review_combustion

VOL. 15, NO. 8, AUGUST 1977 AIAA JOURNAL 1063

Swirl Flows in Combustion: A Review

David G. LilleyConcordia University, Montreal, Canada

I. Introduction

RECENTLY, concentrated research effort has been ex-pended on understanding and characterizing the

combustion aerodynamics of swirl flow burning processes ofgaseous, liquid, and solid fuels. Economical design andoperation of practical combustion equipment can befacilitated greatly by estimates made from complementaryexperimentation and modeling studies. Such work combinesexperimental and theoretical combustion aerodynamics withsophisticated computational fluid dynamics and its im-provement and use will reduce the cost of developmentprograms significantly. Detailed surveys of these studies areto be found in the literature.M1

Swirling flows result from the application of a spiralingmotion, with a swirl velocity component (also known as atangential or azimuthal velocity component) being impartedto the flow via the use of swirl vanes, in axial-plus-tangentialentry swirl generator or direct tangential entry into thecombustion chamber. Experimental studies show that swirlhas large-scale effects on flowfields: jet growth, entrainment,and decay (for inert jets) and flame size, shape, stability, andcombustion intensity (for reacting flows) are affected by thedegree of swirl imparted to the flow. This degree of swirlusually is characterized by the swirl number S, which is anondimensional number representing axial flux of swirlmomentum divided by axial flux of axial momentum timesequivalent nozzle radius. In this context, for comparisonpurposes it is worth noting that swirl vane angle 0 and swirlnumber S are related approximately by

5=- tan</>« - tan</> (1)

for dh <^d, so that vane angles of 15, 30, 45, 60, 70, and 80,for example, correspond to 5 values of approximately 0.2,0.4, 0.7, 1.2, 2.0, and 4.0. Here 100% efficiency also isassumed for the swirl vanes, which deteriorates as the vaneangle increases.

The effect of a low degree of swirl (weak swirl, 5< —0.4) isto increase the width of a free or confined jet flow: jet growth,entrainment, and decay are enhanced progressively as the

degree of swirl is increased. At higher degrees of swirl (strongswirl, S> —0.6), strong radial and axial pressure gradients areset up near the nozzle exit, resulting in axial recirculation inthe form of a central toroidal recirculation zone, which is notobserved at weaker degrees of swirl. In particular, swirl isused extensively as an aid to efficient clean combustion in avariety of practical situations: gasoline engine, diesel engine,gas turbine (including central toroidal recirculation zone),industrial furnace, utility boiler, and many other practicalheating devices, including small domestic home furnaces.Recent interest also is being shown in rotary (Wankel) andstratified charge engines in our desire for efficiency andcleanliness. In design situations, the engineer has co seek anoptimum path between irreconcilable alternatives of, forexample, efficiency and pollution.m5

Consideration is given to the major features of thecharacterization of swirl flow combustion, with emphasis onapplication to practical combustors. Recent experimentalwork is surveyed in Sec. II, with special regard to the maineffects of swirl on the performance, stability, and combustionintensity of flames in combustors. Since solution of the basicgoverning equations yields predictions that are realistic only ifthe physical processes are sufficiently well expressed inmathematical form and suitable computational methods ofsolution are employed, these details are discussed in Sec. III.The treatment is brief, since extensive reviews are available inthe literature. It is possible to predict major features of theseswirling flows; some solutions are exhibited in Sec. IV. TheClosure summarizes the achievements and current status.

II. Experimental WorkAlmost all industrial flames have the form of turbulent jets

issuing from round orifice burners. Sometimes the fuel gas isintroduced through a central jet (maybe premixed) and theremaining air through an annulus surrounding it, so thatdouble concentric jets are formed. If the fuel enters as liquiddroplets or coal particles, it is either atomized or sprayed fromthe central region, again with a surrounding annulus of air.Either the primary or the secondary (or both) is given a certaindegree of swirl to enhance the jet and flame characteristics.Tangentially fired equipment differs from wall-fired

David G. Lilley is currently an Associate Professor in the Department of Mechanical Engineering, ConcordiaUniversity, Montreal, Canada, with responsibilities for teaching and research in fluid dynamics and combustion,with the development and application of theoretical combustion aerodynamics being of prime concern. He wasborn in England and obtained his education at Sheffield University, from which he received the B.Sc. and M.Sc.degrees in Mathematics in 1966 and 1967 and the Ph.D. degree in Engineering in 1970. His academic careerincludes two years lecturing in Mathematics and Computing at Sheffield Polytechnic, three years as ResearchAssociate in Mechanical Engineering at Cranfield Institute of Technology, and one year as Visiting AssociateProfessor in Chemical Engineering at the University of Arizona, prior to taking up his current appointment.During this time, he has concentrated on the modeling and prediction of swirl flows with application to furnaceand combustion chamber design. He is a corporate member of five technical societies, and Associate Fellow ofAIAA, and has been a member of the AIAA Technical Committee on Fluid Dynamics (1974-1977).

Presented as Paper 76-405 at the AIAA 9th Fluid and Plasma Dynamics Conference, San Diego, Calif., July 14-16, 1976; submitted Aug. 3,1976; revision received April 25, 1977.

Index categories: Combustion Efficiency; Reactive Flows; Combustion and Combustor Designs.

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1064 D. G. LILLEY AIAA JOURNAL

r / R

0 10 20 30 40 50 60 70AXIAL DISTANCE, Cm

Fig. 1 Streamlines in swirling annular freejet; S =1.57 (Ref. 16).

0 0.4 0,8 1,2 1,6 2.0 2.4

M R /M Q

Fig. 2 Variation of recirculated mass flow in freejets with swirlnumber.5

equipment in that no swirl is imparted to the incomingstreams, but these streams are directed so as to aim tangen-tially at the fireball that results in the center. These swirleffects, documented at length in Refs. 1-70, now arediscussed.

A. Swirling FlowsExtensive studies of the effect of swirl on jet flows have

been made and reported elsewhere,1"4 for both single anddouble concentric nozzle flows, free and confined. As anintroduction to this literature, some of the salient featuresnow are discussed. General effects of introducing swirl onturbulent jets are to cause an increase in width, rate of en-trainment, and rate of decay in the jets as the degree of swirl isincreased progressively. Pressure fields are induced to balancecentrifugal forces, and the decay of swirl caused by shear andmixing with surrounding fluid sets up adverse axial pressuregradients. The form of the radial distribution of time-meanaxial velocity depends on the degree of swirl S imparted to theflow. For weak swirl, the distribution remains Gaussian inform, with the maximum velocity on the axis of the jet. As theswirl number is increased, the radial spread of the jet in-creases, and, for jets with swirl greater than a certain criticalswirl number (approximately 5 = 0.6), the forces due to theaxial adverse pressure gradient exceed the forward kineticforces and the flow reverses its direction in the central regionof the jet, in the vicinity of the nozzle. At 5=0.64, the lengthof the reverse flow region is 4 jet diameters.

For combustion applications, one of the most significantand useful phenomena of swirling jet flows is the recirculationbubble generated centrally for supercritical swirl numbers.From the point of view of long-time mean averages, bound-aries of the recirculation bubble and reverse flow zones arewell defined. The flows generally are associated with highrates of shear and values of turbulence intensity so that in-stantaneously large-scale spatial fluctuations of boundariesand stagnation points occur. Streamlines calculated frommeasured time-mean velocity distributions are shown for a

1-0

o

1-0

2-0

z / dFig. 3 Size and shape of reverse flow zone in freejets from annularvane swirlers with straight exits.5'20

swirling annular freejet (issuing from a swirl generator) with5=1.57 in Fig. I.16 The recirculation bubble plays an im-portant role in flame stabilization by providing a hot flow ofrecirculated combustion products and a reduced velocityregion where flame speed and flow velocity can be matched.Flame lengths and distance from the burner at which theflame is stabilized are shortened significantly.

Of course, the precise effect of swirl on a flowfield is foundto depend on many factors as well as the swirl number: forexample, nozzle geometry (the presence of a central hubencourages a larger recirculation zone, as does the addition ofa divergent nozzle), size of enclosure if any (central recir-culation zones are much more pronounced in enclosures thanthose of comparable freejets), and the particular exit velocityprofiles (recirculation zones tend to the larger when the flow isproduced via swirl vanes as opposed to an axial-and-tangential entry swirl generator).

Turbulence intensity reaches very high levels in recir-culation bubbles. On the reverse flow boundary, where themean velocity is zero, the local turbulence intensity tends toinfinity. Measurements of all six different turbulent stresscomponents show strong variations of absolute turbulencekinetic energy levels and strong nonisotropy of the stressesand associated turbulent viscosity.17 The exchange coef-ficients are found to be functions of the degree of swirl andposition in the flowfield, as can be shown also by analyticaland numerical inverse solution procedures applied to thesimpler situation of weakly swirling jets and flames.18*19

The size and shape of the recirculation zone and associatedregion of high turbulence are critical to flame stability,combustion intensity, and performance. Regardless of thetype of swirl generator (apart from hubless vane swirlers), the"eye" of the recircualtion eddy always occurs very close tothe nozzle exit, and streamline patterns similar to those of Fig.1 also result. The main differences lie in the recirculated massflow produced, and Fig. 2 shows that there is good correlationbetween the swirl number 5 and recirculated mass flowMR/M0 for free swirling jets.4 Here the suffices R and 0stand for reverse and initial values. The presence of an oil gunat the throat of a swirl generator appears to halve MR/M0\the presence of a divergent outlet has a disproportionatelylarge effect of greatly increased MR/M0 for a given swirlnumber. Although the point of onset of reversed flowgenerally is taken to occur at approximately 5 = 0.6, it is clearthat divergent exit nozzles substantially reduce thisrequirement.5

The size and shape of the reverse flow zone depend prin-cipally on the degree of swirl, as shown in Fig. 3, and angle ofdivergence of the outlet. The figure shows the effect of swirlfor annular vane swirlers with straight exits.5'20 The trends,even though there are experimental difficulties in takingmeasurements in regions of low velocity, are evident. As theswirl number (associated with vane angle) is increased, thenarrow recirculation zone becomes longer, reaching amaximum at about 5= 1.5, and subsequently becomes shorterand wider at 5>2. Recirculation zones produced by swirlgenerators (that is, axial-plus-tangential entry swirlgenerators) generally are much smaller than those produced

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AUGUST 1977 SWIRL FLOWS IN COMBUSTION: A REVIEW 1065

by swirl vanes, for a given swirl number. Since mass flowrates at similar swirl numbers are similar, it is clear thathigher reverse flow velocities, higher velocity gradients,higher turbulence levels, and higher rates of mixing areassociated with the much more compact reverse flow zonefrom the swirl generator.

