Abstract : The problem of calculating the motion of an incompressible inviscid fluid with a free surface is formulated as a variational principle. The result is in the form of an expansion in powers of the wave height. The theory is specialized to the linear case where it is demonstrated that the variational principle is of the free boundary condition type. A procedure for calculating the natural frequencies and modes of the shallow and the deep tank by applying the Rayleigh-Ritz procedure to solution of the variational formulation is discussed. An approximate procedure for calculating the sloshing modes and frequencies of a tank of intermediate depth in terms of the solutions for shallow and deep tanks is suggested. The results of numerical calculations for conical tank are presented in the form of mode shape diagrams and frequency charts. (Author)
{"title":"Variational Solution of Fuel Sloshing Modes","authors":"H. R. Lawrence, C. J. Wang, R. Reddy","doi":"10.2514/8.7443","DOIUrl":"https://doi.org/10.2514/8.7443","url":null,"abstract":"Abstract : The problem of calculating the motion of an incompressible inviscid fluid with a free surface is formulated as a variational principle. The result is in the form of an expansion in powers of the wave height. The theory is specialized to the linear case where it is demonstrated that the variational principle is of the free boundary condition type. A procedure for calculating the natural frequencies and modes of the shallow and the deep tank by applying the Rayleigh-Ritz procedure to solution of the variational formulation is discussed. An approximate procedure for calculating the sloshing modes and frequencies of a tank of intermediate depth in terms of the solutions for shallow and deep tanks is suggested. The results of numerical calculations for conical tank are presented in the form of mode shape diagrams and frequency charts. (Author)","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125709809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Recent Advances in Transient Surface Temperature Thermometry","authors":"J. G. Hall, A. Hertzberg","doi":"10.2514/8.7440","DOIUrl":"https://doi.org/10.2514/8.7440","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134560389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stagnation laminar heat transfer at hypersonic speeds depends on the rate of recombination of the dissociated air behind the detached shock wave. This paper is concerned with the case of a large recombination t ime compared to the t ime of diffusion across the boundary layer. The conditions of existence of such a "frozen flow" and i ts coupling with the dissociation lag behind the shock are discussed. In order to account for finite catalytic recombination rates at the wall, a nonsimilar boundary condition is introduced which can be reduced to similarity for stagnation flow only. In this latter case, Lees' ( l ) 3 and Fay and Ridell's (2) heat transfer solutions are shown to correspond to the l imit ing case of an infinitely fast catalyst. The validity of their solutions is extended to the general case of a wall of finite catalytic efficiency, by introducing a correction factor (p. This factor is a s imple function of the flight condit ion, nose geometry and the wall catalytic recombinat ion rate constant . For a given nose material , the percentage of the heat transfer by catalysis is found to in crease wi th the velocity, the nose diameter and the wall temperature and to decrease with alt itude. Finally, the experimental values obtained for the catalytic recombination rates of oxygen and nitrogen atoms on various surfaces i l lustrate numerically the importance of the nature of the wall on the catalytic heat transfer to a missi le nose . In particular, the superiority of pyrex over metal l ic surfaces stresses the need for more experimental values for glassy and ceramic coatings.
{"title":"On Catalytic Recombination Rates in Hypersonic Stagnation Heat Transfer","authors":"R. Goulard","doi":"10.2514/8.7444","DOIUrl":"https://doi.org/10.2514/8.7444","url":null,"abstract":"Stagnation laminar heat transfer at hypersonic speeds depends on the rate of recombination of the dissociated air behind the detached shock wave. This paper is concerned with the case of a large recombination t ime compared to the t ime of diffusion across the boundary layer. The conditions of existence of such a \"frozen flow\" and i ts coupling with the dissociation lag behind the shock are discussed. In order to account for finite catalytic recombination rates at the wall, a nonsimilar boundary condition is introduced which can be reduced to similarity for stagnation flow only. In this latter case, Lees' ( l ) 3 and Fay and Ridell's (2) heat transfer solutions are shown to correspond to the l imit ing case of an infinitely fast catalyst. The validity of their solutions is extended to the general case of a wall of finite catalytic efficiency, by introducing a correction factor (p. This factor is a s imple function of the flight condit ion, nose geometry and the wall catalytic recombinat ion rate constant . For a given nose material , the percentage of the heat transfer by catalysis is found to in crease wi th the velocity, the nose diameter and the wall temperature and to decrease with alt itude. Finally, the experimental values obtained for the catalytic recombination rates of oxygen and nitrogen atoms on various surfaces i l lustrate numerically the importance of the nature of the wall on the catalytic heat transfer to a missi le nose . In particular, the superiority of pyrex over metal l ic surfaces stresses the need for more experimental values for glassy and ceramic coatings.","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124336766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Project Snooper, A Program for Unmanned Interplanetary Reconnaissance","authors":"M. Willinski, E. C. Orr","doi":"10.2514/8.7442","DOIUrl":"https://doi.org/10.2514/8.7442","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131463218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Heat Transfer in Boundary Layers With Chemical Reactions Due to Mass Addition","authors":"R. Bromberg","doi":"10.2514/8.7425","DOIUrl":"https://doi.org/10.2514/8.7425","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"428 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116538924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Samuel Herrick is Professor of Astronomy at the University of California, Los Angeles. There he instituted courses and research in celestial mechanics and observation theory tha t are now a part of the astrodynamics program of the University. This program can claim the first university course in astronautics. Dr. Herrick's "Astrodynamics and Rocket Navigation" was instituted in 1946, and now the first Ph.D. in the field is his co-author, Dr. Baker. Prof. Herrick has held two Guggenheim Fellowships for his space navigation studies, and is currently consultant for such corporations as Aeronutronic Systems, Rand, Martin-Denver, Librascope, General Precision Equipment, General Electric, Systems Corporation of America and Republic Aviation. He is chairman of the Executive and Space Navigation Committees of the Inst i tute of Navigation, and is an honorary member of tha t society and its British counterpart. His B. A. is from Williams College and his Ph.D. from the University of California, Berkeley. Robert M. L. Baker Jr., presently a Staff Member, Aeronutronic Systems, Inc. and an instructor of courses in Astrodynamics at the University of California, Los Angeles, obtained a B.A. and M.A. in Physics, and a Ph.D. in Engineering (and Astronomy). His specialties are in the fields of celestial mechanics and rarefield gas-dynamics. Dr. Baker is currently engaged in studies concerning spacevehicle Orbits, meteoritics, low density drag and sputtering with particular emphasis on high-speed re-entry from interplanetary orbits.
