towards a unified treatment of fully flashing sprays

International Journal of Multiphase Flow 58 (2014) 168–184

Contents lists available at ScienceDirect

International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Towards a unified treatment of fully flashing sprays

0301-9322/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.08.010

⇑ Corresponding author. Tel.: +49 711 68562173; fax: +49 711 68562317.E-mail addresses: [email protected] (G. Lamanna), hend.

[email protected] (H. Kamoun), [email protected](B. Weigand), [email protected] (J. Steelant).

Grazia Lamanna a,⇑, Hend Kamoun a, Bernhard Weigand a, Johan Steelant b

a Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germanyb ESTEC-ESA (European Space & Technology Centre), P.O. Box 299, 2200 AG Noordwijk, The Netherlands

a r t i c l e i n f o

Article history:Received 8 April 2013Received in revised form 19 August 2013Accepted 28 August 2013Available online 13 September 2013

Keywords:Fully flashing regimeBubble nucleationTransition threshold

a b s t r a c t

This paper presents a systematic study on flashing atomisation, which includes both standards and ret-rograde fluids. A novel data reduction method is proposed in terms of the controlling parameters for(bubble) nucleation. The analysis indicates that bubble nucleation is the rate-controlling process for boththe transition to fully flashing and for the spray lateral spreading. Specifically, the onset condition coin-cides with the surmount of the energy barrier to nucleation. The spray lateral spreading, instead, isdirectly linked to the population of bubble clusters: the larger the population the wider the spray angle.Theoretical aspects of bubble nucleation theory are also reviewed. An interesting conclusion of the anal-ysis is that the experimental trends observed in fully flashing jets are compliant with recent advances innucleation theory. At very high initial superheat, a complex shock wave structure appears around theflashing jets. The novel aspect of this work is that such shock-systems are observed consistently in bothstandard and retrograde substances. This similarity indirectly confirms that, far from the critical temper-ature, the phase transition mechanism is the same for all substances, independently from their degree ofretrogradicity.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Flash-atomisation occurs when a liquid is discharged into a gas-eous environment at an ambient pressure lower than the satura-tion pressure of the fuel. Although flash-boiling is considered tobe detrimental in many technical applications (e.g. the accidentalrelease of flammable and toxic pressure-liquefied gases in the nu-clear and chemical industry), it can have some potential benefits inpropulsion systems. In fact, it is known to produce a fine spraywith enhanced atomisation, to increase the effective spray angleand to decrease the spray penetration. These significant changesin the spray characteristics have an important impact on the fueloxidant mixing and hence on the combustion efficiency, leadingto reduced pollutants’ emissions (Senda et al., 2007). From a heu-ristic point of view, the process of flash-atomisation and vaporisa-tion is clearly described as the subsequent progression ofhomogeneous (or heterogeneous) nucleation, bubble growth(Brown and York, 1962), breakup through bubble disruption, and(superheated) droplet evaporation. Due to its relevance for auto-motive, aerospace and industrial applications, considerable pro-gress has been made in the modelling (e.g., Kawano et al., 2006;Schmehl and Steelant, 2009) and experimental (e.g., Vieira and

Simoes-Moreira, 2007; Desnous et al., 2011) investigation of aflash-atomising liquid spray. In general, the quality of a flashingspray is evaluated in terms of empirical correlations for dropletsizes, velocity distributions, jet spreading angle, and penetrationlengths. The reader is referred to the works of Witlox et al.(2005), Cleary et al. (2007), and Yildiz et al. (2004, 2006) for studiesat atmospheric conditions and to Lecourt et al. (2009) for near vac-uum conditions, just to cite a few. The above mentioned studieshad the merit to provide significant insights into the physics ofsuperheated atomisation. Still, this improved understanding couldnot be conveyed towards the development of a predictive tool forengineering applications, mainly due to the following factors:

� Most experimental data are collected in the dilute region ofthe spray, where the superheated liquid has almost relaxedtowards thermodynamic equilibrium. Hence they can pro-vide only limited information on the mechanism of flash-atomisation.

� The range of applicability of the proposed correlations israther limited, being restricted to the particular fluids(namely water and ethanol) and operating conditionstested. Cleary et al. (2007) tried to extrapolate theseempirical models to other fluids through similarity scalinglaws, expressed in terms of non-dimensional numbers.Despite the noteworthy attempt, considerable research isstill required to corroborate the proposed extrapolationtechnique.

http://crossmark.crossref.org/dialog/?doi=10.1016/j.ijmultiphaseflow.2013.08.010&domain=pdf

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.08.010

mailto:[email protected]






http://www.sciencedirect.com/science/journal/03019322

http://www.elsevier.com/locate/ijmulflow

G. Lamanna et al. / International Journal of Multiphase Flow 58 (2014) 168–184 169

This concise summary on the state-of-the art of superheatedatomisation modelling shows that, in order to predict these phe-nomena and create a proper engineering tool, two conditions haveto be satisfied. First of all, experimental data need to be acquired inthe near-nozzle region (i.e. at axial distances x/D = O(1), where D isthe nozzle diameter). The availability of these data would enable toassess the effect of superheat on the atomisation process and even-tually to formulate these dependencies into a theoretical model forflash-atomisation. Second, in order to properly analyse the data,the data-reduction procedure should establish a direct link withthe theory of bubble nucleation and/or of superheated evaporation.Note that, to-date, a direct connection between the purely fluidmechanical process of atomisation and the kinetics of phase tran-sition (nucleation rate) has only been postulated (e.g., Kurschatet al., 1992), but never verified against experimental data. Further-more, a different phase change mechanism was proposed for retro-grade fluids (e.g., Vieira and Simoes-Moreira, 2007).

In light of these considerations, the present study aims at pro-viding a comprehensive and accurate experimental database onsuperheated atomisation for model validation purposes. The data-base includes data on spray morphology as well as on droplet size,velocity and temperature distributions. As a first step towards thedevelopment of a superheated atomisation model, the transitionthreshold and the spray contour data (i.e. the spreading angle ver-sus axial distance) are correlated as function of the controllingparameters for nucleation. The analysis is extended to both stan-dard and retrograde fluids to find out whether a common phenom-enology can be identified in all cases. If feasible, literature data arealso included to assure the generality of the conclusions.

The outline of the paper is as follows. Section 2 reviews brieflythe most relevant non-dimensional parameters governing flashatomisation and bubble nucleation processes. Section 3 discussesthe different flash atomisation regimes and briefly outlines theavailable theoretical models and/or empirical correlations. Theobjective is to identify the range of disintegration modes, whoseonset and lateral spreading might be solely controlled by thermo-dynamic parameters. Section 4 describes the test facility and post-processing algorithm. Finally, Section 5 discusses the modellingstrategy, the experimental results and the plausibility of the pro-posed model.

2. Nucleate boiling

As mentioned in Section 1, atomisation in superheated fluidsoccurs mostly through nucleate boiling. The superheat level canbe described through two parameters, displayed in Fig. 1. The firstparameter (DT – alias the degree of superheat) is defined as the dif-ference between the fuel injection temperature and the saturationtemperature at the assigned back pressure:

Fig. 1. Flashing parameters.

DT ¼ Tinj � Tsatðp1Þ ð1Þ

The second parameter Rp is defined as the ratio between the sat-uration pressure at the fuel injection temperature and the pre-scribed back pressure:

Rp ¼psatðTinjÞ

p1ð2Þ

Denoting with kb the Boltzmann constant, the thermodynamicrelation

Dl ¼ kbT lnðRpÞ ð3Þ

shows that Rp is directly related to the difference in chemical poten-tial, which represents the ‘‘generalised driving force’’ for the phasetransition process. Hence, Rp (rather than DT as customarily sug-gested) is the most adequate choice to measure the degree of depar-ture from thermodynamic equilibrium in a superheated liquid. Inthe realm of Classical Nucleation Theory (CNT), the number of sta-ble vapor nuclei generated per unit volume and time J is propor-tional to

JCNT /ffiffiffiffiffiffiffiffi2rpm

rexp � DG�

kbTinj

� �ð4Þ

where m is the mass of a liquid molecule and DG⁄ represents theformation energy of the critical cluster

DG�

kbTinj¼ 16pr3

3ðDlÞ2ð5Þ

Following Girshick and Chiu (1990), let us introduce a dimen-sionless surface tension H:

H ¼ a0rkbTinj

ð6Þ

where a0 is the surface area, defined as a0 = (36 p)1/3(vm)2/3. The vol-ume of a molecule vm can be rewritten in terms of macroscopicquantities as vm = M/(ql NA) with ql denoting the liquid density, Mthe molar mass and NA the Avogadro constant. The parameter Hmeasures the relative importance between surface energy (i.e. theenergy required for the creation of a new interface) and thermal en-ergy. Combining Eqs. (3)–(6), the nucleation rate can be expressedas:

JCNT /ffiffiffiffiffiffiffiffi2rpm

rexp � 4

27H3

ðln RpÞ2

" #ð7Þ

Note that Eq. (7) represents simply the non-linearised versionof CNT. The linear version – where the pressure difference(psat(Tinj) � p1) appears instead of ln(Rp) (e.g., Blander and Katz,1975) – is no longer applicable at highly superheated conditions(i.e. at large Rp values). Therefore, throughout this paper, Eq. (7)will be used for the analysis and data reduction procedures ofthe experimental data.

