Xisheng Luo

Generation of cylindrical converging shock waves based on shock dynamics theory

A simple but effective technique is proposed to generate cylindrical converging shock waves. The shock dynamics is employed to design a curved wall profile of the test section in a shock tube. When a planar shock wave propagates forward along the curved wall, the disturbances produced by the curved wall would continuously propagate along the shock surface and bend the shock wave. As an example, the wall profile for an incident shock Mach number of M0=1.2 and a converging angle of 15° is tested numerically and experimentally. Both numerical and experimental results show a perfect circular shock front, which validates our method.

On phase transition in compressible flows: modelling and validation

A physical model for compressible flows with phase transition is described, in which all the processes of phase transition, i.e. nucleation, droplet growth, droplet evaporation and de-nucleation, are incorporated. The model is focused on dilute mixtures of vapour and droplets in a carrier gas with typical maximum liquid mass fraction smaller than 0.02. The new model is based on a reinterpretation of Hills method of moments of the droplet size distribution function. Starting from the general dynamic equation, it is emphasized that nucleation or de-nucleation correspond to the rates at which droplets enter or leave droplet size space, respectively. Nucleation and de-nucleation have to be treated differently in agreement with their differences in physical nature. Attention is given to the droplet growth model that takes into account Knudsen effects and temperature differences between droplets and gas. The new phase transition model is then combined with the Euler equations and results in a new numerical method: ASCE2D. The numerical method is first applied to the problem of shock/expansion wave formation in a closed shock tube with humid nitrogen as a driver gas. Nucleation and droplet growth are induced by the expansion wave, and in turn affect the structure of the expansion wave. When the main shock, reflected from the end wall of the low-pressure section, passes the condensation zone, evaporation and de-nucleation occur. As a second example, the problem of the flow of humid nitrogen in a pulse-expansion wave tube, designed to study nucleation and droplet growth in monodisperse clouds, is investigated experimentally and numerically.

Effects of homogeneous condensation in compressible flows: Ludwieg-tube experiments and simulations

Effects of homogeneous nucleation and subsequent droplet growth in compressible flows in humid nitrogen are investigated numerically and experimentally. A Ludwieg tube is employed to produce expansion flows. Corresponding to different configurations, three types of experiment are carried out in such a tube. First, the phase transition in a strong unsteady expansion wave is investigated to demonstrate the mutual interaction between the unsteady flow and the condensation process and also the formation of condensation-induced shock waves. The role of condensation-induced shocks in the gradual transition from a frozen initial structure to an equilibrium structure is explained. Second, the condensing flow in a slender supersonic nozzle G2 is considered. Particular attention is given to condensation-induced oscillations and to the transition from symmetrical mode-1 oscillations to asymmetrical mode-2 oscillations in a starting nozzle flow, as first observed by Adam & Schnerr. The transition is also found numerically, but the amplitude, frequency and transition time are not yet well predicted. Third, a sharp-edged obstacle is placed in the tube to generate a starting vortex. Condensation in the vortex is found. Owing to the release of latent heat of condensation, an increase in the pressure and temperature in the vortex core is observed. Condensation-induced shock waves are found, for a sufficiently high initial saturation ratio, which interact with the starting vortex, resulting in a very complex flow. As time proceeds, a subsonic or transonic free jet is formed downstream of the sharp-edged obstacle, which becomes oscillatory for a relatively high main-flow velocity and for a sufficiently high humidity.

Parametric study of cylindrical converging shock waves generated based on shock dynamics theory

In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of ...

Experimental investigation of reshocked spherical gas interfaces

The evolution of a spherical gas interface under reshock conditions is experimentally studied using the high-speed schlieren photography with high time resolutions. A number of experimental sets of helium or SF6 bubble surrounded by air for seven different end wall distances have been performed. Distinct flow structures are observed due to the additional vorticity and wave configuration caused by the reshock. In the air/helium case, the deformation of the reshocked bubble is dependent on the development of the penetrating air jet along the symmetry axis of the bubble. In general, two separate vortex rings can be observed, i.e., one develops slowly, and the other approaches and eventually impinges on the shock tube end wall. In the air/SF6 case, two SF6 jets moving in opposite directions are generated and the oscillation of the interface is observed for small end wall distances, while small scale vortex morphologies on the gas interface are found for large end wall distances. The physical mechanisms of the...

