injection, dispersion, and combustion of liquid fuels

Twenty-Fifth Symposium (International) on Combustion/The Combustion Institute, 1994/pp. 333-344

INVITED TOPICAL REVIEW

INJECTION, DISPERSION, AND COMBUSTION OF LIQUID FUELS

W. D. BACHALO Aerometrics, Inc.

Sunnyvale, CA 94086, USA

A review of the research in fuel spray combustion is offered with emphasis on e~cperimentation in spray dynamics. Atomization and fuel-air mixing have been identified as areas in which advancements in the combustion technology are still possible. The development of optical diagnostics has enabled the detailed characterization of fuel spray injection, and subsequent turbulent mixing, in model combustors. Difficulties in making measurements in nonreacting and reacting spray environments, including high drop number densities, drop deformations, nonuniform drop temperatures, refractive index variations, and particle concentration gradients, are discussed. A brief review of experiments in both nonreacting and reacting sprays is provided. Improvements realized in the measurement techniques for drop number density and volume flux are also described. Other areas needing further investigation have been identified. Methods for simultaneously measuring the drop temperature and fuel vapor concentration are under development and some key characteristics of these methods have been outlined. Since the spray drop interaction with turbulent flows in the combustion chamber has a considerable impact on the combustor performance, the parameters and correlations affecting the drop response are reviewed.

Introduction

A considerable percentage of our energy resources is derived from the combustion of liquid fuels in the form of sprays. For this reason, spray formation and liquid atomization have been investigated in order to unravel the mechanisms involved in the liquid breakup [1-7], atomization, and spray drop dynamics [8-14], especially with respect to requirements for combustion. The conditions of the introduction of the spray injection, dispersion, vaporization, and burning of the fuel with stoiehiometric proportions of air in a well-mixed environment affect the combustion stability, efficiency, and pollutant formation. In particular, aerodynamic efficiency of redistribution and mt, cing of the fuel and air in the combustion chamber, and the dilution of the combustion prod- uets to the desired temperature level and proper temperature profile, determine the quality of the combustion and the levels of emissions generated. Of particular concern are the formation of the oxides of nitrogen, carbon dioxide, carbon monoxide, soot, and unburned hydrocarbons.

It is not yet completely clear what the most favorable spray conditions should be for optimum eombustor performance, and thus, research is needed to define the effects of all parameters that influence the combustion process. These parameters are the mean drop size and drop size distribution at each location within the spray plume, drop velocity distribution, drop velocity relative to the air velocity, drop number density (spatial and temporal), and drop temperature. The spray interaction with the turbulent envi-

ronment and its effect upon evaporation affect the mixing and dispersion of the fuel. Aerodynamic mixing of the fuel spray and combustion all transpire under highly turbulent flow conditions, with the drops undergoing heat and mass transfer with the local fuel-air ratios extensively controlled by the aerodynamics.

New trends in combustor development have focused upon the necessity to reduce soot and NO x emissions [14-19]. Sturgess et al. [14] have con- eluded that, for gas turbine eombustors in the near term, the only feasible approaches that can be used to meet the emission standards are changes in the fuel injectors and in the eombustor liner dilution air hole patterns used to further promote mixing. The predicament encountered in the design of eombustors is that schemes implemented to reduce soot lead to an augmentation in NO~ and vice versa, For example, raising the combustion temperature by increasing the combustion zone equivalence ratio reduced CO formation and excess smoke. This was achieved by using airblast fuel injectors to accom- plish finer atomization and improved fuel-air mixing. Unfortunately, the resulting higher combustion temperatures at all operating conditions increased file formation of NOx. Strategies proposed to overcome this dilemma include the use of staged combustion using a rich-burn, quick-quench, lean-burn (RQL) approach. A critical requirement of the approach is the rapid and efficient mixing of the fuel spray with the air, which depends upon the size and shape of the reeireulation zone, the drop size distribution, and

333

334 SPRAYS AND DROPLET COMBUSTION

the design of the air dilution jets, among other fac- tors.

The development of laser-based diagnostics to re- liably characterize the spray size distributions, the drop dynamics, and the turbulent mixing in nonreacting and reacting environments has been timely in terms of the development of advanced combustion technology. The phase-Doppler method [20-22] provides a means for achieving the simultaneous measurements of the spray drop size, velocity, number density, and volume flux in practical sprays [23- 25]. More recently, the method has been combined with rainbow refractometry to enable the simultaneous measurement of the drop temperature. Once deployed, this added capability should serve to provide greater insight into the dynamics and the evaporation and combustion of liquid fuels.

