PERGAMON Progress in Energy and Combustion Science 27 (2001) 483±521 www.elsevier.com/locate/pecs Effervescent atomization S.D. Sovani a, P.E. Sojka a,*, A.H. Lefebvre b a Maurice J. Zucrow Laboratories (formerly Thermal Sciences and Propulsion Center), School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1003, USA b Cran®eld Institute of Technology, and Purdue University, West Lafayette, IN 47907-1003, USA Received 5 May 1999; accepted 5 November 2000 Abstract Effervescent atomization is a method of twin-¯uid atomization that involves bubbling a small amount of gas into the liquid before it is ejected from the atomizer. The technique of bubbling gas directly into the liquid stream inside the atomizer body is essentially different from other methods of twin-¯uid atomization (either internal or external mixing) and leads to signi®cant improvements in performance in terms of smaller drop sizes and/or lower injection pressures. Furthermore, the amount of atomizing gas required is considerably less than what is employed in all other twin-¯uid atomization techniques. Effervescent atomization has been used successfully in a number of applications since its inception over ten years ago. It has been well studied during this period, and the published literature includes experimental and analytical investigations of both atomizer performance and the fundamental mechanisms involved in the atomization process. The literature also includes application-oriented studies that report the development of effervescent atomizers for gas turbine combustors, consumer products, furnaces and boilers, internal combustion (IC) engines, and incinerators. Through these studies a fair appreciation of the capabilities of the technique has been achieved. Continuing work is aimed at exploring the use of effervescent atomization in new areas, as well as acquiring a better understanding of current applications. More in-depth studies are also in progress on the various basic mechanisms that contribute to the overall atomization process. The purpose of this article is threefold. First, to summarize the results obtained from investigations of effervescent atomizer performance embracing wide variations in atomizer design, liquid properties, and operating conditions. Second, to review current theories on the basic mechanisms involved in the atomization process and to discuss the scope for future research. Third, to provide an overview of current applications and to suggest possible areas for future practical applications, including ®re suppression, paint sprays, agricultural sprays, and fuel injection for liquid-rockets and spark-ignition IC engines. q 2001 Published by Elsevier Science Ltd. Keywords: Effervescent; Twin-¯uid; Atomization; Spray Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Description of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Studies on fundamentals of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1. Drop size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.1. In¯uence of injection pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.2. In¯uence of atomizing gas-to-liquid ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.3. In¯uence of liquid type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.4. In¯uence of liquid physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * Corresponding author. Tel.: 11-765-494-1536; fax: 11-765-494-0530. E-mail address: sojka@ecn.purdue.edu (P.E. Sojka). 0360-1285/01/$ - see front matter q 2001 Published by Elsevier Science Ltd. PII: S 0360-128 5(00)00029-0 484 486 488 490 495 495 496 496 497 484 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 3.1.1.5. In¯uence of atomizer internal geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.6. In¯uence of ambient density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.7. In¯uence of atomizing gas molecular weight . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1.8. In¯uence of space and time coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2. Drop velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.3. Patternation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Spray cone angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.5. Spray momentum rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.6. Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Fluid mechanics of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Internal ¯ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2. External ¯ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Applications of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Gas turbine combustors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. IC engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Furnaces and boilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Incineration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Consumer products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Scope for future study and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Experimental studies on basic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1. Atomized liquid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2. Transient spray behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3. Fluid mechanics of effervescent atomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Modeling of the effervescent atomization process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction Most airblast and air-assist atomizers are of the externalmixing type in which the bulk liquid is ®rst transformed into a jet or sheet before being exposed to atomizing gas ¯owing at high velocity. Where internal mixing is employed, the impact between the high-velocity atomizing gas and the liquid takes place within the atomizer body. The effervescent atomizer falls into the category of `internal-mixing' but, in marked contrast to all other types of twin-¯uid atomizers, the atomizing gas is injected into the liquid at very low velocity to form a bubbly two-phase mixture upstream of the discharge ori®ce. Owing to its relatively low density, the gas occupies a signi®cant proportion of the total cross-sectional ¯ow area. This improves atomization by reducing the characteristic liquid dimensions within the discharge ori®ce. The atomization process is further enhanced by the rapid expansion of bubbles at the nozzle exit that shatters the issuing liquid stream into ligaments and drops. Since its inception over 10 years ago [1], effervescent atomization has been a topic of increasing interest and research, as illustrated in Fig. 1. This is attributed to its signi®cant advantages over other atomization methods in certain applications. The effervescent atomization technique was developed in 498 499 500 501 503 504 504 506 507 509 511 512 513 515 516 516 517 517 517 517 517 517 518 518 518 519 519 the late 1980s by Lefebvre and co-workers [1±4]. Although the term `effervescent atomization' was used colloquially right from the outset, it did not appear in any publication until Buckner et al. [5,6] in 1990. Prior to that the technique was described more formally as `aerated liquid atomization' by Lefebvre and co-workers [1±4]. One incentive to the development of effervescent atomization was the drawbacks associated with ¯ash atomization and dissolved gas atomization [7±9]. Flash atomization depends on the rapid evaporation (¯ashing) of a small portion of the liquid. Dissolved gas atomization relies on a dissolved gas coming out of solution to form bubbles. As a result, these techniques apply only to a limited range of liquids that are either highly volatile or which can hold a signi®cant quantity of dissolved gas. To avoid the practical problems associated with ¯ash atomization and dissolved gas atomization, Lefebvre and co-workers [1±3] introduced the technique of effervescent atomization whereby a gas is bubbled into the bulk liquid through an aerator to form a bubbly two-phase mixture upstream of the ®nal discharge ori®ce. This method of atomization is not restricted to volatile liquids or liquids that can hold a substantial amount of dissolved gas. Neither is the choice of gas restricted to those that can dissolve readily into the liquid. Furthermore, the bubble formation S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Nomenclature Roman symbols A Area, m 2 ALR Same as GLR when atomizing gas is air d Diameter, m D Drop diameter in Rosin±Rammler function, m E Entrainment number, dimensionless f Non-dimensional ¯ow behavior index, dimensionless GLR Gas-to-liquid ratio: ratio of mass ¯owrate of atomizing gas through the atomizer to that of liquid, dimensionless K Consistency index, kg/m-s n L length, m m_ Mass ¯ow-rate, kg/s _ M Momentum rate, N p Pressure, Pa pG Injection pressure, Pa q Exponent in Rosin±Rammler function representing drop size distribution width, dimensionless Q Variable in the Rosin±Rammler function representing the fraction of total volume contained in drops of diameter less than D, dimensionless SMD Sauter mean diameter, m process does not involve mass diffusion of dissolved gas to the nucleation sites, as in dissolved gas atomization, or energy diffusion necessary for evaporation, as in ¯ash atomization. These inherently slow processes necessitate the use of expansion chambers in ¯ashing and dissolved gas systems, limitations not found in effervescent atomizers. During the past decade, many detailed experimental studies have been carried out to determine the performance and spray characteristics of effervescent atomizers over wide ranges of operating conditions. The results of these experiments indicate that effervescent atomizers exhibit the following advantages over conventional pressure, rotary, and twin-¯uid atomizers: ² Good atomization can be achieved at injection pressures that are several times lower than those required by other types of atomizers [1,3,4,10]. ² For any given injection pressure, smaller drop sizes are obtained than those produced by more conventional methods of atomization [1,3,4,10]. ² Gas ¯ow-rates are much smaller than those employed in most other forms of twin-¯uid atomization [1,3,4,10]. ² Exit ori®ce diameters are larger than those of other atomizer types having a comparable ¯ow rate. This alleviates clogging problems and facilitates atomizer fabrication [2,5,10,11]. SR v V x X 485 Inter-phase velocity slip ratio, dimensionless Volume, m 3 Velocity, m/s Distance, m Constant in Rosin±Rammler function, m Greek symbols a Void fraction, dimensionless DpG Pressure drop across discharge ori®ce, Pa e A model coef®cient, dimensionless g Deformation rate, s 21 m Viscosity, kg/m-s r Density, kg/m 3 s Surface tension, kg/s 2 t Shear stress, Pa ty Yield shear stress, Pa Subscripts a Ambient gas e Entrained gas g Atomizing gas h Aerator holes j Jet l Ligament L Liquid o Atomizer discharge ori®ce x Conditions at atomizer exit plane ² In combustion applications, effervescent atomizerproduced sprays are conducive to lower pollutant emissions due to the presence of air (atomizing gas) in the spray core [1]. Fig. 1. Publications on effervescent atomization over last 12 years (data consolidated from the list of references). 486 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 2. A typical effervescent atomizer. ² Mean drop size is relatively insensitive to liquid viscosity. This means that a single atomizer can handle a variety of liquids without compromising performance [12±17]. ² Flow velocities in the discharge ori®ces of effervescent atomizers are much lower than those encountered in conventional atomizers because two-phase ¯ows choke at signi®cantly lower velocities than single-phase ¯ows. This reduces ori®ce erosion when handling liquids with solid suspensions [18,19]. ² The device is simple, rugged, and reliable. It requires little or no maintenance and can be operated at low cost [10]. The main drawback of effervescent atomization, which it shares with many other forms of twin-¯uid atomization, is the necessity of having a supply of pressurized gas. However, since the gas ¯ow-rates needed are small, this requirement can often be met with relative ease. 2. Description of effervescent atomization A typical steady-state effervescent atomizer is illustrated in Fig. 2 [21]. It consists of four main components: liquid and gas supply ports, a mixing chamber where the gas is bubbled into the liquid stream, and an exit ori®ce. In the geometry shown in Fig. 2, liquid is supplied to the atomizer through a port at the top and ¯ows down inside a perforated central tube to the exit ori®ce. The gas Ð referred to as `atomizing gas' Ð is supplied to an annular chamber surrounding the perforated central tube. The gas supply pressure is slightly higher than that of the liquid. Being at Fig. 3. Pressure jump at the nozzle exit for two-phase ¯ows at relatively low injection pressures. a higher pressure, the gas ¯ows through the perforations in the central tube into the liquid stream, and forms bubbles. The internal cavity of the central tube serves as the mixing section. The bubbly two-phase mixture formed ¯ows downward and is ejected through the exit ori®ce. A typical effervescent atomizer is approximately 100 mm long with a diameter of 50 mm, though individual designs could measure considerably different. Mixing chamber diameters have ranged from about 5±25 mm in different designs with typical exit ori®ce sizes lying between 0.1 and 2.5 mm. The ef®ciency of effervescent atomizers (in terms of energy needed for atomization) is found to be substantially higher than the ef®ciencies of pressure, rotary, and most forms of twin¯uid atomizers. This advantage over pressure and rotary atomizers stems in part from the fact that effervescent atomization is a twin-¯uid technique. Chawla [18] attributes the better atomization performance of twin-¯uid techniques over single-¯uid techniques to the substantial difference in the speed of sound between single and two-phase media, as discussed below. In a gas±liquid two-phase medium the speed of sound is markedly less than that in either of the individual phases. As an example, Chawla [18] notes that the minimum speed of sound in an air/ water mixture at standard temperature and pressure is 20± 30 m/s, as compared to 300 and 1500 m/s in the individual air and water phases, respectively. Since a two-phase ¯ow through a nozzle chokes at a signi®cantly lower velocity than that at which a singlephase ¯ow would choke, a two-phase ¯ow will experience S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 487 Fig. 4. Possible ¯ow regimes in the discharge ori®ce. a steep pressure jump at the nozzle exit, even at relatively low ¯ow velocities and low injection pressures, as illustrated in Fig. 3. Since atomization quality is greatly enhanced by the sudden pressure drop at the nozzle exit, it is possible to achieve good atomization with two-phase ¯ows even at low ¯ow rates and low injection pressures. Furthermore, due to its low sonic velocity, a two-phase ¯ow can remain choked while ¯owing through ori®ces larger than those required for single-phase ¯ows. As a result, a two-phase ¯ow can provide good atomization even with exceptionally large exit ori®ces. The lower sonic velocity of a two-phase mixture and the consequent pressure jump at the atomizer exit is an advantage that effervescent atomization shares with other internalmixing twin-¯uid atomization techniques. The speci®c reason for the better performance of effervescent atomizers over conventional twin-¯uid atomizers lies in the ¯ow structure immediately downstream of the discharge ori®ce. It is this ¯ow structure that is the distinguishing feature of effervescent atomization. It is described brie¯y in the following paragraphs. The principle of effervescent atomization has been investigated experimentally by Lefebvre and Sojka and their coworkers. Roesler [22] and Roesler and Lefebvre [3,23] conducted experiments to visualize both the two-phase ¯ow inside an effervescent atomizer as it approaches the exit ori®ce and the near-nozzle liquid break-up mechanism. Sojka et al. [12,24,25] also conducted experiments to visualize the two-phase ¯ow issuing from the atomizer exit ori®ce. These investigations into the internal two-phasephase ¯ow and the near-nozzle spray structure have provided useful insights into the principles of effervescent atomization. Roesler and Lefebvre [3,23] observed that the bubbly two-phase mixture formed in the mixing chamber evolves as it ¯ows towards the nozzle exit and may be in either a bubbly or slug ¯ow regime inside the discharge ori®ce, as illustrated in Fig. 4a±c. With bubbly ¯ow, the bubbles discharged from the ori®ce are immersed in the liquid jet. On leaving the ori®ce the bubbles experience a sudden pressure relaxation and expand rapidly, thereby shattering the liquid into drops, as shown schematically in Fig. 5. When the atomizer is operating in the slug ¯ow regime, the rapidly expanding gas slugs similarly break up the liquid. This is a key feature of effervescent atomization. The experiments of Sojka et al. [12,14±16,24,25] showed a similar mechanism of rapidly expanding bubbles shattering the liquid into drops. These workers also investigated the regime where the liquid forms an annular sheath within the discharge ori®ce which subsequently breaks up into thin 488 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 6. Schematic representation of the annular ¯ow, near-nozzle structure observed by Sojka and coworkers [6,24]. 