Atomization regimes of a round liquid jet with near-critical mixing surface at high pressure

Proceedings of the Combustion Institute, Volume 29, 2002/pp. 633–640

ATOMIZATION REGIMES OF A ROUND LIQUID JET WITH NEAR-CRITICAL MIXING SURFACE AT HIGH PRESSURE AKIRA UMEMURA and YUICHIRO WAKASHIMA Department of Aerospace Engineering Nagoya University Nagoya 464-8603, Japan

Among a large number of reports on atomization, little is known about the characteristic feature of atomization occurring in a gas whose temperature and pressure exceed the critical values of the injected fuel. In the present study, microgravity experiments were conducted to examine the high-pressure atomization regimes of a round, SF6 liquid jet injected through a 0.1 mm diameter nozzle into N2 gas. The temperatures of SF6 liquid and N2 gas were fixed at 0.94 and 0.95 times the SF6 critical temperature, respectively, while the pressure of N2 gas was elevated from 1.3 to 2.4 times the SF6 critical pressure, so that the surface of the injected jet was in near-critical mixing state and the value of surface tension was smaller than one hundredth of the standard water value. The following were found. As pressure P increases, surface tension decreases and surface gas density increases, which makes turbulent atomization emerge at lower jet speed. The atomization regime of low-speed jet changes drastically at a certain pressure Pt ⳱ 7.6 MPa. At P ⬍ Pt, hydrodynamic-assisted capillary instability emerges immediately downstream of the nozzle exit and the liquid jet is disintegrated at a wavelength much shorter than one of Rayleigh instability. The analysis of this breakup mechanism identifies a new hydrodynamic-assisted capillary instability, which has the maximum growth rate proportional to jet speed and, thereby, is more unstable at low jet speed than the well-known Taylor instability. The disappearance of this type of capillary instability at P ⬎ Pt demonstrates that there exists a threshold value of surface tension for the capillary instability to be excited. At P ⬎ Pt, the liquid jet breaks into droplets with short spacing at a relatively large distance from the nozzle exit.

Introduction Liquid fuel must be atomized in a high-pressure environment for achievement of fast combustion and high-thermal efficiency. Hence, jet engines, diesel engines, and liquid rocket engines utilize atomization techniques to produce sprays at pressures exceeding the critical pressure of the fuel. Although significant advances have been made recently in the studies of droplet vaporization, ignition, and combustion characteristics [1,2], the mechanism of formation of droplets on which these studies are based is still open to investigation, especially for liquid jets injected into supercritical ambiences. There is a large volume of literature on atomization so far. Various theories based on Rayleigh [3] have been developed for different configurations of liquid jets and atomization regimes of interest [4]. Concerning round liquid jets, a review of Chigier [5] is available to address the advances in experimental atomization research. Three atomization regimes have been identified on the basis of experimental observation mostly at the atmospheric pressure [6]; namely, the Rayleigh, wind-induced, and turbulent atomization regimes. However, the underlying physics of the last two regimes are not fully understood.

Obviously, they will be modified at high pressures. It is easy to imagine that hydrodynamic contributions to liquid breakup will become more important as surface tension becomes small when the surface state of a liquid jet approaches the critical mixing state at high pressure. On the other hand, at such extremely high pressure that continuous phase change takes place, atomization of injected liquid no longer occurs. In fact, for high-speed jets encountered in liquid rocket engines, Mayer and Tamura [7] have observed that fine liquid ligaments formed by turbulent eddies diffuse out into the surrounding gas. Although important for the above-mentioned engines, the instability of a liquid jet with a nearcritical mixing surface, which provides a feature bridging the supercritical fluid jet instability and lowpressure liquid jet atomization, is not studied except for Chen and Sui’s experiment [8]. They examined the atomization of a liquid jet with temperature nearly equal to the critical temperature of a fuel at pressures nearly equal to the critical pressure of the fuel. SF6, which is a non-toxic and non-flammable fluid with critical temperature 318.7 K, pressure 3.76 MPa, and molecular weight 146, was used as a substitute of liquid fuel issued into N2 or CO2 gas.

