COMBUSTION A N D F L A M E 2 9 , 2 2 7 - 2 3 4 (1977)                                                                227

228                                                    F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM

PREDICTION OF FLAME SIZES                                                                                                 ...

        0-050                                                            ...
PREDICTION OF FLAME SIZES                                                                                                 ...
232                                                                                                   F.G. ROPER, C. SMITH...
PREDICTION OF FLAME SIZES                                                                                                 ...
234                                                        F . G . ROPER, C. SMITH, and A. C. CUNNINGHAM

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  1. 1. COMBUSTION A N D F L A M E 2 9 , 2 2 7 - 2 3 4 (1977) 227 The Prediction of Laminar Jet Diffusion Flame Sizes: Part II. Experimental Verification F. G. ROPER,* C. SMITH, and A. C. CUNNINGHAM British Gas Corporation, Watson House, Peterborough Road, London SW6 This paper describes experiments to test the diffusion flame theory given in a previous paper. It is shown that diffusion flame sizes can be predicted for two different burner geometries (circular and slotted ports) by taking the diffusion coefficient of oxygen at a characteristic flame temperature of 1500 K. For the slot burner, the flame size is found to be controlled either by momentum or by buoyancy effects. The transition between the two regimes occurs, as predicted, when the modified Froude number is approxi- mately one. In contrast, if the classical Burke-Schumann theory is used, the diffusion coefficient needed to predict the correct flame size varies by about a factor of six, depending upon the burner geometry and flame conditions. The paper goes on to show that gas compositions in the tail of a diffusion flame may be predicted by the theory already given. It also examines previous experimental work on diffusion flame size in relation to the present work. non-circular burner geometries. A modified theory I. INTRODUCTION was therefore developed in part I of this paper. The present trend towards compact burners and Experimental tests of the new theory are described combustion chambers has caused much interest in the following sections. within the gas industry in the calculation of lami- nar diffusion flame sizes. This subject is of funda- mental scientific interest, but also has many practi- 2. MEASUREMENT OF DIFFUSION cal applications. The latter include: the prediction FLAME SIZE of minimum combustion chamber volume for compact gas appliances; the specification of safety Previous workers, e.g., [1-3, 16, 17], have as- margins needed in appliance design against possible sumed that the diffusion flame ends at the same overload conditions; and assessment of the inter- point as the visible flame. This assumption is often changeability of fuel gases. invalid for hydrocarbon flames, due to the slow It may seem that the many papers already pub- decay of traces of soot or carbon monoxide [15, lished on laminar diffusion flame sizes, e.g., [1-3, 1 9 - 2 1 ] . The diffusion flame height should there- 9, 10, 1 5 - 1 9 ] , have removed the need for further fore be found from the flame gas composition experimental work. However, the previous work rather than visual observation. has concentrated almost completely on the visible The end of the diffusion flame is the point on flame sizes o f circular port burners. Preliminary the flame axis where oxygen and fuel are in the measurements showed that existing theories [1,2] stoichiometric ratio. This point can be found by gave order-of-magnitude errors when applied to gas sampling and analysis, using quartz micro- probes and gas chromatography. However, the method was found to be too slow for general use. * Present address: British Gas Corporation, London Re- It was used to check the following rapid methods search Station, Michael Road, London, S.W.6. Copyright © 1977 by The Combustion Institute Published by Elsevier North-Holland, Inc.
