ILASS 2008

Sep. 8-10, 2008, Como Lake, Italy

ILASS08-A068

HIGH-SPEED VISUALISATION OF LIQUID JET

DISINTEGRATION

Grazia Lamanna∗, Ingo Stotz∗, Bernhard Weigand∗, Johan Steelant◦

∗Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität StuttgartPfaffenwaldring 31, D-70569 Stuttgart, Germany

◦Propulsion and Aerothermodynamics Division (TEC-MPA), ESTEC-ESAKeplerlaan 1, P.O. Box 299, 2200 AG Noordwijk, The Netherlandscorresponding author: e-mail: grazia.lamanna@itlr.uni-stuttgart.de

ABSTRACT

High-speed shadowgraphy was applied to visualise hydrocarbon spray atomisation at elevated pressuresand temperatures. The experiments were performed in the quiescent post-shock region of a double-diaphragm shock tube facility using a heated, fast-response injection system. Test times were in theorder of 4.5 ms with reflected-shock pressures ranging from 10-35 bar and test temperatures of 950 K.The fuel (n-hexane and n-dodecane) was injected right after shock reflection and quasi-steady injectionwas achieved and sustained for about 2.5 ms. Fuel temperature covered both sub- and supercriticalvalues as it was varied between 373.15 and 523.15 K. The acquired images were analysed with respectto the spatiotemporal evolution of the spray, specifically spreading angles and penetration lengths werederived. The influence of the chamber pressure and the fuel temperature on the spray break-up processwas investigated. Increasing chamber pressures (chamber densities) and fuel temperatures result in anenhancement of the spray dispersion measured in terms of jet angles and therefore in a better mixingand vaporisation. As one of the two properties (fuel temperature or chamber pressure) is supercritical,incompressible variable-density gas jet behaviour was observed as certain (subcritical) values for thecorresponding other one were exceeded.

1 INTRODUCTION

Understanding the injection, break-up, mixing and com-bustion processes of fuel sprays is of high importance withrespect to many propulsion systems, such as rocket, jet,(sc)ramjets and direct injection engines. In this study, ashock tube is used to provide basic information on theinjection and disintegration processes of hydrocarbon fuel(e.g. n-dodecane, n-hexane) sprays at elevated fuel and am-bient temperatures and pressures. The experiments com-prise both (conventional) subcritical fuel disintegration aswell as supercritical break-up and are aimed at providinga thorough characterisation of the spray properties as afunction of the thermodynamic state.

The disintegration of (liquid) jets has been ascribed tomany concurring effects, such as surface tension, viscousand aerodynamic forces, liquid turbulence, cavitation phe-nomena and liquid supply pressure oscillations. Depen-ding on the break-up mode, the above mentioned interac-ting factors contribute to the disintegration process withdifferent degree of importance. Extensive reviews on thesubject can be found in Lefebvre (1989), Reitz (1978) andMayer and Telaar (2002). The jet break-up process canbe divided into two macroscopic zones, the primary andthe secondary break-up region. The primary jet break-upmode can be furthermore classified into different regimes(see Figure 1 for details) depending on the injection pres-

sure, velocity and chamber conditions.

Rayleigh-Breakup

1st Wind-Induced Breakup

2nd Wind-Induced Breakup

Atomisation SupercriticalBreakup

Figure 1. Jet disintegration regimes.

A complete theoretical description of the disintegrationprocess is not yet available. An empirical classificationof jet disintegration at atmospheric pressure was given byv. Ohnesorge (1936) using dimensional analysis. The em-pirical transitions between the different regimes of jet di-sintegration (Rayleigh breakup, wind-induced breakup andatomisation) can be described as a function of Ohnesorgenumber versus Reynolds number. More recently, Mayerand Telaar (2002) have extended this empirical classifica-tion and included the supercritical breakup. This classifi-

Paper ID ILASS08-1-7

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cation, strictly valid only at atmospheric pressures, takesinto account the influence of surface tension, viscous, andinertia forces on the disintegration process. With increa-sing chamber pressures (and therefore chamber densities),these empirical boundaries are shifted towards regions atlower Reynolds numbers. This means that the inceptionof wind-induced breakup and atomisation occurs at loweroutlet velocities compared to atmospheric conditions. Athigher chamber densities, the influence of aerodynamicsforces and shear stresses on the jet disintegration processincreases significantly. Lefebvre (1989) showed that therelevance of aerodynamic forces is well represented by thegaseous Weber number, which consists of the ratio of thedisruptive aerodynamic forces and surface tension forces.The increased relevance of the shear stress in a pressurisedgas can be represented by the ratio of liquid to gas visco-sity. Based on these considerations, Czerwonatis and Eg-gers (2001) were able to extend the empirical classificationfor jets to high-pressure conditions by introducing a newnon-dimensional number, defined as the product amongthe Ohnesorge number, the Weber number of the gas phaseand the liquid/gas viscosity ratio.

