PIV measurements of turbulence in an inertial particle plume in an unstratified ambient

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1 PIV measurements of turbulence in an inertial particle plume in an unstratified ambient D.B. Bryant & S.A. Socolofsky Zachry Department of Civil Engineering, Texas A&M University, USA ABSTRACT: A high-speed particle image velocimetry study was conducted to find the mean and turbulent properties of an inertial particle plume in an unstratified ambient. The experiments were conducted in a 2.0m by 1.0m by 1.5m deep tank with 2.0mm particles driving the negatively buoyant plume. The experiments show the plumes to have similar time averaged nondimensional velocity and vorticity profiles within the measured flow rates. Furthermore, the nondimensional turbulent stresses are also similar. The turbulence of the inertial particle plumes was also found by the identification and quantification of the vortices in the plumes. As with the velocity profiles and turbulent stresses, similarity existed across the measured flow rates for the vortex properties. Lastly, the turbulent energy spectra shows a modification to the dissipation of the turbulent energy as the slope is of the spectra is changed from -5/3 to -7/6 as found in bubbly flows. 1 INTRODUCTION Multiphase jets and plumes are common in both environmental and industrial applications, examples including, bubble plumes, droplet plumes, and loop reactors. One subset of multiphase plumes occurring in the environment are negatively buoyant dispersed phase plumes such as sediment plumes and CO 2 sequestration plumes (Wannamaker and Adams 2006). The mean and turbulent properties of multiphase plumes are difficult to measure experimentally since the dispersed phase interferes with measurement methods such as acoustic Doppler velocimetry (ADV) and laser Doppler velocimetry (LDV). Experiments conducted by Bryant et al. (2009) and Simiano et al. (2006) successfully used particle image velocimetry (PIV) to capture the turbulent stresses of bubble plumes. Futhermore, Bryant et al. (2009) analyzed the PIV data using vortex identification methods and found that the largest and most energetic vortices lay along the plume edge in bubble plumes. However, the mean of turbulence properties of inertial particle plumes have not been investigated using high-speed PIV. Beyond turbulent stresses and vortex properties, investigation into the turbulent energy spectra of multiphase plumes are important with previous studies in bubbly pipe flow (Lance and Bataille 1991; Shawkat et al. 2007; Rensen et al. 2005) finding the turbulent kinetic energy dissipation rate changing from the classical slope of -5/3 to -7/6. High-speed PIV has been used successfully by Bryant et al. (2009) to identify changes in the turbulent energy spectra due to the dispersed phase in bubble plumes. This paper presents a high-speed PIV study of an inertial particle plume quantifying the mean flow, turbulent Reynolds stresses, vortex properties, and turbulent energy spectra. The following section will detail the experimental setup, followed by sections explaining the analysis and results of this study.

