Experiments in Fluids [Suppl.] S185±S193 Ó Springer-Verlag 2000
Simultaneous measurement of fluid and dispersed phases in a particle-laden turbulent channel flow with the aid of 3-D PTV Y. Suzuki, M. Ikenoya, N. Kasagi
Abstract Three-dimensional high-de®nition particle tracking velocimetry is successfully applied to simultaneous measurement of ¯uid and dispersed phases in a vertical turbulent water channel ¯ow. Turbulence statistics are substantially modi®ed by the solid particles having a diameter of twice the Kolmogorov length scale. The streamwise turbulence intensity of the ¯uid phase is signi®cantly increased in the channel, whilst it is unchanged at y+ < 20. In contrast, the wall-normal and spanwise components are increased in the whole crosssection. In the center of the channel, the wake behind a solid particle has almost the same streamwise length as that around a sphere in the uniform ¯ow, and particles tend to align in the streamwise direction as they ¯ow downstream. The quadrant analysis shows that the solid particles are densely distributed along the low-speed streaks, especially beneath the ejection event. The difference in traceability of particles to the ejection and sweep events should contribute to the particle agglomeration.
1 Introduction Particle-laden turbulent ¯ows are common in natural and industrial processes, and it is important to understand the underlying physical mechanism, especially in wall turbulence, from both engineering and environmental viewpoints. Recently, turbulence modi®cation by solid particles is also investigated extensively for achieving heat transfer augmentation and/or drag reduction (e.g. Kane 1989; Kurosaki et al. 1986; Hetsroni et al. 1995; Hishida and Maeda 1994). Fessler et al. (1994) found from their experiment in a wind tunnel that solid particles are not uniformly distributed in space and time, but concentrated in the low vorticity regions. Kaftori et al. (1995) showed that particles are densely distributed in the low-speed streaks in their horizontal turbulent channel. These ®ndings indicate that particle clusters are often generated in particle-laden turbulent ¯ows, and they should play an important role in Y. Suzuki (&), M. Ikenoya, N. Kasagi Department of Mechanical Engineering The University of Tokyo, Hongo 7-3-1 Bunkyo-ku, Tokyo 113-8656, Japan e-mail:
[email protected] The authors are grateful to Y. Hamana and Y. Nakashima for their assistance in laboratory work.
turbulence modi®cation. Tsuji et al. (1984) measured a gas±solid two-phase turbulent ¯ow in a vertical pipe by using laser Doppler anemometry (LDA, hereafter). They showed that the effect of solid particle strongly depends on the particle diameter. Kulick et al. (1994) found from their LDA measurement in a vertical turbulent channel ¯ow that turbulence intensity is decreased when solid particles have a diameter smaller than the Kolmogorov length scale, g. Sato and Hishida (1996) simultaneously measured ¯uid and dispersed phases with the aid of digital particle image velocimetry (DPIV). They found that the turbulence intensity is increased for larger particles (dp 3g), but the near-wall behavior of the turbulence statistics have not been explored. Recent development of numerical techniques enables us to carry out direct numerical simulation of particle-laden ¯ows (e.g. Elghobashi and Truesdell 1993; Pan and Banerjee 1997; Boivin et al. 1998), and detailed information on turbulence modulation by particles was provided. However, the effect of various particle parameters on turbulence modulation remains unclear, and there are still many discussions on appropriate approach for the twoway coupling model between ¯uid and dispersed phases (Crow et al. 1996). The objectives of the present study are to provide detailed statistics of both ¯uid and dispersed phases in a particle-laden turbulent channel ¯ow, and to clarify the mutual interaction between near-wall coherent structures and solid particles. To do this, we apply a 3-D particle tracking velocimetry (hereafter, 3-D PTV) system to the simultaneous measurement of velocity vectors of solid and tracer particles.
