Effects of a Recess on Cryogenic Flame Stabilization

D. KENDRICK,† G. HERDING,‡ P. SCOUFLAIRE, C. ROLON, and S. CANDEL*Laboratoire EM2C, CNRS, Ecole Centrale Paris, F-92295 Chatenay-Malabry, France

Flame stabilization is a central issue in propulsion applications. In cryogenic liquid rocket engines this processis controlled by a competition between liquid core breakup, atomization, vaporization, and reaction. It is knownfrom practical experience that cryogenic flame stabilization is improved by recessing the liquid oxygen (LOX)tube with respect to the injection plane. This effect is investigated in this article using model scale experiments.A single jet-flame formed by a coaxial injector fed by LOX and gaseous hydrogen (GH2) is analyzed by imagingthe light emitted by hydroxyl (OH) radicals. To characterize the mean reaction zone structure, the lightemission images are averaged and the resulting image is treated by numerical tomography (based on the Abeltransform). This yields the local volumetric light intensity distribution. This method is used to examine themodifications in the near flame structure due to the LOX tube recess. It is shown that when the LOX tube isrecessed with respect to the injection plane, the flame is stabilized inside the injector, the flame expansion angleis augmented, the thickness of the flame brush and the size of the volume where reaction takes place isenhanced. Effects observed experimentally are quite significant. The phenomenon is interpreted with a simplemodel relying on a one-dimensional description. When the flame develops inside the duct, it produces hot gaseswhich occupy a certain fraction of the available duct area, the hydrogen stream is accelerated, and consequentlythe gas to liquid momentum flux ratio J is augmented. The model provides the values of this quantity in termsof the fraction of vaporized oxygen. The augmented value of J, in turn, leads to a faster breakup of the liquidoxygen core, an improved primary atomization, and a corresponding augmentation of the flame blooming angleand combustion volume. © 1999 by The Combustion Institute

INTRODUCTION

The structure of cryogenic flames poses manyfundamental problems and considerable model-ing difficulties. Mechanisms controlling theflame length and its stabilization are specificallyimportant in the domain of rocket propulsion[1, 2]. The spray characteristics govern in manyways the development of two-phase flames, afact that has been well illustrated in recent years(see for example the detailed investigations ofFarago and Chigier [3], Stepowski et al. [4], andFaeth [5] among many others). New experi-ments have revealed considerable informationon the structure of cryogenic flames near theinjection plane and on the effects of operatingparameters. The geometry of the initial regionhas been visualized with classical (schlieren) aswell as more modern optical methods [6, 7].Emission imaging, elastic light scattering, andplanar laser-induced fluorescence have pro-

vided considerable insight on the complex cou-pling between the liquid oxygen (LOX) jetbreakup, atomization, vaporization, and reac-tion of gaseous hydrogen and oxygen [8–10].Effects associated with operating parametershave been described and the controlling factorshave been identified. The regime of combustionof the droplet spray and the structure of thestabilization zone are now documented in aseries of studies developed by different researchteams [7, 11–13]. Studies of coaxial injectors andtwo-dimensional liquid–gas mixing layers undercold flow conditions [14, 15] have indicated thatthe breakup of the LOX jet is determined by themomentum flux ratio:

J 5rgvg

2

rlvl2 5

Gaseous momentum fluxLiquid momentum flux

(1)

It was shown in particular that the liquid corelength was inversely proportional to the squareroot of J. When the thickness of the coaxialgaseous stream annulus is sufficiently large, theliquid core length may be correlated by lc .6/J1/ 2.

It is also known that the droplet sizes formedafter jet breakup depend on other dimension-

*Corresponding author. Address: Professor Sebastien Can-del, EM2C Laboratory, CNRS, Ecole Centrale Paris, 92295Chatenay-Malabry, France. E-mail: candel@em2c.ecp.fr†Present address: United Technology Research Center,East Hartford, CT 06108, USA.‡Present address: Volkswagen, 38436 Wolfsburg, Germany.

COMBUSTION AND FLAME 118:327–339 (1999)© 1999 by The Combustion Institute 0010-2180/99/$–see front matterPublished by Elsevier Science Inc. PII S0010-2180(98)00168-0

less groups. The Weber number which com-pares inertial and surface tension forces is onecontrolling factor. Experiments indicate, for ex-ample, that the mean droplet diameters result-ing from secondary atomization satisfy a criticalWeber number criterion. Because the momen-tum flux ratio parameter defines to a greatextent the mode of operation of coaxial injec-tors, it has been possible to develop small-scaleexperiments which are representative of realconfigurations by keeping this ratio in the samerange of values (typically around 10 in practicalsystems).