Concerning supercritical disintegration, most studiesconcentrated on the investigation of cryogenic fuels andsurrogates see e.g. (Mayer and Telaar, 2002) and(Chehroudi et al., 2002). In recent reviews, Chehroudiet al. (2003) and Oschwald et al. (2006) analysed in depththe difference between subcritical and supercritical brea-kup in cryogenic fuels. They were able to identify the me-chanism of transition from the wind-induced to the super-critical regime where the jet structure began to resemblea turbulent gas jet with no detectable droplets. The si-milarity between supercritical and turbulent gas jets wasdemonstrated by showing that the experimental jet growthrate agreed well with the theory of incompressible, variabledensity gaseous mixing layers.

The present study focuses on the disintegration of hy-drocarbon fuels, especially on the transition from the ato-misation to the supercritical regime. In the atomisationregime, both aerodynamic forces and shear stresses playa dominant role in controlling the lateral spreading of thejet. Therefore, it is not clear whether and to what extenta reduction in surface tension may affect the ”classical”atomisation process.

In the present study, the injection and chamber condi-tion are varied in such a way as to perform disintegrationexperiments at both subcritical, near-critical, and supercri-tical conditions. The analysis is still at a phenomenologicallevel, since not all jet geometrical parameters have beencorrelated to the available empirical correlations and/ortheoretical predictions in the atomisation regimes. Despitethese limitations, clear trends could be identified, as dis-cussed in Section 4.

2 EXPERIMENTAL SETUP

2.1 ITLR Test Facility

The test facility for jet disintegration studies consists ofa double-diaphragm shock tube (DDST), equipped witha fast-response, heated injector. Test times of the orderof typically 2 − 5ms are attainable with reflected-shockpressures up to 50 bar and typical temperatures of up to

2000K. A more detailed description and qualification ofthe facility is provided in Stotz et al. (2008). Figure 2provides a schematic view of shock tube. The (square) testchamber is equipped with flat flush-mounted fused-silicawindows on both side walls, which cover the full height ofthe duct over a length of 60mm. The fast-response heatedinjector is flush-mounted in the end flange in a way thatfuel is injected perpendicularly to the endwall into the gasbehind the reflected shock wave. Fuel pressures can bevaried between ≈ 100 and 1400 bar, fuel temperatures ashigh as 573.15K can be achieved with the present system.

DriverBuffer/Diaphragms

DrivenSection

Dump TankTestSection

1.0m( 50mm) 8.4m ( 72mm) 3.0m ( 72mm)

InjectionSystem

Figure 2. Schematic drawing of the ITLR double-diaphragm shock tube.

2.2 Optical Setup

The optical layout of the shadowgraph setup is shown inFigure 3. A collimated beam,emitted by a high-power LEDlamp (Luxeon Rebel) and slightly larger than the test-section’s window diagonal, back-illuminates the spray. Thelight is subsequently collected by a parabolic mirror (f =900mm, D = 150 mm) and focused on the CMOS chipof the camera by a Schneider-Kreuznach Super-SymmarHM 5.6/150 objective lens. The optical setup results ina magnification factor of MF = 1:6, which corresponds toan effective optical resolution of about 120µm and yieldsa maximum theoretical velocity without motion blur ofv = 120m/s. The high-speed camera used is a PhotronFastcam SA1. High-speed images were recorded at a reso-lution of 512x96 pixels and 512x160 pixels at acquisitionframe rates of 100,000 fps and 62,500 fps, respectively.

Fuel Spray

Injector

High-SpeedCamera

ObjectiveLens

Parabolic Mirror

Parallel High-PowerLED Illumination

Figure 3. Optical setup for the high-speed imaging expe-riments.