2 3-D high-definition PTV system (3-D HDPTV) Among various particle imaging velocimetry techniques (e.g. Adrian 1991), 3-D PTV has a great advantage of obtaining instantaneous vector distributions in a 3-D volume (e.g. Nishino et al. 1989; Maas et al. 1993; Malik et al. 1993; Guezennec et al. 1994). Unlike particle imaging velocimetry using correlations between successive particle images, it can provide turbulence statistics even in the near-wall region, where the shear rate is very large. The 3-D PTV used in the present study was originally developed by Nishino et al. (1989), Nishino and Kasagi (1989) and Kasagi and Nishino (1992) for single-phase ¯ow measurement. The technique is characterized by its use of three or more TV cameras that observe tracer particles suspended in a ¯ow ®eld from arbitrary viewing direc-
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tions. Three velocity components are simultaneously measured by tracking each particle in 3-D volume. Sata and Kasagi (1992) evaluated the 3-D particle tracking algorithm over multiple time steps by using a modeled Lagrangian time spectra of velocity ¯uctuations. They showed that more than 800 velocity vectors can be obtained by tracking over four time steps. They also found that the size of the search region can be signi®cantly reduced if the turbulence characteristic time scale is suf®ciently larger than the imaging frequency. The improved 3-D PTV system has already been successfully applied to various turbulent ¯ows (Ninomiya and Kasagi 1993; Suzuki and Kasagi 1994; Kasagi and Matsunaga 1995; Suzuki and Kasagi 1999). The present measurement system is shown schematically in Fig. 1. It consists of three high-de®nition CCD cameras (Sony, XCH-1125), three laser disk recorders (Sony, HDL-5800), a digital image processor (Nexus9000), and so on. Stroboscopes synchronized with the TV signal are employed for illumination. Particle images captured by each camera are recorded onto the laser disk at 30 frames/s. Recorded images are then A/D converted and transferred to a workstation, at which further data analysis is carried out. Instantaneous 3-D vectors of tracer and solid particles are obtained from successive four sets of particle images. Details of the particle tracking algorithm and the camera calibration procedure are found in Sata and Kasagi (1992) and Kasagi and Nishino (1992), respectively. A primary system modi®cation in the present study is its use of a high-de®nition image system having 1920 ´ 1024 pixels, which are about eight times larger than that of the conventional NTSC system. With this highde®nition system, the tracer particles can be chosen in such a way that their diameter is much smaller than that of the solid particles. Fig. 2 shows an example of raw image obtained in the present experiment described later. Two kinds of particles can be easily grouped into two subsets, i.e. solid and tracer particles, depending on their image areas. Velocity vectors of both ¯uid and dispersed phases are measured by tracking each of those particles separately.
3 Evaluation of 3-D HDPTV In order to evaluate the yield of velocity vectors and the measurement accuracy of the present system, computer simulation was made with the aid of a direct numerical simulation (DNS) database of a particle-laden turbulent channel ¯ow (Mizuya and Kasagi 1998). The procedure is as follows: (i) generate solid and tracer particles numerically in the ¯ow domain, (ii) calculate particle trajectories by integrating their equation of motion, (iii) store their 3-D position at a regular time interval that corresponds to the image acquisition rate, (iv) project the 3-D position onto image planes of three virtual cameras, and generate synthesized particle images, (v) calculate photographic coordinates of each particle, (vi) reconstruct the 3-D position of particles and track each particle through the above-mentioned procedure as used in the physical experiment. The Reynolds number based on the wall friction velocity us and the channel half-width d is 150. Parameters such as the ¯ow conditions, the measurement volume size, and the camera parameters were given almost the same as those in the present experiment described later. Note that the effect of the two-way coupling between ¯uid and dispersed phases is not taken into account in the DNS database employed. Figure 3a shows the number of tracer particle trajectories NT identi®ed in the virtual measurement of the singlephase ¯ow as a function of the number of particle images IT. In the range of IT considered, NT is increased monotonically, and up to 4000 instantaneous velocity vectors are obtained. Since the maximum value of NT obtained with the NTSC system is about 600 (Ninomiya and Kasagi 1993), we can expect 6±7 times more particle trajectories by using the present high-de®nition system. Figure 3b shows the number of particle trajectories for tracer and solid particles in the particle-laden ¯ow measurement as a function of the number of solid particle images IS. The yield of solid particles NS is increased with increasing IS, while that of tracers NT is gradually decreased. About 1600 and 650 vectors are simultaneously
Fig. 1. 3-D HDPTV system
in Fig. 6. However, this arrangement illuminated particles outside of the measurement volume so that unlike the estimate shown in Fig. 3, the yield of velocity vectors is signi®cantly decreased owing to the increase of overlap among particle images. For the single-phase ¯ow, an average of 1300 instantaneous velocity vectors were obtained, whilst about 400 and 200 vectors were respectively obtained for tracer particles and solid particles in the case of the particle-laden ¯ow.
