Metal Angle Correction in the Cylinder Test

Abstract

Abstract. Cylinder test data shows that the copper wall angle, , increases with time in a given shot and becomes much larger if the wall is at half-thickness. The true velocity is suggested to be that perpendicular to the wall, and this brings full and half-wall data in closer agreement. The equation for calculating the detonation energy density, E d , at each cone relative volume becomeswhere  is the angle of the measuring probe,  m the initial metal density,  o the initial explosive density, R o the initial explosive radius, R and x the later radius and wall thickness, and u  the wall velocity. This provides a unique solution to the energy density that does not require empirical coefficients or standards.(R+x)/cos is the wall length of the cone perpendicular to the cylinder surface and we use this as a description of the constant relative volume. This leads to a definition of the cone relative volume of gas products as beingAs a standard for full-wall cylinders, we take v c relative volumes of 2.43, 4.50 and 7.12 at the scaled wall displacements of 6, 12.5 and 19 mm. For a full-wall copper cylinder at the three points, the wall angles average 10.0, 11.0 and 11.6 degrees. Besides Cylinder test data on copper, previously unpublished framing camera pictures also measure angles for 8 different metals. The angles are a function of wall thickness and relative volume but of nothing else, including the type of metal. For modeling, our simulation code calculates the wall velocity as seen along a particular probe direction, as this is a more realistic comparison to measurements than a zone particle velocity.

Revisiting the Kinematics of the Cylinder Test

“…In Figure 2a, the wall particle velocity, , is compared to the apparent outward radial velocity (i. e., , or what a streak camera would measure) as well as the velocities determined by laser velocimetry, , at three different probe angles ( α =0°, 5°, and 10°). For a standard full‐wall cylinder test, the angles reached by the expanding wall are on the order of 10° to 12°; these values increase to 13°–15° for half‐wall cylinders [14]. As seen in Figure 2a, for such wall angles, velocimetry probes inclined at an angle, α , on the order of 5° will record velocities near the wall particle velocity.…”

“…Equation 10, previously unreported, explicitly relates the cylinder wall angle to measured quantities (i. e., α , , and D ) without resorting to small‐angle approximations (e. g., [6, 14, 31]) or simultaneously solving a system of equations (e.g., [23, 25]).…”

“…Throughout the history of the cylinder test, experimental procedures, diagnostics, and data analysis and interpretation have inevitably evolved due to technological advances. For example, “half wall” cylinders (i. e., wall thickness equal to one twentieth of the cylinder inner diameter) have been used in the past to increase the accuracy of lower resolution diagnostics, such as streak cameras since half‐wall cylinders yield larger velocities during expansion [14]. The advent of laser‐based interferometric velocimetry techniques (e. g., Fabry‐Pérot [15, 16]; Velocity Interferometer System for Any Reflector, VISAR [17]; Photon Doppler Velocimeter, PDV [18]) has rendered half‐wall cylinders obsolete, which presents a benefit given the cost and complexity of machining such cylinders.…”

“…The advent of laser‐based interferometric velocimetry techniques (e. g., Fabry‐Pérot [15, 16]; Velocity Interferometer System for Any Reflector, VISAR [17]; Photon Doppler Velocimeter, PDV [18]) has rendered half‐wall cylinders obsolete, which presents a benefit given the cost and complexity of machining such cylinders. Although an extensive number of literature sources are available (e. g., [6, 8, 9, 11, 13, 14, 19–25]) that describe how to relate measurements from these velocimetry techniques to kinematic aspects of the cylinder test, in this author‘s opinion no widely available single repository exists that is sufficiently detailed, comprehensive, and illustrative. Worthy of note, however, are the contributions of Hill [19, 22] which are similar to the discussion presented herein, although were not published, unfortunately, in the open literature.…”

“…Worthy of note, however, are the contributions of Hill [19, 22] which are similar to the discussion presented herein, although were not published, unfortunately, in the open literature. On the other hand, some publications, presumably inadvertently, contain inaccurate assumptions and equations (e.g., [14], later revised in [6]; [11], later revised in [23, 26]). It is the intention of this article to serve as the aforementioned repository so that the cylinder test may be made more intuitive to those unfamiliar with it.…”