A comprehensive review of spray combustion research is not possible in the limited space available. Several excellent reviews have been written on this subject by Chigier [26], Faeth [27], Law [28], Sirig- nano [29], and Williams [30]. This review is focused on the injection of the atomized fuel, the fuel-air mixing, and the characterization of the subsequent interactions of the fuel spray drops with the complex turbulent air flow in the combustion chamber. The primary emphasis will be upon the experimental ob- servations that have been conducted, and some of the potential measurement problems encountered in spray combustion environments will be addressed. Advances in the spray diagnostics have significantly improved the reliability and detail of the data that may now be obtained,

sprays. Since the phase-Doppler method has been described in great detail in numerous papers, what will be discussed are the measurement characteristics, problems associated with spray combustion characterizations, and the developments in the technology to deal with the problems identified. Of primary concern is the measurement reliability of not only the drop size distributions, but also of the drop number density.

Number Density Limitations:

Operation of the phase-Doppler method, or any other single particle counting method, in high drop number density environments may lead to coincident particle occurrences in the measurement volume. M- though the sample volume can be made very small to ensure a low probability that there is no more than one drop in the sample volume at one time, in the dense spray region, coincident occurrences may give rise to errors. A detailed analysis for estimating the probability of coincident occurrences is given by Ed- wards and Marx [34]. The authors assumed an ideal system in this analysis for which all coincident occurrences were rejected by the instrument logic. Two Poisson filters were employed, one for the spatial distribution of the particles

G = e - ~ (1)

and a second

Spray Characterization Methods

The evolution of spray characterization methods has made an exceptional contribution to our ability to research and understand spray combustion phenomena. The Frannhofer diffraction method described by Swithenbank et al. [31] and others [32- 33] gained acceptance as an efficient and reliable means to obtain Sauter mean diameter (D32) measurements in practical sprays. The method provided a simple line-of-sight measurement of the concentration-based mean diameter. Unfortunately, the method does not provide information on the drop dynamics and is very sensitive to beam steering resulting from refractive index gradients, and hence fails in combustion environments. Interest in measuring the drop size and velocity, as well as the spa- tially and temporally resolved number density and volume flux, led to the development of methods in- corporating the laser-Doppler velocimeter. As a con- sequence of these efforts, the phase-Doppler particle analyzer was developed for spray measurements [20- 22], and it has become a very useful instrument for spray characterization in nonreacting and reacting

e, = e -~ (2)

for the temporal or arrival time statisties. Since the size of the sample volume will be different for different particle sizes, the analysis also accounted for this change in the sample volume. The particles were assumed to be distributed randomly and homoge- neously in space and to have a number density N. The analysis of Edwards and Maix indicated that, for an ideal system, the mean drop size, and partieularly D32, would be reported without significant error even with a low probability for acceptance of the measurements. Only the particle number density and volume flux would have significant error.

In reality, the instrument is imperfect because it may not reject all coincident occurrences. Logic systems including redundant phase measurements, signal-to-noise ratio checks, and signal amplitude measurements have been incorporated into the instruments to prevent erroneous measurements from being made. The performance of the phase- Doppler particle analyzer (PDPA) under conditions of two particles passing the sample volume at one time is described in Sankar et al. [35].


Drop Deforvnations:

When dealing with high-pressure, high-velocity sprays, or sprays in reacting environments in which the high temperatures reduce the surface tension, particular attention must be devoted to the forces on the drop that produce incremental drop deformation, thus causing the drop to deviate from its spherical shape. It is possible to assess the deformation of the drop with the use of the measured mean relative velocity, v, and an estimate of the ambient gas density. The analysis of small deformations and oscilla- tions of a drop in a moving gas by Hinze [36] indicates that the drop deformation will vary as a function of the Weber number given as

- = - 0.047We (3) d

where fi is the radial displacement of each fluid element from its undeformed state. For the drop oscil- lations resulting from a sudden introduction of a drop into the air stream with very" small or very large viscosity, the deformation is

= - 0.085We (4)

which is almost twice that of the steady-state case. In a recent study by Hsiang and Faeth [3], the correlation for a steady disturbance was proposed as

dmax = (1 + 0.07We~ 3. (5)

dmin

Measurement errors of the phase-Doppler instrument resulting from asphericity of the drops can be estimated by assuming that the sphere is deformed aerodynamically into an oblate or prolate spheroid (when the deformations are not extreme). Using simple geometry, the local radius of curvature can be calculated. The local radius of curvature for a drop deformed by a flow in the direction of the measurement beam pair is described by the calculations of Bachalo and Sankar [37]. These results and the data of Alexander et al. [38] show that the measured size will either be larger or smaller than the equivalent sphere, depending on the measurement orientation relative to the axes of the deformed drop. Research- ers have also used drop size measurements simultaneously from two orthogonal beam pair orientations from a two-component system to estimate the deformation of large drops [39]. The drop deformation information is also needed in the correction of the CD for modeling these sprays [18], so such measurements are of value.