Fig. 2. Typical raw image of solid and tracer particles (380 ´ 240 pixels). Note that two successive image ®elds are overlaid in this image
obtained for tracer and solid particles, respectively. Although it is not shown here, the number of erroneous vectors is less than 0.03% of NT, and the turbulence statistics of ¯uid and particle motions obtained are in good agreement with the original DNS data. In the present physical experiment described in the following section, the viewing direction of each camera should be aligned with the incident light in order to obtain uniform image intensity of the particles, since the solid particles employed are opaque and have a light-diffusion surface. Therefore, it is necessary to employ three stroboscopes placed close to individual cameras as shown later
4 Experimental facility and measurement condition As shown in Fig. 4, the present measurement was carried out in a vertical channel, where particle-laden water ¯ows downward. The channel width H and height were 40 and 400 mm, respectively. Tracer particles were suspended in water beforehand and introduced into the ¯ow ®eld at the top of the channel by using a small pump. Solid particles were fed by using a particle loading system mounted above the upper reservoir (see Fig. 5). Particles are uniformly dropped to the centerline of the channel by the action of the roller having many tiny pits on its surface. The test section was located at 50H downstream from the inlet where the single-phase ¯ow should be fully developed. Note that the time period in which the working ¯uid travels from the channel inlet to the test section is two orders of magnitude larger than the particle relaxation time so that the particles should adapt suf®ciently to the turbulent motion of the carrier ¯uid. The test section and the camera setup are shown schematically in Fig. 6. A measurement volume was 50 ´ 25 ´ 25 mm3 in the streamwise (x), wall-normal (y), and spanwise (z) directions, respectively. Since particles in the ¯ow ®eld are observed through a glass window, refraction at the window should be compensated in the camera calibration procedure. In the present study, the Snell's law of refraction is explicitly
Fig. 3. Dependence of yield of particle tracking on the number of Fig. 4. Turbulent water channel ¯ow facility particle images. a single phase ¯ow and b particle-laden ¯ow
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condition is summarized in Table 1. The drag coef®cients of the particles are evaluated with the following formula (Clift et al. 1978):
CD 24
1 0:15Re0:687 =Rep p
1
where Rep is the particle Reynolds number based on the relative velocity between a particle and the surrounding ¯uid. The particle time constant sp is de®ned as
sp
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Fig. 5. Particle loading system
qp dp2 qf 18m
2
Ceramic spherical beads (dp 400 lm, qp/qf = 3.85) were used as solid particles. Their time constant s p nondimensionalized with us and the kinematic viscosity m is 3.6 and in the range where particles are concentrated in the low-speed streaks (Kaftori et al. 1995). The Kolmogorov length scale g was estimated to be 200 lm near the wall, and dp of the solid particles corresponds to about 2g. The volumetric concentration of solid particles is chosen as 3.2 ´ 10)4, where the substantial effect of the two-way coupling is expected (Elghobashi 1994). On the other hand, polystyrene spherical particles (dp 160 lm, qp/qf = 1.01) were used as ¯ow tracers. Their time constant s p is 0.16, and dp of the tracers is somewhat smaller than g. The volume fraction of tracers is about 1.0 ´ 10)4. Therefore, the present particle condition of the tracers is in accordance with that used in Nishino and Kasagi (1989) and Suzuki and Kasagi (1994), where turbulence statistics are obtained with high accuracy. For the single phase ¯ow, the centerline ¯uid velocity U0 is 162 mm/s. The wall friction velocity us was estimated to be 9.07 mm/s by ®tting the velocity distribution in the viscous sublayer to a pro®le predicted by a modi®ed mixing length model (McEligot 1984). The Reynolds number Res based on us and d is 172. For the particleladen ¯ow, U0 = 180 mm/s, us = 10.92 mm/s and Res = 208. Uncertainty intervals associated with the measured instantaneous velocity estimated at 95% coverage by the method of ANSI/ASME PTC 19.1(1985) are 0.06us, 0.17us, and 0.11us in the x, y and z directions, respectively.