Many other results are contained in the re-cent literature and will not be reviewed further.The present investigation concerns the effect ofa recess on the structure of the flame stabiliza-tion region. Recess is here defined as the axialdistance separating the LOX tube exhaust andthe injection plane. A recess is employed inmany rocket motors because it is known to havea positive effect on flame stability. Full-scaleexperiments indicate that the optimum value ofrecess is about equal to the LOX tube diameter.While many experiments have studied how theengine performance changes with recess andestablished practical design rules, basic infor-mation on how recess modifies the flame struc-ture is not available. This article reports de-tailed experiments on this aspect and includes asimple model of the mechanism controlling theprocess. After a brief description of the experi-mental configuration and of the methods ofimaging and numerical processing, it reportsresults which clearly show that recess changesthe flame shape and the heat release distribu-tion in the near field. It is shown that recess andmomentum flux ratio should be considered incombination and that recess has the greatestimpact when the initial momentum flux wouldproduce an imperfect jet breakup and subse-quent atomization. Experimental results are in-terpreted in terms of a simple model whichdescribes the evolution of flow parameters in-side the injection element. This model indicateshow the principal variables change when theflame is stabilized inside the duct. Calculationswith some simplifying assumptions allow a qual-itative understanding of recess effects.

EXPERIMENTAL CONFIGURATION

Experiments were carried out on the cryogeniccombustion facility “Mascotte” shown in Fig. 1.This system designed and operated by ONERAfeatures a combustion chamber equipped with asingle coaxial injector fed with LOX and gas-eous hydrogen (GH2). The mass flow ratesrange from 20 to 100 g s21 for LOX and from 5to 20 g s21 for GH2 (when injected at roomtemperature). In the present experiments, thechamber pressure is limited to 10 bar. Thechamber is of square cross-section with an innerdimension of 50 mm. A stainless steel structureholds two lateral fused silica windows (100 mmlong and 50 mm high). The window internalfaces are cooled by a gaseous helium film. Themass flow rate of helium is negligible and doesnot perturb the main flow. Upper and lowerwindows 100 mm long but only 10 mm wide areused for laser sheet transmission. The combus-tor is constituted of different interchangeablemodules, which permit visualizations of thewhole combustion chamber by placing the trans-parent module at different longitudinal posi-tions. In the present experiments, the visualiza-tion module was placed against the injectionplane, allowing a full view of the initial flame. Aconverging–diverging nozzle made of graphitedefines the operating pressure.

Fig. 1. (a) Schematic view of experimental facility. (b)Schematic view of injector and the flow in the vicinity of theinjection plane.

328 D. KENDRICK ET AL.

Operating Conditions

Similarity between experiments performed atlow pressures on the model scale combustor andoperation at elevated pressures of real enginesis not easily obtained. Among the many possiblesimilarity rules one may choose to conserve themomentum flux ratio J defined above. Thischoice is founded on recent studies on atomiza-tion in coaxial geometries and on older correla-tion methods developed for rocket injectors [2].The mass flow rates of LOX and GH2 areselected in order to preserve the value of themomentum flux ratio at different operatingpressures. This choice leads to variations of themixture ratio E 5 mLOx/mGH2

. In other words,operating conditions at different pressures willcorrespond to the same values of J, but todifferent mixture ratios, E. Such distorsions inoperating parameters are acceptable if they donot change the regime of combustion. Varia-tions in E will have little impact if the chemicalDamkohler number which compares the mixingtime to the chemical time Dac 5 tm/tc remainsin the same range. This condition is well satis-fied as Dac is always much larger than unity forall values used for the mixture ratio (E . 2).Changes in the mixture ratio should not be toolarge, in order to maintain comparable values ofheat release per unit volume, a condition whichis also satisfied in our experiments.

Among the many tests, we only considerthose identified by A and C at a pressure of 10bar, because these typify what is observed atother pressures and operating conditions. Themain characteristic parameters are given in Ta-ble 1. Point A features a sufficiently largemomentum flux ratio to provide good jetbreakup even in the absence of recess. Point Ccorresponds to a low value of J where breakupand atomization are less effective, at least wherethere is no recess.

Imaging Method

A variety of optical diagnostics was used tostudy the cryogenic flames [8–10]. It was shownin these previous studies that considerable in-sight could be obtained by using emission imag-ing in combination with numerical tomography.This technique is exploited to delineate regionsof intense combustion. The data are acquired byplacing an intensified CCD imaging camera atright angles to the combustor axis (Fig. 1). Thedetection matrix features 578 3 384 pixels with12 bits depth, the camera is equipped with aNikon 105 mm f 5 4.5 UV objective. Asemission bands of OH are clearly separatedfrom those of oxygen and water, a UG-5 glassfilter may be used to block radiation above 400nm and two WG 305 filters to suppress radiationbelow 283 nm, while passing 55–80% of thelight emitted between 306 and 320 nm whereOH chemiluminescence is observed. This typeof numerical tomography is suitable if the flameis axisymmetric and if self-absorption of thelight radiated by the flame is not too large.