B. Swirling FlamesThe length of nonswirling fully developed turbulent dif-

fusion flames is unaffected by an increase in velocity througha given burner, in contrast to laminar flames, and in freesurroundings is dependent mainly on thq type of fuel used andthe diameter of the orifice. If the flame is confined in anenclosed furnace, the flame length increases, owing to the lackof entrainment of oxidant and the presence of recirculation,by about 25%, but this depends on the oxygen concentrationof the recirculation gases and degree of confinement Did,where D and d are enclosure and nozzle diameters. Partiallypremixed flames are shorter, and the intensity of combustionis greater, this depending on the degree of premixing.

Phenomena similar to those observed and measured innonreacting swirling flows have been observed and measuredin swirling flames. The recirculation bubble plays an im-portant role in flame stabilization by providing a heat sourceof recirculated combustion products and a reduced velocityregion where flame speed and flow velocity can be matched.Flame lengths and the distance from the burner at which theflame is stabilized are shortened significantly. Direct com-parisons of turbulent flowfields in nonreacting media withthose in flames show that the thermal molecular and atomic

z / dFig. 4 Effect of increasing swirl number on the flame front(maximum temperature) lines in free nonrecirculating swirlingflames.6

&*SW1RL NUMBER

energy changes in the flames induce comparatively smallchanges in the gasdynamic flowfields of recirculating swirlingjets. Reverse flow boundaries and reverse mass flow rates arereduced only slightly with combustion.21

With swirl, the axial velocity radial profile exhibits off-centerline maxima at a short distance downstream of thenozzle (exhibiting reverse flow close to nozzle), as measuredtypically in an industrial furnace. The high-temperature zonefo the flame front is deflected from an annular position forthe fuel jet without swirl to a jet center line position for thecase with swirl. This is due to the increased mixing andreaction rates in the swirling flame. The effect of increasingswirl number on the flame front (maximum temperature) linesin free nonrecirculating flames is shown in Fig. 4, where R= 0/2 is nozzle radius.6 Further details about the effect ofcombustion on reverse flow boundaries, including the effectof mixture ratio, type of fuel entry, etc., may be found inRefs. 1-6.

The reverse flow zone of a recirculation bubble has many ofthe characteristics of a well-stirred reactor in that the tem-perature and gas composition within the reverse flow zone arealmost uniform. This well-stirred zone is fluid-dynamicallyconfined and surrounded by nonreacting room-temperatureair. The levels of temperature and gas composition can becontrolled by the amount and nature of the fuel injected intothe zone, and aerodynamic control is achieved by varying thedegree of swirl. A means thus is available for controlling therates of formation and reaction of carbon and oxides ofnitrogen, and thus, for any particular flame, optimumconditions can be found for minimum net production ofcarbon and nitrogen.

Premixed vane swirled flames in furnaces with expansionratios D/d=2.5 and 5.0 have been studied at Glasgow fromthe aerodynamic and modeling points of view.22 It is foundthat the same swirier can give different velocity patterns as therelative furnace size D is changed, and the size ani shape ofthe central recirculation zone, if present, are primarly func-tions of D and not of d. Correlations between flow types A, B,C, and D and the modified swirl number

= Sd/D (2)

0-1 -

005-

O-1O O-15 O-220s 305 40s 50s

SWIRLER VANE ANGLE 9

O-3 0-4 O-5 O-7SWIRL NUMBER S*

Fig. 5 Swirl number relation to input conditions and flow type.Fig. 6 Variation of reverse mass flow in central recirculation zonewith swirl number S* (Ref. 22).

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based on furnace radius instead of nozzle radius are verysatisfactory and are shown in Fig. 5. The flow types con-sidered are as follows: A, very weak swirl and no significantthrough in velocity on the axis; B, through in velocity on theaxis but no reverse flow; C, weak reverse flow; and D,strongly established central recirculation zone. Transitionbetween these types occurs at values of S* of 0.08, 0.11, and0.18. Furthermore, for a given swirler and a given air-fuelratio (isothermal or burning flow), the 5* values are verysimilar in the two relative furnace sizes. There is a change inthe slopes of both the isothermal and burning characteristicsat a vane angle of about 30°, corresponding in the burningcase to the transition to the formation of a central recir-culation zone. Figure 6 shows the corresponding reverse massflow in the central recirculation zone as a function of 5*, coldor flame conditions, with an expansion ratio D/d=2.5 and5.0.

Recent laser anemometer measurements in free swirlingflow under flame and no-flame conditions have beenreported.23 These include measurements of velocity andturbulent kinetic energy, and they show that substantial in-creases are found in turbulent kinetic energy and velocityfluctuations as a consequence of combustion.

The effect of swirl on flame length is demonstrated bothexperimentally and theoretically using simple models for aturbulent diffusion flame in a cylindrical furnace.24 Hereswirl is imparted only to the annular flow of air, surroundingthe central fuel nozzle, and inlet conditions arestoichiometric. The trends resemble those for the freepremixed flames of Fig. 4.

Stability, mixing, and interaction of multijet natural-gasflames with swirl have been investigated experimentally.25

The effect of burner crowding and separation on the flamelength, for different values of 5, shown in Fig. 7, isrepresentative of the results obtained. It is clear that flamelength increases with increased number of burners, greaterproximity, and lower degree of swirl. The presence of anotherflame in the near vicinity of a flame decreases the surface areathat is in direct contact with the atmosphere, so that en-trainment is hindered. Also, the influence of burner crowdingis found to be even more pronounced in fuel-rich flamesbecause in these cases only small changes in the amounts of airentrained strongly affect the combustion processes. Blow-offlimits of the multiple burner systems are shifted toward thefuel-rich region. For conditions approaching the critical blow-off, a central flame could be lifted or blown off the burnerwhile the surrounding flames remain attached to theirburners.

The effect of swirl on residence time distribution and theperformance and efficiency of combustors are determinedexperimentally in Ref. 26. A comparison of tracer con-centration decay curves obtained for a water model and apulverized fuel furnace for varying degrees of swirl is shownin Fig. 8. The ability to vary the ratio of mean residence timein the perfectly stirred and plug-flow sections of the com-bustor, by varying the degree of inlet swirl, is of greatsignificance in design. A similar investigation on the stabilityand combustion intensity of pulverized-coal flames discussesthe effect of swirl and impingement of the secondary annularair supply.27 Important results are that secondary air swirlleads to a pronounced improvement in the stability of flamesand leads to a reduction in the distance between burner andflame front.

Most complete laser anemometer measurements of swirlingflow under confined conditions, with and without com-bustion, are available recently.28 These were obtained in theImperial College, London, and Harwell furnaces. As anexample, Fig. 9 shows contours of constant velocity for twosets of results, representing isothermal flow and combustingflow. Each set is obtained at two levels of swirl, in anaxisymmetric furnace, using a combustible mixture of air andnatural gas. The boundary and field measurements of three

26

26

24

22

S 2 0

r 18oZ 16UJX

5 "

12

0>2 0«3 0-4SWIRL NUMBER, S

0*5

Fig. 7 Effect of burner crowding and separation on flame length.2

*A•A

O

V

o•

G*6*R001*561-562*242*243-93'9

FURNACEMODELFURNACEMODELFURNACE.MODELFURNACEMODEL

t sec

15 22018 32017 92019 320

Fig. 8 Comparison of tracer concentration decay curves obtainedfrom water model and pulverized fuel furnace for varying degrees ofswirl.26

components of time-mean velocity and corresponding normalstresses were designed to be of good use in the evaluation ofturbulent flow prediction procedures and thus, to this end,necessarily are far more detailed and accurate than previousstudies in the Delft, Ijmuiden, and Karlsruhe furnaces.Results demonstrate, for example, that the regions ofrecirculation under the reacting flow conditions differ sub-stantially from those under nonreacting conditions. Theturbulence is found to be far from isotropic over most of theflowfield. It also is clear that, as a consequence of thecombustion, the velocity fluctuations increase significantlywhen appropriate integrals over the entire flowfield areperformed, thus supporting, in some sense, the hypothesis ofcombustion-generated turbulence.

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At United Technologies Research Center (UTRC), EastHartford, Conn., a substantial effort also has been given tolaser anemometer measurements of turbulent swirlingcombustion flows.29 Measurements were made in the initialmixing region of a confined turbulent diffusion flame. Theaxial and swirl time-mean velocity profiles and the rms andprobability density distribution of the velocity fluctuationsshow that there are significant variations of the mean andtime-dependent flowfields with changes in ambient combustorpressure and inlet-air swirl. These variations have pronouncedeffects on pollutant emissions. Substantial large-scale con-tributions to the total rms turbulent velocity flowfield werefound. These large-scale fluctuations result in large depar-tures from Gaussian turbulence and significant deviationsfrom isotropy over most of the initial region. Such large-scalemotions indicate that turbulence models based on localequilibrium assumptions will not represent the physics ofthese combusting flows adequately. Representative time-meanaxial and swirl velocity profiles at different axial stations,over the full range of ambient combustor pressure and swirl,are appended in the paper.