The classical nucleation theory has been widely criticised forbeing an equilibrium theory and for modelling the critical bubblenucleus by macroscopic thermodynamics and its surface by theplanar surface tension (e.g., Oxtoby and Evans, 1988; Oxtoby,1998). Specifically for nucleate boiling applications, CNT was alsocriticised for predicting a finite energy barrier at the spinodaland for failing to predict the superheat of boiling at relativelylow temperatures (Briggs, 1951). Several modifications of CNThave been proposed to take into account the effect of dissolvedgas (Tucker and Ward, 1975; Lubetkin and Blackwell, 1988), to cor-rect for the erroneous temperature dependence of CNT throughscaling laws (McGraw, 2000) and to improve the accuracy of thepredicted nucleation rates (Delale et al., 2003). It is beyond thepurpose of this paper to assess the accuracy of bubble nucleation

170 G. Lamanna et al. / International Journal of Multiphase Flow 58 (2014) 168–184

theories. A detailed discussion on the limitations of the classicaltheory (in particular for liquid-to-gas transitions) and on alterna-tive approaches can be found in Talanquera and Oxtoby (1995),Oxtoby (1998), and Shen and Debenedetti (2003).

In the context of this paper, our objective is to investigatewhether bubble nucleation rate represents the controlling mecha-nism for the atomisation and lateral spreading of a superheated jet.This conjecture stems from the fact that there are kinetic barriersto first-order phase transitions, resulting in the persistence ofmetastable phases over long periods of time. Only for clusters lar-ger than the critical size it is energetically favourable to grow, lead-ing eventually to irreversible bubble growth and disruption (henceto jet atomisation). Since the growth beyond the critical nucleus isgenerally fast compared to clusters generation, it is then the nucle-ation rate (i.e. the rate of appearance of such critical nuclei) thatdetermines the time scale for the inception of bubble growth andhence for the shattering of the superheated jet. In summary, atlow Rp levels, the corresponding high activation barrier preventsthe onset of nucleation and jet disintegration is caused by theinterplay between aerodynamic, surface and viscous forces. At highsuperheat levels, the onset of nucleation controls the primary (andeventually the secondary) atomisation of the jet. Under thisassumption, the three parameters Rp, H and m (appearing in Eq.(7)), represent the most natural choice for efficiently reducingthe spray angle data into a single model for the jet lateral spread-ing. The validity of this approach is verified in Section 5.

3. Flashing regimes

This section provides a concise review of the different flash-atomisation regimes. The objective is twofold: (1) to review exist-ing models and (2) to identify the disintegration modes, for whichthe shattering of the jet can be considered nucleation-controlled. Afirst classification proposed by Oza (1984) is to distinguish be-tween an ‘‘external flashing’’ and ‘‘internal flashing’’ mode. Inexternal flashing, the jet emerges from the nozzle as a single-phasejet and atomisation occurs at some distance from the nozzle exit.The length of the intact liquid core corresponds to the delay time,during which bubbles are formed and rapidly grow, causing the jetto disintegrate. Examples of external flashing mode are shown inFig. 2b–d for increasing initial superheat. The external flashing re-gime is usually unstable and difficult to control. Right at the nozzleexit, the spray angle is determined by capillary or aerodynamicinstabilities depending upon the efflux velocity. Further down-stream with the onset of external flashing, the lateral spreadingis the result of the interplay among surface tension, aerodynamicforces and thermodynamic instabilities. Furthermore, heat transferand flow fluctuations may enhance or inhibit flash boiling. Conse-quently, it is extremely difficult to predict the jet growth through adeterministic model.

(a) (b) (c) (d)

Rp=1.29 Rp=5.2 RRp=4.73Rp=2.59

Fig. 2. Variation of spray pattern with increasing superheat: (a) mechanical breakup; (acetone.

For higher initial superheat, a two-phase flow may already set-tle within the nozzle (internal flashing or transition regime). Differ-ent spray pattern can be expected depending on the type of nozzle-flow established before discharge. Park and Lee (1994) identifiedthree regimes, namely bubbly, slug and annular flow. At lower de-gree of superheat, the nozzle flow pattern is bubbly flow: the sprayexhibits a long intact core and drops are formed at its side. Byincreasing the superheat, the internal flow pattern changes to slugflow: bubbles collide and coalesce to form large slug bubbles.When the slug flow is discharged from the nozzle, the slug bubblesburst into ligaments and then disintegrate into small droplets. Athigher superheat, the internal flow pattern changes to annularflow, and the spray appears finer and more uniform. A large num-ber of variables govern the inception of the different nozzle flowpattern: the orientation and aspect ratio of the flow channel, thevolumetric and mass flow ratio, the thermo-physical propertiesof the fluids, wettability and surface effects. Recently, Sher et al.(2008) provided a comprehensive review of the different flow pat-tern, extending the previous classification from Park and Lee(1994). The authors also expressed caution in extending this clas-sification to modern atomizer where, due to the short residencetime in the nozzle, the condition of fully developed flow velocitiesdoes not usually apply. Similarly to the external flashing regime,the spray lateral spreading is determined by a number of concom-itant factors, specifically nozzle flow, aerodynamic/capillary forces,and thermodynamic instabilities. This precludes any possibility toderive a generalised phenomenological model for the spray angle.

Independently of geometric factors, a further increase in super-heat level eventually leads to a barrel-shaped, finely atomisedspray, as shown in Fig. 2g. Jet disintegration takes place directlyat the nozzle exit plane with no delay time for the onset of bubblenucleation. This indicates upstream bubble nucleation, either byhomogeneous nucleation via kinetic processes within the bulk li-quid, or by heterogeneous nucleation at the wall’s crevices or atthe nozzle tip. Variations in the initial degree of superheat do notresult in significant changes of the spray morphology: the sprayangle simply becomes wider with increasing superheat. Thisbehaviour might be explained in terms of number density distribu-tions of nucleation sites within the bulk liquid: higher concentra-tion corresponding to wider spray angles. Cleary et al. (2007)termed this disintegration mode the ‘‘fully flashing regime’’. Basedon these considerations and recalling that nucleation is the ratecontrolling process for phase transition, it seems reasonable to as-sume that, limitedly to the fully flashing regime, the initial lateralspreading of the spray is basically controlled by nucleation and toexpress this dependence through a phenomenological model.

Finally, for retrograde fluids at highly superheated conditions, ashock wave structure surrounding the dense jet core has been ob-served (Kurschat et al., 1992; Moreira et al., 2002). Its morphologyis shown exemplary in Fig. 3a, where it is possible to distinguish abarrel shock, a quasi-cylindrical lateral shock and a Mach disc. In

(e) (f) (g)

Rp=37.98Rp=12.97p=8.64

b–d) external flashing; (e, f) transition regime; and (g) fully flashing mode. Fluid:

Fig. 3. Shock structure in a highly superheated spray. Fluid: acetone.

10 −1 10 0 10 110 0

10 1

10 2

10 3

10 4

10 5

Wev

Φ *

Ja

Acetone FlashingEthanol FlashingAcetoneEthanolEnd point CStart point A

Flashing

Mechanical break−up

Transition

Fig. 4. Transition criteria for the onset of flashing according to Cleary et al. (2007).


theoretical models (e.g., Kurschat et al., 1992; Vieira and Simoes-Moreira, 2007), this complex shock structure has been associatedto an abrupt phase change process, which can be described usingthe concept of evaporation waves. Basically, the metastable liquidevaporates rapidly through a phase-change front, assimilated to athin discontinuity. Conservation equations are then establishedacross this discontinuity, assuming thermodynamic equilibriumdownstream of it. The evaporation rate is limited by a maximummass flow rate condition (Chapman–Jouguet condition), corre-sponding to the choking phenomenon. Similarly to an underex-panded gaseous jets, this sonic flow expands further to higherMach numbers to eventually form the above mentioned shock sys-tem. The latter slows down the high-speed flow to match the backpressure in the far field.

Although very similar, the two above mentioned theoreticalmodels inherently entail an important difference. Kurschat’s modeldoes not exclude the occurrence of nucleation and bubble growthwithin the concept of an evaporation wave front. In fact, nucleationis considered the rate-controlling process for the vaporisation rate(e.g., Kurschat et al., 1992, p. 51). Vieira’s model, instead, bypassescompletely the nucleation and growth mechanisms in favour of acomplete adiabatic evaporation discontinuity. In this perspectiveand for very high superheat Rp > 50, the authors proposed a newdisintegration mechanism, where nucleation is inhibited and vig-orous evaporation takes place directly from the surface of themetastable liquid jet. Note incidentally that complete liquid-to-gas evaporation through a discontinuity (or the opposite processthrough a liquefaction shock) is a commonly accepted mechanismfor phase transition in retrograde fluids (see Section 5.1 for moredetails).

In this paper, additional experiments are presented showingthat such phenomenology is not only a prerogative of retrogradefluids. The underlying assumption for both models will be criticallyreviewed on the basis of this new database in Section 5.

