International Journal of Multiphase Flow

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1 International Journal of Multiphase Flow 47 (2012) Contents lists available at SciVerse ScienceDirect International Journal of Multiphase Flow journal homepage: Turbulent exchange mechanisms in bubble plumes Marco Simiano a,, Djamel Lakehal b,1 a ETH Zurich, Laboratory of Nuclear Energy Systems, CH-8092 Zurich, Switzerland b ASCOMP GmbH, CH-8037 Zurich, Switzerland article info abstract Article history: Received 11 December 2011 Received in revised form 5 July 2012 Accepted 17 July 2012 Available online 27 July 2012 Keyword: Multiphase and bubble-laden turbulent flows Turbulent transport and exchange mechanisms in an unstable oscillating bubble plume are investigated using a novel Large-Eddy PIV measurement technique providing simultaneous gas and liquid velocity fields. The flow was generated in a 2 m-diameter vessel with a water depth of 1.5 m for void fractions up to 4% and bubble size of the order of 2.5 mm. Sub-scale turbulent properties of the flow were estimated, revealing an enhanced anisotropic transport of turbulence and energy redistribution mechanism and with strong shear-induced characteristics. It is shown that the plume dynamics contain distinct flow zones, each associated with specific flow events and featuring specific energy exchange mechanisms: the plume-core zone where the flow accelerates, the peak zone where the plume contracts, and a residual external zone where the stresses are relaxed. The turbulent kinetic energy is found to be dominated by the vertical stresses, along the flow direction, notably in the peak zone, a phenomenon associated with the meandering of the central bubble plume. The quantitative estimation of the production terms new explanations of the energy exchange mechanisms between the mean flow and the sub-scale motions within the three flow zones identified. During plume contraction the longitudinal normal- and cross-production terms act as pure generation terms extracting energy from the mean flow; when the contraction is terminated, the shear-induced contribution competes with the normal stress-induced term, which tends to restitute energy back to the mean flow. In the plume-core zone instead, both terms are negligible, except at lower elevations where, because of the strong vertical acceleration of the flow, the contraction occurs and the normal stress-induced restitutes energy to the mean flow. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Turbulence has always occupied a central role in bubbly flow research, with very sparse objectives though, as exemplified in the few sample studies selected here. Experiments of Johansen et al. (1988), Gross and Kuhlman (1992), and Iguchi et al. (1995) for instance focused on the isotropic/anisotropic nature of turbulence in the plume core flow. Iguchi et al. (1991) and Johansen et al. (1988) were interested in comparing the fluctuating and mean velocities in terms of magnitude and shape. In their study of a bubbly jet, Iguchi et al. (1995) evaluated the modulation of turbulence by the bubble-jet volume fraction. The role of large-scale structures on the transport of bubbles in turbulent shear flows was on the other hand a central theme in the studies of Sene et al. (1994). But only a few attempts have dealt with turbulence dissipation in the presence of bubbles (Lance and Bataille, 1991), or more widely bubble-induced agitation (Cartellier et al., 2009), a subject that is markedly of practical importance for chemical/ Corresponding author. addresses: marco.simiano@gmail.com (M. Simiano), lakehal@ascomp.ch (D. Lakehal). 1 Formerly at ETH Zurich, Institute of Energy Technology, Switzerland. process and nuclear engineering. Many more references could be added in the context of modeling using two-equation turbulence models for example, but this is not the scope of the paper. Bubbly flows differ depending on whether they are inertiadominated, like bubbly jets (due to premixed gas and liquid injections), or buoyancy- or gravity-dominated, like bubbly plumes and bubble columns (created by gas injection alone, see the review of Mudde et al. (1997)). One key difference concerns the interplay between sub-scale, shear-induced turbulence and large-scale transients inherent to the stability of the flow itself, i.e. circumferential meandering, vertical pulsations and radial oscillation for the plumes (Delnoj et al., 1999; Simiano et al., 2009) against coherent structures for bubbly jets (Iguchi et al., 1995; Rensen and Roig, 2001; Martinez-Bazan and Lasheras, 2001). The research has been somewhat ambiguous here, notably because the separate contributions of these two phenomena to the global time-averaged characteristics of the flows have never been distinguished properly. The present work expands up on our PIV-based investigations of the transport mechanisms in oscillating bubbly plumes (Simiano et al., 2009) with relatively large void-fractions (up to 4%), precisely with the main objective to discern large-scale from subscale effects. The PIV approach used in Simiano et al. (2009), and whose results are further processed and presented /$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.

