PDA MEASUREMENTS OF TWO-PHASE FLOW STRUCTURE AND PARTICLE DISPERSION FOR A PARTICLE-LADEN JET IN CROSSFLOW*

FAN Jing-yu, XU Song-li, WANG Dao-zeng

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China, E-mail: jyfan@shu.edu.cn

(Received January 19, 2009, Revised March 25, 2009)

PDA MEASUREMENTS OF TWO-PHASE FLOW STRUCTURE AND PARTICLE DISPERSION FOR A PARTICLE-LADEN JET IN CROSSFLOW*

FAN Jing-yu, XU Song-li, WANG Dao-zeng

Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China, E-mail: jyfan@shu.edu.cn

(Received January 19, 2009, Revised March 25, 2009)

The two-phase flow structure and particle dispersion for a dilute particle-laden jet in crossflow (JICF) were experimentally investigated by means of Phase Doppler Anemometry (PDA) measurement. The two-phase flow experiments were conducted for different flow conditions and solid particle parameters, including the ratio of the jet velocity to crossflow velocity, the particle size and mass loading. The experimental results indicate that the fine particles with the size of 70 micron and the mass loading of 0.05% have a minor influence on the mean and fluctuation velocity fields of the two-phase JICF. However, the fine particle transport by the two-phase JICF is dominantly and preferentially affected by the shear layer vortices and exhibits a somewhat enhanced dispersion as compared to the fluid. For the coarse particles with the particle size ranging from 300 micron to 700 micron and the mass loading less than 0.16%, the effect of the particle parameters on the fluid phase is associated with both the anisotropic properties of the flow field and the trajectory deviation of the settling particles from the fluid. Compared to the single-phase JICF, the two-phase JICF laden with the coarse particles is recognized to possess more pronounced mean velocity alteration and turbulence modulation of the fluid phase in the presence of the particles with the larger particle size and higher mass loading.

jet, crossflow, two-phase flow structure, particle dispersion, Phase Doppler Anemometry (PDA) measurement

1. Introduction

A particle-laden jet in crossflow (JICF) is a generic complex two-phase flow, and the transport and dispersion of the particles are not only influenced by the fluid phase properties, such as local turbulence structure, but also responsible for the turbulence modulation due to the feedback from the particles to the fluid phase even with the restriction to the dilute two-phase flow regime. Such flow configuration is relevant to a wide variety of environmental and industrial applications, such as the discharge of sediment-laden domestic and industrial effluent into coastal and estuarine receiving waters, the jet scour in hydraulic engineering, the side-cast jet in waterway dredging engineering, the mixing vessel in chemical process, and so on[1-3].

It is well known that for single-phase JICF, the flow field shows highly three-dimensional and anisotropic properties in the near field, and the complex interaction between the jet and crossflow leads to the formation of a series of main vortical structures, including the shear layer vortices, thehorseshoe vortex, the wake vortices and the Counter-rotating Vortex Pair (CVP), among which the unique CVP is crucial to the flow evolution as well as the enhanced entrainment and mixing rate of the JICF compared to those of a free jet[4]. Numerous experimental and numerical studies have been carried out with regard to the trajectory, the velocity and vorticity fields, and the passive scalar mixing for the single-phase or constant-density JICF[5-9]. And the effect of the wall confinement on the JICF has also been investigated for its relevance to the pollutant discharge into shallow water in our recent work[10-14].

Unlike the single-phase JICF, the particle-laden JICF, however, has not been extensively investigated yet. A relative majority of previous studies concerning two-phase JICF involve air as the fluid phase, whereas few experimental or numerical studies are available for liquid-solid two-phase JICF, resulting in the insufficient understanding concerning both the particle dispersion and turbulence modulation. This is firstly due to that the transport and dispersion of the specific particles can be to a certain extent dominated by the local flow structures of the JICF, which interacts mutually with one another in a complex manner and span over a specific range of spatial and temporal scales, but usually differ from the passive scalar mixing due to the particle inertia and other physical mechanisms by which the particles are likely to follow the fluid phase imperfectly. Furthermore, this is also in part attributed to the difference of the particle-to-fluid density ratio ρp/ρf, where ρpandfρ are the particle and fluid densities, respectively. In the case of gas-solid JICF, owing to the great difference between the particle and gas densities, i.e., ρf/ρp?1, the significant forces acting on the “heavy” particles primarily involve the particle inertia and drag. In addition, the influence of the body force on the particle motion is also of considerable importance in some situations, and the other forces such as the virtual mass force, the Basset force and the lift force are commonly negligible for simplification. For the case of liquid-solid JICF, the particle density ρpis of the same order as the fluid densityfρ, and the above-mentioned simplification, in contrast, is no more applicable to this case[15]. The conventional governing equation for predicting the particle motion in the two-phase flow, such as the Boussinesq-Basset-Oseen (BBO) equation or its modified version, is likely to be excessively complicated to solve for the liquid-solid JICF. The presence of the solid particles further causes a sort of additional complexity to the particle dispersion and turbulence modulation due to the complicated inter-phase interaction, which is still incomplete and difficult to tackle either theoretically or numerically based on the common advection-diffusion equation of the particle transport with practical engineering interest.

