Dynamic characteristic of Converged shock wave and its induced interfacial instability

Student thesis: PhD


When an arbitrarily perturbed interface separating two fluids with different prop- erties is impulsively accelerated by a shock wave, the tiny initial disturbance on the in- terface will grow up and eventually develop into a turbulent mixing state. This distinct hydrodynamic phenomenon is usually called as Richtmyer-Meshkov (RM) instability, which is meaningful for the academic research on hydrodynamic instability, compress- ible turbulent mixing and so on. Besides, it widely exists in lots of engineering appli- cations, including the supernova explosion in large scale and the inertial confinement in small scale. For these great significance, the classical planar RM instability is exten- sively discussed in recent years. However, the physical background of ICF cares more about the interaction of a spherically converging shock wave with a spherically dis- turbed interface, in which the converging RM instability seriously affects the efficiency of focusing on the ignition. Therefore, in order to apply nuclear fusion technology to solve the issue of energy shortage, the direct research on the converging RM instabil- ity is necessary. The converging RM instability has rarely been studied in shock tube circumstance mainly for its difficulties in generation of stable converging shock in lab- oratory conditions. And for its complex mechanism, the converging RM instability has much lesser progress than the planar RM instability. In this work, based on two dif- ferent cylindrically converging shock tubes, which are designed by the shock dynamic method, the cylindrically converging light/heavy single-mode RM instability and the reflection of cylindrical converging shock wave over a plane wedge are studied exper- imentally and numerically. The main work is concluded as follows:
1)In a slender flat cylindrical converging section, which has a converging angle of 15o, the interaction between cylindrical converging shock and several different sinu- soidal disturbed Air/SF6 interfaces are experimentally studied by generating the inter- faces with soap film technique. An undisturbed case is first adopted, showing an evident deceleration phenomenon of the converging interface and revealing the importance of (Rayleigh-Taylor) RT effect in the converging RM instability. Then the disturbed cases verify that the RT stable effect before reshock will decrease the amplitude of disturbance and the RT unstable effect after reshock will promote the occurrence of turbulent mix- ing. Because the pressure on two sides keeps balance during the generation process, the interface has a three-dimensional (3D) minimum feature, and is shown as boundary in- terface and symmetry interface in the schlieren stacked images. A quantitative analysis on the symmetry interface amplitude indicates that, its amplitude orderly goes through a linear growing stage (RM) and a quicker decline stage (RM-RT) before reshock. The discrete Fourier transform is adopted to calculate the 3D theoretical linear growth rate in the first stage, fitting well with the experiments. In the second stage, the long-term ef- fect of the RT stabilization even leads to a phase inversion on the inner interface before the reshock when the initial interface has sufficiently small perturbations. The three- dimensional effect is believed to facilitate the occurrence of this RT phase inversion (RTPI).
2)Then, in order to further study the RTPI phenomenon of converging light/heavy RM instability first found in the experiment, a series of two-dimensional (2D) simula- tions are carried out by 2D upwind CE/SE method. It is found that, in a special azimuthal wave number, smaller initial amplitude will lead to RTPI but larger one will not. An u- nique medium critical state is found between them, accompanied with the appearance of frequency doubling feature,which is caused by nonlinear frequency doubling mech- anism. After finding different critical initial amplitudes for different azimuthal wave numbers, the critical line is acquired. A frequency-truncation phenomenon is found on the critical line: if the azimuthal wave number is smaller than a certain value, no matter how much the initial amplitude is, the RTPI can not happen. This frequency-truncation phenomenon is well predicted by employing Bell’s models. Then the influence of sev- eral physical parameters on the critical line is studied, showing significant correlation with the Atwood number, Mach number and converging radius. This parametric s- tudy indicates that the occurrence of RTPI needs long converging section, high Atwood number and low Mach number, helps explaining why the RTPI has not been found in previous research,.
3)In a slender flat cylindrical converging section, with a converging angle of 25o, the cylindrical converging shock reflection over a plane wedge is investigated experi- mentally and numerically by embedding several wedges with different obliquities in the converging section. The numerical results are in good agreement with the experimen- tal results, both showing different wave structures at different initial incident angles. The smaller initial incident angle leads to whole Regular reflection (RR) process on the wedge, while the bigger initial incident angle leads to whole Mach reflection (MR) process on the wedge. However, the incident angle decreases as the shock converging to the wedge, providing the possibility of wave transition (DiMR→InMR→TRR) in an appropriate medium initial incident angle. Based on the CCW relation, the location of converging shock is captured to calculate the time-varying Mach number, incident angle, detachment criteria angle and von Neumann criteria angle. It is found that, when the initial incident angle locates during a certain range, the wave transition phenomenon can occur on the wedge. The detachment criteria is verified to predict initial reflection type well, i.e., RR or MR, but it fails for the prediction of the continuous transition, i.e., DiMR→InMR. When the initial incident angle is relatively bigger during this range, a hysteresis process is found in the MR→TRR transition and becomes more apparent due to the unsteady effect, and MR is found to persist slightly below the mechanical equilibrium condition.
Date of Award8 Oct 2017
Original languageEnglish
Awarding Institution
  • University of Science and Technology of China
SupervisorXisheng Luo (Chief supervisor), Zhigang Zhai (Co-supervisor) & Chih-yung Wen (Co-supervisor)


  • converging RM instability
  • RT phase inversion
  • critical line
  • frequency truncation
  • converging shock reflection

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