Dense particle cloud dispersion by a shock wave

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<ul><li><p>Shock WavesDOI 10.1007/s00193-013-0432-0</p><p>ORIGINAL ARTICLE</p><p>Dense particle cloud dispersion by a shock wave</p><p>M. Kellenberger C. Johansen G. Ciccarelli F. Zhang</p><p>Received: 30 July 2012 / Revised: 7 February 2013 / Accepted: 8 February 2013 Springer-Verlag Berlin Heidelberg 2013</p><p>Abstract A dense particle flow is generated by the interac-tion of a shock wave with an initially stationary packed granu-lar bed. High-speed particle dispersion research is motivatedby the energy release enhancement of explosives containingsolid particles. The initial packed granular bed is producedby compressing loose powder into a wafer with a particlevolume fraction of p = 0.48. The wafer is positioned insidethe shock tube, uniformly filling the entire cross-section. Thisresults in a clean experiment where no flow obstructing sup-port structures are present. Through high-speed shadowgraphimaging and pressure measurements along the length of thechannel, detailed information about the particle shock inter-action was obtained. Due to the limited strength of the inci-dent shock wave, no transmitted shock wave is produced.The initial solid-like response of the particle wafer accel-eration forms a series of compression waves that eventuallycoalesce to form a shock wave. Breakup is initiated along theperiphery of the wafer as the result of shear that forms due tothe fixed boundary condition. Particle breakup is initiated bylocal failure sites that result in the formation of particle jets</p><p>Communicated by O. Igra.</p><p>The paper was based on work that was presented at the 28th InernationalSymposium on Shock Waves, 1722 July 2011, Manchester, UK.</p><p>M. Kellenberger (B) G. CiccarelliMechanical and Materials Engineering, Queens University,Kingston, ON K7L 3N6, Canadae-mail: kellenbergerm@me.queensu.ca</p><p>C. JohansenMechanical and Manufacturing Engineering,University of Calgary, Calgary, AB T2N 1N4, Canada</p><p>F. ZhangDefense Research and Development Canada-Suffield,Medicine Hat, AB T1A 8K6, Canada</p><p>that extend ahead of the accelerating, largely intact, wafercore. In a circular tube, the failure sites are uniformly dis-tributed along the wafer circumference. In a square channel,the failure sites, and the subsequent particle jets, initiallyform at the corners due to the enhanced shear. The waferbreakup subsequently spreads to the edges forming a highlynon-uniform particle cloud.</p><p>Keywords Dispersion Particle Shock tube</p><p>1 Introduction</p><p>The study of particle cloud dispersion by a shock wave isimportant to many applications. For example, the propaga-tion of shock wave through a dusty gas has been studied formany years [1]. In these studies, the particle volume fractionis insignificant and the particle acceleration can be modeledusing simple drag correlations based on a solid sphere in aninfinite fluid medium. A modern application includes mul-tiphase explosives that compose of a condensed explosivesurrounded with packed micrometric reactive metal parti-cles. The particle dispersion in this application is very com-plicated as the particle flow interaction transitions throughmultiple regimes, each requiring a different treatment. Thesolid volume fraction, p, of the flow is used to identify theregimes [2]. In a granular bed (p &gt; 0.5), forces are alsoexerted through direct contact of the closely packed particles.In a dilute gas-solid flow (p &lt; 0.01), the effects of parti-cle collisions become negligible. Between these two regimesis a dense gas-solid flow (0.1 &lt; p &lt; 0.5). Detonation ofthe explosive generates a shock wave which accelerates andcompacts the particles, and when the shock reaches the parti-cle layer outer boundary, a reflected expansion wave furtheraccelerates the particles. The shock wave initially propagates</p><p>123</p></li><li><p>M. Kellenberger et al.