Flame propagation in a vortex core

COMBUSTION AND FLAME t9, 297-303 (1972)

297

Flame Propagation in a Vortex Core P D MeCORMACK Department o f Mathen~altcal PhysicS. IJmverstty College, Cork lreltmd ,and

K $CI't[ELLEII,G MUELLER, and R. T]SHER Chemwal Group. Aeronautwal Res, arck I aboeatory. Wright-PattersonAFB, Dayton, Ohio

Sequent.as of normal and Schheren photog aph~ illustrate the propagation of combustion m vortex rlngg formed ol premlxed propane and ,lit (or oxygen) Measur~.menIof the mean flame propagation speed and the vortex strength mdlcale lhai ova" the range of strengths used in the eqmpment the relationship is appro ~lmatelylinear

1 introduction The observatm,, of the combustion of vortex rings formed from premtxed p, opane and air, has already been reported [1] The main results fr,,m that m~hal mvestlgatl~on were as follows (=) the flame propagated from the tgn. ion re~aon round both halves of the toms, the two fronts meetmg on the far side, (u) in the time taken to complete the combustz~,n (as indicated by lurmnosaty) the torus remained intact, although( noticeable expansion of the core had occurred, (lU) single flash Schlleren photographs sl3.owed the subsequent transformation of the vortex ring into a bali of hot gas. Tempetature.der~slty effects alone would destroy the stabtht, of the ring, (IV) the measured (mean) ;peed of propagation of the flame front round the ring was avcut 300 cm/sec Tins is much higher than the es~abl).shed laminar flame speed for an unconfined StOlchlometrlc mixture of propane ~nd air (about 200 cm/sec) The turbulent fl.~me speed fi)r propan(.'/an ,~ about 600 era/sac But the gas m a vortex core IS not turbulent The mechanism for the high propagation ~peed was, therefore unknown and so It was deeldv .) to

carry c~ut further, more ~3'stematlc, observatloIt~ on this phenomena, with due objective of estabh~lmg the mechanism at work 2 Experimenttd Eqm'pment and Cahhrd'tlon The vortex rings ¢¢e:e formed as before, by use of a pneumatically driven p m o n at one end of a cyhndrlcal cylinder with a circular orifice at the other end A 7 cm dram onfice was used for most of the work The piston movement was about 1.25 cm and the cylinder thameter was about 22 call (much larger than h~ the first investigation). An eleetlleally operated pneumatic swltdr allowed the pressure to be suddenly applied to the piston and ~hen released A pressure pulse was thereby apphed at the orifice The pressure pulse produced m this way is of relatively |ong duration and considerable gas ts pumpeo out of the cylinder along with rite vortex ring formed Vortex nngs with laige apparent cores are thus formed (the core/ring diameter ratio is hardly very small as required bx Lamb's analysts) [2] The true vortex core (pure solid body rotation) is formed during the pressure rise The gas emerging during the time the pressure is high IS rolled up around the true core and forms a shear layer (.or boundary layer) between the core and the surrounding irrotatlonal fluid. This is sketcl',ed m Fig. 1 The diagram is not to so,de, as theory v,:ould CopyrlghI © t972 by The Combustion tnstltule Pubhshed by American Elsevl(,fPubhshmg Company, tn~.

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mdtcate that the rctatl~onal core would have a dnameter m the region ,,f 10 microns "[he surrounding shear (shp) reguon us about 10,0130 times greater m extent (:~he observed nng dmmeter forming at the orifice us about 1/2 cm) The vortex strength (as measured by the forward velocity of the rl,lg) was varied by varying the magnitude of the pressure pulse to the piston A mnl;e o f "0-1 O0 psi was used Measureme~it of Ihe Vortex Strength In Lamb's model the vortex ring is assumed to be formed in the orifice by a pressure pulse and the m o m e n t u m of the emerging ring ~emams constant

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FLAME PROPAGATIONIN A VORTEX CORE

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(a nomascous vortex'} The theory does not spec,fy the s~ze o¢ ~he core and it assumes that air < < z .,~¢% ~z is the core r~dms and R is the ring radms. it is an idealtz~a model but the behavror t~ prt~dlc~ zs ~ez-onably accurate close to the odfice ]'he relatmn between thevortex strength K ancJ ~'he impulse of the pressure Its gaven by

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where p ;s the fired density Thus tl~e most direct method of deterrunm~ K " would be to lneasur,~ t',e plsssure pu,',se using

transducers Because of the mechamc,d dao~ ~. revolved m operating the piston, this method d,d not prove possible The method adopted was az, mdlrec' one and the results are only quahta;ive (but o" the right order of magnitude) It wa.,, z,~ measure the (mean) velocity of the nngs ovei a dlstan(e .near the orifice, USing two hot-w.ra

probes Now the equation for the forward velocity (on Lamb's theory) zs

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With the measured values of v, the observed R value and an assumed value for a, an ¢stlmate for K can be denved from Eq (2) The calibratzot,~ fi)t a range of onfices of 7-11 cm tha~neter are shown m Fig. 2 It is ~een thtt the velocity-pressure relation ts not linear ahd the rare of increase of velocity xv~ti~ pres~u(e falls off sigmti,.andy aoove abou~ 70 p~l The mltlal rmg~radius (R) was about 7 cm (shghtiy greater than the orifice diameter), assummg a core radius of 0 7 cm, and using the measured value:, of ":e!oe.,ty, the vortex strengths were computed from Eq (2) The resulting curve of vortex strength versus pzsl~on pre,.zure (fo, tile 7