2. The rapidly expanding gas phase has a shattering effect on the liquid ¯ow leaving the nozzle exit greatly enhancing ®ne atomization. The relative contributions made by these two factors vary with operating conditions. Generally, an increase in DpG/pa increases the contribution made by bubble expansion. Both these factors are characteristic features of effervescent atomization that distinguish it from other atomization techniques. Fig. 5. Schematic of the atomization mechanism observed by Roesler and Lefebvre [22,23]. ligaments due to the rapidly expanding gas core (see Figs. 4d and 6). Under the aerodynamic in¯uence of the atomizing and ambient gases the ligaments break up forming fragments that stabilize into drops. Since the liquid occupies only a small portion of the ori®ce cross-section, the diameter of each ligament, and hence the size of drops formed, is considerably smaller than the diameter of the ori®ce. It is emphasized that the supply pressure of the atomizing gas in an effervescent atomizer is only slightly higher than that of the liquid and is just enough to overcome the pressure drop across the holes in the aerator. Thus the relative velocity between the liquid and the gas is usually negligibly small. Unlike other forms of twin-¯uid atomization, effervescent atomization does not make use of the kinetic energy of a gas stream to enhance atomization. Instead it uses the atomizing gas to perform two separate functions: 1. The gas phase forces the liquid to ¯ow through a small fraction of the discharge ori®ce cross section, thus reducing the size of the liquid shreds and ligaments from which the drops are formed. 3. Studies on fundamentals of effervescent atomization The spray characteristics of main interest are drop size and velocity distributions, spray cone angle, patternation (the radial and circumferential distribution of the liquid throughout the spray), spray momentum rate, and entrained gas mass ¯ow-rate. In any atomization process these spray characteristics are dependent on several parameters including liquid physical properties, atomizer internal geometry, and operating conditions. The range of factors that in¯uence the characteristics of an effervescent atomizer-produced spray are presented in Fig. 7. These are the independent variables in effervescent atomization. The dependent variables are the spray characteristics of interest in most applications. The independent variables are classi®ed into categories as indicated by the boxes in Fig. 7. The variables that can be governed directly are listed as operating parameters. They include injection pressure drop and atomizing gas/liquid ratio by mass (GLR). Independent variables associated with the liquid include liquid physical properties and liquid type Ð Newtonian/non-Newtonian and single/multicomponent. Aspects of the atomizer internal geometry that in¯uence the spray characteristics are illustrated in Fig. 8. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 489 Fig. 7. Dependent and independent variables in effervescent atomization. They are described below: ² Outside±in/inside±out gas injection: there are two means of injecting atomizing gas into the liquid inside an effervescent atomizer. The design depicted in Fig. 2 employs `outside±in' gas injection geometry. In this case the liquid ¯ows inside a perforated tube and the atomizing gas is injected into it through holes in the tube wall. Outside±in designs have been used by many workers, including Roesler et al. [3,22,23], Buckner et al. [6,13], Panchagnula and Sojka [19], Satapathy et al. [21], Whitlow et al. [26,27], and Chen et al. [28±30]. The alternative approach is to use `inside±out' gas injection geometry whereby the gas ¯ows inside the perforated tube and bubbles outward into the surrounding liquid. Atomizers employing this concept are shown in Figs. 8 and 9. Inside± out designs have been investigated by Wang et al. [1,4], Lund et al. [14,15], Sutherland et al. [16,17], and Bush et al. [31,32]. The relative merits of the two different methods of gas injection have not yet been examined in detail. Experience suggests that inside±out designs are superior for low liquid ¯ow rates, while outside±in concepts perform better for high liquid ¯ow rates. The main factors that determine the ¯ow regime inside the atomizer exit ori®ce and hence the spray characteristics are as follows. ² Size, number, and location of aerator holes: the size and number of aerator holes can in¯uence bubble size and concentration, while the location of the aerator holes relative to the ®nal exit ori®ce in¯uences the evolution of the bubbly two-phase ¯ow. Fig. 8. Aspects of atomizer internal geometry. 490 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 9. Atomizer design featuring `inside±out' gas injection. ² Mixing chamber size, shape, and location relative to the ®nal exit ori®ce: the geometry of the mixing chamber is important as it governs the evolution of the internal twophase ¯ow. ² Contraction contour at the ori®ce inlet: the ¯ow undergoes a contraction as it enters the exit ori®ce. The contour at the ori®ce entrance in¯uences the ¯ow regime transition within the ori®ce. ² Pore size of ligament control insert: a ligament control insert is a porous plug that can (optionally) be ®xed at the entrance of the ®nal ori®ce, as illustrated in Fig. 10. It has been found that pore size can in¯uence spray characteristics [16]. ² Length and diameter of exit ori®ce: the diameter of the exit ori®ce governs the atomizer ¯ow rate, while the length/diameter ratio has a signi®cant effect on mean drop size. ² Pro®le of ori®ce exit: the edge of the ori®ce at the exit plane may be pro®led to alter spray characteristics. Examples of ori®ce exit pro®les are presented in Fig. 11. ² Number of exit ori®ces: if the two-phase ¯ow inside a multi-hole atomizer is not homogeneous, the sprays produced by individual holes will exhibit different characteristics. Other factors that in¯uence spray characteristics include gas molecular weight and ambient density. In addition to these independent variables, the spray characteristics are also dependent on space coordinates and time. In this section we review studies on the relationships between dependent and independent variables in effervescent atomization. The link between the independent parameters and the spray characteristics is the two-phase ¯ow inside and outside the atomizer. Studies investigating the internal and external two-phase ¯ow provide an understanding of the observed relations between the dependent and independent variables. They are discussed subsequently. Finally we review modeling work that investigates the functional relationships between the dependent and independent variables. A detailed list of the ranges of dependent and independent variables covered in this survey is presented in Table 1. 3.1. Experimental studies This section reviews experimental studies into the functional dependence of spray characteristics on the independent variables (as indicated in Fig. 7). In the following discussion each individual spray characteristic is considered separately and its dependence on the relevant independent S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 491 Fig. 10. Atomizer ®tted with a ligament-control insert [16]. parameters is reviewed in the following order: 1. Operating parameters Injection pressure (or liquid mass ¯ow-rate) GLR 2. Liquid type Newtonian/non-Newtonian Single/multi-component 3. Liquid physical properties Viscosity Surface tension Density 4. Atomizer internal geometry 5. Liquid-to-ambient density ratio 6. Gas molecular weight 7. Space±time coordinates Axial distance from the atomizer Radial distance from the spray centerline Time (transient characteristics) Fig. 11. Examples of indeterminate-origin exit ori®ces [59]. All results reported here were obtained by spraying liquids into ambient air. While the ambient air was at atmospheric temperature in all cases, its pressure was signi®cantly higher than standard atmospheric pressure in Ref. no. Author/s 492 Table 1 Range of parameters Range of independent parameters Dependent parameters investigated Liquid type Atomizing gas GLR Injection pressure Air injection geometry Exit ori®ce geometry Liquid to ambient density ratio 0.001 Nitrogen 2±22% 34.5±690 kPa Inside±out 0.8± , 850:1 1. Drop size 0.001 Air 0.1±5% 173±690 kPa Outside±in 0.5± , 850:1 1. Drop size 0.001 Nitrogen 2±23% 34.5±690 kPa Inside±out ± Air 4±18% 250±1050 kPa Outside±in Consistency index: 400± 840 cPs n21 0.1±13 Air 8.5±34% 0.88±2.0 MPa Outside±in Single ori®ce, 2.4 mm dia. Single ori®ce, 2.5 mm Single ori®ce, 2.4 mm Single ori®ce, 2.5 mm dia. Single ori®ce, mentioned Not mentioned 0.1±25% 207 kPa Inside±out and Outside±in [3] Water [4] Roesler and Lefebvre Wang et al. Water [5] Buckner et al. Coal±water slurry [6] Buckner et al. Glycerine±water± polymer mixtures Single component, Newtonian Single component, Newtonian Single component, Newtonian Two-component, non-Newtonian Three-component, non-Newtonian [11] Loebker and Empie Water±corn syrup mixture Multi-component, Newtonian [13] Buckner and Sojka Buckner et al. [14] Lund et al. [15] Lund and Sojka Hydrocarbon oil [17] [19] Sutherland et al. Panchagnula and Sojka Glycerine±water mixture Glycerine±water mixture Glycerine±water mixture and SNO oil Water, glycerine, SNO oil mixtures Water and other liquids Corn syrup Two-component, Newtonian Two-component, Newtonian Single and two-component, Newtonian Single component, Newtonian Single and twocomponent, Newtonian Single components, Newtonian Single component, Newtonian [20] Sovani et al. ± Newtonian [21] Satapathy et al. Non-combustible Two-component, diesel fuel substitute Newtonian 0.4±0.968 Air 5±40% 1.1±2.4 MPa Outside±in 0.4±0.968 Air 5±40% 1.12±2.35 Outside±in 0.001±0.080 Air 1±7% 239±515 kPa Inside±out 0.002 Air Not mentioned Not mentioned Inside±out 0.001±0.080 Air 0.5±4% 290±780 kPa Inside±out 0.001±0.080 Air 0.5±1.5% 250±800 kPa Inside±out 0.9 Air 2±10% Not mentioned Outisde±in 0.8± , 850:1 1. Drop size 0.5± , 850:1 1. Drop size dia. not , 1000:1 1. Drop size Single ori®ce, 7.5 mm dia. Not mentioned 1. Drop size Single ori®ce, 0.5± 2.5 mm Single ori®ce, 0.5± 2.5 mm dia Single ori®ce, dia. not mentioned 2 1000:1 2. Near nozzle spray structure 1. Drop size , 1000:1 1. Drop size , 800:1 1. Drop size Single ori®ce, dia. not mentioned , 800:1 1. Drop size Single ori®ce, 0.38 mm dia. Single ori®ce, dia. not mentioned Single ori®ce, 3.0 and 4.0 mm dia , 1000:1± 700:1 2. Drop velocity 1. Drop size 2. Near nozzle structure Not mentioned 1. Drop size , 1000:1 0.02±0.08 Air ± ± ± ± ± 0.001±0.010 Nitrogen 1±30% 11.4±33.1 MPa Outside±in Single ori®ce, 0.34 mm 857:1±16:1 dia. 1. Drop size 2. Drop velocity 3. Spray momentum rate 1. Drop size (model studies) 1. Drop size S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Viscosity range (kg/ms) Water Sutherland et al. Ambient conditions Liquid type Lefebvre et al. [16] Atomizer geometry Liquid name [1] [12] Operating parameters Table 1 (continued) Ref. no. Author/s Range of independent parameters Dependent parameters investigated Liquid type Liquid name [24] [25] [26] [27] Roesler and Water Lefebvre Santangelo and Water±corn syrup mixture and SNO oil Sojka Santangelo and Not mentioned Sojka Whitlow and Water Lefebvre Whitlow et al. [28] Chen et al. [29] Chen and Lefebvre Water Viscosity range (kg/ms) Atomizing gas GLR Injection pressure Air injection geometry Exit ori®ce geometry Liquid to ambient density ratio Single component, Newtonian Single and twocomponent, Newtonian Not mentioned 0.001 Air 0±0.8% 173±690 kPa Outside±in , 850:1 1. Internal ¯ow 0.1±0.82 Nitrogen 1±10% 102±1088 kPa Outside±in Single ori®ce, 0.5± 2.5 mm dia. Single ori®ce, 1.5 mm dia. , 1000:1± 700:1 1. Near nozzle spray structure Not mentioned 1±10% Not mentioned Not mentioned 0±60% 69±689 kPa Outside±in 0.2±1.2% 34.5±690 kPa Effervescent pressure swirl Single component, Newtonian 0.001 Not mentioned Air Single component, Newtonian 0.001 Air Water Single component, Newtonian Water±com syrup Single and twomixture and SNO oil component, Newtonian Air 1±8% 0.14±1.8 MPa Outside±in 0.001±0.1 Air 1±35% 0.14±1.8 MPa Outside±in Not mentioned 1. Near nozzle spray structure , 850:1 1. Patternation Single ori®ce , 850:1 Single ori®ce, 1.2± 2.4 mm dia. Single ori®ce 1.2± 2.0 mm dia. 2. Atomizer discharge coef®cient 1. Spray cone angle Outside±in Single ori®ce, dia. not mentioned , 1000:1± 700:1 ± Air 1±10% ± Inside±out Single ori®ce, 0.38± 0.51 mm dia. ± 0.0004±0.001 Air 1±10% Not mentioned Inside±out 0.00275 Nitrogen 1.5±30% 11±33 MPa Outside±in 0.001 Air 0.1±5% 173±690 kPa Outside±in ± Air 2±10% Not mentioned Outside±in Single ori®ce, 0.34 mm dia. Single ori®ce, 0.18± 0.34 mm dia. Single ori®ce, 0.5± 2.5 mm dia Single ori®ce, 1.5 mm dia. Three-component, non-Newtonian Consistency index: 400± 840 cPs n21 Air 8.5±34% 0.88±2.0 MPa Outside±in Single ori®ce, dia. not mentioned Single component Newtonian 0.001 Air 15±85% 930 kPa Outside±in Multi-ori®ce, 1 & 2 mm dia. [32] Bush and Sojka Water and hydrocarbon oils Wade et al. Viscor (calibrating ¯uid) Roesler and Water Lefebvre Geckler and Glycerine±water± Sojka polymer mixtures Single component, Newtonian Single component, Newtonian Single component, Newtonian Three-component, non-Newtonian [36] Buckner and Sojka Glycerine±water± polymer mixtures [37] Li et al. Water 1. A probe for measurement of effervescent spray momentum rate Not mentioned 1. Entrainment , 700:1 1. Drop size , 850:1 1. Internal ¯ow , 1000:1 , 1000:1 1. Near nozzle spray structure 2. Drop size 1. Drop size , 850:1 2. Near nozzle spray structure 1. Patternation (continued on next page) 493 0.14±1.8 MPa Bush et al. 1. Spray cone angle 1. Drop size 1. Liquid mass ¯ow rate 0±12% Water±corn syrup Single and twomixture and SNO oil component, Newtonian ± ± 2. Drop size 1. Drop size , 850:1± 100:1 , 1000:1± 700:1 Air [31] [35] 0.001 Single ori®ce, 1.5 mm dia. Single ori®ce, dia. not mentioned 0.001±0.023 Chen and Lefebvre [34] Ambient conditions Liquid type [30] [33] Atomizer geometry S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 [23] Operating parameters Table 1 (continued) Author/s Range of independent parameters Dependent parameters investigated Liquid type Wade et al. [43] Dutta et al. [44] Lund et al. [45] Lee and Sojka [47] Sojka and Geckler Chin and Lefebvre Chin and Lefebvre Sankar et al. [50] [51] [52] [53] [54] [55] [56] Viscosity range (kg/ms) Atomizing gas GLR Injection pressure Air injection geometry Exit ori®ce geometry Liquid to ambient density ratio A diesel fuel substitute Single component Newtonian 0.0027 Nitrogen 5±30% 11±33 MPa Outside±in Single ori®ce, 0.18± 0.34 mm dia. , 1000:1 Alberta sweet crude oil Alberta sweet crude oil Panchagnula et al. Sovani et al. Newtonian 0.005 Methane 5±20% 135±270 kPa Inside±out Newtonian 0.005 Helium and carbon dioxide mixture 5±50% Not mentioned Inside±out Glycerine±water± polymer mixtures Glycerine±water± polymer mixtures ± Three-component, non-Newtonian Three-component, Non-Newtonian ± Water Single component, Newtonian Single component, Newtonian Water Glycerine±water mixture and SNO100 & SNO-200 oils Luong and Glycerine±water Sojka mixture Sutherland et al. Water and other liquids [59] [64] Liquid type Luong and Sojka Sovani et al. Ambient conditions Liquid name Sutherland et al. Water, glycerine, SNO oil mixtures [57] Atomizer geometry Single and twocomponent, Newtonian Single and twocomponent, Newtonian Two-component, Newtonian Single component, Newtonian ± Air 3±12% 337±653 kPa Inside±out ± Air 2±10% Not mentioned Outside±in ± ± ± ± ± 0.001 Air 0.6±60% 172±848 kPa Inside±out 0.001 Air 5±35% 138±414 kPa Inside±out 0.001±0.080 Air 0.75±3.75% Not mentioned Inside±out Single ori®ce, dia. not mentioned Single ori®ce, 1.5 mm dia. ± Single ori®ce, 4.14 mm dia. Single annular ori®ce, 5 mm dia. Single ori®ce, 0.38 mm dia. 0.030±0.124 Air 1.5±7% Not mentioned Inside±out Single ori®ce, dia. not mentioned 0.02 Air 2% Not mentioned Inside±out 0.001±0.080 Air 0.5±2.0% Not mentioned Inside±out Single ori®ce, dia. not mentioned Single ori®ce, dia. not mentioned Non-combustible Two-component, Diesel fuel substitute Newtonian Not mentioned ± 0.00275 Nitrogen 1±12% 12.6±38.0 MPa Outside±in ± Air 0.5±1% Not mentioned Inside±out ± 0.05 Air ± ± ± Newtonian Single ori®ce, dia. not mentioned Single ori®ce, dia. not mentioned Single hole, 0.34 mm dia. Single ori®ce, dia. not mentioned ± , 700:1 , 460:1± ,5050:1 2. Drop size 1. Drop size 2. Spray cone angles 1. Combustion aspects 1. Drop size 2. Drop velocity Not mentioned 1. Drop size Not mentioned 1. Drop size ± 1. Drop size , 850:1 1. Internal ¯ow , 850:1 1. Drop size , 1000:1± 700:1 2. Mean velocity 1. Drop size 2. Drop velocity 3. Entrainment Not mentioned 1. Drop size Not mentioned 1. Drop size Not mentioned 1. Entrainment 2. Spray momentum rate 322:1±16:1 1. Spray cone angle Not mentioned 1. Entrainment ± 1. Drop size (model studies) S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 [42] Operating parameters 494 Ref. no. