Evolution of a fast flame behind an induction zone

It has been shown that pressure waves can have a large effect on the burning rate of flames. In this paper, the evolution of convection-driven fast flame, which is acoustically linked to a shock wave via an induction zone, is examined in detail. It is found that there is positive feedback mechanism and the asymptotic model breaks down as blow up occurs. Comparison is made between the case of a piston driving a shock wave into a combustible atmosphere with these studies of a shock wave passing through an existing premixed flame. Received 4 August 1995 / Accepted 20 March 1996     

Isochromatic fringe sharpening and interpolation along an isoclinic countour,with application to fracture mechanics

A method is presented for photoelastic analyses whereby fractional fringe orders are determined with enhanced accuracy. It utilizes data from the Tardy compensation method and combines the data by a robust algorithm to produce highly sharpened isochromatic fringe contours in the immediate vicinity of an isoclinic line. Their sharpness provides accurate assessment of fractional fringe orders at a point, relative to that achieved with the broad fringes of the standard Tardy method. Errors introduced by small isoclinic deviations are quantified and found to be inconsequential. The method is well suited to the application of linear elastic fracture mechanics in fracture studies of threedimensional photoelasticity models of complex structures. It is demonstrated for the determination of stress intensity factor at a crack in the solid fuel element of a rocket motor, when the solid fuel is subjected to internal pressure. Other applications are practical, too.     

Turbulent flow structure at concordant and discordant open-channel confluences

Models of flow at river-channel confluences that consist of two concordant confluent channels with avalanche faces dipping into a scour zone are limited because this morphology may be the exception rather than the rule in nature. In this paper the mean and turbulent flow structure in the streamwise and vertical directions at both concordant and discordant laboratory confluences were examined in order to determine the effect of bed discordance on the flow field, and to assess its influence on sediment transport. Instantaneous velocities were measured with a laser Doppler anemometer using a dense spatial sampling grid. The spatial distribution of normal stress varies with bed geometry as bed discordance generates a distortion of the mixing layer between the confluent streams. Turbulent shear stress is larger in the discordant bed case and its peak is associated with the position of the mixing layer whereas for concordant beds the zone of mixing is characterised by a decrease in the Reynolds shear stress. Quadrant analysis also revealed differential dominating quadrants between the two bed geometries which will influence sediment transport routing and, consequently, the resulting bed morphology. These results highlight the need for significant modifications to current models of confluence flow dynamics in order to account for the bed configuration.We would like to thank Phil Fields of the Earth Sciences workshop at Leeds for his skillful construction of the confluence model and continued help during the course of this research. The LDA facility has been funded through grants from the UFC, NERC and University of Leeds. PB thanks NSERC for financial support and the Fonds FCAR for funding an eight month study-visit held at the Department of Earth Sciences, University of Leeds. AGR acknowledges the financial support of NSERC whilst JLB is grateful for the award of a Nuffield Science Foundation Fellowship which facilitated the preparation of this paper. We thank two anonymous reviewers for their constructive criticisms that helped clarifying the paper.     

Aspects of electrical breakdown of liquid insulating material I

Summary The electrical breakdown strength of insulating oil depends on the size of foreign particles which may form bridges in a place of maximum electric stress. This theoretical relation was verified with colloid suspensions of particles of known radius. Mineral oils may deteriorate if the particles unite by the process of flocculation, the occurrence of which depends on the relative magnitudes of the attractive London-Van der Waals forces acting between the particles and the repulsive forces between their ion atmospheres. The possibility of using a mineral oil as an insulator depends on the existence of an upper limit of the size of particle complexes due to the rapid fall-off of the L.-v.d.W. forces at diameters exceeding 500 Å. The latter value of 2r corresponds to a breakdown strength of 1 kV/mm. If acids are being formed, the upper limit of 500 Å will shift towards larger values, and correspondingly the breakdown strength may drop below 1 kV/mm.     

Stress,body force,and momentum balance in mixture theory

Summary A general momentum balance for a mixture constituent is motivated from corpuscular considerations. The interpretations of stress and internal body force in the separate cases of ionic and non-ionic species are indicated. The Gurtin-Oliver-Williams paradox concerning the interpretation of partial stress is resolved, and relations between total and inner stress shown to be more complex than usually assumed. Comparison is made with kinetic theory.