2 142 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) here, could be interpreted as a Large-Eddy PIV, in the sense of Sheng et al., (2000), assuming a dynamic equilibrium of turbulence. The technique provides spatial information of instantaneous 2D-velocity fields simultaneously, which then permits to determine spatial derivatives directly without having to advocate neither the Taylor s hypothesis, nor the isotropic assumption. The experimental results presented in this work were acquired by using an instrumentation technique providing simultaneous measurement of the two phase velocities, and recording the flow structure almost simultaneously with the velocity measurements. The simultaneous measurement of gas and liquid velocities provided by the instrumentation system described in Simiano et al. (2009), strengthens the notion of Large-Eddy PIV approach in the bubble flow context, too. Although not yet fully mastered in laboratories, such simultaneous gas liquid measurements appear to be unavoidable for providing a faithful picture of bubbly flows, in particular when looking at phase relative velocities (Hassan et al., 1992). In this ultimate part of the project, we propose here to discuss new findings relative to the global averages flow quantities along with the energy exchange mechanisms between the oscillating motions and sub-scale turbulence with the mean flow obtained by further post-processing the original experimental data published in Simiano et al. (2009). To avoid confusion, few selected results (Figs. 3 5) of the aforementioned publication were added to support the explanation of these new results. 2. The simultaneous PIV measurement technique The test facility (LINX), Fig. 1, and the simultaneous two-phase PIV measurement system were extensively described in Simiano et al. (2009). Briefely, to set the context of the work, we provide here a general description of the measurement system. The facility is a 2 m diameter vs. 3.4 m height metallic vessel filled with demineralized water, equipped with 12 visualization glass-windows. Gas was injected from 140 hollow needles of 2 mm diameter each uniformly distributed over a circular horizontal plate with a diameter D inj = 150 mm. At about 150 mm elevation, the produced bubbles were ellipsoidal with a shape factor and an equivalent Sauter diameter of e 0.5 and 2.5 mm, respectively. The gas flow rates were tuned to obtain void fractions falling in the range 0.2% < a < 4%. More details can be found in Simiano et al. (2006, 2009). The coordinate system used is such that the vertical axis denotes the elevation (Y) and is measured from the top of the injector needles; the horizontal ones are denoted as X and Z when no assumption of axial symmetry and r otherwise. The vertical (in the flow direction) and horizontal (in the radial direction) velocity components are denoted as v and u, respectively. The liquid and the gas phases were recorded simultaneously by seeding the liquid with fluorescent particles and observing the laser light reflected by the bubble surfaces (Simiano et al., 2009). The plume was observed at three different elevations through the superimposed windows. For each investigation three series of images were acquired: one long-time acquisition of 4000 pairs of images for each phase at 0.5 Hz (about 133-min measurements), and two short-time acquisitions of 2000 pairs of images at 15 Hz (more than 2-min acquisition). The PIV window used for both phases consists of a field of view of about mm with a resolution of 207 lm/pixel; each velocity vector was calculated over an interrogation region (IR) of pixels (about mm) with 50% overlap. The total vector field consisted of 30 columns by 30 rows of vectors placed at the center of their respective IRs. To analyze the flow dynamics in terms of characteristics scales, we proceed by estimating the energy dissipation rate based on the gas flow rate and the total volume of gas in the vessel (v G ), assuming that this quantity is proportional to the rate of rise of air bubbles: e = v G gq w V T, where q w is the density of water, V T is the terminal rise bubble velocity and g is the gravitational acceleration. This should give e m 2 /s 3, yielding a length scale of the order of g ¼ðm 3 =eþ m, and a time scale of the order of s k ¼ðm=eÞ 1 2 4: s. For an equivalent bubble diameter of 2.5 mm, which is the average bubble diameter measured in our experiment, the relaxation time of the bubbles is roughly s b ¼ V T 2g 15. The results presented here were obtained by further elaborating the data acquired during the measurement campaign I 4 described in the test matrix (Table I of Simiano et al., 2009). This deliberate choice is motivated by the fact that Case I 4, with air mass flowrate Fig. 1. Bubble plume experiment in the LINX facility (left). Top view schematic of the experimental setup used to detect simultaneously the instantaneous bubble plume position and the velocity fields of the two phases (right).