3 DATA REDUCTION

3.1 Postprocessing

The extraction of accurate spray geometrical data fromthe shadowgraph images requires image processing thatreduces background noise and enhances the image contrast

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without altering the spray contour.Illumination inhomogeneities due to temporal fluctuati-

ons as well as spatial non-uniformities of the light distribu-tion are accounted for by normalising each image to a refe-rence image, thus the background intensity of all images ofan experimental series is homogenously distributed and ata constant value. Afterwards, the images are filtered witha (two-dimensional) hybrid, edge-preserving median filterto reduces the background noise, caused by the shock tubeflow, without influencing the shape of the spray.

Subsequently, the spray images are thresholded to se-parate the spray from the background. Unfortunately,the contour of an atomising and evaporating spray is notclearly confined, as it is made up, especially in the outerregion, of a mixture of liquid fuel, ambient test gas, fuelvapour and, depending on the test conditions, supercriticalfluid. On this account, the results may depend on the levelon which the spray images are thresholded, as the spraycontour marks the smooth transition between the sprayand the ambient test gas. For this purpose, a sensitivityanalysis was performed. For threshold levels between 40and 70% of the background intensity, the deviations in thespray angles are usually smaller than 1 deg. All tests re-ported in the following sections, are evaluated using a 50%threshold, which represents an intermediate value amongthose physically reasonable.

Additionally, subpixel interpolation is applied to incre-ase the spatial resolution of the images, which enhances theaccuracy of the analysis. This improvement in accuracy isparticularly relevant for the region closer to the nozzle,where a shift of the spray contour by a single pixel maycause high deviations from the ”real” value. As an examplefor the resulting images, Figure 4 shows the temporal evo-lution of an n-hexane spray injected at a chamber pressureof p5 = 35bar and a fuel temperature of Tf = 523.15K.

3.2 Definition of the Jet Parameters

In the evaluation of the spray characteristics, the follo-wing macroscopic parameters will be considered: (local)jet spreading angle, spray tip length and velocity (in thestart up phase) and dark (dense) core length. Their geo-metrical definition is illustrated in the bottom image ofFigure 4. In the present work, the axial distribution of thelocal spreading angle θi(x) is considered, as it provides abetter physical insight in the spatiotemporal evolution ofthe (fuel) spray and its interaction with the surroundingtest gas. The spreading angle is directly related to therate of gas entrainment into the jet and is influenced bythe forces acting on the jet at the nozzle exit. Dependingon the chamber and injection conditions, the local sprea-ding angle may vary along the axis, as shown in Figure 5.The picture shown here is the average image, composed of150 single snapshots (during ”quasi-steady” injection) of asingle experiment. For a more accurate description of thelateral spreading of the spray and to facilitate the com-parison among literature data, it is therefore advisable toinvestigate the axial distribution of the local spray angleθ(x).

In literature, two different characteristic lengths are of-ten employed to describe the axial penetration of the spray:the spray tip length Lspray and the dense core length Lcore.The spray tip penetration (axial growth rate) is calculatedfrom the extent of the spray contour during the start-upprocess of the injection. Using the spray lengths of all

Jet spreading angle

NozzleSpray contour

θ(x)

x

y

Spray tip length & velocity

Figure 4. Example of a series of spray shadowgraphimages (time between images ∆t = 160µs) and definitionof jet parameters.

images and the chosen frame rate of the camera, the (tran-sient) velocity of the spray tip vspray can be derived.

The liquid or dense core length of the jet is a measurefor the axial penetration of the jet/spray core into the testenvironment. The ”liquid core” can be either specified asthe intact core (connected liquid) or as the dense core (highliquid/gas density ratio). The dense core length is calcu-lated in a similar manner as the spray tip length, albeitwith a much smaller threshold (2% of the background in-tensity level), in order to include only the dense (i.e. dark,low-intensity) parts of the spray. Although this quantityis rather arbitrary and also dependent on the threshold le-vel chosen, it is still a useful measure to compare differentconditions among each other, to classify break-up processesand to identify steady state injection conditions, providedthe threshold level is consistent through the analysis.

Spray contour

Constant angle

min. max.Intensity

Figure 5. Average image of the spray.