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Sommario Una relazione generale di bilancio della quantità di moto per un costituente di una mistura è ricavata sulla base di considerazioni particellari. Interpretazioni di stress e forza interna di volume sono fornite per costituenti sia carichi sia neutri. In tal modo il paradosso di Gurtin, Oliver e Williams sull'interpretazione degli stress parziali viene risolto e, inoltre, le relazioni tra stress totali e parziali risultano in generale più complesse di quanto si assuma solitamente. Infine si effettua un confronto con la teoria cinetica.

     

Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz number is small and the Nahme number is non-zero and can be large. Thus the flows are fully-developed and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity. Gz Graetz number - h half-height of channel or disc - h ^* half-height of polymer melt region in channel or disc - L length of channel or pipe - m viscosity shear-rate exponent - Na _Q Nahme number based on flowrate - Na _P Nahme number based on pressure drop - Na _PL lower critical value of Nahme number based on pressure drop - Na _PU upper critical value of Nahme number based on pressure drop - Na _P Nahme number based on pressure gradient - p pressure - P pressure drop - Q volumetric flowrate - r radial coordinate in pipe or disc - R radius of pipe - Re Reynolds number - R _i inner radius of disc - R ₀ outer radius of disc - R ^* radius of polymer melt region in pipe - T temperature - T _m melting temperature of polymer - T ₀ reference temperature - T _w wall temperature - u axial velocity in pipe or channel or radial velocity in disc - w width of channel - x axial coordinate in channel - y transverse coordinate in channel or disc - z axial coordinate in pipe - thermal conductivity of molten polymer - thermal conductivity of frozen polymer - heat capacity of molten polymer - viscosity temperature exponent - dimensionless transverse coordinate in channel or disc - ^* dimensionless half-height of polymer melt region in channel or disc - dimensionless temperature - ^* dimensionless wall temperature - µ viscosity of molten polymer - µ ₀ consistency of molten polymer - dimensionless pressure drop - dimensionless pressure gradient - density of molten polymer - dimensionless radial coordinate in pipe or disc - _i dimensionless inner radius of disc - ^* dimensionless radius of polymer melt region in pipe - dimensionless velocity     

Optimal blunt-nosed figures of revolution in a gas of different rarefactions

Many studies have been made of the optimization of the shape of bodies in a gas stream. However, the majority of these have been made for supersonic and hypersonic flow in the limiting case of a continuum [1], and only a few studies have been made [1–3] for the case of flow over a body of a rarefied gas (mainly a free molecular stream). In the present paper, the problem of shape optimization is considered for hypersonic flow of a gas of different rarefactions over a body. Numerical methods are used to investigate the influence of the Reynolds number on the shape and drag of optimal figures of revolution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 158–161, May–June, 1980.     

Flow birefringence of dilute solutions of polyethyleneoxide of high molecular weight at high rates

Summary Birefringence and orientation angle of solutions of Polyox WSR 301 in the concentration range of 50 to 1350 ppm have been measured up to 8000 s^–1. A few marked differences with ordinary flexible polymers have been evidenced: (i) a very low value of the extinction angle at high shear rate, which could be attributed to an unusually high molecular weight; (ii) the independence of this angle on the concentration, which is due to the variation of the flexibility with the concentration, as shown by the study of the concentration dependence of the segmental optical anisotropy; (iii) the concentration dependence of the elongation shows a plateau value forc 150 ppm, which may come from a concentration dependent and reversible association process, as shown from reduced viscosity measurements.

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Zusammenfassung Es wurden die Doppelbrechung und der Orientierungswinkel von Polyox-WSR 301-Lösungen im Konzentrationsbereich 50–1350 ppm bis zu Schergeschwindigkeiten von 8000 s^–1 gemessen. Dabei wurden einige ausgeprägte Unterschiede gegenüber normalen flexiblen Polymeren gefunden: (i) ein sehr niedriger Wert des Auslöschwinkels, was auf ein ungewöhnlich hohes Molekulargewicht schließen läßt: (ii) die Unabhängigkeit dieses Winkels von der Konzentration, was von einer Änderung der Flexibilität mit der Konzentration herrührt, wie sie durch die Untersuchung der Konzentrationsabhängigkeit der optischen Anisotropie der Segmente aufgezeigt wird; (iii) die Existenz eines Plateaus in der Konzentrationsabhängigkeit der Streckung beic 150 ppm, welches auf einen konzentrationsabhängigen reversiblen Assoziationsvorgang hindeutet, der auch durch Messung der reduzierten Viskosität nahegelegt wird.

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With 5 figures