5 Experimental results In total, 10 000 and 20 000 instantaneous velocity ®elds were obtained for single- and two-phase ¯ows, respectively. Statistics were calculated as ensemble averages of velocity vectors grouped into small data cells depending on their distance from the wall. The wall-normal interval of each data cell was set to be 0.2 mm (2m/us). The number of samples in each data cell is 5000±30 000. Figure 7 shows the distribution of the probability Fig. 6. Test section and camera setup density of velocity vectors tracked. The increase of solid particle near the wall indicates that they are concentrated incorporated into the camera parameters (e.g. Maas et al. in the near wall region. Since the yield of velocity vectors somehow depends on the distance from the wall, the 1993). In the present study, two separate measurements were present data are not equivalent to the number density of carried out. For the single-phase ¯ow, only tracer particles particles. However, a separate ¯ow visualization experiwere introduced into the ¯ow, whilst both tracer and solid ment also shows that solid particles often ¯ow along the particles were fed to the particle-laden ¯ow. The particle wall, once they approach the wall. The probability density
Table 1. Particle condition
Diameter, d
Speci®c density, q=qf
Terminal velocity, uS
Time constant, sp
Tracer particle (polystyrene)
150±180 lm (1.7 m=us )
1.01
0.12 mm/s
1.45 ms 0.16 m=u2s
Solid particle (ceramic beads)
380±412 lm (4.2 m=us )
3.85
87.2 mm/s
31.9 ms 3.6 m=u2s
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Fig. 7. Probability density of velocity vectors
of tracer particles has a peak in the buffer region, and is decreased near the wall in both single and two-phase ¯ows. The reason for the inhomogeneous distribution of the tracked paths is unresolved, but the number density should be homogeneous, because the preferential concentration should not be expected for the tracers with their small time constant. The pro®les of streamwise mean velocity (U) are shown in Fig. 8. They are nondimensionalized by us for each ¯ow condition. The present result of the single-phase ¯ow is in good agreement with the DNS data of Kim et al. (1987). In the particle-laden ¯ow, the ¯uid velocity is slightly increased in the viscous sublayer. The velocity gradient in the logarithmic region is somewhat smaller than that of the single-phase ¯ow, so that the KaÂrman constant should be modi®ed by the presence of the dispersed phase. The mean velocity of the solid particle is shifted upward due to the terminal velocity us (=8us). The particle Reynolds number based on the terminal velocity us is about 33, where the vortex shedding behind particles does not occur (e.g. Wu and Faeth 1993; Johnson and Patel 1999). The slip velocity between solid particle and ¯uid is decreased at y+ < 10, since the drag coef®cient of particle is increased near the wall (Clift et al. 1978). The present result is not in accordance with the LDA data of Kulick et al. (1994), which shows signi®cant slip velocity in the viscous sublayer. This disagreement is probably due to the facts that the time constant of their glass and copper particles, is 2±3 orders of magnitude larger than that of the present experiment, and that the developing region of their channel is too short for the particles to adapt to the ¯ow ®eld. The distributions of rms velocity ¯uctuations are shown in Fig. 9. In the single-phase ¯ow, the rms values are again in good agreement with the DNS data of Kim et al. (1987). In the particle-laden ¯ow, the streamwise
Fig. 8. Mean streamwise velocity pro®les of ¯uid and dispersed phases
Fig. 9. Root-mean-square velocity ¯uctuations of ¯uid and dispersed phase. Keys as in Fig. 8
component urms is unchanged at y+ < 20, while it is signi®cantly increased in the central region of the channel and becomes as large as 2us. On the other hand, the wallnormal and spanwise components are markedly increased
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center line as shown in Fig. 10; u0 v0 becomes zero at around y+ = 170, which should be y+ = 208 for a symmetric ¯ow. At this moment, the reason for the lack of symmetry of the ¯ow ®eld is unresolved, but it might be due to the particle concentration near the wall is much different between two opposite channel walls. The turbulence production rate Pk due to the shear stress,
