The Zeldovich spontaneous reaction wave propagation concept in the fast/modest heating limits

2016 ◽  
Vol 791 ◽  
pp. 439-463 ◽  
Author(s):  
D. R. Kassoy
Keyword(s):  
Induction Period ◽  
Heating Rate ◽  
Time Scale ◽  
Hot Spot ◽  
High Activation ◽  
Post Induction ◽  
Spontaneous Reaction ◽  
Reaction Wave ◽  
Mechanical Disturbances ◽  
High Temperature High Pressure

Quantitative mathematical models describe planar, spontaneous, reaction wave propagation (Zeldovich, Combust. Flame, vol. 39, 1980, pp. 211–214) in a finite hot spot volume of reactive gas. The results describe the complete thermomechanical response of the gas to a one-step, high-activation-energy exothermic reaction initiated by a tiny initial temperature non-uniformity in a gas at rest with uniform pressure. Initially, the complete conservation equations, including all transport terms, are non-dimensionalized to identify parameters that quantify the impact of viscosity, conduction and diffusion. The results demonstrate unequivocally that transport terms are tiny relative to all other terms in the equations, given the relevant time and length scales. The asymptotic analyses, based on the reactive Euler equations, describe both induction and post-induction period models for a fast heat release rate (induction time scale short compared to the acoustic time of the spot), as well as a modest heat release rate (induction time scale equivalent to the acoustic time). Analytical results are obtained for the fast heating rate problem and emphasize the physics of near constant-volume heating during the induction period. Weak hot spot expansion is the source of fluid expelled from the original finite volume and is a ‘piston-effect’ source of acoustic mechanical disturbances beyond the spot. The post-induction period is characterized by the explosive appearance of an ephemeral, spatially uniform high-temperature, high-pressure spot embedded in a cold, low-pressure environment. In analogy with a shock tube the subsequent expansion process occurs on the acoustic time scale of the spot and will be the source of shocks propagating beyond the spot. The modest heating rate induction period is characterized by weakly compressible phenomena that can be described by a novel system of linear wave equations for the temperature, pressure and induced velocity perturbations driven by nonlinear chemical heating, which provides physical insights difficult to obtain from the more familiar ‘Clarke equation’. When the heating rate is modest, reaction terms in the post-induction period Euler equations exhibit a form of singular behaviour in the high-activation-energy limit, implying the need to use a nonlinear exponential scaling for time and space, developed originally to describe spatially uniform thermal explosions (Kassoy, Q. J. Mech. Appl. Maths, vol. 30, 1977, pp. 71–89). Here again the result will be the explosive appearance of an ephemeral spatially uniform high-temperature, high-pressure hot spot. These results demonstrate that an initially weak temperature non-uniformity in a finite hot spot can be the source of acoustic and shock wave mechanical disturbances in the gas beyond the spot that may be related to rocket engine instability and engine knock.

scholarly journals Forcing Spring Growth of Rhododendron ‘Nova Zembla’ Rooted Cuttings

1983 ◽  
Vol 1 (1) ◽  
pp. 3-4
Author(s):  
John R. Havis
Keyword(s):  
Induction Period ◽  
Night Temperature ◽  
Rooted Cuttings ◽  
Post Induction ◽  
C 50 ◽  
Growth Induction ◽  
C 63

Growth induction treatments of 17°C (63°F) minimum night temperature (MNT) for 14 days beginning on February 15 or March 1 subsequently gave equal growth of Rhododendron ‘Nova Zembla’ rooted cuttings at post-induction MNT of 5°C (41°F). Neither 14 days of 10°C (50°F) MNT before or after the induction period nor 3-hr light breaks (2300 to 0200 hr) during the induction period further benefited growth. One mature flush of growth was produced by the end of May on plants kept at MNT of 5°C following induction, whereas 2 flushes were produced on plants maintained at continuous 17°C MNT from February 15. Both groups matured a third flush by the end of September.