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 12. Variation of spray SMD with injection pressure and GLR [26]. certain experiments as mentioned at appropriate places in the following discussion. 3.1.1. Drop size Spray mean drop size and drop size distribution are the parameters of greatest interest in most applications. They have been investigated in most of the effervescent atomization studies reviewed in this article. 3.1.1.1. In¯uence of injection pressure. Mean drop size is strongly in¯uenced by injection pressure. Among the works reviewed, Lefebvre et al. [1,4] measured drop sizes at the lowest reported injection pressure (34.5 kPa) while Satapathy 495 et al. [21] and Wade et al. [33,42] obtained drop size data at the highest reported injection pressure (33 MPa). Most studies indicate that spray mean drop size is reduced by an increase in injection pressure [1±4,21,22,26,28,33±42]. Usually, the effect of a change in injection pressure is more pronounced at low injection pressures than at high injection pressures. The in¯uence of injection pressure on Sauter mean diameter (SMD) is illustrated in Figs. 12 and 13. The experimental data shown in Fig. 12 were obtained at the relatively low injection pressures that are of interest for gas turbine and spray coating applications [26], whereas the high injection pressures used to acquire the data contained in Fig. 13 are typical of those employed in diesel engines [21]. The drop sizes in Fig. 12 were measured on the spray axis 152 mm downstream of the discharge ori®ce while those in Fig. 13 were similarly measured on the axis at a distance of 100 mm downstream of the discharge ori®ce. The bene®cial effect of an increase in injection pressure in promoting ®ner atomization is clearly evident in these ®gures. An exception to the general rule that higher injection pressures improve atomization has been observed by Buckner et al. [12,13] in their studies on effervescent atomizerproduced sprays of Newtonian liquids having viscosities up to 0.968 kg/m-s. For these high-viscosity liquids they found that SMD was largely independent of injection pressure. Similar ®ndings were made by Buckner and Sojka [5,6,36], Geckler and Sojka [35], and Geckler [38] for highly viscous non-Newtonian liquids. Several workers have investigated the in¯uence of injection pressure on drop size distributions [1,3,4,26,28]. In all Fig. 13. Variation of spray SMD with injection pressure and GLR [21]. 496 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 cases the Rosin±Rammler function [10] was used to represent the distribution of drop sizes in the spray. It is usually expressed in the form  q D 1 2 Q ˆ exp 2 1† X where Q is the fraction of the total volume contained in drops of diameter less than D, and X and q are constants that are determined empirically. The exponent q provides a measure of the spread of drop sizes. Large values of q indicate narrow drop size distributions and vice versa. For most practical sprays the value of q lies between 1.8 and 3.5. Lefebvre et al.'s [1,4] initial studies on effervescent atomization indicated that the Rosin±Rammler parameter q decreased with increasing injection pressure, but in subsequent experiments by Chen et al. [28] and Whitlow et al. [26] the value of q remained fairly constant, regardless of changes in injection pressure. This disparity could be due to differences in atomizer geometry. The early studies employed the inside±out method of gas injection, with the gas injected into the liquid well upstream of the atomizer exit ori®ce, whereas the later studies employed outside±in gas injection, with the gas injected much closer to the exit ori®ce. However, a more likely explanation for the different results obtained in the two sets of experiments is the different range of GLRs over which they were conducted. It is now clear that Lefebvre et al.'s [1,4] initial studies were carried out with the atomizer operating almost entirely in the slug ¯ow regime, whereas the later experiments of Chen et al. [28] and Whitlow et al. [26] were con®ned mainly to the bubbly ¯ow regime, corresponding to a much lower range of GLRs (by a factor of ®ve). More detailed information on drop size distributions for effervescent atomizer-produced sprays, is contained in Dutta et al. [43], Lund et al. [44], and Lee and Sojka [45]. 3.1.1.2. In¯uence of atomizing gas-to-liquid ratio. The atomizing gas-to-liquid ratio by mass (GLR) is an important operating parameter in most applications since it is desirable to minimize the amount of atomizing gas supplied while maintaining a small mean drop size. Most of the studies reviewed in this article contain data illustrating the variation of spray mean drop size with changes in GLR. As mentioned earlier, effervescent atomizers operate at signi®cantly lower GLRs than most other types of twin-¯uid atomizers. Among the works reviewed, SMD data have been acquired for the lowest GLR (0.001) by Roesler and Lefebvre [3,22] and for the highest GLR (0.85) by Li et al. [37]. All the experimental evidence shows that spray SMD is a non-linear function of GLR, with mean drop size decreasing rapidly as GLR is increased from zero to around 0.03 and thereafter decreasing at a slower rate with further increase in GLR. A typical plot of SMD versus GLR is presented in Fig. 12. Several workers have examined the in¯uence of GLR on drop size distributions [1,3,4,26,28]. The early experiments of Lefebvre et al. [1,4] showed that q decreased with an increase in GLR but, as discussed above, this result is relevant only to the slug ¯ow regime. Of more practical interest are the results obtained by Roesler and Lefebvre [3], Whitlow and Lefebvre [26], and Chen et al. [28] for the bubbly ¯ow regime. These workers found that the distribution parameter q remained fairly constant, irrespective of changes in GLR. 3.1.1.3. In¯uence of liquid type. Most effervescent atomizerproduced sprays are formed using Newtonian liquids (see Table 1). Buckner and Sojka [6,36,46] studied the effervescent atomization of non-Newtonian liquids. They formulated mixtures of water, glycerine and xanthan gum polymer to form liquids with non-Newtonian rheological behavior. The rheological behavior was characterized by a power law relationship between the shear stress exerted on the ¯uid and its deformation rate: t ˆ ty 1 K g_ f 2† where t represents the shear stress, t y represents the yield shear stress, gÇ represents the rate of deformation, K is the consistency index, and f is a dimensionless ¯ow behavior index. Buckner and Sojka [6,36,46] found that spray SMD for a non-Newtonian liquid is larger than that for a Newtonian liquid with the same apparent viscosity. They attributed this phenomenon to the yield stress associated with the polymeric non-Newtonian liquids they used. They also reported that SMD does not vary with changes in K or f. Fig. 14 is typical of the results obtained. When considered along with other data obtained by Buckner and Sojka Fig. 14. In¯uence of liquid type on spray SMD [36]. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 [6,36,46], it indicates no consistent change in SMD with K, regardless of the air/liquid ratio and injection pressure employed. The non-Newtonian liquids used in spray applications can exhibit visco-elastic behavior [38]. The effect of liquid visco-elasticity on spray characteristics was studied by Geckler [38], Geckler and Sojka [35,47] and Lee and Sojka [45]. These researchers formulated mixtures of water, glycerine and polyethylene oxide (a polymer) to form liquids with different visco-elastic behavior. They found that SMD increased as the liquid visco-elasticity increased, either by increasing the polymer concentration in the mixture, or by extending the polymer chain length (i.e. increasing polymer molecular weight). Lee and Sojka [45] provide plots of drop size distribution for sprays of visco-elastic liquids. In some cases, they observed multi-modal drop size distributions (i.e. having multiple peaks) which they attributed to the simultaneous occurrence of different modes of primary breakup. Based on the work of Ferguson et al. [48], Lee and Sojka [45] surmised that the polymeric liquid they sprayed underwent phase change in the atomization process leading to two modes of breakup. The ®rst mode, termed `cohesive fracture', formed large drops while the second mode, termed `capillary failure', formed small drops. Buckner and Sojka [5] and Jardine [49] studied the characteristics of effervescent atomizer-produced sprays of multi-phase liquids. They sprayed mixtures of ground coal, water, and a polymer and noted that mean drop size did not change appreciably with changes in the size or quantity of solid particulate in the mixture. 3.1.1.4. In¯uence of liquid physical properties. The studies reviewed in this article used a variety of liquids spanning a wide range of physical properties (see Table 1). Among these studies, mean drop sizes are reported for the lowest liquid viscosity (0.001 kg/m-s) in several publications, and 497 for the highest viscosity (0.968 kg/m-s) by Buckner and Sojka [12,13]. Other workers have also examined the variations in mean drop size with change in liquid viscosity, including Lund et al. [14], Sutherland et al. [16,17], and Satapathy et al. [21]. Buckner and Sojka [12,13] found mean drop size to be independent of liquid viscosity, while Lund et al. [14] and Sutherland et al. [16,17] observed only a small effect of viscosity on drop size. Some of the results obtained by Lund et al. [14] are presented in Fig. 15. They show that a fourfold increase in viscosity produced only around a 15% increase in SMD. However, the experiments of Satapathy et al. [21], conducted at considerably higher injection pressures (11±33 MPa) than those employed in other studies (0.2±2.0 MPa), showed mean drop size to be strongly dependent on liquid viscosity and to increase markedly with an increase in viscosity. The in¯uence of liquid surface tension on atomization quality was studied by Lund et al. [14] and Sutherland et al. [16,17]. These researchers formulated mixtures of glycerine and water to produce liquids with different surface tensions. Spraying a liquid of 0.020 kg/m-s viscosity at an injection pressure of 377 kPa into atmospheric ambient pressure, Lund et al. [14] observed that SMD decreased appreciably when the surface tension was raised from 0.030 to 0.067 kg/s 2, as illustrated in Fig. 16. On the other hand, Sutherland et al.'s [16,17] measurements for the same two liquids indicated that SMD remained constant within the range of experimental uncertainty upon changing the surface tension from 0.030 to 0.067 kg/s 2. Sutherland et al.'s [16,17] ®ndings are different from Lund et al.'s [14] results possibly because the former researchers used an atomizer ®tted with a ligament-control insert while the atomizer of the latter workers did not have such an insert. Note that conventional atomizers invariably produce smaller drops as the surface tension is reduced [10]. Lund et al. [14] rationalized their unexpected results with the help Fig. 15. In¯uence of liquid viscosity on spray SMD [14]. 498 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 16. In¯uence of surface tension on spray SMD [14]. of a primary atomization 1 model that is based on the instability of ligaments in the near-nozzle region of the spray. This model is discussed later in this article. Although it neglects secondary atomization, 2 the Lund et al. model was able to accurately predict the scaling of drop size with surface tension because the experiments were conducted at low-mass ¯ow rates where primary atomization tends to be dominant [10]. Luong and Sojka [54,55] report the effect of liquid physical properties on spray unsteadiness. Using a phase/Doppler particle analyzer these researchers measured droplet sizes and velocities and deduced probability distributions of interparticle time (de®ned as the ratio of inter-particle distance to particle velocity). From a range of experiments conducted using liquids with different physical properties, these researchers concluded that spray unsteadiness increases with a decrease in viscosity and/or an increase in surface tension. 3.1.1.5. In¯uence of atomizer internal geometry. The atomizer internal geometry controls the gas±liquid ¯ow structure inside the atomizer and may strongly in¯uence atomizer performance. Several different atomizer designs have been described in the literature. Some of the studies reviewed in this article speci®cally consider the in¯uence of atomizer internal geometric parameters on mean drop size (see Table 1). The effect of the size and number of aerator holes on spray mean drop size was studied by Wang et al. [4] for an atomizer with inside±out gas injection, and by Roesler 1 Primary atomization indicates the ®rst breakup of the continuous liquid jet issuing out of the atomizer into fragments. 2 Secondary atomization refers to the subsequent breakup of liquid fragments formed in primary atomization into smaller fragments. and Lefebvre [3,22,23] for an atomizer with outside±in gas injection. They showed that multi-hole aerators produce slightly narrower drop size distributions than single-hole aerators with the same effective hole area. However, no explanation was offered for this effect. According to Chin and Lefebvre [50], an important geometric parameter in¯uencing spray mean drop size is the ratio of the ®nal discharge ori®ce area to the total area of the aerator holes (Ao/Ah). Their study showed that at low GLRs (,0.05), atomizers with low values of Ao/Ah (0.13± 0.28) produced ®ner sprays than those produced by atomizers with high values of Ao/Ah (2.64±3.1). They attributed this difference to the lower velocity at which the atomizing gas is injected into the liquid when the total area of gas injection holes is large (low Ao/Ah). This promotes the bubbly ¯ow regime inside the atomizer that has been reported to give the most ef®cient atomization [3,22,23,51]. Wade [40] and Wade et al. [42] studied how the location of the aerator holes relative to the ®nal discharge ori®ce affects mean drop size. They observed that mean drop size decreases when the aerator holes are located farther from the atomizer discharge ori®ce. They attributed this behavior to (unspeci®ed) changes in the internal ¯ow structure. Chin and Lefebvre [50] found that the convergence angle at the inlet of the exit ori®ce had little effect on spray mean drop size, provided it was less than 1208. The effect of ®nal discharge ori®ce diameter on drop size was examined by several investigators [1,3±5,13, 22,23,26,27,33,37,42], most of whom reported that drop size is largely independent of the ®nal discharge ori®ce diameter. However, Wang et al. [4] found that the smallest injector ori®ce (0.8 mm) provided the ®nest atomization at the lowest injection pressures, while the largest diameter ori®ce (2.4 mm) performed slightly better at higher injection pressures. Similar trends were observed by Wade [40] and Wade et al. [42] who measured the drop sizes produced by S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 499 Fig. 17. Discharge ori®ce geometries studied by Satapathy et al. [21]. an effervescent atomizer when operating at a very high injection pressure (33 MPa). They noted that the mean drop size decreased slightly as the diameter of the ®nal discharge ori®ce was increased from 0.18 to 0.34 mm. No arguments were put forward to explain this observation, but it could be due to the reduction in ori®ce length/diameter ratio, as discussed below. In all cases, the differences in drop size exhibited by nozzles of different injector-ori®ce diameter were always quite small. The conclusion to be drawn is that atomization performance is fairly insensitive to discharge ori®ce diameter. Chin and Lefebvre [50] found that the length to diameter ratio (l/d) of the ®nal discharge ori®ce had a signi®cant effect on atomization performance, with mean drop size decreasing as the l/d ratio was reduced. They attributed this to the lower frictional losses associated with a reduction in ori®ce l/d ratio. Satapathy [41] and Satapathy et al. [21] compared the drop sizes produced using the two different discharge-ori®ce geometries shown in Fig. 17. With the stepped ori®ce, atomization occurred inside the ori®ce as the ¯ow expanded suddenly. Drops impinged on the walls of the ori®ce, decelerated, and then coalesced, leading to much higher drop sizes than those obtained with the plain-ori®ce atomizer. Whitlow et al. [27] measured drop sizes for a `conicalsheet' effervescent atomizer. This atomizer is designed to eject the two-phase ¯ow through an annular passage in such a way as to form a hollow-cone spray. The dependence of spray mean drop size on injection pressure and GLR was found to be similar to that of plain-ori®ce effervescent atomizers. When operating at low injection pressures and GLRs, SMD increased slightly with an increase in width of the annular passage, but the in¯uence of this width on SMD diminished with an increase in either pressure or GLR. At the highest operating pressure (0.5 MPa), SMD became independent of gap width at all GLRs. Multi-ori®ce effervescent atomizers were studied by Whitlow et al. [27], Li et al. [37] and Dutta et al. [43] Whitlow et al. concluded that the performance characteristics of multi-hole atomizers are generally the same as those of single-hole atomizers for the same l/d ratio in the ®nal discharge ori®ce. Li et al. [37] found that changing the number of discharge ori®ces had no effect on mean drop size. Dutta et al. [43] made no performance comparison of their atomizer with a similar single-ori®ce atomizer. Sutherland et al. [16] studied the performance of effervescent atomizers ®tted with ligament-control inserts. The unique feature of this design is the inclusion of a porous plug located immediately upstream of the nozzle discharge ori®ce, as illustrated in Fig. 10. Some of the results obtained are shown in Fig. 18. Generally, it was found that this type of atomizer produces lower drop sizes than similar atomizers without a ligament control insert. It was also noted that mean drop size decreases with a decrease in the pore size of the ligament control insert. 