3 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) thoroughly discussed in Simiano et al. (2009); in what follows we restrict reporting the findings to some pertinent conclusions. The oscillatory behavior of the plume consists mainly of a stochastic motion of the plume around its axis, with plume width and horizontal cross-section fluctuations increasing with distance from the injector. While the inner part of the plume evolves nonhomogeneously, with marked clusters of bubbles interacting with turbulence structures, the horizontal cross-section fluctuates, shrinks and stretches in all directions, as can be inferred from the instantaneous plume-edge reconstructions of Fig. 3. Further, the relatively long period of data acquisition (a few minutes) revealed that the position of the plume adheres to a symmetric PDF with respect to its mean central position. The centerline of the bubble plume position showed a slow meandering process with a period of the order of a minute. This natural instability was found to be negligible close to the injector, but grows consistently with the axial distance before reaching saturation further downstream. This finding justifies the use of classical time averages close to the injector (results discussed next). Far away from the injector, use was made of conditional averages to clarify the impact of the plume instability on the turbulent transport mechanisms. 4. Mean flow field near injection Fig. 2. Two dimensional false color map of the average void fraction at the injection rate of 15 NLiter/min. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) of 15 NLiter/min, delivers the highest void fraction at injection (a 0 = 4.07%), which is indeed more interesting to study since most earlier contributions had dealt with lower void fraction level; the cross-sectional average value (over 0 < r < 150 mm), a s, was 1.45%, see Fig. 2. The water level in the tank reached 1.5 m above the top of the injector. 3. Large-scale events: bubble oscillation and meandering Plume meandering could be defined as any displacement of its structure away from the injector centerline; instantaneous plume diameter fluctuations are deliberately correlated here to plume oscillations, and assumed to be independent from the deviations of the plume from its centerline. In comparison to plume oscillations, meandering mechanisms are relatively slow motions displacing the flow from the injector center and thus from the observation plane. These two events constituting the dominant large-scale motions of the plume structure in the vessel are not necessarily part of the turbulence but they are part of the fluctuating velocity components. The two classes of scenarios can be classified as individual energetic events in the sense of Farge (1992),as they are coherent, non-periodic, in non-equilibrium and interacting with the sub-scale part of the spectrum that constitutes turbulence. These large-scale motions could be superimposed on a wide range of smaller-scale (or sub-scale) motions, ranging from typical swarm-of-bubbles size all the way to the dissipation scales, controlled by the Reynolds number. This latter issue is beyond the scope of this paper, because of the limitation in data acquisition of the present PIV technique. An Image-Acquisition System (IAS, Fig. 1) was used to record images of the bubble plume in two vertical planes from two perpendicular directions. The technique was particularly useful for the characterization of the flow structure (Simiano et al., 2009). A detailed analysis of the plume meandering and fluctuations and the resulting impact on the mean and turbulent flow fields is 4.1. Mean liquid flow profiles Liquid flow profiles are perhaps more interesting to discuss, since the gas-phase velocity distributions close to the injector are simply flat, with centerline values steadily increasing with elevation (results not shown here). The vertical (streamwise) and horizontal (radial) liquid velocity profiles near the injector plotted in Fig. 4a and b better reflect the evolution of the plume structure, featuring steep velocity gradients with sharp peripheral edges. In particular, the streamwise liquid-phase velocity varies substantially with elevation (Y direction) and radial extension. The sharp edges correspond to the peaks of the liquid vorticity shown in Fig. 4b, v L is much higher than L. At higher elevations (Y > 312 mm), the streamwise velocity profiles evolve substantially reaching a higher centerline velocity (up to 0.4 m/s) and smoother edges, reflecting the contraction of the plume. In summary, when comparing the liquid velocity gradients, one could observe that at all locations close to the injector in the plume core region (r < mm), the most vigorous gradient L, followed by L. It is very interesting to note that in the inner core region (r < 50 mm), immediately after gas injection ðy < 312 v L is negligible and is dominated by L; the tendency is inverted further downstream (Y > 312 mm), where while L is decreasing, is increasing. The behavior of the liquid velocity gradients in the core region (encompassing the inner and peripheral regions) reflects the plume contraction feature discussed previously in the context of Figs. 2 and 3: the signature of plume contraction is such v L v L (flow acceleration) are suddenly promoted at the expense of L (flow retraction). In the plume peripheral region ð50 < r < 70 L exhibits a very strong drop, while L re- mains negligibly small. In general, the two v L and L are important only in the core zone near the centerline of the plume (r < 30 mm). The liquid vorticity defined by: x L v L L ; is a very interesting flow measure in bubbly flows, since it helps gain insight into the oscillatory behavior of the plume. In the light of the previous discussion of the liquid velocity gradients, it v L ð1þ

