Transition study for asymmetric reflection between moving incident shock waves

The transition criteria seen from the ground frame are studied in this paper for asymmetrical reflection between shock waves moving at constant linear speed. To limit the size of the parameter space, these criteria are considered in detail for the reduced problem where the upper incident shock wave is moving and the lower one is steady, and a method is provided for extension to the general problem where both the upper and lower ones are unsteady. For the reduced problem, we observe that, in the shock angle plane, shock motion lowers or elevates the von Neumann condition in a global way depending on the direction of shock motion, and this change becomes less important for large shock angle. The effect of shock motion on the detachment condition, though small, displays non-monotonicity. The shock motion changes the transition criteria through altering the effective Mach number and shock angle, and these effects add for small shock angle and mutually cancel for large shock angle, so that shock motion has a less important effect for large shock angle. The role of the effective shock angle is not monotonic on the detachment condition, explaining the observed non-monotonicity for the role of shock motion on the detachment condition. Furthermore, it is found that the detachment condition has a wavefunction form that can be approximated as a hybrid of a sinusoidal function and a linear function of the shock angle.

Shock induced aerobreakup of a droplet

The multiscale dynamics of a shock–droplet interaction is crucial in understanding the atomisation of droplets due to external airflow. The interaction phenomena are classified into wave dynamics (stage I) and droplet breakup dynamics (stage II). Stage I involves the formation of different wave structures after an incident shock impacts the droplet surface. These waves momentarily change the droplet's ambient conditions, while in later times they are mainly influenced by shock-induced airflow. Stage II involves induced airflow interaction with the droplet that leads to its deformation and breakup. Primarily, two modes of droplet breakup, i.e. shear-induced entrainment and Rayleigh–Taylor piercing (RTP) (based on the modes of surface instabilities) were observed for the studied range of Weber numbers $(We\sim 30\text{--}15\,000)$ . A criterion for the transition between two breakup modes is obtained, which successfully explains the observation of RTP mode of droplet breakup at high Weber numbers $(We\sim 800)$ . For $We > 1000$ , the breakup dynamics is governed by the shear-induced surface waves. After formation, the Kelvin–Helmholtz waves travel on the droplet surface and merge to form a liquid sheet near the droplet equator. Henceforth, the liquid sheet undergoes breakup processes via nucleation of several holes. The breakup process is recurrent until the complete droplet disintegrates or external drag acting on the droplet is insufficient for further disintegration. At lower Weber numbers, the droplet undergoes complete deformation like a flattened disk, and a multibag mode of breakup based on RTP is observed.

Evolution of artificial disturbances in a shear layer at M=1.43

The evolution of artificial disturbances in a laminar boundary layer on a flat plate model in the presence of an incident shock wave is considered. The flow is supersonic with the freestream Mach number M = 1.43. The study is carried out by hot-wire anemometry. A dielectric barrier discharge is used to generate disturbances. Data on the distribution in space of the average and non-stationary components of the mass flow are obtained. Disturbances created by the discharge and their evolution along the separation zone are recorded.

Numerical simulation of the interaction of the disturbed boundary layer with an incident shock

Interaction of the disturbed supersonic boundary layer with an incident oblique shock wave is studied numerically with eddy-resolving numerical simulations. Eigenmodes of the linear stability theory are used to generate the inflow boundary layer disturbances. The evolution of unstable boundary-layer disturbances, effects of the incident shock on the disturbances, effects of the disturbances on the boundary layer separation, flow dynamics in the separation zone, and laminar-turbulent transition are studied.

Numerical Study of Air Flow Induced by Shock Impact on an Array of Perforated Plates

This study is focused on the propagation behavior and attenuation characteristics of a planar incident shock wave when propagating through an array of perforated plates. Based on a density-based coupled explicit algorithm, combined with a third-order MUSCL scheme and the Roe averaged flux difference splitting method, the Navier–Stokes equations and the realizable k-ε turbulence model equations describing the air flow are numerically solved. The evolution of the dynamic wave and ring vortex systems is effectively captured and analyzed. The influence of incident shock Mach number, perforated-plate porosity, and plate number on the propagation and attenuation of the shock wave was studied by using pressure- and entropy-based attenuation rates. The results indicate that the reflection, diffraction, transmission, and interference behaviors of the leading shock wave and the superimposed effects due to the trailing secondary shock wave are the main reasons that cause the intensity of the leading shock wave to experience a complex process consisting of attenuation, local enhancement, attenuation, enhancement, and attenuation. The reflected shock interactions with transmitted shock induced ring vortices and jets lead to the deformation and local intensification of the shock wave. The formation of nearly steady jets following the array of perforated plates is attributed to the generation of an oscillation chamber for the inside dynamic wave system between two perforated plates. The vorticity diffusion, merging and splitting of vortex cores dissipate the wave energy. Furthermore, the leading transmitted shock wave attenuates more significantly whereas the reflected shock wave from the first plate of the array attenuates less significantly as the shock Mach number increases. The increase in the porosity weakens the suppression effects on the leading shock wave while increases the attenuation rate of the reflected shock wave. The first perforated plate in the array plays a major role in the attenuation of the shock wave.

Blast mitigation by perforated plates using an explosive driven shock tube: study of geometry effects and plate numbers

This work is set in the context of blast mitigation based on geometric means, namely perforated metallic plates or grids. When a shock wave passes through a perforated plate, the flow field is modified, and new shock waves are created, as well as regions of vortices and turbulence in which the energy of the wave can be dissipated. In this study, an explosive driven shock tube (EDST) was used to visualize the interaction of a blast wave with perforated plates or with a piece of cast metallic foam. Additionally, the overpressure and the impulse of the reflected blast wave on a wall located downstream were assessed. The use of an EDST allowed the evaluation of the mitigation capacity under a high dynamic loading. Several combinations of perforated plates were tested, varying the geometry and the number of plates, as well as switching between two different spacings. When the shock wave collided with a plate, we observed that part of the incident shock wave was reflected by the plate, while the remaining wave was transmitted through it. Downstream of the plate, both the overpressure and the impulse were reduced, this effect being more prominent as the porosity of the plates decreased. When two plates were placed as obstacles, this phenomenon of reflection/transmission was repeated twice consecutively, further reducing the downstream reflected overpressure and impulse. An array of three plates or a piece of metallic foam were even more effective in mitigating the blast wave. Varying the distance between two or three plates had no effect on blast mitigation.

Adjoint-based optimisation of detonation initiation by a focusing shock wave

An optimisation study of a shock-wave-focusing geometry is presented in this work. The configuration serves as a reliable and deterministic detonation initiator in a pulsed detonation engine. The combustion chamber consists of a circular pipe with one convergent–divergent axisymmetric nozzle, acting as a focusing device for an incoming shock wave. Geometrical changes are proposed to reduce the minimum shock wave strength necessary for a successful detonation initiation. For that purpose, the adjoint approach is applied. The sensitivity of the initiation to flow variations delivered by this method is used to reshape the obstacle’s form. The thermodynamics is described by a higher-order temperature-dependent polynomial, avoiding the large errors of the constant adiabatic exponent assumption. The chemical reaction of stoichiometric premixed hydrogen-air is modelled by means of a one-step kinetics with a variable pre-exponential factor. This factor is adapted to reproduce the induction time of a complex kinetics model. The optimisation results in a 5% decrease of the incident shock wave threshold for the successful detonation initiation.