633

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ENERGY PRODUCTION—Drop and Spray Flames Thermocouple(K-type) Pressure gauge N2 gas

Glass wool Vent cover

Electric band heater Heater power

Test section

High speed video camera

N2

Lamp Lens TV monitor /video recorder

PC video capturing ˚

Sapphire window Liquid SF6 Solenoidal valve

Nozzle Pressure gauge SF6 reservoir Thermocouple(K-type) Liquid SF6

Handling high pressure liquid pump

Fig. 1. Schematic of microgravity experiment setup.

The jet was issued vertically downward and the resulting spray angle was measured. The low-speed jet exhibited a vortical structure and seemed to be affected by the effect of gravity. In the present study, we conducted similar experiments in microgravity but with a different motivation to disclose a new feature which is overlooked in the past studies, that is, the hydrodynamic-assisted atomization characteristics of low-speed, near-critical mixing surface jet. Another motivation of this study is to get insight into turbulent atomization at high pressures. Developed from Dombrowski’s turbulent atomization model [9], it is now an established concept that fibers (ligaments) are peeled off the liquid surface by the action of hydrodynamic forces and then break into droplets. There is a recent numerical study supporting this cascade of liquid fragmentation [10]. An important point is that, at the stage of droplet formation, the velocity difference between the ligament and surrounding gas has reduced to a small value, because, otherwise, the ligament keeps deforming to a thinner one. Therefore, the observation of a lowspeed round liquid jet issued into a stagnant gas provides a basis to explore the breakup mechanism of ligaments involved in the turbulent atomization of high-speed jet. At low pressure, surface tension is large and gas density is small, so that the breakup of the liquid column obeys the Rayleigh mechanism. However, at high pressure, the small surface tension of the near-critical mixing surface jet makes hydrodynamic force effective to deform the liquid surface at small relative velocity, and a hydrodynamic-assisted liquid breakup process will become a main mechanism to produce droplets from ligaments. Hence, we examined the breakup process of the lowspeed liquid jet with a near-critical mixing surface in detail.

Experimental Method The schematic of the microgravity experiment setup is shown in Fig. 1 [11]. Following Chen and Sui, we used SF6 as a substitute for liquid fuel. SF6 liquid at 300 K was injected through a 0.1 mm diameter nozzle into N2 gas of 308 K which was confined in a thermally controlled, high-pressure chamber with inner diameter 100 mm and height 230 mm. In a 4 s duration of microgravity experiment, the jet speed U varies from about 1 m/s to zero, so that all atomization regimes relevant at a given pressure were captured in two runs with a different jet speed range. The back-lighted, magnified picture of the jet near the nozzle exit was taken with a high-speed video camera (1000 frames/s, shutter speed 1/12,000 s) through two 40 ␾ optical glass windows attached to the chamber. The N2 gas pressure P was changed from 5 to 9.1 MPa to examine the pressure dependence of atomization regime at various jet speeds. Remarks on Experimental Condition Near-Isothermal Flow When intensive vaporization occurs, it is difficult to obtain clear back-lighted images in microgravity because, without natural convection, a thick, dense SF6 vapor layer formed on the jet surface deflects light by lens effect. Therefore, the temperatures of SF6 liquid and N2 gas were set close to room temperature and the chamber pressure was elevated considerably above the SF6 critical pressure in order to produce a near-critical mixing surface jet with small vaporization rate. Consequently, the flow field realized in each microgravity experiment was almost isothermal, and the occurrence of unsteady transcritical phenomena [12] and sophisticated temperature control could be avoided. Because the ambient gas contains no SF6 vapor initially, SF6 liquid vaporizes and diffuses into the ambient gas. Thus, a thin SF6 vapor layer is formed on the near-critical mixing surface due to low diffusivity. (Note that the diffusion coefficient vanishes at the critical mixing surface [10]). Heat required for vaporization is supplied from both sides of the surface, which is at a lower temperature. However, since the latent heat in the near-critical mixing condition is small, the surface temperature drop is not significant. It should be noted that, according to the corresponding-state principle, the present experimental condition simulates the phenomena which would occur for a decane liquid jet of about 670 K issued into an air of temperature 700 K, which roughly corresponds to the condition encountered in diesel engines. Realization of Near-Critical Mixing Surface For the two-component system under consideration, the existence of liquid surface depends not only

