Detonation Velocity as Function of Curvature from Diameter Effect Data

Abstract

Dn(k) (normal detonation velocity as function of curvature) is usually calibrated from rate stick breakout data. Using this approach, it is often found that sections of the Dn(k) curve, obtained from sticks of different diameters, do not agree at overlapping k ranges. We therefore ask if it is possible to calibrate Dn(k) from diameter effect data, and show that this is indeed possible. We use for that an indirect calibration procedure: 1) assume a Dn(k) curve; 2) for different values of the steady rate stick detonation velocity Ds, integrate the two front shape ODEs until the boundary angle is reached, and record the resulting diameter d; and 3) compare the resulting Ds,d pairs to the experimental diameter effect curve. We show here that by appropriately correcting the assumed Dn(k) curve, we can easily get agreement with the experimental diameter effect curve, thereby completing the calibration procedure. As a byproduct we show that the Dn(k) curve must have a limit curvature, or otherwise the failure stick diameter is not reproduced. Finally, we apply the same procedure to predict the size effect (like diameter effect, but for nonstick geometries) and the breakout curves for other steady detonations.