Front Tracking of Shock and Combustion Waves by an Optimal Transport Framework

EasyChair Preprint 4413

Abstract

When we are studying gas explosions it is a challenging task to find the position, the velocity, and the shape of the flame and the shock wave. In lab experiments, state-of-the-art has been to use the sensors like pressure transducers to measure velocities. One drawback of this technique is the limited number of sensors that can be placed inside a test rig. An alternative to these sensor-based measurements is to use a high-speed camera whereupon the position, shape, and velocity can be derived from the recorded images.

An Unnormalized Optimal Transport framework was implemented in Python to provide the route of propagation by the recorded high-speed video. This route was then used for front tracking by three different methods. These methods are classified as Divergence, Transport, and Matrix method. The Transport and the Divergence method were analyzed with both synthetic images and recorded high-speed video frames. Unfortunately, the Matrix method was only applicable to noise-free synthetic images. The Transport method provided better results than the Divergence method. The velocity of the shock wave and the shock angles were therefore calculated using the front tracked from Unnormalized Optimal Transport in combination with the Transport method. Preliminary results indicate that our findings are in accordance with results obtained with sensor-based measurements. Moreover, the Unnormalized Optimal Transport framework can also uncover velocities between the location of the transducers.

Keyphrases: Front Tracking, Unnormalized Optimal Transport, shock wave

@booklet{EasyChair:4413,
  author    = {Sabin Bhattarai and Ola Marius Lysaker and Dag Bjerketvedt},
  title     = {Front Tracking of Shock and Combustion Waves by an Optimal Transport Framework},
  howpublished = {EasyChair Preprint 4413},
  year      = {EasyChair, 2020}}