335

Mass Flux and Number Density Measurements:

Measurements of the local mass flux and number density are important capabilities of the phase- Doppler instrument. Several reports have indicated successful measurements of these quantities [22,23,25,40]. However, there also have been reports indicating large variances in the measurements. There are several explanations for these discrepan- cies, including nonuniformities in the spray patterns, large variations in the drop trajectories as a function of drop size, measurements of only a single velocity component, drop deformation, and excessive drop number densities. A problem has been the possible inability of the instrument to detect and process signals from small drops that produce signals with low signal-to-noise ratio (SNR). A signal processor based on the discrete Fourier transform (DFT) that provides the optimum method for signal frequency and phase measurement has been developed [41] to overcome this problem. The reliable detection of the smallest particles in the size distribution that also possess the lowest SNR has been enhanced with the invention and development of the Fourier transform burst detector (FTBD) (Ibrahim and Bachalo, 1994, U.S. Patent 5,289,391). Signal detection is now based upon the relative coherence or SNR of the signal and serves to detect and process signals with SNR as low as - 6 dB or lower. The relevance of the signal processor development is that the dependence of the measurements on the instrument setup parameters has been minimized [42].

The method used for determining the number density has also been improved. Use of the transit time, or time required for the drop to pass through the sample volume, has reduced the error due to random drop trajectories and false triggers of the burst detector. The number density is obtained as

tg(i,j) 1 j

N = -- Tt} (6)

A critical factor is the in situ determination of the sample volume when measuring sprays in complex swirling flows in eases where only two simultaneous velocity components are being measured. In these environments, the light-scattering intensity approach [43] appears to offer promise for resoMng this problem. Recent comparisons of the measured number densities with beam extinction measurements have shown good agreement [42]. Incorporation of the signal intensity validation and a better understanding of the trajectory-dependent light scattering [44] have allowed more reliable measurements of the largest drops in the distributions and, consequently, the vol- llme flux.


Nonuniform Drop Heating:

In combustion environments, the effect of nonuniform temperature within the drop on the drop size measurements may be another potential source of error. The liquid heating time, rn, which is defined as the penetration time of a drop by a thermal dif- filsion wave from the surface to its center, is discussed by Sirignano [29]. The estimation of the drop heating time for spherically symmetric heating was estimated as

r H = plCld~/421 (7)

and the drop lifetime was presented as

rL = pad~/8pD log(1 + B) (8)

and the ratio is

Cl . , r.__H_n = 2 - - log(1 + B). (9) TL /~l Cp

Note that the ratio is independent of the drop diameter, indicating that the problem of nonuniform temperature may occur over all initial drop sizes. De- pending on the conductivity, specific heats, and transfer number, the drops may be at nearly uniform temperature or show large temperature gradients. Law and Sirignano [45] provide information on the drop radial temperature distributions for spherically symmetric drop vaporization. Schneider and Hirle- man [46] investigated the influence of spherically symmetric refractive index gradients on the size measurements of spherical particles larger than the light wavelength. The resulting error in the size measurement is approximately _+5% for 30 ~ forward scatter detection in the severest condition.

Drop Temperature Meas~trenwnts:

Accurate drop temperature in a reacting spray is an important parameter that needs to be measured and that will allow further insight into drop heating, vaporization, and heat and mass transfer during the combustion of fuel sprays. Although various spectro- scopic and nonspectroscopic techniques have been considered for drop temperature measurements [47,48], the successful measurement of individual drop temperatures in complex reactive environments has not been possible, to date. The use of exciplex fluorescence has been demonstrated [47], but unfortunately, the fluorescence is quenched in an oxygen environment. Furthermore, liquid fuels may contain aromatic hydrocarbons, which can produce fluorescence emissions that will mask the fluorescence spec- trum of the dopants. Currently, a method is under development to allow the nonintrusive, in situ, simultaneous measurements of the drop size, velocity,

and temperature in a turbulent swirling and recirculating flow field [49]. The method is based on the measurement of the rainbow angle [50], which depends upon the drop index of refraction. For single- component fuels, the dependence of the refractive index as a function of temperature is known. This method is also affected by the nonuniform heating of the drop [51], which may cause errors in the measurements. The problem is currently under investigation.

Massoli et al. [52] suggested a second approach for measuring the drop index of refraction, which in- volves measuring the light-scattering intensity ratio of the horizontally polarized light (incident and scat- tered) at two scattering angles, InH(33)/I~(60). Their results were in excellent agreement with the rainbow method. With the index of refraction varia- tion resulting from temperature changes (~n/6T)p known, the drop temperature can be derived. For uniformly heated drops and a single-component fuel, an accuracy of + 5 ~ was claimed. The simultaneous measurement of the refractive index also provides information for correcting the drop sizing for index of refraction effects.