</p><p>through a granular particle bed, and much later after the pas-sage of the shock wave, the particles are further dispersed bythe radial combustion product flow forming a cloud. In thisapplication, it is important to understand the dispersion of theparticles as the energy release from the particles maintainsthe pressure in the shock sphere, thereby increasing the shockwave impulse [3]. The particle dispersion phenomenon variesfrom early time when the particle volume fraction is large, tolater time where the volume fraction is very small and the flowis considered a dilute gas-solid flow, i.e., similar to a dusty-gas flow. The particle dispersion phenomenon responsiblefor very late time dispersion has been studied extensively inthe past and is relatively well understood. However, for theearly time dispersion of a granular bed, as the particle cloudexpands, a dense gas-solid flow exists which has not receivedmuch attention and is not very well understood [2].</p><p>Reactive multiphase flow models have been used to sim-ulate the acceleration and dispersion of the particle cloudthat occurs in multiphase explosives [4]. The fidelity of thesimulations is severely limited by the physical drag modelsthat take into account the interactions in the dense gas-solidflow [2]. In order to develop an accurate particle drag modelthat describes particle acceleration in the dense flow regime,representative experimental data need to be generated. Large-scale experiments have been carried out with spherical multi-phase explosive charges to visualize the global particle clouddispersion [5]. Controlled shock wave experiments are nec-essary to gain understanding of the fundamental physics ofthe dense supersonic gas-solid flow interactions and obtainquantitative data concerning the particle cloud dispersion.Shock tube experiments have been carried out in the pastbut typically the particle suspension method influences theshock flow [4], and the particle size is not typical of mul-tiphase explosives. Recently, shock tube experiments werecarried out by Wagner et al. [6] looking at the interaction ofa shock wave and a gravity-fed particle curtain. The roughly3 mm thick particle curtain, consisting of 100 m sized sodalime particles, had an estimated particle volume fraction ofp = 0.15, which is in the dense gas-solid flow regime.Schlieren photography was used to visualize the interac-tion of the particle curtain with 1.67 and 1.95 Mach num-ber shocks. The dispersion was characterized by tracking thedownstream and upstream edges of the particle cloud. Thevideos show that the interaction of the shock wave with theparticle curtain produces a transmitted and reflected shock</p><p>wave. Immediately following the shock interaction, the parti-cle cloud accelerates and grows axially. The cloud dispersionwas found to be exactly the same for both shock strengthstested. The particle curtain only extended 87 % of the full76 mm width of the channel. As will be discussed later, thegap between the particle curtain and the shock channel glassside-wall is necessary to prevent sticking of the particles andthe subsequent obscuring of the cloud upstream edge. Thedrawback is that the gaps on either side of the curtain intro-duce three-dimensional effects. For example, diffraction ofthe incident shock wave past the gap shows up as thickeningof the shock wave in the schlieren image [6].</p><p>This paper reports on shock tube experiments lookingat the acceleration and dispersion of 100 m-sized alu-minum oxide particles [7]. By pure coincidence, the experi-mental conditions are very similar to those of the Wagneret al. experiment, i.e., similar shock tube cross-sectiondimensions, shock wave strength, and particle size. The maindifference between the experiments is in the initial particlecloud volume density. The novel feature of the present exper-iments is the initial configuration of the particles in the formof a free-standing wafer covering the entire shock tube cross-section. This method allows absolute control over the initialparticle distribution without the use of flow obstructing struc-tures.