2 2 PHYSICAL MODEL The PIV experiments in this study are performed in a glass-walled tank measuring 1.0m by 2.0m by 1.5m deep in the Ocean Engineering Wave Tank Laboratory of the Zachry Department of Civil Engineering at Texas A&M University. The plume is generated with particles having an average diameter of 2mm and specific gravity of 2.5. These particles are delivered through a funnel system at the water surface to minimize any initial velocity. The mass flow rate of the inertial particles for case A, B, and C are , , and kg/s respectively. The characteristic length to the asymptotic region of the plume from the diffuser is given by Bombardelli et al as (1) where g is the gravitational constant, Q g is the volumetric flow rate at the diffuser,! is the entratinment coefficient, taken as 0.083, and w b is the slip velocity of the inertial particles found to be approximately 0.4 m/s. Comparing the length scale, D, and the distance from the diffuser to the field of view 51.4 cm, the inertial particle plume should be within the asymptotic region. The plane of observation is illuminated by a 10 Watt Argon-Ion laser. A high-speed Phantom camera with a resolution of 1024 by 1024pixels captured a 12.4 by 12.4cm region every 2.22ms (450Hz) with an exposure time of 200!s. The Phantom camera has an internal memory of 2 GB allowing for 2,000 images to be stored during the experiment with a total of 10,000 images captured for each flow rate. 3 ANALYSIS Before PIV analysis of the captured images can occur, the inertial particles must be removed using image processing techniques. This pre-processing removes the inertial particles based on size and brightness leaving only the seeding particles which move with the liquid phase of the plume. The PIV analysis is performed in DaVis (LaVision 2002) using a multi-pass crosscorrelation PIV analysis of decreasing interrogation window sizes, 32 by 32 pixel to 16 by 16 pixel, with 50% overlap. This analysis resulted in velocity vectors on an 8 by 8 pixel grid corresponding to a 0.97 by 0.97mm grid. Errant vectors are removed using a median filter which compares the value of a vector with the root mean square of neighboring vectors. Due to the removal of the inertial particles and errant vectors, the velocity fields are missing some velocity vectors. These missing velocity vectors are interpolated using a krigging interpolation scheme. The final velocity fields are used to calculate the vorticity and local swirl strength, defined as the imaginary portion of the eigenvalue of a two-dimensional velocity gradient tensor (Adrian et al. 2000). The local swirl strength has been shown to identify vortices in the flow, working well even in regions of high shear. The size of the vortex is defined as the area of a contiguous region of nonzero swirl strength. By matching the local swirl strength contours with the corresponding vorticity field, the size, circulation, and enstrophy of each vortex identified in the flow can be calculated (Bryant et al. 2009). Finally, using the velocity, vorticity, and vortex properties the mean flow and turbulent properties of an inertial particle plume can be quantified. 4 RESULTS The velocity fields are used to find both the mean and turbulent properties of the inertial particle plumes. The nondimensional time averaged velocity (subplot a) and vorticity (subplot b) profiles are shown in Figure 1. Velocity and vorticity profiles are nondimensionalized by the absolute value of the time averaged centerline vertical velocity, v c, and the plume radius, r. The plume radius is found as the distance from the plume center to the point at which the time averaged velocity is 1/e of v c. Figure 1 shows self-similartiy for the velocity and vorticity profile within the measured buoyancy fluxes and as expected the vorticity profile corresponds to the de-

3 rivative of the velocity. The horizontal velocity, u, shows a negative value outside of the plume edge which corresponds to the entrainment of fluid into the plume from the ambient. Figure 1. Average nondimensional velocity profile (a) and nondimensional vorticity profile (b) of the inertial particle plumes for case A, B, and C. Figure 2 presents the profile of the time averaged vertical turbulent stress, v"v" and u"v. Unlike the velocity profile and vorticity which used the centerline velocity, v c, the local velocity, v(x), was needed to collapse the time averaged turbulent stresses. The nondimensional turbulent stress increases from the center to the plume edge. The other time averaged turbulent stress component, u"u', was also calculated and collapsed similarly to the results presented in Figure 2. Figure 2. Average nondimensional trubulent stress versus position in the plume for case A, B, and C. The probability of the nondimensional vortex size for each inertial particle flow rate (subplot a) along with the average nondimensional vortex size versus position in the plume (subplot b) is presented in Figure 3. The vortex size which corresponds to the surface area in PIV crosssection is nondimensionalized by the plume radius, r, squared. Subplot (a) shows that the distribution of vortex size collapses into a single PDF for all the inertial flow rates tested in this study. As expected the occurrence of large vortices is much smaller than that of small eddies agreeing with the concept of turbulent energy cascade. Furthermore, subplot (b) shows that the average vortex size is also similar for all the tested flow rates and that the largest vortices exist between 0.5 and 1.0 of the plume radius, in the region of highest vorticity in Figure 1. The average size of the vortices diminish after the plume edge due the lack of turbulent energy input from either the inertial particle wake or shear layer instabilities.