  2. 2. 228 F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM PUMP TO which were developed for measuring diffusion WASTE flame size. 2.1. Diffusion Flame Size from Carbon Jl To J.R 4- II OUTERANALYSERS 71 II Monoxide Concentrations DRAUGHT MANIFOLD . .~ PROOF Part I of this paper has shown how diffusion theory ENCLOSURE can predict the escape of carbon monoxide (CO) through a heat exchanger above the burner. For a heat exchanger at the end of the diffusion flame, VIEWING the calculated CO concentrations were (dry-air- WINDOW EXCHANGE~ free basis): circular port 0.08%; slot burner 0.3%. These values were almost constant for the fuel VIEWING/ L~ I I gases and primary aerations used in the present BURNERI ISL°r WINDOW H work. The same method was used here in reverse; the diffusion flame heights were found from the SECONDARY SECONDARY measured concentrations of CO entering a heat ex- AIR AIR changer at various heights above the burner. The method was tested experimentally as described in Fig. 1. Apparatus for measurement of diffusion flame height from the escape of carbon monoxide through a section 4.4. heat exchanger. The heat exchanger was a water-cooled array of 2-ram-i.d. stainless-steel tubes. The combustion products passing through it were analysed for CO of soots formed from low molecular weight hydro- and CO 2 by nondispersive I.R. analysers. The carbons [22]. This procedure yielded the soot sampling rate through the heat exchanger was high concentrations integrated along the light beam of enough to minimise distortion of the flame im- the densitometer. The flames studied in this way pinging on the heat exchanger. The CO concentra- were axisymmetric. The results were deconvoluted tions (corrected for dilution by excess secondary to yield local soot concentrations, in a way similar air) were then independent of the sampling rate. to that used for axisymmetric flame interfero- For the slot burner a double manifold was con- grams [23]. The detection limit was better than nected to the heat exchanger as shown in Fig. 1, 0.3 ng mm - a of soot, in a volume 1 mm a. so as to sample combustion products from above The soot concentration profiles were found to the central regions of the burner. This eliminated show a common pattern. The soot oxidation zone end effects, so that the flame heights corresponded moved inwards from the edge of the flame to to an infinitely long slot burner. A similar sam- cover its entire width, implying a large degree of piing arrangement was used for the circular port chemical control. So the question arose of how the burner, but without the inner manifold. soot concentration profiles are related to the diffu- sion flame height. Obviously, the maximum soot 2.2. Diffusion Flame Size from concentration occurs at a point where net soot Soot Concentrations formation stops and oxidation starts. The axial Soot concentrations were measured using a sensi- soot maximum must be the point where hydro- tive dual-beam optical densitometer at a wave- carbons are replaced on the flame axis by oxygen. length of 575 nm. The burner and flame contain- This conclusion was confirmed experimentally by ing soot were traversed automatically through one flame gas composition measurements. light beam of the densitometer, by a motorized In other words, if hydrocarbons were the only traverse rig. The resulting absorption profiles were fuel species present in the flame, the axial soot digitized and recorded on punched tape. They maximum would be the end of the diffusion were then analysed on an IBM 1130 computer flame. But for the methane/air flame investigated, using data on the specific extinction coefficients sufficient hydrogen and carbon monoxide were