</p><p>2 Experimental setup</p><p>The shock tube consists of a 1.96-m long, 10-cm diameterdriver, a transition section, and a driven section consisting offive 0.6 m long, 7.6 cm square sections as shown in Fig. 1. Thetransition section is 0.75 m long. Some experiments used a6.99-cm inner-diameter acrylic tube inserted into the channelto obtain a circular cross-section. A double diaphragm isused to precisely control the driver pressure at the time ofdiaphragm rupture. Helium (298 K) is used in the driver andatmospheric air is used in the driven section. Piezoelectricpressure transducers are flush-mounted on the top surface ofthe driven section, see Table 1 for transducer locations. Oneof the driven section channel segments is equipped with glasswindows for flow visualization. A single-pass shadowgraphsystem is used in connection with a Photron SA5 high-speedvideo camera to record the shock trajectory and the particlecloud movement. In some cases, a front-lit, direct video was</p><p>Fig. 1 Schematic of shock tube showing the positions of the wafer, optical section, and the pressure transducers</p><p>123</p></li><li><p>Dense particle cloud dispersion by a shock wave</p><p>Table 1 Pressure transducer distances from diaphragm</p><p>Transducer P3 P4 Particle wafer P5 P6 P7 P8</p><p>Distance (m) 1.511 1.816 1.969 2.051 2.203 2.356 2.508</p><p>Fig. 2 a Die used to compress powder into the plate cavity, b particlewafer loaded in the plate</p><p>taken when passing parallel light through the optical sectionwas not possible. The camera is triggered when the shockwave reaches location P3. The camera field-of-view covershalf the length of the optical section window shown in Fig. 1.</p><p>The particles are initially configured in a wafer that islocated between P4 and P5, as seen in Fig. 1, 1.97 m down-stream of the diaphragm and 8.5 cm upstream of the edge ofthe optical section window. The particle wafer is created bycompressing 70 g of aluminum oxide powder into a 7.6-cmsquare cavity machined into a 6.4-mm thick plate. The alu-minum oxide is compressed using a 75-ton hydraulic pressthat compresses the powder into the plate cavity using thedie shown schematically in Fig. 2a. A photograph showingthe wafer in the plate cavity is shown in Fig. 2b.</p><p>As shown in Fig. 1, the plate containing the powder waferis sandwiched between two flanges such that the cavity linesup with the channel cross-section area. This ensures that theparticle wafer uniformly fills the entire shock tube cross-section such that no air bypass is possible following shockreflection. The initial position of the wafer between flangesmakes it impossible to capture the initial shock and parti-cle wafer interaction using the shadowgraph video system.Attempts to slide the wafer into the optical section field-of-view near P5 resulted in unacceptable gaps forming betweenthe wafer and the inner-channel walls. The wafer has a par-ticle volume fraction p = 0.48, and the aluminum oxidepowder has a mean particle diameter of 100 m.</p><p>Videos were processed using the computer programImageJ to create binary black-and-white frames using a colorthreshold to define the cloud area. The binary images wherethen processed using a code developed in MATLAB thatallowed for the tracking of the particle cloud position. Thecloud front referred to in this paper was defined as the averageof the leading and trailing edges of the front.