Mixing and Evaporation:

Experiments designed to study the mixing of the air streams in a swirling flow have utilized the approach of tagging the seed particles in the flow in one region with a fluorescent dye [53]. Particle tagging allowed the separation of fluid arriving from the outer part of the flow from the air flowing through the swirler. A method for the measurement of the path-averaged hydrocarbon vapor concentration in fuel sprays has been described by Billings and Drall- meier [54] and Drallmeier and Peters [55]. Detec- tion of the light extinction simultaneously at two wavelengths allowed the measurement of the vapor in transient sprays.

Fuel Injection

Numerous practical means for supplying the nee- essary energy to the liquid to break the liquid into small drops have been considered for the atomization of fuels. Pressure swirl atomizers have found a wide range of acceptance for use in gas turbine, industrial, and domestic combustors, as well as in other combustors, because of their simplicity and low cost. These atomizers are being superseded by various airblast and air-assist atomizers [56]. Other approaches receiving attention are electrostatic atomizers [57], ultrasonic atomizers, and hybrid pressure swirl atomizers using piezoelectric crystals to excite the in- stability modes [58]. To improve the atomization for gas turbine and industrial combustors, which would then reduce the smoke and soot formation, prefihn-

INJECTION, DISPERSION, AND COMBUSTION OF LIQUID FUELS 337

ing airblast atomizers were developed [59]. Varia- tions of this design that include fuel swirl are com- monly used in high-compression-ratio gas turbojet engines. An extensive discussion of the design parameters affecting airblast atomizer performance is given by Lefebvre [56]. With pressure swirl atomizers, the high liquid injection pressure leads to liquid velocities that greatly exceed the velocity of the surrounding air velocity. The liquid kinetic energy, turbulence, and shear forces dominate the breakup [60,61], with the air flow playing a more passive role. Alternatively, with airblast and air-assist atomizers, the high relative velocity between the liquid sheet and the air is now furnished by the air, with the liquid injected at low velocity. These atomizers produce better spray uniformity, higher combustion efficiency, lower smoke production, and a lower pattern factor [14], although there are some differences of opinion on this observation.

The radial distribution of the axial velocity of the spray produced by airblast atomizers is quite different from that of the pressure swirl atomizer [62,63]. For an airblast atomizer, the large drops have the lowest velocity, whereas the small drops (D10 - 10 /lm) at the center of the distribution have the highest velocity. For this reason, the airblast atomizer appears to produce a more favorable condition for combustion since the large drops that require a greater residence time for evaporation are moving at a velocity that is approximately 10 times slower, which also allows more time for interaction with the swirling recirculating flow. The atomization air in the airblast atomizer also contributes to the mixing and sup- plies additional air for combustion. With the pressure swirl atomizer, it is the large drops that are typically moving at velocities an order of magnitude or more faster than the small drops. Thus, the relative difference in the drop velocities in the two types of atomizers may be the factor leading to the reduction of the soot formation and improved performance. Odgers et al. [64] report finding no measurable effect of drop size on combustion efficiency. The authors claim that, in almost all previous studies, some other parameter was changed as well as the drop size.

Drop Collisions a n d Coalescence:

Drop collisions and coalescence in the dense spray region, as well as in the dilute spray, have been described as a reason for the development and evolution of drop size distributions with downstream distance in the spray. The probability for drop collisions can be estimated from a knowledge of the drop speed relative to other target drops and the drop number density. For example, the swept volume, f2 i, for a drop of diameter di to collide with a drop of mean diameter D10, moving at a mean relative velocity, L~i, is

f2 i _ n,__,(d. 2 + Dlo) 2 viti. (10) 4

This approximation indicates the dependence of the swept volume on the relative velocity and the possible interaction time, t i. Assuming a spatial Poisson distribution of particles of number density N particles per cm 3, then

I~ = Nf2ie -N~ (11)

where Pci is the probability of a collision for the particle of diameter d, with another particle of mean diameter D10 within time ti, based on the probability of another particle existing in the swept volume, f2 i. The description is complicated by the facts that drops of different size may be traveling at velocities (magnitude and direction) that are a function of their size and location in the developing spray and that drops will decrease in size and velocity because of evaporation.

Particle collisions may lead to coalescence, breakup, or a rebound depending on several parameters, including the Weber and Ohnesorge numbers [65,66]. In a recent paper, Qian and Law [67] suggest there are five distinct collision regimes: bouncing, coalescence with minor deformation, coalescence with substantial deformation, coalescence followed by separation for near head-on collisions, and coalescence followed by separation for off-center collisions. Numerical simulations of drop collisions by Nobari and Tryggvason [68] considered off-center collisions.