4 144 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) Fig. 3. Time sequence of 3D plume reconstructions produced using information obtained with the two-directional video recording system; gas injection rate of 15 NLiter/ min. that the vorticity plotted in the third panel of Fig. 4 evolves according to the location, featuring a complex radial distribution with elevation: close to the injection x L is dominated by L in the inner core region and v L at the periphery. Far downstream from the injector, the dominating quantity across the entire plume core L. Sim- iano et al. (2009) have shown that the shape and downward evolution of the mean flow profiles including in particular the relative velocity (not discussed here) and vorticity are intimately tied to vortices created at the periphery of the bubble plume. The high-liquid vorticity at the peripheral zone near injection is indeed associated with intermittent vortices which form at the plume edge (in the thin shear layer) and travel upward pushed by the sort of pumping action induced by the plume oscillation. These peripheral vortices are quickly deformed before vanishing in the form of momentum diffusive mechanisms resulting from the interaction of the bubbles with the flow Simiano et al. (2009) Energy exchange mechanisms The results shown in Fig. 5 were already presented in Simiano et al. (2009) and are repeated here only for the seek of clarity. Briefly, in the of isotropic Eddy Viscosity Modeling (EVM) concept where the Reynolds stresses (s yy ) are linearly linked to eddy viscosity s yy ¼ v 0 Lv 0 L ¼ 2=3K L t and turbulent kinetic energy (TKE) defined by K: K ¼ 1 2 u0 L u0 L þ v 0 Lv 0 L þ w0 L w0 L v 0 Lv 0 L indeed does not show explicitly the contribution L, in con- trast to what is manifestly suggested by Fig. 5a and b, but that L only. In contrast to single-phase, thin shear-layer flows, both normal stresses u 0 L u0 L and v 0 Lv 0 L are actually generated by the combined action of L and L, L L, respectively, in total odds with the EVM concept reflected by the above Eq. (2). The way EVM models behave is such that there is practically no energy exchange accounted for between the normal stresses (and TKE), which is obviously not the case judging from our results. Equation (2) is simply inadequate to represent the Reynolds stresses appropriately. Important contributions for s yy, and for s xx are not taken into account by the mode to estimate the normal stresses. Even without considering the full Reynolds Stress Model (RSM), starting with a more elaborate modeling strategy like Algebraic Stress Modeling (ASM) or Non-Linear Eddy Viscosity models show that the EVM fails in this context. Under specific conditions of equilibrium and mild departure from isotropy, the ASM model ð2þ ð3þ

5 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) Fig. 4. Average liquid velocities and vorticity at the injection rate of 15 NLiter/min and at various elevations. representation of the stresses contrasts with Eq. (2) and delivers the following form of the mechanical normal stresses (we will discuss the buoyancy counterpart next) (Launder, v 0 Lv 0 L ¼ 2=3K C S 4=3Ke v 0 Lv 0 L Lv u0 0 L L u 0 L u0 L ¼ 2=3K C S 4=3Ke u 0 L L u0 L Lv u0 0 L L where C S is a model coefficient that depends on the flow (generally taken equal to 0.26 for wall flows). Clearly, ASM models (with no ð4þ ð5þ Fig. 5. Globally averaged Reynolds stresses profiles of the liquid phase at gas injection rate of 15 NLiter/min, at various elevations. The numbers and the arrows indicate the peak positions of the stresses at different elevations. preference a priori) alone can provide a better description of what may be expected to occur in the flow under study here, since they take into account the contribution v and. Calibrating model coefficients C S is beyond the scope of this paper; the intention here is to rather highlight the weakness of simple eddy viscosity modeling to explain the turbulent transport mechanisms in these flows. Further, characterizing subscale turbulence radially from the core to the peripheral zones and outward is made by estimating the turbulence intensity at several crossflow locations:

