Application of the minimum entropy production principle to shock reflection induced by separation


Shock waves are generally generated by a decrease in the flow area for an object moving with high speeds exceeding that of sound. Consequently, multiple shocks are present in various flow problems which may in one way or another intersect with each other or the surfaces generating them. Pioneered by Mach in the late nineteenth century, the study of different shock configurations has attracted significant attention of researchers to date.

For instance, in earlier published literature, the transition between the regular reflection and Mash reflection have been attributed to the fact that the reflection solution is a function of the pressure and deflection angle. Unfortunately, in stable Mach reflection and regular reflection, the prediction of the reflected solution has remained difficult. Therefore, researchers have been looking for alternatives and have identified the application of the second law of thermodynamics based on the principle of minimum entropy production as a promising solution.

To this note, Nanjing University of Aeronautics and Astronautics scientists: Dr. Chengpeng Wang, Dr. Longsheng Xue and Dr. Keming Cheng from the College of Aerospace Engineering investigated both experimentally and theoretically, the separation-based shock reflection configurations. Fundamentally, unlike the initial studies that emphasized on the influence of the upstream conditions and shock configurations, the authors further took into consideration the downstream conditions which exist in many applications such as combustion chambers and isolators. Their work is currently published in the journal, Journal of Fluid Mechanics.

Briefly, the research team commenced their work by first cross-examining the relationship between the downstream flow, upstream flow, and the different shock configurations. Next, based on the existing research contributions, an analytical method was developed in which a minimum entropy production was employed to predict the transition between the Mach reflection and the regular reflection as well as the separation shock angle. In particular, the newly considered downstream flow conditions were measured using an equivalent back-pressure technique variable. Eventually, a solution path obeying the minimum entropy production principle was determined for regular reflection domain and compared to that obtained for the experimental results.

The authors observed that the results were similar to the exciting experimental results. For instance, it was noted that for solutions obeying the minimum entropy production principle, it was much easier to predict the shock angles induced by separation and the transition between the regular reflection and Mach reflection. Furthermore, further analysis indicated that a solution path resided in the overall regular reflection domain and the shock polar line.

In summary, Chengpeng Wang and colleagues successfully developed employed the minimum entropy production principle to investigate separation-induced shock reflections.  To actualize their research work, they designed a model comprising of two ramps of 7° each and tested each of them with Mach number 5 in a free-stream flow. They noted that a steady shock reflection is obtaining before the solution path reaches the incident polar line after which it become consistently unstable. Altogether, the implementation of the solution path will pave the way for efficient determination of the incident shock angles and stable shock configurations.

Application of the minimum entropy production principle to shock reflection induced by separation - -Advances in Engineering
Figure 1 The reflected shock solution path that fulfills the minimum entropy production.


Wang, C., Xue, L., & Cheng, K. (2018). Application of the minimum entropy production principle to shock reflection induced by separationJournal of Fluid Mechanics, 857, 784-805.

Go To Journal of Fluid Mechanics

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