HIGH-PRESSURE LIQUID JET ATOMIZATION N2 gas temperature T(Å)Å (reduced)

Åõ Surface observed (jet & falling droplets) Å: Jet has surface but no falling droplets Å~ No surface observed

61.5 (1.05)

45.5/3.76 (1.00,1.00)

5.64 (1.5)

a

7.52 (2.0)

b c

N2 gas pressure P(MPa) (reduced)

9.40 (2.5)

d

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As the pressure is increased from a to e, the surface state approaches the critical mixing state. At pressures exceeding point e, the jet has no surface. For reference, the experimental conditions of Chen and Sui are also shown in the figure. Pressure Dependence of Surface Tension

e

29.6 (0.95) SF6 liquid temperature (27Å) Chen & Sui exper. range

Fig. 2. Existence of surface for a SF6 liquid jet injected into high-pressure N2 gas. SF6 liquid jet of 300 K has the surface for the N2 gas state on the lower side of the solid curve. The broken line expresses the SF6-N2 critical mixing condition speculated from the present experimental data. Points a–e denote the N2 gas conditions used in the microgravity experiment.

on the chamber pressure but also on the temperatures of injecting SF6 liquid and surrounding N2 gas [12]. To identify the condition which realizes a nearcritical mixing surface jet, we examined the existence of liquid surface by injecting the SF6 liquid of 300 K upward into the N2 gas at various values of pressure and temperature under normal gravity. The results are shown in Fig. 2. When falling drops were observed, we judged that the jet had the surface and marked the gas condition with an open circle on the figure. We marked a triangle or a cross for the gas condition when no falling droplets were observed. Although the dynamics of a ‘‘low-speed’’ jet may be significantly influenced by gravity, the thermodynamic state (existence of surface) of a ‘‘high-speed’’ jet is not significantly affected by gravity. Therefore, this laboratory experiment provides a simple method to find the appropriate microgravity experiment conditions. It is notable that the jet has the surface up to more than twice the SF6 critical pressure for the N2 gas of 308 K. Points a–e show the experimental conditions adopted in the microgravity experiments.

Droplets formed from the jet often collide and coalesce. We estimated the value of surface tension by measuring the period of oscillatory deformation of a coalesced droplet [13,14]. The result is shown in Table 1 together with other properties. The measured value of surface tension rapidly decreases with increasing pressure and vanishes at a pressure between 9 and 10 MPa. Since water exposed to air at the standard state has the surface tension of about 70 dyn/cm, the jets produced in the microgravity experiments of conditions c–e have a surface tension of less than one hundredth of this water value.

Analysis of Experimental Results Figures 3ai and 3bi show a sequence of video images for P ⳱ 7 MPa (point c in Fig. 2) and 9.1 MPa (point e), respectively. The small jet speed U was measured from the video images, while the high jet speed was calculated from the variation of SF6 tank pressure recorded. The liquid flow injected from the nozzle is laminar for U ⬍ 1.4 m/s. The two sequences show that the atomization regime changes significantly with jet speed and pressure. We can identify two distances from the nozzle exit, where appreciable surface deformation is observed first (‘‘instability emergence distance’’) and the jet breaks into droplets (‘‘breakup distance’’). Their variations with jet speed at various pressures are shown in Fig. 4. The following are found from these experimental results, which will reveal how the atomization of high-pressure liquid jet is affected by the thermodynamic state of the jet surface through the changes in surface tension and surface gas density.

