Shock-cylinder Interaction Research Articles

Deformation and mutual influence of two cylindrical water columns in tandem subjected to shock wave

Abstract The interaction between shock waves and multiple cylinders, referred to as shock–cylinder interaction (SCI), is an important phenomenon in science and engineering. However, its underlying physical mechanisms remain unclear. This study entailed the numerical simulation of the aerobreakup of two tandem water columns subjected to a high-speed gas flow by using an adaptive mesh refinement (AMR)-based diffusion-interface model. The objective was to elucidate the changes in water–column deformation patterns over a wide range of Weber numbers. Statistical analysis was performed to examine the deformation of the water columns in vertical directions. Results reveal distinct deformation patterns between the two columns as the Weber number increases. Additionally, an extended exponential stretching law model was devised, and its improved capability to predict the deformation patterns was demonstrated.

Effects of interface diffusion and shock strength on shock-accelerated SF6 cylinder

The effects of interface diffusion and incident shock strength on the evolution of a shock-accelerated SF6 cylinder are numerically instigated. These two effects are manifested by measuring two essential issues that determine the material mixing of a shock–cylinder interaction (SCI), namely, the variations of the cylinder area and the material line length. Three interface types (with one sharp interface and two diffuse interfaces) and five incident shock strengths (Mach number ranges from 1.21 to 2.00) are examined. The numerical results provided in the present study show that both these effects play important roles in deforming the SF6 cylinders and the corresponding cylinder area and material line stretching. The cylinder area variation histories of the present results prove that the one-dimensional theoretical prediction of Giordano and Burtschell [“Richtmyer–Meshkov instability induced by shock–bubble interaction: Numerical and analytical studies with experimental validation,” Phys. Fluids 18, 036102 (2006)] applies not only to those sharp interface cylinders but also to these diffuse interface cylinders. The material line stretching histories prove that the exponential law of Yang et al. [“Applications of shock-induced mixing to supersonic combustion,” AIAA J. 31, 854 (1993)] applies well for diffuse interfaces but not for sharp interfaces. It is found that the exponential growth of the material line for the diffuse cylinders is dominated by the mass transport, and that the secondary instabilities only play their role in the primary vortex region. Finally, a predictive law of the development of material line length on the basis of circulation prediction theory is built. It is interesting that the use of the original circulation prediction model can be extended in such a way.

A moving embedded boundary approach for the compressible Navier-Stokes equations in a block-structured adaptive refinement framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1,91,92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds – acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries – an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re=40, an inline oscillating cylinder at Re=100, and a transversely oscillating cylinder at Re=185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

Effects of aspect ratio on shock-cylinder interaction

Interaction of a planar shock wave with a discontinuous \(\hbox {SF}_6\) elliptic gas cylinder surrounded by air is investigated. Special attention is given to the effects of aspect ratio on wave pattern, interface evolution, and material mixing. An ideal discontinuous two-dimensional gas cylinder is created by the soap film technique in experiments, and the shocked flow is captured by schlieren photography combined with a high-speed video camera. The surface of the gas cylinder is clear enough to observe the shock motions, and the distinct interface boundaries allow us to extract more details. As aspect ratio varies, the shock focusing process is quite different. For the prolate gas cylinder, an inward jet is produced although an internal shock focusing firstly occurs. The inward jet has never been observed in membraneless prolate ellipse experiments probably because the inward jet is so faint due to less vorticity generation on membraneless interface that it is difficult to be observed. For the oblate gas cylinder, a secondary vortex pair, which has not been described clearly in previous work, is derived from the downstream interface. The material lines at early stages are extracted from experiments, which grow faster as aspect ratio increases. The interfacial area, the mean volume fraction and the mixing rate are presented from computations, and the results show that the increase of aspect ratio promotes the mixing between gases.