塞缪尔·赫里克是加州大学洛杉矶分校的天文学教授。在那里，他开设了天体力学和观测理论的课程和研究，这些课程和研究现在是该大学天体动力学项目的一部分。这个专业可以称得上是航天学的第一个大学课程。赫里克博士的《天体动力学和火箭导航》创立于1946年，现在该领域的第一位博士是他的合著者贝克博士。Herrick教授曾两次因其空间导航研究获得古根海姆奖学金，目前担任航空电子系统公司、兰德公司、马丁-丹佛公司、Librascope公司、通用精密设备公司、通用电气公司、美国系统公司和共和航空公司等公司的顾问。他是英国导航学会执行委员会和空间导航委员会主席，也是该学会及其英国同行的荣誉会员。他在威廉姆斯学院获得学士学位，在加州大学伯克利分校获得博士学位。Robert M. L. Baker Jr.，现任Aeronutronic Systems, Inc.职员，加州大学洛杉矶分校天体动力学课程讲师，获得物理学学士和硕士学位，工程学(和天文学)博士学位。他的专长是天体力学和磁场气体动力学。Baker博士目前从事有关航天器轨道、陨石、低密度阻力和溅射的研究，特别强调从行星际轨道高速再入。
{"title":"Recent Advances in Astrodynamics","authors":"S. Herrick","doi":"10.2514/8.7418","DOIUrl":"https://doi.org/10.2514/8.7418","url":null,"abstract":"Samuel Herrick is Professor of Astronomy at the University of California, Los Angeles. There he instituted courses and research in celestial mechanics and observation theory tha t are now a part of the astrodynamics program of the University. This program can claim the first university course in astronautics. Dr. Herrick's \"Astrodynamics and Rocket Navigation\" was instituted in 1946, and now the first Ph.D. in the field is his co-author, Dr. Baker. Prof. Herrick has held two Guggenheim Fellowships for his space navigation studies, and is currently consultant for such corporations as Aeronutronic Systems, Rand, Martin-Denver, Librascope, General Precision Equipment, General Electric, Systems Corporation of America and Republic Aviation. He is chairman of the Executive and Space Navigation Committees of the Inst i tute of Navigation, and is an honorary member of tha t society and its British counterpart. His B. A. is from Williams College and his Ph.D. from the University of California, Berkeley. Robert M. L. Baker Jr., presently a Staff Member, Aeronutronic Systems, Inc. and an instructor of courses in Astrodynamics at the University of California, Los Angeles, obtained a B.A. and M.A. in Physics, and a Ph.D. in Engineering (and Astronomy). His specialties are in the fields of celestial mechanics and rarefield gas-dynamics. Dr. Baker is currently engaged in studies concerning spacevehicle Orbits, meteoritics, low density drag and sputtering with particular emphasis on high-speed re-entry from interplanetary orbits.","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125990816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Brachistochronic Thrust Program for a Rocket Powered Missile Traveling in an Isothermal Medium","authors":"A. Miele","doi":"10.2514/8.7427","DOIUrl":"https://doi.org/10.2514/8.7427","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123543818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boundary Layers With Chemical Reactions Due to Mass Addition","authors":"C. B. Cohen","doi":"10.2514/8.7422","DOIUrl":"https://doi.org/10.2514/8.7422","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116608203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Experimental Study of High-Frequency Combustion Pressure Oscillations","authors":"M. J. Zucrow, J. Osborn","doi":"10.2514/8.7420","DOIUrl":"https://doi.org/10.2514/8.7420","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"418 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126701781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Flame Stabilization in the Boundary Layer of Heated Plates","authors":"R. Ziemer","doi":"10.2514/8.7400","DOIUrl":"https://doi.org/10.2514/8.7400","url":null,"abstract":"","PeriodicalId":304231,"journal":{"name":"Journal of Jet Propulsion","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1958-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129684579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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