3.1. Transition thresholds

The transition from mechanical break-up to fully flashing is vis-ualised in Fig. 2 for an acetone spray. As can been seen, the spraymorphology changes gradually with increasing superheat. To date,only a few authors tried to derive criteria for predicting the onsetof flashing and its sub-regimes. The objective of this subsectionis to revise the available correlations and their underlying assump-tion. By analysing bubble growth rates in superheated liquids,Kitamura et al. (1986) derived experimentally the critical super-heat corresponding to complete external flashing (i.e. the metasta-ble liquid core disintegrates at a certain distance from the nozzle).The basic assumption is that flashing phenomena are controlledsolely by bubble growth rates, which can be shown to be propor-tional to a modified Jacob number Ja, defined as

Ja ¼ cplDThfg

ql

qvð8Þ

where cpl and ql are the specific heat and density of the liquid, hfg isthe enthalpy of vaporisation. All properties are evaluated at the ori-fice temperature. The vapor density qv is evaluated at the ambientpressure and injection temperature. The main drawback of Kitam-ura’s criterion is its scarce relevance for technical applications.Complete external flashing, in fact, is not only difficult to control,but it does not guarantee a complete and fine atomisation of thesuperheated jet. Cleary et al. (2007) extended the work of Kitamuraon transition and introduced two distinct thresholds, shown inFig. 4. Point A represents the upward limit for mechanical breakup:beyond this point, macroscopic bubbles alter the evolution andmorphology of the spray (see e.g. Fig. 2b). Point C denotes the onsetof the fully flashing regime. The new transition thresholds (A and C)are simply translated compared to Kitamura‘s criterion and wereobtained empirically. The experimental database included waterand ethanol jets, flashing at atmospheric condition in nozzles withdifferent aspect ratios (1.7 6 L/D 6 50). The correlations for condi-tions A and C are reported below (Cleary et al., 2007):

Start point A : JaU ¼ 55We�1=7v ð9Þ

End point C : JaU ¼ 150We�1=7v ð10Þ

where Wev ¼ Dqvu20=r is the vapor Weber number and u0 denotes

the nozzle discharge velocity. The correction factor U wasderived empirically by correlating experimental bubble growth rates(Kitamura et al., 1986). It provides the attenuation in bubblegrowth rate (and hence the increase in critical Ja number) due to


the simultaneous growth of an increasing number of bubbleclusters and is defined as

(a) Steel nozzle (b) Lapped steel nozzle

Fig. 5. Influence of surface properties and materials on the flash atomisationprocess. Fluid: water. Pinj = 500 kPa. L/D = 5. Superheat: DT = 40 K. Courtesy ofGünther and Wirth (2011).

Table 1Range of test conditions attainable in the ITLR test bench.

Quantity Symbol Unit Range

Injection pressure pinj MPa 0.1–8

U ¼ 1� exp �2300qvqL

� �� ð11Þ

Fig. 4 shows the classification of the present experiments fol-lowing Cleary’s transition model (Cleary et al., 2007) for fully flash-ing sprays. Along each curve, the back pressure is constant and thedegree of superheat increases when proceeding from low to high Janumbers. As can be seen, highly superheated, fully flashing jets –corresponding to high Ja numbers – are all located well abovethe transition line (green1 curve). At intermediate and low Ja num-bers, the experimental data (hollow symbols for non-flashing jets) lieclose or below the proposed correlation. This agreement is remark-able considering the uncertainty in the evaluation of the Wev num-ber. The injection velocity u0, in fact, is estimated on the basis ofthe measured mass flux (Cleary et al., 2007) or assuming an empir-ically determined discharge coefficient (this work). Note that smallvariations in u0 may shift the curves significantly along the transition(green) line and thus affect the quality of the prediction.

Despite the good agreement, the proposed correlation for pointC suffers three main limitations from a theoretical point of view:

� an inappropriate choice of the thermodynamic ‘‘driving force’’;� an inappropriate choice of the rate controlling process for the

fully flashing regime;� wettability and surface roughness effects are not taken into

account.

Concerning the first remark, we point out that the difference inchemical potential Dl is the correct ‘‘driving force’’ for promotingphase transition. The choice of Ja as correlation parameter assumesindirectly the temperature difference [DT = Tinj � Tsat(p1)] as thepertinent driving force, which is not correct. Recalling the thermo-dynamic relation, Eq. (3), it is immediately clear that a betterchoice would be the parameter Rp. The latter is directly propor-tional to the chemical potential difference and is expressed interms of thermodynamic variables, which can be directly mea-sured during an experiment (e.g. pressure). It is, therefore, veryunluckily that the proposed correlation can have a general validity.The successful application to our own data is most probably due tothe similarities in geometry, materials and fluids employed for theexperiments.

Concerning the second critical remark, the identification of bub-ble growth as the rate controlling process is certainly justified forpoint A (i.e. upper boundary for mechanical breakup – magentaline in Fig. 4). Indeed, the latter coincides with the inception oflarge macroscopic bubbles within the liquid bulk, as shown exem-plary in Fig. 2. Hence the characteristic time for such phenomena isrelated to the process of bubble growth. For the onset of the fullyflashing regime (point C), however, the preceding discussion (seeSections 2 and 3) has already shown that it is the nucleation ratethat determines the time scale for the inception of irreversiblebubble growth and hence for flash atomisation.

Concerning the third remark, it is well known that surfaceroughness and wettability can promote or inhibit the onset of het-erogeneous nucleation. The influence of these factors on the tran-sition to the fully flashing internal regime is very welldemonstrated by the investigations of Günther and Wirth (2011,2012), shown exemplary in Fig. 5. Here a superheated water jet(DT = 40 K) is discharged from two very similar nozzles. They aregeometrically identical, but made of different materials: steel and

1 For interpretation of color in Fig. 4, the reader is referred to the web version ofthis article.

lapped steel, respectively. As can be seen, the heterogeneous nucle-ation process is inhibited in the lapped steel nozzle (compared tothe steel nozzle) due to its reduced surface roughness. As a result,only external flashing is observed. This result is in agreement withrecent published data on bubble nucleation enhancement on roughsurfaces (McHale and Garimella, 2010). The authors measured thedensity of active nucleation sites on rough and polished surfaces.Polished surfaces require comparatively much higher superheatsto sustain active nucleating cavities in agreement with Hsu’s crite-rion (Hsu, 1962). In Günther and Wirth (2012), the comparison isextended to a Teflon nozzle. In this case, nucleation is enhancedthanks to its hydrophobic properties (i.e. poor wettability). In liter-ature, hydrophobic zones are well known to act as promoters ofnucleation sites (Phan et al., 2009b; Suk, 2010). Consequently,transition to fully flashing occurs at lower superheats (DT = 30 K)compared to a steel nozzle (DT = 40 K), as shown in Günther andWirth (2011, 2012).

Based on these considerations, in Section 5.3.1 an alternativecriterion is proposed for the onset of the fully flashing regime(point C).

4. Experimental part

4.1. Test facility

The test bench (C2) at the Institute of Aerospace Thermodynam-ics (ITLR) is designed for performing flash atomisation and vapori-sation experiments at low pressure and medium vacuumconditions. The operating conditions for the facility are summa-rised in Table 1. The facility comprises a pressurising and ventingsystem, a liquid tank, a modified diesel injector, a glass-windowedvacuum chamber and a vacuum pump. The liquid fuel is fedthrough a capillary tube to the nozzle. A gas bottle (typically nitro-gen) is connected to the liquid reservoir and provides the drivingforce for pushing the liquid column through the nozzle. The nozzlebody is made of stainless steel and can withstand high thermal andmechanical loads. The nozzle tip is a simple cylindrical orifice witha diameter D = 150 lm and an aspect ratio L/D = 6. With this setup,

Injection temperature Tinj K 308–428Back pressure p1 kPa 0.5–40Pressure ratio Rp – 0.3–1000

Table 2Constancy of pressure during test time: comparison among different facilities.

ONERAa SISEAb ITLR

Injection time 10 s 4 s 20 msRate of pressure increase 118 Pa/s 45 Pa/s <13 Pa/sPressure rise during test time 1180 Pa 180 Pa <0.26 Pa

a Lecourt et al. (2009).b Moreira et al. (2002).

Fig. 7. Schematic layout of the optical setup.


the injection pressure pinj can be varied between 0.1 and 8 MPa andmaintained constant during an experimental run. The vacuumchamber can be either connected directly to a vacuum pump orto a large tank, if a longer test-time is needed. To monitor the backpressure (p1), the chamber is instrumented with a vacuum trans-ducer (MKS – Baratron 390). A schematic view of the vacuumchamber is shown in Fig. 6. The cylindrical test section is 400mm long and has a diameter of 250 mm. Four circular windows(/ = 160 mm) are installed at 90� apart from each other to allowvisualisation of the spray and optical diagnostics. To monitor thetemperature, three thermocouples are flush-mounted along thechamber’s walls. On the top flange, a heated fuel injector ismounted and its temperature is monitored through a PIDcontroller.

To guarantee a high accuracy and reproducibility of the exper-iments, the injector has to meet a number of requirements. A firstessential requisite is the use of a fast-response injector, character-ised by short transient times for attaining steady-state injection.This way only a small amount of fuel is injected in the chamberand no significant change in the back pressure (and hence in thedegree of superheating) is observed. A second requirement is thepossibility of varying the injection conditions (i.e. pressure andtemperature) independently and over a wide range, representativeof the operating conditions of modern propulsion systems. Finallythe injection system has to be pressure and vacuum sealed. Theinjector chosen is a standard automotive fuel injector, which canoperate reliably at low-pressure conditions thanks to an ad hoc de-sign of the nozzle needle. It has got a characteristic response timeof roughly 0.4 ms and is capable of establishing steady-state condi-tions within about 1 ms. Short transient times can be achieved bystoring pressurised fuel inside the injector, thus strongly reducingthe nozzle flow start-up time. Thereby, fuel pressurisation andinjection are decoupled, which facilitates the regulation of the fueltemperature as well. This implies that the fuel can be directlyheated within the injector itself so that the target fuel temperatureis immediately obtained at the beginning of the injection event.With the present facility, injection times of 20 ms can be achievedwith no appreciable change in back pressure. Table 2 shows a com-parison between the stability of our test conditions compared tothose of other facilities employed for similar studies.