  3. 3. PREDICTION OF FLAME SIZES 229 also present for the ratio (diffusion flame height/ 0'004 height to axial soot maximum) to equal 1.15. For consistency, this correction was applied to all the / o 2'0 CH4] flames containing soot, although it made slightly [] j t.-2 CH41] I Z ~ I)0quot;2 CH4II r 0 /quot; poorer the agreement between diffusion flame :/ c 'tf 0 / heights measured from soot and carbon monoxide 0'003 concentrations. 3. EXPERIMENTAL CONDITIONS CH4 /,8quot;9/ /o /I vJ CH4 [1%8 9~IT The burners used in this work were: (A) Circular co I2o.9]+, ~ , ,4-0 * 0quot;00: REF ,5) I I~ ¢ port burner, diameter 0.36 to 10.2 mm; (B) straight slot burner, water cooled at 60°C. Length 90 ram, I width 0.33 to 9.0 mm. •,* :, 27,0-3{,o,,.,,,,}-, The burners were placed within an enclosure, to control the secondary air flowrate and composi- 0 .ol tion. Soot measurements were performed only on the circular port burner, with an enclosure cross- section which varied from 30 × 30 mm to 50 × ,Z; ° T© 100 ram. The secondary air flow rate was varied from two to five times the stoichiometric require- I I 1quot;0 2quot;0 3quot;0 ments. These changes were found to have no effect on flame height. The apparatus for measurements I In {1+1/s1 of carbon monoxide escape is shown in Fig. 1. The enclosure had a cross-section 250 × 250 ram, with Fig. 2. Circular port diffusion flame sizes found from a secondary air velocity of 0.05 m/sec for the measurement of carbon monoxide escape. The fuel gas circular port and 0.075 m/sec for the slot burner. compositions are given in Table 1. 4. RESULTS AND DISCUSSION TABLE1 4.1. Circular Port Diffusion Flame Sizes Gas The equation derived in part I for the diffusion Mixture See Figs. flame height (H) of a circular port burner was: Letter No. Composition (H/Q) = {47rDo In (1 1/S)}-I(To/Tf) °'67, + (1) A 3 95% CH4 + 5% C3H8 B 3 90% CH4 + 10 %C3H8 where the symbols are defined in the nomencla- 2,3 87% CH4 + 13% C3H8 C ture (Part I). The proportionality between H and 3 50% CH4 + 50% AIR D 3 33% C3H8 + 67% AIR E flow rate Q was found to hold except at very low 3 47% CH 4 + 35% H 2 + 10% C2H 6 F flow rates, where axial diffusion reduced flame + 4% C3H 8 + 4% N 2 size. Equation (1) was tested by plotting (H/Q) G 2 30% CH 4 + 35% H 2 + 29% C3H 8 against {ln (1 + l/S)} - x for the fuel gases shown + 1 C4HIO + 5% CO2 % in Figs. 2 and 3. 2 65% CH4 + 35% H2 2 49%CH4+ 35% H2 + 16% C3H8 The flame sizes found from CO escape are 3 49% CH4 + 26% H2 + 25% C3H8 shown in Fig. 2 for primary aerations from 25 to 3 14% CH 4 + 48% H 2 + 14% C2H 4 95% of stoichiometric. The figure includes a value + 24% N 2 of H/Q for a CO/air diffusion flame, deduced from
  4. 4. F. G. ROPER, C. SMITH, and A. C. CUNNINGHAM 230 0-050 an average value in Eq. (2) below: (H/Q) = (1.33 10 - 3 mm - 2 sec){ln (1 + I/S)} - 1 . (2) X 0,0t.0 X A comparison of Eqs. (1) and (2) gave an esti- r mate of Tf as 1500 K, which seems a reasonable H/0=1quot;/,0 10-3{1- mean temperature for the flame regions control- 0.030 ling diffusion. D O was taken as the diffusion co- 'E efficient of oxygen, calculated from Leonard- E i Tl__q Jones viscosity fitted parameters [8]. (D O = 20 mm 2 sec - 1 at 293 K.) L~ 0'020 ' SYMBOL FUEL GAS CH4 O 4.2. Slot Burner Diffusion Flame Sizes A ,r'~ C2H6 C2 HL The values of Tf and Do found above may be used C2 H2 X // C3H8 to calculate diffusion flame sizes for a straight slot Y C3H6 + GAS A 0.010 burner. Substituting these values into Eqs. (23)- 7 OA$ B U GAS C (25) of part I. GAS D GAS E 0 OAS K Momentum Control.quot; GAS L GAS F tl 20 30 bQM4~2To I ! HM = (.086 (3) mm - 2 sec) In{ I quot;11s) / Fig. 3. Circular port diffusion flame sizes found from soot concentrations within the flame. The fuel gas composi- Buoyancy Control: tions are given in Table 1. H B = (.20 mm - 4 / 3 sec 213)(Q4(94/aL4)l/3 (4) Transition Region: the results of Hess [15]. For flames where H >> II1+v, / -] burner diameter (d), the points lie close to the 338(HM~312/3 1 ~H = (4~(HB) 3 straight line in Fig. 2. This linear relationship fol- lows from Eq. (1) if Tf and Do are constant. The points which lie significantly below the line in Fig. (5) 2 have ratios (H/d) less than about six, so that The mean acceleration quot;aquot; of the flame gases due axial diffusion cannot be ignored. to buoyancy is needed in Eq. (4) to predict HB. Vitiation of primary and secondary air had a large effect on the flame sizes in Fig. 2. A reduc- We will treat quot;aquot; as an empirical constant. For fuel tion of only 10% in oxygen concentration in- gases premixed with a substantial proportion of creased H by up to 60%, as predicted by Eq. (1). air, the maximum possible