JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER Vol. 16, No. 3, July– September 2002 Highly Expanded Flashing Liquid Jets J. R. Sim˜ oes-Moreira, ¤ M. M. Vieira, † and E. Angelo † Universidade de S˜ ao Paulo, 05508-900 S˜ ao Paulo, Brazil Results are presented of experiments with highly expanded ashing liquid jets along with a one-dimensional nu- merical model. The experiments were carried out with liquid iso-octane jets issuing from a small conical convergent nozzle into a low-pressure chamber. Images of the expanding jet off the nozzle exit section were obtained from a schlieren setup using a charge-coupled device camera. Analyses of these images enabled a qualitative visualization of the ashing jet structure and geometry. At very low backpressures, it has been observed that the emerging jet was formed by a central liquid core, and the phase change process occurred on the surface of that liquid core, giving rise to a sonic two-phase ow. In addition, it is also inferred that the freshly formed two-phase ow proceeded further to higher velocities and Mach numbers to terminate eventually with a complex shock wave structure to adjust pressures, as usual. A one-dimensional numerical analysis is carried out. The sudden phase change in the metastable liquid jet surface is modeled as an evaporation wave, for which the jump equations are solved. Next, the supersonic expansion of the two-phase mixture downstream of the evaporation wave is analyzed in a radial direction. The one-dimensional calculation yielded the radial position of the shock wave location. It has been found that the numerical results are consistent with the experimental data. Introduction I N some situations,a pressurizedliquidmay suddenlybe exposed to a low-pressure environment. If the environmental pressure is somewhat lower than the corresponding saturation pressure, the liquidwillundergoa fastphasetransitionprocess,commonlyknown as liquid ashing. Liquidashingstudiesarerelevanttoa multitudeof industrialand technological elds. As examples, one can mention the following: 1) Disastrous industrial accidents have occurred as a consequence of rupturing a pressurized liqueed gas storage tank. In the litera- ture, this phenomenon is known as boiling liquid expanding vapor explosion. 1 2) The liquid fuel preheatingprocess 2 has been investi- gated as a method of increasing fuel atomization for improvement of fuel injector technology. 3) Flashing mechanisms occurrence in expansiondevicesof refrigerationcycleshave been studied, 3 which may be a source of intense noise. 4) In the 1960s and 1970s, the nu- clear industry provided motivation for the study of the ashing phe- nomenon as it could occur in case of rupture 4 of pressurized water pipes.5)Otherapplicationsincludeseawaterdesalinationprocesses and ashing liquid jet analyses, 5;6 in a more fundamental sense. The experiments were carried out with liquid iso-octane (C 8 H 18 / jets issuing from a small conical convergent nozzle into a low- pressure chamber. Photographic documentation revealed the exis- tence of three liquid jet regimes: 1) continuous, 2) partially atom- ized, and 3) abrupt liquid evaporation with a two-phase supersonic expansion usually terminated by shock waves. Regime 1 occurred at backpressuresabove the vapor pressure at the initial testing tem- perature, so that no evaporation would occur. Regime 2 occurred at intermediate backpressure values. In the last situation, at very low backpressures(case 3), it has been inferred from photographic documentation 6¡9 (also Figs. 1– 4) that no phase transition or nu- cleation sites are observed in the liquid jet at the exit plane of the Received 4 June 2001; presented as Paper 2001-3036 at the AIAA 31st Fluid Dynamics Conference, Anaheim, CA, 11– 14 June 2001; revision re- ceived 26 February 2002; accepted for publication 28 February 2002. Copy- right c ° 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on conditionthat the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0887-8722/02 $10.00 in correspondence with the CCC. ¤ Professor, Escola Polit´ ecnica, SISEA—Alternative Energy Systems Laboratory, Mechanical Engineering Department, P.O. Box 61548; jrsimoes@usp.br. † Doctoral Student, Escola Polit´ ecnica, SISEA—Alternative Energy Sys- tems Laboratory, Mechanical Engineering Department, P.O. Box 61548. nozzle. Examination of still pictures taken using different photo- graphictechniques 6¡9 at a high shutterspeedallows one to conclude that the jet emerging from the nozzle remains in the liquid phase. In addition, a liquid core is usually visible down to several nozzle diameters, whereas ashing takes place on the surface of this liquid core. With the usual assumption of incompressibleow, the simpli- ed version of Bernoulli’s equation along with the measured mass ow rate implies that the emerging liquid must be highly super- heated or metastable at the nozzle exit section, that is, the liquid state has entered deeply into the metastable region. This description is validfor a low chamberpressure,that is,a backpressurevaluesub- stantially below the saturation pressure corresponding to the initial injection temperature. The main reason for working iso-octane is related to its retro- grade behavior, which means that a high degree of evaporation can bereachedduringa liquidashingprocess.As a consequence,retro- grade substances are quite suitable for documenting ashing liquid experimentsbecausea less dense cloud of dropletsshould surround the metastable liquid core, which evidently allows better and clearer pictures. A proper discussion of the retrograde behavior may be found in Refs. 10– 12. According to experimental data on mass ow measurements, choking-typebehavioris observedas the backpressureis decreased, while keeping the liquid injection conditions unchanged (also see Fig. 5). This brings up a puzzling question: Why does the ow be- come choked if (metastable) liquid phase emerges from the nozzle? It is well known that the speed of sound in liquids is far greater than that of vapors and gases and that the liquid cannot become easily choked, except at extremely high injection pressures, neither of which occurred in the aforementioned experiments nor in those discussed in this paper. Basedonexperimentalobservations,thispapercontributestoelu- cidating the ashing liquid jet problem. The present ndings of a metastableliquid jet emergingfrom the nozzle corroboratethe work carried out by previous researchers (see Refs. 5– 8, among others). The exiting jet comprises a liquid core from which a high-speed two-phaseoworiginates.Also,themetastabletwo-phaseowtran- sition region is circumscribed by an interface that surrounds that metastable liquid core. This interface has been well studied using the concept of evaporation waves, which are phase change discon- tinuities similar to deagration waves in a combusting gas. 7;10;11;13 Theevaporationwavetheoryleadsto adistinctivesolutioncalledthe Chapman– Jouguet (C– J) point. As is well known, the C– J solution means that the two-phase ow is sonic in relation to the evaporating interface. 415