A Control System for Microwave Processing of Materials

1999 ◽  
Vol 122 (1) ◽  
pp. 253-261 ◽  
Author(s):  
P. Groombridge ◽  
A. Oloyede ◽  
E. Siores
Keyword(s):  
Control System ◽  
Heating Rate ◽  
Hot Spot ◽  
Maximum Output Power ◽  
Microwave Processing ◽  
Maximum Output ◽  
Automated Control ◽  
Epoxy Adhesives ◽  
Automated Control System ◽  
Engineering Plastics

This paper discusses a control system for microwave processing of materials. Microwave joining of ceramics and drying of timber are currently industry practices while microwave joining of engineering plastics and curing of epoxy adhesives are still being researched. In this study, all materials are processed in rectangular sections of waveguide fed by a magnetron with a maximum output power of 2 kW operating at 2.45 GHz. The most significant problems encountered when processing these materials are: (i) maintaining proper tuning to ensure maximum power transfer, (ii) thermal runaway, where the heating rate proceeds so rapidly that the material burns within a few seconds, and (iii) hot spot development, where localized regions heat up at a faster rate than adjacent regions. A computerized automated control system has been developed to alleviate these processing problems and has been successfully employed in joining a range of ceramics and engineering plastics, curing epoxy adhesives and drying wood. Results of preliminary tests obtained using the developed prototype are presented. [S1087-1357(00)71701-1]

Granite Recrystallization - The Key to an Alternative Strategy for HLW Disposal?

2003 ◽  
Vol 807 ◽  
Author(s):  
Fergus G. F. Gibb
Keyword(s):  
High Temperature ◽  
Time Scale ◽  
Spent Nuclear Fuel ◽  
Environmental Safety ◽  
Economic Benefits ◽  
Alternative Strategy ◽  
High Level Waste ◽  
Viable Option ◽  
High Level ◽  
High Temperature High Pressure

ABSTRACTAn alternative strategy is proposed for the disposal of spent nuclear fuel (SNF) and other forms of high-level waste (HLW) whereby the integrity of a mined and engineered repository for the bulk of the waste need be preserved for only a few thousand years. This is achieved by separating the particularly problematic components, notably heat generating radionuclides (HGRs) and very long lived radionuclides (VLLRs) from the waste prior to disposal. Such a solution requires a satisfactory means of disposing of the relatively minor amounts of HGRs and VLLRs removed from the waste. This could be by high-temperature very deep disposal (HTVDD) in boreholes in the continental crust [1,2]. However, the viability of HTVDD, and hence the key to the entire strategy, depends on whether sufficient melting of granite host rock can occur at suitable temperatures and whether the melt can be completely recrystallized. The high-temperature, high-pressure experiments reported here demonstrate that granite can be partially melted and completely recrystallized on a time scale of years, as opposed to millennia as widely believed. Furthermore, both can be achieved at temperatures and on a time scale appropriate to the disposal of packages of heat generating HLW. It is therefore concluded that the proposed strategy, which offers, environmental, safety and economic benefits, could be a viable option for a substantial proportion of HLWs.

scholarly journals Silver Precipitation Using Sodium Dithionite in Cyanide Media

2017 ◽  
Vol 56 (2) ◽  
Author(s):  
Isauro Rivera ◽  
Guillermo Juárez ◽  
Francisco Patiño ◽  
Iván A. Reyes ◽  
Antonio Roca ◽  
...  
Keyword(s):  
Activation Energy ◽  
Induction Period ◽  
Kinetic Parameters ◽  
Room Temperature ◽  
Chemical Precipitation ◽  
Sodium Dithionite ◽  
High Activation ◽  
Residual Content ◽  
Silver Precipitation ◽  
Reaction Orders

The nature of the reaction and the main parameters affecting Ag precipitation rate in the system Ag<sup>+</sup>-CN<sup>-</sup>-S<sub>2</sub>O<sub>4</sub><sup>2-</sup> are studied. From the results obtained, a process of chemical precipitation for Ag recovery is proposed, using an environmentally-friendly reducing reagent (sodium dithionite, Na<sub>2</sub>S<sub>2</sub>O<sub>4</sub>), leaving a residual content of Ag into the permitted environmental levels (-1 Ag). The levels of CN<sup>-</sup> in liquids wastes are of the order of 0.816 mol L<sup>-1</sup>, and they can be treated by ozonization processes for inerting cyanide. The results obtained indicate that Ag precipitation is achieved in less than 1 hour, with recoveries close to 99%, at room temperature. Silver precipitation is characterized by an induction period followed by a precipitation period, leaving a metal amount in solution less than 1 mg L<sup>-1</sup>. The main kinetic parameters studied lead to obtain the following apparent reaction orders: with respect to the initial [S<sub>2</sub>O<sub>4</sub><sup>2-</sup>] was <em>n</em> = 1.675, with respect to [CN<sup>-</sup>] was -1.24, with respect to [OH<sup>-</sup>] was ≈0 (between 10<sup>-4</sup> and 10<sup>-2</sup> mol L<sup>-1</sup>) and with respect to the initial [Ag<sup>+</sup>] was 0.524. An activation energy of 77 kJ mol<sup>-1</sup> was obtained. Under these conditions, Ag precipitation in the system Ag<sup>+</sup>-CN<sup>-</sup>-S<sub>2</sub>O<sub>4</sub><sup>2-</sup> is controlled by chemical reaction, characterized by high activation energy, and is independent of the hydrodynamic variables of the system.