value of quot;aquot; is approxi- mately g(Tf/To - 1) ~ 40 m sec - 2 . In practice, The flame sizes found from soot concentrations are plotted in Fig. 3, which again shows that this value will be reduced by momentum losses to (H/Q) ~ (in (1 + l/S)} - 1 . A change in burner the surrounding air. The values of H observed and predicted from diameter from 0.36 to 1.0 mm was found to re- duce (H/Q) by 10%. In this case axial diffusion can Eq. (5) are shown by the solid points in Fig. 4. be ignored, as (H/d) > 50. The effect seems to be The fuel gas was methane, with primary aerations from 30 to 80% of stoichiometric. H was deter- due to buoyancy, and is discussed in Section 5. mined as in section 2.1. For flames where buoy- The equations of the lines in Figs. 2 and 3 ancy effects were small, the predicted and observed differ only slightly, so it seems permissible to take
  5. 5. PREDICTION OF FLAME SIZES 231 width (b) for momentum control and independent I/,0 of b for buoyancy controlled flames, as predicted E E 120 from Eqs. (3) and (4). I ~100 From part I, the criterion for buoyancy effects to be negligible is that the modified Froude num- o x + Jr uJ •:.tl_~f ber Fr >> 1. Figure 5 shows that the transition :::) 80 from momentum to buoyancy control occurs M M NU B O A C O ETM U YN Y when Fr ~ 1. C N R LE C N R LE O T OL D O T OL D FLAMES FLAMES , T.gORY 4.3. Diffusion Flame Sizes from I~ ,•quot; PART T Burke- Schumann Theory ~la~quot; TER HO Y LU The results given above can be used to test the II I I I I I I l I Burke-Schumann (B-S) theory of diffusion flame 0 20 40 60 80 100 120 11.0 160 180 size [1]. On this theory, the diffusion coefficient CALCULATED VALUE OF H-rnm found from the circular port flame sizes is 60 mm 2 Fig. 4. Experimental and predicted diffusion flame sec- 1 , equivalent to diffusion at 575 K. If this heights for slot burner. The 45 ° line shows where the points should lie for complete agreement between theory coefficient is used to predict flame sizes for the and experiment. slot burner, the results are the crosses shown in Fig. 4. When buoyancy can be neglected, the observed flame sizes are about six times larger values of H agreed well, regardless of the value than predicted by the B-S theory. The results taken for quot;aquot;. When buoyancy effects were sig- imply a diffusion coefficient for the slot burner nificant, good agreement was found if quot;aquot; was (on the B-S theory) of 10 mm 2 sec- 1 , equivalent taken as 25 m sec - 2 , 60% of the maximum value. to diffusion at 190 K. The points for buoyancy However, this value is not critical; a 50% increase controlled flames are scattered, but the ratios in quot;aquot; decreases H e by only 12%. (Hexperimental/Hpredieted) are lower than for Figure 5 shows the transition from momentum momentum controlled flames. In other words, to buoyancy control as the slot width increases. buoyancy effects decrease flame size. The opposite The curve in Fig. 5 shows the value of (H/Q) cal- effect would be expected by the B-S model, where culated from Eq. (5) taking a = 25 m sec- 2 . It can an increase in gas velocity due to buoyancy should be seen that (H/Q) is proportional to the slot increase flame height. 4.4. Experimental and Calculated 500 Flame Gas Compositions The concentration profiles of CO, CO2, and 0 2 z,O0 were calculated for the tail of a methane/air flame with primary aeration 60%. The method described in Part I was used, with the values of Do, Tf, and E Io quot;aquot; from the present work. The results are com- ~2oo pared with experiment in Figs. 6(a) and (b). / ! l IBUOVANCV CONTROLLED FLAM In the region close to the flame axis and just ° '~/ ~F r = l ~ - ] I , above the primary flame zone, the measured CO and 0 2 concentrations are greater than calculated. Fr > > 1 (MOMENTUM CONTROLLED FLAME) This implies that conditions there have not yet reached equilibrium. But the remainder of the BURNER SLOT W I D T H - m m profiles show good agreement between theory Fig. 5. Transition from momentum to buoyancy control and experiment. In particular, the width of the for slot burner flame. The solid line is the calculated profiles agrees well with the calculated values. For curve.
