The time evolution of the width of the turbulent mixing zone arising from the late development of Richtmyer-Meshkov instability is investigated in this work. This is achieved by means of the analysis of time-resolved Schlieren images obtained with a given set of shock-tube experiments. The post-reshock growth rate of the mixing zone width is found to be nearly insensitive to the development state of the mixing at the time of reshock

Bouzgarrou, Ghazi

Bury, Yannick

Haas, Jean-François

Jamme, Stéphane

Joly, Laurent

English

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 To cite this document: Bouzgarrou, Ghazi and Bury, Yannick and Jamme, Stéphane and Joly, Laurent and Haas, Jean-François Experimental determination of the growth rate of Richtmyer-Meshkov induced turbulent mixing after reshock. (2013) In: 29th International Symposium on Shock Waves - ISSW29, 14-19 Jul 2013, Madison, USA. Open Archive Toulouse Archive Ouverte (OATAO)  OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.  This is an author-deposited version published in: http://oatao.univ-toulouse.fr/  Eprints ID: 9282 Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@inp-toulouse.fr  Experimental determination of the growth rateof Richtmyer-Meshkov induced turbulentmixing after reshockG. Bouzgarrou1, Y. Bury1, S. Jamme1, L. Joly1, and J.-F. Haas21 IntroductionThe Richtmyer-Meshkov Instability (RMI) develops when a shock wave impul-sively accelerates an initially perturbed interface between two gases of differentdensity, promoting their mixing inside a delimited zone, hereafter denoted the mix-ing zone (MZ). This mixing is a key issue for inertial confinement fusion process.It also finds applications in many different scientific and engineering issues, e.g. insupernova explosion or supersonic combustion [1]. In the context of inertial con-finement fusion, the characterization of the RMI-induced mixing zone initiated bya shock and further amplified by a reshock is largely based on the temporal evolu-tion of integral parameters such as the width of the MZ. This is classically achievedthrough shock tube experiments involving the time-resolved acquisition of Schlierenimages. From the initial shock/interface interaction, the global evolution of the MZgrowth rate is found to experience a succession of five consecutive phases: 1) lin-ear increase, 2) asymptotic increase, 3) strong decrease (recompression of the MZinduced by the reshock), 4) linear increase, 5) asymptotic increase.Among the various studies focusing on this topic [2, 3], recent works have ex-plored the dynamics of a RMI-initiated MZ with a reshock. In their study aboutthe growth rate evolution of the mixing zone consecutive to a reshock [4], Leinovand co-authors report that the post reshock growth rate, corresponding to the fourthphase, is largely independent of pre reshock conditions. These results differ fromthose obtained by Counilh et al. [5], where the mixing width after reshock is foundto depend on pre reshock conditions. Since these various results were obtained viadifferent post processing strategies of Schlieren images, one can thus question therelevance of a specific post processing methodology in the determination of themixing dynamics.1Universite´ de Toulouse, ISAE, 10 Avenue Edouard Belin, F-31055 Toulouse, France · 2CEA, DAM,DIF, F-91297 Arpajon, FranceIn an attempt to unravel this question, we propose to analyze a given set of shocktube experiments using various image processing algorithms in order to analyse thebehaviour of the MZ growth rate after reshock.2 Experimental set-upThe experimental apparatus used in this study consists of a 5m long, 130mm squarecross section vertical shock tube. A schematic of the experimental setup is givenin figure 1(a). An incident Mach 1.2 shock wave is generated by impacting a My-lar diaphragm, initially separating the driven and the driver sections of the shocktube, using a blade cutting device. The shock wave travels upward and crosses anair/sulphur hexafluoride (SF6) interface, which sets the Atwood number at 0.67.Both gases are initially separated by a thin nitrocellulosic membrane (0.5µm thick)trapped between two square-meshed grids. The lower grid ensures the mechanicalresistance of the membrane under hydrostatic pressure of the heavy gas. The up-per grid imposes a three-dimensional initial perturbation of wavelength equal to itsmesh size. Pressure histories of the flow in the shock tube are obtained using fivepiezoelectric pressure transducers. The acquisition frequency is fixed to 2.5 MHz.The incident Mach number is determined via the two pressure transducers PPT1and PPT2, located at 315 and 115mm below the interface respectively. In the testsection, two additional