6 146 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) T v ¼ v 0 Lv 0 L þ 2 u0 L u0 L v 2 L þ u2 L Fig. 6b compares the turbulence intensity profiles at different elevations. Near the plume center, Tv reaches about 10 40% and is somewhat more pronounced at lower elevations. Moving to the plume periphery, it increases up to % at its extreme edge. In Fig. 6b, three distinct flow zones can be identified, which can be individually associated with specific flow events (i.e. contraction, acceleration), and specific energy transports (production, dissipation), too. In the plume-core zone, the turbulence intensity is controlled by flow acceleration. The peak zone is the region where the plume contracts, and where turbulence production occurs, a phenomenon marked by the contraction of the steep liquid profiles. At the edge of the plume starting at r = 80 mm, turbulence intensity presents a plateau pointing to an entrainment effect. In fact, at this radial distance the vertical velocity is already approaching zero and so do the normal stresses v 0 Lv 0 L (Fig. 4a and b). It is rather the radial normal stresses u 0 L u0 L that are still active and sustain the entrainment-induced inward flow motion. Finally, the higher turbulent intensity in the zone defined as background turbulence zone is the result of the small residual amount of fluctuations normalized by a low average liquid velocity. Fig. 6. Turbulent kinetic energy (TKE) and turbulence intensity profiles at several elevations, for the 15 NLiter/min flow rate. ð6þ 4.3. Postulates, definitions and formulation Now that the three flow zones were identified, each with specific turbulent transport and intensity of fluctuations, it becomes interesting to further explore the subsequent energy exchange mechanism in these regions by looking at the relevant terms in the transport equation of the Reynolds stresses. The purpose here is to clarify the interaction of the mean flow with the fluctuating field from an energy-exchange point of view; forward- and backscatter of energy. Firstly, we postulate an analogy between the bubbly plumes rising in quiescent liquid and gravity-driven plumes involving two miscible fluids with different densities (Ruzicka et al., 2001). There exist of course limitations to the analogy due to differences in the physical processes involved in these two situations. The analogy primarily rests (for the mean quantities, and in terms of the bulk averaged equations) on the relative slip velocity between the dispersed and continuous phase (slip velocity) being smaller than the mean flow in the plume. Since the bubbles are too large to be affected by Brownian motion, there is no molecular diffusion in the gas flow where the bubbles are rather transported by the turbulent motions in the liquid phase; the bubbles can also experience bubble bubble interactions. The analogy would be acceptable for bubble sizes smaller than the Kolmogorov scale, which is not the case in our experiments. However, the PIV technique used here does not permit to resolve these length scales and the analysis is restricted to the dynamics of low frequency, which we believe to be the most significant ones for plume development. In the framework of this flow description obviously borrowed from the Large-Eddy Simulation of turbulent flows-, the analogy with a buoyancy driven fluid mixture is thus meaningful (Ruzicka et al., 2001). The role of the mixture-concentration fluctuation is now played by the fluctuation of the void fraction (in both cases one should speak about an apparent density), in which case the production of turbulent stresses (s ij ) in the liquid phase should involve both shear-induced and buoyancy-induced contributions now due to fluctuating void fraction field, denoted by P ij and C ij, respectively: P ij þ C ij ¼ u 0 j i u0 k þ u 0 i u0 k g Dq k q ðd iku 0 j a0 þ d jk u 0 i a0 Þ ð7þ The inertia term scales as u 02 S, where S is a measure of the velocity gradient, while the buoyancy term scales as ag u 0 Dq/q. The ratio of these two contributions is obviously high in the lower part of the plume where gradients are strong, and small in the upper part. In other words, term C ij is inefficient in creating/ destructing turbulence stresses and kinetic energy in the lower region near the injector. The key player in the energy exchange mechanism remains the shear-induced contribution P ij, the components of should dictate the forward backward energy transfer and redistribution. But prior to evaluating these components, let us turn back to the derivation of the average turbulent stresses equations for two-phase dispersed flows within the inter-penetrating media two-fluid formulation (Elghobashi and Abou-Arab, 1983), which contrasts with the mixture-based postulate advanced above in that energy production is driven by P ij defined above, augmented by an interfacial contribution translating P I ij the transfer of kinetic energy across a control volume larger than the bubbles: P ij þ P I ij ¼ ð1 aþ j u0 i u0 k þ u 0 i u0 k þ i u0þ j n k d I ð8þ k where n i stands for the unit vector to the bubble surface and d I for the delta function centered at the interface. While there is no reason a priori to neglect P I ij, the range of length scales associated with this