3.1.1.6. In¯uence of ambient density. The effect of ambient gas density on spray mean drop size has been reported in a number of works. Chen et al. [28] investigated the effect of ambient density on the performance of an effervescent atomizer operating in the medium injection pressure range (0.14±1.8 MPa). It was found that a continuous increase in ambient gas density (above normal atmospheric) caused SMD to rise to a maximum value and then gradually decline. They attributed this characteristic to the combined effect of two different atomization processes. The basic effect of an increase in air density is always to improve atomization by raising the Weber number. However, at low ambient gas pressures, the atomization process is further enhanced by the release of energy contained in the bubbles. This additional source of energy declines with an increase in ambient air pressure, becoming zero when the latter attains the same value as the static pressure in the discharge ori®ce. At this condition the mean drop size attains its maximum value. These workers also noted that ambient density had no signi®cant effect on the width of the drop size distribution (as represented by the Rosin± Rammler parameter, q). Satapathy et al. [21] studied the in¯uence of ambient density on the performance of a high injection pressure (11.4±33.1 MPa) effervescent atomizer. At the lowest injection pressures they found that mean drop size increased with an increase in ambient density, as shown in Fig. 19. At 500 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 18. In¯uence of liquid viscosity and GLR on spray SMD for an atomizer with a ligament control insert [16]. higher injection pressures (22±33 MPa) the spray mean drop size was not affected by ambient density. These apparent differences between the results reported by Chen et al. [28] and Satapathy et al. [21] could be due to the different manner in which their experiments were Fig. 19. In¯uence of ambient pressure on spray SMD [21]. conducted. In Chen et al.'s [28] experiments the ratio DpG/ pG was kept constant to ensure that variations in ambient gas density did not affect the ¯ow velocity through the atomizer. Satapathy et al. [21] followed a different approach; they kept the injection pressure constant while varying the ambient pressure. This meant that any increase in ambient pressure was accompanied by a reduction in DpG/pa. Thus, in one case the investigation considered the combined effects of an increase in ambient pressure with a corresponding increase in injection pressure differential, while in the second case the results show the combined effect of an increase in ambient pressure with a decrease in injection pressure differential. Both sets of data are equally valid, but it is important to bear in mind that they represent two different modes of atomizer operation. 3.1.1.7. In¯uence of atomizing gas molecular weight. The in¯uence of atomizing gas molecular weight on the performance of an effervescent atomizer was studied by Lund et al. [44]. These workers found that an increase in this parameter led to a small increase in spray mean drop size, as illustrated in Fig. 20. They attributed this effect to shrinkage of the gas core and the resultant thickening of the liquid annulus inside the ®nal discharge ori®ce as gas molecular weight (and density) increased. Lund et al. [44] also found that the Rosin±Rammler distribution parameter q S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 501 Fig. 20. In¯uence of atomizing gas molecular weight and GLR on spray SMD [44]. decreased slightly with an increase in atomizing gas molecular weight. 3.1.1.8. In¯uence of space and time coordinates. The axial variation of mean drop-size in an effervescent atomizerproduced spray was studied by Whitlow and Lefebvre [26]. They employed low injection pressures (69±689 kPa) with outside±in gas injection, and measured mean drop sizes at different axial locations between 102 and 254 mm downstream of the atomizer discharge ori®ce. They found that axial distance had little effect on mean drop size for low GLRs (,0.008), but for higher GLRs (.0.010) mean drop size increased by up to 20% with an increase in downstream distance. This increase in mean drop size was attributed to the combined effects of evaporation and drop coalescence. Panchagnula and Sojka [19] experimented with a high viscosity liquid and obtained similar results, showing only a minor effect of downstream distance on mean drop size. Lund and Sojka [15] also studied the variation of mean drop size with axial distance downstream of the atomizer discharge ori®ce for a range of injection pressures from 0.24 to 0.52 MPa. They also observed a small increase in mean drop size with an increase in axial distance, which they attributed to drop coalescence. Lund and Sojka [15] developed a kinetic drop coalescence model and its prediction of a 0.5 mm increase in SMD with 1 cm increase in axial distance from the atomizer tip was found to match with the experimental observations. In the respect of SMD variation with axial distance from the atomizer, effervescent sprays are partially similar to sprays formed by airblast atomizers and pressure-atomized sprays. Zelina et al. [74] report that the SMD of airblast atomizers decreases initially (by approximately 10%) as the axial distance from the atomizer is increased but increases slightly (by roughly 5%) beyond a certain axial distance (25±35 mm). For a Diesel injector (which is essentially a pressure atomizer), Hardalupas et al. [75] report that SMD decreases signi®cantly (by about 50%) as the axial distance is increased up to distances between 200 and 400x/do, beyond which mean drop size is seen to increase slightly (by approximately 10%). Unlike Zelina et al. [74] and Hardalupas et al. [75], none of the effervescent atomization researchers have reported drop size in close proximity to the atomizer and hence effervescent spray characteristics cannot be compared with those of other atomizers in this region. However, like airlast and pressure atomized sprays, effervescent sprays are seen to exhibit a slight increase in mean drop size with an increase in axial distance from the atomizer in the region signi®cantly downstream of the atomizer. The radial variation of mean drop size in an effervescent atomizer-produced spray was examined by Panchagnula and Sojka [19], Lund and Sojka [15] and Sankar et al. [52]. Lund and Sojka's [15] experiments at low injection pressures (0.24±0.52 MPa) showed SMD increasing as the point of measurement was moved radially outward from the spray axis. This ®nding is consistent with the behavior of conventional pressure-swirl and twin-¯uid atomizers, and is to be expected since larger drops penetrate further against the aerodynamic drag forces due to their greater momentum. Similar observations were made by Sankar et al. [52] and also by Sutherland et al. [53] who examined the effect of a ligament-control insert on the radial variation of mean drop size. The presence of this insert appeared to have little effect, with mean drop size again increasing as the point of measurement was moved away from the spray axis. The only exception to the general rule that SMD increases with an increase in radial distance are the ®ndings of Panchagnula and Sojka [19] which showed fairly constant values of mean drop size at all radial locations within the spray cone. Fig. 21 is typical of the results obtained in this investigation. According to Panchagnula and Sojka [19] this radial uniformity of drop sizes within the spray is due to high turbulence levels causing rapid and complete mixing of drops. Very little consideration appears to have been given to the 502 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 21. In¯uence of radial position within spray on SMD [19]. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 possibility of transient variations of drop size in effervescent sprays, although such sprays were tested for unsteadiness by Luong and Sojka [54,55]. They transformed droplet arrival time data, measured using a PDPA, into inter-particle time distributions for various drop size bins. Their study indicated that effervescent sprays are inherently unsteady. This observation was supported by Bush and Sojka [32] who studied the entrainment characteristics of effervescent atomizer-produced sprays. They concluded that the observed variations in spray entrainment number for different liquids were due to different levels of spray unsteadiness. Sutherland et al. [16,56] conducted spray entrainment experiments similar to those performed by Bush and Sojka [32], but they used an atomizer with a porous ligamentcontrol insert ®tted upstream of the exit ori®ce. For a range of liquids Sutherland et al. [53] found that the addition of this insert reduced the variation in entrainment number to lower levels than those observed by Bush and Sojka [32]. They deduced that the presence of the insert damped the ¯uctuations in the two-phase ¯ow entering the exit ori®ce, thereby reducing spray unsteadiness. Another method of alleviating spray instabilities is by controlling the liquid velocity approaching the gas injection holes. According to Chin and Lefebvre [50], a liquid velocity of around 5 m/s represents a satisfactory compromise 503 between the con¯icting requirements of good stability and low pressure loss. 3.1.2. Drop velocity Knowledge of spray mean drop velocity and drop velocity distribution is important in several applications. For example, drop velocity in¯uences ®nish quality in paint sprays and transfer ef®ciency in consumer product and agricultural sprays. The effect of injection pressure on drop velocity was examined by Panchagnula and Sojka [19] and Sankar et al. [52]. As expected, they observed that drop velocities increase with increasing injection pressure. These workers also investigated the effect of gas/liquid ratio on drop velocity. They found that drop velocity increased steadily with an increase in GLR and concluded that the larger mass of atomizing gas exerted greater aerodynamic drag force on the drops, causing them to move faster. Lund et al. [44] studied the effect of atomizing gas molecular weight on drop velocity. They reported that numberaveraged drop velocity decreases with an increase in gas molecular weight. For any given GLR, as the gas molecular weight (and hence its density) is increased, the liquid phase occupies a larger portion of the cross-sectional area and thus discharges at a lower velocity. Panchagnula and Sojka [19] studied the radial and axial Fig. 22. In¯uence of radial position within spray on normalized drop velocity [19]. 504 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 variation of drop velocity in the spray produced by an effervescent atomizer featuring outside±in gas injection. Fig. 22 shows some of their results on the effect of radial distance on normalized mean velocity (normalized by the centerline velocity). The measurements clearly indicate that drop velocity is a maximum at the spray centerline and falls off rapidly with increase in radial distance from the centerline. Similar studies were conducted by Lund and Sojka [15] for an atomizer featuring inside±out gas injection, and by Sutherland et al. [53] for an atomizer ®tted with a ligament-control insert. All these studies show that drop velocity decreases with increasing axial distance downstream of the atomizer and with increasing radial distance away from the spray axis. Similar characteristics have been observed in the sprays produced by pressure and twin¯uid atomizers. No information is available in the literature on the effects of liquid type, liquid physical properties, atomizer internal geometry, and ambient gas density on drop velocities in effervescent sprays. importance in several areas. In combustion applications, local heat release rate and species concentration depends on the radial distribution of fuel. As mentioned above, for paint and coating sprays the radial liquid distribution determines both transfer ef®ciency and ®nish quality. Whitlow and Lefebvre [26] studied the radial liquid distribution in effervescent sprays for a single injection pressure and two values of GLR. The results indicate that the liquid mass ¯ux initially increases with increasing radial distance from the spray axis, reaching a maximum about half way between the spray axis and the outer edge of the spray, after which it decreases with any further increase in radial distance. There appears to be little or no available information on the effects of injection pressure, liquid type and physical properties, atomizer internal geometry, ambient gas density, atomizing gas molecular weight, or axial distance downstream of the atomizer on the radial distribution of liquid mass in an effervescent atomizer-produced spray. 3.1.3. Patternation The radial distribution of liquid mass within a spray is of 3.1.4. Spray cone angle The spray cone angles produced by conventional Fig. 23. Rapidly expanding spray cone downstream of atomizer exit. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 505 Fig. 24. Variation of spray cone half-angle with injection pressure and GLR [57]. single-ori®ce effervescent atomizers were investigated by Chen and Lefebvre [30], Wade et al. [42] and Sovani et al. [57]. Chen and Lefebvre conducted their experiments at intermediate injection pressures (0.14±1.8 MPa) while Wade et al. and Sovani et al. con®ned their experiments to high-injection pressures (11±38 MPa). The results obtained by all these workers show that spray cone angle increases monotonically with an increase in injection pressure. Chen and Lefebvre noted that the sprays produced in effervescent atomization have wider cone angles (by a factor of around 2) than the sprays produced by plain-ori®ce pressure atomizers. They attribute this wider spray angle to the rapid expansion of the atomizing gas bubbles downstream of the atomizer exit ori®ces. A photograph illustrating this rapid spray expansion is presented in Fig. 23. Wade et al. and Sovani et al. observed that the spray cone angle widened with an increase in GLR. They postulated that this increase in cone angle is due to the greater energy available for expansion of the atomizing gas core as it exits the atomizer. A typical plot representing the variation of cone half-angle with GLR and injection pressure is presented in Fig. 24. The cone half-angle values shown in this ®gure are typical of those obtained with single-ori®ce atomizers when operating at high injection pressures (20± 30 MPa). Chen and Lefebvre [30] observed a similar increase in spray cone angle with an increase in GLR. However, after attaining a maximum value the cone angle then declined slightly with a further increase in GLR. According to Chen and Lefebvre, this reduction in cone angle beyond its peak value is due to the reduction in bubble energy which occurs when continual increase in GLR causes the internal ¯ow structure to change gradually from the bubbly to the annular ¯ow regime. Chen and Lefebvre [30] also examined the effects of liquid viscosity and surface tension on spray cone angle. They found that reducing liquid viscosity and/or surface tension increased the spray cone angle, as illustrated in Figs. 25 and 26, respectively. The effect of ambient gas density on spray cone angle was investigated by Chen and Lefebvre [30] and Sovani et al. [57]. At low GLRs, where the atomizer operated in the bubbly ¯ow regime, Chen and Lefebvre found that an increase in ambient density caused the cone angle to contract. At higher GLRs, with the atomizer operating in the annular ¯ow regime, ambient density appeared to have little effect on cone angle. In contrast to these ®ndings, Sovani et al. [57] observed that spray cone angle widened with an increase in ambient gas density. For a proper interpretation of these results it is necessary to bear in mind that Sovani et al.'s experiments were carried out at extremely high injection pressures 506 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 25. In¯uence of liquid viscosity on spray angle [30]. Fig. 26. In¯uence of surface tension on spray angle [30]. (12.6±38.0 MPa), to enhance their relevance to diesel fuel injection, whereas Chen and Lefebvre's experiments were conducted at much lower injection pressure (0.24± 0.60 MPa), which is the range of interest for paint sprays and other spray coatings. Moreover, unlike Chen and Lefebvre, and Sovani et al. held the injection pressure at a ®xed value in their experiments while varying the ambient pressure. Thus, effectively, they reduced the injection to ambient pressure ratio as they increased the ambient pressure. This is another possible cause for the difference between Chen and Lefebvre's and Sovani et al.'s observations. The experiments of Chen and Lefebvre [30] and Sovani et al. [57] show that the total included cone angle of sprays produced by plain-ori®ce effervescent atomizers is always less than 238. This maximum angle is perfectly satisfactory for most applications, but there are some exceptions, one notable example being the fuel injectors employed in gas turbine engines which usually require spray cone angles of around 908. Whitlow et al. [27] addressed this problem by testing two different types of effervescent atomizer, both of which were designed to eject the two-phase ¯ow in a manner which yielded a wide spray cone angle. One atomizer was a plain-ori®ce design that featured four equispaced exit holes drilled at an angle of 408 from the central axis of the atomizer. The other atomizer, called the `conical-sheet' atomizer, ejected the two-phase ¯ow through an annular passage in such a way as to form a hollow-cone spray. Both atomizers performed very satisfactorily, and exhibited the same characteristics as plain-ori®ce airblast atomizers in regard to the effects of GLR and injection pressure on mean drop size and drop-size distribution. Of special interest is that the conicalsheet atomizer was entirely free of the ¯ow and spray instabilities that are often encountered with plain-ori®ce effervescent atomizers when operating at exceptionally high values of GLR. This absence of any form of instability suggests that the annular ¯ow passage of a conical-sheet atomizer promotes a ¯ow structure that is inherently more stable than the cylindrical passage of a plain-ori®ce atomizer. This is one of the reasons why Colantonio [58] elected to use the conical-sheet atomizer in his researches on low-emissions combustion. 