrated that his linear modelpredictions of shock cell spacing agreewith the experimental results of Powell[20] and Hammitt [21] for under expandedrectangular jets with aspect ratios greaterthan 4. His predications of screech tonefrequencies based on the weakest linkhypothesis [22] were in agreement with theexperimental results of Krothapalli [16]and Powell [23].

A number of experimental and numericalstudies were conducted to Investigate

under-expanded circular jets of gas particleflows. Both Lewis et al. [24] andSommerfeld [25] observed a forward shift inthe Mach disk with increased particleloading. However, computational studieseither predicted a rearward shift in the Machdisk location [26,27,28], or under predicted[25] the forward shift.

Hamed et al. [29,30] conducted numericalsimulations of gas-particle flows todetermine the effect of particle loading insupersonic 2DCD nozzles. The computedresults at over-expanded conditions withinternal shocks in the nozzle [29], indicatedthat both shock strength and shock inducedflow separation region are reduced withincreased particle loading. Subsequently, theeffects of particle sublimation and inter-phase energy exchange were included in thenumerical simulations of CO2 pellet-blastingnozzles [30].

The purpose of the present investigation isto characterize the shock structures in over-expanded rectangular jets plumes. Schlierenphotographs are presented for over-expanded rectangular jets in quiescentatmosphere to show the effect of nozzlepressure ratio on the shock structure and jetmixing. The results indicate that the mixingrate is high along the jet’s minor axis at thehigher nozzle pressure ratios, but decreasesas the nozzle pressure ratio is reduced. Inover-expanded rectangular particle-ladenjets, the shock strength was found todecrease as the nozzle pressure ratio wasreduced.

Experimental MethodExperiments were carried out in a blowdown facility with the jet discharging in thequiescent laboratory air. The air supplied bya compressor that pressurizes the ambient airup to 200 psig was filtered, dried and storedin a high-pressure reservoir consisting of 7

tanks with a total volume of 102 m3. Thetotal temperature was equal to that of thesurrounding, and the total inlet pressure tothe nozzle was controlled and maintainedconstant during the testing by a pressureregulator. A particle feeder was designedand manufactured to provide steady stateflow of particles at pressures up to 150 psi.The particles were injected four metersupstream of the nozzle inlet to insure goodmixing of the particles with the air.

Visualization of the supersonic jet andshock structure was obtained byshadowgraph and Schlieren photography,with 100-watt mercury-vapor lamp as acontinuous light source. Two 12” diameterparabolic mirrors with a focal length of72” were arranged in the Z-shapeconfiguration to redirect the light from thesource through the test section and onto ascreen. In the Schlieren arrangements, aknife-edge was placed at the focal point ofthe mirror and oriented horizontally.

A two-component LDV system withconventional optics manufactured byAerometrics Inc. was used in the presentstudy. The blue wavelength (488nm) andgreen wavelength (514.5nm) lines from a5-watt Spectra Physics argon-ion laserwere used to create the LDV measurementvolume. Velocities up to 570m/s could bemeasured using transmitting optics frontlens with a focal length of 1000mm and abeam spacing of 32mm. The scattered laserlight from the seeding particles in the testsection was collected in the forwardscattered mode by a 500mm (focal length)receiving lens situated 20o off the forwardscatter axis. The transmitting and receivingoptics were mounted on two fixed tripods.Traversing the measuring volumethroughout the flow-field was achieved bymounting the test nozzle on a computer-controlled 2D traverse mechanism. A two-

channel Real-time Signal Analyzer (RSA)was used to process the LDV signal.Doppler frequency information from thesignal analyzer was passed to a personalcomputer. Control of the RSA was managedby the personal computer via Data View(DV) software package. The softwareintegrated the data acquisition process withthe nozzle traversing mechanism, yieldingautomatic traversing capability duringtesting. The high-pressure particle feederwas used to seed the flow with 1-2µmdiameter aluminum oxide particles.