C. Pollutant FormationConcentrating on pollutant formation in combustion,

detailed experimental results for the influence of aerodynamicphenomena are available from UTRC.30 Average con-centration levels of the pollutants nitric oxide NO, nitrogendioxide NO2, carbon monoxide CO, and unburned hydro-carbons were measured at the exit of an axisymmetriccombustor over a significant range of operating conditions. Inaddition, detailed species concentrations, temperature, andvelocity maps were obtained throughout the combustor forseveral representative operating conditions. Gaseous fuel(natural gas, methane, or propane) issued through a centralround tube, mixing and burning with the airstream within the1.8-m-long cylindrical combustor. Liquid propane was used

Isothermal flow

3 2 1 0 1 2 3

as the fuel in some of the tests. Major combustor inputparameters were varied over substantial ranges: overall fuel-air equivalence ratio, 0.5-1.3; air-fuel velocity ratio, 0.1-40.0;inlet air swirl number, 0.0-0.6; air flow rate (kg/sec), 0.09-0.14; inlet air temperature (°K), 730-860; and combustorpressure (atm), 1.0-7.0.

It was found that elevated pressure and swirl result in a shiftfrom chemistry- to mixing-limited behavior and create"unmixedness" in the flowfield, producing high local tem-peratures in an annular region around the centerline, which inturn enhances NO formation and consumption ofhydrocarbons. Aerodynamic flame stabilization, achievedwithout the benefit of swirl or physical flame holders insystems having large air-fuel momentum flux ratios, producesstrong stirring that results in reduced temperatures, low NOformation, and hydrocarbon consumption rates.

The NASA Lewis annular combustor includes a uniqueconcept that has demonstrated substantial potential for loweroxides of nitrogen NOX emissions.31'37 The combustor isdivided into 48, 72, or 120 individual swirl-can modulesarranged in two or three concentric rows, respectively, whichdistribute combustion uniformly across the annulus. Earlydesigns of these modules with swirler plates did not pay muchattention to fuel atomization and mixing within the individualmodules. It now is recognized that oxides of nitrogen, soot,and unburnt hydrocarbons formed in the small reaction zonescan be frozen and omitted from the exhaust. More attentionnow is being devoted to the control of mixing and im-provement of fuel atomization in each individual module, allof which now are designed specifically for low oxides ofnitrogen emissions. Results show that swirl-can combustorsproduce oxides of nitrogen levels substantially lower thanconventional combustor designs. These reductions are at-tributed to reduced dwell time resulting from short combustorlength, and quick mixing of combustion gases with diluentair, and to uniform fuel distributions resulting from the swirl-can approach. At low power conditions, the levels of carbonmonoxide and unburnt hydrocarbon emissions normallywould rise to quite high values, but these can be reducedsomewhat by radial staging of fuel into just one or twomodule rows. At present, a swirl flow annular combustor fortest in-house is being designed, including radial fuel stagingcapability; it complements the swirl-can module approach andis discussed further in Sec. II. D.

Nitrogen oxides NOX are formed (primarily as nitric oxideNO) during the combustion process as thermal NO (resultingfrom the high-temperature thermal fixation of atmosphericnitrogen in the air supply, as primarily with gas and oil fuels)or as fuel NO (resulting from the nitrogen in the fuel, as withoil and coal fuels). Thermal NO formation in gaseous systemshas been studied extensively. The controlling mechanism inthe postflame zone is an extended version of that proposed byZeldovich. In the flame zone, significant amounts of NO areformed very rapidly as prompt NO, and these are believed tobe the result of high oxygen atom concentrations produced bythe hydrocarbon combustion process and of other undefinedcarbon-nitrogen reactions.38 The mechanism for fuel NOformation is not well established, although recent work in-

VELOCITYm/s«c-<

1919265227

1 2r /R

Fig. 9 Contours of constant velocity for swirl numbers of 0 and 0.52,for isothermal and combusting flow.28

1 2 " S

Fig. 10 Nitric oxide NO emission curves for 1.76-MW pulverizedcoal flame (5% excess air; injector A is 0.115 m diam; others are 0.060mdiam).43

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dicates that it is the primary source of NO formation inpulverized coal flames.148

The evidence about the effect of swirl on pollutant for-mation shows that precise effects depend on the preciseconfiguration being considered. As far as oxides of nitrogenNOX are concerned, the effect of swirl may enhance itsproduction or not. Generally, increased swirl 1) increasesentrainment of cooled combustion products and therebydecreases thermal NO, 2) increases local oxygen availabilityand thereby increases fuel NO (and possibly also increasesprompt NO), and 3) increases combustion intensity and soincreases thermal NO.

Prompt NO may be dealt with under the second category,where swirl increases local oxygen availability. There are twoeffects of this. Hydrocarbon radicals react more with oxygenrather than forming a nitrogen-containing hydrocarbonradical, which is essential for the prompt NO mechanism,38'39

and so reduce prompt NO formation. On the other hand, anynitrogen-containing free radical has more oxygen availablewith which to react, which leads to the greater production ofprompt NO. There is no evidence as yet to decide which ofthese competing effects of swirl predominates. Details ofother pollutant formation studies are relegated to thereferences40'44; other work is described in Sec. III. B., withadditional referencing. As an example of the effect of swirl onthe level of flue gas nitric oxide concentrations, for differenttypes of fuel injector, Fig. 10 shows the results obtained at theInternational Flame Research Foundation, Ijmuiden,Holland, for pulverized coal flames.43 Details of the fuelinjectors used in these studies, and similar results for large-scale gaseous diffusion flames, are available in Ref. 44.

D. Centrifugal EffectsRecent work at United Technologies Corp., Florida,45"48

and ONERA, France,49'50 has been concerned with thefavorable centrifugal force effects on combustion. Tests in acombustion centrifuge demonstrate that the increased"buoyancy" produced can increase flarnespeeds significantlyover turbulent flamespeeds, which control combustion ratesin conventional burners. In the past, when attempts have beenmade to increase the turbulent flamespeed to higher values,the pressure drop required to produce the turbulence wasprohibitive, or flame stabilization problems occurred athigher velocities. Tests show that centrifugal force can be usedto increase flame propagation rates by an additional factor of4 or more.47

The models were developed47 to predict the flame-spreading rate at various burner conditions (bubble theory offlame propagation) and the extinction limits of flames at veryhigh centrifugal force values (based on classical heat-transfercorrelations), respectively. The effects of Reynolds numberon turbulent flamespeeds and on limiting bubble sizes ingravitational fields also were measured. The validity of theexperimental model was confirmed by testing a subscale 15-in.-diam swirl augrnentor,48 which uses precombustion swirlvanes to swirl the flow and produce a centrifugal field thatincreases the burning rate of the combustible mixture. Fuel isinserted into the swirling flow by spray rings, and the flamebubbles move quickly to the center because of the buoyanteffect of the hot burned gases in the cold unburned gases,igniting the fuel-air mixture as they go. Since the bubble speedcan be many times greater than turbulent flamespeed inconventional augmentors, shorter lengths or higher burningefficiencies result (see Fig. 11). The swirl augrnentor has theadded performance advantage of being unaffected bypressure and Mach number changes, and pressure losses areless than conventional augmentors. This has led to the designof a full-scale swirl augrnentor, for advanced versions of anAir Force turbofan engine, which is predicted to reduce thefuel consumption and increase the stability of the engine.47

Guided by these studies, a swirl flow annular combustor isbeing developed at NASA Lewis Research Center. It has

100

80

60

40

! 20

0

D ExO Ex

———— MoE

• L/D

L/D =

>eri mental Daperi mental Dadel With Bubqua! to Pilot

/= 1.37/̂

B

0.914 '

ta (L/D = O.ita (L/D = 1.Cble DiameterHeight

r̂

14)17)

/a

20 30Swirl Angle - deg

50

Fig. 11 Comparison of experimental and theoretical results ataugmentor equivalence ratios between 0.95 and 1.05 (Ref. 48).

radial fuel staging capability. One outer row of swirl-canmodules may be used exclusively under idle conditions. Atother conditions, fuel also may be injected further inward,directly into an annular swirling flow region, caused by swirlvanes positioned around the annulus further upstream. Atpresent, this swirl flow annular combustor is being in-vestigated. A full-scale plastic model already has been builtfor flow studies, and tests currently are in progress withannular swirl vane angles of from 25 ° to 45 °.

In general, the application of swirl in combustion systems,usually to the annular air surrounding the primary fuel outlet,leads to increased rates of mixing (higher turbulence) and ashorter, more intense stable flame. Under certain cir-cumstances, however, swirl can have the opposite effect andlead to reduced rates of mixing (laminarization) and a longerlazy flame. Such an example is a turbulent jet flame, burningin the core of the rotating flowfield set up by the rotation of acylindrical wire screen.51'52 Without rotation, a typicalturbulent jet flame is observed; with rotation, the flamebecomes stably confined in the vortex core. This centrifugalstabilization of the flow reduces mixing and entrainment,leading to a considerable increase in flame length, up to afactor of about 5. Similar phenomena are observed in firewhirls, dust devils, tornadoes, hurricanes, waterspouts, etc.,and characterizations of these geophysical phenomena are ofgreat interest themselves.53

E. Vortex EffectsSwirling flows, with particular emphasis on the

phenomenon of vortex breakdown (the formation of a freestagnation point and recirculation zone in the vortex core offlows with significant stream wise vorticity), have been studiedfor some time at Cornell.54'55 A gas-turbine-like combustorusing vortex breakdown to stabilize combustion has beeninvestigated, where a confined double concentric jet con-figuration is used, with premixed fuel (methane) and air in theinner jet and air in the outer jet. Swirl may be induced in bothinner and outer jets with the sense of rotation the same oropposite (coswirl or counterswirl). The objectives were tolearn more about the influence of swirl and vortex breakdownon combustion and to evaluate the potential of this con-figuration as a practical device.

