Shock waves should not be shocking — engineers across scientific fields need to be able to precisely predict how the instant and strong pressure changes initiate and dissipate to prevent damage. Now, thanks to a team from YOKOHAMA National University, those predictions are even better understood.
In work published on Aug. 19 in the Physics of Fluids , the researchers detailed how computational models used to simulate shock wave behavior represents the "very weak shock waves" in a way that is distinctly different from both theoretical predictions and physical measurements.
Shock waves comprise the pressure that pushes out from an explosion or from an object moving faster than sound, like a supersonic jet. Weak shockwaves refer to the same changes in pressure, density and velocity, but they are much smaller than the larger waves and move closer to the speed of sound. However, current computational modeling approaches have difficulty accurately representing these very weak shock waves, according to co-author Keiichi Kitamura, professor, Faculty of Engineering, YOKOHAMA National University.
"Shock waves cause instantaneous compression, resulting in increased entropy; thus, precise computations of flows involving shock waves are crucial," said co-author Keiichi Kitamura, professor, Faculty of Engineering, YOKOHAMA National University.
Entropy refers to disorder, which in seeming contradiction to expected physical behaviors, increases as the wave moves. That disorder is at the crux of shock wave simulations, according to Kitamura. Conventional computational approaches categorize very weak shock waves as "diffused," but that label doesn't account for the wave's more nuanced variables, especially as it moves.
"Finite volume methods are commonly utilized to address the discontinuity in numerical simulations as they can conserve variables even at shock discontinuities," Kitamura said, explaining that finite volume methods refer to the specific number of cells used in a computational representation. "However, computing shock waves using finite volume methods is not always stable and, under certain conditions, presents challenges owing to their discontinuous nature."
In an analysis focused on understanding the specific properties of numerically represented shock waves, the researchers found that the final state of a moving shock wave can be classified into three regimes: dissipated, transitional and thinly captured. It appeared, Kitamura said, that uninterrogated numerical simulations automatically adjusted assumed physical parameters of a shock wave to make it match the calculated entropy.
"This work identified the mechanism of the diffused weak shocks — it was caused in the entropy generation process within the numerically expressed shockwaves," Kitamura said. "Our findings will bridge the understanding gap between theoretical and physical weak shock waves, which could potentially contribute to safer, more economical and more accurate designs of future rockets and supersonic aircraft."
Gaku Fukushima, postdoctoral researcher in the Department of Mechanical Engineering at Université de Sherbrooke in Canada, served as the corresponding author on this paper. At the time of the research, Fukushima was a Japan Society for the Promotion of Science postdoctoral fellow at YOKOHAMA National University.
The Japan Society for the Promotion of Science supported this research.