Therefore, the experimental investigation presented in this article is focused on the flow structure and particle-fluid interplay with regard to dilute liquid-solid two-phase JICF by means of Phase Doppler Anemometry (PDA) measurements, thus making quantitative assessment of the two-phase flow feature and the particle dispersion as well as the impact of the particle parameters, e.g., the particle size and mass loading, on the fluid phase under different flow conditions.

2. Experimental facilities and measurement techniques

The experiments were carried out in an open channel flume with a rectangular test section of 2.0 m in length, 0.25 m in width and 0.5 m in height. Both sidewalls and bottom wall of the channel flume were made of glass plates allowing visual observation and laser optical access to the interior of the flow field over the entire test section length. The recirculated water (as the crossflow fluid with the densityfρ close to 1000 kg/m3) of the channel flume was supplied from a large rectangular water tank of 1.6 m in depth, 1.3 m in length and 2.1 m in width. The particle-laden jet was gravity-driven from a small water tank with the auxiliary system, consisting of a weir plate in the interior to maintain constant water head and a stirrer arrangement to keep the added particles well mixed during the experiments, located above the channel flume, and then injected continuously and vertically downward into the crossflow from a long cylindrical pipe with an internal diameter d of 5.5 mm during the experiments. The jet pipe was vertically positioned at about 1.2 m downstream of the test section inlet, and the nozzle velocity uj, which exhibited a velocity profile of fully developed pipe flow, could be regulated using a rotator flowmeter. To avoid local disturbance on the free surface of the channel flow, the jet nozzle was adjusted and placed slightly beneath the free surface of the crossflow about 1cm. The required velocity uc(nearly fully developed velocity profile) and water depth H of the channel flow could be obtained by suitably adjusting both the rotating speed of a frequency-controlled centrifugal water pump and the opening of a tail gate located at the end of the channel flume.

The present experiments were performed at five jet-to-crossflow velocity ratios (R=uj/uc=2, 4, 6, 8 and 10), and the water depth H was fixed (H/d =20) in each run. The operating conditionswere achieved by altering the jet nozzle velocity ujand keeping the crossflow velocity ucfixed for convenience. The Reynolds number Rej(based on the jet nozzle velocity ujand diameter d) varied from 1.43×103to 7.15×103in the experiments, and the Reynolds numbers Rec(based on the crossflow velocity ucand water depth H) was 1.56×104.

Two types of the solid particles (glass beads with a refractive index of 1.51) were used in the two-phase flow experiments, namely (1) the fine particles with the mean diameter D of 70 μm and the density of ρp=1050kg/m3, and (2) the coarse particles with the mean diameters D ranging from 300 μm to 700m μm and the density of ρp=2450kg/m3. For the fine particles, the particle-fluid mixture of the smaller water tank was directly supplied from the large water tank, and the smaller and larger water tanks were connected by a bypass pipe through which the surplus particle-fluid mixture spilling over the weir plate in the small water tank was drained into the large one, indicating the fine particles seeding both the jet and crossflow fluid. For the coarse particles, the particle-fluid mixture of the smaller water tank was supplied from an additional agitator tank by a submerged pump, which generated sufficiently strong circulations inside the tank and kept the particles well mixing in suspension, and the bypass pipe was alterably connected between the smaller water tank and the agitator tank, namely the coarse particles only seeding the jet fluid. Furthermore, the addition of the particles should meet two essential requirements: there were sufficient particles for statistically reliable measurements at each measuring position, and besides, the overall particle mass (or volume) loading should be low enough and thus the flow field was limited to the dilute liquid-solid two-phase flow regime. To this end, the added particle concentration was properly chosen, and the fine particle mass loading φ (defined as the ratio of the particle to fluid mass flow rates) was 0.05% while the coarse particle mass loading φ=(0.08%, 0.16%).

