Blast wave induced unsteady flow at the shock tube opening

TL;DR

The paper investigates unsteady blast-driven flow at the opening of an open-ended rectangular shock tube using a wire-explosion source to generate blasts in the range $Ma_s=1.2-1.8$. It combines high-speed Schlieren, Mie-scattering, and PIV measurements with an approximate blast-wave model based on a power-law density behind the front and an energy scale $E_0$, alongside a boundary-condition analysis at the exit via the method of characteristics. A steady-outlet pressure boundary condition best reproduces the observed phenomena, including supersonic efflux, embedded shocks, PM expansion fans, and reshock formation, while revealing a previously undocumented shedding of embedded shocks and complex CVR dynamics. The study discusses the limitations of one-dimensional modeling and various boundary conditions, providing a framework for improved boundary treatments in highly transient blast-driven flows exiting open tubes. Overall, the results advance understanding of transient jet formation from open-ended shock tubes and have implications for safety assessment and propulsion-related applications involving blast waves and shock-tube venting.

Abstract

Shock tubes have been a crucial device, facilitating studies across a wide range of practical applications. An open-ended shock tube employing the wire-explosion technique with a rectangular cross section is used in the present study to generate blast waves over a Mach number range of 1.2-1.8, enabling detailed investigation of unsteady compressible flow at the tube opening. The blast wave produces a complex flow field comprising a compressible vortex ring with a trailing jet, and several transient structures, including embedded shocks, inward-moving shock or reverse shocks, shear layers, and Prandtl-Meyer expansion fans. An approximate model based on a power-law density profile describes the blast evolution inside and outside the tube, with the equivalent source deduced from measured shock trajectories. The blast wave-tube exit interaction is analyzed using the method of characteristics with alternate exit boundary conditions. A steady-pressure outlet best reproduces experimental observations, predicting supersonic efflux, embedded shocks, expansion waves, and circulation production. Several previously unreported unsteady features, including reverse shock or "reshock" formation and embedded shock shedding, are documented. The findings highlight the intricate dynamics of various features associated with such highly transient, blast-driven flows emanating from an open-ended shock tube.

Figures (22)

• Figure 1: Schematic illustrating experimental setup (a) Wire explosion based shock tube and the rectangular cross-section of the cavity (b) Two primary orthogonal views for flow visualisation - Front View and Side view (c) Schlieren imaging setup to visualise the shock wave and the density gradients in the compressible vortex flow (d) Particle image velocimetry (PIV) setup to assess flow fields using tracers and a planar laser sheet illuminating one of the principal planes.
• Figure 2: Schlieren imaging of the flow evolution near the shock tube exit illustrating primary blast wave, diffracted shockwave, expansion wave, compressible vortex ring (CVR) and reverse shock wave from the front view at (a) lower blast energy at $V_c=6kV$ (b) higher blast energy at $V_c=10kV$ and the side view at (c) $V_c=6kV$ (d) $V_c=10kV$.
• Figure 3: (a) Schematic illustrating the asymmetric evolution of the compressible vortex ring (CVR) displaying kinks, unsteady deformations, and axis switching. (b) Schlieren images from the front view (FV) and side view (SV) superimposed over a time period illustrating an asymmetric flow. The red dotted box illustrates the shock tube cavity. Top: FV and Bottom: SV for $V_c=6kV$ (c) Superimposition of processed schlieren images (gradient operation), showing the trajectory of the kinks over the unstable CVR through yellow arrows. Left: FV and Right: SV for $V_c=6kV$ (d) Diagonal view of the vortex ring. Left: $V_c=6kV$ with slender vortex and Right: $V_c=10kV$ with curved embedded shock.
• Figure 4: (a) Schematic illustrating the blast wave transmission across the tube exit (b) Line schlieren: Temporal evolution of the centerline intensity of the Schlieren imaging of the front view, plotted as a contour diagram for blast energy $V_c=8kV$, illustrating evolution of the significant flow features. $z-t$ diagram extracting spatiotemporal information of the significant flow features for blast energies (c) $V_c=6kV$ (d) $V_c=10kV$, where $z/D_e=0$ marks the tube exit. CVR: compressible vortex ring; PM: Prandtl-Meyer wave
• Figure 5: (a) Time series of the blast wave velocity near the tube opening, illustrating significant decay outside the exit. Arrival properties of the blast wave at the tube exit at different charging voltages (b) Shock Mach number $Ma_{se}$ (c) Arrival time $t_{se}$. (d) Prediction of the arrival characteristics based on the model and (e) corresponding characteristic length $R_{0,in}$ values associated with blast energy from the system inside the shock tube. (f) Normalised blast wave trajectories inside the shock tube and comparison with the model.