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I. Relaxation Time of One-Dimensional, Laminar Deflagration for First Order Reactions. II. Reflection and Transmission of Electromagnetic Waves at Electron Density Gradients


Albini, Frank Addison (1962) I. Relaxation Time of One-Dimensional, Laminar Deflagration for First Order Reactions. II. Reflection and Transmission of Electromagnetic Waves at Electron Density Gradients. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TYH3-ZQ11.


Part I

The one-dimensional, time-dependent equations describing laminar deflagration are solved by an integral method, under the assumption of a physical model for the flame structure and behavior, with restrictions on the type of deviation from steady-state behavior. By virtue of application of a hot-boundary approximation of the von Kármán type, certain sensitive integrals are expressed in a form independent of the temperature profile assumed. Two cases are considered: the "thermal theory" neglecting diffusion, and the case of unity Lewis number (temperature/concentration similarity). Only first order reactions are considered. Arguments supporting the generality of the results are included, along with a discussion of accuracy, and some comparison with experimental work. Graphical display of the results anticipates the utility of the theory for correlating and cross-checking experimental data.

It is concluded that the relaxation time is closely related to the time required for the gas undergoing rapid chemical reaction to pass through the flame.

Part II

The interaction of an electromagnetic wave with a mildly ionized gas is described by an ensemble average treatment of electron motion, and under this description, electromagnetic wave propagation parameters derived. Motivated by the fact that mildly ionized gases in general exhibit inhomogeneous boundary regions, exemplary transition zones are described in terms of varying electron density but constant collision frequency, in order to simplify the solution of wave problems. The half-space reflection problem with a linear transition zone is solved exactly and under two approximations. It is discovered that the reflection and transmission coefficients are strong functions of zone thickness for thin zones. A piecewise-linear transition zone solution exemplifies the procedure for constructing an approximate solution to an arbitrary profile and illustrates the relative insensitivity of reflection and transmission coefficients to detailed zone structure. The "slab" reflection problem with symmetrical, linear transition zones is solved exactly, and it is discovered that the basic periodicity of reflection and transmission coefficients with slab thickness is unchanged, although shifted to higher values of slab thickness/wavelength. The text is supported by fairly extensive graphical presentation of results.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mechanical Engineering and Philosophy)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Minor Option:Philosophy
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marble, Frank E.
Thesis Committee:
  • Marble, Frank E. (chair)
  • De Prima, Charles R.
  • Jahn, Robert G.
  • Papas, Charles Herach
  • Rannie, W. Duncan
Defense Date:1 January 1962
Funding AgencyGrant Number
Hughes Aircraft CompanyUNSPECIFIED
Daniel and Florence Guggenheim FoundationUNSPECIFIED
Record Number:CaltechTHESIS:07262011-115318209
Persistent URL:
Related URLs:
URLURL TypeDescription ItemArticle in CaltechAUTHORS
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6547
Deposited By: Benjamin Perez
Deposited On:26 Jul 2011 20:23
Last Modified:22 Nov 2023 21:18

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