Light emission images provide the instanta-neous signal integrated over the line of sight(i.e., over a line orthogonal to the axial direc-tion). It is clearly not possible to deduce thelocal values from an observation under a singleviewing angle. However, the instantaneous im-ages may be averaged and the resulting datamay be processed through an Abel transform todetermine the mean volumetric light intensitydistribution. This processing relies on the Abeltransform [10, 16, 17]. The principle of theprocessing method is shown schematically inFig. 2. A special case of the Radon transform,the Abel transform is adequate if the object (theflame) that is being projected is axisymmetricand if self-absorption of the light radiated byOH radicals is not too important. Rotationalsymmetry of the flame is not exactly verified

TABLE 1

Operating Conditions

PointPressure

(bar)TGH2

(K)mLOX

(g/s)mGH2

(g/s)vLOX

(m/s)vGH2

(m/s) E JWe

(3103)

C-10 10 289 50 15.8 2.23 207 3.2 6.5 12.6A-10 10 289 50 23.7 2.23 308 2.1 14.5 28.2

329CRYOGENIC FLAME STABILIZATION

because the flow is confined by a chamber witha square cross-section. One expects howeverthat the distorsion associated with the cornervortices will remain small, allowing applicationof the Abel transform. The second condition isalso approximately satisfied in the present ex-periments.

We will see in what follows that the emissionimages have an aspect that differs markedlyfrom that of the processed (Abel-transformed)images. One should recall that the detectedimages are formed by line-of-sight integrationwhich “weights” the local intensity distributionby the optical path length. The tomographicprocessing restores the actual distribution ofvolumetric light radiation.

RESULTS AND DISCUSSION

Consider the results obtained by taking aver-ages of instantaneous emission images corre-sponding to the operating points C-10 and A-10.Figures 3 and 4 give the measured emissiondistributions for the two injectors (with andwithout recess). The injector geometry is shownon the left of each figure. The flow is from leftto right, in these and in all the following figures.

Liquid oxygen flows through the central tubewhile hydrogen is conveyed in the annularspace. One may note that the data feature acertain level of noise. The averaging was carriedout over 140 images, each image being exposedover a period of 10 ms. The number of images islimited by the test duration, the exposure time isset sufficiently short so that each image willprovide an “instantaneous” view of the flame.The exposure time could have been madelonger but the information about the instanta-neous flame pattern would have been lost. Thefluctuation level in the average images is how-ever acceptable for the present purpose, and wewill show that it allows an adequate determina-tion of the mean flame structure.

Recess modifies the region of OH emission ina significant way. The flame zone blooming ismuch more important in the presence of recess.The increase in expansion angle is quite notablefor the two operating points. The effect is morenoticeable for point C-10. The flame rapidlyoccupies a large volume, indicating that theLOX jet breakup and mixing are faster whenthe LOX tube is recessed. The previous obser-vations are important but as already stressed inthe previous section, one should remember thatemission images are obtained by integratingover the line of sight. Each instantaneous imageis a projection of the emitting volumes on aplane. This representation does not provide anaccurate view of the mean flame structure be-cause the distribution of light emission isweighted by the optical path through the flame.This explains why the signal reaches its maxi-mum some distance from the injection plane.

Numerical tomography based on the Abeltransform provides more precise information onthe distribution of volumetric light intensity.The numerical transform is applied to the aver-age emission images and yields Figs. 5 and 6which correspond to the operating conditionsC-10 and A-10. The data exhibit a certain noiselevel corresponding to the fluctuations seen inthe average images and also to the Abel trans-formation. The transform was applied sepa-rately to the upper and lower parts of eachimage. A comparison of the resulting trans-formed data thus gives an indication of thestatistical value of the results.

Figures 5 and 6 significantly differ from the

Fig. 2. (a) Schematic view of line of sight OH*-emissiondetection. (b) Principle of algebraic reconstruction used toinvert the signal Sp( x, y) recorded by the camera. Inversionof the matrix A allows calculation of volumetric lightemission i( x, r).

330 D. KENDRICK ET AL.

Fig. 3. Average emission images. Operating pointC-10, p 5 10 bar. (a) Injector with recess. (b)Injector without recess.

Fig. 4. Average emission images. Operating point A-10,p 5 10 bar. (a) Injector with recess. (b) Injector withoutrecess.

331CRYOGENIC FLAME STABILIZATION

Fig. 5. Images calculated by numerical tomographybased on the Abel transform. Operating point C-10,p 5 10 bar. (a) Injector with recess. (b) Injectorwithout recess.

Fig. 6. Images calculated by numerical tomographybased on the Abel transform. Operating point A-10, p 510 bar. (a) Injector with recess. (b) Injector withoutrecess.