Experimental study of Richtmyer-Meshkov instability in a cylindrical converging shock tube

The interaction of a cylindrical converging shock wave with an initially perturbed gaseous interface is studied experimentally. The cylindrical converging shock is generated in an ordinary shock tube but with a specially designed test section, in which the incident planar shock wave is directly converted into a cylindrical one. Two kinds of typical initial interfaces involving gas bubble and gas cylinder are employed. A high-speed video camera combined with schlieren or planar Mie scattering photography is utilized to capture the evolution process of flow structures. The distribution of baroclinic vorticity on the interface induced by the cylindrical shock and the reflected shock from the center of convergence results in distinct phenomena. In the gas bubble case, the shock focusing and the jet formation are observed and the turbulent mixing of two fluids is promoted because of the gradually changed shock strength and complex shock structures in the converging part. In the gas cylinder case, a counter-rotating vortex pair is formed after the impact of the converging shock and its rotating direction may be changed when interacting with the reflected shock for a relatively long reflection distance. The variations of the interface displacements and structural dimensions with time are further measured. It is found that these quantities are different from those in the planar counterpart because of the shock curvature, the Mach number effect and the complex shock reflection within the converging shock tube test section. Therefore, the experiments reported here exhibit the great potential of this experimental method in study of the Richtmyer-Meshkov instability induced by converging shock waves.

A cylindrical converging shock tube for shock-interface studies

A shock tube facility for generating a cylindrical converging shock wave is developed in this work. Based on the shock dynamics theory, a specific wall profile is designed for the test section of the shock tube to transfer a planar shock into a cylindrical one. The shock front in the converging part obtained from experiment presents a perfect circular shape, which proves the feasibility and reliability of the method. The time variations of the shock strength obtained from numerical simulation, experiment, and theoretical estimation show the desired converging effect in the shock tube test section. Particular emphasis is then placed on the problem of shock-interface interaction induced by cylindrical converging shock waves. For this purpose, membrane-less gas cylinder is adopted to form the interface between two different fluids while the laser sheet technique to visualize the flow field. The result shows that it is convenient to perform such experiments in this facility.

GPU accelerated CESE method for 1D shock tube problems

In the present study, a GPU accelerated 1D space-time CESE method is developed and applied to shock tube problems with and without condensation. We have demonstrated how to implement the CESE algorithm to solve 1D shock tube problems using an older generation GPU (the NVIDIA 9800 GT) with relatively limited memory. To optimize the code performance, we used Shared Memory and solved the inter-Block boundary problem in two ways, namely the branch scheme and the overlapping scheme. The implementations of these schemes are discussed in detail and their performances are compared for the Sod shock tube problems. For the Sod problem without condensation, the speedup over an Intel CPU E7300 is 23 for the branch scheme and 41 for the overlapping scheme, respectively. While for problems with condensation, both schemes achieve higher acceleration ratios, 53 and 71, respectively. The higher speedup of the condensation case can be ascribed to the source term calculation which has a local dependence on the mesh point and the SOURCE kernel has a higher acceleration ratio.

On interaction of shock wave with elliptic gas cylinder

The interaction of a planar shock with one elliptic heavy-gas (SF6) cylinder surrounded by air is investigated experimentally. By changing the aspect ratio of the elliptic cylinder, the influence of the initial shape on the evolution of the interface is visualized by a series of dynamic photos utilized by a high-speed camera. It is found that the longer the axis perpendicular to the shock front, the faster and the severer the deformation of the gas cylinder. This can be explained mainly by the different amount of vorticity produced by the misalignment between the density gradient and the pressure gradient. When the vertical axis is much longer than the horizontal axis, the vorticity production is mainly concentrated at the upper and lower corners, which rolls up in time, and results in a structure of big vortex-pair. When the horizontal axis is much longer than the vertical axis, the baroclinic vorticity production distributes at almost every position along the interface, which leads to a faster rolling up of vortices, and even second vortex may develop at later times.Graphical Abstract

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.