  6. 6. 232 F.G. ROPER, C. SMITH, and A. C. CUNNINGHAM /• I ~ ENO OF I POSITION OF 10 PRIMARY FLAME DIFFUSION] FLAME ] ZONE [] [] Io 22 l ol [J CO2 EXPERIMENTAL POINTS I I ] 20 . . . . CO2 CALCULATED LINE CO EXPERIMENTAL POINTS- []/~CALCULATED ,--~7 I I--I co CALCULATED LINE / EXPERIMENTAL SPECIES I 181 POINTS [ [ quot;~/quot; LINE o 02 EXPERIMENTAL POINTS / Z 06 A =limp 16 - - 02 CALCULATED LINE / .,/ J; r A CO i:ilquot; [] CO2 (I: P'5 o [ 02 / Z % ILl i (..) z/, % O (J quot;.o I / o / quot;,, I o / o/o',,,, ¢ '~~ o Td / quot;2,.. o ,F~ ~,4wquot;~i, -quot;rquot;--~._ X ;, 60 - - 70 80 90 100 HEIGHT ABOVE BURNER-ram I I I I I I l I -5 0 5 10 32 3/, 36 38 40 /.6 /.2 /./. TIME -millisecs RADIAL DISTANCE -ram (a) (b) Fig. 6. Concentration profiles for circular port burner-comparison of theory and experiment: (a) Axial profiles, (b) radial profiles 60 mm above the burner. comparison, the classical Burke-Schumann theory 5. C O M P A R I S O N WITH O T H E R W O R K would predict profiles less than half the observed When a comparison was made with previous work width. for the visible flame size (HF) of a circular port The predictions of CO escape into a heat ex- burner, a linear relationship was found between changer above the burner are compared with (HF/Q) and (In (1 + l/S)} - 1 . The graph was simi- experiment for the circular port flame described lar to Fig. 3 (where H replaced HF) except that above and for two slot burner flames. The diffu- the linear relationship now extended from town sion flame height was found from the local gas gas to butane. The graph was restricted to flame compositions, as previously described. For the sizes where soot was present, as the significance circular port flame the agreement between experi- of quot;bluequot; flame sizes is doubtful. The results of ment and predictions is very good. For the slot the present work in general agreed well with Refs. burner, the experimental and calculated profiles [1, 3, 12, 15-17] for the laminar flow region are approximately parallel, and differ at most by where HF De Q. However, an anomaly occurred 8% of the flame height (see Fig. 7).
  7. 7. PREDICTION OF FLAME SIZES 233 A The effect of axial diffusion on flame size, Ill 1quot;0 found in section 4.1, is also confirmed by other SYMBOL BURNER FLOW RATE, mls -1 workers. For short flames of butane, Savage [17] METHANE PRIMARY AIR C RCULAR found that the ratio (Hp~eaietea/Hobservea) de- quot;--0-- 6ram I 0' 9quot;6 554. quot;--quot;D---- 0 8mm pended on the Reynolds number within the SO LT 25.9 124 l, (3 mm ..°.°~ .... burner-which in turn is proportional to (H/d). SLOT 18quot; 0 103 When plotted in this way, the results of Savage (,o and Barr (given in Ref. [17]) agree fairly well with the present work. t! o ~°C. b The effect of buoyancy on flame size was in- 0_ V.. vestigated by Edelman et aL [9], using a numeri- o ~- cal method which ignored axial diffusion. Their g results show that a tenfold decrease in Fr reduces ~t ~ IE (H/Q) by only 7%, in the range 10- 1 > Fr > quot;~. O ~02 quot;~ E]A X 10 - 5 . 5 . This agrees with the experimental results %,% z © °.% . quot;...'... of the present work and those of Hess [15]. o w 0 quot; -~ O 6. CONCLUSIONS 0quot;6 0quot;7 0quot;8 0-9 1'0 1-1 12 13 1''t LIJ HEIGHT ABOVE BURNER CL DIFFUSION FLAME HEIGHT (1) Experimental verification has been obtained for the theory given in part I for the diffusion Fig. 7. Carbon monoxide concentrations in the combus- tion products sampled through a heat exchanger com- flame sizes of axisymmetric and straight slot parison of theory and experiment. burners. (2) Concentration profiles in the tail of the for propylene. The ratio (HF/Q) for this gas was flame may be predicted by diffusion theory, as- much greater than for propane although the two suming the flame gases to be in thermodynamic diffusion coefficients should be similar. The effect equilibrium. This assumption is not valid in the did not occur for the values of (H/Q) in Fig. 3. region just above the primary flame zone. The explanation is that, when soot concentra- (3) Diffusion flame sizes may be found experi- tions are high, a soot oxidation zone follows the mentally from measurements of soot or carbon diffusion flame, causing a large increase in visible monoxide within the flame. Visible flame sizes flame size. This point was shown clearly by Lee only approximate to the diffusion flame size when et al. [21]. Reed and Roper [20] have also shown sufficient secondary air is present, and when small that the length of the soot oxidation zone in- concentration of soot are present within the flame. creases as the soot concentrations increase and as The authors are glad to acknowledge the help the secondary air supply decreases. Soot escape of Dr. M. E. Nolan, Dr. K. Thompson, and Mr. was found to occur when the ratio (soot oxidation B. C. Dutton in the computation o f equilibrium length/H) reached a value close to one. flame gas compositions. They also wish to thank The visible length of hydrocarbon flames at the their colleagues at Watson House for many helpful point where air starvation just caused soot escape discussions, and British Gas for permission to pub- (//smoke) was measured by Vaerman [18]. He lish this paper. found that (Hsmoke/Q) cc S for olefins and paraf- fins up to C7. This is equivalent to two of the pre- vious conclusions: that (H/Q) ~ {In (1 + l / S ) } - 1 , REFERENCES and that (soot oxidation length/H) is constant at the point of soot escape. (For the fuel gases con- and Schumann, T . E. W., Ind. Eng. 1. B u r k e , S. P., cerned, (In (1 + l/S)} - 1 - S ) . Chem. 20, 998 (1928).