3.1.5. Spray momentum rate Spray momentum rates are of interest in many applications because they in¯uence the entrainment characteristics and penetration distance of the spray. These properties are especially important in internal combustion (IC) engines because they determine the effective usage of air available for combustion. Momentum rates of effervescent atomizer-produced sprays have been measured by Bush et al. [31], Sutherland et al. [53,56], Panchagnula and Sojka [19], and Satapathy et al. [21]. All these investigators used an instrument developed by Bush et al. [31] for measuring the momentum rate of twophase free ¯ows. Bush et al. [31] made momentum rate measurements at a low injection pressure (0.515 MPa), while Panchagnula and Sojka's experiments were conducted at an intermediate level of injection pressure (3.8 MPa). Satapathy et al.'s experiments were carried out at the highest reported injection pressures (11±31 MPa). Sutherland et al.'s measurements were made on a ligament-controlled effervescent atomizer at the same injection pressure used by Bush et al. (0.515 MPa). All these workers studied the variation of spray momentum rate with injection pressure and GLR. As expected, their observations showed that spray momentum rate increased almost linearly with an increase in injection pressure and/or liquid mass ¯ow rate. They also found that spray momentum S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 507 Fig. 27. In¯uence of liquid ¯ow rate and GLR on spray momentum ¯ux [31]. rate increased linearly with an increase in GLR, which they attributed to the higher discharge velocity of the gas phase produced by an increase in GLR. A typical plot of spray momentum rate versus GLR is presented in Fig. 27. Satapathy et al. found that spray momentum rate became independent of GLR within the limits of experimental uncertainty at high injection pressures. This observation suggests that in a high pressure atomizer the increase in momentum rate due to higher gas velocity is offset by the decrease in momentum rate resulting from the reduction in liquid ¯ow rate. The in¯uence of liquid physical properties on spray momentum rate has been examined by Bush et al. [31] and Sutherland et al. [56]. Bush et al.'s results showed that spray momentum rate increases with increasing liquid viscosity. This ®nding was unexpected since an increase in viscosity should increase the dissipative losses inside the atomizer and thereby reduce the momentum rate. According to Bush et al. their result might be due to compressible phenomena and inter-phase shear in the ¯ow inside the atomizer. Bush et al. [31] and Sutherland et al. [53] found that spray momentum rate decreased slightly with an increase in liquid density. This was attributed to the decrease in liquid velocity that must occur if the density is increased and the liquid mass ¯ow rate is held constant. Sutherland et al. [56] compared the momentum rate of a spray produced using a ligament-controlled effervescent atomizer with the data reported by Bush et al. [31] for an atomizer having no ligament-control insert. The spray momentum rate for the atomizer ®tted with an insert was found to be lower, and this was attributed to the loss of momentum suffered by the two-phase mixture as it ¯owed through the insert. 3.1.6. Entrainment Entrainment is the process whereby ambient gas is drawn into the spray envelope as it expands downstream of the atomizer discharge ori®ce. It has important consequences in many spray applications. In combustion systems, entrainment affects the local equivalence ratio and hence the local temperature, heat-release rate, and species concentration. Entrainment also strongly in¯uences transfer ef®ciency and ®nish quality in paint and coating sprays, and is clearly an important consideration in spray drying applications. The entrainment of ambient gas into effervescent sprays has been studied by Bush [77], Sutherland et al. [53,56] and Panchagnula et al. [59]. Bush and Sojka used an atomizer operating at an injection pressure of 1.1 MPa, while Sutherland et al. used an atomizer ®tted with a ligamentcontrol insert operating at the same injection pressure. Panchagnula et al. used the same atomizer and the same 508 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 28. Schematic of global entrainment measurement method [31]. injection pressure as Sutherland et al. However, they changed the external geometry of the discharge ori®ce and studied its effect on entrainment. All researchers measured global entrainment rates using a measuring device developed by Bush and Sojka [32]. As shown in Fig. 28 the apparatus consists of a cylindrical chamber that surrounds the spray. The chamber has a circular opening at its lower end whose diameter is maintained almost exactly equal to the diameter of the spray at that axial location. This arrangement enables the spray to pass unhindered from the chamber to the atmosphere, but does not allow air to escape from the chamber to the atmosphere past the spray envelope. Air continuously ¯owing to the atmosphere from inside the spray cone is the net amount of air entrained by the spray inside the chamber. To compensate for the air entrained by the spray and carried out of the chamber through the spray cone, a continuous air supply is provided to the chamber through its porous side wall. The air ¯ow is accurately regulated such that air supplied to the chamber just equals the amount of air entrained by the spray. This equality is ensured by a micro-manometer that measures the difference between the chamber pressure and the atmospheric pressure. The ¯ow rate of air supplied to the chamber is measured using a rotameter. The ability of a spray to entrain gas is represented by the parameter `normalized entrainment', which is the ratio of the entrained gas mass ¯ow rate to the mass ¯ow rate of the liquid discharged through the atomizer, me/mL. Bush and Sojka [32] observed that the normalized entrainment at any given axial distance downstream of the atomizer was directly proportional to the liquid mass ¯ow-rate. They also found that the normalized entrainment at any given axial distance downstream of the atomizer ori®ce increased almost linearly with an increase in GLR. This was attributed to the corresponding increases in atomizing gas and liquid velocities at the exit plane of the discharge ori®ce. Similar observations were reported by Sutherland et al. [53]. Bush and Sojka [32] and Sutherland et al. [53] studied the effects of liquid viscosity and surface tension on entrainment. Both groups noted that entrainment is increased by an increase in either of these properties. Bush and Sojka [32] hypothesized that variations in viscosity and surface tension affect entrainment by changing the near-nozzle structure of the spray, but no detailed description of the mechanism involved was provided. Sutherland et al. [53,56] studied the entrainment characteristics of sprays produced by an atomizer ®tted with a ligament-control insert. This modi®cation appeared to have little effect on entrainment characteristics although the rates of entrainment were lower. This was attributed to the loss of momentum suffered by the twophase mixture as it ¯owed through the porous insert. Panchagnula et al. [59] examined the effect of changes in atomizer exit geometry on the entrainment rates of sprays produced by ligament-controlled effervescent atomizers. They found that entrainment rates for a pro®led exit ori®ce can be appreciably different (by up to 50%) than for a plainori®ce exit. They also reported that entrainment rates were higher for the double-point crown than for the single-point crown pro®le (see Fig. 11). The dependence of entrainment rate on axial distance downstream of the atomizer was studied by Bush and Sojka [32], Sutherland et al. [53,56] and Panchagnula et al. [59]. All these workers found that the amount of gas entrained into the spray was linearly proportional to the S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 509 Fig. 29. Typical entrainment characteristics of an effervescent atomizer [32]. axial distance downstream of the atomizer under all conditions. A typical plot of normalized entrainment versus downstream distance (normalized by the atomizer discharge ori®ce diameter) is presented in Fig. 29. Most research on the entrainment characteristics of effervescent sprays has tended to connect the entrained gas mass ¯ow-rate to the momentum rate of the spray via a nondimensional entrainment number. According to Ricou and Spalding [60] the normalized gas entrainment rate of a steady single-phase gas jet is directly proportional to the axial distance downstream of the injector ori®ce. They expressed this relationship as: r s 4 x re m_ e ˆE p do m_ j rj 3† where me/mj is the normalized entrainment, E the entrainment number, x the distance downstream of the discharge ori®ce, do the diameter of the discharge ori®ce, and r e and r j the densities of the entrained gas and the gas in the jet. Eq. (3) can be used to express the non-dimensional entrainment number E in terms of the entrained gas mass ¯ow-rate and jet momentum rate as: m_ e E ˆ q _ j re x M 4† Çj Ç e is the entrained gas mass ¯ow-rate, and M where m momentum rate of the jet at the exit plane of the discharge ori®ce. Bush and Sojka [32] conducted an analysis for twophase jets similar to that of Ricou and Spalding for singlephase gas jets. They obtained the following expression for normalized entrainment: r s   re GLRrL 1 SRrg † 1 m_ e 4 x 1 GLR ˆE p do SR rL rg m_ L 5† where SR is the inter-phase velocity slip ratio at the exit plane of the atomizer discharge ori®ce. Bush and Sojka calculated entrainment numbers using Eq. (5), after determining SR by measuring the atomizing gas and liquid mass ¯ow rates and the spray momentum rate. Ricou and Spalding [60] found that the entrainment number for steady gas jets remained constant at 0.32 for jet Reynolds numbers higher than 25,000. However, Bush and Sojka [32] found that the entrainment number for effervescent sprays was not constant and varied with operating conditions. They attributed this variability to the inherent unsteadiness of these sprays. Support for this hypothesis is provided by the ®ndings of Sutherland et al. [53,56] who observed fairly constant values of entrainment number when using an atomizer with a porous insert ®tted just upstream of the exit ori®ce. As discussed above, this insert reduces spray unsteadiness by damping the ¯uctuations in the two-phase ¯ow entering the exit ori®ce. 3.2. Fluid mechanics of effervescent atomization The dependent variables in effervescent atomization that represent the spray characteristics of most interest are linked to the independent variables through the two-phase ¯ow inside and outside of the atomizer. Independent variables such as operating parameters, gas and liquid physical properties, and various aspects of atomizer internal geometry, govern the ¯ow inside the atomizer. This internal ¯ow in 510 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 turn controls the external ¯ow structure that determines the dependent variables such as drop size and velocity through primary and secondary atomization. Thus, an investigation of the ¯uid mechanics of effervescent atomization is essential for understanding the relationships between spray characteristics and the range of independent parameters that are empirically observed to in¯uence these characteristics. The internal ¯ow in an effervescent atomizer is more complex than in most single and twin ¯uid atomizers, since it involves internal mixing of the liquid with the atomizing gas and the evolution of the two-phase, gas± liquid mixture as it ¯ows through the atomizer and out through the discharge ori®ce. Some aspects of the internal two-phase ¯ow and the external ¯ow structure downstream of the discharge ori®ce are illustrated in Figs. 4±6 and 30±33. As noted above, atomizing gas and liquid are conveyed to the atomizer through supply ports. The gas is supplied at a pressure slightly higher than that of the liquid and is bubbled into the liquid through a perforated aerator tube. The bubbly two-phase mixture evolves in the mixing chamber as it ¯ows toward the discharge ori®ce. Its evolution is in¯uenced by the gas injection geometry (outside±in/inside±out), the shape and size of the mixing chamber, the contraction contour upstream of the ®nal discharge ori®ce, the injection pressure, the gas/liquid ratio, and the liquid physical properties. The two-phase ¯ow may be in a bubbly, slug, or annular ¯ow regime as it enters the ®nal exit ori®ce. The gas phase expands rapidly as it discharges from the ori®ce and the liquid phase breaks up into ligaments. These ligaments rapidly become unstable and disintegrate into fragments that either undergo further breakup or stabilize forming relatively large drops. The following basic two-phase ¯ow phenomena are of interest with regard to the ¯uid mechanics inside and outside an effervescent atomizer. They are also represented in Fig. 30. Mixing chamber ± Bubble formation ± Transport and evolution of bubbles in a moving liquid stream (coalescence/breakup) ± Motion of individual phases Fig. 30. Fundamental two-phase ¯ow phenomena involved in effervescent atomization. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 511 Fig. 33. Near-nozzle spray structure for a visco-elastic liquid [38,47]. Fig. 31. Near-nozzle spray structure produced by bubble explosions [12,24]. Contraction upstream of the ori®ce ± Transition of the ¯ow regime as a two-phase mixture ¯ows through a contraction ± Two-phase ¯ow through porous media (in the case of ligament-controlled atomizers) Fig. 32. Illustration of near-nozzle `tree and root' spray structure [12,24]. Discharge ori®ce ± Two-phase ¯ow in a small/micro diameter pipes ± Compressibility aspects in two-phase ¯ows Outside the atomizer ± Free expansion of a pressurized two-phase ¯ow ± Motion of individual phases ± Ligament formation ± Primary breakup ± Secondary breakup In the following two sections we review the studies on the ¯ow inside and outside of an effervescent atomizer. 