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

Abstract

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.