G. Jourdan

Experimental study on a plane shock wave accelerating a gas bubble

A detailed experimental study of the interaction between a planar shock wave and an isolated spherical gas inhomogeneity is presented here. Different configurations have been considered: a shock wave moving from one gas into another, of similar density, lower density and one of higher density. Sequences of shadowgraph pictures obtained during the same run provided useful insights into several mechanisms such as shock wave reflection, refraction and focusing, distortion of the bubble interface, and vortex formation. Based on these sequences, the changes with time in the characteristic bubble sizes were plotted and the results showed that the influence of the shock wave Mach number is significantly greater in the case of light gas bubbles. The displacement of the inhomogeneity relative to the surrounding gas was determined and compared to Rudinger and Somers’ model. In all the cases studied, although the measurements were found to agree well with the theoretical predictions, in the initial acceleration phas...

Drag coefficient of a sphere in a non-stationary flow: new results

The drag coefficient of a sphere placed in a non-stationary flow is studied experimentally over a wide range of Reynolds numbers in subsonic and supersonic flows. Experiments were conducted in a shock tube where the investigated balls were suspended, far from all the tube walls, on a very thin wire taken from a spider web. During each experiment, many shadowgraph photos were taken to enable an accurate construction of the spheres trajectory. Based on the spheres trajectory, its drag coefficient was evaluated. It was shown that a large difference exists between the sphere drag coefficient in steady and non-steady flows. In the investigated range of Reynolds numbers, the difference exceeds 50%. Based on the obtained results, a correlation for the non-stationary drag coefficient of a sphere is given. This correlation can be used safely in simulating two-phase flows composed of small spherical particles immersed in a gaseous medium.

Experimental investigation of the shock wave interaction with a spherical gas inhomogeneity

The interaction of a shock wave with a spherical gas inhomogeneity (soap bubble) is experimentally investigated using a high speed camera shadowgraph diagnostic. Negative, close to zero, and positive density jumps across the bubble interface are studied for weak incident shock waves. For each case, the bubble length and height evolutions have been determined, as well as the generated vortex diameter and pair spacing from only one run. We point out that in all cases, after the shock bubble compression phase, the bubble and surrounding gaseous mixing length is linear with time.

An experimental and numerical investigation of the dependency on the initial conditions of the Richtmyer-Meshkov instability

The nonlinear evolution of 2D single-mode Richtmyer-Meshkov instabilities is investigated through experiments in shock tube and numerical simulations. In our shock tube, the interface is materialized by a thin membrane attached to a stereo-lithographed grid. The purpose of this study is to compare experimental and numerical results, verify that using a higher Mach number for the incident shock wave (Misw) than in a previous study [C. Mariani, M. Vandenboomgaerde, G. Jourdan, D. Souffland, and L. Houas, “Investigation of the Richtmyer-Meshkov instability with stereolithographed interfaces,” Phys. Rev. Lett. 100, 254503 (2008)] drastically reduces the deleterious effects of the membrane remnants, explore the effect of a high initial amplitude at the interface on the growth of the perturbation, and understand the lack of roll-up structures in the nonlinear phase of the instability. Using grayscale gradient rather than gray level, a new processing of the raw pictures is developed. Numerical simulations run wi...

Experimental investigation of the propagation of a planar shock wave through a two-phase gas-liquid medium

We conducted a series of shock tube experiments to study the influence of a cloud of water droplets on the propagation of a planar shock wave. In a vertically oriented shock tube, the cloud of droplets was released downwards into the air at atmospheric pressure while the shock wave propagated upwards. Two shock wave Mach numbers, 1.3 and 1.5, and three different heights of clouds, 150 mm, 400 mm, and 700 mm, were tested with an air-water volume fraction and a droplet diameter fixed at 1.2% and 500 mu m, respectively. From high-speed visualization and pressure measurements, we analyzed the effect of water clouds on the propagation of the shock wave. It was shown that the pressure histories recorded in the two-phase gas-liquid mixture are different from those previously obtained in the gas-solid case. This different behavior is attributed to the process of atomization of the droplets, which is absent in the gas-solid medium. Finally, it was observed that the shock wave attenuation was dependent on the exchange surface crossed by the shock combined with the breakup criterion

Hot-wire method for measurements of turbulent mixing induced by Richtmyer-Meshkov instability in shock tube

Abstract. A constant temperature hot-wire anemometry method is applied to the study of mixing zones induced by the interaction of a shock wave with Mach number 1.25 in air with air/helium (heavy/light), air/argon or air/krypton (light/heavy) initially plane interfaces. The single wire gauge is positioned at various locations along the shock tube axis. At the present stage of our investigation, although the analysis of the hot-wire signal is not achieved yet, we report the interesting concept of using hot-wire anemometry as a diagnostic method for shock tube studies of the Richtmyer-Meshkov instability. Based on this preliminary work, we discuss prospective experimental signal conversion, in order to provide some new results for this field of investigation, in particular for resolving characteristics of the turbulent mixing zone which is of most interest.