The double concentric swirler configurations of the variousNASA Lewis swirl modules31"36 (studied for application inaircraft jet engines) are very similar to those of the presentstudy. Early studies of vortex breakdown indicate54 that thesize and position of the recirculation zone and its associatedturbulence field could be influenced by swirl level, relativeswirl direction, and jet velocity ratio. It seemed desirable andfeasible to use these flow parameters to match flow conditionsto operating conditions. Of special interest was the possibilityof using a very lean inner jet to limit the formation of oxidesof nitrogen NOX (without sacrificing carbon monoxide COand unburned hydrocarbon emission performance), coupledwith a large recirculation zone and intense turbulence tocounteract the loss of stability due to lean operation.Qualitative observations of the combustion process, blow-off

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limits, exhaust temperatures, and emissions of oxides ofnitrogen NOX and carbon monoxide CO from the combustorare reported in Ref. 54.

More recently,55 composition, temperature, and velocityprofiles have been presented for different values of swirl,equivalence ratio, and inner-to-outer jet axial velocity ratio.Combustion efficiency as determined by chemical andthermal analysis also was reported. Relative swirl directionand magnitude are found to have significant effects onexhaust gas concentrations, exit temperatures, and com-bustion efficiencies. Counterswirl generates a large recir-culation zone, a short luminous combustion zone, and largeslip velocities and turbulence in the interjet shear layer. Lownitric oxide NO levels are observed for maximum counterswirlconditions and lean mixtures. However, this is accompaniedby low combustion efficiency, as indicated by the relativelyhigh carbon monoxide CO and methane CH4 levels and lowexhaust gas temperatures. It is concluded that quenching dueto rapid mixing in the interjet shear layer is the main con-tributor to this, and this is confirmed by results obtained bychanging outer swirl and jet velocity ratio.55

It often has been assumed that the mean flow from vortexchambers is axisymmetric. Recent studies56"58 have shown thisto be true only for low swirl numbers and low Reynoldsnumbers. For a given swirl number (5>0.6), when the flowreaches a certain critical Reynolds number, the vortexbreakdown instability develops. The initial manifestationusually is comprised of a nearly symmetric swelling of thevortex core, enclosing a recirculating bubble of fluid. In thewake of this disturbance, another spiral instability oftenoccurs in which the central forced-vortex region starts toprecess about the axis of symmetry. This so-called precessingvortex core lies near to the boundary of the mean reverse flowzone, which now has become quite large, between the zeroaxial velocity line and zero streamline, and it is responsible forthe very high levels of turbulence and mixing which have beenmeasured in swirl generators. There is now three-dimensional(3-D) time-dependent turbulent flow, which has dramaticeffects on the stability, rate of mixing, combustion intensity,and flame length. The range of stable burning can be extendedwell into the region of fuel-lean mixture ratios. Although theprecessing vortex core is useful for mixing the reactants, it cangive rise to combustion oscillations and the emission of unduenoise and other pollutants.59 As the precessing vortex coreleaves the exit, it soon is dissipated, and an axisymmetricmotion ensues.

There is, however, another instability associated with theprecessing vortex core and the exit. Near the throat region, theeddies and mixing processes are mainly in the tangential-axialplane, but at the exit a large eddy is formed in the radial-axialplane, just inside the path of the vortex core. This is stable atlow Reynolds numbers, but as the Reynolds number is in-creased the eddy is shed alternately from either side of theexit. This is a continuous process, with the eddy being peeledoff continuously by the precessing vortex core. It is called the

RADIAL SECTION (EXIT)

radial-axial eddy. A schematic of the flow patterns occurringwith the precessing vortex core is shown in Fig. 12.

It may be shown that the precessing vortex core can becharacterized by intensity and frequency parameters.56"58

Excitation of the frequency and amplitude of the precessingvortex core substantially increases the pressure loss, whereasdamping reduces the pressure loss. A turbulent axial jet offluid introduced along the central axis of the swirl generatorreduces the rate and radius of the precession. With swirlingcombusting flow, either an intense excitation of the precessionoccurs, or a large-scale damping occurs, depending on themode of fuel entry.

Premixed combustion appears to be the only method bywhich the precessing vortex core is excited to higherfrequencies and intensities as compared to the isothermalstate. A fairly linear relationship between frequency andReynolds number is found for a combustion case, similar tothat for an isothermal case. Frequencies are, however, in-creased by a factor of 2 or 4, dependent on flow rate andmixture ratios. Blow-off limits of this type of flame are wide.Any other mode of fuel entry (diffusion flame with axial ortangential entry) damps the precessing vortex core with largepositive radial density gradients. Frequencies with axial fuelentry are some 50% higher than those for tangential fuelentry. Stability limits with tangential fuel entry are poor.Intensities for the oscillations substantially reduced for thesetwo modes of fuel entry (as compared to very high values forthe premixed flame), and the amplitude is damped by some 3to 4 orders of magnitude. A nondimensional frequencyparameter / D3 /Q (where / is frequency, D is chamberdiameter, and Q is mass flow) is shown to be adequate fordescribing the variation of frequency with Reynolds number,for both the isothermal and flame states.56'58

The unpleasant characteristics of the presence of aprecessing vortex core in industrial burners can be improvedby better control of both the aerodynamics and thedistribution of reactants in the burner. With this objective, amultiannular swirl burner recently has been developed59

which has wider stability limits, better turn-down ratio, andhigher volumetric heat release rate than the conventionalsingle annular tangential entry (or vane type) swirl flamestabilizer. High volumetric heat release rates are achievedmatching the concentrations and directions of flow ofreactants in such a way that regions of high fuel concentrationoverlap regions of high shear stress in the flow. No evidenceof the precessing vortex core is found with this burner. Theburner consists of eight concentric annular divergent nozzles,with the inner end of each nozzle aligned with the outer end of

RECIRCULATED

Fig. 12 Isothermal and premixed combustion flow patternsdominated by the processing vortex core; note the large dissipativeprecessing vortex core inside the swirler and the radial-axial eddybeing shed from the exit.56'58

^ <£*;......._ ...— —— —— —— COMBUSTION

Fig. 13 Stabilization of pressure iet oil flame by internalculation zone in swirling annular jet. *'60

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the adjacent inner nozzle. Fuel and air may be suppliedtangentially to alternate annuli; tests are being made withalternate rings coswirling and counterswirling.

F. Liquid Fuel FlamesOther work has been concerned with liquid fuel flames.61'70

Practical oil flames are usually in the form of one or two basictypes.

1) The first type is turbulent jet diffusion flames, in whichthe oil is atomized by high-pressure air or stream (blast-atomized) and where the momentum of the fuel spray is sohigh that it is quite sufficient for the entrainment of com-bustion air necessary to complete the combustion. Thesignificant dimensions of the flame, such as length and angleof spread, can be calculated from turbulent jet theory basedon the fuel-atomizing agent spray as the momentum source.

2) The second type is pressure jet flames, in which themomentum of the spray is small in comparison with themomentum of the airflow. In this case, the characteristicdimensions of the flame will depend more on the airflowpattern than on the fuel spray.

The interaction of a pressure jet oil spray with the recir-culation zone from a swirling annular jet in the Ijmiudenfurnace is shown schematically in Fig. 13.60 The figure showsstreamline airflow patterns as calculated from mean velocitymeasurements under isothermal conditions, with details fromoil flame photographs superimposed, so as to give thecomposite picture. In order to obtain flame stabilization, aregion of the flowfield must be found where the flame speedmatches the forward flow velocity, and also the heat suppliedmust be sufficient to initiate the combustion process. Within arecirculation zone, the forward flow velocity is reduced untilit reaches zero at the reverse flow boundary, and thus a regionof the flow always can be found where local flame speed willmatch local forward velocity. Since the recirculation eddygenerally passes through the flame front, recirculationcombustion products are carried toward the burner and passthrough the spray, carrying small droplets to the flame frontand thus forming a flame front, as shown in the figure. Thesize and strength of the recirculation zone can be controlled bythe degree of swirl in the airflow system. By adjusting theangle of the oil spray to match the size and strength of therecirculation zone, optimum conditions can be found forgood flame stabilization, high combustion efficiency, andminimum production of pollutants.61 Recent work on liquidfuel swirling flames is discussed in Refs. 63-70.

G. SummaryTo summarize the experimental evidence, the design of

swirl burners for practical combustion equipment is still verymuch an art in which the practical experience of the designeris paramount.61 The use of bladed swirlers is one of the mosteffective means of generating swirl, and there does not appearto be a very significant difference between flat-bladed andaerodynamically shaped swirier blades. An outlet diffuserincreases the size of a recirculation zone, and the use of adivergent angle of 35° and a diffuser length of 1.5D has

Fig. 14 Prediction oflongitudinal decays withswirl for inert jets (xexperimental, 0 pre-dicted). 123

provided good results in practice. The ability to move theswirler in the burner along the outlet diffuser is a simple andeffective means of controlling the degree of swirl. Somesimple aerodynamic measurements of the flow distribution atinlets to the windbox and the shape of the reverse flow zoneusing a total head tube with forward- and rear-facing holescan be of considerable help to the burner designer. In oil-firedflames, the matching of the spray angle to the flow patternswithin and around the recirculation zone is important in orderto minimize smoke formation in the outer or inner regions ofthe flame. The objective of current research is to characterizethese types of flows in a logical scientific fashion, so aidingfuture designers.