in the whole region. Therefore, the anisotropy measure of the Reynolds normal stresses is drastically changed from the wall to the channel center. Although vrms and wrms near the wall are increased with Res (Moser et al. 1998), the magnitude of increase in the present two-phase ¯ow is more than the Reynolds number effect. Sato and Hishida (1996) also showed that urms is somewhat increased when glass beads (d+ = 5, s p 3:5) are employed, although the deviation of the rms values presently obtained over the single-phase ¯ow data are much larger. Elghobashi and Truesdell (1993) found in their DNS of isotropic particle-laden turbulence that turbulence intensity is increased selectively in the direction of gravity, while the turbulence energy is redistributed to the other two directions through the pressure±strain correlation. The present data are in accordance with their DNS result. Gore and Crowe (1989) propose a correlation map for turbulence modulation based on the ratio between particle diameter and the turbulence length scale, and Elghobashi (1994) suggests another map based on the ratio between particle time constant and the turbulence time scale. However, the present experimental condition falls in the turbulence reduction range in both maps, and neither is in accordance with the behavior of the turbulence intensity presently obtained. Thus, neither the time scale ratio nor the length scale ratio should be a single parameter for turbulence modulation when the gravity force is present. The rms velocity ¯uctuations of solid particles are smaller than those of the ¯uid phase at y+ > 20, while the streamwise and wall-normal components become larger close to the wall. Note that the particle terminal velocity us is varied among particles, since the solid particle used in the present study has a ®nite variance in its diameter as shown in Table 1. However, the standard deviation in us estimated is about 0.2 us, and thus its unwanted contribution to urms of the solid particle should be negligible. Figure 10 shows the pro®les of Reynolds shear stress u0 v0 . Although the turbulence intensity is markedly modi®ed in the particle-laden ¯ow, this component is only slightly increased. Therefore, the correlation between u0 and v0 is substantially decreased by the presence of solid particles. It is noted that the velocity ®eld in the two-phase ¯ow becomes somewhat asymmetric about the channel
is shown in Fig. 11. It is evident that Pk is unchanged despite the substantial increase of the turbulent ¯uctuations at y+ > 20. Although it is not shown here, the viscous and turbulent diffusion terms in the transport equation of the turbulence kinetic energy are also unchanged in the two-phase ¯ow. Therefore, the signi®cant increase of urms at y+ > 20 should be attributed to the direct turbulence production due to the solid particle, although the vortex shedding behind particles is not expected as mentioned before. Figure 12 shows contours of the streamwise ¯uid velocity around a solid particle in the x±z plane. About 100±200 samples are employed to obtain these ensemble averages of ¯uid velocity in each data cell. The streamwise velocity is accelerated in the wake of the solid particle (x+ < 0), and the length of the wake region is increased with increasing distance to the wall. This is because the increasing characteristic turbulence time scale near the center of the channel is much larger than that close to the wall. The isolines of 1us in Fig. 12 correspond to about 12.5% of us, which persists more than 50 viscous length scales downstream in the center of the channel. According to the similarity solution of the wake behind a sphere in a uniform ¯ow (Schlichting 1977), the corresponding streamwise position is 16 dp, which is about 64 viscous units in the present experimental condition. Therefore, the wake presently observed in the channel center has a streamwise length comparable to that in the uniform ¯ow case. Figure 13 shows the probability density of solid particles around a solid particle. There are observed the regions
Fig. 10. Pro®les of the Reynolds shear stress
Fig. 11. Distribution of the production rate of turbulence kinetic energy
Pk
u0 v0
oU ; oy
3
upstream and downstream of a particle, where the probability has a peak, and it is pronounced near the channel center. Therefore, the solid particles should tend to align in the streamwise direction as they ¯ow downstream, especially away from the wall, which results in the increase in the streamwise ¯uid velocity upstream of the solid
