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.

中文翻译：

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三点路径预测的新经验公式的开发

本文开发了一个新的经验公式，用于在不规则冲击反射情况下预测三点路径。使用二维轴对称多材料任意拉格朗日-欧拉公式的数值模拟被用来获得流体密度数据。使用流体密度和节点坐标数据，确定流体密度梯度，然后用于生成数值纹影图像。根据这些图像，推导出三点路径，并与统一设施标准 (UFC) 和自然资源保护委员会 (NRDC) 的模型以及公开文献中的两个模型进行比较。发现数值导出的三点路径与最近发表的公开文献中针对典型地面范围的冲击波传播范围高达 6 m 的模型预测的路径非常吻合。考虑到整个距离范围，发现三点路径的不同模型与数值模型的一致性取决于所考虑的爆炸场景，即按比例缩放的装药高度。对于小尺度电荷高度，UFC 模型和最近公开文献中发表的模型与数值结果的吻合度比其他两种模型更好，而 NRDC 模型与大体积的数值结果吻合度最好。 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?缩放充电高度。根据数值计算结果，提出了三点路径预测的新经验公式，