Thermophysics and Aeromechanics, 2008, Vol. 15, No. 3

Influence of dispersed phase on the turbulent structure of submerged axisymmetric impact jet A.P. Belousov Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia Е-mail: [email protected] (Received April 18, 2007, final revision April 2, 2008) The PIV/LIF method was used to experimentally examine turbulent characteristics of a submerged gassaturated axisymmetric impact jet. A novel method to analyze the dynamics of vortex formations is proposed, making it possible to obtain spectral characteristics of turbulent motion at low sampling frequency. A comparison of data obtained with theoretical models is reported. Key words: turbulent flows, gas-liquid flow, PIV/LIF method, impact jet, spectrum of turbulent pulsations.

Investigation into the influence of dispersed phase on turbulent characteristics of gas-liquid flows is an important problem since water-bubble mixtures are widely used in many technological processes. Presently, ample experimental data on the problem are available, many of them, however, being contradictory, hampering the development of adequate physical models. For instance, it was shown in [1−4], where comparatively large bubbles, about 0.5 cm in size, were used, that the power exponent of –5/3 in the Kolmogorov spectrum smoothly decreases to –8/3, pointing to instantaneous dissipation of turbulent energy in the wake region of the bubbles ascending in the liquid. On the contrary, in [5−7] the classical –5/3-spectrum was observed even in flows with 25-% gas content. To explain this discrepancy, the authors of [8] introduce the bubble parameter

b=

αU R2 2u0′2

.

(1)

Here, α is the volume content of the gas phase, UR is the ascent velocity of bubble in the liquid at rest, and u0′ is the pulsating velocity in the absence of bubbles. At b > 1 the primary influence on the flow is assumed to be exerted by the ascending bubbles, and the slope of the spectral curve in this case obeys the law of –8/3. In the opposite case of b < 1 the bubbles present tracers that weakly modify the turbulent characteristics relative to the law of –5/3. A comparison with experimental data by other workers proved the above parameter to be, in the majority of cases, a good qualitative criterion defining the effect of gas bubbles on the turbulence. © A.P. Belousov, 2008

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Fig. 1. Submerged axisymmetric impact jet. 1 ⎯ gas-liquid mixture, 2 ⎯ electrodynamic vibration generator, 3 ⎯ nozzle, 4 ⎯ impact surface.

The purpose of the present study was to experimentally examine the effect of gas bubbles on turbulent characteristics of the flow with the PIV/LIF (Particle Image Velocimetry/Light Induced Fluorescent) method. The model was a submerged axisymmetric impact jet. The flow under study is shown in Fig. 1. A gas-liquid mixture 1 circulates in a closed contour involving a test section, a pump, a tank, pipe connections, and control probes. The test section is a rectangular reservoir prepared from organic glass and having dimensions 200×200×300 mm. Nozzle 3 (d = 15 mm) is introduced into the reservoir through its bottom so that the gas-liquid stream impinges normally onto impact surface 4. For generation of large-scale vortical structures, a standard ESE-201 electrodynamic vibration generator 2 was used, connected through bellows with the stilling chamber. The flow was examined with the PIV/LIF method whose schematic is shown in Fig. 2. Radiation emitted by Nd:YAG pulsed laser 1 (532 nm, second harmonics) is converted, by anamorphotic optical system 2, into light sheet 3, which defines the flow section to be examined. The laser gives out, in succession, two flashes. The radiation reemitted by the tracers and bubbles passes through light filters 5 and 6. Since, as tracers, fluorescent particles are used, the light scattered by these particles has a frequency lower than the laser-emitted frequency. Thus, camera 7 registers a bubble image 9, and camera 8, a tracer image 10. The data gained are analyzed by complex 11. The majority of commercially available PIV systems feature poor time resolution. The time between two successive measurements is long, amounting to one second, which hampers the determination of spectral properties of pulsating velocity. In the literature, one-of-a-kind systems are described making it possible taking pictures at a high filming speed (up to 35 thousand frames per second); such setups, however, have rather

Fig. 2. Measuring system. 1 ⎯ laser beam, 2 ⎯ anamorphotic converter, 3 ⎯ laser sheet, 4 ⎯ nozzle, 5 and 6 ⎯ light filters with a transmission peak in the green and red portions of the spectrum, respectively, 7 and 8 ⎯ ССD cameras, 9 ⎯ bubble image, 10 ⎯ tracer image, 11 ⎯ processing system.

