Gas Particle Nozzle Flows

Kliegel, J. R.

doi:10.1016/b978-1-4832-2759-7.50090-x

Cited by 55 publications

(7 citation statements)

References 7 publications

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“…However, we argued above that for the rates of gas pressure and density change envisaged in eruptions, the assumption of good thermal contact for most of the particles seems adequate (Sparks & Wilson 1976; and so u, plays a role in the motion equivalent to that of the speed of sound in gases. A number of more detailed treatments of the flow of gas/solid dispersions exist (So0 1961;Kliegel 1963;So0 1967;Cole, Bowers & Hohbs 1969;Kieffer 1977). The present treatment is similar to those of KLiegel and Cole et al, but differs in that the relative velocities of the particles and gas are negligible and a constant temperature is assumed.…”

Section: Variables and Equationsmentioning

confidence: 89%

Explosive volcanic eruptions -- IV. The control of magma properties and conduit geometry on eruption column behaviour

Wilson

Sparks

Walker

1980

Geophysical Journal International

626

363

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Plinian air-fall deposits and ignimbrites are the principal products of explosive eruptions of hgh viscosity magma. In this paper, the flow of gas/ pyroclast dispersions and high viscosity magma through various magma chamber/conduit/vent geometries is considered. It is argued that after the first few minutes of an eruption magma fragmentation occurs at a shallow depth within the conduit system. Gas pressures at the fragmentation level are related to exsolved gas contents by consideration of the exsolution mechanism.The sizes of blocks found near vents imply that gas velocities of 200 to 600 m s-' commonly occur. These velocities are greater than the effective speed of sound in an erupting mixture (90-200ms-') and the transition from subsonic to supersonic flow is identified as occurring at the depth at which the conduit has its minimum diameter. The range of values of this minimum diameter (-5 to -100 m) is estimated from observed and theoretically deduced mass-eruption rates.The energy and continuity equations are solved, taking account of friction effects, for numerous geometries during the evolution, by wall erosion, of a conduit. Conduit erosion ceases, near the surface, when an exit pressure of one atmosphere is reached. Eruption velocities are found to depend strongly on exsolved magma gas content and weakly on radius of conduit and friction effects. Assuming water as the main volatile phase, velocities of 400-600 m s-l for plinian events imply magma water contents of 3-6 per cent by weight, Three scenarios are presented of eruptions in which: (1) conduit radius increases but gas content remains constant; (2) conduit radius increases and gas content decreases with time; and (3) conduit radius remains fured and gas content decreases. These models demonstrate that the reverse grading 118 L. Wilson, R. S. J. Sparks and G. P. L. Walker commonly observed in plinian air-fall deposits is primarily a consequence of conduit erosion, which always results in increasing eruption intensity and eruption column height with time. The models also show that a decrease in gas content as deeper levels in a magma chamber are tapped or an increasing vent radius as conduit walls are eroded leads to the prediction of a progression from air-fall activity through ignimbrite formation to cessation of eruption and caldera collapse.

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Section: Variables and Equationsmentioning

confidence: 89%

Explosive volcanic eruptions -- IV. The control of magma properties and conduit geometry on eruption column behaviour

Wilson

Sparks

Walker

1980

Geophysical Journal International

626

363

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“…3 ' 4 Brown 5 was able to predict nozzle efficiency based on theoretically determined thermal and velocity lags; however, the test firings of Kliegel and Nickerson 6 revealed the actual performance loss attributed to lags to be considerably smaller than predicted in each instance. Brown was not successful in obtaining experimental verification of the theoretical velocity lag.…”

Section: Gas-particle Flow Systemsmentioning

confidence: 84%

“…where a and b are constants. Therefore, the particle growth rate would be of the exponential form ln(dD*/dt) = n -mt (4) Accordingly, Fig. 4 was plotted as shown.…”

Section: Effect Of Pressure and Residence Timementioning

confidence: 99%

Performance of solid propellants containing metal additives

Cheung

Cohen

1965

AIAA Journal

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Test firings of solid propellant research rockets were made to study effects of propellant composition, pressure, and engine size on the exhaust oxide particle size, and on the composition of the solid exhaust products. The experimental results of this work and those reported by others were analyzed collectively to provide a reasonable description of the aluminum combustion and oxide condensation processes in solid propellant rocket motors. Combustion of aluminum was found to occur in the vapor phase, and was essentially complete in the engines studied although some combustion took place in the nozzle. The experimental results indicate that condensation of the oxide vapor can be described by first-order chemical kinetics. Further particle growth by agglomeration appears likely. The effect of two phase flow was found to be significant in the motors tested and reached a maximum in motors of a certain size. In motors where this loss is large, significant improvement in delivered performance can be realized by reducing the aluminum content.

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“…Equations (11)(12)(13)(14)(15)) form a complete system that can be solved numerically for the variables dp, P, QG, A, and e. Such calculations must start from prescribed conditions at the nozzle inlet which may be arbitrarily selected. One may assume that the flow originates from the reference reservoir, but the assumption of equilibrium in the reservoir is incompatible with the velocity ratio according to Eq.…”

Section: Equations For Steady Nozzle Flowmentioning

confidence: 99%

Gas-particle flow in convergent nozzles at high loading ratios

Rudinger

1970

AIAA Journal

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Nozzle flows of gas-particle mixtures are analyzed for particle loadings for which the particle volume may not be negligible. Nozzle shapes are such that the particle velocity is a constant fraction of the gas velocity. The influence of various parameters which enter into the analysis is discussed. For loading ratios greater than about five, the gas and particle temperatures remain substantially constant for the entire flow, and the assumption of isothermal flow reduces the flow equations to algebraic relationships. Throat conditions then can be obtained directly without having to compute the entire flow. A procedure is outlined to evaluate the ranges of the loading ratio for which the assumption of either isothermal flow or of negligible particle volume keeps errors below a desired level, and it is found that these ranges may overlap. An important intermediate range of the loading ratio therefore exists, typically from about five to fifty, for which both simplifying assumptions are permissible with a resultant extreme simplification of the relationships.Nomenclature a = speed of sound of gas A = cross-sectional area of nozzle c p = specific heat of gas at constant pressure c = specific heat of particles CD = drag coefficient D = diameter of particles F = thrust g = acceleration of gravity /s P = specific impulse K = velocity ratio, Up/Uo k = thermal conductivity of gas m = mass flow rate of gas Nu = Nusselt number p -pressure P = dimensionless pressure, p/p r R = individual gas constant Re = Reynolds number, poD(uo -up)/n T = temperature u = velocity U = dimensionless velocity, u/a r = $u/oL r x = distance coordinate X = dimensionless distance coordinate, l8fj,x/a r ppD* a = equilibrium speed of sound in the gas-particle mixture jS = density ratio in the reservoir, PG.T/PP -y = ratio of the specific heats of the gas F = ratio of the specific heats for equilibrium in the gas-particle mixture, Eq. (20) 5 = specific heat ratio, c/c p e = volume fraction of the particles f = ratio of sound speeds, a r /a r 77 = loading ratio e = dimensionless temperature, T/T r fj, = viscosity of gas p = density Subscripts and superscripts G = gas P = particles

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Gas Particle Nozzle Flows

Cited by 55 publications

References 7 publications

Explosive volcanic eruptions -- IV. The control of magma properties and conduit geometry on eruption column behaviour

Explosive volcanic eruptions -- IV. The control of magma properties and conduit geometry on eruption column behaviour

Performance of solid propellants containing metal additives

Gas-particle flow in convergent nozzles at high loading ratios

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