Elementary reaction rates from post-induction-period profiles in shock-initiated combustion

1973 ◽  
Vol 14 (1) ◽  
pp. 61-75 ◽  
Author(s):  
W.C. Gardiner ◽  
W.G. Mallard ◽  
M. McFarland ◽  
K. Morinaga ◽  
J.H. Owen ◽  
...  
Keyword(s):  
Induction Period ◽  
Reaction Rates ◽  
Elementary Reaction ◽  
Post Induction

scholarly journals The Sensitivity of the Isentropic Slope in a Primitive Equation Dry Model

2008 ◽  
Vol 65 (1) ◽  
pp. 43-65 ◽  
Author(s):  
Pablo Zurita-Gotor
Keyword(s):  
Surface Temperature ◽  
Heating Rate ◽  
Mass Flux ◽  
Time Scale ◽  
Diabatic Heating ◽  
Return Flow ◽  
Mean Flow ◽  
Primitive Equation ◽  
The Mean ◽  
Flow Changes

Abstract This paper discusses the sensitivity of the isentropic slope in a primitive equation dry model forced with Newtonian cooling when the heating is varied. This is done in two different ways, changing either the radiative equilibrium baroclinicity or the diabatic time scale for the zonal-mean flow. When the radiative equilibrium baroclinicity is changed, the isentropic slope remains insensitive against changes in the forcing, in agreement with previous results. However, the isentropic slope steepens when the diabatic heating rate is accelerated for the zonal-mean flow. Changes in the ratio between the interior and the boundary diffusivities as the diabatic heating rate is varied appear to be responsible for the violation of the constant criticality constraint in this model. Theoretical arguments are used to relate the sensitivity of the isentropic slope to that of the isentropic mass flux, which also remains constant when the radiative-equilibrium baroclinicity is changed. The sensitivity of the isentropic mass flux on the heating depends on how the gross stability changes. Bulk stabilities calculated from isobaric averages and gross stabilities estimated from isentropic diagnostics are not necessarily equivalent because a significant part of the return flow occurs at potential temperatures colder than the mean surface temperature.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

The E-ring: interactions with plasma and implications for its evolution

1984 ◽  
Vol 75 ◽  
pp. 599-602
Author(s):  
T.V. Johnson ◽  
G.E. Morfill ◽  
E. Grun
Keyword(s):  
Time Scale ◽  
Particle Density ◽  
High Energy ◽  
Particle Removal ◽  
Density Region ◽  
Drag Forces ◽  
Orbit Evolution ◽  
History Of ◽  
Ring Particle ◽  
Ring Material

A number of lines of evidence suggest that the particles making up the E-ring are small, on the order of a few microns or less in size (Terrile and Tokunaga, 1980, BAAS; Pang et al., 1982 Saturn meeting; Tucson, AZ). This suggests that a variety of electromagnetic and plasma affects may be important in considering the history of such particles. We have shown (Morfill et al., 1982, J. Geophys. Res., in press) that plasma drags forces from the corotating plasma will rapidly evolve E-ring particle orbits to increasing distance from Saturn until a point is reached where radiation drag forces acting to decrease orbital radius balance this outward acceleration. This occurs at approximately Rhea's orbit, although the exact value is subject to many uncertainties. The time scale for plasma drag to move particles from Enceladus' orbit to the outer E-ring is ~104yr. A variety of effects also act to remove particles, primarily sputtering by both high energy charged particles (Cheng et al., 1982, J. Geophys. Res., in press) and corotating plasma (Morfill et al., 1982). The time scale for sputtering away one micron particles is also short, 102 - 10 yrs. Thus the detailed particle density profile in the E-ring is set by a competition between orbit evolution and particle removal. The high density region near Enceladus' orbit may result from the sputtering yeild of corotating ions being less than unity at this radius (e.g. Eviatar et al., 1982, Saturn meeting). In any case, an active source of E-ring material is required if the feature is not very ephemeral - Enceladus itself, with its geologically recent surface, appears still to be the best candidate for the ultimate source of E-ring material.

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