3

4 RESULTS

4.1 Test conditions

The experiments were performed in the region behind thereflected shock wave. The test pressure p5 was varied bet-ween 10 and 35 bar while the test temperature was fixed ata target value of T5 = 950K. The fuel back-pressure wasset so as to maintain a constant pressure difference betweenfuel reservoir and test chamber of ∆pf = pf −p5 = 200 bar.As the effect of fuel preheating was to be investigated, threedifferent fuel temperatures were selected: Tf = 373.15 ,448.15 and 523.15K. The test conditions of the presentstudy are summarised in Table 1.

Condition No. p5 [bar] T5 [K] ρ5 [kg/m3]I 10.0 ± 0.05 952 ± 6 5.1 ± 0.04II 27.5 ± 0.04 951 ± 5 13.6 ± 0.09III 35.0 ± 0.16 949 ± 8 17.5 ± 0.14

Table 1. Chamber conditions of the experiments performed in thepresent study. Test pressures, temperatures and densities were de-rived from the incident shock Mach number Ms. The uncertaintiesquoted are the standard deviations of different experiments.

Two fuels n-dodecane and n-hexane were tested usinga nozzle with a rounded inlet, an inner diameter of D =236µm and a length to diameter ratio of L/D = 4 . Inorder to thermodynamically characterise the experimen-tal conditions, the reduced temperature and pressure areintroduced. They are defined as the ratio of the actualto the critical fuel temperature (Tr = Tf/Tc), the ra-tio of the chamber pressure to the critical fuel pressure(pr = p5/pc) respectively. In the case of n-dodecane, prvaries in the range 0.55 ≤ pr ≤ 1.91, while Tr lies between(0.57 ≤ Tr ≤ 0.79). For n-hexane, the reduced tempera-ture varies in the range of 0.73 ≤ Tr ≤ 1.03 and the reducedpressure between 0.33 ≤ pr ≤ 1.15. The most significantdifference between the two experimental campaigns is that,for n-hexane, an excursion above the critical point is possi-ble both in temperature and pressure, while for n-dodecanethe initial fuel temperature is below its critical value.

4.2 Results for n-Dodecane

The influence of the chamber pressure p5 (density ρ5) onthe spray dispersion and penetration is shown in Figure 6.As a first remark, note that the results for p5 = 27.5 barand p5 = 35bar are generally very similar, whereas thosefor p5 = 10bar differ considerably. In terms of redu-ced thermodynamic parameters, this means that as soonas Tr ≥ 0.79 and pr ≥ 1.50, subcritical jet disintegra-tion starts to deviate from ”standard” atomisation. Theterm ”standard” atomisation refers to the fact that sprea-ding angle increases with an increase in chamber den-sity. This represents an established trend for the atomi-sation regime, in agreement with the experimental obser-vations of e.g. Hiroyasu and Arai (1990), Naber and Sie-bers (1996), Chehroudi et al. (1985). The most strikingdifference is traceable in axial distribution of the time ave-raged (t = 2 − 4.5 ms) jet spreading angle, shown in Fi-gure 6(a)-6(b). For a reduced pressure much smaller thanone (pr ≈ 0.5), the spray angle is almost constant for thewhole observable distance and only a very faint increaseis found. As the reduced parameters are increased, butstill remaining in the subcritical region (i.e., pr ≥ 1.5 and

0.68 ≤ Tr ≤ 1), the jet disintegration can be divided intwo distinct zones. In the near-nozzle region (up to aboutx/D ≈ 40), fairly constant angles are observed. In thedownstream region, the spray angles increase with a nearlylinear slope. As a general trend, higher pressures and den-sities lead to larger spray angles at all axial positions. Theposition at which the curves start to diverge coincides ap-proximately with the onset of the breakup region at t = t0(breakup time, following the terminology of Hiroyasu andArai (1990)). For t > t0 the spray is slowed down and theinfluence of higher chamber pressure becomes more rele-vant through the enhanced gas entrainment. This region,further downstream of the nozzle tip, is dominated by tur-bulent shear-layer mixing effects.