4.2. Optical setup

The optical layout of the shadowgraph setup is shown in Fig. 7.As the light source, a short-pulsed, high-power LED (LUXEON Re-bel) is used to back illuminate the spray. A more detailed descrip-tion of the illumination system can be found in Stotz (2011). Thelight is collected by a parabolic mirror and focused on the camera’schip (Photron Fastcam SA1) by an objective lens. The pixels of the

Fig. 6. Schematic layout of the ITLR-C2 facility.

camera have an edge length of 20 lm and the LED lamp produceslight pulses with a width of about 200 ns (FWHM). These parame-ters yield a maximum theoretical velocity without motion blur ofabout 600 m/s. In the present study, the maximum spray velocityis always lower than 100 m/s and therefore sharp images of thejets can be acquired with the current settings. Synchronisation ofcamera and light source is achieved by slaving the light source tothe internal clock of the high-speed camera. The high-speed cam-era has a maximum resolution of 1024 � 1024 pixel at 5400 fps, itsminimum shutter time is 1 ls, its dynamic range is 12 bit. For thepresent investigation, the camera resolution has been adapted tothe region of interest, resulting in a higher frame rate. The resolu-tion and magnification settings applied in the test runs are summa-rised in Table 3. For a magnification factor M of 1:1, the actualoptical resolution is 20 lm/pixel. The latter decreases to roughly80 lm/pixel, when the optical setup is set to a magnification factorM of 1:4.

Note that, in order to visualise the shock structure at highsuperheat conditions, it is necessary to operate the LED in contin-uous mode. During pulsed operation mode, in fact, light refractionthrough the weak shock structure is hardly detectable during thevery short illumination time (�200 ns). For detecting weak shocks,it is necessary to set the camera exposure time to 1 ls as a neces-sary compromise between the need to minimise motion blur andto visualise weak refraction effects.

4.3. Post-processing

This section describes the post-processing algorithm, used toextract the spray geometrical data from the high-speed shadow-graphy images. The used Matlab code was developed by Stotzet al. (2008). For accurate results, the image processing algorithmmust reduce the background noise and enhance the image contrast

Table 3High-speed camera settings.

Resolution Frame rate (fps) Magnification

256 � 784 22,500 1:4512 � 440 30,000 1:1

[mm]

[mm

]

1 2 3 4

4

2

0

−2

−4

θx / D = 20 x

y

Fig. 9. Definition of the local jet spreading angle.


without altering the spray contour. As a first step, illuminationinhomogeneities due to temporal fluctuations as well as spatialnon-uniformities of the light distribution are corrected by normal-ising each image to a reference image. In this way, the backgroundintensity of all images from an experimental series is homoge-neously distributed and set at a constant value. Then a median fil-ter is applied to the normalised images to reduce the backgroundnoise, without affecting the shape of the spray. Afterwards, thespray images are thresholded to separate the spray from the back-ground. Fig. 8 illustrates schematically the three different phases ofthe image processing scheme.

Once the spray contour has been defined, its upper and lowerbranch yi(x) are subsequently used to calculate the upper and low-er half of the local spreading angles hi(x) according to

tan½hiðxÞ� ¼yiðxÞ � yið1Þ

Dx; i ¼ upper; lower ð12Þ

The total spray angle, shown in Fig. 9, is then calculated at dif-ferent axial positions (x/D = 2, x/D = 5, x/D = 10, x/D = 20, x/D = 60)as:

hðxÞ ¼ hupperðxÞ � hlowerðxÞ ð13Þ

By applying Eq. (13) to all acquired images, temporally and spa-tially resolved information on the lateral spreading of the jet isgained.

The uncertainty in the determination of the local spray angle ismostly due to the limited spatial resolution of the camera chip andto non-uniformities in the light distribution. They are responsiblefor the erroneous positioning of the spray contour during post-pro-cessing, and hence affect directly the reliability of the spray anglepredictions. Since the spray angle is expressed as a function of thespray contour h(x) = f[y(x)], its standard deviation ystd has been

Fig. 8. Image proce

calculated at each axial position x, assuming as sample a popula-tion of 30 images. The random error is then determined as:

Dyr ¼2ystdffiffiffiffiffiffi

30p ð14Þ

The systematic error depends upon the pixel size and is relatedto the impossibility to capture displacements of the jet contourwithin one pixel. Therefore the systematic error is fixed toDys = 20 lm (i.e. 1 pixel). By applying the Gaussian error propaga-tion law to the global error (Dy = Dyr + Dys), the correspondinginaccuracy in the determination of the spray angle can be

ssing scheme.


determined. Note that the largest error amounts to 3% and isobserved mostly in highly superheated jets, thus providing goodconfidence in the reliability of the model predictions (Kamounet al., 2010).

4.4. Overview test conditions

As test fluids, acetone, ethanol and isooctane are selected. Therationale for this choice is threefold: (1) to facilitate comparisonwith literature data; (2) to include in the test matrix highly super-heated conditions, as encountered in spacecraft operations; and (3)to compare the behaviour of standard and retrograde fluids. Thelatter are substances of high complexity, characterised by an in-creased ability of the molecule to store internal energy (i.e. sub-stances with large molar specific heat). Thanks to thischaracteristic, phase transitions on a molecular scale are facilitatedin retrograde fluids, since they can absorb or release amounts ofenergy that exceed the latent heat of vaporisation and are not lim-ited by heat conduction. A widely used quantity, capable of charac-terising the degree of retrogradicity of a substance, is thecharacteristic heat capacity c�v ¼ c0

v ðTcÞ=Rs. It is defined as theideal-gas heat capacity at the thermodynamic critical temperaturec0

vðTcÞ normalised by the specific gas constant Rs. From correspond-ing state calculations, it can be shown that the limiting value for afluid to be classified as retrograde is c�v ¼ 11:2. In practical applica-tions, however, it is found – on the basis of energy considerations –that a molar specific heat of c0

v ðTcÞ > 24Rs is required for observingretrograde gas-dynamics effects (e.g., Thompson and Sullivan,1975). The fluid properties and test conditions are summarised inTable 4. Note that the injection temperature is selected in such away that Tinj is always lower than the equilibrium temperature cor-responding to the injection pressure [Tinj < Tsat(pinj)]. This repre-sents a necessary requisite to avoid boiling inside the liquidreservoir. For all experiments, the injection velocity is kept rela-tively low (below 40 m/s) so that Rayleigh breakup is the referencestate in absence of non-equilibrium evaporation effects.

5. Results and discussion

This section presents the main findings of a systematic study onsuperheated jet atomisation. The objective of this paper is to gain abetter insight in the physics of the fully flashing disintegration pro-cess and to translate this understanding in a phenomenologicalmodel. As it is best to proceed in a systematic way, we start witha small digression on some thermodynamic features of retrograde

Table 4Overview of test conditions. For all test cases: pinj = 106 Pa, T1 = 293 K.

Fluid Quantity Unit Range

Ethanol Tinj K 308–389c�v ¼ 10:7 p1 kPa 2–40

Rp – 0.3–196DT K �21 to 113Tc K 514M kg/kmol 46.07

Acetone Tinj K 303–373c�v ¼ 12:18 p1 kPa 2–40

Rp – 0.9–186DT K �1.3 to 126Tc K 508M kg/kmol 58.08

Isooctane Tinj K 313–420c�v ¼ 36:63 p1 kPa 2–40

Rp – 0.32–165DT K �31 to 145Tc K 544M kg/kmol 114.23

fluids. Then we will proceed with a comparative analysis of thespray characteristics in both retrograde and ‘‘standard’’ fluids.Examining differences and similarities in the spray morphologyand relating them to the possible phase-transition mechanismswill help ruling out the non-relevant physical processes. Finally,an hypothesis is formulated on the controlling mechanisms forflash-atomisation. Accordingly, new criteria are proposed for char-acterising both the onset of the fully flashing regime and the lateralspreading of the jet. Both criteria are verified through comparisonwith experimental data.

5.1. Preliminary thermodynamic considerations

In the context of this paper, we are interested in highlightingthe possible difference in the mechanism of phase transition be-tween retrograde and regular fluid behaviour when a liquid isbrought to a metastable state by a rapid decompression. This dif-ference is related to the shape of the two-phase dome, whichexhibits the tendency to lean over to the right with increasing c�v ,as shown schematically in Fig. 10a. For regular fluids, there is anabsolute limit to the maximum achievable metastability dictatedby the thermodynamic stability requirement (@p/@v)T < 0 and rep-resented by the vapor and liquid spinodals, shown in Fig. 10b.Within this metastable region, evaporation takes place via bubblenucleation and growth in the metastable region. In this case, thevaporisation rate is mainly determined by the rate of latent-heatabsorption (Thompson et al., 1986). For retrograde fluids (i.e.c�v > 24), phase transition is also possible in the unstable regionthrough an adiabatic evaporation wave. The latter can be seen asa gas-dynamics discontinuity for which the upstream state issuperheated liquid and the downstream state a vapor–liquid equi-librium mixture. The estimated time for these transitions is veryshort – roughly 1–2 ns – (Gülen, 1994), such that there is a reason-able chance that nucleation and bubble growth process are by-passed in favour of a complete adiabatic transition from liquid-to-gas through a rarefaction discontinuity. In this case, the vapori-sation rate is limited by the condition of maximum local mass flux(sonic condition or Chapman–Jouguet solution).