III. Modeling and Prediction

A. Basic Governing EquationsIn the modeling and prediction of swirl flow combustion,

one is involved with simulating the problem via simultaneousnonlinear partial differential equations. These may beparabolic (boundary-layer type) but are more often elliptic(recirculating type), and the solution scheme differs accordingto the category and is discussed in Sec. III. C. The turbulentflux (Reynolds) equations of conservation of mass,momentum, stagnation enthalpy, and chemical species, whichgovern the flow of turbulent chemically reactingmulticomponent mixtures, may be solved for time-meanpressure, velocity, temperature, and species mass fractions,provided that the further thermodynamic and turbulent fluxunknowns are specified prior to solution. Often considerationis given to a simplified main exothermic reaction between justtwo species, fuel and oxidant; this and other assumptions leadto many simplifications. The reaction then is characterized byequations for 1) mfu (mass fraction of fuel), h (stagnationenthalpy), and/(mixture fraction mox-imfu, where / is thestoichiometric ratio) for a premixed flame; 2) h and / for adiffusion flame; or 3)/for a diffusion flame in an adiabatic,nonreacting, and impervious chamber with only two inletstreams of fuel and oxidant. Solution for a variable g (meansquare fluctuating component of fuel concentration) allows aturbulent diffusion flame to have a thick reaction zone or apremixed flame to burn fuel at a rate dependent on eddy-breakup concepts.

Further equations are required to simulate turbulence, two-phase effects, radiation, pollutant formation, etc., but acentral point of the theory is that all of these equations aresimilar to laminar flow ones, but the variables are time-meanquantities, and the fluxes for momentum, stagnation en-thalpy, and the chemical species are composed of two parts,the laminar and turbulent parts, the latter of which are relatedto correlations of turbulent fluctuations. These must bespecified via a turbulence model, often, by analogy with thelaws of Newton, Fourier, and Fick for laminar flows, usingturbulent exchange coefficients relating fluxes to localgradients and then Prandtl, Schmidt, and rO (and other)viscosity numbers relating other exchange coefficients to theprimary component of turbulent viscosity fjLrz. In turbulencetheory, isotropy is the term that connotes the existence of ascalar turbulent viscosity at points in the flowfield. If theturbulent viscosity is not equal with regard to different stress-rate of strain directions, the term nonisotropy is used, and theratios of the other component with the primary component ofturbulent viscosity are called rd (and other) viscosity numbers,by analogy with Prandtl-Schmidt numbers.

All of these linkages and complexities in the equationsprovide a high degree of nonlinearity in the total problem andgive the numerical analysis of fluid flow its peculiar difficultyand flavor. The similarity between the differential equationsand their diffusional relations allows them all to be put in thecommon form

d_dt (3)

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where the exchange coefficient assumptions have been in-voked. Here <£ is a general dependent variable, and equationsmay be solved for </> equal to time-mean axial, radial, andswirl velocities u, v> w, stagnation enthalpy h, fuel massfraction mfu, mixture fraction /, turbulent kinetic energy &,and dissipation rate e, and mean square fluctuating com-ponent of fuel concentration g = m'fu2 (and possibly othervariables as well). The equations differ not only in their ex-change coefficients but also, and primarily, in their finalsource terms S^. Specific details about the equations may befound in the literature.1'71'80

B. Simulation of the Physical ProcessesClosure and completeness of the governing equation set are

effected by means of models of the physical processes takingplace within the combustion system. Either our knowledge ofthese processes or computer size limitations restrict the degreeof sophistication to be used in any simulation. The simulationproblems have been reviewed extensively elsewhere71"80 andwill be touched on only obliquely here. Briefly, the four mainprocesses to be modeled are as follows:

1) Turbulence, where models of the exchange coefficienttype and direct stress specification type have been applied toswirling flows, and currently energy-length models are to berecommended and in particular the k = e model, where e= kL5/t, and £ is the macrolength scale of turbulence.81'82 Arecent conference highlights current work in this area.83

2) Radiative transfer, where the integrodifferentialequations may be represented by Hotter s "zone method"84

or one of the "flux methods" for one, two, or three fluxsums.78'85 (The former is more exact but difficult to in-corporate with hydrodynamics; the latter is less rigorous butsimple to employ.)

3) Chemical reaction, including the simulation of premixedand diffusion flames,71'86 the complex equations representingthe route to pollutant formation,87'95 techniques for handling"stiff" kinetics96'104 (where widely differing reaction ratecoefficients require special techniques for handling sourceterms), and the effect of turbulence structure on time-meanchemical reaction rates.86'105'111 Realistic simulation ofcomplex chemistry in turbulent reacting flows is probably thearea in combustor modeling which will prove to be mostuseful to study, and the results of which will be most fruitfulto apply in practical design situations.112

4) Two-phase phenomena, for solid fuel particles andliquid droplets, including infinite drag assumptions for smallparticles113 and ordinary differential equations for largerparticle trajectories,114 and studies on the rate of burning ofdroplets, clouds, and sprays.115"118

C. Computational MethodsAll combustor problems entail the solution of many

simultaneous nonlinear equations, including up to threevelocity components, pressure, stagnation enthalpy, andspecies concentrations. Since their equations are all similar inform, the same solution algorithm can be used for all of them.Problems are classed according to the degree of realism andrefinement, as represented by their dimensionality (thenumber of independent variables from three space dimensionsand time) and type (parabolic or elliptic). The flowclassification of parabolic [possessing one coordinatedirection with first- but without second-order derivatives:boundary-layer type with prominent directions(s)] or elliptic(possessing second-order derivatives in all coordinatedirections: recirculating type with upstream influence)governs the type of boundary conditions required andsolution method. Marching methods are appropriate for theformer (flows with weak swirl) and relaxation methods forthe latter (flows with strong swirl). The problems, methods,and solutions are discussed in Refs. 119-147. Papers presentedat two recent conferences highlight both experimental andtheoretical studies in the fluid mechanics of combustion. 146>147

Problem classification is generally into one of the followingcategories:

1) 2-D marching methods, for axisymmetric 2-D parabolicboundary-layer flows: weak swirl (approximately 5<0.4), 1-D storage, automatic expanding grid using non-dimensipnalized streamfunction \l/ instead of r as the radialcoordinate, and implicit solution procedure. 122~125

2) 2-D relaxation methods, for axisymmetric 2-D ellipticrecirculating flows: strong swirl (approximately 5>0.6), 2-Dstorage, streamfunction-vorticity ^ = co or primitive pressure-velocity p-u-v formulation, and Gauss-Seidel or line-by-lineSIMPLE (semi-implicit method for pressure-linkedequations) solution procedure. 126~138

3) 3-D marching methods, for 3-D parabolic boundary-layer flows: nonaxisymmetric, weak swirl, 2-D storage, primi-tive formulation, and SIMPLE solution procedure.128'145

4) 3-D relaxation methods, for 3-D elliptic recirculatingflows: nonaxisymmetric, strong swirl, 3-D storage, primitiveformulation, and SIMPLE solution procedure.138-145

The essential differences between the various availablecomputer codes (and those that are not available) include thecomplexity of the equation set for the simulation of thephysical processes, the storage requirements, the location ofvariables in the grid space system, the method of deriving thefinite-difference equations that are incorporated, and thesolution technique. In primitive pressure-velocity variableformulations, a staggered grid system normally is used, asrecommended by Los Alamos for its special .attributes. Incomputational fluid dynamics, the "best" representation ofthe convection and diffusion terms is essential to the accuracyand convergence or stability of the iteration scheme ormarching procedure. At high call Reynolds numbers, a certaindegree of "upstream differencing" is essential using upwinddifferencing, a hybrid formulation or the Los Alamos zip,donor cell, etc., techniques, for example.75 Solutionprocedures vary from Gauss-Seidel point methods67 to moreefficient line-by-line SIMPLE methods68'74 for steady-stateproblems, with corresponding explicit and SIMPLE methodsfor associated transient problems. The application of finite-element computational methods to combustor problems, withcomplex boundary geometry and complex boundary con-ditions to apply, is in its infancy; further work in this fertilearea will be most useful.137

IV. Sample PredictionsCalculations often are performed with a nonuniform grid

system of about 500 nodes in the flowfield, and the solutiontime required to solve 10 simultaneous equations is typically10 min of CDC 6600 CP time, although this decreases in theabsence of swirl to about 5 min and in the absence of swirl andcombustion to about 2/2 min. Most relaxation procedures forelliptic problems are under-relaxation on new values, coef-ficients, and source terms, although this under-relaxation isset to be less effective as the iteration procedure nears con-vergence, so that the initial stabilizing effect does not hinderthe final convergence rate. Final convergence is decided byway of the well-known fractional-change criterion or theresidual source sum criterion, the latter generally beingrecommended. The results discussed below compare ex-perimental evidence and predicted characteristics of weaklyand strongly swirling, free and confined, jets and flames.

A. Weakly Swirling FlowsSince details of the prediction of weakly swirling jet and

flame structures have been published already, only highlightsof the computations are discussed here. Predictions are madewith both the Prandtl mixing length and energy^-length tur-bulence models so as to confirm suitable extensions of themodels to swirl flows.123 Computations with either modelproduce longitudinal decays of um and wm which comparewell with experimental data (see Fig. 14). The primary use of

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swirl in a jet is to increase the angle of spread and rate ofdecay of axial velocity. The half-angle a (u/um=0.5) ispredicted to increase with swirl according to

Table 1 Development parameters for jets and premixed(mfu =0.245) jet flames

= 4.8+14 S (4)

as found experimentally.4 These and other results123 agreewell with the data and show that the effect of swirl onisothermal jet growth, entrainment, and decay may bepredicted well. To make such isothermal computations, onehas to solve four simultaneous parabolic partial differentialequations for «, rw, k, and Z, where Z=kT. The com-putation cited uses m = n = 1 .

Premixed flames (mfu= 0.245) with initial fuel/air ratiowell outside the flammability limits have been studied ex-perimentally.4 Predictions have been made125 with an eddy-breakup reaction model and turbulence simulated in a mannersimilar to the form used in the prediction of inert jets.123

Eight parabolic partial differential equations are solved for u,rw, k, kt, h, mfu, mox-imfu, and g. Predicted longitudinaldecays of um and wm compare well with experimental results,and there is a progressive increase in them as S increases. It isto be noted, however, that the velocity decays are slower thanin cold swirling jets. This is largely because of the temperatureand density changes, and a consequence of this gas expansionis increased axial and radial velocities, giving a reduced rate ofdecay of um and a wider jet initially.

