Reactive flow and the size effect

The detonation reaction rate in mus(-1) is derived from Size Effect data us ing the relation - DUs(partial derivativeU(s)/partial derivativey)(-1), whe re y = 1/R-o, where U-s is the detonation velocity for a ratestick of radiu s R-o and D is the infinite-radius detonation velocity. These rates are gen erally not constant with radius and have pressure exponents ranging from < -5 to >5. JWL++, a simple Reactive Flow code, is run with one rate constant on many samples to compare its rates. JWL++'s pressure exponents vary from about 0.5 to 2.5, and failure occurs outside this range. There are three c lasses of explosives: (1) those for which the pressure exponent is between 1 and 2 and the rate is nearly constant (e.g. porous urea nitrate): (2) hig her pressure explosives with a concave-down shape and large positive pressu re exponents (dense TNT); and (3) explosives with negative pressure exponen ts and concave-up shapes (porous PETN). JWL++ fits only the first class wel l and has the most trouble with class 3. The pressure exponent in JWL++ is shown to be set by the shape of the Size Effect curve - a condition that ar ises in order to keep a constant reaction rate for all radii. Some explosiv es have too much bend to be modeled with one rate constant, e.g. Comp. B ne ar failure. A study with creamed TNT shows that the rate constant need not be changed to account for containment. These results may well be pertinent to a larger consideration of the behavior of Reactive Flow models.