7 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) Mean to fluctuating fields, and vice versa The shear-induced contribution P ij, which could indeed be evaluated from measurable quantities without need of modeling, encompasses three components of interest, namely: P xx ¼ 2 s þ s xy ; ð9þ v P yy ¼ 2 s yy þ s xy 6 4 fflffl{zfflffl} ðaþ ; ð10þ fflffl{zfflffl} ðbþ Fig. 7. Production tensor terms, at 15 NLiter/min, close to the injector. interfacial transfer should be comparable to the bubble size, and the eddies formed in bubble wakes dissipate by viscous effects rather quickly because of their short characteristic time scale (Lance et al., 1991; Chahed et al., 2003); both flow features cannot be resolved in this experiment. As a consequence, provided the flow is dilute (say a smaller than 10%), this interphase transfer term is almost balanced by an associated dissipation rate, so that the remaining key player in the energy exchange mechanism is the shearinduced production P ij. and P xy ¼ s yy þ s þ 2s v : ð11þ For simplicity, the liquid velocity subscript L is now omitted. Terms s yy, s xx and s xy represent the Reynolds normal and shear stress terms estimated previously and discussed within the context of Fig. 5. We proceed by first identifying the dominant terms. The three components, P xx, P yy, and P xy, are plotted in Fig. 7 at several elevations. The distribution of the production terms reveals the anisotropic generation mechanisms of turbulence in this flow. Because of entrainment effects ( < 0 in the plume core), P xx features significant values very close the injector. As was to be expected, however, the dominant term in the balance is P yy, being substantially active in the peak zone where vortices interact with the outer surface of the plume. At very low elevation, P yy shows high peaks at about r = 60 mm, in line with the liquid-velocity gradients already shown in Fig. 4a, and the turbulent kinetic energy depicted in Fig. 6a. At higher elevations the production becomes weaker and shifts its peak towards the center. To better understand the phenomena, the two terms (A and B) in Eq. (10) are analyzed in Fig. 8, at three elevations. Term A denotes the normal contribution of the stress tensor and of the velocity gradient in the flow direction. Term B denotes instead the turbulence production by the shear stress and the transversal gradient of the liquid vertical velocity. Close to the injector, Fig. 8a suggests that both terms contribute positively to the production, in what was previously identified as peak zone. In this case the normal contribution dominates the others because of the longitudinal deceleration of the liquid which occurs just above the injector. In fact, while in the plume-core zone the flow is strongly accelerated, it decelerates in the peak zone because of plume contraction. The production in the plume-core zone is dominated by v, reflecting the acceleration of the flow. This phenomenon contributes to P yy (considering always s yy P 0), with weakly negative and significant positive amounts in the plume-core and peak zones, respectively. A higher elevations, 338 and 438 mm, B in Eq. (10) relating to the direct interaction of shear with mean flow plays a dominant role because of the strong transversal gradient of the vertical liquid v. In contrast to the lower elevation, the contraction has already occurred and the velocity profile does not present steep gradients anymore (Fig. 4a). The transversal shear-induced production is thus balanced by the normal contribution (A), which acts rather as a destruction term (sucking energy) also in the peak zone, since the flow is rather weakly accelerating across its entire section. Further away from the plume injection, the radial evolution of the dominant term P yy is shown in Fig. 9a for the 719 and 1143 mm elevations. P yy decreases at higher elevation and becomes very small. Observing in detail the two terms constituting P yy (see Eq. (10)) helps understand its evolution. At an elevation

8 148 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) 141 Fig. 8. Comparison of the two components, s v yy and xy, of the production tensor term P yy at 15 NLiter/min, close to the injector. Fig. 9. Production tensor terms for the gas flow rate of 15 NLiter/min. of 719 mm, term B is indeed dominant, showing a turbulent field clearly controlled by the transverse velocity gradient. However, term A makes a similar contribution to the production term P yy for small radial distances, while at the plume periphery it makes a slight opposite contribution. The sign change is due to the fact that at this elevation, despite a continued increase of the cross-sectional average vertical velocity of the liquid, there is a redistribution of local velocities, flattening the radial velocity profiles. This leads to a negative velocity in the plume center, while it is positive farther away. At higher elevations, Fig. 9c, A follows roughly the same trend and has similar values, while B has already lost its strength because of the flat velocity profiles. In conclusion, during plume contraction, in the peak zone, terms A and B act as pure generation terms extracting energy from the mean flow. When the contraction is terminated, the shear-induced contribution competes with the normal-stress-induced term, which tends then to restitute energy back to the mean flow.