Transient Fuel Injection

Diesel Injection:

Transient spray injection such as that used in diesel and spark ignition (SI) engines shows some unique atomization characteristics. Diesel injection may take place into a relatively quiescent environment at pressures of approximately 15 atm and at injection pressures of between 50 and 180 MPa [69]. The important combustion parameters are the fuel penetration, mixing, and vaporization. These parameters depend upon the spray drop velocity and trajectory, the drop size distribution, and the turbulent gaseous flow field. Tsao et al. [70] note that injection rate and duration are also important parameters since they influence the pressure rise in the cylinder after ignition. It was recognized that just fine atomization was not sufficient for achieving efficient combustion, since the spray must be able to penetrate into the chamber under a range of chamber conditions. If the drops are too small, rapid evaporation will occur, and the fuel vapor and flame will not penetrate far enough into the combustion chamber. In- jector parameters such as the number of orifices in


the injector, hole size and length of the orifice hole, and the hole angle all affect the performance [69]. Interaction of the spray with the air swirl in the chamber and the squish serve as effective mechanisms in the mixing and vaporization of the fuel spray.

The increasing restrictions on NOx and particulate emissions from diesel engines have led to some in- novative approaches in reaching these goals. Konno et al. [71] attempted to augment turbulent mixing during injection with the use of an auxiliary ehamber. A high-pressure air-fuel jet was injected into the main combustion chamber after the start of the main injection. This was reported to result in a factor of 3 reduction in particulate production. Golding [72] observed a similar improvement when injecting a meth- ane-air jet to enhance the turbulent mixing late in the injection cycle. Tow et al. [73] showed promising results in terms of NOx and particulate reductions when using staged or split injections. A variety of multiple injection strategies were examined in addi- tion to ramped injections in which the rate of change of the fuel injection was varied. This work followed the earlier work of Bower and Foster [74], who indicated that the fuel-air mixing could be enhanced by the augmented fuel spray penetration achieved with the split injection. Predictions using the modi- fied KIVA code made by Patterson et al. [18] indicated that fuel injection at lower pressure resulted in increased soot emissions, but an increase to very high pressures has a limited usefulness in reducing soot and NO~ emissions.

Detailed measurements of the drop size and velocity of transient diesel injection were obtained by Koo and Martin [75,76]. They observed that the fac- tors affecting the drop size and velocity were the fuel properties, pump speed, fuel quantity delivered, the needle lift, and the combustion chamber geometry.

Spark Ignition Engines:

Spark ignition (SI) engines using port fuel injection (PFI) also show a strong dependence of the emissions and performance on the atomization quality and fuel-air mixing [77-80]. As with diesel applications, the atomization is highly transient and must be accomplished over a wide range of operating parameters. Dementhon and Vannobel [80] investigated the injection of fuel into the manifold of a SI engine operating with gasoline. Their interest was in the effect of the manifold and combustion chamber aerodynamics on the fuel-air mixing. Depending on the angle of injection and the air flow, fuel films also formed on the valve and valve seat. Fuel injection into a manifold with similar flow conditions was investigated by Nemecek et al. [77].

Turbulent Dispersion

Information on the spray characteristics produced by the various atomizers operating in a quiescent environment is useful for the basic development of these systems. However, one might ask whether such studies are relevant for spray combustion applications since the injection generally takes place in highly turbulent swirling flows with recirculation and reaction. The drop size distributions and even the spray formation mechanisms may be significantly al- tered by the interaction with the ambient turbulent flow. Furthermore, the high-temperature combustion environment reduces the surface tension of the liquid and rapidly evaporates drops smaller than 10 #m in times on the order of milliseconds.

Turbulence Coupling:

Sprays are generally injected into the flow with sufficient momentum to significantly alter the continuous-phase flow field, at least locally. Thus, turbulence coupling between the dispersed phase and the continuous phase needs to be considered. Near the injector, the dispersed phase generally dominates the gas-phase turbulence in the host environment. A degree of turbulence is generated by the liquid during the spray formation and by the wakes of the drops in the dense spray region. Further downstream, two- way coupling exists between the dispersed phase and the gas. The drop number density is still high, and relatively large velocities still exist between the drops and the gas phase. Simultaneously, the gas-phase turbulence of the surrounding swirling flow and the turbulence that was induced by the injection velocity upstream begin to have a greater influence on the redistribution of the smaller drops within the spray. However, the spray number density and the drop slip velocities are still high enough to produce a significant effect upon gas-phase turbulence. Further downstream, the drops are dispersed by a combination of the spray axial and radial momentum and the interaction with the turbulent flow field, so the number density and slip velocities decrease substantially. The coupling is one way again in this region, but from the gas-phase turbulence to the dispersed phase. The dispersed phase now has an insignificant effect upon the gas phase.