TABLE 1 Characteristic properties

Pressure P (MPa) 5.0 6.0 7.0 8.0 9.1

Surface Tension r (dyn/cm)

Bulk Gas-to-Liquid Density Ratio q/q*

Bulk Gas-to-Liquid Viscosity Ratio l/l*

Liquid Ohnesorge number (Z)

2.0 1.1 0.4 0.09 0.02

0.04392 0.05101 0.0593 0.06468 0.07126

0.254 0.243 0.235 0.219 0.218

0.00461 0.00646 0.01107 0.02405 0.05260

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Fig. 3. Atomization regimes of a round liquid jet with near-critical mixing surface.

Pure Hydrodynamic Instability

Fig. 4. Variations of characteristic distances of capillary instability with jet speed at various pressures. Experimental plots: xˆ, station where the jet surface deformation grows to an appreciable degree; ⳯, station where the jet breaks into droplets.

To understand the underlying physics of the observed atomization regime change, we start by considering the hydrodynamic instability of laminar jet flow in the neglect of capillary effect. The thickness of the gas-phase shear layer developing on the jet surface grows according to d ⳱ 1.72 冪vx/U, where v and x denote the gas dynamic viscosity and axial distance from the nozzle exit, respectively. A similar shear layer develops on the liquid side, but it grows more slowly. Thus, the type of instability excited on the jet differs, depending on whether d is greater than the jet radius a or not. The curve xa in Fig. 4 expresses the station where d becomes equal to a for P ⳱ 5 and 9.1 MPa. When the jumps in density and viscosity at the surface are relatively large, the liquid jet behaves like a rigid body for the surrounding gas, so that the gas-phase shear flow has a property similar to the wall boundary layer flow. This implies that the flow instability excited upstream of xa must be of the Blasius type (responsible to viscosity) [15], and

HIGH-PRESSURE LIQUID JET ATOMIZATION

introduces, in Fig.4, another curve xt ⳱ (Rec/1.72)2 (v/U) where local Reynolds number Re ⳱ Ud/v grows up to the critical Reynolds number Rec ⳱ 520. (Our linear stability analysis (omitted) shows that the critical Reynolds number does not change so much until the liquid surface becomes very close to the critical mixing state.) The excited instability wave has a wavelength of O(d). On the other hand, downstream of xa, the flow becomes unstable due to the presence of an inflexion point in the axial velocity profile. The wavelength of this instability wave is of O(a). Hence, two regimes, ‘‘low-jet-speed regime’’ and ‘‘high-jet-speed regime,’’ may be identified using the value of jet speed, Uc, at the intersecting point of the two curves xa and xt Atomization in High-Jet-Speed Regime U ⬎ Uc Once the gas-phase flow becomes turbulent and the fluctuating gas velocity is large enough to overcome the surface tension, the liquid surface will be largely deformed to lead to turbulent atomization. Thus, the decrease in surface tension and the increase in surface gas density with increasing pressure make turbulent atomization occur at lower jet speed as seen in Fig. 3. Atomization in Low-Jet-Speed Regime U ⬍ Uc The liquid jet upstream of xa may be destabilized by the presence of surface tension (capillary instability). At relatively low pressures, surface tension is relatively large. Therefore, Taylor (or Rayleigh) type of instability [16,17] emerges immediately downstream of the nozzle exit where the shear layer is thin and the velocity difference between liquid and gas phases is large. As it moves downstream, this capillary instability couples with the hydrodynamic flow instability, leading to the disintegration of the helically or axisymmetrically deformed liquid jet. At first glance, this atomization feature resembles the familiar one with atmospheric-pressure water jets, but it is found that more effective hydrodynamic mechanisms are involved in the jet disintegration process as described later. Since droplets are formed only through the excitation of axisymmetric instability, in what follows we focus our attention to such a low-speed jet that the typical, axisymmetric disintegration of liquid jet occurs. The most interesting feature found from Fig. 3 is that a drastic change (disappearance of Taylor instability) occurs at a certain pressure Pt between 7 and 8 MPa. Our laboratory experiment with finer increment of pressure disclosed that this change occurs at 7.6 MPa. Since, in this experiment, the value of surface tension most significantly changes with pressure, the drastic change in atomization regime demonstrates that (1) the instability appearing immediately downstream of the nozzle exit at P ⬍ Pt