332 D. KENDRICK ET AL.

original emission images of Figs. 3 and 4. Themaximum intensity is now located in the initialregion near the injection section. The volumet-ric light intensity keeps the same order ofmagnitude in this region and then diminishesslightly with increasing axial distance.

When there is no recess, the flame is initiallycylindrical and envelopes the LOX jet. Theflame then progressively moves away from thecentral axis and the emission zone becomesthicker. The flame brush appears as a “thickshell” surrounding the spray of LOX dropletsand the vaporized oxygen. The emission regionfeatures a maximum size at about 9 dLOX fromthe injection plane. Beyond this section, thediameter of the flame diminishes slowly withdistance.

When the LOX tube is recessed, the flame isthicker near the injection plane, it expandsrapidly and assumes a conical shape. At agreater distance the flame appears again like athick quasi-cylindrical shell. For both operatingpoints (C-10 and A-10) the flame zone expandsfaster and occupies a broader region in thechamber. The effect of recess is also more

pronounced for point C-10 but is nonethelessquite visible for point A-10.

Theoretical Interpretation

The interpretation of the effect of recess wouldrequire a detailed analysis of the flow fieldwhich is established inside the injector element.This is outside the scope of the present study. Itis however possible to investigate the phenom-enon with a simplified one-dimensional repre-sentation. This model will be used to calculatethe axial evolution of the flow when the flame islocated inside the injector duct. We will onlydescribe the main steps of this analysis and showthat the flame expansion observed experimen-tally may be related to the acceleration of thegaseous stream of hydrogen. This accelerationresults from the presence of the flame inside theduct and the associated flow of hot products.The momentum flux ratio is augmented underthese conditions, precipitating the LOX jetbreakup and subsequent atomization, vaporiza-tion, and reaction.

The analysis deals with the configurationsketched in Fig. 7 and uses the notations gath-ered in Tables 2 and 3. The LOX tube endsection is designated by the superscript (0) whileconditions in the injector end section (e) haveno superscript. To analyze the compound flowestablished in the duct, it is assumed that:

● The LOX velocity does not change;● The pressure is uniform at each section;● The different streams flowing in each section

may be treated as one-dimensional;● Friction on the duct wall may be neglected.

In this formulation all the flow variables evolvein the axial direction due to mass and momen-

Fig. 7. Geometry of injector with recess.

TABLE 2

Conditions Prevailing at Section (0)

LiquidOxygen

LOX

GaseousHydrogen

GH2

HotProducts

p

Mass flow rate m10 m2

0 0Velocity U1

0 U20 —

Density r10 r2

0 —Cross-section A1

0 A20 0

Pressure p0 p0 —

TABLE 3

Conditions Prevailing at Section (e)

LiquidOxygen

LOX

GaseousHydrogen

GH2

HotProducts

p

Mass flow rate m1 m2 mp

Velocity U10 U2 Up

Density r10 r2 rp

Cross-section A1 A2 Ap

Pressure p p p

333CRYOGENIC FLAME STABILIZATION

tum transfer between the different streams. As aconsequence, the pressure changes by anamount p 2 p0 which will be evaluated in whatfollows.

It is worth underlining that the treatment isnot globally one-dimensional. The streams flow-ing at each section feature different velocitiesand different densities. This is a “compoundflow.” Similar descriptions are successfully usedto analyze situations (found in the propulsiondomain) including the mixing between hot andcold streams injected in a channel or nonuni-form flows in nozzles. It has been used torepresent flame spreading in afterburners [18].

Between sections (0) and (e) a certainamount of oxygen is vaporized and this is con-veniently expressed by

mGO25 bm1

0 (2)

where b is the fraction of vaporized oxygen.This fraction will be evaluated later but it istypically of the order of 1023 to 1022 (this willbe estimated below). The oxygen vapor reactswith hydrogen according to H2 1 1

2 O2 3 H2Oor equivalently F 1 sO 3 (1 1 s)P indicatingthat 1 kg of fuel (hydrogen) requires s kg ofoxidizer (oxygen) to give (1 1 s) kg of products(water vapor). Because the chemical time of thereaction is so short, it is reasonable to assumethat gaseous oxygen reacts instantaneously withhydrogen. As a consequence, the amount ofreacted hydrogen is

~mGH2!r 5

mGO2

s5

bm10

s(3)

The resulting mass flow rate of hot products isthen given by:

mp 5 mGO21 ~mGH2

!r 5 bm10 s 1 1

s(4)

It is convenient to introduce a geometricalparameter s representing the total injectionarea divided by the LOX injection area: s 5A0/A1

0 and the global mixture ratio E 5 m10/m2

0.This yields m2 5 m2

0(1 2 bE/s).Mass balance relations and some algebraic

rearrangements yield (see Appendix A for de-tails):

U2

U20 5

r20

r2

~s 2 1!