Concerning the region near the nozzle tip, ”standard”atomisation is observed for pr = 0.55 and Tr ≤ 0.68.However, at supercritical chamber pressures and higher(but subcritical) reduced temperatures (Tr ≥ 0.79), thejet angles appear to diverge from the density dependenceobserved at lower pressures. As can be clearly seen inFigure 6(b), the spray angle (near the nozzle tip) hardlychanges as the chamber pressure is increased from 27.5to 35 bar. Furthermore, as the reduced temperature isincreased to ≈ 0.8 (i.e. Tf = 523.23 K), the spreadingangle approaches the lower limit of incompressible, fullydeveloped jets (i.e. tan(θ) ≈ 0.2), already at values ofthe ambient-gas to fuel density ratio of the order of 0.02(i.e. ρch/ρf ≈ 0.02 − 0.03). A similar behaviour was alsofound experimentally by Chehroudi et al. (2002) for thetransition from the second-wind induced breakup regimeand marked as the onset of supercritical disintegration.Note that for atomisation experiments performed at muchlower reduced temperatures (Tr ≈ 0.4), the transition to-wards incompressible jet behaviour is predicted for muchlarger density ratios ((i.e. ρch/ρf ≈ 1) (see e.g. Naberand Siebers (1996)). This seems to suggest that, in thenear-nozzle region, the spray disintegration in the subcri-tical regime start to resembles more and more that of anincompressible jet, as soon as the injection/chamber con-ditions approach the critical values of the injectant.

The spray tip length during the first phase of fuel injec-tion is given in Figure 6(c). During the first 300 − 400µs,the penetration and thus the velocity of the spray tip isvery similar for all three pressures investigated. At thispoint, the spray tip gets noticeably decelerated for the twohigher pressures, while it remains on a fairly constant ve-locity for the lower pressures 10 bar. After about 800µs,an observable difference is also found for 27.5 and 35 bar.Spray tip velocities can thus be assumed to be constantin the initial stage of jet propagation (inertia-dominated).After a certain time t0, to which Hiroyasu and Arai (1990)refer to as the break-up time of the spray, the spray is re-markably slowed down. This deceleration is stronger forhigher chamber pressure (density) and occurs noticeableearlier as the resistance of the gas is higher the denser itgets. The spray tip penetration, as well as the time of thetransition between the linear behaviour and the attenuatedgrowth, decreases with increasing chamber pressure.

During this deceleration phase, the spray penetrationis attenuated and follows a power function of the formLspray ∼ t

c (c < 1). The spray tip velocities vspray, de-rived from the temporal evolution of tip lengths, are allsmaller than 90m/s, which is significantly smaller than

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the calculated ideal theoretical velocity vtheo ≈ 230m/s fora differential pressure ∆p = 200 bar at the orifice outlet.This leads to the conclusion that the spray disintegrationalready starts shortly after or directly at the nozzle outlet.

As can be seen in Figures 6(d) and 6(e) the dark corelength Lcore, indicated by the 2%-intensity contour of thespray, reflects similar behaviour at the beginning of the in-jection as the spray tip length. After about 1ms, it thenabruptly comes to rest and stays constant for the rest ofthe test time. As an effect of the reduced aerodynamicresistance, these (constant) values are larger for smallerchamber densities. For the highest temperature, the dis-crepancies of the dark core penetration vanish and, for allchamber pressures (densities), virtually equal lengths arefound.

In addition to the chamber pressure, the influence of thefuel temperature was investigated. Its influence on the lo-cal spreading angle is shown in Figures 7(a) and 7(b). Ascan be seen, the fuel temperature has only a marginal influ-

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Jet s

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(a) Time averaged spreading an-gle θ versus axial distance,Tf=448.15 K

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(c) Spray tip length Lspray ver-sus time, Tf=448.15 K

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(d) Dark core length Lcore ver-sus time, Tf=448.15 K

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(e) Dark core length Lcore versustime, Tf=523.15 K

Figure 6. Influence of the chamber pressure on the jetspreading angle θ, the spray tip length Lspray and the darkcore length Lcore (fuel: n-dodecane).

ence on the jet spreading angle. For low reduced pressures(pr = 0.5 , i.e. p5 = 10 bar), differences are observed inthe upstream region close to the nozzle, which follows the”classical” atomisation behaviour. It is not surprising thatthe fuel temperature has only an indirect impact on thejet spreading angle. In fact, the fuel temperature affectsindirectly the ambient-gas to fuel density ratio by redu-cing the fuel density. This circumstance implies slightlylarger spreading angles for increasing fuel temperatures,as confirmed by a visual inspection of Figure 7(a). Athigh reduced pressures (pr = 1.9 , i.e. p5 = 35bar) andfor Tr ≥ 0.68 (Tf ≥ 448.15K), the fuel temperature haspractically no impact at all on the lateral spreading of thejet. In fact, at these reduced thermodynamic parameters,the spray behaviour (in the near-nozzle region) evolves to-wards the behaviour of an incompressible jet and thereforeit is completely insensitive to variations in the ambient-gas to fuel density ratio. Concerning the region furtherdownstream of the nozzle, aerodynamic forces and turbu-lent mixing dominate the lateral spreading of the jet. Thisexplains the convergence towards a similar value regardlessof the specific value of the fuel injection temperature.