Figure 15 shows longitudinal variations with swirl of Tc,the centerline temperature, and mfu , the total mass flow rateof unburned fuel. 125 Notice that Tc increases more rapidly as5 increases, indicating the more rapid mixing of hot com-bustion products with the cooler, higher-velocity core region.Observe also that mfu decreases more rapidly as 5 increases,indicating the more rapid consumption of fuel per unit lengthof flame. Predicted flame front lines (loci of temperaturemaxima) accord well with the experimental ones of Fig. 4, andit is clear that the length of the flame decreases markedly withswirl and that there is a progressive increase in the initialwidth (at z/d= 10) of the flame as S increases. Flame lengthsmay be compared favorably with experimental values, asTable 1 shows. Downstream development of these jets andflames often is characterized by the parameters A (for axialvelocity decay) and a (for jet half- angle), defined by

um/umo=A(Poo/pm.m)°'sd/(z + a) (5)

(6)

where m stands for station maximum, o for orifice value, pfor density, oo for ambient conditions, and min for minimumvalue. Recommendations for a, A, a, and flame lengths aregiven in Table 1.

Fig. 15 Predicted longitudinal Tc (centerline temperature) and rhfu(mass flow rate of unburned fuel) variations for partially premixed jetflames (nifu - 0.245) (x experimental).125

Jet (S < 0.4)aid 2.3A 6.8/(l +6.S52)a 4.8 + 145

Flame length /d

Flame (5< 0.23)35 + 100515 + 105

2.2 + 543 - 1005

B. Strongly Swirling JetsThe forms of strongly swirling free and enclosed jets,

issuing from vane swirlers and swirl generators, have beenpredicted using the /?-o> and p-u-v approaches.74'128 Theproblem is elliptic, requiring the relaxation solutiontechnique. Initially, enclosed flow in a cylindrical chamberwas predicted solving three equations for \j/> u/r, and rw witha simple algebraic turbulent viscosity formula.74 Results forthe length of central recirculation zone, axial distance toimpingement, and velocity decays are encouraging whencompared with experimental data, in view of the use of anaive turbulence model in the computations. More recently,the primitive-variable approach has been used to predictsimilar flows; then equations are solved for/?, u, v, w, k, and e(where the additional complexity of the two-equation k-eturbulence model has been included). Again results show goodagreement with experiment.128 As an example, Fig. 16 showspredicted streamlines and recirculation zone for a free annularjet from an axial-plus-tangential entry swirl generator withswirl number 5=1.5. There is a striking resemblance to asimilar experimental figure (see Fig. 1), but the recirculationzone is predicted slightly too wide and too short.

An enclosed swirling flow in an axisymmetric furnaceconfiguration recently has been predicted76 by an advancedprimitive code with advanced turbulence and combustionmodels. The predictions with chemical reaction suppressedare discussed here (those with chemical reaction are discussedin the next section); for brevity, only those for axial velocitydistribution are considered. Figures 17 and 18 show predicted

Fig. 16 Predicted streamlines (——) and recirculation zone (—) fora free annular jet (from an axial-plus-tangential entry swirl generator)with swirl number S = 1.5 (Ref. 128).

1.67

1.34

Fig. 17 Radial profiles ofmean axial velocity: swirl

- number = 0, isothermal° flow.76

.17

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Fig. 18 Radial profiles ofmean axial velocity: swirlnumber = 0.52, isothermalflow.76

2

0

1010210

20

^__

Ufc—~ •— . ^ -

[_ ,^LL._ - _ ,. _^-— ̂ __f/v/\» — •— •

2.672.33

2

1

.67 9"N

.33

.17

.067in r

- 2

NO REACTION

- 2

REACTION

30 60 90 30 60 90* *

Fig. 20 Effect of swirl vane angle on central recirculation zonelength (0predicted).74

r 1.0CJ

Lfuel "P

z/dFig. 19 Predicted streamlines (—) and flame envelope (---) in acombustion chamber (swirl vane angle 60°, primary velocity up =0.5us, overall air-fuel ratio 30:1).74

axial velocity radial profiles at a variety of axial stations (Df isfurnace diameter) and compare them with experimental datafor 5 = 0.0 and 0.52, respectively. In each case, there is nocentral jet velocity. Predicted results are very close to themeasurements. Some of the effects of swirl are apparentimmediately: a recirculation zone near the nozzle, off-centerline maxima, and more rapid decay in the downstreamdirection. Although not shown here, absolute values ofturbulent kinetic energy are much higher (a factor of 3) in theswirling case in the initial region and extend further in theradial direction. However, their decay in the downstreamdirection is also quicker, indicating again that the interestingpart of the flowfield is shorter and wider with the applicationof swirl.

C. Strongly Swirling FlamesPredictions for a strongly swirling diffusion flame in a

cylindrical combustion chamber require the use of a 2-Delliptic program. In Refs. 74 and 126, a streamfunction-vorticity formulation is used, solving four partial differentialequations for \l/, u/r, nv, and/. A simple algebraic formula isused to specify the turbulent viscosity. Figure 19 illustrates acomputation74 for a cylindrical combustion chamber whichhas many of the features of practical equipment: fuel and airinput at one end, exit for combustion products at the other,arrangement of the air inlet as an annular orifice surroundingthe fuel inlet, a device for causing the air to enter with aswirling motion, and a thick annular lip between the air andfuel inlets. The expansion ratio Did is 2. Sizes are such thatequal axial velocities of the primary fuel stream up andsecondary airstream us give overall stoichiometric conditions(air-fuel ratio APR = 15). It needs to be stressed that moresatisfactory turbulence and reaction models now exist; thepredictions shown are intended as demonstrative, and, assuch, the following conditions are taken at the inlet: pressurep = 25 atm, temperature T= 850 K, and u = 36 m/sec.

The computations show some interesting features74 andstriking differences between the nonswirling and stronglyswirling (vane angle 0 = 60° corresponding to a swirl numberS=1.2 approximately) cases. The presence of strong swirlcauses a toroidal vortex to form in the middle of the com-bustion chamber, in addition to the recirculation near the

entrance provoked by the sudden enlargement of the cross-sectional area. It also shortens the flame. Both of these effectsare well known to combustion engineers, who strive to utilizethe recirculation of hot combustion products and the bluff-body effect of this zone as an aid to the combustion process.

The vane angle has a strong effect on the existence (orotherwise) and size of the central recirculation zone. Shown inFig. 20 is the length of this zone as a function of vane angle <t>for a variety of values of up (and hence AFR): on the leftwhen no reaction is allowed to take place, and on the rightwith reaction.74 In both cases, the zone lengthens as </> in-creases for a given up (AFR). Reduction of up promotes theexistence of the zone and lengthens it for a given vane angle.The third point to note is that, with chemical reaction sup-pressed, zone lengths generally are longer: the presence ofreaction, gas expansion, and increased velocity tend toshorten, and in some cases destroy (for example, 60° vaneswith up = us), the zone as compared with its nonreactingcounterpart. Despite this, zone lengths for low values of up(high values of AFR) are quite comparable, especially athigher degrees of swirl. This is because in these cases theflames are short and trapped upstream of the recirculationzone as opposed to encompassing it. Predicted also, and asexpected experimentally, is that reduction of up (increase inAFR) and/or increase in vane angle <j> progressively reducesthe flame length and improves the temperature traversequality (uniformity of temperature) across the exit from thecombustor. Some general observations are that the presenceand increase in size of a central recirculation zone are en-couraged by increasing D/d, having a central hub in the inletflow dh>Q, increasing dh/d, reducing primary velocity (alsoshifts zone more upstream), increasing swirl number of swirlvane angle, and suppressing chemical reaction.38 For com-bustors, an optimum swirl strength for reasonable recir-culation zone and pressure loss is about 5= 1.15 or swirl vaneangle <£ = 60 when D/d=2y although recent work suggests thatS based on chamber diameter D rather than nozzle diameter dgives a better guide to similarity of flow downstream of theinlet for different Did systems.22

More recently, a strongly swirling enclosed premixed flamehas been considered with a primitive pressure-velocityvariable code, suitably amended to include the k-e turbulencemodel and the simple exothermic one-step chemical reac-tion.128 The results of application of the aforementionedadvanced primitive-variable code (with advanced turbulenceand combustion models) to flows with chemical reaction noware. discussed.76 Three combustion models are considered:model 1, diffusion flame; model 2, diffusion flame with thickflame region because of turbulence, calculation of g requiredfrom its governing partial differential equation; and model 3,finite reaction rate, deduced from the lesser of the Arrheniusand eddy-breakup models, calculating g either from itsgoverning partial differential equation or its reduced local-equilibrium algebraic equation. Figures 21 and 22 showsample calculations of axial velocity at x/Df= 1.0 and 1.5, at

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swirl numbers of .5=0.0 and 0.52, respectively. Results showthe presence of a central toroidal recirculation zone, andfurther downstream more uniform velocity profiles across thechamber, in the swirl case of the latter figure. Comparisonwith experimental data suggests that combustion model 2 isslightly preferable over model 3, with model 1 a poor third.This results from inadequacies in the detail of model 3 ratherthan the concept of recognizing finite-rate chemical reactions.Temperature field calculations are in close agreement witheach other, but unfortunately there are no experimental datawith which to compare them. These and other results showclearly the effect of swirl on furnace flames, both ex-perimentally observed and theoretically predicted: swirlgenerally leads to flatter, more uniform velocity distributionsacross the chamber, a wider region of higher temperatureshifted further away from the axis, and higher initial values,but lower later values, of kinetic energy of turbulence.