Spray Interactions with Turbulent Flows:

In recent years, there has been a considerable interest in the Study of the interaction of the spray drops and the air flow swirl as a result of the need to develop smaller clean-burning engines while main- taining performance. Recirculation, generated by augmenting the swirl, which reduces the axial momentum of the flow and, combined with the positive streamwise pressure gradient, results in a reversed-


flow region, is also used to increase the residence time and enhance mixing. When contemplating such concepts as the rich-burn, quick-quench, lean-burn method for NOx reduction, it is imperative that rapid mixing in the initial fuel-rich zone is achieved without formation of pockets of near-stoichiometric burning. The mixing time depends on the size of the recirculation zone, the drop size distribution, and the degree of turbulence. A combination of the injector air, the swirler air, wall-cooling air, and the dome- cooling air all contribute to the supply of active air that also drives the fuel-air mixing [14,81]. The shear flows created by the swirl, which in some cases have counter-rotating components, and the wall jets, will produce large-scale eddies with which the spray drops must interact and, consequently, enhance the large-scale turbulent mixing.

The smallest turbulent length scales will be on the order of the drop diameters. It is known that the restoring force or drag needed to change the particle velocity to the velocity of the gas in the new sur- roundings is generated by the relative or slip velocity, so the fuel droplets will essentially always lag the flow. The degree of the velocity lag depends upon the flow acceleration, turbulence intensity, and mass of the drops. No matter how small the drops, they will be buffeted by the flow with random velocities having large variations in magnitude and direction. It may therefore be misleading to estimate evapora- t-ion rates and heat and mass transfer based on the studies of drops in a quiescent environment or as drops moving in a quasi-laminar environment.

Drop Response to Turbulence:

Several studies have been conducted to elucidate the interaction of particles with highly turbulent flows [82-87]. The drop drag correlation of Torobin and Ganvin [88] was validated experimentally for a polydisperse collection of drops in a turbulent air flow by Ruddff et al. [89]. The drop response to the large-scale eddies is assumed to be most important to the dispersion of the spray drops in the flow since it is the large-scale turbulent motion that is most effective in transporting the range of drop sizes over distances on the scale of the flow field. The analysis of Hinze [82] led to the expression that approximates the drop response as

d,n )]1,2

< ,P_do + fl (12) A LV \ p

where A is the macroscale of the turbulence, u ' is the root-mean-square (rms) of the velocity fluctuations, and fl is given by

fl = 1 + p - - (13) 2pd

339

which is approximately equal to 1 for a large density ratio between the drop and the gas. For the basic case of a subsonic jet of exit diameter D emanating into still air at an exit velocity U, the expression reduces to

] 1/2 dm C

Pd (14)

where C is an empirical constant, u'/U is the actual turbulence intensity, and Reo is the jet exit Reynolds number. As an example, for an axisymmetric jet with C = 0.4 at a jet Reynolds number of approximately 16,000, the largest drops that will respond well to the turbulence fluctuations are 5.0 pm. Thus, for sprays within a highly turbulent flow, a preponderance of the drops will significantly lag the large-scale turbulent fluctuations. As stated earlier, the implication is that the evaporation and heat transfer for drops in a quiescent environment will not be representative of the actual situation.

The response of the drops to large-scale eddies also has been described in terms of the Stokes number [90] as

1A St = - - - (15)

where v is the relative velocity between the particle and the eddy convection velocity. For a transit Stokes number greater than 1, the drop is likely to respond to the turbulent eddy. Dring and Suo [90] suggested that, for a drop within a large-scale eddy, the magnitude of the centrifugal forces relative to the Stokes drag forces may be estimated by the centrifugal Stokes number given as

18v p (16) St~ - ~vd2 P,I

where ~v is the angular velocity. The largest drop that will adequately respond to

the motion of the small-scale eddies was derived from the Stokes law particle relaxation and the Kol- mogorov time scales zk = (v/e) ~ as [82]

where e is the local turbulence dissipation rate, x is the distance from the jet exit, and D is the exit diameter of the jet. For a first approximation, z/z k = 1 was taken as a reasonable choice to provide a lower bound to determine whether the drop size, or more accurately the drop mass, is small enough to respond to the smallest turbulent scales in the flow. At a jet


Reynolds number of 16,000 (jet mean velocity of 50 m/s), the diameter of a water drop meeting the above criteria is 0.3/tm. Therefore, none of the drops in a typical spray can be expected to respond to the Kol- mogorov time scales in a turbulent jet. Hence, the drops will always experience a relative velocity that is random in trajectory and magnitude relative to the drop moving at the mean flow velocity, or the local velocity of the large-scale motion.