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is caused by the presence of surface tension, and (2) there exists a threshold value of surface tension for the capillary instability to be excited. Thus, we may subdivide the low jet speed regime atomization into two types: ‘‘low-pressure type’’ at P ⬍ Pt and ‘‘highpressure type’’ at P ⬎ Pt. High-pressure type Note that the above-mentioned jet laminarization at P ⬎ Pt takes place where the shear layer is stable in the absence of surface tension. Surface tension contributes to hydrodynamics only through surface deformation. Small-surface deformation, which plays a similar role of disturbance to the Blasius type laminar flow, will be suppressed, unless the surface tension is so large that the flow induced by the surface tension pressure overwhelms the stabilizing effect of viscous flow. In addition, the application of Taylor theory to the near-critical mixing surface jet shows that the thin, dense SF6 vapor layer formed on the near-critical mixing surface also suppresses the excitation of Taylor instability. Therefore, the observed jet laminarization is found to be caused by the decreased surface tension and increased gas density which are intrinsic to the near-critical mixing surface jet. However, this does not mean that the liquid jet is not disintegrated at all. According to Weber’s analysis [18], a liquid column is unstable for the disturbance of wave number ka ⬍ 1 if Ohnezorge number Z ⳱ l*/冪rq*(2a) is less than unity. In the present experiment, Z takes a value of at most O(0.01) at P ⳱ 9.1 MPa. Therefore, the laminarized SF6 liquid jet must be disintegrated somewhere downstream. In fact, Fig. 3b shows the formation of droplets with small spacing at large distances from the nozzle exit. Low-pressure type Figure 4 shows that there is a jet speed range for which both instability emergence distance and breakup distance decrease with decreasing jet speed (U ⳱ 0.3⬃1 m/s). Interestingly, the breakup distance is located near the curve xa and the difference between instability emergence distance and breakup distance is almost independent of jet speed. These facts imply that the growth rate of the relevant instability is proportional to U/a (not U/d) and that the instability is coupled with the jet flow instability. Except at very small jet speeds for which Rayleigh instability becomes dominant, similar jet instability emerges at smaller jet speeds even though the emergence of capillary instability is fixed at the nozzle exit. The droplet formation process at such small jet speeds is especially interesting and we discuss it in the next section. Mechanism of Liquid Breakup at Short Wavelength Figure 3aii shows the disintegration process of the liquid jet issued with U ⳱ 0.1 m/s (liquid Weber

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Fig. 5. Breakup wavelength (solid circle) of O(1)-liquid Weber number jet shown in Fig. 3aii, plotted on RayleighTaylor solution diagram. The Rayleigh-Taylor theory yields unstable waves in the shadowed region. Axisymmetric breakup is impossible in the hatched region. The wavelength of most unstable wave at each Weber number is shown by the solid line.

N2 gas flow

Gas pressure acting on liquid surface Small Surface tension

Recirculating flow Dense SF 6 vapor layer

Fig. 6. Hydrodynamic-assisted breakup mechanism.

number We ⳱ qU2a/r ⳱ 1.66) at P ⳱ 7 MPa. The jet speed does not change significantly during the short period. The deformation of the liquid jet is approximately axisymmetric. Unlike Rayleigh instability, the liquid jet breaks into droplets without the formation of satellite droplets. In the figure, the