For a liquid with high heat capacity, the transition from regularto retrograde phase changes has been investigated by Thompsonet al. (1986). The authors showed that retrograde behaviour willoccur provided the energy stored in the molecular degrees of free-dom is large compared to the latent heat. Since the latent heat de-creases with temperature, it results that substances with largevalues of c�v always show retrograde behaviour over some rangeof temperatures along the liquid–vapor coexistence curve. How-ever, at low temperatures (i.e. far away from the critical point)all substances will exhibit regular phase change behaviour. Thecharacteristic heat capacities c�v for the three fluids considered hereare listed in Table 4. As can be seen, only isooctane can exhibit ret-rograde phase change behaviour. It is therefore interesting to ana-lyse whether the phenomenology and spray patterns observed forall three substances are mutually consistent and evolve in a similarmanner. If confirmed, this circumstance would then provide anindirect confirmation that bubble nucleation and growth are thecontrolling physical processes for the shattering and vaporisationof a superheated jet.

5.2. Flow visualisation results

This section discusses the main features of fully flashing spraysfor both standard and retrograde fluids. Three aspects are mainlyconsidered for the analysis: spray morphology and lateral spread-ing, transition threshold Rp,tr at the onset of the fully flashing re-gime and the inception of a complex shock wave structure athighly superheated conditions (i.e. Rp > 50). Whenever feasible,

Liquid

Vapour Two-phase region

0

1 0

1

Critical point T

specific entropy

Regular fluid: cv* < 11

Liquid

Vapour

Two-phase region

0

1

Critical point T

specific entropy

Retrograde fluid: cv* > 24

(a)

Liquid spinodal curve

Vapour spinodal curve

p

specific volume

metastable regions

unstable region

(b)Fig. 10. (a) Temperature-entropy diagrams of substances with increasing characteristic heat capacities c�v and (b) schematics of the two-phase dome for a pure fluid.

Fig. 11. Examples of fully flashing sprays. Top row: case 1; Middle row: case 2; Bottom row: case 3. Test conditions reported in Table 5.

Table 5Test conditions for Fig. 11.

Fluid Tinj (K) p1 (kPa) Rp


the evaluation of experimental findings is substantiated by theo-retical considerations in an attempt to identify the controllingphysical processes for superheated jet disintegration.

EthanolCase 1 389 20 19Case 2 374 8 29Case 3 389 8 48

AcetoneCase 1 342 20 8Case 2 374 20 19Case 3 374 8 47

IsooctaneCase 1 389 20 8Case 2 382 8 16Case 3 405 8 28

5.2.1. Spray morphology and angleFig. 11 shows examples of fully flashing sprays for three differ-

ent fluids and varying degrees of superheat. The corresponding testconditions are listed in Table 5. At a phenomenological level, allimages bear a close resemblance. Regardless of the initial super-heat Rp, the sprays exhibit the characteristic bell-shaped formand are finely atomised. Estimated drop sizes are below 30 lm,based on the fact that droplets cannot be clearly resolved evenwith the resolution of 20 lm/pixel. Note that this estimation ofdrop sizes is in agreement with the classification of Witlox et al.(2007). The authors estimated the Sauter Mean Radius (SMR) tobe 30 lm at the onset of the fully flashing regime. With increasingsuperheat level, the SMR decreases and the spray becomes widerwhile preserving its bell-shape. Right at the nozzle exit plane, thespray angle may reach values as high as 160� depending upon

the initial degree of superheat Rp, as illustrated in Fig. 12. Despitethese similarities, predicting the jet lateral spreading or thetransition threshold for the superheat parameter Rp,tr is notstraightforward. The spray angle, for example, is not a univocal

Fig. 12. Spray angle as function of initial superheat Rp. Axial location: x/D = 5.

1

10

100

1.0E+051.0E+041.0E+03

Rp,tr

p [Pa] Ethanol Acetone

Fig. 13. Variation of Rp,tr with back pressure.


function of the initial superheat Rp, as can be deduced from Fig. 12.This is particularly true at the onset of the fully flashing regime,where the rapid increase of spray angle with superheat is fluid-dependent. Subsequently, upon attainment of a threshold valueof about 140–150�, only a weak dependence on Rp is observed,without any noteworthy difference between retrograde andstandard fluids.

From the analysis of the spray angle data, the following conclu-sions can be drawn. First, the initial lateral spreading of the jet can-not be attributed to aerodynamic/inertial effects. In the frameworkof mechanical breakup, it is well-known that, for a given nozzlegeometry (i.e. aspect ratio L/D), the spray angle increases linearlywith the chamber density and never exceeds a value of 20� (e.g.,Abramovich, 1963; Chehroudi et al., 2002). Consequently, the largespray angles observed in the fully flashing regime cannot be attrib-uted to density stratification effects. Second, retrograde phasetransitions can also be excluded since the same phenomenologyis observed for ethanol c�v ¼ 10:7 and isooctane c�v ¼ 36:6 jets. Fur-thermore, the physics of retrograde phase change is not consistentwith the experimental observations. Retrograde transitions foreseea complete adiabatic vaporisation of the superheated liquid withina gas dynamic discontinuity and the attainment of thermodynamicequilibrium downstream of it. If the jet is discharged in a super-heated liquid state and nucleation is bypassed, then the liquid coreshould resemble a Rayleigh jet (see e.g. Fig. 2a) and the vaporisa-tion front should start directly from the outer jet periphery leadingto a complete vaporised mixture just downstream of it. This theo-retical trend is not supported by the experimentally observedspray patterns (Fig. 11) and opening angles (Fig. 12). Third, the de-gree of superheat Rp is not the controlling parameter for the onsetof the fully flashing regime and the associated spray angle. This fol-lows directly from Fig. 12: the spray angle data do not merge into asingle curve and exhibit a significant scatter in the onset region.

5.2.2. Transition thresholdAs mentioned already in the previous section, the onset of the

fully flashing regime does not occur at a specific superheat value.To the contrary, the transition threshold Rp,tr varies with test fluidand back pressure. This case is best exemplified in Fig. 13. As canbe seen, Rp,tr – i.e. the excess in chemical potential Dltr requiredfor the onset of the fully flashing regime – increases with decreas-ing back pressure. To date, none of the available theoretical modelsor correlations (e.g., Kurschat et al., 1992; Vieira and Simoes-Moreira,2007; Cleary et al., 2007) provides an explanation for the observedphenomena. This is mainly ascribable to the fact that there is stillno clear understanding of the physical mechanism and drivingforces controlling the inception of the fully flashing regime andits development.

5.2.3. Shock wave structuresThis section examines the evolution of flashing sprays at highly

superheated conditions (i.e. Rp > 50). Figs. 14 and 15 present exam-ples of shock structures surrounding fully flashing isooctane andacetone sprays, respectively. As can be seen, the morphology of thisshock system is very similar for both fluids. This qualitative simi-larity is further corroborated in quantitative terms in Fig. 16. Herethe maximum lateral extent r1 of the shock wave structure, definedin Fig. 3b, is plotted in non-dimensional coordinates. The correla-tion parameter on the x-axis takes into account different factors:degree of metastability, injection conditions and nozzle geometry.Noteworthy is that the radius r1 increases steadily with the degreeof metastability and the same dependency is observed for all sub-stances, independently from their retrograde behaviour. An over-view of the test conditions for the experiments performed bythese authors and by Vieira and Simoes-Moreira (2007) is givenin Table 6. Note that this is the first time that such shock structuresare detected in regular fluids.

We recall from Section 3 that, in literature, there is a generalconsensus on the mechanism leading to the generation of theshock structure (e.g., Kurschat et al., 1992; Vieira and Simoes-Moreira, 2007). Discrepancies are instead present with referenceto the mechanism of phase transition. Vieira and Simoes-Moreira(2007) assume a complete adiabatic transition from liquid-to-gasthrough a rarefaction discontinuity; whereas Kurschat et al.(1992) were among the first to suggest a direct link between nucle-ation rate and flash-atomisation. The additional data presentedhere indicate that Kurschat et al.’s model adheres better to theexperimental observation. In fact, the only possibility to justifythe similar vaporisation behaviour between isooctane c�v ¼ 37

� �and acetone c�v ¼ 12

� �is to postulate that for both substances the

transition from liquid-to-vapor occurs through the ‘‘standard’’ pro-cesses of bubble nucleation and growth. This conclusion is alsosupported by the thermodynamic analysis of Thompson et al.(1986). The authors predicted regular fluid behaviour for retro-grade substances at low reduced temperatures (T/Tc), as it is thecase for the isooctane experiments (see for details Tables 4 and 6).

A logical sequence of events is therefore the following. Upondischarge from the nozzle, the rapid depressurisation induces bub-ble nucleation and jet disintegration through bubble bursting. Atvery high superheat, the rapid expansion right at the nozzle exitis not sufficient to relax the system to thermodynamic equilibriumand sustained vaporisation takes place within the two-phase flowregion. Since the maximum mass flow rate is limited by the soniccondition (Chapman–Jouguet point), this induces a supersonicexpansion flow terminated by a shock wave to match the ambientpressure. With increasing Rp (alias Dl) increases also the total

Rp = 43 Rp = 57

Rp = 85 Rp = 171

Fig. 14. Variation of the spray structure with increasing values of the parameter Rp. Fluid: isooctane.

Fig. 15. Variation of the spray structure with increasing values of the parameter Rp. Fluid: acetone.


vaporised fuel mass and hence the associated vapor pressure. Thisresults in a stronger supersonic expansion and in a wider shockstructure of increased strength, as depicted in Fig. 16. Since in reg-ular evaporation the absorption of latent heat controls the rate ofvaporised mass, this shock system will be clearly visible at compar-atively lower superheat for substances with a lower enthalpy ofvaporisation (e.g. isooctane). For fluids with a high enthalpy ofvaporisation (e.g. ethanol), the shock structure is completelyembedded within the two-phase flow and requires novel optical

techniques for its detection. Evidence for the existence of such flowacceleration and associated shock structures is provided inKamoun and Lamanna (2012) and in the Supplementary onlinematerial for this article.