Metamodels for Interphase Heat Transfer from Mesoscale Simulations of Shock–Cylinder Interactions

Macroscale computations of shocked particle-laden flows rely on closure laws to model the heat transfer between the fluid and particle phases. Typically, closure models are semiempirical and obtained for a limited range of parameters because experiments can be difficult and expensive to perform. This paper describes an approach to obtain closures for heat and momentum exchanges from ensembles of high-fidelity mesoscale computations of shock–cylinder interactions. The simulations are performed for flow over a single cylinder for a wide range of Reynolds and Mach numbers . The results are used to construct a metamodel for the drag coefficient and the Nusselt number correlation using a modified Bayesian kriging method. To study the effects of the particle volume fraction , mesoscale computations are performed for cylinder clusters and the and are calculated. The metamodel shows that, although the Nusselt number is primarily a function of the , the and also significantly affect the interphase heat transfer. In particular, the Nusselt number first decreases until and increases for values of . The results show that compressibility and viscous effects must be taken into account to provide accurate closure laws for interphase heat transfer in shocked particle-laden flows.

Effects of Atwood number on shock focusing in shock–cylinder interaction

The evolution of shock-accelerated heavy-gas cylinder surrounded by the air with different Atwood numbers ( $$A_t=0.28, 0.50, 0.63$$ ) is investigated, concentrating on shock focusing and jet formation. Experimentally, a soap film technique is used to generate an ideal two-dimensional discontinuous gas cylinder with a clear surface, which can guarantee the observation of shock wave movements inside the cylinder. Different Atwood numbers are realized by different mixing ratios of $$\hbox {SF}_6$$ and air inside the cylinder. A high-speed schlieren system is adopted to capture the shock motions and jet morphology. Numerical simulations are also performed to provide more information. The results indicate that an inward jet is formed for low Atwood numbers, while an outward jet is generated for high Atwood numbers. Different Atwood numbers will lead to the differences in the relative velocities between the incident shock and the refraction shock, which ultimately results in the differences in shock competition near the downstream pole. The morphology and feature of the jet are closely associated with the position and intensity of shock focusing. The pressure and vorticity contours indicate that the jet formation should be attributed to the pressure pulsation caused by shock focusing, and the jet development is ascribed to the vorticity induction. Finally, a time ratio proposed in the previous work for determining the shock-focusing type is verified by experiments.

A lattice Boltzmann method for simulation of multi-species shock accelerated flows

ABSTRACTA numerical scheme for simulating multi-species shock accelerated flows using lattice Boltzmann approach has been proposed. It uses the moment conservation approach of Yang, Shu, and Wu and extends it to multi-species fluid problems. The multi-species method of Wang et al. has been modified by use of a predictor–corrector approach. This has helped in preventing the pressure oscillations while handling multi-species. Simulation of 2D shock cylinder interaction with this solver has shown good agreement with the experimental data and could capture material discontinuity and unsteady shocks. The simulation of a single mode Richtmyer–Meshkov instability showed that the solver is able to capture the development of spike and bubble as per the experimental findings of Aure and Jacobs. The dissipation in the proposed scheme was further reduced by the use of fifth-order weighted essentially non-oscillatory (WENO). Validated with multiple problems, this method has been found to capture shock instability with good accuracy with a check on pressure oscillations.

Numerical analysis on shock-cylinder interaction using immersed boundary method

The problem of shock interaction with a rigid circular cylinder has been investigated using a compressible immersed boundary method coupled with high-order weighted-essentially non-oscillatory (WENO) scheme. First, the accuracy of the developed code is validated. Then, influences of the incident shock Mach number on the flow-field structure and dynamic drag coefficient, as well as time evolution of the flow field are studied. For different shock Mach number, the flow structure shows very different features. At a given dimensionless time, both the normalized shock detachment distance and the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder decreases with increasing shock Mach number. However, location of the upper triple point varies non-monotonically with shock Mach number. For a case with given shock Mach number, the trajectory of the upper triple point and the time evolution of the normalized vertical distance from the highest point of the primary reflected shock to the centerline of the cylinder can both be predicted by linear correlation. Nevertheless, the time evolution of the normalized shock detachment distance is biased to be non-linear. Meanwhile, time evolution of force exerted on the cylinder is quite unsteady for a case with given shock Mach number and given cylinder diameter. For small shock Mach number, there exists a negative valley, and it disappears when the incident shock Mach number increases to a large value, e.g., 1.7. Furthermore, correlations to predict the occurrence of the peak drag and its value under different shock Mach numbers have been proposed.