movements of constricted parts of the liquid jet and droplet centers are indicated by solid and broken lines, respectively. It is found that droplets are formed with small spacing. The shadowed region in Fig. 5 shows the condition for which the dispersion equation, derived from the combined Rayleigh [3] and Taylor [16] theories, yields unstable waves. The measured breakup wavelength (solid circle) is outside of the shadowed region, suggesting that the observed disintegration is brought about in a different mechanism from the classical theories. When a liquid column breaks up at a small wavelength, the generator lines of the column surface must take a large value of curvature at the constricted part. This implies that the effect of surface tension due to this generator’s deformation cancels the effect of surface tension due to the circumferential curvature and tends to stabilize the column deformation. Therefore, there must be other effects for the short-wavelength breakup to occur. One possibility is that the gas pressure acting on the constricted part becomes greater than the gas pressure acting on the swelling part in the formation of waketype gas flow around the liquid column. If their pressure difference is large enough, the flow induced in the liquid column can overwhelm the stabilizing effect of generator’s deformation (see Fig. 6). The near-critical mixing surface jet of liquid Weber number greater than unity has such a property, because Reynolds number Re ⳱ Ua/m ⳱ (m*/m)We1/2/Z takes a value greater than O(10) and the density of the SF6 vapor on the surface is comparable with the liquid density. Note that the gas pressure acting on the deformed liquid jet has a distribution similar to that of a series of spheres placed in a uniform stream U of relatively large Reynolds number [19] and has the same order of pressure variation as the gas stagnation pressure 0.5 qU2. In addition, the internal liquid flow, induced by the action of shear stress from the gas flow, also favors the breakup of the liquid jet (see Fig. 6). This hydrodynamic-assisted breakup mechanism, newly identified in the present study, is different from the Taylor instability which has been conventionally referred to as wind-assisted instability, because the Taylor instability is based on Bernoulli’s theorem and relies on a very large velocity difference between gas and liquid phases. In fact, in the realm of linear stability theory, the contribution of the surface gas pressure variation caused by the shear layer with thickness comparable with the jet radius is approximately proportional to the surface displacement and the gas dynamic pressure of the relative motion, yielding a maximum growth rate proportional to the relative velocity U [20], which is greater, at low jet speed, than the Taylor instability’s maximum growth rate proportional to U3. This is considered to be the reason why the present experiment shows the strong, short-wavelength instability at O(1)-liquid Weber number.

HIGH-PRESSURE LIQUID JET ATOMIZATION

The same hydrodynamic-assisted breakup mechanism may work in the high-pressure type, too, but at distances far downstream from the nozzle exit. Figure 3bii shows the successive formation of a droplet at the tip of liquid jet with a short distance of separation between droplets. The jet speed is 0.03 m/s and the liquid Weber number is 0.68. It should be noted that no other appreciable capillary deformation of the liquid column appears upstream of the deformed jet tip except that caused by the purely hydrodynamic instability. We numerically simulated the deformation process of a semi-infinitely long liquid column initiated by the rounding of the liquid column tip by surface tension. The result showed the formation of a spheroidal liquid bulb with length comparable with the column diameter at the liquid jet tip, but this liquid bulb tended to oscillate like the deformation of a spherical droplet and could not be pinched off from the upstream liquid column without the aids of hydrodynamic actions. Since the disintegration of an O(1)-gas-Webernumber jet may be regarded as the elementary process of turbulent atomization, the above-mentioned mechanism provides a candidate atomization mechanism of high-speed jet (usually, tens to hundreds of meters per second), which results in a dense spray consisting of fine droplets with much shorter spacing than that due to the Rayleigh mechanism. Since the droplets produced at short spacing are in the wake of leading droplets, they make pairs and coalesce to enlarge their spacing downstream. Conclusion Microgravity experiments were conducted to characterize the atomization regimes of a round liquid jet with near-critical mixing surface encountered in the formation of high-pressure sprays. The following were found. The gas-to-liquid density ratio nearly equal to unity and the very small surface tension of near-critical mixing jet make possible the disintegration of the liquid jet at short wavelength at relatively small velocity difference between liquid and gas phases. The instability identified in the present experiment has the maximum growth rate proportional to the relative velocity and is different from neither the wellknown Rayleigh instability (with growth rate independent of relative velocity) nor Taylor instability (with maximum growth rate proportional to the cubic power of relative velocity). As a result, the breakup occurs at small relative velocity. The shortwavelength breakup can be realized with the aid of the internal liquid flow induced by the shearing stress and pressure acting on the surface which are

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caused by the wake type of gas shear layer flow. There is a threshold value of surface tension for Taylor type instability to be excited. Acknowledgment The present study was partially supported by the Grantin-Aid for Scientific Research from Monbusyo and Space Forum, Japan.