5.3. Data analysis

In order to bring the entire scope of experimental data into amore unified and coherent framework, the only plausible

Fig. 16. Normalised shock wave radius versus correlating parameter. �Data takenfrom Vieira and Simoes-Moreira (2007).

Table 6Test conditions for highly superheated jets.

Fluid SISEAa ITLRIsooctane Isooctane and acetone

pinj 0.25–0.7 MPa 1 MPaTinj 329–350 K 313–420 Kp1 0.2–0.4 kPa 40–2 kPaRp 9–451 1–145L/D 25.8 6.67

a Vieira and Simoes-Moreira (2007).

Table 7Summary of test conditions for Fig. 17. Fluid: ethanol. pinj = 106 Pa, T1 = 293 K.

p1 Tinj (K) Rp (–) v (–)

40 (kPa) 319 0.6 53366 4.37 1.67374 5.75 0.93

10 (kPa) 311 1.61 75350 9.67 1.13366 17.5 0.44

4 (kPa) 307 3.27 13.4334 12.5 1.41350 24.2 0.57

Table 8Summary of test conditions for Fig. 18. Fluid: acetone. pinj = 106 Pa, T1 = 293 K.

p1 Tinj (K) Rp (–) v (–)

40 (kPa) 342 3.89 7.39350 4.94 4.27366 7.69 1.63

10 (kPa) 311 5.20 11.7342 15.6 1.81358 24.8 0.84

6 (kPa) 311 8.67 6.81327 15.5 2.80350 32.9 0.89


explanation is to assume a direct functional dependence betweenbubble nucleation and spray broadening in the fully flashingregime. These considerations led to the formulations of thefollowing two hypotheses.

Hypothesis 1 (Spray angle). Large depressurisation rates, asencountered in the discharge of a pressurised liquid in a lowpressure environment through an orifice or an atomiser, may leadto the onset of homogeneous or heterogeneous nucleation (e.g. bydissolving volatile gas). As a result, a uniform distribution ofbubbles within the bulk metastable liquid is obtained. Whenexposed to a low pressure environment, these bubbles burstalmost immediately since they cannot withstand the high pressuredifference between the Laplace pressure (inside the bubble) andthe low ambient pressure. These manifold of micro-bursting eventscause the instantaneous broadening of the liquid spray.

This hypothesis explains the experimental trend of increasingspray angle with superheat Rp. Higher Rp values correspond tohigher nucleation rates, and therefore to an increased numberof micro-bubbles bursting within the bulk liquid and finer atom-isation. As soon as a threshold of roughly 150� in the openingangle is reached, however, the spray morphology and angle(see Figs. 11 and 12) become relatively insensitive to further in-crease in the initial superheat. This behaviour can be explainedin light of recent advances on the theoretical description ofnucleation in confined space (e.g., Schmelzer and Abyzov,2011; Kozíšek et al., 2011). The authors demonstrated thatdepletion of the liquid phase (i.e. volume reduction in the parentphase) results in an increase of the energy barrier to nucleation.On the other hand, the number of nuclei formed inside the par-ent phase (e.g. a droplet or a melt) changes only slightly with itsvolume. Consequently, in a superheated liquid jet (practicalexample of a confined volume), the high nucleation and growthrates typical of the fully flashing regime will rapidly lead to asignificant reduction of the liquid volume. The associated in-crease in the activation barrier will therefore prevent any furtherincrease of the nucleation rate at higher Rp values and, hence, inthe spray lateral spreading. Note that the proposed mechanismon the role of nucleation for flash-atomisation can also explainthe recent experimental findings of Cleary et al. (2007) and Wit-lox et al. (2007). The authors observed a rapid decrease in thedroplet SMD at the onset of flashing (point C, defined in Eq.(10) and plotted in Fig. 4), which is consistent with the increaseof the nucleation rate with superheat (i.e. finer atomisation).After a certain threshold (e.g., Witlox et al., 2007, p. 32), theSMD exhibits an appreciably slower decay till it reaches aconstant minimum value for very high initial superheat. At theseconditions, volume depletion effects become significant andinhibit an increase in nucleation rate, thus explaining theconstancy of the droplet SMD with increasing superheat. Finally,Hypothesis 1 is also fully consistent with the physics of highlysuperheated jets, as reported in Section 5.2.3. If the maximumattainable expansion at the nozzle outlet is limited by the kinet-ics of nucleation in confined volumes, this implies that theresidual superheat can only be dismissed through a sustainedevaporation front. As explained previously, this leads to strongersupersonic expansion flows and to wider shock structures ofincreased strength with increasing Rp values.

Hypothesis 2 (Transition threshold). If the spray lateral spreadingand atomisation is controlled by bubble nucleation, then it isreasonable to assume that also the onset of the fully flashingregime is linked to the onset of nucleation. In this hypothesis, theenergy barrier to nucleation should then represent also thethreshold to the inception of the fully flashing regime. Hence, forgiven injection conditions, transition will occur at a specificsuperheat Rp,tr at which the surplus in chemical potential Dl willbalance the work made by surface tension to form the new phase.In non-dimensional term, this is equivalent to state that their ratiomust be of order one.


In the following sections, the validity of these hypotheses is ver-ified by demonstrating that the controlling variables for nucleationcan be employed for reorganizing the experimental data into areduction procedure that enables to predict both the onset of fullyflashing and the spray angle.

5.3.1. Transition conditionThe objective of this section is to corroborate Hypothesis 2 and

identify a suitable criterion for predicting the onset of the fullyflashing regime. We revert therefore to nucleation theory and spe-cifically to the non-dimensional expression for the energy barrier

v ¼ DG�

kbTinj¼ 16pr3

3ðDlÞ2¼ H3

ðln RpÞ2ð15Þ

If v is smaller than one, then the excess in chemical potentialsuffice to overcome the work done to form a new surface, thusdetermining the onset of nucleation and consequently the transi-tion to the fully flashing regime. To verify this hypothesis, we havecalculated the value of the energy barrier for the three different re-gimes: mechanical breakup, transition region and fully flashing re-gime. A selection of images with the associated value of the

Before onset p = 40 kPa

= 53 =

p = 10 kPa

= 75 =

p = 4.0 kPa

= 13.4 =

Fig. 17. Energy barrier associated with mechanical breakup (left), transition region (ce

parameter v is presented in Figs. 17 and 18 for two different fluids:ethanol and acetone, respectively. As can be seen, the mechanicalbreakup regime corresponds always to values of v P O(10). Atthe onset (transition region), the energy barrier is always of orderone and the spray still exhibits a few macroscopic liquid filaments.As soon as the parameter v drops below one, the superheated jetsbecome finely atomised and no macroscopic ligaments are ob-served any longer.

Note that this trend reproduces consistently for all experimentsconsidered in this work, as shown in Fig. 19. Here the energy bar-rier is plotted versus the Wev number. For a constant back pressure,the parameter v decreases progressively with increasing superheatRp in agreement with the prediction from nucleation theory. Corre-spondingly, the disintegration process evolves from mechanicalbreakup towards the fully flashing regime. Two important consid-erations can be drawn from the analysis of the transformed exper-imental data. First, the new transition criterion v = O(1) shows amarkedly different dependence upon the Wev number, when com-pared to Cleary’s correlation. Second, a certain scatter is observedconcerning the accurate determination of the onset value. Graphi-cally, this is represented by the grey area (exp. onset region) inFig. 19. In order to fully understand the implications of these

Onset Full Flashing

1.67 = 0.93

1.13 = 0.44

1.41 = 0.57

ntre), fully flashing regime (right). Fluid: ethanol. Test conditions listed in Table 7.

Before onset Onset Full Flashing p = 40 kPa

= 7.39 = 4.27 = 1.63

p = 10 kPa

= 11.7 = 1.81 = 0.84

p = 6.0 kPa

= 6.81 = 2.80 = 0.89

Fig. 18. Energy barrier associated with mechanical breakup (left), transition region (centre), fully flashing regime (right). Fluid: acetone. Test conditions listed in Table 8.

Fig. 19. Variation of the v parameter as the sprays evolve from mechanical breakup to the fully flashing regime.


remarks, both aspects are analysed in details in the ensuingdiscussion.

Concerning the independence upon the Wev number, this fol-lows directly from thermodynamic considerations. In the newlyintroduced criterion, the onset is univocally determined by the

kinetic condition v = O(1). Therefore the Wev number, which mea-sures the relative importance of aerodynamic versus surface ten-sion forces, has no impact in controlling the onset of (hetero)- orhomogeneous nucleation within the nozzle or at its exit plane.An interesting aspect of the new transition criterion v = O(1) is that

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

250 290 330 370 410 450

Satu

ratio

n pr

essu

re [M

Pa]

T [K]

p ,1

p ,2

Rp,tr1

Rp,tr2

Fig. 20. Adaptation of the transition threshold with back pressure: a phenomeno-logical illustration.

p = 40 kPa

p = 20 kPa

p = 10 kPa

p = 8 kPa

p = 6 kPa

p = 4 kPa

p = 2 kPa

Corr.

