{"title":"Diffusion in laminar flame jets","authors":"H.C. Hottel , W.R. Hawthorne","doi":"10.1016/S1062-2896(49)80034-1","DOIUrl":null,"url":null,"abstract":"<div><p>The lengths and concentration patterns offlames from circular nozzles burning in free air have been determined over a wide range of velocities with several nozzle diameters and for various gases and primary air-gas ratios. As the nozzle velocity is increased from zero the flame, burning under conditions of diffusional mixing with air, increases in length until a transition occurs to turbulent combustion with a consequent change in flame length to a value which is substantially independent of further increase in velocity.</p><p>the present paper covers that portion of the data related to laminar jets and to transition phenomena. The progress of combustion is treated analytically, assuming that molecular diffusion is controlling and that the concentration of oxygen and fuel are zero at the flame interface. A relation is obtained between the time of flow of fuel gas to the flame tip and the proportion of nozzle fluid and air required for complete combustion as follows:</p><p><span><span><span><math><mrow><mrow><mn>1</mn><mo>/</mo><mrow><msub><mi>θ</mi><mi>f</mi></msub><mo>=</mo><mn>4</mn><msub><mrow><mo>log</mo><mo></mo></mrow><mi>e</mi></msub><mrow><mo>(</mo><mrow><mfrac><mrow><mn>1</mn><mo>+</mo><msub><mi>a</mi><mi>t</mi></msub></mrow><mrow><msub><mi>a</mi><mi>t</mi></msub><mo>−</mo><msub><mi>a</mi><mn>0</mn></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mrow></mrow></math></span></span></span></p><p>where <em>θ<sub>f</sub></em>=4<em>D<sub>v</sub>t<sub>f</sub>/D<sup>2</sup> D<sub>v</sub></em>=molecular diffusivity <em>t<sub>f</sub></em>=time of flow from nozzle to flame tip <em>D</em>=nozzle diameter <em>a<sub>t</sub></em>=mols air/mol fuel gas for complete combustion <em>a<sub>0</sub></em>=mols air/mol fuel gas in nozzle fluid When the flame is short the time of flow is proportional to flame length, <em>L</em>; for longer flames, the generalized flow-time for a given nozzle fluid, <em>θ<sub>f</sub></em>, should be a function of <em>L/D</em>, volumetric flow rate, <em>Q</em>, diffusivity, <em>D<sub>v</sub></em>, and the Grashof group which enters wherever the major force overcoming viscous drag is one of buoyancy. The actual relationship is established empirically from data on flames of carbon monoxide and of city gas. For flames longer than 6 inches, issuing from nozzles of diameters 0.125 to 0.82 inches, the following relation is suggested: <em>L</em>=<em>A</em> log <em>Qθ<sub>f</sub>+B</em>, where <em>A</em> and <em>B</em> are constants depending only on the fuel gas and the primary air-fuel ratio.</p><p>Data on phenomena of transition from laminar to turbulent flow in the flame jet are also presented.</p></div>","PeriodicalId":101204,"journal":{"name":"Symposium on Combustion and Flame, and Explosion Phenomena","volume":"3 1","pages":"Pages 254-266"},"PeriodicalIF":0.0000,"publicationDate":"1948-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1062-2896(49)80034-1","citationCount":"103","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Combustion and Flame, and Explosion Phenomena","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1062289649800341","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 103
Abstract
The lengths and concentration patterns offlames from circular nozzles burning in free air have been determined over a wide range of velocities with several nozzle diameters and for various gases and primary air-gas ratios. As the nozzle velocity is increased from zero the flame, burning under conditions of diffusional mixing with air, increases in length until a transition occurs to turbulent combustion with a consequent change in flame length to a value which is substantially independent of further increase in velocity.
the present paper covers that portion of the data related to laminar jets and to transition phenomena. The progress of combustion is treated analytically, assuming that molecular diffusion is controlling and that the concentration of oxygen and fuel are zero at the flame interface. A relation is obtained between the time of flow of fuel gas to the flame tip and the proportion of nozzle fluid and air required for complete combustion as follows:
where θf=4Dvtf/D2 Dv=molecular diffusivity tf=time of flow from nozzle to flame tip D=nozzle diameter at=mols air/mol fuel gas for complete combustion a0=mols air/mol fuel gas in nozzle fluid When the flame is short the time of flow is proportional to flame length, L; for longer flames, the generalized flow-time for a given nozzle fluid, θf, should be a function of L/D, volumetric flow rate, Q, diffusivity, Dv, and the Grashof group which enters wherever the major force overcoming viscous drag is one of buoyancy. The actual relationship is established empirically from data on flames of carbon monoxide and of city gas. For flames longer than 6 inches, issuing from nozzles of diameters 0.125 to 0.82 inches, the following relation is suggested: L=A log Qθf+B, where A and B are constants depending only on the fuel gas and the primary air-fuel ratio.
Data on phenomena of transition from laminar to turbulent flow in the flame jet are also presented.
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