Shock-induced multi-mode, multi-layer and multi-phase interface evolution

Student thesis: PhD


Richtmyer-Meshkov (RM) instability occurs when an initial perturbed interface separating different materials is impacted by an impulsive acceleration (e.g. shock wave), later the interface perturbation grows and eventually the whole interface lay- er transits to the turbulence. RM instability plays an important role in a wide range of applications, such as the inertial confinement fusion (ICF), the supernova explosion and the scramejet engine, etc. Besides, RM instability is a significant academic object in studying the gas dynamics, the vortex dynamics and the turbulence. RM instability has attracted lots of attention around the world, such as the Lawrence Livermore National Laboratory and the Los Alamos National Laboratory in the U.S.A., the Commissari- at a l’Energie Atomique Laboratory in France and the China Academy of Engineering Physics in China, etc. In the previous research on RM instability, the single-mode RM unstable interface evolution attracted most attention because of the simplest mathematic pattern of a cosine wave. However, in the applications, the initial interface perturba- tion is always random, i.e. multi-mode. But the dependence of a multi-mode interface evolution on the initial spectrum has not been fully understood yet. In addition, the ICF capsules consist of multiple layers of different materials in a spherical geometry. But there were few research on the interface coupling mechanism and the waves’ effect in- volved in the multi-layer RM unstable systems. What’s more, the ICF capsules consist of materials of different phases, including solid, liquid, gas and plasma, etc. But the RM instability on the multi-phase system has been scarcely investigated. In the present study, we separately investigate the RM instability coupled with multi-mode perturba- tion, multi-layer configuration and multi-phase system with experiments, simulations and theoretical analyses.
First of all, the shape controllable quasi-two-dimensional single-mode perturbation interface and quasi-single-mode perturbation interface were generated with the extend- ed soap film technique. Shock-tube experiments on the single-mode interface evolu- tion and quasi-single-mode interface evolution were performed. It was found that the quasi-single-mode is dominated by only one mode and the mode-competition effect can be ignored in the weakly nonlinear stage. Here, a simple nonlinear theory was estab- lished for predicting the quasi-single-mode interface amplitude growth by summing the amplitude growth of finite number of the constituted modes. More constituted modes needed in the sum to match the experiment indicates the more pronounced deviation of the quasi-single-mode interface shape from a single-mode one. Next, the evolu- tion of a quasi-single-mode interface without or with non-periodic portions impacted by a shock wave was experimentally investigated. It was found that the non-periodic portion significantly changes the balanced position of the initial interface perturbation, and which therefore influences the ratios of the spike width to the bubble width. As a result, the non-periodic portion influences the whole interface perturbation growth. Later, the evolution of a complicated multi-mode perturbation interface consisted by multiple dominated modes induced by a shock wave was investigated. By considering both the mode-competition mechanism and nonlinear effect, a universal nonlinear the- ory for predicting the time variant each mode amplitude growth and total mixing width growth was established, and which was validated with our well-designed shock-tube experiments and the data extracted from literature.
Second, RM instability of a heavy gas layer was experimentally investigated. Us- ing the extended soap film technique, five kinds of gas layer with two sharp interfaces were generated such that the perturbation growth on each interface was concerned. It was found that both the interface-coupling effect and the wave’s effect obviously influ- ence the two interface perturbation growth. It was the first time to quantify the addi- tional Rayleigh-Taylor (RT) instability induced by the rarefaction waves in a heavy gas layer evolution. Besides, the interfacial instability induced by rarefaction waves on a heavy/light interface was numerically investigated. The RT instability and the equiv- alent RM instability induced by rarefaction waves were separately well predicted by modifying the nonlinear models previously proposed with the consideration of the vari- able acceleration and the growth rate transition from RT instability to RM instability.
Third, the interaction of a shock wave and a droplet embedded with a vapor cavity was first experimentally studied. The vapor cavity inside a droplet was generated by depressurising the surrounding air to the saturation pressure in the test section of a shock tube. Both the relative size and position of the vapor cavity to the droplet influence the deformation of both the vapor cavity and the droplet. The phase change accelerates the droplet breakup. We clearly captured the transverse jet induced by RM instability and other mechanisms. We also proposed a modified Rayleigh-Plesset equation to predict the cavity-collapse within the finite volume of a droplet.
Last, the nonuniform strength of lasers utilized in driving ICF leads to initial rip- pled shock wave. In the present study, a rippled shock wave induced non-standard RM instability was experimentally investigated. Here, a rippled shock wave was generated by a planar shock wave diffracting solid cylinders. And the evolution of an unperturbed interface induced by a rippled shock wave was concerned and a modified linear theory was established to quantify the non-standard RM instability.
Date of Award31 May 2020
Original languageEnglish
Awarding Institution
  • University of Science and Technology of China
SupervisorXisheng Luo (Chief supervisor), Zhigang Zhai (Co-supervisor) & Chih-yung Wen (Co-supervisor)


  • Richtmyer-Meshkovinstability
  • multi-mode
  • multi-phase
  • multi-layer
  • shock- tube experiment

Cite this