Evaluation of the existing triple point path models with new experimental data: proposal of an original empirical formulation

Boutillier, Johanna; Ehrhardt, Loic; Mezzo, Sébastien de; Deck, Caroline; Magnan, P.; Naz, P.; Willinger, Reinhard

doi:10.1007/s00193-017-0743-7

Cited by 12 publications

(13 citation statements)

References 10 publications

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“…The extension of the study to greater distances showed that the evolution of height of the Mach stem actually follows a parabolic law as expected from Ref. 29 rather than a linear law as done in Ref. 13.…”

Section: Evolution Of the Mach Stemsupporting

confidence: 51%

“…In the context of blast wave studies, empirical models have been developed to predict the variation of the Mach stem length generated by the reflection of strong shock waves. 29 These models describe a parabolic 29 or a cubic 30 growth of the Mach stem height. Recent studies reporting experiments of weak shock reflection but at a larger scale than the present experiment showed a good agreement with a cubic law.…”

Section: Evolution Of the Mach Stemmentioning

confidence: 99%

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Irregular reflection of spark-generated shock pulses from a rigid surface: Mach-Zehnder interferometry measurements in air

Karzova

Lechat

Ollivier

et al. 2019

The Journal of the Acoustical Society of America

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The irregular reflection of weak acoustic shock waves, known as the von Neumann reflection, has been observed experimentally and numerically for spherically diverging waves generated by an electric spark source. Two optical measurement methods are used: a Mach-Zehnder interferometer for measuring pressure waveforms and a Schlieren system for visualizing shock fronts. Pressure waveforms are reconstructed from the light phase difference measured by the interferometer using the inverse Abel transform. In numerical simulations, the axisymmetric Euler equations are solved using finite-difference time-domain methods and the spark source is modeled as an instantaneous energy injection with a Gaussian shape. Waveforms and reflection patterns obtained from the simulations are in good agreement with those measured by the interferometer and the Schlieren methods. The Mach stem formation is observed close to the surface for incident pressures within the range of 800 to 4000 Pa. Similarly, as for strong shocks generated by blasts, it is found that for spherical weak shocks the Mach stem length increases with distance following a parabolic law. This study confirms the occurrence of irregular reflections at acoustic pressure levels and demonstrates the benefits of the Mach-Zehnder interferometer method when microphone measurements cannot be applied.

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Section: Evolution Of the Mach Stemsupporting

confidence: 51%

Section: Evolution Of the Mach Stemmentioning

confidence: 99%

Irregular reflection of spark-generated shock pulses from a rigid surface: Mach-Zehnder interferometry measurements in air

Karzova

Lechat

Ollivier

et al. 2019

The Journal of the Acoustical Society of America

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“…Four models are available in the open literature to calculate the triple point path. They are the Unified Facilities Criteria (UFC) curves (UFC 3-340-02 [4]), the empirical formula of Kinney and Graham [5], Natural Resources Defense Council (NRDC) [6], and Boutillier et al [7]. UFC published ten curves of the triple point path, for example, Figure 2-13 of UFC 3-340-02 [4].…”

Section: Models Of Triple Point Pathmentioning

confidence: 99%

“…The units for the height and the weight in the equation are centimetre and kiloton, respectively. Although this formula is originally obtained from nuclear explosions, it can also be used for conventional high-explosive tests [2,7]. It should be noted that a high explosive is about twice as effective at forming an air blast compared to a nuclear detonation.…”

Section: Models Of Triple Point Pathmentioning

confidence: 99%

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Development of a new empirical formula for prediction of triple point path

2020

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This paper develops a new empirical formula for the prediction of the triple point path in irregular shock reflection cases. Numerical simulations using a two-dimensional axisymmetric multi-material arbitrary Lagrangian–Eulerian formulation are employed to obtain the data of fluid density. Using the data of fluid density and nodal coordinates, the gradients of fluid density are determined and then used to generate numerical schlieren images. Based on these images, the triple point paths are derived and compared with the models of the Unified Facilities Criteria (UFC) and Natural Resources Defense Council (NRDC) as well as two models from the open literature. It is found that the numerically derived triple point paths are in good agreement with those predicted by a recently published model in the open literature for the typical ground range of shock wave propagation of up to 6 m. Considering the whole distance range, it is found that the agreement of different models of the triple point path with the numerical ones depends on the considered blast scenario, i.e., the scaled charge height. For small-scaled charge heights, the model of the UFC and the recently published model in the open literature are in better agreement with the numerical results than the other two models, whereas the NRDC model has the best agreement with the numerical results for large-scaled charge heights. Based on the numerical results, a new empirical formula is proposed for the prediction of the triple point path, which is valid for a wide range of the scaled charge heights from 0.5 to 3.5 m/kg1/3 and scaled ground distances up to 15 m/kg1/3.

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