P D M¢CORMACK, K SCHLLLI'R,G MUELLER, and R TISdFR

300

cm unfice) ~s shown m Fig 3 Above about 70 ps~ the rate of mcrea,,e to vorte,, strength falls off drasucallv 3 Flame Propagation Speed Measurement A ghgntly fuel-rich mtxture of propane and air was fed to the vortex generator via rotameters The vortt,x nngs were lgmted by the corona discharge from a sharp wire charged to 12,000 V. at a posmon aoou I 30 em from the orifice A Fastax camera operating a~ 1,000 frames/sec photographed the combus~lon as the ring appr,)acned the camera head-on Figure 4(a)-(g) shows a sequence of the burning process For these particular photographs the mixture was augmen ted wWa boron 6*chlortde Tlus produ~.ed a green flame t~ ,¢h,ch the film is mo~t sensmve Normally flus addatwe was ,rot used

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The time interval from ~gmtlon to the meeting of the two flame fronts wa,, measured frc~m the developed fihn whllch had timing marks ( 1,000 per second) on it Assuming a nng s, ze equal to the orifice size gwes a lower estimate of ~he d~stance travelled by the flame front m this mte~va~ and leads to a lower hmlt for the mean propagation speed The measurement of flame speed was made at various voJtex strengths-achieved, as pointed out m Sec 2, by varymg the vortex generator ptMon pressure Measurements were made with a sequence of increasing pressures and then a sequence of decreasing preosure's and average time ll'Jtervals determined The resulting graph of flame speed ',ersus vortex ~trength ~s shown in F~g. 5 Over the. range of ,ortex strengths avadable, the flame speed appears

P];oto~aph~,." ~cquen~e of vortex ring combustion

301

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to increase apprt~x~nately linearly w~th vortex strengq't Mea,;urements using a propane/oxygen mtxture were also made and two points are plotted m Fig 5 The flame speeds are increased by a factor o f abou! 1 35 over the propane/azr ease. Normally the factor is about 1.5 However, as some dilutton with air IS unavoidable in the vortex generator used. thzs lower factor *s not ~urpnsmg In the earlier work the flame speed was lower than those recorded here But only d 2 5 cm orifice was used, and a much smaller plstorl and chamber The maximum pressure was well oelow 20 ~s~ and so presumably the vortex strength was considerably less than the Iowes. value used m this work It was found that w~th the partteular piston and chamber used the ~ cm orifice produced the best re,,ults and ~t was used almost e×cluswely

Mo~e SchleerenPhotographs Irt an attempt to learn more about the phenomenon, ~t was decided to take high-speed Schheren F,hotogrzphs

Fz°,e. 5 [lame speed vs vortex strength

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£.~;) Fig 7 Schhelen ~cquence of vortex nng eombusUon

The hyouz adopted is ,~nown m Fig 6 A ,~lercury vapor lamp was the source and two 2.5 m tac.al length nnnols were used Instead of a knife edge. an ell)ptlcal Schheren spot was substituted There was more than enough hght intensity in tile diffracted field and so a less sensmve film was used and the camera speed increased to 2,000 lrames per see. Owing to the bulk of the generator, the hght beam from the first mirror passed through the vortex at an angle of about 25 ° to the uormal to the plane of the ring F~gure.,, 7(.~)-(h) show a sequence o f pnnts from the 16 m m mo~e film Figure 7(a) ,.s z, Schheren photograph with only tile igmtlon probe and thscharge m the ;ie[d of wew Figure 7(~) sb,~ws the vortex ring b~re lgmt,on and approaching the ~gmter Figure 7(c) is just after igruhon has started Figures 7(d)-([') slto~ )he progress o~ the Oame (as e,adenced by hot g~ses) Figures 7(g) and 7(h) show the combustion dying out, and tke brea~ up of the ring as it moves o'al of the field of 'clew The hght beam is also ~,!v"r~,-g.the gas emerging from the orifice as a

.let, wluch ts apparent m the central opemng of tIae vortex nng The center of the field of view appears bright for th:s reason 4 Concluding Remarks The experiments have estabhshed that (a) the flame propagation speed Ln a vortex ring formed of premlxed propane and mr As slgmficantly higher than that obse~ed m a quiescent gas mlxtule, (b) the speed appears tc increase approxaraately hnearly with the vortex strength As the flame temperature for propan,.~/mr ts about .~200°K, the expected speed of propagation would be about 200 cm/sec ar, d the turbvlent flame speed [3] would be at most about 6(70 cm/sec In the 7 cm vortex ring eombusaon, speeds well over 1000 ~.m/sec h~ve [teen observed Thus it is unhkely that turbulence m the vortex could be the sole source of the enhance,] flame speed lX~oreover, it is generally accepted that the

FLAME PROEM :ATION IN A VORTEX CORE vortex ~.c re is characterized by solid-body rotation al'td Ihl:, ,s inconsistent Wlt]t a t u r b u l e n t structure References i McCcrmcck, P D , P.oc Royallnsh Academy 71 Sec A. Nc 6 ( ; 9 7 1 ) 2 Lamb, H . Hydrodynamics. Dover. New York (19451

303 3 Gersteln, M , and Dugger, ~ L, m Basic Co~.stderanons tn the Combttxrlorl of t~,droca-bon I:ud~ with Air (H C Ba.mett and R R Hubbard, ~.ds L Report 1300. NACA. waslungton. D C ( 19571, Chap 5

{Rccetved December 19 71. re'.'lsed t,er~ton received May 19 72)