Shock induced Richtmyer-Meshkov instability in the presence of a wall boundary layer

An experimental investigation on gaseous mixing zones originated from the Richtmyer-Meshkov instability has been undertaken in a square cross section shock tube. Mass concentration fields, of one of the two mixing constituents, have been determined within the mixing zone when the shock wave passes from the heavy gas to the light one, from one gas to an other of close density, and from the light gas to the heavy one. Results have been obtained before and after the coming back of the reflected shock wave. The diagnostic method is based on the infrared absorption of one of the two constituents of the mixing zone. It is shown that the mixing zone is strongly deformed by the wall boundary layer. The consequence is the presence of strong gradients of concentration in the direction perpendicular to the shock wave propagation. Finally, it is pointed out that the mixing goes more homogeneous when the Atwood number tends to zero.

MODELING OF RICHTMYER-MESHKOV INSTABILITY-INDUCED TURBULENT MIXING IN SHOCK-TUBE EXPERIMENTS

A turbulence transport model for the analysis of shock interface interaction-induced turbulent mixing is presented. Results given by the one-dimensional (1-D) version of this model are compared with data obtained in shock-tube experiments. Calibrations are made from an air/He interface destabilized by a 1.3 incident shock wave Mach number, taking into account the successive interactions with the different reshocks on the shock tube end wall. Then, using the same set of model constants, different gas pairs with both various Atwood and incident shock wave Mach numbers are considered, in order to point out the influence of these main parameters on the results. Mixing zone thickness time evolutions and 1-D density profiles are presented and directly compared with experimental results. Profiles of other variables such as the space integral of the turbulent kinetic energy ∫k dx, translation energy ∫ρux2 dx, and the ratio ∫ρk dx/∫ρux2 dx, given by the computations, are also shown. Using two different initializat...

Modelling spherical explosions with turbulent mixing and post-detonation

This paper addresses post detonation modelling in spherical explosions. One of the challenges is thus related to compressible turbulent mixing layers modelling. A one-dimensional flow model is derived consisting in a reduced two-phase compressible flow model with velocity drift. To reduce the number of model parameters, the stiff velocity relaxation limit is considered. A semi-discrete analysis is used resulting in a specific artificial viscosity formulation embedded in the diffuse interface model of Kapila et al. [Phys. Fluids 13(10), 3002–3024 (2001)]10.1063/1.1398042. Thanks to the velocity non-equilibrium model and semi discrete formulation, the model fulfils the second law of thermodynamics in the global sense and uses a single parameter. Multidimensional mixing layer effects occurring at gas-gas unstable interfaces are thus summarized as artificial viscosity effects. Models predictions are compared against experimental measurements of mixing layer growth in shock tubes at moderate initial pressure ...

Study of the Interaction between a Shock Wave and a Cloud of Droplets

The pressure histories obtained when a shock wave propagates into an air-solid particle medium is well known: the overpressure jump decreases, as the shock wave propagates into the mixture and is followed by a pressure build-up corresponding to the velocity relaxation processes. In the present paper, an air-water droplet mixture interacting with a shock wave has been studied and the comportment of the pressure traces was found significantly changed in comparison to the interaction with a air-solid particle mixture. This is attributed to the ability of the droplets to deform and fragment into finer ones. This phenomenon, known as secondary atomisation, widely reviewed by Gelfand[1] and by Guildenbecher[2], affects both the pressure histories and the impulse induced by the shock wave. We have previously studied the influence of the height of cloud of droplets on shock wave propagation [3]. In the present work, we focus our attention on the influence of the droplet diameter on the attenuation of shock wave propagating into the air-water mixture. Moreover, predictions obtained by 1D numerical simulations are compared to the experimental results. The necessity to introduce a secondary atomisation model to fit the experimental behaviour is then underlined.