~s 2 1! 1 b 2 br1

0

rp

U10

Up

1 1 ss

z S1 2bEs D (5)

The fraction of LOX vaporized in the injectorduct, b, is typically quite small b ,, 1 and theprevious expression may be simplified

U2

U20 .

r20

r2

s 2 1

s 2 1 2 br1

0

rp

U10

Up

1 1 ss

(6)

The product stream velocity Up may be esti-mated from a local balance of momentum be-tween reactants and products at one section.The pressure is uniform across the section, thevaporized oxygen has a velocity U1

0 while theGH2 being reacted has a velocity U2. One maywrite:

mpUp 5 mGO2U1

0 1 ~mGH2!rU2 (7)

This yields Up 5 sU10 1 U2/(s 1 1). In all

practical applications U10 ,, U2

0 and one mayalso consider at this level that U2 . U2

0. Thevelocity of products may then be estimated byUp . U2

0/(1 1 s).The momentum balance, Eq. 7, written for

the local flame element does not involve thepressure. This is because we assume it to benearly uniform across the flame. A change ofpressure will appear however in the global mo-mentum balance written between two differentaxial sections (see Eq. 9). This pressure changecorresponds to the acceleration of the flow,which is itself a consequence of vaporizationand reaction of some of the LOX injected.

The situation is reminiscent of that in otherfluid flow problems. For example, in a boundarylayer over a flat wall, pressure is nearly uniformat each section while a pressure gradient mayexist in the axial flow direction and has pro-found effects on boundary layer development.Another example is premixed flame spreadingin a channel, as in afterburners [18]. Here again,the pressure difference across an element of theflame front is quite small (of the order of M2),but the pressure changes from the entrance ofthe channel to the exhaust due to the accelera-

334 D. KENDRICK ET AL.

tion of the hot stream. At each local section, thepressure is essentially uniform while the axialchange of pressure has a finite value.

In compressible flow at relatively low Machnumber, changes in density are slower thanchanges in velocity and one may assume thatr2

0 . r2. Substituting the expression obtained forUp, the velocity ratio for GH2 becomes:

U2

U20 5

1

1 2b

s 2 1r1

0

rp

U10

U20

~1 1 s!2

s

(8)

According to this expression, the change inhydrogen velocity is larger if the fraction b ofvaporized LOX increases. For a fixed injectorgeometry (s 5 const) and for given injectionvelocities, the hydrogen velocity ratio changeswith the product b(r1

0/rp)(U10/U2

0). Even smallvalues of b will affect the velocity ratio becauseof the large density ratio r1

0/rp between theLOX and gaseous products of reaction. Onemay then expect that the hydrogen stream willbe accelerated and that this will change themomentum flux ratio. If J0 and J respectivelydesignate the momentum flux ratios at the (0)and (e) sections one finds J/J0 . (U2/U2

0)2

which, in combination with Eq. 8, provides adirect estimate of the value of J in the exhaustsection (e). We later give numerical estimates ofthe change in momentum flux ratio, but first wederive an expression for the pressure changewhich accompanies the process.

Global Momentum Balance

The pressure loss associated with the hydrogenstream acceleration is evaluated from a globalmomentum balance between sections (0) and(e). If the pressure at each section is uniformand designating by p0 and p as the pressures inthe LOX injection section and in the exhaustsection, the balance of momentum over a con-trol volume limited by these two sections is:

r10~U1

0!2A10 1 r2

0~U20!2A2

0 1 p0A0 5 r10~U1

0!2A1

1 rpUp2Ap 1 r2U2

2A2 1 pA0 (9)

It is again assumed that the LOX velocity doesnot change U1 5 U1

0. The previous expression

divided by r10(U1

0)2A10 may then be cast in the

form:

A10 2 A1

A10 1 J0 A2

0

A10 2

rpUp2

r10~U1

0!2

Ap

A10

1p0 2 pr1

0~U10!2

A0

A10 5 J

A2

A10 (10)

where J0 and J respectively designate the mo-mentum flux ratios in sections (0) and (e). Thisrelation may be rearranged by using results anddefinitions given in Appendix A and reproducedbelow:

A1

A10 5 1 2 b

Ap

A10 5 b

r10

rp

U10

Up

1 1 ss

A20

A10 5

A0 2 A10

A10 5 s 2 1

A2

A10 5 s 2 1 1 b 2 b

r10

rp

U10

Up

1 1 ss

Substituting these expressions gives

b 1 J0~s 2 1! 2 bUp

U10

1 1 ss

1 sp0 2 pr1

0~U10!2

5 JFs 2 1 1 b 2 br1

0

rp

U10

Up

1 1 ss G (11)

Introducing the expression for Up, and using thefact that b ,, 1 (one may drop terms containingb but not those including the product br1

0/rp),one obtains after a number of rearrangements:

p0 2 pr2

0~U20!2 5

s 2 1s

SU2

U20 2 1D (12)

According to this expression the pressure lossp0 2 p is directly proportional to the change inhydrogen velocity U2 2 U2

0.

