{"title":"湍流气体射流中的混合和燃烧","authors":"W.R. Hawthorne , D.S. Weddell , H.C. Hottel","doi":"10.1016/S1062-2896(49)80035-3","DOIUrl":null,"url":null,"abstract":"<div><p>Visible flame lengths and concentration patternshave been obtained in turbulent jets of flame formed by combustible gas issuing from circular nozzles into stagnant air. The nozzle velocities were above those which, in a previous paper, were found necessary to insure that the mixing should be turbulent. As a basis for analysis of the data a simplified treatment is presented for mixing of nozzle and ambient fluids in a vertical jet. The simplifying assumption of constant velocity and composition in a cross-section normal to the axis of flow is combined with a force-momentum balance, continuity, and the perfect gas laws to obtain a relation between mean concentration and jet spread. The relation allows for initial difference in density of nozzle and ambient streams, density variation due to combustion, and buoyancy. The qualitative agreement between the analysis and the experimental data on visible flame lengths and axial concentration patterns indicates plainly that the process of mixing resulting from the momentum and buoyancy of the jet is the controlling factor in determining progress of the combustion. For tree flames in which the effects of buoyancy are small (high nozzle velocity, small diameter) the analysis leads to the following simple relation for the length of free turbulent flame jets:</p><p><span><span><span><math><mrow><mrow><mi>L</mi><mo>/</mo><mi>D</mi></mrow><mo>=</mo><mfrac><mrow><mn>5.3</mn></mrow><mrow><msub><mi>C</mi><mi>τ</mi></msub></mrow></mfrac><msqrt><mrow><mfrac><mrow><msub><mi>T</mi><mi>F</mi></msub></mrow><mrow><msub><mi>α</mi><mi>T</mi></msub><msub><mi>T</mi><mi>N</mi></msub></mrow></mfrac><mrow><mo>[</mo><mrow><msub><mi>C</mi><mi>τ</mi></msub><mo>+</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msub><mi>C</mi><mi>τ</mi></msub></mrow><mo>)</mo></mrow><mfrac><mrow><msub><mi>M</mi><mi>S</mi></msub></mrow><mrow><msub><mi>M</mi><mi>N</mi></msub></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></msqrt></mrow></math></span></span></span></p><p>where <em>L</em>=visible flame length <em>D</em>=nozzle diameter <em>T<sub>F</sub></em>=adiabatic flame temperature, absolute <em>T<sub>N</sub></em>=absolute temperature of nozzle fluid <em>M<sub>S</sub>, M<sub>N</sub></em>=molecular weights of surrounding and nozzle fluids, respectively <em>C<sub>T</sub></em>=mol fraction of nozzle fluid in the unreacted stoichiometric mixture <em>α<sub>T</sub></em>=mols of reactants/mols products, for the stoichiometric mixture. It is to be noted that fuel gas flow rate is no factor, as long as it is great enough to prodace a turbulent jet. Although data for testing this relation covered the small range of port diameter of 0.12 to 0.30 inches, a wide variety of fuels was studied, including propane, acetylene, hydrogen, carbon monoxide, city gas, mixtures of carbon dioxide with city gas, and mixtures of hydrogen with propane. Turbulent flame lengths varying from 40 to 290 nozzle diameters are predicted with average and</p></div>","PeriodicalId":101204,"journal":{"name":"Symposium on Combustion and Flame, and Explosion Phenomena","volume":"3 1","pages":"Pages 266-288"},"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)80035-3","citationCount":"249","resultStr":"{\"title\":\"Mixing and combustion in turbulent gas jets\",\"authors\":\"W.R. Hawthorne , D.S. Weddell , H.C. Hottel\",\"doi\":\"10.1016/S1062-2896(49)80035-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Visible flame lengths and concentration patternshave been obtained in turbulent jets of flame formed by combustible gas issuing from circular nozzles into stagnant air. The nozzle velocities were above those which, in a previous paper, were found necessary to insure that the mixing should be turbulent. As a basis for analysis of the data a simplified treatment is presented for mixing of nozzle and ambient fluids in a vertical jet. The simplifying assumption of constant velocity and composition in a cross-section normal to the axis of flow is combined with a force-momentum balance, continuity, and the perfect gas laws to obtain a relation between mean concentration and jet spread. The relation allows for initial difference in density of nozzle and ambient streams, density variation due to combustion, and buoyancy. The qualitative agreement between the analysis and the experimental data on visible flame lengths and axial concentration patterns indicates plainly that the process of mixing resulting from the momentum and buoyancy of the jet is the controlling