pressure transducers PPT3 and PPT4 are flush-mounted at43 and 213mm above the interface respectively. A fifth pressure transducer PPT5is flush-mounted on the endwall of the test section. Time-resolved Schlieren visu-alizations are recorded thanks to a high-speed Phantom V12 camera. The data rateof the image recording is fixed to 27000 images per second with a spatial resolutionequal to 512×384 pixels2.Several configurations are considered in order to analyze the interaction of areshock with a MZ at different stages of its development (see (X − t) diagram onfigure 1(b)). To this avail two parameters, driving the spatio temporal evolution ofthe MZ, are considered: the length of the test section, hereafter denoted L, whichfixes the arrival time of the reshock on the travelling mixing zone, and the wave-length of the initial perturbation (imposed by the upper grid mesh size), hereafterdenoted λ . For convenience of reference, each experiment is referenced as CλL , basedon the values of L and λ . As such a first set of experiments C1.8L is conducted, whereL is varied from 100 to 300mm, in steps of 50mm, for an upper grid mesh sizeof λ = 1.8mm. This set of experiments is complemented with a second serie ofexperiments C12.1L , for which a λ = 12.1mm initial perturbation is considered forL = 250mm and L = 300mm. The temporal evolution of the MZ width, before andafter its interaction with the reshock, is investigated through the analysis of post-processed Schlieren images, following specific filtering algorithms detailed in thenext section.(a) (b)Fig. 1 Description of the experimental apparatus (a) and (X-t) diagram of the experiment (b).Letters W, T and R used in the acronyms refer to ‘wave’, ‘transmitted’ and ‘reflected’ respectively.3 Image processing methodologyTwo distinct image post-processing algorithms have been developped in order to de-tect the MZ boundaries, based on spatial or frequential filtering techniques respec-tively. The spatial-based filtering approach decomposes into first, a median-filteringof the raw images, second an Otsu binarization and last an edge-based segmentationmethod (Canny filter) displaying the boundaries of the MZ. The frequency-basedfiltering approach consists in first, applying a 2D Fast Fourier Transform (FFT) onthe raw images, second high-pass filtering the previously transformed images in or-der to eliminate the low frequency components of the image associated with thehomogeneous zones, last applying the inverse FFT, revealing the boundaries of theMZ.Once the boundaries of the MZ have been revealed by these two approaches, aregion of interest (ROI) is then selected around the MZ inside each image, near thecenter of the tube in order to get rid of wall effects. For each column of the ROI, twopixels can be found as the boundaries, one on each side of the MZ. Therefore, thelocal width of the MZ in each column is obtained by subtracting the X−coordinateof these two pixels. The overall width of the MZ is finally determined by averagingall the widths of the MZ obtained in all the columns of the ROI.As an illustration figure 2 shows the boundaries of the mixing zone as detected bythe spatial and frequential filters respectively, before and after reshock. It has to benoticed that the spatial filter is found to be more sensitive to the transient presence,near the MZ, of spurious waves or membrane fragments that limit its efficiencyin retrieving continuous boundaries on the whole history of the phenomenon (notillustrated here).(a) (b)Fig. 2 Schlieren images of the MZ at different instants for L = 250mm. Colored lines illustratethe boundaries obtained from (a) spatial algorithm, (b) frequential algorithm. Upper line: beforereshock; lower line: after reshock.(a) (b)Fig. 3 Temporal evolution of the MZ width obtained with spatial (−∗−) and frequential (−◦−)filters for λ = 1.8mm. (a) L = 250mm, (b) L = 300mm. Symbols: measurements. Solid lines:tendency curves.Figure 3 presents the temporal evolution of the MZ width for cases C1.8250 andC1.8300. It shows that analogous evolutions of the MZ thickness are obtained from bothspatial and frequential post processing algorithms. Similar growth rate evolutionsare also observed when applying these two approaches for all the other consideredcases. However, due to the previously mentioned robustness issues of the spatialfilter, the latter provides a limited number of measurement points in comparisonwith the frequential one. As such and for sake of conciseness the analysis will thushereafter be limited to the frequential filter.4 Results and discussionFigure 4 illustrates the topology of the MZ before its interaction with the reshock,for L = 300mm and for λ = 1.8mm (a) and λ = 12.1mm (b). Figure 5 summarizesthe temporal evolution of the MZ width for experiments C1.8L and C12.1L .Figure 4 clearly shows that the global shape of the MZ is affected by the wave-length of the initial perturbation. Indeed, just before reshock and contrary to thecase C1.8300, the MZ that develops in case C12.1300 depicts large corrugations on its upperboundary and spikes on its lower boundary. This emphasizes the influence of thewavelength of the initial perturbation on the topology of the MZ.