D. Three-Dimensional FlowsThe discussion is restricted to two particular combustor

flows: one78 is a furnace flame without swirl, and most of theinteresting part of the flow is without axial recirculation; andthe other79'139 is the flame in a section of an annular com-bustor, where the inlet boundary conditions favor thegeneration of a swirling motion in the flowfield. Figure 23shows the results of computations for a steady methanediffusion flame in a square-sectioned adiabatic furnace,where dimensions and conditions are similar to those usedexperimentally in the Ijmuiden furnace.78 In this preliminarywork, no advanced turbulence model was incorporated, theturbulent viscosity being computed from a simple algebraicexpression that gives approximate turbulent jet values ofturbulent viscosity in the inlet jet part of the flow. The resultsshow cross sections of the flowfield at four locations Ay B, C,and £>, going downstream in the flow direction from left toright. Contour plots in the frames allow interpretation of theentire 3-D flowfield of regions of unburnt fuel and tem-perature. Results that are not shown here indicate that theforward-moving jet of fuel quickly entrains the combustionair, causing a recirculation of hot combustion products in the

Fig. 21 Radial profiles ofmean axial velocity: swirlnumber = 0, combustingflow.76

model

1 2 3

n n—2—rr/d

Fig. 22 Radial profiles ofmean axial velocity: swirlnumber = 0.52, combustingflow.76

corner regions, from which the further entrainment by the jetis supplied. Of course, the symmetrical entry of the fuel andair, and the absence of swirl, insures no circulation of gas inthe sectional plane: all vector velocities in the cross sectionsare radially outward from the main-direction centerline.Inspection of the results shown in the figure reveal otherphysically realistic features: the flame boundary, taken to bethe fuel-air interface, widens at first with distance from theinjector nozzle, and then diminishes to zero; temperaturemaxima occur at the flame envelope; and nonuniformities oftemperature diminish as the furnace exit is approached.

The second flow considered is a diffusion flame in a sectionof an annular combustor, shown schematically in Fig.24.79,139 xwelve equations are solved, including those for thetwo-equation k-e turbulence model and a six-flux radiationmodel. The flow is fully 3-D and exhibits a complex recir-culation pattern. A significant swirling motion developsmainly because of the upstream injection of dilution air alongthe top boundary, but also because of the spreading of thefuel jet flame and the circulation produced by the lateral air.The location and angle of injection of the lateral air alsocontribute to significant axial recirculation against the mainflow direction. The discussion here is restricted, however, tothe ensuing temperature field and, in particular, to thetemperature distribution at the outlet, which is especiallyinteresting to the combustion-chamber designer who wishes tohave a good temperature traverse quality.

Several outlet temperature distributions are shown in Fig.24, each resulting from a different set of inlet boundaryconditions. Part A represents the standard situation: fuel andair entering at 600 K at all locations, fuel and top wall filmcooling air entering at 100 m/sec, some inlet air through holesat upstream boundary averaged as 1 m/sec over the entire

Air

Products

iB C

Regions of unburnt fuelox

fu

ox

fu

ox

fu

ox

0fu

Temperature T/Tin

Fig. 23 Predictions for a diffusion flame in an adiabatic furnace.1

FLAME-TUBE WALL

AIR

^-e-KV-;>J>v}r Y YFILM-COOL i NO siL FUEL'GAS V, RECIRCULATING

Fig. 24 Influence of bound-ary conditions on outlettemperature distributions foran annular combustor.79'139

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area, and lateral air entry 200 m/sec normal to the top surfaceand - 200 m/sec in the axial z direction, that is, at 45° in theupstream direction. Part B shows what happens when the topwall air film is injected at five times its standard value: theuniformity of the temperature is significantly greater.Comparison of the part C and part D contours with those ofthe standard result of part A reveals that the direction of entryof the lateral air radically alters the temperature pattern anddoes so in an understandable way. For the standard conditionof part A, the axial velocity of the 200-m/sec vertical velocitylateral air is - 200 m/sec, in part C it is 0 m/sec and in part Dit is + 200 m/sec. Clearly these and other design variations inboundary conditions are simple to incorporate and can be ofgreat help to the combustor designer. The temperaturedistributions here are far from uniform; none of the onesshown is good enough from the points of view of efficiencyand turbine inlet temperature requirements. Clearly thecombustor being considered is not at a stage of developmentwhich the engine designer could accept.

V. ClosureThe extremely favorable effects of applying swirl to in-

jected air and fuel in combustion systems have been knownand utilized for many years. Only recently, however, hassystematic study been aimed at understanding and charac-terizing the observed phenomena. Advances in the ex-perimental study, modeling, and prediction of combustorswirl flows were reviewed here. Increasingly detailed ex-perimental observations are being modeled with increasingrealism, both in the simulation of the physical processesoccurring and solution of the resulting governing equations.A few general hypotheses now are linking together a largenumber of previously disconnected experimental data andbeing incorporated into general computer programs. Practicalapplication of numerical predictions now is providingdesigners with adequate results more cheaply and quickly thancurrently possible by experimental means, which, in turn, isproviding a powerful stimulus to their further development.

AcknowledgmentThe author sincerely would like to thank the following for

helpful discussions: J. M. Beer, A. A. Boni, L. S. Caretto, N.A. Chigier, R. S. Fletcher, R. J. Gelinas, F. C. Lockwood, N.R. L. Maccallum, D. W. Pershing, N. Syred, and J. H.Whitelaw. Many thanks are due to Science Applications Inc.,La Jolla, Calif., for funds to cover part of this work, whichwas performed while the author was acting as a Consultant tothe Energy and Environmental Sciences Division.

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9IOdgers, J., "Combustion Modeling within Gas TurbineEngines," AIAA Paper 77-52, Los Angeles, Calif., Jan. 24-26, 1977.

92Boccio, J. L., Weilerstein, G., and Edelman, R. B., "AMathematical Model for Jet Engine Combustor PollutantEmissions," NASA CR-121208, March 1973.

93Rai, C. and Siegel, R. D. (eds.), "Air: II. Control of NOX andSOX Emissions," American Inst. of Chemical Engineers, SymposiumSer. 148, Vol. 71, 1975.

94Altenkirch, R. A. and Mellor, A. M., "Predicting Emissions forPrevaporizing Combustors via Continuum Flow Techniques," 16thSymposium (International) on Combustion, The Combustion Inst.,Pittsburgh, Pa., 1977.

95Cernansky, N. P., "Formation of NO and NO2 in a TurbulentPropane/Air Diffusion Flame," Dept of Mechanical Engineering,Univ. of California, Rept. UCB-ME-74-5, Berkeley, Calif., Nov.1974.

96Butler, T. D. and O'Rourke, P. J., "A Numerical Method forTransient Reacting Flows in two Space Dimensions," 16th Sym-posium (International) on Combustion, The Combustion Inst.,Pittsburgh, Pa., 1977.

97Magnussen, B. F. and Hjertager, B. H., "On MathematicalModeling of Turbulent Combustion with Special Emphasis on SootFormation and Combustion," 16th Symposium (International) onCombustion, The Combustion Inst., Pittsburgh, Pa., 1977.

98Quan, V., Bodeen, C. A., and Teixeira, D. P., "Nitric OxideFormation in Recirculating Flows," Combustion Science andTechnology, Vol. 7, 1973, pp. 65-75.

"Pratt, D. T., "Calculation of Chemically Reacting Flows withComplex Chemistry," Studies in Convection, edited by B. E.Launder, Vol. 2, Pergamon Press, Oxford, 1976.

IOOWormeck, J. J. and Pratt, D. T., "Computer Modeling ofCombustion in a Longwell Jet-Stirred Reactor," 16th Symposium(International} on Combustion, The Combustion Inst., Pittsburgh,Pa., 1977.

101 Hindmarch, A. C., "GEAR: Ordinary Differential EquationSystem Solver," Lawrence Livermore Lab., Univ. of Calif., Rept.UCID-30001, Rev. 3, Dec. 1974.

102Young, T. R. and Boris, J. R., "A Numerical Technique forSolving Stiff Ordinary Differential Equations Associated withReactive-Flow Problems," Naval Research Lab., Memo. Rept. 2611,Washington, D.C., July 1973.

103Scaccia, C. and Kennedy, L. A., "Calculating Two-Dimensional Chemically Reacting Flows," AIAA Journal, Vol. 12,Sept. 1974, pp. 1268-1272.

104Boni, A. A., Chapman, M., Cook, J. L., and Schneyer, G. P.,"Computer Simulation of Combustion in a Stratified ChargeEngine," 16th Symposium (International) on Combustion, TheCombustion Inst., Pittsburgh, Pa., 1977.

105Spalding, D. B., "A General Theory of Turbulent Combustion;The Lagrangian Aspects," AIAA Paper 77-141, Los Angeles, Calif.,Jan. 24-26, 1977.

106Spalding, D. B., "The Eddy Break-Up Model Applied toConfined Turbulent Steady Flames," AIAA Paper 77-98, LosAngeles, Calif., Jan. 24-26, 1977.

107Spalding, D. B., "Development of the "Eddy Breakup" Modelof Turbulent Combustion," 16th Symposium (International) onCombustion, The Combustion Inst., Pittsburgh, Pa., 1977.

108Spalding, D. B., "The Escimo Theory of Turbulent Com-bustion," Dept. of Mechanical Engineering, Imperial College, Rept.HTS/76/13, London, 1976 [extension of 16th Symposium (In-ternational) on Combustion paper].

109Spalding, D. B., "Mathematical Models of Turbulent Flames: AReview," Dept. of Mechanical Engineering, Imperial College, Rept.HTS/75/1, London, 1975; see also Ref. 86, 1976, pp. 1-25.

110Edelman, R. B. and Harsha, P. T., "Some Observations onTurbulent Mixing with Chemical Reactions," AIAA Paper 77-142,Los Angeles, Calif., Jan. 24-26, 1977.

1HGouldin, F. C., "Role of Turbulent Fluctuations in NO For-mations," Combustion Science and Technology, Vol. 9, 1974, pp. 17-23.

