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Evolution of a shock wave moving Through an expansion

Introduction

This study examines how shock waves evolve far downstream of an abrupt expansion in a duct. When a normal shock passes over a step change in cross-section, it experiences strong reflections, vortex formation, and pressure fluctuations. Over time, the shock front tends to recover into a uniform normal shock — but the transient path to this state is complex and poorly understood. We combine experiments, large-eddy simulations (LES), and geometrical shock dynamics (GSD) to uncover the mechanisms that drive this evolution.

Experimental System

Experiments are performed in a 40 × 40 mm shock tube fitted with a 2-m-long test section to capture long-duration flow development. The duct includes back-facing steps of varying heights (expansion ratios 1.75–3.25). High-speed Schlieren imaging (up to 140 kHz) and 26 pressure transducers provide detailed spatiotemporal measurements of the shock wave and the unsteady pressure field. This setup reveals both the near-step transient behavior and the far-downstream recovery process.

Numerical Simulations

The experimental findings are complemented by:

  • 3D LES, solving the compressible Navier–Stokes equations with high-order schemes, validated against experiments.

  • Geometrical Shock Dynamics (GSD), adapted with corrections for expanding geometries, to provide simplified predictive models for shock propagation velocity.

Together, these methods give a full picture of shock front dynamics across different Mach numbers (1.1–1.8) and expansion ratios (up to 5).

Results and Insights

  • Immediately after expansion, the shock wave slows down and becomes curved, producing strong reflections and vortices near the corner.

  • A triple point (TP) forms and reverberates between the duct walls, creating a train of reflected shocks that extend downstream.

  • These repeated reflections induce large pressure fluctuations that persist long after the initial shock has passed.

  • Further downstream, the shock front gradually straightens and approaches a pseudo-steady velocity.

  • Scaling laws show that the downstream shock velocity depends on the expansion ratio and the far-downstream shock speed, enabling simple predictive relations.

Conclusions

The research provides new insight into how shocks recover after abrupt expansions:

  • The corner geometry triggers strong initial instabilities.

  • The triple point dynamics drive the shock train and extended unsteadiness.

  • Despite this complexity, the final outcome can be predicted with a simple scaling law.

These findings deepen the fundamental understanding of compressible flows with area changes and aid in the design of engineering systems like jet engines, pressure-relief devices, and protective ducts

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Shock Evolution

Shock Evolution

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Evolution of a shock wave moving Through an area contruction

Introduction

This project investigates how shock waves behave when they encounter sudden contractions inside ducts of different shapes. Although shock reflections are a classic subject in compressible flow, their dynamics in confined geometries are still not fully understood. By combining high-speed Schlieren experiments with advanced large-eddy simulations (LES), we aim to reveal how contraction geometry alters reflection patterns, vortex formation, and the redistribution of flow energy.

Experimental System

The experiments are carried out in a custom-built shock tube. A pneumatic fast-opening valve generates controlled shock waves that travel through a square-section duct. At the test section, the flow encounters one of four contraction geometries:

  • Forward-facing step (90°)

  • 15° wedge

  • 45° wedge

  • Quadrant profile

High-speed Schlieren imaging captures the evolution of the shock wave and the associated density gradients, enabling direct visualization of flow structures that evolve within microseconds of the initial interaction.

Numerical Simulations

To extend beyond the limitations of the physical setup, we perform three-dimensional LES simulations. These simulations solve the unsteady compressible Navier–Stokes equations using a solver developed at the Technion CFDLAB. The method combines:

  • A monotonicity-preserving scheme for inviscid fluxes.

  • A fourth-order explicit scheme for diffusive fluxes.

  • Runge–Kutta time integration for stability.

The simulations are validated against the experiments, showing strong agreement, which gives confidence in their predictive ability for configurations that are not accessible experimentally.

Results and Insights

The results demonstrate that geometry is the key factor governing shock dynamics:

  • In the step case (90°), the transmitted shock remains normal and produces the strongest reflection.

  • In sloped geometries (15° and 45° wedges), the incoming shock undergoes complex reflection processes that lead to multiple reflections behind the contraction.

  • The 45° wedge generates regular reflections, while the 15° wedge produces Mach reflections, significantly changing the transient flow.

  • The quadrant profile smooths the interaction, weakening reflections and shortening the transient period.

The excellent match between Schlieren images and LES simulations confirms the reliability of the numerical framework.

Conclusions

This study highlights the critical role of contraction geometry in shaping shock reflections, flow evolution, and transient pressure loads. While sharp steps produce strong reflections and prolonged unsteadiness, smoother profiles minimize reflections and stabilize the flow more quickly.

Understanding these dynamics not only advances the fundamental science of compressible flows but also provides practical insights for designing ducts, nozzles, and flow passages in engineering systems where shock control and energy redistribution are crucial.

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Time series of experimental images showing the shock wave evolution after it impinges the four different geometries, with an incoming Mach number of M=1.4.

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Comparison between experimental Schlieren images (top row) and LES simulations (bottom row) for three contraction geometries: (a) 15â—¦ wedge, (b) 45â—¦ wedge, and (c) front-facing step, at representative times after shock interaction

Publication

1. Gichon, Y., Jose, J. T., Chandravamsi, H., Evron, Y., & Ram, O. (2024). The dynamics of shock wave propagation far downstream of an abrupt area expansion. Journal of Fluid Mechanics, 997, A30.

Contact Us

The Transient Fluid Mechanics laboratory
tfml@technion.ac.il

California Energy building, Floor -1, Suite 11,  Faculty of Mechanical Engineering, Technion, Haifa, 3200003


Omri Ram
omri.ram@technion.ac.il
Dan-Kahn Building, Room 402, Faculty of Mechanical Engineering, Technion, Haifa, 3200003

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