An Estimate of the Vaporized Fraction ofOxygen

It is interesting now to estimate the rate ofvaporization from the LOX jet. For this we usean expression for the convective rate of vapor-

335CRYOGENIC FLAME STABILIZATION

ization from a liquid surface placed in a gaseousstream. According to [19]

m 0v 51C Fr2D~U2 2 U1!

x G1/ 2 ln ~1 1 BT!

BT0.15 (13)

where r, D, and BT are respectively the densityof oxygen, its diffusivity in the gaseous phase,and the Spalding transfer number BT 5 cp(T2

2 T1)/Lv. The constant C is 3.67 according to[19]. Because relations of the type Eq. 13 areusually obtained by assuming that the productrD2 is constant, one may estimate this group atany reference temperature (for example Tref 5293 K). Sufficiently far from critical conditions,the diffusivity D varies inversely with pressure.From these considerations one may write:

rD2 5 S prTref

D2

D~Tref, pref!pref

p(14)

where pref may be taken equal to 1 bar. Thetotal mass flow rate of vaporized oxygen mGO2

may be evaluated by integrating the vaporiza-tion rate given by Eq. 13 over the LOX jetsurface. For simplicity, we assume that thissurface is smooth and cylindrical with a diame-ter dLOX and an axial extent a. This last quantityis equal to the recess size (here a 5 dLOX). Toaccount for corrugations of the surface and forsome droplets torn away from the liquid core,one may insert an empirical factor h . 1relating the real surface area to the cylindricalsurface area. Integration of Eq. 13 yields:

mGO25 S2h

C D @r2D~U20 2 U1

0!a#1/ 2

zln ~1 1 BT!

BT0.15 pdLOX (15)

The integration assumes that the flow velocitiesU1 and U2 are constant. This is acceptable inorder to estimate a small quantity, b, and moreaccurate representations of U1 would only in-troduce second-order terms. Dividing Eq. 15 bym1

0 5 r10pdLOX

2 U10/4 gives:

b 5 S8h

C DS r

r10DFS D

dLOXU10D

zU2

0 2 U10

U10

adLOX

G1/ 2 ln ~1 1 BT!

BT0.15 (16)

To estimate b one uses Eq. 14, with D(Tref, pref)5 0.244 1024 m2 s21, and take h . 1.5, BT .10. It is also assumed that recess is one diame-ter a 5 dLOX. Values of velocities are thoseincluded in Table 1. One finds b 5 0.9 1022 forpoint C at 10 bar and b . 1.0 1022 for point Aat 10 bar.

Numerical Application

The previous results may be used to obtainnumerical estimates of ratio J/J0 and of thepressure loss ( p0 2 p)/r2

0(U20)2. These expres-

sions depend on two parameters which are fixedby the injector geometry [s 5 (12/5)2] and theoperating conditions (s 5 8, U1

0, U20 are given in

Table 1, r10 5 1140 kg m23). The product stream

density may be estimated with the perfect gaslaw rp 5 p/(rpTp) where rp is the gas constantfor products. At p 5 10 bar, rp 5 0.72 kg m23.

The vaporized fraction of oxygen cannot bedetermined with precision and it is thereforesuitable to plot the normalized momentum fluxratio J/J0 and the pressure coefficient ( p0 2p)/r2

0(U20)2 as a function of b for the estimated

range of values of this quantity. Figures 8 and 9show that the momentum flux increases with thevaporized fraction and that, correspondingly,the pressure loss increases simultaneously. Forpoint C-10, the momentum flux ratio J is ap-proximately 2.2 times its initial value J . 14.2.The pressure loss coefficient for that point isnearly 0.4, corresponding to a pressure differ-

Fig. 8. Variation of the momentum flux ratio J as a functionof the vaporized LOX fraction. Plot displays the ratio of themomentum flux ratio divided by its initial value J0. Operat-ing conditions A and C at p 5 10 bar. Recess a 5 dLOX.Open circles correspond to estimated values of b.

336 D. KENDRICK ET AL.

ence p0 2 p . 13,900 Pa. The change in J mayhave a marked effect on the LOX jet breakup. Itis known that breakup is most sensitive to thevalue of this quantity: if J is below 10, jetbreakup is delayed, whereas above this criticalvalue it is improved. The core length alsochanges with the inverse of J1/ 2. Previous exper-iments have shown that operating conditions C,without recess, lead to poor atomization [13].The LOX tube recess modifies this situation toa great extent by changing the momentum fluxratio. The liquid core breakup is improved, as isevident from the expansion of the flame in thevicinity of the injection plane.

