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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenFri, 08 Dec 2023 22:30:59 +0000Quasi-steady gas phase assumption for a burning droplet
https://resolver.caltech.edu/CaltechAUTHORS:20171025-145418174
Authors: Bellan, Josette; Summerfield, Martin
Year: 1976
DOI: 10.2514/3.7172
[No abstract]https://authors.library.caltech.edu/records/28exa-zc769Model for Studying Unsteady Droplet Combustion
https://resolver.caltech.edu/CaltechAUTHORS:20171025-134801561
Authors: Bellan, Josette; Summerfield, Martin
Year: 1977
DOI: 10.2514/3.60621
The concept of a reduced boundary condition at the surface of a droplet is used to develop a theory of unsteady droplet burning. This theory utilizes a quasi-steady gas-phase assumption, which has been shown to be realistic for a wide range of droplet sizes at low pressures. The most significant consequence of the theory is that the problem of unsteady droplet burning is reduced to the solving of a single diffusion-type nonlinear partial differential equation having one of its boundary conditions determined by an algebraic function of the quasi-steady gas-phase variables. This reduced boundary condition incorporates the entire dependence of the solution on fuel characteristics, chemical kinetics, and thermal properties of the gases. An experiment is proposed for determining this boundary condition so that the nonsteady droplet combustion problem can be solved for a realistic situation. By using additional assumptions, a numerical estimate of the boundary condition has been made.https://authors.library.caltech.edu/records/8pa46-q3b75Theoretical examination of assumptions commonly used for the gas phase surrounding a burning droplet
https://resolver.caltech.edu/CaltechAUTHORS:20171023-143538311
Authors: Bellan, Josette; Summerfield, Martin
Year: 1978
DOI: 10.1016/0010-2180(78)90054-8
A finite reaction-rate model is compared to three commonly used flame-sheet models. The latter differ in their treatment of the evaporation from the surface and the value used for the molecular weights in the evaporation law. All four models are applicable to both steady and unsteady burning of droplets. Further, they account for variations of droplet radii and allow for differences in ambient conditions. Numerical results (obtained forn-decane) show that if the radius of the droplet is 10^(−2) cm the thin-flame approximation is excellent at 10 atm if the droplet surface temperature is not close to either the boiling point or the ambient temperature. However, this approximation is unacceptable at 1 atm. Among the three flame-sheet models, the one using non equilibrium evaporation at the surface and individual molecular weights best approximates the finite reaction-rate theory. However, this agreement breaks down for smaller droplets with lower surface temperatures, or for air with a larger oxygen content. These conclusions are independent of the chosen kinetics. The Clausius-Clapeyron approximation is shown to be excellent away from the boiling point for R = 10^(−2) cm. However, as the droplet surface temperature approaches the boiling point, or the droplet radius decreases, this assumption leads to considerable errors in the evaporation rate and also distortion of the thermal layer. Even larger errors are obtained when an average molecular weight is used. Here, large underestimates of the evaporation rate and great distortions of the thermal layer of the droplet are obtained. In spite of these errors, all models agree well at wet-bulb conditions.https://authors.library.caltech.edu/records/gyf7g-fcx53A preliminary theoretical study of droplet extinction by depressurization
https://resolver.caltech.edu/CaltechAUTHORS:20171019-134640679
Authors: Bellan, Josette; Summerfield, Martin
Year: 1978
DOI: 10.1016/0010-2180(78)90100-1
Depressurization-induced extinction of droplets is demonstrated using an unsteady liquid-phase theory and a previously presented quasisteady gas-phase model. Numerical results show that depressurization of the gas phase causes extinction of both regressing and nonregressing droplets. For nonregressing droplets it is found that at fixed droplet size the extinction pressure is a decreasing function of the initial depressurization rate; thus results are explained in terms of the time lag needed by a droplet to respond to a change in pressure. Regressing droplets, which extinguish more rapidly than constant-size ones, show the same type of behavior. Extinction boundaries, evaluated as functions of the initial temperature profile, show that whereas for constant-size droplets the extinction pressure is a strong decreasing function of the temperature, for regressing droplets this dependence is very weak and an asymptote is reached as the temperature increases. Results obtained by varying the initial pressure show that the extinction pressure is an increasing function of the initial pressure for regressing droplets. For constant-size droplets this function is nonmonotonic and reaches a maximum at the initial pressure for which the initial temperature profile is the wet-bulb state. The thermal conductivity of the liquid phase has almost no influence on the extinction boundary.https://authors.library.caltech.edu/records/5agj3-ywp32The Physics of Rockets
https://resolver.caltech.edu/CaltechAUTHORS:20151125-103838789
Authors: Seifert, Howard S.; Mills, Mark M.; Summerfield, Martin
Year: 2015
Although the Chinese are credited with the use of gunpowder rockets as early as several centuries B.C., and Hero of Alexandria invented a steam jet propulsion device about 100 B.C., most of the serious effort to develop rockets has occurred in the last three decades. Goddard in America made a complete study of rocket performance in 1914. The German all-out rocket program commenced in 1935 culminating in the V-2, which was first fired in September of 1944. Since 1938, intensive rocket research has been carried out by a number of American agencies, including a basic theoretical contribution by Malina in 1940.
The present paper will concern itself only with that type of jet propulsion device designated as a "pure" rocket, i.e., a thrust producer which does not make use of the surrounding atmosphere. This restriction excludes propulsive duct devices such as the "turbojet" engine used in jet propelled airplanes of the P-80 type. No attempt will be made to discuss the aerodynamics of bodies moving at supersonic speeds, the electronic problems of rocket missile guidance and control, the measurement of physical quantities in the upper atmosphere, or the properties of weapon rockets. Even omitting these interesting fields, the science of rocketry embraces many phases of physics and chemistry, as will appear in later sections.https://authors.library.caltech.edu/records/j0gm6-emy63