The spray tip velocity is hardly influenced by the fueltemperature. All spray tip traces develop very similarlyand almost collapse to a single curve. This holds for allchamber pressures investigated, i.e. the rate of spray tippropagation Lspray is dominated by the resistance due toaerodynamic forces and the kinetic energy of the fuel at thenozzle outlet. As expected the dark core length Lcore inturn is strongly influenced by the initial jet temperature,as increased temperatures lead to enhanced evaporationand thus to shorter penetration of the dense spray core.Similar behaviour is observed for all chamber pressures.

4.3 Results for n-Hexane

The most significant difference between the two experimen-tal campaigns is that, for n-hexane, an excursion abovethe critical point is possible both in temperature and pres-sure as the critical temperature of n-hexane (507.9K) isnoticeably below that of n-dodecane (658.7K). More spe-cifically, reduced temperatures were varied in the rangeof 0.73 ≤ Tr ≤ 1.03 and reduced pressures between0.33 ≤ pr ≤ 1.15.

Figure 8 provides an overview of the influence of thechamber gas pressure (density) on the jet break-up pro-cess for a subcritical (Tr = 0.73 ) and a supercritical(Tr = 1.03 ) reduced temperature. At subcritical tempe-ratures and low subcritical (see Figure 8(a)) ”standard”atomisation behaviour is observed in the near-nozzle re-gion, i.e. the spreading angle increases with increasingchamber densities. In the region further downstream ofthe nozzle, the lateral spreading of the jet is controlledby turbulent mixing and gas entrainment and, similarly tothe n-dodecane experiments, much more sensitive to thechamber density.

Figure 8(b) shows the pressure dependence of the jetspreading angle at a (supercritical) reduced temperatureTr = 1.03. As can be seen, the jet lateral spreading in thenear-nozzle region is independent of the chamber pressureand tends to the limit of tan(θ) ≈ 0.2 already at a re-duced (subcritical) pressure of pr = 0.91. As for all otherexperiments, the downstream region (x/D ≥ 40) resemblesthe behaviour of a turbulent mixing layer and the lateral

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TFuel

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(a) Time averaged spreading an-gle θ versus axial distance,p5=10 bar

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(b) Time averaged spreading an-gle θ versus axial distance,p5=35 bar

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(c) Spray tip length Lspray ver-sus time, p5=35 bar

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(d) Dark core length Lcore ver-sus time, p5=35bar

Figure 7. Influence of the fuel temperature on the jetspreading angle θ, the spray tip length Lspray and the darkcore length Lcore (fuel: n-dodecane).

spreading is a function of the chamber density.The spray length during the initial phase of the injec-

tion process is plotted in Figure 8(d) for the (supercritical)fuel temperature Tf = 523.15K (Tr = 1.03 ). At the verybeginning, the penetration and thus the velocity of the jetis virtually equal for all pressures investigated. Thereaf-ter, the tip gets decelerated and the penetration depth isshorter for increasing chamber pressure. Comparing theseobservations with those for subcritical injection (fuel tem-perature Tf = 373.15K, Tr = 0.73 ) does not show anyqualitative differences (see Figure 8(c)). This implies thatthe propagation of the spray tip is governed solely by in-ertia and aerodynamic forces.

For n-hexane, the dark core length is only influencedslightly by the chamber pressure and more noticeably forcooler fuel temperatures. For Tf = 373.15K (Tr = 0.73 )slightly longer dark core lengths are observed for p5 =10bar (pr = 0.33 )(see Figure 8(e)), whereas for p5 = 27.5or higher (pr ≥ 0.91), the dark core length levels out ata constant value regardless of the chamber pressure value.If the reduced temperature Tr is increased to values > 1(see Figure 8(f)), no major difference is observed in thedark core lengths. Similarly to the results obtained for n-dodecane, the fuel temperature, rather then the chamberpressure, seems to be the controlling parameter for thedark core length.