(a) (b)Fig. 4 Schlieren images of the MZ just before reshock for L = 300mm. (a) λ = 1.8mm, (b) λ =12.1mm.(a) (b)Fig. 5 Temporal evolution of the MZ width obtained with the frequential filter for (a) λ = 1.8mm,L = − ⊲− 100, −△− 150, −⋄− 200, −− 250 and −◦− 300mm ; (b) L =300mm, −− λ =1.8mm, −− λ = 12.1mm. Symbols: measurements. Solid lines: tendency curves interrupted atthe time of the interaction between the reshocked MZ and RW.As expected, the analysis of figure 5(a) reveals that the temporal evolution of theMZ width, obtained before reshock for the different values of L considered in casesC1.8L , obeys a similar assymptotic trend until the MZ interacts with the reshock. In-deed as L is increased, the reshock occurs at different development times of the MZ,imposing a greater or lesser MZ width at the time of reshock, comprised betweenh = 10mm for L = 100mm and h = 14mm for L = 300mm. In addition the influ-ence of the wavelength of the initial perturbation (λ = 1.8mm v.s. λ = 12.1mm forL = 300mm), illustrated in figure 5(b) imposes slightly different assymptotic lawsof the MZ width temporal evolution, leading to a larger MZ at the time of reshockwhen the wavelength is larger. Moreover and as previously evoked, the global topol-ogy of the MZ in case C12.1300 is also quite different from the case C1.8300.Despite those differences it is remarkable to note that, independently of either thedevelopment state of the MZ (figure 5(a)) or the wavelength of the initial perturba-tion (figure 5(b)), the reshock causes the compression of the MZ to a fairly uniquewidth of h = 7mm.After the reshock, the evolution of the MZ width fits a similar trend for all thecases C1.8L and C12.1L . It initially experiences a linear growth rate, between t = 0msand t = 0.15ms, characterized by a slope close to dh/dt ≈ 21m/s. It should benoticed that this value is in good accordance with the empirical law defined by [6].The post reshock evolution of the width of the MZ thus appears to be only weakly,if not, affected by its prior-to-reshock history. For subsequent instants the growthrate tends to decrease. However it is no more possible to determine a meaningfulassymptotic analytical law since the expansion waves reflected from the endwall,referred to as RW on the (X − t) diagram (figure 1(b)), quickly interacts with thereshocked MZ (about 1ms after the reshock for L = 300mm).AcknowledgmentsThis work is supported by CEA, DAM, DIF under grant number 09-37-C-SACO.References1. Brouillette M. : The Richtmyer-Meshkov instability. Annu. Rev. Fluid Mech. 34, pp. 445-468(2002)2. Vetter M., Sturtevant B. : Experiments on the Richtmyer-Meshkov instability of an air/SF6interface. Shock Waves. 4, pp. 247-252 (1995)3. Erez L., Sadot O., Oron D., Erez G., Levin L.A., Shvarts D., Ben Dor G. : Study of themembrane effect on turbulent mixing measurements in shock tubes. Shock Waves. 10, pp.241-251 (2000)4. Leinov E., Malamudi G., Elbaz Y., Levin L., Ben-Dor G., Shvarts D. and Sadot O. : Ex-perimental and numerical investigation of the Richtmyer-Meshkov instability under re-shockconditions. J. Fluid Mech. 626, pp. 449-475 (2009)5. Counlih, D., Haas, J.F., Schwaederle´, L. : Measurements of turbulent mixing within an air/SF6shocked and re-shocked interface. In 10th International Workshop on the Physics of Com-pressible Turbulent Mixing, Paris, France (2006)6. Mikaelian K.O. : Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkovinstabilities. Physica D. 36, pp. 343-57 (1989)

Counlih,D.,Haas,J.F.,Schwaederl´ e,L.:Measurementsofturbulentmixingwithinanair/SF6 shocked and re-shocked interface.

Experimental and numerical investigation of the Richtmyer-Meshkov instability under re-shock conditions.

Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface.

Study of the membrane effect on turbulent mixing measurements in shock tubes.

The Richtmyer-Meshkov instability.

Turbulent mixing generated by Rayleigh-Taylor and Richtmyer-Meshkov instabilities.

Experimental determination of the growth rate of Richtmyer-Meshkov induced turbulent mixing after reshock

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Experimental determination of the growth rate of Richtmyer-Meshkov induced turbulent mixing after reshock

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