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1

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Circular streamline model of shaped-charge jet and slug formation with asymmetry (1994)

Curtis, J. P. ; Kelly, R. J.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 75 (1994), S. 7700-7709

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The formation of a jet as a result of the collapse of a shaped charge liner in the presence of asymmetry is considered. The development of a satisfactory analytic formation model based on the assumption of incompressible fluid flow requires the solution of the classically indeterminate problem of the collision of two unequal streams. A method of closing the problem is presented. It rests on the assumptions that there is a stagnant core region and that the flows of material from the impinging streams into the jet and slug turn by following circular streamlines with no decrease in speed. Balances of the centrifugal forces with the pressure in the stagnant core, relations derived from the flow geometry, the equation of mass conservation, and Bernoulli's law provide the mathematical statement of the problem. These equations are manipulated to produce a reduced set of four equations in four unknowns, enabling a solution to be determined. This analytic solution predicts that both the jet and the slug are deflected by the same acute angle from the line of bisection of the angle between the impinging streams. The percentages of material in each stream which turn to form the jet are the same. The new model recovers analytically the classical Birkhoff, MacDougall, Pugh, and Taylor [J. Appl. Phys. 19, 563 (1948)] jet formation model in the symmetric case. It also yields the correct analytic result for the head-on collision of two streams of equal speeds but differing widths. More generally the model predicts an approximately linear dependence of the off-axis jet velocity component on the percentage difference in the stream speeds and a similar dependence for the widths. The predicted absolute values of the off-axis velocity are greater for a given difference in the stream speeds than for the same percentage difference in the widths. Finally, fair agreement with some previous experimental work on the collision of streams of unequal widths is demonstrated.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.356601

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2

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Variational approach to the calculation of the radii in the stagnant core model of shaped charge jet formation (1994)

Curtis, J. P. ; Kelly, R. J. ; Cowan, K. G.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 76 (1994), S. 7731-7740

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The formation of a jet and slug from a collapsing shaped charge liner can be viewed, by appropriate choice of reference frame, as the result of two fluid streams impinging upon each other. In this article we consider this formation process and develop further the concept of a stagnant core model. In this model a core region of material is supposed to be stationary at the junction where the liner material turns to form the jet and slug. In our two-dimensional treatment the boundaries of the core region and the free streamlines are assumed to be arcs of circles and the main problem is to determine the radii of these boundaries. However, unlike in previous work, a nonuniform flow field is assumed to exist in the circular flow region from the outset. The nonuniform flow field we derive needs to be matched with the (assumed) uniform flow in the impinging stream. To accomplish this a transition region in the impinging stream is postulated. Consideration of the mass and momentum balances in this region leads to further model equations. The first of these balances gives a relation between the radii of the free streamline and the stagnant core boundary. It is shown that there are no physically acceptable exact solutions to the model equations when the energy is minimized. However a very accurate approximate solution is shown to exist. This solution leads to an expression for the liner speed on the core boundary which is identical to the critical speed used in a recent study on the formation of incoherent jets. Physically sensible values of the free streamline radius are also shown to result from this approximate solution.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.357948

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3

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Axisymmetric instability model for shaped charge jets (1987)

Curtis, J. P.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 61 (1987), S. 4978-4985

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: As a shaped charge jet stretches it breaks up into a series of particles along the jet axis of symmetry. These particles are frequently of approximately the same length, suggesting the existence of a critical wavelength for which the growth of an initial surface disturbance is greatest. Following the failure of earlier one-dimensional models to reproduce this critical wavelength effect, this paper addresses the problem using the axisymmetric equations of motion and boundary conditions of continuum mechanics. Certain simplifying assumptions are made, which enable the analysis of the growth of a small initial sinusoidal disturbance for a range of wavelengths including that suggested by observation of break-up by flash radiographic experiments. The disturbance growth equation derived is of a complicated and singular nature. Under certain initial conditions it can approximately predict from the experimental data the observed critical wavelength.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.338317

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4

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On the effect of asymmetries on the jet from a linear shaped charge (1990)

Pack, D. C. ; Curtis, J. P.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 67 (1990), S. 6701-6704

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The jet from a linear-shaped charge is formed by the collapse of the wedge-shaped liner brought about by the passage of the detonation wave through the surrounding explosive. There is a variety of possible sources of asymmetry which can affect this process. The thickness distributions along each face of the liner may vary. The detonation wave may traverse the liner asymmetrically. The quantity or other properties of the explosive adjoining the liner arms may differ. In such situations the velocities imparted to opposite liner elements at equal distances from the intersection of the arms will in general be different. Thus a pair of liner elements which do meet will in general have started from different distances down their respective liner arms, and will not meet on the axis of symmetry of the charge. This effect causes the process of formation of the jet at the meeting point to occur asymmetrically. This paper presents an investigation of this phenomenon. We generalize the classical analysis of the symmetric steady-state collapse of a liner to include the asymmetries we have described. We present an extension of the classical jet formation theory to the asymmetric case by making several simple physical assumptions. We consider an example of a typical asymmetry in liner thickness and recover values for the off-axis velocity of the jet of the order observed in experiments.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.345107