9 M. Simiano, D. Lakehal / International Journal of Multiphase Flow 47 (2012) In the plume-core zone instead, both terms are negligible, except at lower elevations where, because of the strong vertical acceleration of the flow, plume contraction occurs imposing the normal-stressinduced to restitute energy back to the mean flow. This is a very important result for modeling in particular, demonstrating the weakness of the isotropic RANS models where the complex energy exchange mechanism is ignored. It is also intriguing to see whether RSM can reproduce this effect Impact on turbulence modeling The analysis of the results presented in the previous section has clearly highlighted the separate roles of the interaction of the normal and the shear stresses with the mean flow (via velocity gradients) to the generation of s xx and s yy. EVM modeling approaches were found to be afflicted with a serious drawback, in that they do not allow the representation of energy redistribution between individual normal stresses and turbulent kinetic energy. In steady-state conditions, the contradiction could be alleviated by resorting to Algebraic or full RSM, which could to some extent be capable to correctly capture the interaction between the stresses and the mean flow, but again without a preference as to the model details and constants. The instantaneous plume oscillation/meandering, and scale separation and history effects are only within reach of LES (Lakehal et al., 2002), or to some extent V-LES (short for very large-eddy simulation). It clearly appears that under such oscillating conditions, ASM and RSM models will also fail to predict the energy exchange mechanisms since these seem to depend locally on the flow evolution. 5. Conclusions The results of an intensive experimental investigation of a bubble plume exhibiting three-dimensional unstable motions were presented. A two-camera PIV system was used to measure simultaneously the velocity fields of the two phases. Sub-scale turbulent properties of the flow were estimated, revealing an anisotropic transport mechanism with strong shearinduced characteristics in the lower injection segment. The analysis of the turbulent stresses helped identify distinct flow zones in the plume, each associated with specific flow events and featuring specific energy exchange mechanisms: the plume-core zone where the flow accelerates, the peak zone where the plume contracts, and a residual external zone where the stresses are relaxed. The global turbulent kinetic energy was found to be dominated by the vertical stresses, notably in the peak zone where the stresses attain levels four times larger than in the acceleration zone. A further quantitative estimate of the turbulence production terms was carried out in order to analyze the more global energy exchange mechanisms between the mean flow and the sub-scale motions within the three flow zones identified. The decomposition of the global stress production term has revealed that the different contributions behave differently from one flow zone to the other. Near the injector in the more stable flow zone, the transverse normal-stress-induced production dominates in the plume-core zone, promoted by flow entrainment. The same quantity acting in the longitudinal direction prevails however in the peak zone due to plume contraction. The cross-production term is rather important in the intermediate region located between the plume core and plume contraction areas. Interpreted in terms of energy exchange mechanism, during plume contraction the longitudinal normal- and cross-production terms act as pure generation terms extracting energy from the mean flow, while when the contraction is terminated, the shear-induced contribution competes with the normal-stress-induced