A PDA was used to measure the velocity, size and concentration distributions of the particles in the flow field. Besides the solid particles, the tracer particles (spherical glass beads) with the mean diameter of approximately 10 μm and the density of 1050 kg/m3were also added to both the jet and crossflow fluid, thus allowing the simultaneous measurements of both phases by the discrimination method according to their size difference. The transmitting and receiving optics of the PDA (Dantec Fiber PDA) system were mounted on a three-dimensional traversing system controlled by a computer. To improve signal-to-noise ratio and reach high data-collecting rate, the receiving and transmitting probes of two-component PDA were on the both sides of the channel flume (namely using forward scatter mode), respectively, and the receiving probe was mounted at a scattering angle of about 30oin order to ensure high scattering intensities for the seeding particles, as illustrated in Fig.1.

Fig.1 Installation of PDA measurement system

The maximum samples and the maximum acquisiti4on time for the PDA measurement were set to be 2×10 and 300 s, respectively. The data rate could reach to 1 kHz or so throughout the measurement due to the presence of sufficient particles in the flow field. The mean and turbulence properties of both phases at about 30 positions along the vertical direction y (where the y axis was directed upward andy=0 was located at the bottom wall), which were on each vertical centreline of the channel flume, were measured in the experiments. The lowest measurement position was properly chosen depending on the jet penetration while the top one was kept 92 mm (corresponding to y/ d≈16.7) away from the wall. During the course of the profile measurements, the variable moving steps of the traversing system were used to obtain the detailed data in the vicinity of the large velocity gradient positions. The PDA measurement covered eight different sections in the downstream of the jet nozzle from the proximal position x/ d=1 up to the far fieldx/ d=30 along the streamwise directionx (where the x axis was directed downstream and x=0 was located at the streanwise position of the jet nozzle).

3. Results and analyses

3.1 Flow evolution and particle number concentration

distribution for fine particles

Fig.2 Mean velocity profiles of both phases at each vertical centreline (R=6)

The gross flow feature of the single-phase JICF has been revealed both experimentally and numerically in literature, and the flow field of the JICF is dependent primarily on the jet-to-crossflow velocity ratio R. In the near field, the momentum-dominated jet at the relatively high velocity ratio penetrates into the crossflow, and is subsequently deflected and aligned with the crossflow. In the present experiments, the flow fields of the JICF laden with the fine particles at different jet-to-crossflow velocity ratios yield a somewhat fundamental similarity with respect to the trajectory, the mean and fluctuation velocity profiles in the near and far fields, and thus only the results at a specific operating run, namely R=6, are presented in detail.

Figure 2 shows the evolution of the mean velocity profiles of both phases at different vertical centrelines from the proximal position x/ d=1 up to the far field x/ d=30. In general, the mean velocity profiles of both phases appear to be more anisotropic in the near field than those in the far field. This is attributed to the effect of the induced vortical structures on the evolution of the mean velocity field, in respect that these vortices, such as the shear layer vortices and the CVP, stem from the formation and evolution of the skewed shear layer in which the initial momentum gradually decays due to the entrainment between the jet and the ambient crossflow.

It can be also observed from Fig.2 that the mean velocity profiles of both phases are basically similar in either the near field or the far field, indicating that the fine particles are likely to follow the fluid motion nearly exactly. However, at a few measurement positions in the near field, as indicated by the arrows in Fig.2(a), there is a somewhat tiny difference between the particle and fluid phases in the vicinity of the peak position, and the measured results indicate that the maximum inter-phase slip streamwise velocity at these specific positions is less than 0.1ucin magnitude.

The turbulence fluctuation properties of the particle and fluid phases can be analyzed in terms of their corresponding root-mean-square (rms) velocities. The evolution of the fluctuation velocity profiles of both phases at various vertical centrelines are plotted in Fig.3. It can be seen from the figure that the rms velocity distributions of both phases can be single- or double-peaked in magnitude, which is also due to the anisotropic flow structure produced by the jet/crossflow interaction. For example, the double-peaked vrmsdistributions of both phases occur in the near field due to the effect of the upper and lower shear layers between the skewed jet and the surrounding crossflow, while the single-peakedvrmsdistributions of both phases occur in the far field due to the effect of the downwash between the CVP. Despite of a rather slight difference between bothphases with regard to the fluctuation velocity in the lower shear layer, as indicated by the arrows in Fig.3, the amplitudes of the rms velocity distributions for both phases are still similar to a great extent.

