Evolution of a shock wave moving Through a local nerrow section

Introduction

When a shock wave encounters a narrowing inside a conduit, it interacts with the geometry and produces multiple reflected shocks. Understanding these interactions is essential for predicting unsteady pressure loads and flow separation in confined flows.

This study investigates, both experimentally and numerically, the transient dynamics of shock interaction with a smooth, sinusoidal narrowing. By varying the blockage ratio (the maximum reduction in cross-sectional area) and the axial length of the narrowing, we reveal how geometry controls shock reflections, transmitted shocks, and the impulsively driven downstream flow.

Experimental and Numerical Methods

• A shock tube with an axisymmetric sinusoidal narrowing was used to generate controlled test cases.

• High-speed Schlieren imaging and wall pressure measurements captured shock reflections and transmitted waves.

• Numerical simulations were performed under identical conditions and validated against experiments, showing excellent agreement (Figure 1).

Results and Insights

• Effect of obstacle length:

  • Shorter or longer narrowing lengths (at constant blockage ratio) strongly influence the initial reflected shock and the onset of flow detachment.

  • These differences carry downstream and alter the transmitted shock structure in the early stages (Figure 2).

• Pseudo–steady state (after ~1 ms):

  • The influence of length diminishes, and blockage ratio becomes the dominant factor controlling reflected shock strength.

  • The transmitted shock still varies with geometry, but its sensitivity to blockage ratio is weaker (Figure 3).

• Geometric coupling:

  • While blockage ratio governs steady reflected shock strength, the combination of length and height shapes the detailed shock patterns that evolve downstream.

Conclusions

This study shows that:

• Obstacle length mainly affects the short-time transient interaction immediately after shock impact.

• Blockage ratio strongly controls the steady reflected shock intensity.

• The combined geometry determines the rich variety of shock structures that develop in the flow field.

These findings contribute to the design of conduits and flow passages where shock control and unsteady load mitigation are critical.