Drop Interaction with Large-Scale Eddies:

Experiments have been conducted to aid in the understanding of the particle interaction with the turbulence [9,91-95]. The initial studies [9] focused on the redistribution of the spray when interacting with turbulent swirling flows with recirculation and the time-averaged spray drop dynamics. Time-resolved measurements were then applied in the measurements of a spray flame. These results showed possible evidence of clustering of the drops at a period that correlated with the shedding frequency of the dilution air flow [95]. The formation of clusters due to the interaction with turbulence has been the subject of several studies [94-96].

An illustrative example of the basic mechanisms of the cluster formation was given by Hancock et al. [94] using a novel flow visualization technique. The method involved the injection of water drops into a TiCl4-1aden gaseous flow, which then forms TiO2 particles of approximately 1/zm in diameter. The visualization method clearly showed how small drops with a mass that can respond to the vortex will tend to accumulate in the core of the vortex. It is easy to anticipate that spray drops in the size range between the 1-/zm particles and the 70-/~m drops will have a continuum of responses from being entrained in the vortex to only showing a small deflection in the trajectory. An experimental investigation of the interaction of a spray with large-scale eddies was conducted by Bachalo et al. [86,91] in an effort to quantify the drop response to the eddies at various flow Reynolds numbers and the fundamental mechanisms in drop dispersion and cluster formation.

8--2 ln(1 + B)

f l _ Cp (19) Pa

with the symbols described in the nomenclature. The values o f t for heptane, for example, were ,6 = 0.96 for a single drop and fl = 0.47 for a uniform spray. For a monodispersed drop stream combustion of kerosene, the total combustion time tc was approxi- mated as

�9 c = 2 .5 • 10- a3 (20)

where do is the initial drop diameter in micrometers. Typical drop combustion times are 0.25 ms for a 10- /*m drop and 25 ms for 100-/lm drops. Note that, at a mean velocity of 20 m/s, a 10-/~m drop will travel approximately 2 mm, and 100-/am drops will travel 200 mm during this time, which may be well beyond the flame zone.

Researchers have assumed that the drops will rapidly acquire the velocity of the air stream, so the drop Reynolds number and the enhancement of the heat and mass transfer from the drop by the relative motion disappear [64]. However, the basic analysis on the drop response to the turbulence indicates that this is not the case, as the drops do not equilibrate with the turbulent flow velocity fluctuations. Because the drops are more likely to lag the smaller scale turbulent fluctuations, it may be concluded that these smaller scale fluctuations will be more effective in increasing the local convection and, hence, the drop mass transfer rates. Chin and Mongia [98,99] have studied the effects of temperature on the drop breakup, and convection on drop evaporation. They show that, at Re d greater than 50, the evaporation time with forced convection is approximately one-half that of the stagnant case [98]. Gokalp et al. [100] have also investigated the influence of turbulence on the global transfer rates from heptane and decane drops.

Spray Combustion Measurements

Spray Evaporation and Combustion

Drop evaporation has been the subject of extensive studies with the focus being on single drops, as well as on sprays. Unfortunately, most of these studies have considered isolated drops in quiescent or very low turbulence environments, as discussed in the review by Beer and Chigier [97]. The drop evaporation is described as [64]

r~ = ~- (18)

where

The development of the phase-Doppler particle analyzer has enabled the detailed measurement of drop size and velocity and the number density and volume flux in realistic spray combustion environments [63,95,101-105]. Bachalo et al. [95] obtained drop size and velocity measurements in an unconfi- ned fuel spray combustion and observed the appar- ent formation of drop clusters that had a periodicity that correlated with the shedding frequency of the coannular dilution air flow. Edwards and Rudoff [105] obtained measurements of the drop size and velocity in a research furnace of 0.57 m in diameter and 0.93 m in height. The size-classified mean velocity of the spray drops showed a maximum velocity

INJECTION. DISPERSION, AND COMBUSTION OF LIQUID FUELS 341

difference between the 2-/~m drops and the 40-/2m drops of approximately 10 rrds. Williams [106] sug- gests that drops of 100/~m in alia, meter with relative velocities on the order of 10 cm/s will be extin- guished. Thus, the penetration of these drops beyond the flame zone may be expected, resulting in excess unburned hydrocarbon (UHC) emissions. The fact that the large drops escape the combustion is clearly visible in the flame photographs of Presser et al. [103].

Gas-phase and spray drop size and velocities were measured by Bulzan [107] for a simplex air-assist atomizer operating in a swirl coflow air stream used to stabilize the flame. Anisotropic turbulence was observed, with the axial and radial velocity fluctuations being much larger than the angular velocity fluctuations. Measurements of the flow velocity and turbulence parameters, as well as the drop size and velocity, for an airblast atomizer operating on methanol were reported by McDonell and Samuelsen [62]. Both nonreacting and reacting conditions were also considered. They found that the effect of the reaction had only a minor effect on the mean velocity and turbulence intensity at an axial station of 50 mm (the beginning of the reaction zone). Anisotropy of the turbulence was observed to increase with reaction.