Fig.3 Rms velocity profiles of both phases at each vertical centreline (R=6)

Fig.4 Particle number concentration CNprofiles at each vertical centerline

On the whole, the addition of the fine particles exerts a minor influence on the mean and fluctuation velocity fields of the two-phase JICF. The mean and fluctuation velocity profiles of both phases show the strong three-dimensionality and anisotropic characteristics in the near field, and tend to be relatively uniform in the far field.

In addition, the particle number concentration CNcan be measured by means of PDA. The fine particles are transported in suspension by the fluid phase, and have no appreciable particle settling within the near field. To eliminate the resulting absolute error related to the particle concentration measurement, the particle number concentration CNat each measuring position is normalized by the average value Cavat each vertical centreline. It can be seen from Fig.4 that the particle number concentration is markedly nonuniform throughout the flow field, and the double-peaked CNdistributions occur in the near field, indicating that the particle preferential concentration occurs proximately downstream of the jet exit. With increasing downstream distance, the vertical range between the two CNpeak positions tends to be expanded and shifted downwards, and this trend is maintained even up to the far field.

Fig.5 Comparison between the peak positions of vrmsand CNat each vertical centreline

To identify the relationship between the particle dispersion and the local flow structure of the two-phase JICF, the corresponding double-peaked positions of the particle number concentrationCNtogether with the rms velocity fluctuation vrmsare simultaneously plotted at each vertical centreline for x/ d ≤6 within the near field, as shown in Fig.5. It is clearly observed from Fig.5 that the double-peaked positions of the CNare closely associated with those of vrms, indicating the considerable consistent propensity to their relative orientation, that is, the double-peaked positions of the CNare located, relative to the jet trajectory, outside those of the vrms. This indicates that the fine particles exhibit a somewhat enhanced dispersion as compared to the fluid, and tend to migrate toward the outer edge of the jet shear layer.

It can be further inferred that even at relatively low mass loading φ=0.05%, the fine particle transport by the two-phase JICF in the near field is dominantly affected by the shear layer vortices, and the particle dispersion, depending upon the local flow structure and the Stokes number, is radically different from the passive scalar mixing, due to the superimposition of both the interdependent and compatible effects, namely the strong inter-phase interaction and the jet/crossflow interaction.

3.2 Effect of coarse particle size on the fluid phase

For the case of the two-phase JICF laden with the coarse particles, the corresponding particle Stokes numbers are as large as O(102) for the different sized particles in the range of 300 μm-700 μm, and it can be inferred that owing to the particle inertia and gravity, the coarse particles do not follow the fluid motion perfectly, resulting in an appreciable separation between the coarse particle and fluid motions. Large numbers of the particles are concentratively deposited on the bottom wall downstream of the jet exit, and the particles remaining in suspension are able to follow the large-scale fluid motion partly, subsequently giving rise to nonuniform gravitational deposition pattern along the farther downstream direction. Special attention is hereby paid to the impact of the main particle parameters, including the particle size and mass loading, on the fluid phase in the near field, and the results obtained from the PDA measurements are only given at the specific position (x/ d=4) in the near field for simplicity.

Figures 6 and 7 depict the mean and fluctuation velocity profiles of the fluid phase for the two-phase JICF at relatively low mass loading φ=0.08%, respectively. For comparison, the corresponding results of the single-phase JICF under the same flow condition are also given. It is observed from Fig.6 that the effect of the particle size on the mean streamwise velocity component u is more noticeable than that on the mean vertical velocity component v. In particular, there is a local region, located in the vicinity of the minimum u position, where the effect of the particle size on the mean streamwise velocity distributions is much more remarkable than elsewhere. With increasing particle size, the streamwise velocity component u of the fluid tends to increase in amplitude. It is noted that the minimum streamwise velocity component uis an indication of the jet/crossflow interaction, corresponding to the most intense entrainment between the particle-laden jet and the crossflow. Consequently, the inter-phase momentum exchange in this local region is thereby enhanced and transferred to the fluid, resulting in the increasing streamwise velocity in amplitude.

Fig.6 Mean velocity profiles for single- and two-phase JICFs (R=6,x/ d=4)

Fig.7 Rms velocity profiles for single- and two-phase JICFs (R=6,x/ d=4)

On the other hand, the turbulence modulation of the fluid phase by the coarse particles is a little detectable, as shown in Fig.7, and the addition of the coarse particles appears to augment the fluctuation velocity of the fluid phase in an indeterminate manner as compared to the single-phase case. In this regard, the different sized coarse particles remaining in suspension, even with the relatively large Stokes number at the same vertical centreline lead to a discrepant reduction in the particle concentration, and thus augment the fluid turbulence to a decreasing degree at relatively low mass loading.

