![]() ![]() ![]() The freely fit values of A result in larger radii at early time. This is a result of the A coefficient, which acts as a non-dimensional shock wave radius at \(t^*=0\). Fits 1 and 2 asymptote toward a constant non-dimensional radius value. Inspection of the Dewey curve fit in ( 15) reveals that it is a dimensional equation. Insights into blast data and explosive energy release are obtained via scaling and comparison with the universal curve fits. The goal of the present work is to compare the recent universal scaling approaches to each other and to traditional methods for representing shock wave radius versus time data. Both works have demonstrated that a singular shock wave radius versus time curve appears to exist that can characterize all explosive formulations, which appears to be a contradiction of the concept that each explosive has a unique shock wave radius versus time profile. ![]() Both of these new scaling approaches demonstrated good agreement with experimental data for explosive testing across orders of magnitude of scaling, and the identification of clear strong and weak shock limits to the curve fits. Similarly, recent work by Diaz and Rigby developed a theoretical description of shock wave position and Mach number versus time starting from analysis of the hydrodynamic equations of motion . The work identified a single shock wave radius versus time relationship for a range of explosive formulations. Recent work by Wei and Hargather presented a new scaling approach that demonstrated the ability to scale explosively driven shock waves in air and water. The idea of TNT equivalence as a function of radius means that the shock propagation from each explosive material is specific for that explosive, and detailed measurements of shock wave position versus time for each explosive material should be recorded. Calculation of TNT equivalence is frequently reported as a single number , or more recently a TNT equivalence as a function of position from a charge . This is traditionally used to compare energy release to the energy release of TNT, resulting in a “TNT equivalence” . The variations in this region result in different estimations of energy release or blast strength between the curve fits.įor explosions of the same mass of different energetic materials, the scaling can yield an equivalent energy release between the two materials. The universal shock wave profiles are all found to be relatively similar, but with slight variations in a transition region of non-dimensional radii \(0.15\lesssim R^*\lesssim 2\). The nonlinear profile, originally developed by Dewey, is examined here, and a universal non-dimensional form of the equation is proposed. These two universal shock wave profiles are examined here relative to each other and relative to a commonly used nonlinear shock wave profile, which is fit to experimental data for individual explosive materials. Recently, two universal shock wave radius versus time profiles have been presented in the literature, which demonstrate the ability to represent explosively driven shock wave profiles for all explosive sources in any fluid environment. Explosively driven shock wave radius versus time profiles are frequently used to document energy release and relative explosive performance. ![]()
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