For point A-10, the recess also changes themomentum flux by a smaller factor (.1.74).This yields a value of J . 25 and a correspond-ing pressure difference p0 2 p . 20,000 Pa.The effect on the flame development will be lessmarked in this case because the initial momen-tum flux ratio J0 belongs to the suitable rangeand leads to rapid breakup and good primaryatomization. The effect on the flame is never-theless visible, indicating that breakup is accel-erated and atomization improved.

According to the present model, recessing ofthe oxygen tube will have the greatest impact ifthe initial momentum flux ratio is smaller thanthe critical value ( Jc ; 10) required for “cor-rect” LOX jet breakup. To be effective we haveseen that the vaporized fraction of LOX shouldbe of the order of 1%, which corresponds to theestimated value of b. Recessing will still beeffective for values of b above 0.4%.

One may also try to use the model to predicttrends with respect to operating pressure. For afixed area ratio s and for similar values of theinitial momentum flux ratio J0, the model indi-cates that a recess will be more effective atlower pressure. The controlling parameter is

b

s 2 1r1

0

rp

U10

U20

~1 1 s!2

s(17)

As b evolves as p1/ 2 and rp changes as p, thisgroup diminishes as p21/ 2 and the change inGH2 velocity, given by Eq. 8 diminishes.

This corresponds well to what is observed:data obtained at p 5 5 bar (not shown) indicatethat flame expansion is greater than that ob-served at 10 bar. A recess is more effective atlower pressure. One should note, however, thatoperation at higher pressures requires a de-crease in the area ratio s 5 A0/A1

0 and this willrestore the effectiveness of the recess.

The previous results are all based on the ideathat changes in the hydrogen stream momen-tum control the injector operation. Momentaassociated with the gaseous oxygen and the hotproducts are not considered and we do notdescribe the possible “barrier” effect resultingfrom the presence of the flame. To justify thispoint, it may be reasoned that a layer of hotproducts and gaseous oxygen and a flame “bar-rier” are present in the two configurations con-sidered (recess and no recess). Thus the mainchange seen by the LOX jet is the change inGH2 momentum. One may further argue thatthe GH2 momentum is dominant because themass flow rate of gaseous oxygen and hot prod-ucts is of the order of 1% of mLOX. Thecorresponding mass flow rate is small and theassociated momentum is negligible. The flamebarrier effect would be perhaps slightly morepronounced in the recessed situation.

CONCLUSION

The article deals with the effect of a recess oncryogenic flame stabilization for the case of acoaxial injector, without swirl. Numerical to-mography based on Abel’s transform is used toprocess average images of the light emitted byOH radicals and deduce the structure of themean flame. The data show that a recess of one

Fig. 9. Variation of the pressure coefficient ( p0 2 p)/r2

0(U20)2 as a function of the vaporized LOX fraction.

Curves correspond to operating conditions A and C at p 510 bar. Recess a 5 dLOX. Open circles correspond toestimated values of b.

337CRYOGENIC FLAME STABILIZATION

LOX tube diameter enhances the flame expan-sion rate and augments the width of the flamevolume. The phenomenon is explained with asimple one-dimensional analytical model whichdescribes the flow inside the injector. Becausethe flame develops inside the duct, it produceshot products which occupy a certain fraction ofthe available duct area. The hydrogen gas isaccelerated and consequently the momentumflux ratio J is augmented. This leads to a fasterbreakup of the liquid jet, improved primaryatomization, and a corresponding augmentationof the flame expansion angle and combustionvolume. The data gathered in this article pro-vide original information on effects of injectorgeometry on cryogenic flame stabilization andmay be used to guide modeling efforts.

This work was supported in part by SEP andCNES. D.K. had a Chateaubriand fellowship, thedoctoral fellowship of G.H. was provided byCNES and DLR. Technical support was providedby E. JeanBart, Y. Le Teno, G. Lucas, and G.Coeur-Joly (EM2C). The Mascotte team (L.Vingert, A. Mouthon, and R. Barraud) of ONERAprovided essential help. We wish to thank thereviewers and Prof. Derek Bradley for commentswhich have helped us clarify various aspects.

REFERENCES

1. Burick, R. J., J. Spacecraft 9:326–331 (1972).2. Gill, G. S. (1978). A Qualitative Technique for Concen-

tric Tube Element Optimization, Utilizing the Factor(Dynamic Head Ratio-1). AIAA Paper 78–76.

3. Farago, Z., and Chigier, N., Atomizat. Sprays 2:137–153(1992).

4. Stepowski, D., Cessou, A., and Goix, P., Combust.Flame 99:516–522 (1994).

5. Faeth, G., Twenty-Sixth Symposium (International) onCombustion, The Combustion Institute, Pittsburgh,1996, pp. 1593–1612.

6. Mayer, W., and Tamura, H., J. Propuls. Power 12:1137–1147 (1996).

7. Mayer, W., Schik, A., Schweitzer, C., and Schaffler, M.(1996). Injection and Mixing Processes in High PressureLOX/GH2 Rocket Combustors. AIAA Paper 96-2620.