3.3 The effect of the coarse particle mass loading on

the fluid phase

The effect of the coarse particle mass loading, in combination with the particle size, on the fluid phase is considered in the experiments. Figures 8 and 9 depict the mean velocity profiles for different particle sizes and mass loading rates for the single- and two-phase JICFs. Note that the results of the single-phase JICF is referred to those at φ=0.

Fig.8 Mean velocity u profiles for single- and two-phase JICFs (R=6,x/ d=4)

It can be noted from Figs.8 and 9 that in the range of the particle mass loading under consideration, namely φ=0.08% and 0.16%, the jet penetration for the two-phase JICF at various mass loading rates are almost similar to that for the single-phase JICF, since the mean velocity peak positions of the fluid phase have no appreciable change. Similarly, in the local region in the vicinity of the minimum u position, the strong momentum exchange between the particles and the fluid is sufficient for altering the streamwise velocity profiles of the fluid phase, and this trend is more pronounced at higher mass loading. While the effect of the particle mass loading on the mean vertical velocity component v occurs primarily in the lower shear layer, and the amplitude of the vertical component of the fluid velocity tends to increase in the presence of the particles with the higher mass loading. It should be noted that beneath the lower shear layer, the effect of the particle mass loading on the mean vertical velocity v is inconsistent with that in the lower shear layer, which might be due to the distinct mutual interaction mechanism, such as the particle-wall collision.

Fig.9 Mean velocity v profiles for single- and two-phase JICFs (R=6,x/ d=4)

The fluctuation velocity profiles of the fluid phase at different particle sizes and mass loading rates are plotted in Figs.10 and 11. The effect of the particle mass loading on the mean and fluctuation velocity distributions of the fluid phase is more pronounced for the coarse particles with the size of 500 μm than that with the size of 300 μm. With increasing particle size and mass loading, the turbulence modulation of the fluid phase by the coarse particles occurs to an increasing degree, especially in the lower shear layer.In this local region, the coarse particles are less susceptible to the fluid motion due to their high inertia, and the inter-phase interaction at high mass loading plays an important role in the fluid phase, indicating that the coarse particles tend to enhance the fluid turbulence due to both their crossing trajectory effect and the vortex shedding from the particles.

Fig.10 Rms velocity urmsprofiles for single- and two-phase JICFs (R=6,x/ d=4)

4. Conclusions

In this article, the two-phase flow structure and particle dispersion characteristics of a dilute particleladen JICF have been experimentally investigated by means of PDA measurement. The liquid-solid two-phase flow experiments have been conducted for different flow conditions and solid particle parameters, including the jet-to-crossflow velocity ratio, the particle size and mass loading. The following conclusions can be drawn from the experimental results:

(1) The fine particles with the size of 70 micron and the mass loading of 0.05% have a minor influence on the mean and fluctuation velocity fields of the two-phase JICF. However, the particle transport by the two-phase JICF in the near field is dominantly and preferentially affected by the shear layer vortices and exhibits a somewhat enhanced dispersion as compared to the fluid due to the superimposition of both the interdependent and compatible effects, namely the strong inter-phase interaction and the jet/crossflow interaction. This is radically different from the passive scalar transport and mixing in the single-phase JICF.

Fig.11 Rms velocity vrmsprofiles for single- and two-phase JICFs (R=6,x/ d=4)

(2) For the coarse particles with the particle size ranging from 300 micron to 700 micron and the mass loading less than 0.16%, the effect of the particle parameters on the fluid phase is associated with both the anisotropic properties of the flow field and the trajectory deviation of the settling particles from the fluid in the near field, resulting in the inconsistent trend concerning the mean flow and turbulence modulation in various local regions.

(3) Compared to the single-phase JICF, the two-phase JICF laden with the coarse particles is recognized to possess more pronounced mean velocity alteration and turbulence modulation of the fluid phase in the presence of the particles with the larger particle size and higher mass loading.

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10.1016/S1001-6058(09)60022-6

* Project supported by the National Natural Science Foundation of China (Grant Nos. 10572084, 10972134), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20050280008).

Biography: FAN Jing-yu (1968-), Male, Ph. D., Associate Professor

WANG Dao-zeng,

E-mail: dzwang@staff.shu.edu.cn