Conservation equation summary

For the purposes of looking at them together and drawing some observations, we collect the conservation equations. 

Written in cylindrical coordinates and specialized for a perfect-gas mixture the conservation laws are  

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The crystalline inorganic monopropellants decompose directly from the solid to the vapor phase and are approximately described by the above mentioned theoretical work, in spite of the fact that the gas phase processes are simplified. However, the double-base propellants and other organic materials liquefy before vaporizing. In their combustion, so-called foam and fizz zones occur before the vapor phase processes. Much work has been done attempting to apply the conservation equations to the series of processes. This work forms the basis for the summary by Geckler (G3). It is the viewpoint of this author that too many parameters are determined empirically in this application of the theory, so that useful extrapolations are not possible. One must admire the manipulative skill of the early workers in this field and also their determination to formulate a complete theory. When and if the rate parameters become available, a useful theory will be developed with the aid of this early work. 

All fluid flow problems involve solution of the equations that express conservation of mass, momentum, and energy. In what follows we give a brief summary of the governing equations and simplification of them. Details may be found in Ref 27. The conservation equations take the form... 

Chapter 2 contains a summary of the basic concepts of kinetic theory of dilute and dense gases. This theory serves as basis for the development of the continuum scale conservation equations by averaging the governing equations determining the discrete molecular scale phenomena. This method is an alternative to, or rather both a verification and an extension of, the continuum approach described in Chap. 1. These kinetic theory concepts also determine the basis for a group of models used describing granular flows, further outlined in Chap. 4. 

In summary, we have so far seen that there are two types of boundary conditions that apply at any solid surface or fluid interface the kinematic condition, (2-117), deriving from mass conservation and the dynamic boundary condition, normally in the form of (2-122), but sometimes also in the form of a Navier-slip condition, (2-124) or (2-125). When the boundary surface is a solid wall, then u is known and the conditions (2-117) and (2-122) provide a sufficient number of boundary conditions, along with conditions at other boundaries, to completely determine a solution to the equations of motion and continuity when the fluid can be treated as Newtonian. 

The experimental techniques and theoretical interpretations of PES data have been discussed in detail in numerous articles and books. Some detailed reviews were published recently in this series1. Other reviews are too numerous to list so we shall mention only some of the more recent ones2-4. Our aim is not to give a detailed coverage of PES, but rather to provide a summary of PES methods which were used in studies of the electronic structure of gold and silver compounds. What all PES methods have in common is the basic phenomenon of photoionization, in which a photon of known energy hv becomes absorbed by the material and induces subsequent ejection of an electron (photoionization). The law of conservation of energy applied to the process can be expressed by equations 1 and 2,... 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

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