Results and DiscussionThe convergent divergent nozzle used in thecurrent experimental study has an exit-to-throat area ratio of 2.79 for a design Machnumber, Md of 2.5 and a design pressureratio, NPRd, of 19.4. The rectangular crosssection is 25.4mm x 4.92mm at the exitplane for an aspect ratio (AR) of 5.1. Testswere performed over a range of nozzlepressure ratios, NPR, between 4-9. Thechange in NPR was achieved by changingthe inlet stagnation pressure to operate in theexternal over-expanded regime.

Figure 1a and 1b show Schlierenphotographs of the jet in the major andminor axis planes at different nozzlepressure ratios. The figure shows that theshock strength as well as the total number ofshock cells in the jet plume decrease as thenozzle pressure ratio decreases. The visualjet spread rate along the minor axis is seento decrease as the nozzle pressure ratiodecreases. On the other hand, the visual jetwidth in the major plane does not exhibitnoticeable spread, nor does it change withthe nozzle pressure ratio.

Sample contours of the axial jet velocityfrom LDV measurements in the major axisplane at NPR = 9, are presented in Fig. 2.The velocities are normalized by the speed

of sound, ao, based on the measured nozzleinlet stagnation temperature, while thedistance is normalized by the nozzle minoraxis width, h. The measurements wereobtained up to x/h=16.6 on an 81 × 41mesh by traversing the nozzle in 2mmincrements in both vertical and horizontaldirections. The corresponding centerlinevelocity variation along the nozzle axis isshown in Fig. 3. The centerline velocitydecay is reproduced in a log-log plot inFig. 4. One can see that the decay rateapproaches the classical x-1 line past theshock cell zone.

The distance from the jet exit to the firstshock intersection with the jet centerline,L1 and the average distance betweensubsequent shock intersections with the jetcenterline, LS, as determined from theSchlieren photographs at the differentnozzle pressure ratios are presented in Fig.5. Both first and subsequent shock celllength are seen to increase with increasedNPR. The shock cell length was alsofound to increase with nozzle pressureratio in underexpanded jets [31, 17]. Therate of increase was dependant on thenozzle design Mach number [31], and onthe shape of the jet cross section [17]. Therate was higher for elliptic and highest forrectangular jets, compared to circular jetsof the same equivalent diameter [17].

Test results were obtained for two-phaserectangular jets at different particle loadingratios. Long grain rice, was used tosimulate the cylindrical shaped CO2 pelletsin Coldjet’s blasting nozzles. The materialdensity, mean diameter and length of theparticles are 750 kg/m3, 1.5mm , and 5mmrespectively. A particle separator wasplaced downstream from the jet to collectthe suspended particles. Schlierenphotographs of the jet at different particleloading ratios are shown in Fig. 6 for

NPR=9.0. The photographs clearly showthat as the particle loading increases, theshock strength as well as the number ofshock cells decreases. Shock attenuation wasalso predicted in the case of internal shocksin a 2DCD nozzle operating at NPR muchless than the design value [29].

AcknowledgementsThis work was sponsored by NSF GrantCTS-9812837. The authors would like toacknowledge the valuable help of Prof. S.M. Jeng, and to thank Mr. R. DiMicco forhis support.

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Figure 1a. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).

NPR=9.0

NPR=8.5

NPR=8.0

NPR=7.5

NPR=7.0

Major axis plane Minor axis plane

Figure 1b. Schlieren photographs of a rectangular jet at different nozzle pressure ratios (7.0-9.0).

NPR=6.0

NPR=5.5

NPR=5.0

NPR=4.5

NPR=4.0Major axis plane Minor axis plane

Figure 2. Axial velocity contours (NPR=9.0).

Figure 3. Jet centerline velocity variation (NPR=9.0).

Figure 4. Jet centerline velocity decay (NPR=9.0)

Figure 5. Effect of nozzle pressure ratio on shock cell length.

L1 Ls Ls

Figure 6. Schlieren photographs of rectangular jet at different particle loadings (NPR=9.0).

Particle loading = 0%

Particle loading = 12%

Particle loading = 15%

Particle loading = 30%

Particle loading=60%