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moderate spatial resolution and require data gathering and storage systems with special characteristics to be used. In some cases, the time Fourier transform can be replaced with the spatial transform; yet, in practice such situations are seldom encountered. Thus, there arises a necessity to search for a new universal method which would be independent of data acquisition frequency and flow geometry. According to modern concepts, the turbulent flow has a complex structure [9] involving various vortex formations differing in shape and sizes. By the sizes of vortex formations, average sizes are meant, and distinction between small-scale and large-scale vortices is made. The flow velocity pulsations registered by local probes (hot-wire anemometer, optical fiber, LDA) are due to the motion of variously scaled vortical structures. Following the determination of the velocity and sizes of these structures, pulsating characteristics of the flow can be predicted. Data concerning the vortical structures can be obtained from instantaneous flow velocity fields calculated by the PIV system. Presently, there are many proposed methods enabling reliable detection of vortices both in simple cases with vortices that are easy to identify from instantaneous vorticity fields and in complex cases in which the vortex motion is masked by a strong transverse gradient of flow velocity (mixing or boundary layer). Thus, the PIV system offers an efficient tool to examine the internal turbulence structure. In the present study, to determine characteristics of vortical structures (size, position of the center of mass), we analyzed the two-dimensional field of flow velocity  V ( xi , yi ) calculated by the PIV system, calculated the field of vorticity I ( xi , yi ) , and identified the location of vortices I > Ithre (Ithre = 0.2⋅Imax). The kinetic energy contained in a vortex-formation slice of thickness l = xi – xi−1 = = yi – yi−1 is given by E=

1 3 2 2 ρ l ∑ I 2 ( xi , yi ) ⎡⎢( xi − x0 ) + ( yi − y0 ) ⎤⎥ . ⎣ ⎦ 8 i

(2)

Here, ρ is the density of the liquid, and x0 and y0 are the coordinates of the center of mass of the vortical structure. Summation in (2) is to be performed over the region M occupied by the vortex (Fig. 3). The experiment was carried out at Reynolds number 12 500. Here, Re = U0d/ν, ν is the kinematic viscosity coefficient, and U0 is the mean flow velocity. The distance H between the nozzle exit plane and the impact surface was 30 mm (H/d = 2). The mean size of the gas bubbles was 400 μm, and their volume content at the nozzle exit plane, about 4.5 %. The excitation frequency was chosen such that to correspond to Strouhal number 0.5 (an optimal value for the formation of large-scale vortical structures). This frequency was synchronized with the taking pictures frequency, so that the camera registered a picture that involved several spatially localized coherent structures. The latter made it possible to carry out a statistical analysis and examine the action of the dispersed phase on variously scaled vortical structures. Let us evaluate the bubble parameter b in our experiments. The ascent velocity of

Fig. 3. Calculation of the kinetic energy contained in a vortex-formation slice of thickness l. 411

Fig. 4. Regions from which data were sampled.

gas bubbles UR in the liquid at rest can be estimated as UR =

2 grb2 , 9ν L

where g is the free-fall acceleration, rb is the bubble radius, and νL is the kinematic viscosity of the liquid. Substituting values, for the present experiment we obtain a velocity of 9 cm/s. According to formula (1) the bubble parameter is about 0.02; it can, therefore, be expected that the presence of the gas phase will not substantially distort the power law of −5/3. The main processes causing the formation, development, and dissipation of vortices are: convection (advection), production (generation), diffusion and, at the late state of breakup, dissipation (conversion to heat) [9]. During the turbulent-diffusion process, large vortices disintegrate into smaller vortices in which inertial phenomena still prevail over viscous phenomena. The vortices in the “inertial range of scales” take part in convection and turbulent diffusion; they, however, are negligibly affected by viscosity. Further general degradation of vortices finally results in their transformation in small vortices acted upon already by viscous diffusion with subsequent viscous dissipation of kinetic energy into heat. Of course, such a cascade scheme only roughly reproduces the actual processes in turbulent flows yet adequately reflects the common tendencies.

Fig. 5. Analysis of vortex-formation dynamics in one-phase (а) and two-phase (b) flows. 412

Fig. 6. Number of vortex formations versus vortex-formation size for regions A+B+C+D. Flow: one-phase (1) and two-phase (2).

