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Chemically Reactive Turbulent Vortex Rings H Chemically reactive turbulent vortex rings H. Johari Department of Mechanical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609 (ReGeived 2 November 1993; accepted 22 June 1995) Employing an aqueous acid-base reaction, the minimum mixing rate of turbulent vortex rings was investigated in a water tank. Vortex rings were generated by a simple apparatus with a cylindrical geometry. The released fluid surrounding the vortex core mixed very rapidly when compared with the fluid in the toroidal core. Moreover, the fluid within the core did not mix uniformly in the azimuthal direction. The normalized distance a vortex ring must travel, in order to completely mix with the ambient fluid to a specific volumetric ratio, depends on the aspect ratio of the generating cylinder. Scaling arguments are presented that relate the above distance to the spreading rate and the generating apparatus parameters. Due to the very small net entrainment rate of vortex rings, the detrainment of core material cannot be ignored when the mixing rate of the core is considered. © 1995 American Institute of Physics. I. INTRODUCTION other free shear flows, is dependent on the generating appa­ ratus geometry as well as the Reynolds number. 11 It has also A vortex ring is created when a fluid parcel is impul­ been reported that at far downstream locations, a turbulent sively discharged from a circular opening into a quiescent vortex ring may undergo a transformation that changes the environment. Vortex rings have been studied for more than a spreading rate.11•12 At present there does not exist a method century primarily due to their ability to transport mass and of predicting the spreading rate of a turbulent vortex ring, momentum for a relatively long distance with little mixing. even if its generating geometry and initial Reynolds number The application of vortex rings to industrial practices has are known. also been discussed in the literature. For example, Turner1 In the context of mixing, the entrainment and detrain­ studied the feasibility of transporting pollutants to high alti­ ment rates of the bubble, as well as the mixing rate of the tudes via buoyant vortex rings. It has also been suggested vortex core, are important. Since vorticity is concentrated in that vortex rings can be employed to improve the mixing of a small area associated with the vortex core, the core region fuel injected into a high-speed cross-flow.2 Knowledge of the has the slowest mixing rate. Based on tlie appropriately av­ mixing rate in vortex rings is crucial in the above examples, eraged velocity measurements, Glezer and Coles9 were able as well as other applications. to determine the net entrainment rate of the bubble. The en­ There exists a large body of work on the formation, trainment processes in vortex rings were qualitatively de­ structure, and stability of laminar vortex rings.3-5 At large scribed by Auerbach13 on the basis of flow visualization Reynolds numbers, vortex rings are either turbulent at birth studies. Detailed planar measurements of a passive scalar or become turbulent after going through·a transition phase.6 (dye concentration) field within the initial phases of a lami­ 4 A major difference between laminar and turbulent vortex nar vortex ring enabled Southerland et al. 1 to calculate the rings is that turbulent rings leave mixed fluid in their wake. A local (fine-scale) mixing rate. The present study is concerned with the molecular scale concise review of vortex rings was recently carried out· by Shariffand Leonard.7 mixing rate of turbulent vortex rings, as revealed by an iso­ Maxworthy8 conducted flow visualization studies of tur­ thermal chemical reaction . (acid-base neutralization) in the bulent vortex rings and described the flow in terms of a core large Schmidt number regime. Of particular interest is the of very fine-scale turbulence surrounded by a co-moving depen'dence of the mixing on the vortex generator geometry "bubbie." Ambient fluid was observed to get entrained into and Reynolds number. Scaling arguments that provide the the bubble; a small portion was retained while the rest was distance within which the vortex core mixes to a certain ejected into the wake after mixing with the vortex fluid. volumetric ratio are presented in Sec. III. Experiments were These observations were later corroborated by Glezer and performed to measure the core mixing rate and to verify the Coles.9 Maxworthy also presented arguments for the celerity validity of the proposed scaling. of the vortex bubble, which are in contrast to the classical self-similar scaling (based on the conservation of impulse II. APPARATUS assumption). Johrison10 used an alternative power law to de­ scribe the motion of turbulent vortex ririgs. The experiments were conducted in a transparent acrylic Even the available data