Interaction of a weak shock wave with a discontinuous heavy-gas cylinder

The interaction between a cylindrical inhomogeneity and a weak planar shock wave is investigated experimentally and numerically, and special attention is given to the wave patterns and vortex dynamics in this scenario. A soap-film technique is realized to generate a well-controlled discontinuous cylinder (SF6 surrounded by air) with no supports or wires in the shock-tube experiment. The symmetric evolving interfaces and few disturbance waves are observed in a high-speed schlieren photography. Numerical simulations are also carried out for a detailed analysis. The refracted shock wave inside the cylinder is perturbed by the diffracted shock waves and divided into three branches. When these shock branches collide, the shock focusing occurs. A nonlinear model is then proposed to elucidate effects of the wave patterns on the evolution of the cylinder. A distinct vortex pair is gradually developing during the shock-cylinder interaction. The numerical results show that a low pressure region appears at the vortex core. Subsequently, the ambient fluid is entrained into the vortices which are expanding at the same time. Based on the relation between the vortex motion and the circulation, several theoretical models of circulation in the literature are then checked by the experimental and numerical results. Most of these theoretical circulation models provide a reasonably good prediction of the vortex motion in the present configuration.

Three-dimensional effects in shock-cylinder interactions

The shock-cylinder interaction is important for understanding the mixing of fluids by impulsively accelerated material interfaces. The flowfield development is highly sensitive to the initial conditions, which can be difficult to fully characterize in experimental facilities. In this work, simulations based on experimental measurements are used to model the initial flowfield at the Los Alamos shocktube facility. While nominally two-dimensional, our simulations show the initial column has significant axial variation. These numerical solutions are then used as the initial conditions for three-dimensional simulations of the shock-cylinder interaction. A genuinely three-dimensional flowfield develops as a consequence of the initial, axial variation of the cylinder.

Shock tube investigation of hydrodynamic issues related to inertial confinement fusion

A shock tube investigation of two hydrodynamic issues related to inertial confinement fusion (ICF) is undertaken. ICF is a promising source of energy for the future. There has been a considerable increase in the interest in ICF with the development of the National Ignition Facility (NIF). However, much remains to be investigated before a useful yield is obtained from a fusion reaction for power generation. The physics involved in carrying out a fusion reaction combines hydrodynamics, plasma physics and radiation effects superimposed on each other, at extremely small scales, making the problem very complex. One such phenomenon occurring in the deuterium-tritium pellet implosion is the Richtmyer-Meshkov instability occuring at each layer of the fuel which results in the mixing of the ablator with the fuel. This causes dilution of the fuel and reduces the yield of the reaction. Another issue is the impulsive loading of ICF reactor cooling tubes due to the shock wave produced as a result of the fusion reaction. These tubes must withstand the impulse of the shock wave. A shock tube provides an ideal environment to study these issues at large geometric scales with the isolation of hydrodynamics from other effects. A new vertical, square shock tube has been designed specifically for the purpose of studying these fluid flow phenomena from a fundamental point of view. The shock tube is vertical, with a large square inner cross-section and is designed to allow for the release of a $M=5$ shock into air at atmospheric pressure. In this paper, we describe the new shock tube and related instrumentation in detail and present a few preliminary results on the Richtmyer-Meshkov instability and shock-cylinder interactions.