</p><p>Time (ms)</p><p>Dis</p><p>tan</p><p>cefro</p><p>mD</p><p>iaph</p><p>ragm</p><p>(m)</p><p>Pre</p><p>ssu</p><p>re(b</p><p>ar)</p><p>0 1 2 3 4 51.4</p><p>1.6</p><p>1.8</p><p>2</p><p>2.2</p><p>2.4</p><p>2.6</p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>P3</p><p>P4</p><p>P5</p><p>P6</p><p>P7</p><p>P8</p><p>Reflected Shock(434 m/s)</p><p>Incident Shock(695 m/s)</p><p>Block Front(Average 204 m/s)</p><p>Precursor Shock(Average 391 m/s)</p><p>Reflected Shock(311 m/s)</p><p>Initial Block Position</p><p>Fig. 3 Diagram showing pressure traces as well as shock and blocktrajectories for an 11-bar abs. helium driver</p><p>3 Results and discussion</p><p>3.1 Delrin block</p><p>Reference tests were performed with a loose-fitting solidDelrin block placed in the same location as the particlewafer. The block was of the same mass as the particle waferand was inserted inside the channel. The data from one suchexperiment with a driver pressure of 11 bar absolute is pro-vided in Fig. 3. The pressure traces recorded at P3 through P8(see Fig. 1 for transducer locations) are shown in Fig. 3. Thereference of all pressure transducers is ambient atmosphericpressure (initial driven section pressure). Also shown arethe high-speed video captured trajectories of the block andthe shock wave that forms downstream. The incident shockwave reflects off the upstream side of the block producing areflected shock wave that propagates back toward the driversection. The reflected shock wave corresponds to the secondpressure rise in the pressure signals recorded at P3 and P4 inFig. 3. A straight dotted line connects points on P3 and P4(corresponding to shock time-of-arrival) showing the aver-age trajectory of the incident and reflected shock wave. The695 m/s (Mach number equal to 2) incident shock wave pro-duces a 311-m/s and 14.5-bar reflected shock wave imme-diately after reflection that subsequently accelerates as itpasses through the contact surface. This compares to the-oretical fixed-surface normal reflection values of 348 m/sand 15.2 bar. The deviation could be attributed to the blockacceleration and high pressure air leakage past the blockdue to a loose fit. The interaction of the shock wave withthe block results in acceleration of the block to a relativelyconstant velocity of 204 m/s. The piston-like motion of theblock produces a weak shock wave that propagates at a veloc-ity of 391 m/s. The weak precursor shock wave could also</p><p>123</p></li><li><p>M. Kellenberger et al.</p><p>(a)</p><p>Time (ms)</p><p>Dis</p><p>tan</p><p>cefro</p><p>mD</p><p>iaph</p><p>ragm</p><p>(m)</p><p>Pre</p><p>ssu</p><p>re(b</p><p>ar)</p><p>0 1 2 3 4 51.4</p><p>1.6</p><p>1.8</p><p>2</p><p>2.2</p><p>2.4</p><p>2.6</p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>P3</p><p>P4</p><p>P5</p><p>P6</p><p>P7</p><p>P8</p><p>Incident Shock(581 m/s)</p><p>Reflected Shock(343 m/s)</p><p>Cloud Front(Average 250 m/s)</p><p>Reflected Shock(316 m/s)</p><p>Initial Wafer Position</p><p>(b)</p><p>Time (ms)</p><p>Dis</p><p>tan</p><p>cefro</p><p>mD</p><p>iaph</p><p>ragm</p><p>(m)</p><p>Pre</p><p>ssu</p><p>re(b</p><p>ar)</p><p>0 1 2 3 4 51.4</p><p>1.6</p><p>1.8</p><p>2</p><p>2.2</p><p>2.4</p><p>2.6</p><p>0</p><p>10</p><p>20</p><p>30</p><p>40</p><p>Precursor Shock(Average 472 m/s)</p><p>Coud Front(Average 248 m/s)</p><p>Incident Shock(589 m/s)</p><p>Reflected Shock(350 m/s)P3</p><p>P4</p><p>P7</p><p>P5</p><p>P8</p><p>P6</p><p>Reflected Shock(317 m/s)</p><p>Initial Wafer Position</p><p>Fig. 4 Diagram showing pressure traces for 6.5 bar abs. helium driver. Shock and block trajectories with the camera field-of-view covering a thefirst half of the optical section, b the second half of the optical section</p><p>originate from the small amount of gas that initially bypassesthe block around the edges. The acceleration of the blockand bypassing of some of the reflected shock gas producesa shallow pressure gradient between the block and the pre-cursor shock wave. The high pressure air behind the blockmoves downstream with the block that is manifested as atravelling shock-like pressure pulse observed in the P5 to P8signals in Fig. 3. The pressure behind the block decays as theblock propagates down the channel, and the high pressuregas region expands as the distance between the block and thereflected shock increases.</p><p>3.2 Particle wafer-square cross-section</p><p>Results with the particle wafer obtained from two testsperformed with a 6.5-bar absolute driver pressure andatmospheric pressure in the driven section is show...</p></li></ul>

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