JWL++ is a simple Reactive Flow model that includes time‐dependent reaction in prompt detonation. It consists of a Murnahan unreacted equation of state, a JWL reacted EOS, a mixer for the two EOS's and a single‐time‐constant exponential rate. The mixing can be done by four ways, using either pressure or pressure plus artificial viscosity in the rate, and also using either an analytic function or a pressure equilibrator. The model reproduces the Size Effect and detonation front curvature. Detonation failure can also be induced. JWL++ propagates also through an arbitrary geometry in 3‐D without the need for pre‐run program burn calculations. It is slower than a JWL/program “Burn” but faster than “Ignition & Growth”.
The detonation reaction rate in μs−1 is derived from Size Effect data using the relation – DUs(∂Us/∂y)−1, where y =1/Ro, where Us is the detonation velocity for a ratestick of radius Ro and D is the infinite‐radius detonation velocity. These rates are generally 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 classes 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) higher pressure explosives with a concave‐down shape and large positive pressure exponents (dense TNT); and (3) explosives with negative pressure exponents and concave‐up shapes (porous PETN). JWL++ fits only the first class well 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 arises in order to keep a constant reaction rate for all radii. Some explosives have too much bend to be modeled with one rate constant, e.g. Comp. B near 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.
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