Chehroudi and Ghaffarpour [108] investigated the effects of swirl and dilution air flow rates on the shape and stability of a kerosene flame on a model combustor, with comparisons made of the noncom- busting and combusting cases. Their flow visualization showed nonuniformly distributed separated fin- gerlike regions of visible flames wrapped around the spray sheath. These structures were possibly due to large-scale eddies formed by the swirling flow. In- vestigations by Li et al. [109,110] explored the combustion and flame extinction of methanol sprays con- veyed by nitrogen into a counterflowing oxygen stream. Detailed measurements showed the expected slight increase in Da2 as the flame was encountered. The number density showed a dramatic decrease within the flame and was approximately three orders of magnitude less than in the nonburn- ing ease.

Summary and Conclusions

Improvements in the combustion performance and reduction of pollutant emissions, including NO x and soot, are primary objectives of combustion research and development. It has been recognized that improvements in combustion may be realized through a better understanding of the fuel atomiza- B tion, injection, and aerodynamic mixing in the corn- Co bustor. Spray formation and atomization have re- cz eeived a good deal of attention both through the cp research on the detailed studies of spray formation D mechanisms and the development of advanced at- D10

omization techniques. There is a need for further research on the impact of the spray quality on the combustion efficiency and pollutant formation. Several parameters, such as the drop penetration, evaporation rate, drop reaction to the mean swirling flow and to the large-scale turbulent fluctuations, need to be quantified in terms of their influence on the combustor performance.

Developments in the instrumentation have provided the means to obtain reliable experimental data on the sprays, and spray interactions with the turbulent flow in nonreacting and reacting environments. Reliable measurements in these difficult environments require the most sophisticated methods, such as real-time Fourier analysis signal detectfion and processing, and logic systems to prevent or at least minimize errors. Measurement methods continue to be developed to provide better accuracy and reliability in the spray combustion environments, which are characterized as highly three-dimensional turbulent two-phase flows with recireulation. Measurements of the gas-phase turbulence in the presence of the dispersed phase require the adoption of careful seeding procedures. Simultaneous in situ drop temperature measurements are being attempted in an effort to add another dimension to the information needed to understand the drop dynamics and vaporization.

Drop response to the turbulent flow has a significant effect on the mixing and distribution of fuel in the eombustor. Basic analyses show that even the smallest drops will not follow the small-scale turbulent fluctuations. Drop vaporization and mass transfer rates are dependent upon the relative velocity between the drops and the gas phase. Thus, studies of interactions between sprays and turbulence continue to be an important area of research. It also appears that turbulence modeling efforts have not reached the point of predicting the spray behavior in highly turbulent flows. Future experimental research must focus on the fundamental mechanisms associated with the spray interaction with the turbulence and the formation of localized voids and regions of high spray concentration (clusters), as this phenom- enon produces fuel-rich and fuel-lean pockets leading to soot and NOx formation. Careful experimental studies need to be conducted on the evaporation of sprays in a controlled environment, with parameters such as the turbulence levels and drop concentra- tions being varied and measured.

Nomenclature

transfer number drag coefficient liquid specific heat gas specific heat at constant pressure jet exit diameter linear mean diameter


D32 Sauter mean diameter d drop diameter dm largest drop to respond adequately to large-

scale turbulence dmi n minor axis of deformed sphere dma x major axis of deformed sphere d 1 axis parallel to the measurement axis de axis perpendicular to the measurement axis do initial drop diameter N drop number density P joint Poisson probability Pa probability of a drop collision Pt temporal Poisson probability Px spatial Poisson probability Red drop Reynolds number ReD jet Reynolds number St Stokes number St c centrifugal Stokes number T t total time for the sample ti drop interaction or observation time tg period of the drop passage of the probe vol-

ume U jet exit velocity u' rms turbulent velocity fluctuations V probe sample volmne V, sample volume for the particles in size

class i v i mean relative velocity of drop size class, d i v relative velocity, drop to gas We Weber number, We = pv2d/a x distance from the jet exit

Greek Symbols

c

Y 21 2 A /l y

P Pd o T TH rE Zk re Zc

radial displacement of fluid element, drop deformation

local turbulence dissipation rate particle rate in size class di liquid thermal conductivity gas thermal conductivity macroscale of turbulence dynamic viscosity kinematic viscosity gas density drop liquid density surface tension characteristic drop response time liquid heating time drop lifetime Kolmogorov time scales evaporation time combustion time swept volume by the drop angular velocity

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