on the spreading rate of coni­ water tank having dimensions 1.2X1.2X 1.5 m deep. The cally growing turbulent vortex rings have a wide range with vortex generating apparatus consisted of an acrylic cylinder the smallest reported valuen of 0.5X10-3 and the largest sealed on the top by a valve and on the bottom by a thin value8 of 12X10-3. This is in contrast to the consistent mea­ sliding stainless steel plate. The cylinder was positioned on surements of spreading rates of other free shear flows. The top of a 30 em square platform with the sliding plate resting spreading_ rate of vortex rings, generally much smaller than on the platform. The sliding plate is needed to separate the d 2420 Phys. Flui s 7 (10), October 1995 1 070-6631/95/7(10)/2420/8/$6.00 © 1995 American Institute of Physics Downloaded 23 Jul 2013 to 130.166.29.139. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions resulting in maximum HID ratios of 1.5, 2, and 4 for 10.1, 7.5, and 3.8 em diam cylinders, respectively. Classically, vortex rings have been visualized by mark­ ing the vortex fluid with an inert dye. Such a visualization provides an integrated external view appropriate for mea­ surement of global properties. Recently, planar laser-induced fluorescence techniques have been employed for visualiza­ tion of the intimate details of vortex cores in selected planes.6•14 In the present experiments, an aqueous acid-base neutralization reaction along with a pH indicator (phenol­ 2 phthalein) was employed. The tank fluid contained a 10- platform molar acidic (H2S04) solution. Phenolphthalein, in ethanol solution, was mixed with the released fluid, which was a weak alkaline (NaOH) solution. The indicator had a purplish color in the alkaline solution. Upon mixing with the ambient fluid to a prescribed volumetric ratio </J, the indicator was rendered colorless. Here <P is the acid-base stoichiometric ratio, the ratio of volume (mass) of acidic solution required to neutralize a unit volume (mass) of the alkaline solution. In this manner the location of the last parcel to molecularly mix with the ambient fluid could be determined. The distance from the generator exit to this location was termed "reaction length." The reaction length is a measure of the minimum molecular scale mixing in the vortex ring, since the time scale of the acid-base reaction is short compared with the fluid mechanical time scales. The density difference between the released and tank fluid was kept below 0.1 %, thereby minimizing any buoyancy related effects. FIG. 1. Schematic of vortex ring generator vortex core (not to scale). and Figure 2 compares two turbulent vortex rings, one marked by an inert dye while the other containing the pH indicator. Both were generated from the same (10.1 em chemically reactive reservoir and ambient fluids. The plat­ diam) cylinder. The "bubble" fluid, as well as the wake, are form had a circular opening underneath the cylinder. The clearly visible in the inert dye vortex. However, the chemi­ vortex generator assembly was placed above the water tank cally reactive vortex ring reveals only the toroidal core, since such that the sliding plate was at the free surface. Three the rest of the released fluid has mixed with the ambient fluid different cylinders with 3.8, 7.5, and 10.1 em diam could be and has been neutralized (except for a small portion near the placed in the apparatus. A schematic drawing of the vortex vortex generator). Eventually, the core will also mix and dis­ generator is shown in Fig. 1. color when the vortex ring reaches its reaction length. This The released fluid was fed into the cylinder with the technique has previously been used to measure the mixing valve in the open position. The valve was closed subse­ rate in turbulent jets.15•16 quently and the fluid was allowed to become quiescent. The The weight of the fluid slug above the free surface of the sliding plate was pulled back smoothly, leaving the released tank provided the necessary impulse for the motion, in the fluid in contact with the tank fluid. Although care was taken present vortex generator. In order to calculate the impulse I, to minimally disturb the interface between the two fluids, a the velocity time history during the discharge is needed. If laminar wake appeared due to the motion of the plate. A one neglects the effects of boundary layers, the velocity time crude estimate of 3 cm/s for the plate velocity results in a history could be found from the unsteady Bernoulli's equa­ maximum boundary layer displacement thickness of 0.32 em tion. Neglect of the boundary layer thickness is justifiable, for the largest cylinder. The width of the wake, which would since the resulting area contraction at the end of a run be twice this value, is still small in comparison with the amounts to about 1.5 and 3% for the large and small cylin­ cylinder dimensions.
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