  8. 8. 234 F . G . ROPER, C. SMITH, and A. C. CUNNINGHAM 13. Goldburg, A., and Cheng, Sin-L, Comb. Flame 9, 2. Hottel, H. C., and Hawthorne, W. R., Third Sympo- sium on Combustion, Flame and Explosion Phe- 259 (1965). nomena, Williams and Wilkins, Baltimore, 1949, p. 14. Powell, H. N., and Browne, W. G., Sixth Sympo- sium Ilnternational) on Combustion, The Com- 254. 3. Wohl, K., Gazley, C., and Kapp, N., Third Sympo- bustion Institute, Pittsburgh, 1956, p. 918. sium on Combustion, Flame and Explosion Phe- 15. Hess, K., quot;Flame Length and Flame Stability,quot; nomena, Williams and Wilkins, Baltimore, 1949, Dissertation, Karlsruhe T.H., 1965. 16. Barr, J., Fourth Symposium {International) on p. 288. Combustion, Williams and Wilkins, Baltimore, 1952, 4. Clarke, J. F.,Proc. Roy. Soc. A. 296, 519 (1967). 5. Melvin, A., Moss, J. B., and Clarke, J. F. Comb. p. 765. 17. Savage,L. D., Comb. Flame 6, 77 (1962). Sci. Tech. 4, 17 (1971). 6. Williams, F. A., Combustion Theory, Addison- 18. Vaerman, J.,Ind. Chem. Beige. 32,653 (1967). 19. Jones, J. M., and Rosenfeld, J. L. J., Combust. Wesley, Massachusetts and London, 1965. Flame 19,427 (1972). 7. Carslaw, H. S., and Jaeger, J. C. Conduction of Heat 20. Reed, S. B., and Roper, F. G., Gas Council Research in Solids, Oxford University Press, 1947. Communication GC 186, presented to the Autumn 8. Fristrom, R. M. and Westenberg, A. A., Flame Struc- Research Meeting of the Institute of Gas Engineers, ture, McGraw-Hill, New York and London, 1965. 9. Edelman, R. E. Fortune, O. F., Weilerstein, G., 1971. 21. Lee, K. B., Thring, M. W., and B6er, J. M. Combust. Cochran, T. H., and Haggard, J. B., Fourteenth Flame 6,137 (1962). Symposium (International) on Combustion The 22. Dalzell, W. H., and Sarofim, A. F., Trans. ASME J. Combustion Institute, Pittsburgh, 1973, p. 399. Heat Transfer 91,100 (1969). 10. Cochran, T. H., and Masiea, W. J., Thirteenth Sym- 23. Pearce, W. J., Optical Spectrometric Measurement o f posium {International) on Combustion, The Com- High Temperatures, University of Chicago Press, bustion Institute, Pittsburgh, 1971, p. 821. 1960. 11. Fay, J. A., J. Aeronautical ScL 21,681 (1954). 12. Goudie, G. O., quot;Mixing and Combustion of Gas Received 14 June 1976; revised 12 January 1977 Jets,quot; PhD Thesis, University of Glasgow, 1967.