Fig. 21. Spreading angle as function of log R2pH

3

, evaluated at x/D = 20. Fluid:ethanol.


it provides a simple and logical explanation for the experimentallyobserved trend on the dependence of Rp,tr with back pressure (seeFig. 13). For a better clarity, Fig. 20 provides a phenomenologicalillustration of the relevant variables. Let us denote with Rp,tr1 the‘‘transition’’ superheat at the injection temperature Tinj,1 and backpressure p1,1. If we now lower the back pressure to p1,2, thenew ‘‘transition’’ threshold Rp,tr2 will occur at a lower injectiontemperature Tinj,2 < Tinj,1. This is simply a result of the monotonicincrease of saturation pressure with temperature. On the otherside, due to the associated increase in surface tension, a compara-tively higher degree of superheat Rp,tr2 > Rp,tr1 (i.e. chemical poten-tial surplus) is required to balance the energy of formation of thecluster and meet the condition v2(r2, Rp,tr2) < 1. Note that this isthe same effect measured by Cleary et al. (2007). The authors alsodetected an increase in the superheat required for transition (i.e.increase in the Ja number) with decreasing Wev (i.e. lower chamberdensities). This trend, however, was simply obtained by fitting theexperimental data. In this work, instead, the above mentionedtrend is justified on the basis of nucleation theory by the need toovercome the energy barrier for the onset of nucleate boiling.The above results can be generalised by stating that: for a givenback pressure, the steeper the saturation pressure curve, the lowerthe injection temperature for the onset of the fully flashing regime.The corresponding transition threshold Rp,tr, however, is higher incompliance with the transition criterion v = O(1).

Concerning the scatter in the quantitative calculation of thetransition threshold, this is directly related to limitations of theClassical Nucleation Theory (CNT). CNT is known to provide anaccurate prediction of the number of molecules in the critical nu-cleus, but not of the activation barrier. The latter is strongly depen-dent on the fluid temperature and only weakly dependent on Rp.McGraw and Laaksonen (1996) demonstrated that there is a sys-tematic displacement between barrier heights in the classical anddensity functional theories and that such displacement is only afunction of temperature. The authors then introduced scaling lawsto correct for the wrong temperature dependence of CNT. Thevalidity of this correction is supported by theoretical arguments(e.g. the nucleation theorem) and by experiments. As stated earlier,in our experiments the onset of flashing occurs at distinctly lowertemperatures with decreasing back pressures. Consequently, theomission of the temperature scaling correction in the calculationof the activation barrier v will certainly have an impact on theaccuracy of the transition criterion. Another factor hampering theaccurate determination of the onset is the exclusion of heteroge-neous effects (e.g. due to wettability and surface roughness) inthe calculation of the energy barrier.

Despite these limitations, the present analysis has the merit tocast the calculation of the onset condition within the correct theo-retical framework. Furthermore, the accuracy of the predictionscan be improved by incorporating recent advances on nucleationmodelling in the expression of the activation barrier. Noteworthy,in this context, the work of Shen and Debenedetti (2001). Theauthors extended the thermodynamic analysis of McGraw andLaaksonen and developed scaling laws for bubble nucleation. Con-cerning the effect of surface topography on the nucleation process,Phan et al. (2009b,a) proposed a new approach to the nucleationmechanism and introduced the concept of macro and micro-con-tact angle to clarify the nexus between wetting characteristicsand nucleate boiling. Nam and Ju (2008), on the other side, intro-duced a modified bubble nucleation model that is consistent withthe drastic reduction in superheat for the onset of vapor nucleationon hydrophobic surfaces. Inclusion of such corrections in the for-mulation of the parameter v would then enable to independentlyassess and corroborate the different formulations of CNT.

5.3.2. Spreading angleThe objective of this section is to investigate whether, limitedly

to the fully flashing regime, a direct functional dependence be-tween the spray lateral spreading and bubble nucleation exists(i.e. validity of Hypothesis 1). As already described in Section 2,the population of bubble-clusters is basically depending upon thefollowing variables: the mass of a liquid molecule m, the superheatparameter Rp and the dimensionless surface tension H. The analy-sis basically consists in defining an efficient data reduction schemefor processing the spray angle data as function of the controllingvariables for nucleation. The reduction scheme should be validover a wide range of back pressures, superheat levels and test flu-ids, while providing a realistic representation of the spray contourwith a minimum impact on its accuracy.

To verify whether a direct relationship between the populationof bubble clusters (i.e. the nucleation rate) and the spray angle ex-ists, the following combination of non-dimensional parameters istaken: R2

pH3. This set of variables is derived by linearising the

dependence of the energy barrier to nucleation upon the term(lnRp)�2 – see Eq. (7). Then a correlation is established betweenthe non-dimensional group R2

pH3 and the spray angle, as shown

in Fig. 21 on a logarithmic scale. This data reduction mechanism re-lies on the following reasoning. All experimental data entering thecorrelation have to meet simultaneously the following three crite-

Fig. 22. Spreading angle versus the parameter log R2pH

3

, evaluated at x/D = 15 forthree different fluids.

Fig. 23. Generalised correlations for the local spray angle, evaluated at differentaxial position. Validity range: 1 < Rp < 196, 2 < p1 < 100 kPa and three differentfluids.


ria: (1) to overcome the energy barrier to nucleation; (2) widerspray angles should correspond to larger nucleation rates (i.e. high-er Rp); and (3) due to volume depletion effects (see Section 5.2 fordetails), a logarithmic growth of the bubble-nuclei population isanticipated.

As can be seen in Fig. 21, the proposed data reduction schemeyields a very good description of the jet lateral spreading overthe entire range of back pressures. In an attempt to extend thisanalysis to other fluids, we point out that the non-dimensionalgroup log R2

pH3

does not include the influence of the kinetic

pre-factor on the nucleation rate (see Eq. (7) for more details).The latter controls the kinetics of molecular collisions and its orderof magnitude is largely determined by the mass of a liquid mole-cule m. This implies that, for a given value of the parameterlog R2

pH3

, substances with a lower molecular weight M (see

Table 4) will exhibit a wider spray angle. Fig. 22 confirms thisprediction and indirectly corroborates the functional dependencebetween the nucleation rate and the jet lateral spreading.

Following the same reasoning, we scaled the non-dimensionalgroup R2

pH3 by the quantity m2 and repeated the data reduction

procedure for different axial distances (x/D = 2, 5, 10, 15, 20 and40). The result of this exercise is shown in Fig. 23. Note that thedata for the location x/D = 20 have not been included in the plot,since they almost exactly overlap with the data acquired at x/D = 15 due to the barrel shape of the spray. As can be seen, it is pos-sible to establish a universal relation between the parameter� ¼ logðR2

pH3=m2Þ and the spray angle for each axial distance (with

x/D 6 40). Note that the proposed correlations cover a wide rangeof test conditions both in terms of superheat levels and back pres-sures (as summarised in Table 5) and are not limited to a single testfluid. This represents a noteworthy result when compared to thehuge scatter in literature data, where for each test fluid and backpressure a new empirical correlation is proposed.

For each axial position, then, a single analytical function can bederived to predict the spray angle as function of the parameter �.An example of this exercise can be found in Kamoun et al. (2010).

6. Conclusions and outlook

We have presented a unified treatment of the fully flashing dis-integration regime, valid for both standard and retrograde fluids.Bubble nucleation is identified as the rate-controlling process forthe transition to fully flashing. Specifically, the onset conditioncoincides with the surmount of the energy barrier to nucleationand is expressed in quantitative terms by the condition v = O(1).The latter basically represents the point where the excess in chem-ical potential, proportional to ln(Rp), equals the surface energywork. Comparison with the transition criterion based on the Janumber reveals a markedly different dependence upon the Wevnumber and the fluid properties. An important nontrivial predic-tion obtained by the newly introduced onset criterion is the in-crease of Rp,tr with decreasing back pressure, which is alsocorroborated by the experiments.

We have also explored the connection of the spray lateralspreading to bubble nucleation. By scaling the spray angle withthe (kinetic) controlling parameters for nucleation, it was possibleto derive a phenomenological model for predicting the spray con-tour in the near-nozzle region (x/D < 20). The model establishes adirect correlation between the jet lateral spreading and the popu-lation of bubble clusters: the larger the population the wider thespray angle. An important aspect of this correlation is that theexperimental observations fully adhere to the predictions of nucle-ation theory in small volumes (Kozíšek et al., 2011). In confinedvolumes, numerical solutions of the kinetic equation foresee an in-crease in the energy barrier to nucleation with depletion of the li-quid phase, while the number of critical nuclei stays basicallyconstant. This theoretical result is consistent with the logarithmicgrowth of the spray angle with Rp and the constancy of the Sautermean diameter at large Rp (Witlox et al., 2007), as they both corre-late directly with the population of bubble clusters.

The direct correlation between nucleation theory and spraymorphology has another important implication. Due to volumedepletion effects, secondary nucleation events can be excludedand the subsequent evolution of the superheated jet is basicallycontrolled by the vaporisation process. Since in regular vaporisa-tion the absorption of latent heat dominates, it follows that fluidswith a low heat of vaporisation (e.g. isooctane) will vaporise muchfaster, as corroborated by the experiments in this work. At high ini-tial superheat (typically Rp > 50), a second condition intervenes tolimit the rate of vaporisation: namely the attainment of the localmaximum mass flux (sonic condition). This gives rise to a super-sonic source flow, terminated by a complex shock structure tomatch the ambient pressure (Kurschat et al., 1992). The same


phenomenology is observed consistently in both standard andretrograde fluids, at least for low reduced injection temperatures(i.e. Tinj/Tc < 0.8). This result indirectly confirms bubble nucleationand growth as the controlling mechanisms for spray atomisationin the fully flashing regime. They represent, in fact, the only possi-bility to achieve fast vaporisation rates thanks to the exponentialincrease in the surface area and hence in the mass transport.