factor in determining progress of the combustion. For tree flames in which the effects of buoyancy are small (high nozzle velocity, small diameter) the analysis leads to the following simple relation for the length of free turbulent flame jets:</p><p><span><span><span><math><mrow><mrow><mi>L</mi><mo>/</mo><mi>D</mi></mrow><mo>=</mo><mfrac><mrow><mn>5.3</mn></mrow><mrow><msub><mi>C</mi><mi>τ</mi></msub></mrow></mfrac><msqrt><mrow><mfrac><mrow><msub><mi>T</mi><mi>F</mi></msub></mrow><mrow><msub><mi>α</mi><mi>T</mi></msub><msub><mi>T</mi><mi>N</mi></msub></mrow></mfrac><mrow><mo>[</mo><mrow><msub><mi>C</mi><mi>τ</mi></msub><mo>+</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msub><mi>C</mi><mi>τ</mi></msub></mrow><mo>)</mo></mrow><mfrac><mrow><msub><mi>M</mi><mi>S</mi></msub></mrow><mrow><msub><mi>M</mi><mi>N</mi></msub></mrow></mfrac></mrow><mo>]</mo></mrow></mrow></msqrt></mrow></math></span></span></span></p><p>where <em>L</em>=visible flame length <em>D</em>=nozzle diameter <em>T<sub>F</sub></em>=adiabatic flame temperature, absolute <em>T<sub>N</sub></em>=absolute temperature of nozzle fluid <em>M<sub>S</sub>, M<sub>N</sub></em>=molecular weights of surrounding and nozzle fluids, respectively <em>C<sub>T</sub></em>=mol fraction of nozzle fluid in the unreacted stoichiometric mixture <em>α<sub>T</sub></em>=mols of reactants/mols products, for the stoichiometric mixture. It is to be noted that fuel gas flow rate is no factor, as long as it is great enough to prodace a turbulent jet. Although data for testing this relation covered the small range of port diameter of 0.12 to 0.30 inches, a wide variety of fuels was studied, including propane, acetylene, hydrogen, carbon monoxide, city gas, mixtures of carbon dioxide with city gas, and mixtures of hydrogen with propane. Turbulent flame lengths varying from 40 to 290 nozzle diameters are predicted with average and</p></div>\",\"PeriodicalId\":101204,\"journal\":{\"name\":\"Symposium on Combustion and Flame, and Explosion Phenomena\",\"volume\":\"3 1\",\"pages\":\"Pages 266-288\"},\"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)80035-3\",\"citationCount\":\"249\",\"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/S1062289649800353\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symposium on Combustion and Flame, and Explosion Phenomena","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1062289649800353","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Visible flame lengths and concentration patternshave been obtained in turbulent jets of flame formed by combustible gas issuing from circular nozzles into stagnant air. The nozzle velocities were above those which, in a previous paper, were found necessary to insure that the mixing should be turbulent. As a basis for analysis of the data a simplified treatment is presented for mixing of nozzle and ambient fluids in a vertical jet. The simplifying assumption of constant velocity and composition in a cross-section normal to the axis of flow is combined with a force-momentum balance, continuity, and the perfect gas laws to obtain a relation between mean concentration and jet spread. The relation allows for initial difference in density of nozzle and ambient streams, density variation due to combustion, and buoyancy. The qualitative agreement between the analysis and the experimental data on visible flame lengths and axial concentration patterns indicates plainly that the process of mixing resulting from the momentum and buoyancy of the jet is the controlling factor in determining progress of the combustion. For tree flames in which the effects of buoyancy are small (high nozzle velocity, small diameter) the analysis leads to the following simple relation for the length of free turbulent flame jets:
where L=visible flame length D=nozzle diameter TF=adiabatic flame temperature, absolute TN=absolute temperature of nozzle fluid MS, MN=molecular weights of surrounding and nozzle fluids, respectively CT=mol fraction of nozzle fluid in the unreacted stoichiometric mixture αT=mols of reactants/mols products, for the stoichiometric mixture. It is to be noted that fuel gas flow rate is no factor, as long as it is great enough to prodace a turbulent jet. Although data for testing this relation covered the small range of port diameter of 0.12 to 0.30 inches, a wide variety of fuels was studied, including propane, acetylene, hydrogen, carbon monoxide, city gas, mixtures of carbon dioxide with city gas, and mixtures of hydrogen with propane. Turbulent flame lengths varying from 40 to 290 nozzle diameters are predicted with average and
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