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5

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The formation of jets from shaped charges in the presence of asymmetry (1992)

Brown, J. ; Curtis, J. P. ; Cook, D. D.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 72 (1992), S. 2136-2143

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The jet from a nominally axisymmetric shaped charge is formed by the collapse of the typically conical liner under the high pressures resulting from detonation of the explosive around it. Where asymmetries are present the velocities imparted to the elements of the liner at a given axial distance from the cone tip will vary as a function of the azimuthal angle among other variables. In general these elements will not meet at all. Conversely a pair of liner elements that do meet will in general have started from different axial positions, and will meet away from the nominal axis of symmetry of the charge. This effect renders the formation process asymmetrical. Consequently the jet particles have an off-axis velocity component which can substantially degrade the penetrative capability of the charge. A complete analysis of asymmetrical liner collapse and jet formation is presented for the case where the liner is axisymmetric, but there is an azimuthal variation in liner projection velocity. The classical analysis of symmetric liner collapse and jet formation is extended to include this type of asymmetry. Earlier work on linear shaped charges, particularly a model for asymmetric jet formation, is drawn upon to consider plane sections of the liner individually. A fully three-dimensional analysis is then achieved by the combination of the results for these sections. This analysis is implemented in a computational model and example results are presented and compared in as far as is possible and meaningful with previous theoretical and experimental results. Good agreement with the previous theoretical work is obtained, and the values of the off-axis velocity components predicted are of the orders observed in the limited experimental data as yet available.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.352329

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6

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A limit of validity of the straight line hypothesis in shaped charge jet formation modeling (1997)

Curtis, J. P.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 82 (1997), S. 107-111

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: A particular problem in the field of shaped charge jet formation modeling concerns the collision of two fluid streams of different widths and speeds. It is commonly assumed that the flow is incompressible, and that the velocity of the fluid in any of the streams is constant across and normal to its cross section. Then the well-known classically indeterminate mathematical problem arises. In the shaped charge context the indeterminacy of the problem has been addressed by making three assumptions about the flow. Several models have assumed that conservation of kinetic energy holds, and have applied Bernoulli's Law to equate the speeds of the jet and slug in a frame moving with the collision point. One natural choice for the third and final assumption is that the jet and slug lie in a straight line when viewed in this frame, the so-called straight line hypothesis. In this article the inclination of this line relative to the bisector of the two colliding streams is expressed as a function of the parameters of the incoming streams. It is shown that the angle between the jet and the incoming stream supplying momentum at the greater rate increases with the size of the angle between the incoming streams until it reaches a maximum value. It then decreases to zero. It is known that the straight line hypothesis is a good approximation for low values of the angle between the incoming streams, but becomes increasingly inaccurate as this angle increases. The above maximum appears to correspond to the limit of validity of the straight line hypothesis. Recommendations for the utilization of the existing formation models to achieve best accuracy are made, based on this limit.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.365854

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7

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On analytic modeling of casing and liner thickness variations in a shaped charge (1994)

Kelly, R. J. ; Curtis, J. P. ; Bremer, M.

[S.l.] : American Institute of Physics (AIP)

Journal of Applied Physics 75 (1994), S. 96-103

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ISSN: 1089-7550

Quelle: AIP Digital Archive

Thema: Physik

Notizen: The jet from a shaped charge is formed by the collapse of its typically conical liner under the high pressures resulting from a detonation front. Nominally the charge is axisymmetric and the jet travels along the axis of symmetry of the charge. However, when asymmetries are present in the shaped charge the velocities imparted to liner elements at a given axial distance from the cone tip will be different. Thus the jet formation process becomes asymmetrical and a nonzero off-axis component of the jet velocity is generally produced. Such an off-axis component can cause considerable degradation in the penetration achieved by the jet. In this article a recent novel approach to the modeling of shaped charge liner collapse with constant liner projection velocities in the presence of asymmetries is generalized to include Randers–Pehrson acceleration of the liner elements. The Gurney formula for an asymmetric closed sandwich is used for the limiting liner element speed in the Randers–Pehrson model and it is shown how the required mass elements may be calculated in a shaped charge application. Simple illustrative models are used to describe thickness variations in the shaped charge casing and liner.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1063/1.355768

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