For n-hexane, the fuel temperatures were varied fromsubcritical to supercritical values, as possible differences inthe disintegration mode were to be investigated. The in-fluence of the fuel temperature is shown in Figure 9. Theaxial variation of the jet spreading angle θ is given in Figu-res 9(a) and 9(b), for subcritical (pr = 0.91) and supercri-tical (pr = 1.15) reduced pressures. For both reduced pres-

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(a) Time averaged spreading an-gle θ versus axial distance,Tf=373.15 K

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= 27.5 bar

p5

= 35 bar

(d) Spray tip length Lspray ver-sus time, Tf=523.15 K

0 1000 2000 3000 40000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Dar

k co

re le

ngth

/ 2%

−C

onto

ur p

enet

ratio

n L

Cor

e [m

m]

p5

= 10 bar

p5

= 27.5 bar

p5

= 35 bar

(e) Dark core length Lcore ver-sus time, Tf=373.15 K

0 1000 2000 3000 40000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Dar

k co

re le

ngth

/ 2%

−C

onto

ur p

enet

ratio

n L

Cor

e [m

m]

p5

= 27.5 bar

p5

= 35 bar

(f) Dark core length Lcore versustime, Tf=523.15 K

Figure 8. Influence of the chamber pressure on the jetspreading angle θ, the spray tip length Lspray and the darkcore length Lcore (fuel: n-heptane).

sures, two distinct zones can again be identified (close tothe nozzle exit (up to x/D ≈ 40) and further downstream).In the near nozzle region, the standard atomisation processevolves slowly towards gas jet behaviour, identified by thelimit tan(θ) ≈ 0.2, as soon as the fuel temperature is incre-ased beyond the critical value Tr = 1.03. The downstreamzone in turn is quite insensitive to the initial fuel tempera-ture, equal values are found for different fuel temperaturesand equal chamber conditions.

No influence on the spray tip length and its velocity wasobserved for all fuel temperatures for both subcritical (Fi-gure 9(c)) and supercritical (Figure 9(d)) chamber pressu-res p5. This also shows that the dominating parameter forspray propagation is the chamber pressure/density, as thisprovides the resistance to the penetrating jet. Variationsin the evaporation rate due to different fuel temperaturesonly play (if any) a minor role.

The dark core length, in turn, exhibits a strong depen-dence upon the fuel temperature. In general, an increase inthe fuel temperature leads to shorter dark core lengths (see

6

0 10 20 30 40 50

0

2

4

6

8

10

12

14

16

18

20

Axial position [mm]

Jet s

prea

ding

ang

le θ

[°]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(a) Time averaged spreading an-gle θ versus axial distance,p5=27.5 bar

0 10 20 30 40 50

0

2

4

6

8

10

12

14

16

18

20

Axial position [mm]Je

t spr

eadi

ng a

ngle

θ

[°]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(b) Time averaged spreading an-gle θ versus axial distance,p5=35 bar

0 500 1000 1500 2000 25000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Spra

y le

ngth

LSp

ray

[mm

]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(c) Spray tip length Lspray ver-sus time, p5=27.5 bar

0 500 1000 1500 2000 25000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Spra

y le

ngth

LSp

ray

[mm

]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(d) Spray tip length Lspray ver-sus time, p5=35 bar

0 1000 2000 3000 40000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Dar

k co

re le

ngth

/ 2%

−C

onto

ur p

enet

ratio

n L

Cor

e [m

m]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(e) Dark core length Lcore versustime, p5=27.5 bar

0 1000 2000 3000 40000

5

10

15

20

25

30

35

40

45

50

Time t [µs]

Dar

k co

re le

ngth

/ 2%

−C

onto

ur p

enet

ratio

n L C

ore

[mm

]

TFuel

= 373.15 K

TFuel

= 448.15 K

TFuel

= 523.15 K

(f) Dark core length Lcore versustime, p5=35bar

Figure 9. Influence of the fuel temperature on the jetspreading angle θ, the spray tip length Lspray and the darkcore length Lcore (fuel: n-heptane).

Figure 9(f)), regardless of whether the chamber pressure isbelow or above the critical value. This can be clearly seenby comparing Figures 9(e) and 9(f).

