Introduction

   From the earliest days of the universe, massive explosions have been responsible for the chaotic separation of structured materials. During the explosion process, shockwaves (or shock shells) are formed due to gradients in pressure and heat released from the detonation’s center. Interacting with the surrounding environment, the pressure and temperature gradients bend the path of optical rays traced to the viewer from the background. The video frame below from this source captures the pressure- and temperature-induced refractive index changes, as the hills in the background are seen to “bend” around the shock shell.

Detonation Simulation

   Unfortunately, the ability to see a detonation only slightly improves our ability to understand it better, let alone the chance of understanding the geometry of the explosive device. Luckily, physics and detonation experts have poured countless hours into developing high-fidelity physics-based models to simulate pressure, temperature, and velocity profiles of various detonation scenarios. One such software is CTH from Sandia National Laboratories. For a well-defined detonation and its environment, the software is able to produce 1-dimensional spatiotemporal data of the detonation’s shockwave.

   Once calculated, the software produces a variety of parameters describing the shockwave in time and space. Among these parameters are location (XLOC), location offset (DX), pressure (PM+2), temperature (TK), and refractive index (nRefrac). Each parameter can be plotted to provide visual intuition from the results.

   But understanding a change in refractive index is not the same as simulating the effects of the change in refractive index. In other words, having the refractive index values as a function of position will not result in a simulation of what the camera would see of the same explosion defined in CTH. To achieve this goal, more infrastructure is needed. Upon closer inspection, CTH’s refractive index data is not continuous, but is broken into a finite number of steps, each step characterized by a single refractive index value.

   Since the data are already tabled, they can be easily imported into a 3D computer-aided design (CAD) software. Mixed with a bit of Python, softwares like Blender are able to translate the refractive index data (below, left) into a series of concentric hemispherical shells. In this technique, the thickness of each shell exactly matches the thickness of the spatial shell thickness calculated by CTH. The result is a visual representation of the tabulated CTH data.

   When the concentric layers are modeled in Blender, each layer is given a unique material identification number which can then be tied back to a specific material in an optical properties database — this is relatively easy to accomplish, since the refractive index of each layer is already calculated by CTH; pressure and temperature become unimportant.

Placing the explosion

   Once the nested refractive index profile is defined, radiometrically-accurate ray tracing software like DIRSIG can be used to import the nested CAD geometry representing the shockshell and tie each material to an optical property database. Although there are caveats and the ray tracing can take some time, the end result is interesting.

   The final layout used in this study is shown in the top illustration of the above image set. The word “Google” indicates the real-world elevation data that was used to import and create a life-size mountain in the background. In the scene, a person (green stick figure) stands with a camera, the limits of the camera’s frame outlined by the red rectangle. As seen by the person, the scene includes a shockshell (shown with the gold hemisphere) and the moutains in the background, just as in the initial image from the detonation video.

Physical interpretation

   Interestingly, the shock shell produced by converting the CTH data into a CAD model and importing it into an optical ray tracing program produces the same effect on the mountain in the background! Illustrated in the bottom image (right), the individual shock shells can be seen. The outermost shock shells are also seen to bend the outline of the mountain along the direction of the shockwave, similar to the image at the opening of this article.

   One final benefit of using radiometrically accurate ray tracing software as the final simulation piece is that it has the ability to produce non-intuitive simulation results. For instance, DIRSIG has the ability to track not just the amplitude of light as a function of wavelength in the scene, but it can also track each of the Stokes parameters of each ray. This means that additional questions can be asked, such as “Does the shockwave have a notable degree of linear polarization (DoLP)?” The answer to this question, it turns out, is Yes it does (albeit a very weak signature). The DoLP for the nested shock shells is shown in the above image.

Conclusion

This article discussed one technique to circumvent expensive detonation experiments with highly validated numerical models. By fusing specialized heat and pressure models of detonation shock shells with modern CAD software, we were able to create a virtual explosion and place the explosion in a physically-accurate scene! The scene was then processed by a radiometrically accurate model to produce surprising insights such as the polarimetric signature from the outer shock shells. Although each component took a long time to run, they can be run in parallel on high-performance clusters, reducing the speed and cost of each model.