8. Herding, G., Snyder, R., Souflaire, P., Rolon, C., andCandel, S., Proceedings of the Conference on PropulsiveFlows in Space Transportation Systems, Bordeaux,France, 1995, pp. 1–14.

9. Herding, G., Snyder, R., Scouflaire, P., Rolon, C., andCandel, S., Twenty-Sixth Symposium (International) onCombustion, The Combustion Institute, Pittsburgh,1996, pp. 2041–2047.

10. Herding, G., Snyder, R., Rolon, C., and Candel, S., J.Propuls. Power 14:146–151 (1998).

11. Pal, S., Moser, M. D., Ryan, H. M., Foust, M. J., andSantoro, R. J., in Proceedings of the Central and EasternStates Sections of the Combustion Institute, New Or-leans, 1993.

12. Guerre, S., Bazile, R., and Stepowski, D., Twenty-SixthSymposium (International) on Combustion, The Com-bustion Institute, Pittsburgh, 1996, pp. 105–111.

13. Snyder, R., Herding, G., Rolon, C., and Candel, S.,Combust. Sci. Technol. 124:331–373 (1997).

14. Hopfinger, E., and Lasheras, J. C., in Proceedings of the6th International Conference on Liquid Atomization(A. J. Yule and C. Dumouchel, Eds.), Begell House,New York, 1994, pp. 110–117.

15. Villermaux, E., in Proceedings of the 3rd InternationalSymposium on Space Propulsion, Beijing, China, 1997.

16. Beyler, C. L., and Gouldin, F. C., Eighteenth Sympo-sium (International) on Combustion, The CombustionInstitute, Pittsburgh, 1981, pp. 1011–1019.

17. Hughey, B. J., and Santavicca, D. A., Combust. Sci.Technol. 29:167–190 (1982).

18. Marble, F. E., and Candel, S., Seventeenth Symposium(International) on Combustion, The Combustion Insti-tute, Pittsburgh, 1978, pp. 761–769.

19. Glassman, I., Combustion, Academic Press, San Diego,1987.

Received 27 April 1998; revised 18 November 1998; accepted28 November 1998

APPENDIX A. DERIVATION OF EQ. 5

We begin by writing mass balance equations forthe LOX, GH2, and hot products. It is reason-able to assume that the LOX velocity in the coredoes not change U1 5 U1

0 and that the LOXdensity is constant r1

0 5 r1 5 rLOX 5 const. Inthe initial section (0) and in the final section (e)the LOX mass flow rates are respectively m1

0 5r1

0U10A1

0 and m1 5 r10U1

0A1. Combining thesetwo expressions:

A1

A10 5

m1

m10 5

m10 2 bm1

0

m10 5 1 2 b (A1)

To evaluate the area Ap occupied by products ofthe reaction, the mass flow rate of products maybe written as mp 5 rpUpAp with mp 5bm1

0(1 1 s)/s. This yields:

br10U1

0A10 1 1 s

s5 rpUpAp

from which one deduces

338 D. KENDRICK ET AL.

Ap

A10 5 b

r10

rp

U10

Up

1 1 ss

. (A2)

The area occupied by LOX and hot products isthen such that

A1 1 Ap

A10 5 1 2 b 1 b

r10

rp

U10

Up

1 1 ss

(A3)

We later estimate the velocity of the hot prod-ucts Up but first calculate the ratio of the area ofhydrogen stream to the initial LOX streamA2/A1

0. For this we start from A2 5 A0 2 ( A11 Ap) where A0 designates the total injectionarea. One has:

A2

A10 5

A0

A10 2

A1 1 Ap

A10

It is convenient to introduce the area factor s 5A0/A1

0, the total injection area divided by theLOX injection area. Thus,

A2

A10 5 s 2 1 1 b 2 b

r10

rp

U10

Up

1 1 ss

(A4)

One may now evaluate the hydrogen flow veloc-ity U2 or more precisely the ratio of this velocity

to its initial value (U2/U20). For this we use a

mass balance for the GH2 stream

m2 5 r2U2A2 5 m20 2

b

sm1

0 5 m20S1 2

bEs D

(A5)

Now m20 5 r2

0U20A2

0 and

U2

U20 5

r20

r2

A20

A2S1 2

bEs D 5

r20

r2

A20

A10

A10

A2S1 2

bEs D(A6)

As A0 5 A10 1 A2

0 one finds that:

A20

A10 5

A0

A10 2 1 5 s 2 1

Using Eq. A4 for A2/A10 yields:

U2

U20 5

r20

r2

~s 2 1!

~s 2 1! 1 b 2 br1

0

rp

U10

Up

1 1 ss

z S1 2bEs D (A7)

339CRYOGENIC FLAME STABILIZATION