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

Abstract

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.