ON FLAME PROPAGATION IN EXPLOSIVE MIXTURES OF GASES: II. ON THE DECOMPOSITION FLAME OF OZONE

1956 ◽  
Vol 34 (3) ◽  
pp. 324-330 ◽  
Author(s):  
Robert Sandri
Keyword(s):  
Diffusion Coefficient ◽  
General Theory ◽  
Numerical Integration ◽  
Flame Propagation ◽  
Approximation Method ◽  
Flame Velocity ◽  
Good Agreement

The general theory developed in an earlier paper of the author is applied to the ozone explosion. Values of the linear flame velocity are computed under the assumption of constant enthalpy and, without this assumption, for different values of the reduced diffusion coefficient. The results do not differ very much and are found to be in very good agreement with experiments. They are further compared to the results which were obtained by Hirschfelder et al. by exact numerical integration and by Kármán and Penner by an approximation method and are found to be between the values obtained by these authors.

ON FLAME PROPAGATION IN EXPLOSIVE MIXTURES OF GASES: III. FLAME PROPAGATION IN MIXTURES OF METHANE AND NITROGEN AIR, HELIUM AIR, AND ARGON AIR

1956 ◽  
Vol 34 (3) ◽  
pp. 331-337 ◽  
Author(s):  
Robert Sandri
Keyword(s):  
Temperature Distribution ◽  
General Theory ◽  
Oxygen Atom ◽  
Flame Propagation ◽  
Flame Velocity ◽  
Flame Zone ◽  
End Products ◽  
Atom Chain ◽  
Experimental Values ◽  
Good Agreement

The general theory developed in an earlier paper of the author is applied to the combustion of mixtures of methane and nitrogen air, helium air, and argon air where dissociation of the end products is negligible. The oxygen atom chain is assumed to be rate-determining. Absolute values of the flame velocity are computed for mixtures containing 8% of methane and for the stoichiometric mixtures. The results are found to be in very good agreement with experimental values. Dependence on pressure is likewise found to be in very good agreement with experiments. The temperature distribution in the flame zone is also computed.

scholarly journals Relationship between the Transport Coefficients of Polar Substances and Entropy

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 13
Author(s):  
Ivan Anashkin ◽  
Sergey Dyakonov ◽  
German Dyakonov
Keyword(s):  
Experimental Data ◽  
Thermal Conductivity ◽  
Diffusion Coefficient ◽  
High Pressures ◽  
Thermal Conductivity Coefficient ◽  
Good Description ◽  
Transport Coefficients ◽  
Viscosity Coefficient ◽  
Wide Region ◽  
Good Agreement

An expression is proposed that relates the transport properties of polar substances (diffusion coefficient, viscosity coefficient, and thermal conductivity coefficient) with entropy. To calculate the entropy, an equation of state with a good description of the properties in a wide region of the state is used. Comparison of calculations based on the proposed expressions with experimental data showed good agreement. A deviation exceeding 20% is observed only in the region near the critical point as well as at high pressures.

scholarly journals Construction et Precision de Nouvelles Theories Planetaires

1979 ◽  
Vol 81 ◽  
pp. 61-67 ◽  
Author(s):  
P. Bretagnon ◽  
J. Chapront
Keyword(s):  
Solar System ◽  
General Theory ◽  
Numerical Integration ◽  
Classical Type ◽  
Minor Planets ◽  
Secular Variations ◽  
Planetary Theories

At the Bureau of Longitudes the construction of planetary theories have been developed in three directions: A general theory of the motion of the four largest planets in the solar system is in the course of development at the Faculty of Sciences at Lille by L. Duriez (1977) following the methods of V. A. Brumberg and J. Chapront (1973). Theories of the classical type with secular variations of the motions of all of the planets from Mercury to Neptune are being completed at the Bureau of Longitudes. They are constructed by P. Bretagnon and J. L. Simon (1975, 1978). The numerical complement to all of these studies, numerical integration, a representation of the solution by Tchebychev series, are being carried out by P. Rocher as concerns the motions of minor planets, and by J. Piranx for the action of Pluto on Uranus and Neptune in the framework of theories with secular variations.

Shape of a Wire in a Centrifugal Field—Application to Quasi-Circular Bare Filament Flywheels

1983 ◽  
Vol 105 (2) ◽  
pp. 221-226 ◽  
Author(s):  
G. Genta
Keyword(s):  
Numerical Calculation ◽  
Stress Distribution ◽  
Numerical Integration ◽  
Equilibrium Equation ◽  
Series Solution ◽  
Field Application ◽  
Centrifugal Field ◽  
Low Speed ◽  
Theoretical Results ◽  
Good Agreement

In order to calculate the stress distribution in bare filament rotors it is necessary to evaluate with good approximation the shape taken by the wires in the centrifugal field (sometimes referred to as “polar catenary”). This problem is usually solved via a numerical integration of the equilibrium equation of the wire. In this paper a series solution of the same equilibrium equation is obtained. The calculation of the stress distribution in the rotor, which is an interative one and requires the evaluation of the shape of each wire several times, becomes faster and can be performed also in those conditions in which the numerical calculation failed (i.e., at low speed, when the “subcircularity” of the wires is too great to be taken into account in that way). Photographic and photoelastic tests are in good agreement with theoretical results.