3.2.1. Internal ¯ow Roesler and Lefebvre [3,23] carried out the only reported experimental study on the ¯ow inside an effervescent atomizer. These researchers constructed an atomizer with a transparent section upstream of the ®nal discharge ori®ce. Photographic studies were conducted on the internal twophase ¯ow as it approached and passed through the exit ori®ce. The two-phase ¯ow characteristics observed immediately upstream of the discharge ori®ce were related to the near-nozzle spray structure downstream of the ori®ce and the mean drop size in the spray. Experiments were conducted using water and air over a range of pressures from 0.14 to 0.55 MPa and a range of GLRs from 0.005 to 0.10. At low GLRs the photographs show that single bubbles ¯ow one after another through the exit ori®ce, as illustrated in Fig. 5. As the jet discharges from the atomizer the bubbles contained within it expand rapidly and shatter the jet into ligaments and drops. With increasing GLR the number of bubbles within the mixing chamber increases until eventually a GLR is reached above which the bubbles start to coalesce and form voids in the ¯ow. This marks the end of the bubbly 512 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 ¯ow regime and the onset of the slug-¯ow regime. At this condition the spray may exhibit unsteadiness. Further increase in GLR suppresses these instabilities and the slug-¯ow regime gradually transitions into the annular¯ow regime whereby the ¯ow structure in the discharge ori®ce comprises a round jet of gas surrounded by a thin annular sheet of liquid, as shown in Fig. 4d. Roesler and Lefebvre's measured values of SMD, when plotted against gas/liquid ratio, show a continual reduction in SMD with an increase in GLR, with little to indicate the transitions between bubbly, slug, and annular ¯ow regimes. Chin and Lefebvre [51] used another approach for studying the effect of operating parameters, various aspects of atomizer internal geometry, and liquid physical properties on the ¯ow inside an effervescent atomizer. By applying data previously reported in the literature for two-phase ¯ows inside horizontal and vertical pipes to the ¯ow inside an effervescent atomizer, they were able to reach certain conclusions. Their results were presented in the form of ¯ow regime plots with traces representing the transition between different ¯ow regimes as one or more ¯ow variables are changed. They used these plots to show that an increase in injection pressure always extends the range of GLRs over which bubbly ¯ow can be maintained. For vertical ¯ows, it was found that an increase in GLR caused the ¯ow regime in the mixing chamber to transition from bubbly to slug, and then ®nally to annular ¯ow. In general, the ¯ow pattern in the discharge ori®ce is bubbly at low GLRs and annular at high GLRs. At very high GLRs (.0.40) the twophase ¯ow inside the ®nal discharge ori®ce is fully dispersed and discharges from the ori®ce in the form of drops suspended in the atomizing gas. Chin and Lefebvre noted that an increase in liquid viscosity promotes bubbly ¯ow in the mixing chamber, while the effect of surface tension is contrary to that of viscosity and signi®cantly smaller. Although Roesler and Lefebvre [3,23] correctly identi®ed the transition from bubbly ¯ow to slug ¯ow and the associated unsteadiness of the spray, they used this information only to de®ne an upper limit to the range of GLRs investigated. In a subsequent investigation, Whitlow and Lefebvre [26] studied the transition from bubbly ¯ow to slug ¯ow in more detail. They used a single-ori®ce atomizer operating at pressures from 0.069 to 0.69 MPa and GLRs from 0 to 0.06. Determination of the end of the bubbly ¯ow regime involved visual observations of the steadiness of the air and water supply pressures, and any other visual or audible sign that might indicate a change in the spray. At the lowest pressures investigated, the changeover from bubbly to slug ¯ow was abrupt and easily identi®ed. At higher pressures, the changeover was more gradual and determination of the transition point was more subjective. By assuming one-dimensional, steady ¯ow in the mixing chamber, Whitlow and Lefebvre showed that the maximum GLR at which the atomizer could remain in the bubbly ¯ow regime was given by GLRmax ˆ  rg rL  1 amax 2 1 21 6† where r g and r L are the gas and liquid densities, respectively, and a max the void fraction at the termination of the bubbly ¯ow regime. The void fraction, a , is de®ned as the ratio of the ¯ow area occupied by the gas to the total ¯ow area of the mixing duct. Whitlow and Lefebvre's [26] experimental data for air and water indicated that a max remained fairly constant at around 0.82. Hence, from Eq. (6)   rg GLRmax ˆ 4:6 7† rL Note that this equation relates only to the upper limit of GLR for operation within the bubbly ¯ow regime. As mentioned above, atomizers will operate quite satisfactorily at higher GLRs and will exhibit lower mean drop sizes with an increase in GLR. Very little information is contained in the literature on the bubble sizes involved in effervescent atomization. Roesler [3] employed a specially designed probe to collect quantitative data on bubble sizes in the two-phase ¯ow upstream of the discharge ori®ce. As expected, he observed a decrease in bubble size with an increase in injection pressure. The bubble size was also found to decrease slightly with an increase in GLR. This effect was attributed to the increase in gas injection velocity associated with a rise in GLR. 3.2.2. External ¯ow A detailed investigation of the near-nozzle structure of effervescent sprays was carried out by Santangelo and Sojka [24,25]. These workers used focused-image holography to visualize the structure of the spray near the atomizer discharge ori®ce. Their atomizer featured outside±in gas injection geometry and was operated in a low injection pressure range (0.1±1.1 MPa). Liquids spanning a range of physical properties were sprayed. Under different operating conditions Santangelo and Sojka observed two distinctly different regimes of near-nozzle structure. For GLRs less than 0.02, they noted that individual gas bubbles ¯owed in sequence through the exit ori®ce and were surrounded by a liquid sheath. A slug of liquid followed each bubble. After discharging from the ori®ce the gas bubbles expanded rapidly, exploded, and shattered both the surrounding liquid sheath, and to some extent, the liquid slug into ®ne shreds. An artist's rendition of this bubbly ¯ow breakup mechanism is presented in Fig. 31. At GLRs greater than 0.05 the atomizer operated in the annular-¯ow regime. The central gas core created by the coalescence of individual gas bubbles expanded rapidly and broke up the annular sheath into a ring of ligaments. The near-nozzle structure in this regime resembled a tree with the annular liquid sheath forming a S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 hollow trunk and the ligaments forming branches. An artist's interpretation of this is presented in Fig. 32. In both the bubbly and annular ¯ow regimes, the ligaments were observed to break up into fragments that stabilized forming drops. As the GLR was increased beyond 0.05 it was observed that the tree structure was maintained but the `trunk' became progressively shorter. An increase in GLR also caused the structure to evolve from a smaller number of thicker ligaments to a larger number of thinner ligaments. This explains the decrease in spray mean drop size with an increase in GLR as reported by several researchers. Buckner and Sojka [12] took high-speed photographs to study the near-nozzle spray structure when ¯owing highviscosity Newtonian liquids. They observed the same bubble expansion and liquid-shattering mechanisms as those observed by Roesler and Lefebvre [3,22,23] and Santangelo and Sojka [23,24]. They also took shadowphotographs of the near-nozzle region of the spray and found a diamond-like pattern that they assumed was gas expansion and compression waves emanating from the atomizer discharge ori®ce. This observation con®rms that under conditions of high DpG/pa the two-phase ¯ow is choked as it leaves the ori®ce. It also helps to explain the results obtained by several researchers that indicate that spray mean drop size is constant over a range of ori®ce diameters. Geckler [38] and Geckler and Sojka [47] studied the near nozzle structure of sprays formed with visco-elastic (nonNewtonian) liquids using focused image holography. For such liquids the near nozzle structure is not characterized by the typical bubble expansion mechanism or the trunk with branching ligaments mechanism. Owing to the elastic properties of the liquid, an annular net-like structure is observed over a wide range of GLRs, as illustrated in Fig. 33. Sutherland et al. [16] studied the near-nozzle structure of the sprays produced by a ligament-controlled effervescent atomizer. Their observations were very similar to those of previous workers [3,12,22±25]. Even with the insert ®tted immediately upstream of the atomizer discharge ori®ce, the two-phase ¯ow discharged in the form of a central gas core surrounded by a ring of ligaments. The size of the ligaments, however, was controlled by the size of the pores on the insert. Little information is available on the near-nozzle structure of sprays produced by effervescent atomizers when operating at high injection pressures (.10 MPa) or with very small ori®ces (,0.5 mm diameter). Furthermore, the effect of atomizer internal geometry or ambient density on the near-nozzle structure has not been investigated. 3.3. Modeling Effervescent atomization involves complex two-phase phenomena that are dif®cult to model. It is not surprising, 513 therefore, that only a few modeling studies have been reported in the literature. The substantial bene®ts of having a comprehensive atomization model that would be able to predict spray characteristics from inputs of atomizer geometry and operating characteristics are obvious. Signi®cant efforts have recently been directed at the development of such overall models for several atomization processes. (An example is the work of Liao et al. [72] who are developing a comprehensive model for pressure-swirl atomization.) An ideal, comprehensive model of effervescent atomization would have the capability to predict spray characteristics from ®rst principles. With an input of values for independent parameters such as injection pressure, GLR, and liquid physical properties, the model would be able to predict spray characteristics such as drop size and velocity distributions, spray momentum rate, etc. The probable structure of such a model is illustrated in Fig. 34. As indicated in this ®gure, a comprehensive model of effervescent atomization would need to have sub-models for phenomena such as ¯ow-regime transition and compressible two-phase ¯ow inside an ori®ce. Some researchers have formulated portions of such a comprehensive model. Their efforts have concentrated mostly on modeling the external ¯ow, for which detailed experimental investigations are described in the literature [22±25]. Similar detailed experimental studies on all aspects of the internal two-phase ¯ow have not yet been conducted, due in part to the considerable dif®culties involved in building a transparent atomizer. Consequently, sub-models for effervescent atomizer internal ¯ows are unavailable at this time. External ¯ow sub-models have been reported by Buckner and Sojka [6,36], Lund et al. [14], and Panchagnula and Sojka [19]. The models of Buckner and Sojka and Lund et al. were aimed primarily at predicting spray mean drop size. Buckner and Sojka [6,36] developed a model for predicting the spray mean drop size from a knowledge of atomizing gas and liquid mass ¯ow rates and liquid physical properties. They considered a control volume that enveloped the spray cone extending downstream from the atomizer exit plane. Global conservation of mass, momentum, and energy were applied to the control volume. Atomizing-gas and liquid velocities at the nozzle exit plane, necessary for determining the momentum and energy entering the control volume, were estimated from a correlation available in the literature for void fraction and inter-phase velocity slip ratio [61]. Atomizing-gas and liquid velocities leaving the control volume were assumed to be equal and were determined from conservation of mass and momentum. The total energy entering the control volume was equated to the total energy leaving the control volume to obtain a relation for spray SMD. The energy entering the control volume was assumed to be the sum of the atomizing gas and liquid kinetic energies and the surface energy of the gas bubbles embedded in the liquid. The energy leaving the control volume was 514 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 Fig. 34. A comprehensive model for effervescent atomization. assumed to be the sum of the atomizing gas and liquid kinetic energies and the surface energy of the drops. The following relation was obtained for spray SMD: SMD ˆ 12s 2 1 eGLR V 2 2 ‰ V 2 r{V Lx gx Lx 1 eGLR VLgx † Š=‰1 1 eGLRŠ} 8† where s and r represent the liquid surface tension and density, GLR represents the atomizing gas-to-liquid ratio by mass, and V represents velocity. The subscript L indicates liquid, g indicates atomizing gas, and x indicates conditions at the atomizer exit plane, e is a model coef®cient that is determined from the experimental data. Buckner and Sojka [36] reported that predictions made by this model matched the experimental data within 25%. A more fundamental model was developed by Lund et al. [14] for predicting drop size from a knowledge of atomizing gas and liquid mass ¯ow rates, liquid physical properties, and atomizer exit geometry. The model, which is fully consistent with the visualization studies of Santangelo and Sojka [24,25], employed an available stability analysis of these structures to determine the size of drops formed. It assumed that the two-phase atomizing gas and liquid mixture is discharged from the atomizer in the form of a S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 central gas core surrounded by an annular liquid sheath. The sheath disintegrates into a ring of ligaments that further break up and form drops due to the aerodynamic in¯uence of the surrounding gas. Lund et al. used a correlation reported in the literature to determine the void fraction and inter-phase slip ratio for the annular liquid±gas ¯ow emanating from the atomizer discharge ori®ce. They calculated the thickness of the annular liquid sheath from the void fraction and ori®ce diameter, and then assumed that this annular sheath splits up into several cylindrical ligaments each having almost the same diameter as the thickness of the annular sheath. The stability analysis reported by Weber [62] for the breakup of cylindrical liquid jets was applied to the ligaments and the size of the fragments broken off from the ligaments was calculated. The size of drops formed was calculated assuming that each fragment stabilized to form one drop. Secondary atomization was neglected. From this model Lund et al. obtained the following expression for spray SMD: "  1=2 #1=3 3 p 3 3mL SMD ˆ 2pd 1 1 1 p 9† 2 rL s L d1 where d1 represents the ligament diameter and r L, m L and s denote the liquid density, viscosity, and surface tension, respectively. Lund et al.'s model is of special interest because it is based entirely on ®rst principles and contains no empirical constants. As illustrated in Figs. 15 and 16 the accuracy of this model increases with an increase in ALR. Drop-size is over-predicted by approximately 25% (compared to corresponding experimental data) for ALRs below 0.02 but is predicted to within about 5% of the measured values at ALRs of 0.04 and more. As mentioned above, the Lund et al. model incorporates the stability analysis performed by Weber [62] for cylindrical liquid jets. This analysis does not take into account the aerodynamic effect of the gas surrounding the (assumed) cylindrical ligament. In effervescent atomization, however, there is always a relative velocity between the atomizing gas and the liquid that can have a signi®cant effect on ligament breakup. Sutherland et al. [16] improved Lund et al.'s model by incorporating the effect of relative velocity between the atomizing gas and the liquid, by replacing Weber's stability analysis with the stability analysis of Sterling and Sleicher [63]. Furthermore, instead of the slip ratio correlation used by Lund et al. for determining atomizing gas and liquid velocities at the atomizer exit, Sutherland et al. actually measured spray momentum rates to obtain the atomizing gas and liquid velocities at the atomizer exit. With these modi®cations, Sutherland et al. obtained good agreement between model predictions and experimental data. The experimentally observed variations of spray mean drop size with injection pressure, GLR, liquid viscosity, surface tension, and ligament-control insert pore size were well predicted by the model, as shown in Fig. 18. 515 Sovani et al. [20,64] also modi®ed the Lund et al. model to predict drop size distributions for effervescent sprays. Any practical atomizer produces a range of drop sizes rather than just a single drop size due to the stochastic phenomena involved in the atomization process. Sovani et al. included such stochastic phenomena in the Lund et al. model in the form of variations in gas±liquid relative velocity and liquid physical properties. The variations were introduced in the form of discrete probability functions (DPFs) and the drop size distribution was obtained in the form of another DPF. Their results indicate that the drop size distribution width is a strong, non-linear function of mean and ¯uctuating gas±liquid relative velocities and is largely unaffected by variations in liquid physical properties. Panchagnula and Sojka [19] developed a model for predicting drop velocity pro®les in effervescent sprays. They modeled the spray as a variable-density, singlephase turbulent jet and used an expression for velocity pro®le reported in the literature [65] for such jets. This expression relates the velocity at any point in the jet to the jet momentum rate. Panchagnula and Sojka modi®ed this relation, using expressions for the momentum rate of an effervescent spray, and expressed droplet velocity in terms of the operating parameters (liquid mass ¯ow-rate and GLR) and the densities of the liquid, atomizing gas, and ambient gas. They found that the experimental data agreed with the model predictions to within approximately 15%. 