Decaying rapidly, small-scale vortices are incapable of storing, for any long time, and carry over in the downstream direction, information about perturbations produced in upstream flow regions. The kinetic energy of large vortices is the order of the specific energy of the average local motion. Then, this energy decreases as the scale diminishes to become negligible in the case of fine vortices. In the present paper, we report on a statistical analysis of vortex-formation sizes as dependent on the type of the flow (one-phase or two-phase) and on the location of vortex structure. A stationary picture comprising several coherent structures was put to analysis. The statistical array was formed by about 2000 fields of instantaneous velocity. Figure 4 shows the flow regions from which data were drawn. Located at the left is the axis of symmetry of the jet, and atop, the impact surface. Regions A, B, C, and D correspond to the coherent structure at its various developmental stages. In region A we have a fully formed structure, and in regions B, C, and D, downstream variation of this structure. Shown in Fig. 5 are the experimental data. It is seen from the figure that the size distribution of vortex formations in the mixing layer displays two peaks. The right peak refers to large-scale coherent structures, and the left peak, to smaller vortices. In the downstream direction, the vortex formations decrease in size to disappear in region D. The presence of the gas phase (about 4.5 %) suppresses the large-scale structures, this circumstance being manifested in a larger size spread of vortices (see Fig. 5, b), and accelerates the dissipation of these structures. Consider the total distribution of vortex formations over their sizes NA + NB + NC + ND, where Ni is the number of vortices in the region i. Figure 6 shows

Fig. 7. Fraction of the energy stored in fixedscale vortices. Flow: one-phase (1) and twophase (2).

Fig. 8. Е versus ω (inertial interval) at ω = U0/λ; one-phase (1) and two-phase (2) −5/3 flows, power law ω (3). 413

that the major contribution to the total number of structures is made by small-scale formations in the range of scales in which viscous dissipation of energy takes place. The number of vortices in the one-phase and two-phase flows shows no substantial changes. Let us now construct the energy spectrum according to (2). The distribution obtained (see Fig. 7) complies with the commonly accepted idea of the fraction of turbulent energy contained in fixed-scale vortices. In the inertial interval the energy of large structures formed over the initial length of the jet gets gradually transferred to smaller formations to finally dissipate in small-scale structures. It is seen from Fig. 7 that the dispersed phase suppresses the development of large-scale formations. Yet, the influence on the power law of −5/3 remains negligible (see Fig. 8); this finding well agrees with previous observations made in [1−8]. To summarize the study, several conclusions can be drawn. The application range of PIV systems for studying turbulent processes was extended to cover a wider region. Data concerning the effect of dispersed phase on turbulent characteristics of axisymmetric impact jet were obtained. It was shown that the presence of gas bubbles in the flow causes variation of statistical characteristics defining the size distribution of large-scale structures (the dispersion increases), and promotes dissipation of these structures. REFERENCES 1. M. Lance and J. Bataille, Turbulence in the liquid phase of a bubbly air ⎯ water flow, in: Martinus Nijhoff (Ed.), Proc. NATO Specialists Meeting, Spitzensee, Germany, 1983. 2. M. Lance and J. Bataille, Turbulence in the liquid phase of a uniform bubbly air ⎯ water flow, J. Fluid Mech., 1991, Vol. 222, Р. 95−118. 3. S.K. Wang, S.J. Lee, O.C. Jones, and R.T. Lahey, Statistical analysis of turbulent two-phase pipe flow, J. Fluid Engng., 1990, Vol. 112, Р. 89−95. 4. I. Michiyoshi and A. Serizawa, Turbulence in two-phase bubbly flow, in: Proc. Japan ⎯ US Seminar on Two-Phase Flow Dynamics, 1984, July 29 ⎯ August 3, Lake Placid, USA. 5. R.F. Mudde, J.S. Groen, and H.E.A. Van den Akker, Liquid velocity field in a bubble column: LDA experiments, Chem. Engng. Sci., 1997, Vol. 52, P. 4217−4224. 6. R.F. Mudde and T. Saito, Hydrodynamical similarities between bubble column and bubbly pipe flow, J. Fluid Mech., 2001, Vol. 437, P. 203−228. 7. Z. Cui and L.S. Fan, Turbulence energy distribution in bubbling gas ⎯ liquid and gas ⎯ liquid ⎯ solid flow systems, Chem. Engng. Sci., 2004, Vol. 59, P. 1755−1766. 8. J. Rensen, S. Luther, and D. Lohse, The effect of bubbles on developed turbulence, J. Fluid Mech., 2005, Vol. 538, P. 153−187. 9. L.G. Loitsyansky, Mechanics of Liquids and Gases, Begell House, New York, 1995.

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