Relativistic Hartree–Fock–Roothaan wavefunctions for atoms

1985 ◽  
Vol 63 (7) ◽  
pp. 1550-1552 ◽  
Author(s):  
Takashi Kagawa ◽  
Gulzari Malli
Keyword(s):  
Numerical Integration ◽  
Integration Method ◽  
Basis Functions ◽  
Numerical Integration Method ◽  
Hartree Fock ◽  
Orbital Energies ◽  
Good Agreement

Relativistic Hartree–Fock–Roothaan (RHFR) wavefunctions have been calculated for a large number of atoms up to radon (Z = 86) under the point nucleus approximation using STO's as basis functions. The calculated total as well as orbital energies are in very good agreement with the corresponding results obtained by the numerical integration method.

ON FLAME PROPAGATION IN EXPLOSIVE MIXTURES OF GASES: I. GENERAL THEORY

1956 ◽  
Vol 34 (3) ◽  
pp. 313-323 ◽  
Author(s):  
Robert Sandri
Keyword(s):  
Temperature Distribution ◽  
Flame Propagation ◽  
Energy Equation ◽  
Approximation Formula ◽  
Flame Velocity ◽  
System Of Differential Equations ◽  
Flame Zone ◽  
Method Of Solution ◽  
Set Up ◽  
Numerical Method Of Solution

The system of differential equations of flame propagation is set up and discussed. It is shown that, without any major influences being neglected, the energy equation can be reduced to the form[Formula: see text]with the boundary conditions[Formula: see text]Some qualities of the solutions of this equation are discussed and a simple numerical method of solution is described. The flame velocity V0 is found as an eigenvalue of the energy equation. The temperature distribution in the flame zone can then be found by an ordinary quadrature. Further, an approximation formula for finding V0 directly is derived[Formula: see text]where F(η) is proportional to [Formula: see text]and has a maximum for η = ηm.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

Toward a General Theory of Cutting: A Relationship Between the Incident Power Density and the Cut Speed

1975 ◽  
Vol 97 (1) ◽  
pp. 116-122 ◽  
Author(s):  
K. A. Bunting ◽  
G. Cornfield
Keyword(s):  
Thermal Properties ◽  
General Theory ◽  
Power Density ◽  
Experimental Results ◽  
Energy Utilization ◽  
Incident Power ◽  
Incident Power Density ◽  
Good Agreement

A relationship between the power density incident on a material and the resulting cut speed is developed in terms of the thermal properties of the material. The expression obtained is general and is shown to be in good agreement with experimental results. It is shown that the efficiency of energy utilization is influenced by the incident power density and the jet diameter. The theory indicates that to maximize cut speed and energy utilization the jet diameter should be as small as possible consistent with an attainable power density.

The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities

1986 ◽  
Vol 170 ◽  
pp. 199-232 ◽  
Author(s):  
P. W. Carpenter ◽  
A. D. Garrad
Keyword(s):  
Viscous Fluid ◽  
Numerical Integration ◽  
Critical Velocity ◽  
Finite Length ◽  
Irreversible Processes ◽  
Infinite Length ◽  
Material Damping ◽  
Compliant Surfaces ◽  
Sommerfeld Equation ◽  
Good Agreement

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

scholarly journals The Modeling of Nitrogen Mass Transport in CoCr Alloys

2016 ◽  
Vol 36 (331) ◽  
pp. 19-26
Author(s):  
Akvilė Petraitienė
Keyword(s):  
Diffusion Coefficient ◽  
Plasma Nitriding ◽  
Nitrogen Concentration ◽  
Nitrogen Adsorption ◽  
Nitrogen Diffusion ◽  
Depth Profiles ◽  
Swelling Rate ◽  
Cocr Alloy ◽  
Kinetics Of ◽  
Good Agreement

Abstract The kinetics of plasma nitriding of CoCr alloy below temperatures of nitrides formation and mechanisms of nitrogen penetration are analyzed by proposed kinetic modeling in this article. Proposed nitrogen diffusion model is based on the trapping – detrapping (TD) model and developed taking into account the effect of the concentration dependent diffusivity of nitrogen, nitrogen adsorption on the surface of alloy and surface swelling process. The model indicates the influence of chromium atoms to nitrogen atoms diffusivity. The model consists of time and depth dependent diffusion, which is described by a partial differential equation, and it is solved by using Crank – Nicolson finite difference method. By fitting of experimental nitrogen depth profiles, it is shown that nitrogen diffusion coefficient varies with nitrogen concentration according to Einstein-Smoluchowski relation. Nitrogen depth profiles in plasma nitrided medical grade CoCr alloy (ISO 5831 – 12) at T = 400 °C for 1, 4 and 20 hours calculated on the basis of this model are in good agreement with experimental nitrogen profiles. Furthermore, the swelling process is showed and analyzed, derived the dependency of swelling rate on nitriding duration – the swelling rate is inversely proportional to the square root of nitriding duration. The obtained diffusion coefficient value and the swelling process rates satisfy the experimental data form Ref. The derived model explains physical processes during plasma nitriding and allows obtaining nitrogen depth profiles for any requisite nitriding duration.

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