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Research Papers: Fundamental Issues and Canonical Flows

# Laser Doppler Velocimetry Measurements in Turbulent Gaseous Mixing Induced by the Richtmyer–Meshkov Instability: Statistical Convergence Issues and Turbulence Quantification

[+] Author and Article Information
Ghazi Bouzgarrou

Institut Supérieur de l'Aéronautique et
de l'Espace (ISAE),
Université de Toulouse,
10 avenue Edouard Belin,
Toulouse 31400, France
e-mail: ghazi.bouzgarrou@isae.fr

Yannick Bury

Institut Supérieur de l'Aéronautique et
de l'Espace (ISAE),
Université de Toulouse,
10 avenue Edouard Belin,
Toulouse 31400, France
e-mail: yannick.bury@isae.fr

Stéphane Jamme

Institut Supérieur de l'Aéronautique et
de l'Espace (ISAE),
Université de Toulouse,
10 avenue Edouard Belin,
Toulouse 31400, France
e-mail: stephane.jamme@isae.fr

Laurent Joly

Institut Supérieur de l'Aéronautique et
de l'Espace (ISAE),
Université de Toulouse,
10 avenue Edouard Belin,
31400 Toulouse, France
e-mail: laurent.joly@isae.fr

Jean-Francois Haas

CEA, DAM,
Arpajon DIF F-91297, France

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 28, 2013; final manuscript received March 24, 2014; published online July 9, 2014. Assoc. Editor: Stuart Dalziel.

J. Fluids Eng 136(9), 091209 (Jul 09, 2014) (12 pages) Paper No: FE-13-1201; doi: 10.1115/1.4027311 History: Received March 28, 2013; Revised March 24, 2014

## Abstract

A statistical characterization of the turbulent flow produced in a vertical shock tube dedicated to the study of the Richtmyer–Meshkov instability (RMI) is carried out using laser Doppler velocimetry (LDV), time-resolved Schlieren images, and pressure histories. The time evolution of the phase-averaged velocity field and the fluctuating velocity levels produced behind the shock wave (SW) are first investigated for different configurations of a pure air homogeneous medium. This allows us to determine the background turbulence of the experimental apparatus. Second, the RMI-induced turbulent air/sulfur hexafluoride ($SF6$) mixing zone (TMZ) is studied both in its early stage of development and after its interaction with a reflected shock wave (RSW) (reshock phenomenon). Here, the gaseous interface is initially produced by a thin nitrocellulosic membrane trapped between two grids. One of the most consistent issues regarding such a process is the generation of a large number of fragments when the incident SW crosses the interface. These fragments are likely to corrupt the optical measurements and to interact with the flow. This work seeks to clarify the influence of these fragments on the statistical determination of the velocity field. In particular, it is shown that statistical convergence cannot be achieved when the fragments are crossing the LDV measurement volume, even if a significant number of identical experiments are superimposed. Some specific locations for the LDV measurements are, however, identified to be more favorable than others in the air/$SF6$ mixing configuration. This finally allows us to quantify the surplus of turbulence induced by the reshock phenomenon.

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## References

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Bouzgarrou, G., Bury, Y., Jamme, S., Joly, L., and Haas, J., 2013, “Experimental Determination of the Growth Rate of Richtmyer–Meshkov Induced Turbulent Mixing After Reshock,” Proceedings of the 29th International Symposium on Shock Waves, Madison, WI, July 14–19.
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## Figures

Fig. 1

Description of the experimental apparatus

Fig. 2

Illustration of the pattern of the initial perturbation

Fig. 3

Schematic (X-t) diagram representative of a homogeneous experiment

Fig. 4

Convergence curves of the first- and second-order statistics at different time steps located between the incident and RSWs, resulting from the cumulation of 40 identical experiments in pure air configuration: (a) mean X-velocity and (b) RMS fluctuating X-velocity

Fig. 5

Evolution of (a) the mean X-velocityU¯, and (b) the RMS fluctuating X-velocityu'2¯ (blue symbols, left vertical axis): Conf1 (upper) and Conf2 (lower). Number of samples used for the calculation of the statistics on each time step of the discretized velocity signal (black dashed line, right vertical axis). The red horizontal line corresponds to the number of samples necessary to obtain convergence. The origin of time on the figure corresponds to the instant of passage t0 of the incident SW on the LDV probe volume at X=43 mm.

Fig. 6

(a) PPT3 static pressure signals (X = 43 mm above the interface) for Conf1 (green) and Conf2 (red) over the whole phenomenon history, and (b) concurrent evolutions of the mean X-velocity (blue symbols) and PPT3 static pressure (red dashed line), enlarged around the velocity plateau between the incident and RSWs for Conf2. The origin of time on the figure corresponds to the instant of passage t0 of the incident SW on the LDV probe volume at X = 43 mm.

Fig. 7

Schlieren images of the perturbations generated by the SW in pure air (Conf1). The black cross on the images indicates the location of the LDV probe volume at X = 43 mm. The origin of time on the figure corresponds to the instant of passage t0 of the incident SW on the LDV probe volume.

Fig. 8

Evolution of (a) the mean X-velocityU¯, and (b) the RMS fluctuating X-velocityu'2¯ (blue symbols, left vertical axis): Conf3. Number of samples used for the calculation of the statistics on each time step of the discretized velocity signal (black dashed line, right vertical axis). The red horizontal line corresponds to the number of samples necessary to obtain convergence. The origin of time on the figure corresponds to the instant of passage t0 of the incident SW on the LDV probe volume at X = 43 mm.

Fig. 9

Schlieren images of the perturbations generated by the SW in the pure air configuration (Conf3). The black cross on the images indicates the location of the LDV probe volume at X = 43 mm. The origin of time on the figure corresponds to the instant of passage t0 of the incident SW on the LDV probe volume. Here, the dark zone corresponds to membrane fragments.

Fig. 10

Schematic (X - t) diagram of an air/SF6 experiment. Except for the previously defined TMZ acronym, the letters W, T, and R used in the acronyms refer to “wave,” “transmitted,” and “reflected,” respectively.

Fig. 11

Illustration of the TMZ evolution (Conf4). The reader can refer to Fig. 10 for the definition of the acronyms.

Fig. 12

Conf4 LDV measurements of the instantaneous (left-hand column) and mean (right-hand column) X - velocityU and U¯ for the three locations (a) X = 43 mm, (b) X = 135 mm, and (c) X = 150 mm. Here, t0 corresponds to the instant of passage of the incident SW on the LDV probe volume. (Left-hand column) green dashed lines correspond to the temporal location of the TMZ. The red dashed lines depict the temporal location of the blackout. (Right-hand column) number of samples used for the calculation of the statistics on each time step of the resampled velocity signal (black dashed line, right vertical axis). The red horizontal line corresponds to the number of samples necessary to obtain convergence.

Fig. 13

Visualization of the ascending TMZ in its early stage of development and of the following membrane fragments (Conf4)

Fig. 14

Experimental (X - t) diagram of an air/SF6 mixing configuration (Conf4) and associated measured (a) fluctuations (m/s) and (b) turbulence intensity (%). The green and purple numbers correspond to statistically converged or indicative values of the turbulence levels, respectively; “n.c.” refers to nonconverged values.

Fig. 15

Illustration of the influence of the nitrocellulosic membrane on the flow. Enlarged view of the TMZ rear-boundary after reshock. In the experiment illustrated in this figure, the upper grid was replaced by a grid of mesh-size 12.1 mm, leading to the generation of large size membrane fragments. All of the other experimental parameters were kept identical to Conf4 parameters.

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