particle shown in Fig. 12. Thus, the drafting, kissing and tumbling phenomena reported by Fortes et al. (1987) should exist even in the fully-developed turbulent ¯ow. Although the present measurement system cannot track particles located close to each other, a similar result as in Fig. 13 is obtained by a separate 2-D PTV measurement of solid particles in the x±z plane (not shown here). Figures 14 and 15 show conditionally-averaged quantities obtained by the quadrant analysis. The detection point was chosen at y+ = 14, and the threshold in the shear product was set as 0.5 urms vrms. An additional condition for preserving the spanwise asymmetry (Choi and Guezennec 1990) is also employed. Figs. 14a and 15a respectively shows conditionally averaged ¯uid velocity vectors in the y±z plane for the ejection (Q2) and sweep (Q4) events. A quasi-streamwise vortex is clearly observed for both events. For the Q2 event, the streamwise velocity ¯uctuation is negative near the detection point (Fig. 14b), which corresponds to the low-speed streaks. Underneath this region, the particle concentration is signi®cantly large as shown in Fig. 14c. This fact is in good agreement with the previous observation (e.g. Kaftori et al. 1995; Nino and Garcia 1996) that solid particles having s p 4 are accumulated in the low-speed streaks. On the other hand, in
Fig. 12. Contours of ensemble averaged streamwise velocity around a solid particle in the x±z plane. The solid particle is at the origin of the coordinates. a y+ = 14, b y+ = 30 and c channel centerline
Fig. 13. Local concentration of dispersed phase around a solid particle in the x±z plane. Quantities are normalized with mean concentration at the corresponding wall elevation. The solid particle is at the origin of the coordinates. a y+ = 14, b channel centerline
Fig. 14. Conditional averaged quantities in the cross-stream plane associated with the ejection (Q2) event. a Velocity vectors, b contours of streamwise velocity ¯uctuation and c concentration of the solid particles
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Fig. 16. Fraction of occurrence of each quadrant event
¯ow. The turbulence statistics of three velocity components are obtained, and the conditionally-averaged quantities are further calculated with the aid of the quadrant analysis. The following conclusions are derived: 1) The mean slip velocity of solid particles is almost the same as the terminal velocity except in the viscous sublayer. 2) The streamwise turbulence intensity of the ¯uid phase is signi®cantly increased near the center of the channel whilst it is unchanged at y+ < 20. The wall-normal and spanwise components are increased in the entire crosssection of the channel. 3) Since the turbulence production due to the shear stress Fig. 15. Conditional averaged quantities in the cross-stream plane associated with the sweep (Q4) event. a Velocity vectors, b is unchanged, the increase in the turbulence intensity is contours of streamwise velocity ¯uctuation and c concentration attributed to the wake generation downstream of solid of the solid particles particles, which tend to align in the streamwise direction. 4) The solid particles are densely distributed along the the high-speed region associated with the Q4 event, the low-speed streaks, especially beneath the ejection event. particle concentration remains fairly low (Figs. 15b, c). A possible mechanism of the agglomeration is that the Figure 16 shows the fractional occurrence of each traceability of solid particles should be different to the quadrant event of the ¯uid and dispersed phases in the ejection and sweep events. particle-laden ¯ow. At y+ > 10, the fractional occurrence of the Q2 event for the solid particle is less than that of the References ¯uid phase, whilst it is contrary for the Q4 event. There- Adrian RJ (1991) Particle-imaging techniques for experimental fore, the solid particles presently used can follow the ¯uid ¯uid mechanics. Annu Rev Fluid Mech 23: 261±304 motion associated with the Q4 event, but less for the Q2 ANSI/ASME PTC 19.1 (1985) Measurement uncertainty, suppleevent. The spatio-temporal scale of the Q2 event should be ment on instruments and apparatus, part 1, ASME Boivin M; Simonin O; Squires KD (1998) Direct numerical simsmaller than that of the Q4 event, since the Q2 event is ulation of turbulence modulation by particles in isotropic characterized by the multiple intense eruptions from sinturbulence. J Fluid Mech 375: 235±263 gle streak (Bogard and Tiederman 1986), while the regions Bogard DG; Tiederman WG (1986) Burst detection with singleof the Q4 event are wider in the spanwise direction than point velocity measurements. J Fluid Mech 162: 389±413 those of the Q2 event (Robinson 1991). Therefore, it is Choi WC; Guezennec YG (1990) On the asymmetry of structures conjectured that the difference of the traceability between in turbulent boundary layers. Phys Fluids A2: 628±630 the Q2 and Q4 events contribute to the agglomeration of Clift R; Grace JR; Weber ME (1978) Bubbles, drops and particles, Academic Press particles into the low-speed streaks.
6 Conclusions Three-dimensional high-de®nition particle tracking velocimetry is applied to simultaneous measurement of ¯uid and dispersed phases in a turbulent water channel
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