Dynamic Interactions of Rightward-Moving Oblique Shocks with Steady Oblique Shock Waves: Reflection Patterns and Transition Conditions


In high-speed aerodynamics, the interaction of shock waves with each other and with surfaces is a complex phenomenon which can influence the behavior of supersonic and hypersonic flows. These interactions are important in the design and performance analysis of high-speed aircraft, missiles, and space vehicles. The reflection and interference of shock waves lead to changes in pressure, temperature, and flow direction, which can impact the structural integrity and aerodynamic efficiency of these vehicles, therefore, better understanding these interactions is critical for optimal vehicle designs and to ensure safe and efficient operation at high speeds. One specific type of shock interaction that has caught significant attention is the reflection of a rightward-moving oblique shock (RMOS) of the first family over a steady oblique shock wave (SOSW) which is an interaction that can occur in scenarios, such as the flow around supersonic inlets, the interaction of shock waves with control surfaces, and the behavior of shock waves in shock tunnels. However, there are several challenges in studying the reflection of an RMOS over a SOSW including variety of reflection patterns where different types of shock reflection and interference patterns can emerge. Moreover, to determine the conditions under which one type of reflection transitions to another is a complex task and the transition between different shock interference patterns requires a balance of flow parameters and geometric considerations. Furthermore, to predict and validate shock interaction phenomena, it requires advanced numerical simulations and high-fidelity experimental setups to ensure that simulations accurately capture the physics of shock interactions and that experimental data are precise and reliable are ongoing challenges in the field. To this end, new study published in Journal of Fluid Mechanics and led by Dr. Miaomiao Wang, ZhongZiheng Xu, and Ziniu Wu from the Department of Engineering Mechanics at Tsinghua University investigated the reflection of a rightward-moving oblique shock of the first family over a steady oblique shock wave and provided for the first time a comprehensive understanding of the different shock reflection patterns and their transition conditions.

The team conducted a series of advanced numerical simulations to investigate the reflection of a RMOS of the first family over a SOSW. The simulations identified the various reflection patterns and transition conditions, as well as validated theoretical predictions about shock interactions. For instance, in the pre-shock reflection scenario, the incident shock reflected over the pre-interaction part of the SOSW, the researchers identified three types of pre-shock reflection configurations: pre-IV, pre-V, and pre-VI, which corresponds to Edney’s type IV, V, and VI shock interference patterns. The authors found that in the pre-IV reflection, the numerical results showed two triple points forming at the nominal intersection point of the IS and SOR, resulting in a type IV interaction pattern. The shock polars confirmed the theoretical predictions, indicating that the flow behind the shocks reached an equilibrium state. In contrast, the pre-V reflection, the simulations revealed three triple points, characteristic of type V interaction where the shock polars and streamline patterns validated the occurrence of pre-V reflection, with the shocks and slip lines forming a complex network. On the other hand, the pre pre-VI reflection, they found a supersonic jet formed between two slip lines, indicative of type VI interaction and the shock polars demonstrated the presence of both compression and expansion waves, which confirmed the type VI pattern. For post-shock reflection, the incident shock reflected over the post-interaction part of the SOSW. The study identified two main types of post-shock reflection: post-I and post-II, similar to Edney’s type I and II shock interference.

The authors found in post-I reflection, the numerical simulations displayed regular reflection, with the incident shock intersecting the SOSW to create a single triple point. The Mach and pressure contours showed a triangular shock structure, confirming the type I interaction pattern. The time evolution of the shock lengths indicated a pseudo-steady state, and demonstrated self-similarity in the flow field. In post-II reflection, the authors’ results showed Mach reflection, with multiple triple points forming at the interaction of the IS and SNE. The shock polars illustrated the presence of a Mach stem and reflected shocks, and validated the type II interaction. The self-similarity of the flow was evident from the linear relationship between the shock lengths and the non-dimensional time.

The researchers also explored combined pre- and post-shock reflections, and found  these combined configurations to have more complex interaction patterns. For instance, they reported for pre-IV and post-II reflection, the simulations showed that the pre-IV reflection pattern formed at the nominal intersection point of the IS and SOR, while the post-II reflection pattern emerged at the interaction of the IS and SNE. The combined reflection resulted in additional shock interactions and the formation of further triple points, and created a more intricate flow structure. On the other hand, pre-V and post-II reflection, in this scenario, the pre-V reflection pattern was observed at the nominal intersection point, with three triple points characteristic of type V interaction. The post-II reflection pattern was also present, which lead to further reflections over the wedge and the formation of Mach stems. The combination of these patterns resulted in a highly complex shock interaction network. In contrast, pre-VI and post-II Reflection, the pre-VI reflection pattern, with a supersonic jet between two slip lines, was combined with the post-II reflection pattern. They showed that part of the post-II structure merged with the pre-VI pattern, which resulted in a combined shock structure with significant pressure variations along the wedge surface.

In conclusion Dr. Miaomiao Wang and colleagues advanced our understanding of the complex interactions between ROMOS and SOSW. With the better knowledge of the mechanisms of shock interactions, the observations can be directly applied to the design and optimization of high-speed aircraft, missiles, and space vehicles and help improve the aerodynamic efficiency and structural integrity of these vehicles which leads to safer and more effective designs. Moreover, the findings on the shock-on-shock interactions can be used to enhance the performance of supersonic inlets, which are critical components in high-speed propulsion systems. Furthermore, the work can be applied to the design and operation of shock tunnels and wind tunnels, which are essential the testing and validation of high-speed aerodynamic concepts.

About the author

Miaomiao Wang received the B.S. degree in Mechanics from Tianjin University, Tianjin, China, in 2020 and the Ph.D. degree in Fluid Mechanics from Tsinghua University, Beijing, China, in 2024. From 2024 till now, he was a Postdoctoral Research Fellow with school of aerospace engineering of Tsinghua University. Her current research interests include shock interaction and shock reflection problem, especially with moving incident shock. She was the recipient of“Future Scholar Scholarship” in Tsinghua university(2020/08), “National Scholarship for Postgraduate/Graduate students”(2022/12), “Scientific Research and Exploration Single Scholarship” School of aerospace engineering, Tsinghua university, 2022/12. She has win the “Outstanding poster” in JFM/FLOW Symposium China 2023.


Wang M, Xu Z, Wu Z. Reflection of a rightward-moving oblique shock of first family over a steady oblique shock wave. Journal of Fluid Mechanics. 2024;979:A28. doi:10.1017/jfm.2023.988

Go to Journal of Fluid Mechanics.

Check Also

Elucidating Fluid-Structure Interactions: Studying the Propulsion of Flexible Foils - Advances in Engineering

Elucidating Fluid-Structure Interactions: Studying the Propulsion of Flexible Foils