REFERENCES 1. Yang, V., Proc. Combust. Inst. 28:925–942 (2000). 2. Bellan, J., Prog. Energy Combust. Sci. 26:329–366 (2000). 3. Rayleigh, L., Theory of Sound, Vol. 2, Dover Pub., New York, 1945, pp. 351–365. 4. Lefebvre, A. W., Atomization and Sprays, Hemisphere, New York, 1989. 5. Chigier, N. A., in Proceedings of the Fifth ICLASS, Begell House Inc., New York, 1991, pp. 1–15. 6. Reitz, R. D., and Bracco, F. V., in Encyclopedia of Fluid Mechanics, Vol. 3 (N. P. Cheremisinoff, ed.), Gulf, Houston, TX, 1986, pp. 233–249. 7. Mayer, W., and Tamura, H., J. Propul. Power 12:1137– 1147 (1996). 8. Chen, L. D., and Sui, P. C., in Proceedings of the IUTAM Symposium on Mechanics and Combustion of Droplets and Sprays, Begell House Inc., New York, 1994, pp. 307–316. 9. Dombrowski, N., and Fraser, R. P., Philos. Trans. R. Soc. London, Ser. A 247:101–130 (1954). 10. Li, J., Renard, Y., and Renard, M., Phys. Fluids 10:3056–3071 (1998). 11. Wakasima, Y., Hisida, K., and Umemura, A., in Japanese, Trans. Jpn. Soc. Mech. Eng. 68:885 (2002). 12. Umemura, A., and Shimada, Y., Proc. Combust. Inst. 26:1621–1628 (1996). 13. Rayleigh, L., Theory of Sound, Vol. 2, Dover Pub., New York, 1945, p. 373. 14. Antar, B. N., and Nuotio-Antar, V. S., Fundamentals of Low Gravity Fluid Dynamics and Heat Transfer, CRC Press, London, 1993, pp. 172–183. 15. Schlichting, H., Boundary-Layer Theory, McGrawHill, New York, 1979, pp. 438–463. 16. Bachelor, G. K., Collected Works of G. I. Taylor, Cambridge University Press, Cambridge, 1958. 17. Levich, V. G., Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, NJ, 1962, pp. 591–668. 18. Weber, C., Ztachr. f. Agnew, Math. Mech. 11:136–159 (1931). 19. Ramachandran, R. S., and Wang, T. Y., AIAA J. 29:43– 51 (1991). 20. Umemura, A., in Japanese, Trans. Jpn. Soc. Mech. Eng. 68:892 (2002).

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COMMENTS Josette Bellan, Jet Propulsion Laboratory, USA. This is a very nice piece of work. Are you aware of the complementary work of Chehrudy et al. [1,2] showing the change in the fluid breakup as a function of pressure? Their experiments are performed at 1g and show that as the pressure increases, the atmospheric-pressure atomization assumes at near-critical conditions the aspect of fingerlike structures emerging from the jet and dissolving into the surrounding fluid. At supercritical conditions, the jet assumes the characteristics of dense gas with very convoluted structures at the edge of the jet. By changing the composition of the fluid ratio which the jet is injected, they are able to change the critical point of the mixture and change the features of fluid breakup at a given far field pressure from the situation seen when the jet surrounding are composed of a single

chemical species. You may also want to consider the influence of the surrounding fluid composition. REFERENCES 1. Chehrudy, Coy, and Talley, AIAA (1999). 2. Chehrudy, Coy, and Talley, Phys. Fluids, recent paper. Author’s Reply. Thank you very much for your appreciation and valuable information. We were not aware of the authors’ cited papers, but we’ll study them soon. We know, at very high pressures, the liquid jet cannot be atomized and assumes the fingerlike structure, which eventually dissolves into the surrounding fluid. Our paper presents one of the aspects found from our experiments in which we tried to explore the way of transition from the atomization mode to the supercritical fluid jet mode.