4. Applications of effervescent atomization As mentioned in the introduction to this article, effervescent atomizers perform considerably better (i.e. produce sprays having smaller mean drop sizes) than other types of atomizers in many situations. Other signi®cant advantages include larger exit ori®ces, reduced injection pressures, and lower gas ¯ow requirements. These advantages have been exploited in many practical systems; for example, effervescent atomizers can lead to lower pollutant emissions in IC engines due to their ability to produce ®ner sprays than those produced by conventional atomizers for the same injection pressure. This lower injection-pressure requirement can also improve engine ef®ciency by reducing parasitic losses. Most of the studies carried out so far on effervescent atomization were initiated in order to try and overcome some of the drawbacks of the more-established atomizer types. Effervescent atomizers have been designed and tested for a number of applications, including gas turbines [58,66], consumer products, process industry applications, and Diesel engines. A design procedure for different applications has been outlined by Chin and Lefebvre [50]. In the following sections, some of the spray systems to which effervescent atomization has been applied are discussed. The speci®c requirements of each system are listed and the improvements brought about by the use of 516 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 effervescent atomization are described. The literature of relevance to each application is reviewed. 4.1. Gas turbine combustors The fuel injection process plays a major role in the performance of gas turbine combustors especially in regard to pollutant emissions [66]. Increasingly severe emission regulations for both aircraft and industrial gas turbines necessitate continuous improvement of the fuel injection process. In addition, there is an increasing demand for fuel injectors with multi-fuel capability. Finally, gas turbine fuel injectors must provide good atomization over the entire range of fuel ¯ow rates and have low susceptibility to blockage by contaminants and carbon buildup on the nozzle face [66]. Effervescent injectors meet all these requirements more satisfactorily than conventional gas turbine fuel injectors. They are capable of producing ®ner sprays, leading to lower pollutant emissions, and have the capability to handle a variety of fuels due to their relative insensitivity to fuel physical properties. They perform well over a wide range of liquid ¯ow-rates and GLRs, and can provide good atomization over a wide range of operating conditions. They can also have signi®cantly larger ori®ces than those of conventional injectors, thereby reducing clogging problems. Several researchers have contributed toward the development of effervescent fuel injectors for gas turbine combustors. Their work includes most of the studies conducted in the initial stages of development (1987±1993). Notable works are those of Lefebvre [2], Wang et al. [4], Chin and Lefebvre [50], Li et al. [37], and Colantonio [58]. 4.2. IC engines Pollutant emissions and ef®ciency are also of prime concern for IC engines. NOx, unburned hydrocarbons, CO and particulate matter are of most interest. The combustion processes taking place inside the engine govern the quantity of pollutants produced. With tightening emission regulations, engine manufacturers around the world are searching for better technologies to improve the combustion process and reduce pollutant emissions. Lawler et al. [76] conducted experiments with jet ¯ames stabilized on effervescent atomizers. Toulene (C7H8) was the liquid sprayed and methane (CH4) was the atomizing gas. Emission indices of soot, unburnt hydrocarbons and CO were each seen to drop by 80% or more with an increase in GLR from 5 to 15%. These results suggest that the use of effervescent atomization for IC engine fuel injection could possibly lead to drastic decreases in pollutant emissions. In addition, this technique provides good atomization when operating at injection pressures that are several times lower than those of conventional fuel injectors. This would reduce parasitic losses and raise engine ef®ciency. The work of Wade et al. [33,42] established that a high pressure effervescent atomizer spraying `Viscor' (a hydrocarbon fuel with physical properties almost exactly identical to those of Diesel fuel) can produce sub-10 mm sprays when operating at injection pressures less than 35 MPa. Satapathy et al. [21] improved on Wade et al.'s design and developed an injector that produced sub-5 mm sprays when operating at injection pressures less than 28 MPa and GLRs less than 0.02. Their experiments were carried out in a high ambient density environment to simulate the conditions inside the combustion chamber of a modern Diesel engine at the end of the compression stroke. These results demonstrate that the new approach can produce sprays that are comparable to, or ®ner than, those produced by modern conventional Diesel injectors, even though injection pressures may be up to ®ve times lower. However, more work needs to be done to establish combustion advantages/disadvantages of effervescent atomization. 4.3. Furnaces and boilers Most industrial boilers use pressure-swirl atomizers. However, as high grade hydrocarbon fuels become scarce these atomizers will have to be replaced with other designs that can handle less re®ned fuels [52]. Effervescent atomizers are characterized by their ability to perform well for a range of liquids because their performance is relatively insensitive to variations in liquid physical properties. Furthermore they can have larger ori®ces than conventional atomizers, enabling them to handle less re®ned liquids without clogging. Sankar et al. [52] developed a swirl effervescent atomizer for application to industrial and residential boilers. Loebker and Empie [11] designed an effervescent atomizer for spraying a pulping industry by-product (black liquor Ð a viscous liquid of widely varying composition with up to 80% solid suspension) into a heat recovery boiler. The atomizer was designed to meet the optimum drop size requirement of the boiler (2±3 mm mass median diameter). Qualitative and quantitative results were obtained from spray images made using a high shutter speed camera. The qualitative results describe the liquid disintegration process while the quantitative results detail the variation of mean drop size with GLR and viscosity. Images of liquid disintegration mechanisms for the effervescent atomizer were compared with similar images made using a conventional industrial black liquor spray nozzle (Spray Systems Vee-Jet e nozzle). While the near-nozzle structure of the Vee-Jet nozzle showed a mesh of interwoven, unbroken strands of liquid, effervescent atomizer near nozzle structure showed much smaller liquid fragments and drops. Both inside±out and outside±in gas injection geometries were tested and mean drop size was found to be smaller for the latter geometry. The atomizer produced drop sizes less than 5 mm while operating at injection pressures less than 207 kPa and GLRs lower than 5%. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 4.4. Incineration Effervescent atomizers hold promise in waste incineration applications. The ®rst advantage is their relative insensitivity to liquid viscosity. This is especially important when spraying waste products, whose rheological properties cannot be adequately controlled and are often unknown. Secondly, performance is relatively insensitive to the size of the atomizer discharge ori®ce, so larger ori®ces can be used to reduce clogging substantially. Thirdly, the liquid ¯ow velocity in the discharge ori®ce is much lower than that in a conventional atomizer. This greatly reduces erosion problems created by solids suspended in the waste. Furthermore, lower velocities in the ori®ce lead to lower drop velocities. As a result the burnout lengths are shorter and the incinerator can be made more compact. Further information on the application of effervescent atomization to incineration is contained in Panchagnula and Sojka [19]. 4.5. Consumer products Consumer product sprays are commonly produced using dispensers pressurized with hydrocarbon (HC) propellants. They often use volatile organic compounds (VOC) as solvents. VOCs and HCs in aerosol sprays contribute greatly to atmospheric pollution, and it is desirable to replace these compounds with non-polluting substances like water and air. The use of VOCs and HCs is necessitated in current consumer product dispensers by the performance limitations of twin-¯uid and pressure-swirl atomizers. Since effervescent atomizers are known to perform quite well for a range of liquids and atomizing gases with widely varying physical properties, their use makes it possible to replace VOC solvents with water and HC propellants with air without compromising atomizer performance [17]. An important consideration in consumer product dispensers is the amount of propellant gas needed to spray a unit quantity of liquid. The container has to be charged with suf®cient propellant gas to dispense all its contents. It is desirable to minimize the use of propellants in order to keep the size of the dispenser small. This requirement is readily satis®ed by effervescent atomization since it is the most ef®cient means of atomization at GLRs of 0.01 or lower. The work of Sutherland et al. [16,53,56] and Lund et al. [14,44] was targeted at developing an effervescent atomizer for consumer product sprays. The atomizer they developed produced spray mean drop sizes below 70 mm for GLRs less than 0.009. 5. Scope for future study and applications Effervescent atomization is a rapidly expanding ®eld (see Fig. 1). The work carried out so far shows considerable 517 promise for its use in a wide variety of practical applications. An ability to predict atomizer performance is greatly desired since it would signi®cantly reduce time and cost in the design and development cycle. Unfortunately, a comprehensive model of the atomization process is not yet available. Present models need improvements to enhance their accuracy and widen their range of applicability. Hence, there is considerable scope for efforts to model the subprocesses involved in effervescent atomization and to integrate them into a comprehensive model. The areas that we feel warrant further investigations are listed below. The list is presented in the form of topics for possible future research. 5.1. Experimental studies on basic processes 5.1.1. Atomized liquid ² Atomization of visco-elastic liquids with branched or ring polymer structure. Visco-elastic behavior of liquids needs careful consideration since effervescent atomization achieves liquid breakup through the stretching and shattering of a liquid sheath by an expanding gas core, as discussed earlier in Sections 2 and 3.2.2. A large number of polymeric liquids used in spray applications may have branched structures. Such liquids warrant deeper investigation since they are likely to exhibit greater viscoelasticity than straight chain polymers and would exhibit signi®cantly different breakup characteristics than those of the straight chain polymers previously studied [35,38,47]. ² Applications in spraying liquid metals. Liquid metal atomization typically requires the use of low injection pressures and large ori®ces. Since effervescent atomization is able to produce signi®cantly smaller drop sizes under both these constraints it is thought to be a suitable technique for spraying liquid metals. Future efforts should be directed at making a detailed assessment of the suitability of effervescent atomization to this application followed by studies on liquid metal effervescent atomizer performance and investigations of the relevant basic physical problems involved. ² Entrainment characteristics of visco-elastic ¯uid sprays. A wide variety of paints and inks exhibit visco-elastic behavior. In practical applications involving paint sprays the prime concern is the uniformity of the coating formed by depositing the spray on to a surface. Spray entrainment characteristics directly govern the transfer of paint from the atomizer to the painted surface thus in¯uencing coating uniformity. Previous studies directed at the development of effervescent atomizers for paints have studied the effect of ¯uid visco-elasticity on drop size and spray near-nozzle structure. Additional work that considers the practically relevant aspect of spray entrainment characteristics needs to be undertaken. 518 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 5.1.2. Transient spray behavior ² In¯uence of various independent parameters on the unsteadiness of effervescent sprays. To date fairly limited efforts have been directed towards the investigation of unsteadiness in effervescent sprays [54,55]. Spray unsteadiness is highly undesirable in most applications and more detailed investigations are necessary in this area, especially since effervescent atomization is a highly unsteady phenomenon possibly involving exploding gas bubbles that shatter the surrounding liquid into ®ne drops. Future work on this topic can be directed at conducting a parametric study of spray unsteadiness over a range of independent parameters. From such a study the factors that have the greatest effect on spray unsteadiness can be identi®ed and techniques for reducing spray unsteadiness can be developed. ² Development of atomizers for transient injection applications. Several spray applications require atomizers operating in transient mode, a classic example being Diesel injectors. All effervescent atomizers reported to date operate in steady state mode and a signi®cant amount of work needs to be directed towards the development of atomizers for transient spray applications. The primary challenge in the development of transient effervescent atomizers is that of designing the aerator such that it provides the desired gas±liquid mixing throughout the transient spray cycle. ² Transient spray characteristics mapping. The development cycle for transient atomizers should include mapping spray characteristics (drop size, drop velocity, cone angle, etc.) as functions of time. It is anticipated that conventional spray diagnostic instrumentation would be adequate for transient measurements of effervescent spray characteristics. 5.1.3. Fluid mechanics of effervescent atomization ² Further investigation of the internal two-phase ¯ow. Gas±liquid two-phase ¯ow inside the atomizer is an important aspect determining the performance of internal-mixing twin-¯uid atomizers. The current understanding of effervescent atomization internal ¯ow is rather limited. Topics that have not been rigorously investigated previously include gas±liquid mixing inside the mixing chamber, evolution of the two-phase ¯ow through the mixing chamber, and exit ori®ce ¯ow. Work currently in progress at Purdue University is aimed at investigating gas±liquid mixing inside the atomizer at pressures up to 40 MPa using a transparent atomizer. The experimental apparatus used and preliminary ®ndings are reported by Sovani et al. [67,68]. ² Two-phase ¯ow inside the atomizer exit ori®ce. The ¯ow structure inside the ori®ce is thought to have a direct in¯uence on the near-nozzle breakup mechanisms and is a key aspect in the determination of spray character- istics. However, due to signi®cant dif®culty involved in the experimental investigation of two-phase ¯ow in circular micro-ori®ces, there is no work reported on this topic. Relevant works closest to this topic include two recent studies on two-phase ¯ow structure in micro/mini channels. Xu et al. [69] discuss the twophase ¯ow regimes in micro rectangular channels with widths as small as 0.3 mm while Triplett et al. [70,71] report the ¯ow regimes and pressure drops in circular channels with diameters 1 mm and greater. ² Parametric study of near-nozzle spray structure. A comprehensive understanding of the near-nozzle spray structure is indispensable in the process of developing models that can predict spray characteristics. Studies to date have investigated the near-nozzle spray structure over a rather limited range of parameters, as discussed in Section 3.2.2. Further work directed at studying the near-nozzle structure over a wide range of parameters will be helpful for two reasons. First, it would help develop a comprehensive theory for effervescent atomizer near-nozzle breakup. Secondly, it would enable the development of a generally applicable model for predicting spray characteristics of effervescent atomizers. ² The role of two-phase ¯ow compressibility in effervescent atomization. Before the inception of effervescent atomization, Chawla [18] predicted the signi®cant bene®ts of internal mixing twin-¯uid atomization considering the compressibility of two-phase ¯ows, as discussed in detail in Section 2 and Fig. 3. Chawla's [18] approach successfully explains several characteristic features of effervescent atomization including small drop sizes obtained at signi®cantly low injection pressures and relative insensitivity of drop size to exit ori®ce diameter. However, a comprehensive theory clarifying the role of two-phase ¯ow compressibility in effervescent atomization is currently unavailable. Such a theory may lead to fairly simple, yet accurate, models for predicting effervescent atomizer performance. 