4 Figure 3. Average probability distribution function for nondimensionalized vortex size (a) and average vortex size versus position in the plume (b) for all case A, B, C. In addition to the average vortex size, the maximum vortex size can be found. Figure 4 shows the nondimensional maximum vortex size versus position in the plume with peak values around 0.6 times the radius of the plume. As with the average vortex size, the maximum occurs in the region of greatest vorticity and reduces after the plume edge. The length scale of the largest vortices in the flow would be similar to the integral length scale in the flow. The integral length scale in multiphase flows have been shown to be reduced due to the presence of the dispersed phase explaining the integral length scale not being equivalent to the plume radius as expected. Figure 4. Maximum nondimensional vortex size versus nondimensional horizontal position in the plume. Beyond the vortex properties, the turbulent energy spectra have shown modification in bubbly flows. Figure 5 shows the nondimensional turbulent energy spectra for all three flow rates at both the plume center and plume edge. As with other properties, the turbulent energy spectra collapse with the correct nondimensionalization, here being the integral length scale L 1 and the vertical Reynolds stress. Along the plume center, the turbulent energy spectrum was found to have a slope more closely to -7/6 (bold solid line) than the classical -5/3 (bold dashed line). This slope had been identified in bubbly flows by Lance and Bataille (1991), Rensen et al. (2005), and Bryant et al. (2009). However along the plume edge where there is little to none of the dispersed phase (inertial particles), the turbulent energy spectra more closely matches the classical slope of -5/3. This change in the turbulent energy spectra is associated with the input of turbulent energy at a separate length scale, length scale of the dispersed phase, than that of the integral length scale as explained by Balachandar (2009).

5 Figure 5. Nondimensional turbulent energy spectra at the center of the plume (a) and plume edge (b) for case A, B, and C. 5 CONCULSIONS This paper presented a high-speed PIV study of inertial particle plumes and successfully determined the mean and turbulent properties of the liquid phase. Three different flow rates were compared with 2.0mm particles driving the flow as a Phantom camera captured a 12.4 by 12.4cm region. Pre-processing image analysis was successfully used to remove the inertial particles before the PIV analysis. Using the resulting fields it was found that the time averaged nondimensional velocity and vorticity profiles are self-similar within the experimental flow rates when using the centerline velocity and plume radius for nondimensionalization. Futhermore, the nondimensonal turbulent stresses were found to be similar when nondimensionalized by the local velocity, v. Using the local swirl strength as a vortex identification method, vortex properties were calculated including the probability distribution function of the vortex size, average vortex size and maximum vortex size. These properties were found to be similar when nondimensionalized by the plume radius, r. The maximum vortex size suggested the characteristic length scale of the turbulence to be 0.6 of the radius. Finally, the turbulent energy spectra of the plumes in two different locations were compared. As with other multiphase flows, the slopes of the spectra were modified in the region with the dispersed phase to -7/6. This change was in agreement with bubbly flow studies. This study shows the dynamics of inertial particle plumes to be similar to other multiphase plumes. However, more studies will need to be conducted to determine if this is true for all sizes of inertial particles. ACKNOWLEGMENT This research is based upon work supported by the National Science Foundation under Grant No. CTS This support is gratefully acknowledged. REFERENCES Adrian, R. J., Christensen, K. T., and Liu, Z. C Analysis and interpretation of instantaneous turbulent velocity fields. Experiments in Fluids 29: Balachandar, S A scaling analysis for point-particle approaches to turbulent multiphase flows. International Journal of Multiphase Flow 35:

6 Bombardelli, F. A., Buscaglia, G. C., Rehmann, C. R., Rincon, L. E., and Garcia, M. H Modeling and scaling of aeration bubble plumes : a two-phase flow analysis. Journal of Hydraulic Research 45: 617. Bryant, D. B., Seol, D.-G., and Socolofsky, S. A Quantification of turbulence properties in bubble plumes using vortex identification methods. Physics of Fluids 21: Lance, M. and Bataille, J Turbulence in the liquid phase of a uniform bubbly air-water flow. Journal of Fluid Mechanics 222: LaVision GmbH DaVis Flowmaster Software for DaVis 6.2. Goettingen, Germany. Rensen, J., Luther, S., and Lohse, D The effect of bubbles on developed turbulence. Journal of Fluid Mechanics 538: Shawkat, M. E., Ching, C. Y., and Shoukri, M On the liquid turbulence energy spectra in twophase bubbly flow in a large diameter vertical pipe. International Journal of Multiphase Flow 33: Simiano, M., Zboray, R., de Cachard, F., Lakehal, D., and Yadigaroglu, G Comprehensive experimental investigation of the hydrodynamics of large-scale, 3D, oscillating bubble plumes. International Journal of Multiphase Flow 32: Wannamaker, E. J. and Adams, E. E Modeling descending carbon dioxide injections in the ocean. Journal of Hydraulic Research 44:

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