112Lilley, D. G. and Habashi, W. G., "Prediction of SwirlingFlames with Complex Chemistry," Concordia Univ., Montreal,Canada, 1977 (work in progress).

113Gibson, M. M. and Morgan, B. B., "Mathematical Model ofCombustion of Solid Particles in a Turbulent Stream with Recir-culation," Journal of the Institute of Fuel, Vol. 43, 1970, pp. 517-523.

114Crowe, C. T., "Conservation Equations for Vapor-DropletFlows," Proceedings of the 25th Heat Transfer and Fluid MechanicsInstitute, edited by A. A. McKillop, J. W. Baughn, and H. A. Dwyer,Stanford Univ. Press, Stanford, Calif., 1976, pp. 214-228.

115Spalding, D. B., "The Calculation of Combustion Processes,"Dept. of Mechanical Engineering, Imperial College, Rept.HTS/71/41-48, London, 1971.

1I6Lilley, D. G. and Wendt, J. O. L., "Modeling Pollutant For-mation in Coal Combustion," Proceedings of the 25th Heat Transferand Fluid Mechanics Institute, edited by A. A. McKillop, J. W.Baughn, and H. A. Dwyer, Stanford Univ. Press, Stanford, Calif.,1976. pp. 196-213.

117Munz, N. and Eisenklam, P., "The Modeling of a High-Intensity Spray Combustion Chamber," 16th Symposium (In-ternational) on Combustion, The Combustion Inst., Pittsburgh, Pa.,1977.

1I8Westbrook, C. K., "Three Dimensional Numerical Modeling ofLiquid Fuel Sprays," 16th Symposium (International) on Com-bustion, The Combustion Inst., Pittsburgh, Pa., 1977.

1I9Roache, P. J., Computational Fluid Dynamics, Heraiosa,Albuquerque, N. Mex.s 1972.

120 Potter, D., Computational Physics, Wiley, London, 1973.121 Bueters, K. A., Cogoli, J. G., and Habelt, W. E., "Performance

Prediction of Tangentially Fired Utility Furnances by ComputerModel," 15th Symposium (International) on Combustion, TheCombustion Inst., Pittsburgh, Pa., 1975, pp. 1245-1260.

I22Spalding, D. B., "GENMIX: A General Computer Program forTwo-Dimensional Parabolic Phenomena," Dept. of MechanicalEngineering, Imperial College, Rept. HTS/75/17, London, 1975.

123Lilley, D. G., "Prediction.of Inert Turbulent Swirl Flows,"AIAA Journal, Vol. 11, July 1973, pp. 955-960.

124Koosinlin, M. L. and Lockwood, F. C., "The Prediction ofAxisymmetric Turbulent Swirling Boundary Layers," AIAA Journal,Vol. 12, April 1974, pp. 547-554.

125Lilley, D. G., "Turbulent Swirling Flame Prediction," AIAAJournal, Vol. 12, Feb. 1974, pp. 219-223.

126Gosman, A. D., Pun, W. M., Runchal, A. K., Spalding, D. B.,and Wolfshtein, M. W., Heat and Mass Transfer in RecirculatingFlows, Academic Press, London, 1969.

127Gosman, A. D. and Pun, W. M., "Calculation of RecirculatingFlows," Dept. of Mechanical Engineering, Imperial College, Rept.HTS/74/2, London, 1974.

128Lilley, D. G., "Primitive Pressure-Velocity Code for theComputation of Strongly Swirling Flows," AIAA Journal, Vol. 14,June 1976, pp. 749-756.

129Kubo, I. and Gouldin, F. C., "Numerical Calculations of theTurbulent Swirling Flow," Journal of Fluids Engineering, Sept. 1975,pp.310-315.

130Sarnuelsen, G. S. and Starkman, E. S., "Analytical and Ex-perimental Investigation of an Ammonia/Air Opposed Reacting Jet,"Combustion Science and Technology, Vol. 5, 1972, pp. 31-41.

131 Peck, R. E. and Samuelsen, G. S., "Analytical and Ex-perimental Study of Turbulent Methane-Fired Backmixed Com-bustion," AIAA Paper 75-1268, Anaheirn, Calif., Sept. 29-Oct. 1,1975.

132Peck, R. E. and Samuelsen, G. S., "Eddy Viscosity Modeling inthe Prediction of Turbulent Backmixed Combustion Performance,"

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16th Symposium (International) on Combustion, The CombustionInst., Pittsburgh, Pa., 1977.

133 Kennedy, L. A. and Seaccia, C., "Modeling of Gas TurbineCombustors," Proceedings of the International Conference onNumerical Methods in Fluid Dynamics, edited by C. A. Brebbia andJ. J. Connor, Pentech Press, London, and Crane, Russak & Co., NewYork, 1974, pp. 220-239.

134Kennedy, L. A., "Numerical Modeling of Continuous FlowCombustors," AIAA Paper 77-139, Los Angeles, Calif., Jan. 24-26,1977.

135Anasoulis, R. F., McDonald, H., and Buggeln, R. C.,"Development of a Combustor Flow Analysis, Part 1: TheoreticalStudies," Air Force Aero Propulsion Lab., Air Force SystemsCommand, AFAPL-TR-73-98, Pt. 1, Wright-Patterson Air ForceBase, Ohio, Jan. 1974 (see also Pts. 2 and 3).

136Schorr, C. J., Worner, G. A., and Schimke, J., "The AnalyticalModeling of a Spherical Combustor Including Recirculation," 14thSymposium (International) on Combustion, The Combustion Inst.,Pittsburgh, Pa., 1973, pp. 567-574.

137Habashi, W. G. and Lilley, D. G., "A Finite Element Study ofBluff-Body Flameholder Wakes," Ooncordia Univ., Montreal,Canada, 1977 (work in progress).

138Patankar, S. V. and Spalding, D. B., "A Calculation Procedurefor Heat, Mass and Momentum Transfer in Three-DimensionalParabolic Flows," International Journal of Heat and Mass Transfer,Vol. 15, 1972, pp. 1787-1806.

139Patankar, S. V., "Numerical Prediction of Three-DimensionalFlows," Studies in Convection, edited by B. E. Launder, Vol. 1,Academic Press, London, 1975, pp. 1-78.

140Harlow, F. H. and Welch, J. E., "Numerical Calculation ofTime-Dependent Viscous Incompressible Flow of Fluid with Free

Surface (The MAC Method).- The Physics of Fluids, Vol. 8, 1965, pp.2182-2189.

141Amsden, A. A. and Harlow, F. H., "The SMAC Method: ANumerical Technique for Calculating Incompressible Fluid Flows,"Los Alamos Scientific Lab., Rept. LA-4370, Los Alamos, N. Mex.,1970.

142Hjertager, B. H. and Magnussen, B. F., "Numerical Predictionof Three-Dimensional Turbulent Buoyant Flow in a VentilatedRoom," International Center for Heat and Mass Transfer, 7975International Seminar on Turbulent Buoyant Convection, Dubrovnik,Yugoslavia, Aug. 30-Sept. 4, 1976.

143Abou Ellail, M. M., Gosman, A. D., Lockwood, F. C., andMegahed, I. E. A., "A Three Dimensional Procedure for CombustionChamber Flows," AIAA Paper 77-138, Los Angeles, Calif., Jan. 24-26, 1977.

144Paynter, G. C., Birch, S. C., Spalding, D. B., and Tatchell, D.G., "An Experimental and Numerical Study of the 3-D Mixing Flowsof a Turbofan Exhaust System," AIAA Paper 77-204, Los Angeles,Calif., Jan. 24-26, 1977.

145Serag Eldin/M. A. and Spalding, D. B., "Prediction of theFlow and Combustion Processes in a Three-Dimensional CombustionChamber," Dept. of Mechanical Engineering, Imperial College, Rept.HTS/76/3, London, 1976.

146Dussourd, J. L., Lohmann, R. P., and Uram, E. M. (eds.),Fluid Mechanics of Combustion, Americal Society of MechanicalEngineers, Book 100034, 1974.

147Fluid Mechanics of Combustion Processes Meeting, Com-bustion Inst./Central States Sec., March 28-30, 1977.

148Pershing, D. W., private communication, 1976.

From the AIAA Progress in Astronautics and Aeronautics Series...

EXPERIMENTAL DIAGNOSTICS IN GAS PHASECOMBUSTION SYSTEMS—v. 53

Editor: Ben T. Zinn; Associate Editors: Craig T. Bowman,Daniel L. Hartley, Edward \V. Price, and James F. Skifstad

Our scientific understanding of combustion systems has progressed in the past only as rapidly as penetrating experimentaltechniques were discovered to clarify the details of the elemental processes of such systems. Prior to 1950, existing un-derstanding about the nature of flame and combustion systems centered in the field of chemical kinetics and thermodynamics.This situation is not surprising since the relatively advanced states of these areas could be directly related to earlierdevelopments by chemists in experimental chemical kinetics. However, modern problems in combustion are not simple ones,and they involve much more than chemistry. The important problems of today often involve nonsteady phenomena, dif-

.fusional processes among initially unmixed reactants, and heterogeneous solid-liquid-gas reactions. To clarify the innermostdetails of such complex systems required the development of new experimental tools. Advances in the development of novelmethods have been made steadily during the twenty-five years since 1950, based in large measure on fortuitous advances in thephysical sciences occurring at the same time. The diagnostic methods described in this volume—and the methods to bepresented in a second volume on combustion experimentation now in preparation—were largely undeveloped a decade ago.These powerful methods make possible a far deeper understanding of the complex processes of combustion than we hadthought possible only a short time ago. This book has been planned as a means of disseminating to a wide audience of researchand development engineers the techniques that had heretofore been known mainly to specialists.

671 pp., 6x9, illus., $20.00 Member $3 7.00 List

TO ORDER WRITE: Publications Dept., AIAA, 1290 Avenue of the Americas, New York, N.Y. 10019

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