Acknowledgements

This work is performed within the framework of the ESA Net-working and Partnering Initiative (NPI) on ‘‘Modelling superheated(flash) atomisation and vaporisation’’. In addition the financial sup-port of the Carl-Zeiss foundation is gratefully acknowledged.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.ijmultiphase-flow.2013. 08.010.

References

Abramovich, G., 1963. The Theory of Turbulent Jets. The M.I.T Press.Blander, M., Katz, J., 1975. Bubble nucleation in liquids. AIChE J. 21, 833–848.Briggs, L.J., 1951. The limiting negative pressure of acetic acid, benzene, aniline,

carbon tetrachloride, and chloroform. J. Chem. Phys. 19, 970–972.Brown, R., York, J., 1962. Sprays formed by flashing liquid jets. AIChE J. 8, 149.Chehroudi, B., Talley, D., Coy, E., 2002. Visual characteristics and initial growth rates

of round cryogenic jets at subcritical and supercritical pressures. Phys. Fluids14, 850–861.

Cleary, V., Bowen, P., Witlox, H., 2007. Flashing liquid jets and two-phase dropletdispersion. I. Experiments for derivation of droplet atomisation correlations. J.Hazard. Mater. 142, 786–796.

Delale, C.F., Hruby, J., Marsik, F., 2003. Homogeneous bubble nucleation in liquids:the classical theory revisited. J. Chem. Phys. 118, 792–806.

Desnous, C., Cartellier, A., Meyers, N., 2011. Experimental investigation of explosivevaporization of c6f14. In: Taitel, Y. (Ed.), European Two-Phase Flow GroupMeeting, Tel Aviv, Israel.

Girshick, S., Chiu, C., 1990. Time-dependent aerosol models and homogeneousnucleation rates. J. Chem. Phys. 93, 1273–1277.

Gülen, S.C., 1994. On the possibility of shock-induced condensation in thethermodynamically unstable region. J. Non-Equilib. Thermodyn. 19, 375–393.

Günther, A., Wirth, K.E., 2011. Influence of the geometry of cylindrical nozzles onsuperheated atomization. In: 24th European Conf. on Liquid Atomization andSpray Systems, ILASS, Estoril (Portugal).

Günther, A., Wirth, K.E., 2012. Einfluss der Düsengeometrie auf Massenstrom undSpraycharakteristik bei überhitzter Zerstäubung. Chem. Ing. Tech. 84, 1–6.

Hsu, Y., 1962. On the size range of active nucleation cavities in a heating surface. J.Heat Transfer 84, 207–216.

Kamoun, H., Lamanna, G., 2012. Measuring the Velocity Field of a Flashing Jet. TN2000. ESA.

Kamoun, H., Lamanna, G., Weigand, B., Steelant, J., 2010. High-speed shadowgraphyinvestigations of superheated liquid jet atomisation. In: Proc. 22nd Conf. LiquidAtomization and Spray Systems, Paper ILASS2010-109, Cincinnati (USA).

Kawano, D., Ishii, H., Suzuki, H., Goto, Y., Odaka, M., Senda, J., 2006. Numerical studyon flash-boiling spray of multicomponent fuel. Heat Transfer—Asian Res. 35,369–385.

Kitamura, Y., Morimitsu, H., Takahashi, T., 1986. Critical superheat for flashing ofsuperheated liquid jets. Indust. Eng. Chem. Fundam. 25, 206–211.

Kozíšek, Z., Sato, K., Ueno, S., Demo, P., 2011. Formation of crystal nuclei near criticalsupersaturation in small volumes. J. Chem. Phys. 134, 094508(9p).

Kurschat, T., Chaves, H., Meier, G., 1992. Complete adiabatic evaporation of highlysuperheated liquid jets. J. Fluid Mech. 236, 43–59.

Lecourt, R., Barricau, P., Steelant, J., 2009. Spray velocity and drop sizemeasurements in vacuum conditions. Atomization Sprays 19, 103–133.

Lubetkin, S., Blackwell, M., 1988. The nucleation of bubbles in supersaturatedsolutions. J. Colloid Interface Sci. 26, 610–615.

McGraw, R., 2000. Scaling properties of the critical nuclei and nucleation rate. In:Hale, B., Kulmala, M. (Eds.), Nucleation and Atmospheric Aerosols, pp. 85–88.

McGraw, R., Laaksonen, A., 1996. Scaling properties of the critical nucleus inclassical and molecular-based theories of vapor–liquid nucleation. Phys. Rev.Lett. 76, 2754–2757.

McHale, J.P., Garimella, S.V., 2010. Bubble nucleation characteristics in pool boilingof a wetting liquid on smooth and rough surfaces. Int. J. Multiphase Flow 36,249–260.

Moreira, J.S., Vieira, M., Angelo, E., 2002. Highly expanded flashing liquid jets. J.Thermodyn. Heat Transfer 16, 415–424.

Nam, Y., Ju, Y., 2008. Bubble nucleation on hydrophobic islands provides evidence toanomalously high contact angles of nanobubbles. Appl. Phys. Lett., 93.

Oxtoby, D.W., 1998. Nucleation of first-order phase transitions. Acc. Chem. Res. 31,91–97.

Oxtoby, D.W., Evans, R., 1988. Nonclassical nucleation theory for the gas–liquidtransition. J. Chem. Phys. 89, 7521–7530.

Oza, R., 1984. On the mechanism of flashing injection of initially subcooled fuels. J.Fluid Eng. 106, 105–109.

Park, B., Lee, S., 1994. An experimental investigation of the flash atomizationmechanism. Atomization Sprays 4, 159–179.

Phan, H.T., Caney, N., Marty, P., Colasson, S., Gavillet, J., 2009a. How does surfacewettability influence nucleate boiling? C.R. Mec. 337, 251–259.

Phan, H.T., Caney, N., Marty, P., Colasson, S., Gavillet, J., 2009b. Surface wettabilitycontrol by nanocoating: the effects on pool boiling heat transfer and nucleationmechanism. Int. J. Heat Mass Transfer 52, 5459–5471.

Schmehl, R., Steelant, J., 2009. Computational analysis of the oxidizer preflow in anupper-stage rocket engine. J. Propul. Power 25, 771–782.

Schmelzer, J.W.P., Abyzov, A.S., 2011. On the theoretical description of nucleation inconfined space. AIP Adv. 1, 042160(9p).

Senda, J., Wada, Y., Kawano, D., Fujimoto, H., 2007. Improvement of combustion andemissions in diesel engines by means of enhanced mixture formation based onflash boiling of mixed fuel. Int. J. Engine Res. 9, 15–27.

Shen, V., Debenedetti, P., 2001. Density-functional study of homogeneous bubblenucleation in the stretched Lennard–Jones fluid. J. Chem. Phys. 114, 4149–4159.

Shen, V.K., Debenedetti, P.G., 2003. A kinetic theory of homogeneous bubblenucleation. J. Chem. Phys. 118, 768–783.

Sher, E., Bar-Kohany, T., Rashkovan, A., 2008. Flash-boiling atomization. Prog.Energy Combust. Sci. 34, 417–439.

Stotz, I., 2011. Shock Tube Study on the Disintegration of Fuel Jets at ElevatedPressures and Temperatures. Ph.D. Thesis, Universitaet Stuttgart.

Stotz, I., Lamanna, G., Weigand, B., Steelant, J., 2008. Shock tube study onhydrocarbon free jets using high-speed shadowgraphy. In: Proc. of the 15thAIAA Int. Space Planes and Hypersonic Systems and Technologies Conference.

Suk, N.Y., 2010. Surfaces with Controlled Morphology and Wettability for AdvancedPhase Change Heat Transfer Applications. Ph.D. Thesis, University of California(LA), USA.

Talanquera, V., Oxtoby, D.W., 1995. Nucleation of bubbles in binary fluids. J. Chem.Phys. 102, 2156–2164.

Thompson, P., Carofano, G., Kim, Y.G., 1986. Shock waves and phase changes in alarge-heat-capacity fluid emerging from a tube. J. Fluid Mech. 166, 57–92.

Thompson, P., Sullivan, D., 1975. On the possibility of complete condensation shockwaves in retrograde fluids. J. Fluid Mech. 70, 639–649.

Tucker, A.S., Ward, C.A., 1975. Critical state of bubbles in liquid–gas solutions. J.Appl. Phys. 46, 4801–4808.

Vieira, M.M., Simoes-Moreira, J., 2007. Low-pressure flashing mechanisms inisooctane liquid jets. J. Fluid Mech. 572, 121–144.

Witlox, H., Harper, M., Bowen, P., 2005. Flashing liquid jets and two-phasedispersion. In: American Society of Safety Engineers – 7th ProfessionalDevelopment Conference and Exhibition, pp. 236–243.

Witlox, H., Harper, M., Bowen, P., Cleary, V., 2007. Flashing liquid jets and two-phase droplet dispersion II. Comparison and validation of droplet size andrainout formulations. J. Hazard. Mater. 142, 797–809.

Yildiz, D., Rambaud, P., van Beeck, J., 2004. Break-up, droplet size and velocitycharacterizations of a two-phase flashing r134a jet. In: 5th Int. Conf. MultiphaseFlow.

Yildiz, D., Rambaud, P., van Beeck, J., Buchlin, J., 2006. Evolution of the spraycharacteristics in superheated liquid jet atomization in function of initial flowconditions. In: ICLASS.



http://refhub.elsevier.com/S0301-9322(13)00129-8/h0005



















































































towards a unified treatment of fully flashing sprays

Documents