As a concluding remark, we would like to point outthe limitation of the shadowgraph imaging technique ofnot being capable to distinguish between liquid phase anddense gas. It is therefore not clear whether the similaritybetween near critical and supercritical conditions can beextended beyond geometrical parameters (e.g. jet sprea-ding angle or dark core length). With reference to Figure9(f), for example, it is impossible to ascertain whether theinner core of the spray consists of a liquid, dense gas, super-critical fluid or a mixture of all as the reduced temperatureis increased from pr = 0.73 to 1.03.

5 CONCLUSION

Hydrocarbon fuel injection experiments have been conduc-ted in a shock tube to experimentally investigate jet disin-

tegration in the subcritical (atomisation) and supercriticalregime. The fuel was injected into an inert test gas en-vironment (argon), whose temperature was set to a fixedsupercritical temperature while the gas pressure was va-ried from sub- to supercritical values. The injection andbreakup processes were visualised by means of high-speedshadowgraphy. The experiments show that for a reducedpressure much smaller than one, the spray atomises in the”standard” way. As soon as the reduced parameters ap-proach the critical point, the disintegration process can bedivided in two distinct zones: specifically, the near nozzleregion (up to x/D ≈ 40) and the downstream region. Inthe region further downstream of the nozzle, the lateralspreading of the jet is controlled by turbulent mixing andgas entrainment and is therefore much more sensitive tothe chamber density. In the near-nozzle region, the experi-mental results support the hypothesis that the jets behavesimilar to an incompressible gas jet, provided that one ofthe two parameters pr or Tr is larger 1 and the other oneis above a specific value ≈ 0.8−0.9. This statement is cor-roborated by the quantitative agreement of the jet growthrate measurements with those predicted by the theoreticalequations for incompressible gaseous jets.

ACKNOWLEDGMENTS

This work was performed within the Long-Term AdvancedPropulsion Concepts and Technologies (LAPCAT) projectinvestigating high-speed airbreathing propulsion. LAP-CAT, coordinated by ESA-ESTEC, is supported by the EUwithin the 6th Framework Programme Priority 1.4, Aero-nautic and Space, Contract no.: AST4-CT-2005-012282.Further information on LAPCAT can be found on:http://www.esa.int/techresources/lapcat.

The authors are also gratefully indebted to the Landess-tiftung Baden-Württemberg for facilitating the high-speedexperiments entailed in this paper.

References

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B. Chehroudi, D. Talley, and E. Coy. Visual Characte-ristics and Initial Growth Rates of Round CryogenicJets at Subcritical and Supercritical Pressures. Phy-sics of Fluids, 14(2):850–861, February 2002. doi:10.1063/1.1430735.

B. Chehroudi, D. Talley, W. Mayer, R. Branam, J. Smith,A. Schik, and M. Oschwald. Understanding Injectioninto High Pressure Supercritical Environments. In 5th

International Conference on Liquid Rocket Propellants,Chattanooga, USA, October 27–30 2003.

N. Czerwonatis and R. Eggers. Disintegration of LiquidJets and Drop Drag Coefficients in Pressurized Nitrogenand Carbon Dioxide. Chem. Eng. Technol., 24(6):619–624, 2001.

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H. Hiroyasu and M. Arai. Structures of Fuel Sprays inDiesel Engines. Number Doc. No. 900475, 1990.

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W. Mayer and J. Telaar. Investigation of Breakup of Tur-bulent Cryogenic Variable-Density Jets. Atomizationand Sprays, 12(5&6):651–666, 2002.

J. D. Naber and D. L. Siebers. Effects of Gas density andVaporization on Penetration and Dispersion of DieselSprays. In SAE International Congress and Exposition,number SAE Paper No. 960034, 1996.

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Supercritical Environments. Combustion Science andTechnology, 178(1-3):49–100, 2006.

R. Reitz. Atomization and other Breakup Regimes of aLiquid Jet. PhD thesis, Princeton University, Princeton,NJ, 1978.

I. Stotz, G. Lamanna, B. Weigand, and J. Steelant. ShockTube Study on Hydrocarbon Free Jets using High-SpeedShadowgraphy. In Proceedings of the 15th AIAA SpacePlanes and Hypersonic Systems and Technologies Con-ference, number AIAA-2008-2538. AIAA, 28 April – 1May 2008.

W. v. Ohnesorge. Die Bildung von Tropfen an Düsen unddie Auflösung flüssiger Strahlen. Z. Angew. Math. Mech.,16:355–358, 1936.

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