term, which tends then to restitute energy back to the mean flow. In the plume-core zone instead, both terms are negligible, except at lower elevations where, because of the strong vertical acceleration of the flow, the contraction occurs and the normal-stress-induced restitutes energy to the mean flow. Understandably, the energy transfer analysis could not focus in detail on the pressure-correlation terms that control the redistribution of energy between the stresses and with the mean flow. Acknowledgments The authors gratefully acknowledge support from the Emil Berthele Fonds (ETH Zurich). The experiments were performed at the Thermal Hydraulics Laboratory of the Paul Scherrer Institut (PSI). Prof. G. Yadigaroglu and M. Lance are gratefully acknowledged for their input in this work. References Cartellier, A., Andreotti, M., Sechet, P., Induced agitation in homogeneous bubbly flows at moderate particle reynolds number. Phys. Rev. E 80, Chahed, J., Roig, V., Masbernat, L., Eulerian Eulerian two-fluid model for turbulent gas liquid bubbly flows. Int. J. Multiphase Flow 29, Delnoj, E., Westerweel, J., Deen, N.G., Kuipers, J.A.M., Swaaij, W.P.M.V., Ensemble correlation piv applied to bubble plumes rising in a bubble column. Chem. Eng. Sci. 54, Elghobashi, S., Abou-Arab, T., A two-equation model for two-phase flows. Phys. Fluids 26, Farge, M., Wavelet transforms and their applications to turbulence. Ann. Rev. Fluid Mech. 24, Gross, R.W., Kuhlman, J.M., Three-component velocity measurements in a turbulent recirculating bubble-driven liquid flow. Int. J. Multiphase Flow 18 (3), Hassan, Y.A., Blanchat, T.K., Jr, C.H.S., Canaan, R.E., Simultaneous velocity measurements of both components of a two-phase flow using particle image velocimetry. Int. J. Multiphase Flow 18, Iguchi, M., Takeuchi, H., Morita, Z., The flow field in air water vertical bubbling jets in a cylindrical vessel. ISIJ Int. 31 (3), Iguchi, M., Shinkawa, M., Nakamura, H., Morita, Z., Mean velocity and turbulence of water flow in a cylindrical vessel agitated by bottom air injection. ISIJ Int. 35 (12), Johansen, S.T., Robertson, D.G.C., Woje, K., Engh, T., Fluid dynamics in bubble stirred ladles: part i. Experiments. Metall. Trans. B 19B, Lakehal, D., Smith, B.L., Milelli, M., Large-eddy simulation of bubbly turbulent shear flows. J. Turbul. 3, Lance, M., Bataille, J., Turbulence in the liquid phase of a uniform bubbly air water flow. J. Fluid Mech. 222, Lance, M., Marie, J., Bataille, J., Homogeneous turbulence in bubbly flows. J. Fluids Eng. 113, Launder, B., The prediction of forced-field effects, on turbulent shear flow in second-moment closure. Adv. Turbul., 338. Martinez-Bazan, C., Lasheras, J.C., Turbulent transport mechanisms in oscillating bubble plumes. Experimen. Therm. Fluid Sci. 25, Mudde, R.F., Lee, D.J., Reese, J., Fan, L.S., Role of the coherent structures on reynolds stresses in a 2-d bubble column. AIChE J. 43, Rensen, J., Roig, V., Experimental study of the unsteady structure of a confined bubble plume. Int. J. Multiphase Flow 27, Ruzicka, M.C., Draho, J., Fialov, M., Thomas, N.H., Effect of bubble column dimensions on flow regime transition. Chem. Eng. Sci. 56, Sene, K.J., Hunt, J.C.R., Thomas, N.H., The role of coherent structures in bubble transport by turbulent shear flows. J. Fluid Mech. 259, Sheng, J., Meng, H., Fox, R.O., A large eddy piv method for turbulence dissipation rate estimation. Chem. Eng. Sci. 55, Simiano, M., Zboray, R., de Cachard, F., Lakehal, D., Yadigaroglu, G., Comprehensive experimental investigation of the hydrodynamics of largescale, 3d bubble plumes. Int. J. Multiphase Flow 18, Simiano, M., Lakehal, D., Lance, M., Yadigaroglu, G., Turbulent transport mechanisms in oscillating bubble plumes. J. Fluid Mech. 633,