5.2. Modeling of the effervescent atomization process ² Creation of a comprehensive model for the overall atomization process. As discussed in Section 3.3, a comprehensive model for the overall atomization process is currently unavailable. Such a model would have the ability to predict spray characteristics from ®rst principles given inputs of atomizer geometry, operating parameters and liquid physical properties. A signi®cant amount of work needs to be done to develop submodels for the individual ¯ow phenomena involved and integrate them into one comprehensive model. ² Model for two-phase ¯ow inside the atomizer exit ori®ce. A particularly challenging part of the comprehensive model is the submodel for two-phase ¯ow in the atomizer exit ori®ce. Such a model should be able to predict the ¯ow structure, gas and liquid velocities, pressure, and S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 void fraction at the exit plane. Two challenges in the development of this submodel are the small geometric scales and the unavailability of experimental data. A useful reference is the work of Xu et al. [69] who have proposed models for predicting ¯ow regime transitions in micro channels of rectangular cross-section. While these models would serve as helpful references, they cannot be directly applied to the exit ori®ce ¯ow since they are developed for ¯ows in rectangular channels at pressures close to the atmospheric pressure. Furthermore, these models only predict regime transition and are incapable of predicting quantitative ¯ow parameters like gas and liquid velocities and void fraction. ² Improvement of Lund et al.`s [14] primary atomization model. The only presently available model for primary atomization is that proposed by Lund et al. [14]. There are three limitations to this model. First, it is applicable only if the two-phase ¯ow in the atomizer exit ori®ce is in the annular regime. Second, it uses a simplistic scheme based on geometric considerations for predicting the breakup of the annular liquid sheath issuing from the atomizer into ligaments. Third, the model uses a linear stability analysis for ligament breakup. Consequently, Lund et al.'s [14] model can be improved signi®cantly by expanding its range of applicability to all possible exit ¯ow regimes, by using a circumferential stability analysis for the breakup of the annular liquid sheath into ligaments, and by performing a non-linear stability analysis for the breakup of individual ligaments into drops. ² Primary atomization model for non-Newtonian liquids including visco-elastic substances. Another drawback of the Lund et al. [14] model is its inapplicability to non-Newtonian liquids. An experimental investigation of the near-nozzle structure of effervescent sprays of visco-elastic liquids is reported by Geckler and Sojka [35,47], as discussed in Section 3.2.2. Their results may be used in the development of a primary atomization model for visco-elastic ¯uids. Efforts in this direction are currently being undertaken at Purdue University. Refer to Babinsky [73] for details. 6. Summary Effervescent atomization is a form of internal-mixing twin-¯uid atomization in which an atomizing gas is bubbled into a liquid and the resulting two-phase mixture is discharged from the atomizer ori®ce. Atomizers that embody this concept are found to produce ®ner sprays than those produced by conventional single and twin ¯uid atomizers while operating at much lower injection pressures. The atomizing gas-to-liquid ratios needed for effervescent atomization are signi®cantly lower than those of other forms of twin-¯uid atomization. In addition, problems of clogging of the discharge ori®ce are greatly reduced. Effervescent atomizers have a characteristic drawback compared to other single-¯uid atomization techniques Ð 519 the need for a supply of pressurized atomizing gas. However, this requirement can be often met fairly easily since the device performs well at low gas/liquid ratios. Work on effervescent atomization was ®rst reported in the late 1980's. Since then it has become a ®eld of growing scienti®c and technical interest. Current literature includes parametric studies of spray characteristics (drop size and velocity distributions, spray cone angle, spray momentum rate, patternation and entrainment) for a variety of atomizer designs. The fundamentals of various processes involved have been investigated and a partial understanding of some basic principles has been accomplished. Preliminary models for performance predictions have been developed. Work in progress is directed at applying the technique to a number of applications. Further work is needed to gain a deeper understanding of the fundamental mechanisms and two-phase ¯ow phenomena involved. A comprehensive model for predicting performance is currently unavailable and needs to be developed. References [1] Lefebvre AH, Wang XF, Martin CA. Spray characteristics of aerated-liquid pressure atomizers. AIAA J Prop Power 1988;4(4):293±8. [2] Lefebvre AH. A novel method of atomization with potential gas turbine application. Indian Defence Sci J 1988;38:353±62. [3] Roesler TC, Lefebvre AH. Studies on aerated-liquid atomization. Int J Turbo Jet Engines 1989;6:221±30. [4] Wang XF, Chin JS, Lefebvre AH. In¯uence of gas injector geometry on atomization performance of aerated-liquid nozzles. Int J Turbo Jet Engines 1989;6:271±80. [5] Buckner HN, Sojka PE, Lefebvre AH. Effervescent atomization of coal-water slurries. ASME Publ 1990;PD-30:105±8. [6] Buckner HN, Sojka PE, Lefebvre AH. Effervescent atomization of non-Newtonian single phase liquids. Proceedings of the Fourth Annual Conference on Atomization and Spray Systems, Hartford, Connecticut, 1990. p. 93±7. [7] Sher E, Elata D. Spray formation from pressure cans by ¯ashing. Ind Eng Chem Process Des Dev 1977;16:237±42. [8] Marek CJ, Cooper LP. US Patent No. 4,189,914, 1980. [9] Solomon ASP, Rupprecht SD, Chen LD, Faeth GM. Flow and atomization in ¯ashing injectors. Atomization Spray Technol 1985;1(1):53±76. [10] Lefebvre AH. Atomization and sprays. New York: Hemisphere, 1989. [11] Loebker D, Empie HJ. High mass ¯ow-rate effervescent spraying of high viscosity Newtonian liquid. Proceedings of the 10th Annual Conference on Liquid Atomization and Spray Systems, Ottawa, ON, 1997. p. 253±7. [12] Buckner HE, Sojka PE. Effervescent atomization of high viscosity ¯uids. Part 1: Newtonian liquids. Atomization Sprays 1991;1:239±52. [13] Buckner HN, Sojka PE, Lefebvre AH. Aerated atomization of high viscosity Newtonian liquids. Proceedings of the Third Annual Conference on Liquid Atomization and Spray Systems, Irvine, California, 1989. p. 98±102. 520 S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 [14] Lund MT, Sojka PE, Lefebvre AH, Gosselin PG. Effervescent atomization at low mass ¯ow rates. Part 1: the in¯uence of surface tension. Atomization Sprays 1993;3:77±89. [15] Lund MT, Sojka PE. Effervescent atomization at low mass ¯ow-rates. Part 2: the structure of the spray. Proceedings of the Fifth Annual Conference on Liquid Atomization and Spray Systems, San Ramon, CA, 1992. p. 233±7. [16] Sutherland JJ, Sojka PE, Plesniak MW. Ligament controlled effervescent atomization. Atomization Sprays 1997;7(4):383± 406. [17] Sutherland JJ, Panchagnula MV, Sojka PE, Plesniak MW, Gore JP. Effervescent atomization at low air±liquid ratios. Proceedings of the Eighth Annual Conference on Liquid Atomization and Spray Systems, Troy, MI, 1995. p. 74±7. [18] Chawla JB. Atomization of liquids employing the low sonic velocity in liquid/gas mixtures. Proceedings of the Third International Conference on Liquid Atomization and Spray Systems, LP/1A/5/1-7, 1985. [19] Panchagnula MV, Sojka PE. Spatial droplet velocity and size pro®les in effervescent atomizer-produced sprays. Fuel 1999;78:729±41. [20] Sovani SD, Sojka PE, Sivathanu YR. Prediction of drop size distributions from ®rst principles: the in¯uence of ¯uctuations in relative velocity and liquid physical properties. Atomization Sprays 1999;9(2):133±52. [21] Satapathy MR, Sovani SD, Sojka PE, Gore JP, Eckerle WA, Crofts JD. The effect of ambient density on the performance of an effervescent atomizer operating in the MPa injection pressure range. Submitted for publication. [22] Roesler TC. An experimental study of aerated-liquid atomization. PhD thesis, Purdue University, 1988. [23] Roesler TC, Lefebvre AH. Photographic studies on aeratedliquid atomization, combustion fundamentals and applications. Proceedings of the Meeting of the Central States Section of the Combustion Institute, Indianapolis, Indiana, Paper 3, 1988. [24] Santangelo PJ, Sojka PE. A holographic investigation of the near nozzle structure of an effervescent atomizer produced spray. Atomization Sprays 1995;5:137±55. [25] Santangelo PJ, Sojka PE. Focused image holography as a dense spray diagnostic. Appl Opt 1994;33(19):4132±6. [26] Whitlow JD, Lefebvre AH. Effervescent atomizer operation and spray characteristics. Atomization Sprays 1993;3:137±56. [27] Whitlow JD, Lefebvre AH, Rollbuhler JR. Experimental studies on effervescent atomizers with wide spray angles. AGARD (Advisory Group for Aerospace Research and Development) Conference Proceedings, vol. 536, 1993. p. 38/1±38/11. [28] Chen SK, Lefebvre AH, Rollbuhler JR. In¯uence of ambient air pressure on effervescent atomization. J Propulsion Power 1993;9(1):10±15. [29] Chen SK, Lefebvre AH. Discharge coef®cients for effervescent atomizers. Atomization Sprays 1994;4(3):275±90. [30] Chen SK, Lefebvre AH. Spray cone angles of effervescent atomizers. Atomization Sprays 1994;4(3):291±301. [31] Bush SG, Bennett JB, Sojka PE, Panchagnula MV, Plesniak MW. Momentum rate probe for use with two-phase ¯ows. Rev Sci Instrum 1996;67:1878±85. [32] Bush SG, Sojka PE. Entrainment by effervescent sprays at low mass ¯owrates. Proceedings of the Sixth International [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] Conference on Liquid Atomization and Spray Systems, Rouen, France, 1994. p. 609±15. Wade RA, Sojka PE, Gore JP. Effervescent atomization using high supply pressures. Proceedings of the 9th Annual Conference on Liquid Atomization and Spray Systems, San Francisco, CA, 1996. p. 263±70. Roesler TC, Lefebvre AH. Studies on aerated-liquid atomization. ASME Winter Annual Meeting, Boston, Massachusetts, Paper 87-WA/HT-17, 1987. Geckler SC, Sojka PE. High mass ¯ow rate effervescent atomization of viscoelastic ¯uids. ASME 1993;FED-Vol. 178/HTD-Vol. 270:109±15. Buckner HE, Sojka PE. Effervescent atomization of high viscosity ¯uids. Part 2: non-Newtonian liquids. Atomization Sprays 1993;3:157±70. Li J, Lefebvre AH, Rollbuhler JR. Effervescent atomizers for small gas turbines. American Society of Mechanical Engineers, 94-GT-495, 1994. 1±6. Geckler S. Effervescent atomization of visco-elastic liquids. MS thesis, Purdue University, 1994. Panchagnula MV. High mass ¯ow rate effervescent atomization. MS thesis, Purdue University, 1994. Wade RA. Combustion applications of effervescent atomization. MS thesis, Purdue University, 1996. Satapathy MR. The effect of ambient density on the performance of an effervescent Diesel injector. MS thesis, Purdue University, 1997. Wade RA, Weerts JM, Sojka PE, Gore JP, Eckerle WA. Effervescent atomization at injection pressures in MPa range. Atomization Sprays 1999;9(6):651±67. Dutta P, Gore JP, Sivathanu YR, Sojka PE. Global properties of high liquid loading turbulent crude oil 1 methane/air spray ¯ames. Combustion Flame 1994;97:251±60. Lund MT, Jian CQ, Sojka PE, Gore JP, Panchagnula MV. The in¯uence of atomizing gas molecular weight on low mass ¯ow rate effervescent atomization. ASME J Fluids Engng 1998 (in press). Lee WY, Sojka PE. The in¯uence of ¯uid viscoelasticity on low mass ¯owrate effervescent atomization. ASME 1996;FEDVol. D65 178/HTD-Vol. 270:129±35. Sojka PE, Buckner HN. Effervescent atomization of highly viscous multiphase non-Newtonian ¯uids. Annual Meeting of the International Fine Particle Research Institute, Albuquerque, New Mexico, 1991. Geckler SC, Sojka PE. Effervescent atomization: limitations due to viscoelasticity. Proceedings of the Seventh Annual Conference on Liquid Atomization and Spray Systems, Bellevue, WA, 1994. p. 181±5. Ferguson J, Hudson JE, Warren BCH. The breakup of ¯uids in an extensional ¯ow-®eld. J Non-Newtonian Fluid Mech 1992;44:37±54. Jardine J. Effervescent atomization on non-Newtonian ¯uids at high ¯ow rates. MS thesis, Purdue University, 1991. Chin JS, Lefebvre AH. A design procedure for effervescent atomizers. ASME J Engng Gas Turbines Power 1995;117:226±71. Chin JS, Lefebvre AH. Flow regimes in effervescent atomization. Atomization Sprays 1993;3:463±75. Sankar SV, Robart DM, Bachalo WD. Swirl effervescent atomizer for spray combustion. ASME HTD 1995;317± 312:175±82. S.D. Sovani et al. / Progress in Energy and Combustion Science 27 (2001) 483±521 [53] Sutherland JJ, Sojka PE, Plesniak MW. Entrainment by ligament-controlled effervescent atomizer-produced sprays. Int J Multiphase Flow 1997;23:865±84. [54] Luong JTK, Sojka PE. Unsteadiness in effervescent sprays: the in¯uence of ¯uid physical properties. Proceedings of the 10th Annual Conference on Liquid Atomization and Spray Systems, Ottawa, ON, 1997. p. 248±52. [55] Luong JTK, Sojka PE. Unsteadiness in effervescent sprays. Atomization Sprays 1997;9:87±109. [56] Sutherland JJ, Sojka PE, Plesniak MW, Gore JP. Entrainment by low air±liquid ratio effervescent atomizer produced sprays. Proceedings of the Ninth Annual Conference on Liquid Atomization and Spray Systems, San Francisco, CA, 1996. [57] Sovani SD, Chou E, Sojka PE, Gore JP, Eckerle WA, Crofts JD. High pressure effervescent atomization: effect of ambient pressure on spray cone angles. Fuel 2000;80(3):427±35. [58] Colantonio RO. Application of jet shear layer mixing and effervescent atomization to the development of a low NOx combustor. PhD thesis, Purdue University, 1990. [59] Panchagnula MV, Kuta TJ, Sojka PE, Plesniak MW. Modifying entrainment in ligament-controlled effervescent atomizerproduced sprays. Proceedings of the 10th Annual Conference on Liquid Atomization and Spray Systems, Ottawa, ON, 1997. p. 35±39. [60] Ricou FP, Spalding DB. Measurements of entrainment by axisymmetric turbulent air jets. J Fluid Mech 1961;11:21±32. [61] Ishii M. One dimensional drift-¯ux mode and constitutive equations for relative motion between phases in various two-phase ¯ow regimes. Argonne National Laboratory Report, 1977. p. 47±77. [62] Weber C. Disintegration of liquid jets. Z Angew Math Mech 1931;11(2):136±59. [63] Sterling A, Sleicher C. The instability of capillary jets. J Fluid Mech 1975;68(3):477±95. [64] Sovani SD, Sojka PE, Sivathanu YR. Predictions of drop size distributions from ®rst principles: joint-PDF effects. Atomization Sprays 2000;10(6):587±602. [65] White FM. Viscous ¯uid ¯ow. New York: McGraw-Hill, 1992. [66] Lefebvre AH. Gas turbine combustion. New York: Hemisphere, 1983. 521 [67] Sovani SD, Sojka PE, Gore JP, Crofts JD, Eckerle WA. Internal ¯ow structure of an effervescent diesel injector. Paper No. 99-ICE-181, ICE-Vol. 32-2, ASME Spring Technical Conference, 1999. [68] Sovani SD, Sojka PE, Gore JP, Crofts JD, Eckerle WA. Effervescent Diesel injection: injector internal ¯ow and its in¯uence on spray quality. Proceedings of the Eighth International Conference on Liquid Atomization and Spray Systems, Pasadena, CA, 16±20 July 2000. [69] Xu JJ, Cheng P, Zhao TS. Gas±liquid two-phase ¯ow regimes in rectangular channels with mini/micro gaps. Int J Multiphase Flow 1999;25:411±32. [70] Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski. Gas±liquid two-phase ¯ow in microchannels. Part I: twophase ¯ow patterns. Int J Multiphase Flow 1999;25:377±94. [71] Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski. Gas±liquid two-phase ¯ow in microchannels. Part II: void fraction and pressure drop. Int J Multiphase Flow 1999; 25:377±94. [72] Liao Y, Sakman AT, Jeng SM, Benjamin MA. A comprehensive model to predict simplex atomizer performance. J Engng Gas Turbines PowerÐTrans ASME 1999;121(2):285±94. [73] Babinsky E. Predicting drop size distributions from ®rst principles for non-Newtonian ¯uids. MS thesis, Purdue University, 2000. [74] Zelina J, Rodrigue A, Sankar S. Fuel injector characterization using laser diagnostics at atmospheric and elevated pressures. AIAA Paper No. AIAA-98-0148, 36th Aerospace Sciences meeting and Exhibit, Reno, NV, 12±15 January 1998. [75] Hardalupas Y, Taylor AMKP, Whitelaw JH. Characteristics of the spray from a diesel injector. Int J Multiphase Flow 1992;18(2):159±79. [76] Lawler A, Wade RA, Sojka PE, Gore JP. Flame length and pollutant emission characteristics of effervescent atomizer/ burner stabilized jet ¯ames, combustion fundamentals and applications. Proceedings of the Technical Meeting of the Central States Section of the Combustion Institute, 1996. [77] Bush SG. Entrainment by effervescent sprays at low mass ¯ow rates. MS thesis, Purdue University, 1994.