Particle–turbulence interaction and local particle concentration in sediment-laden open-channel flows

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Journal of Hydro-environment Research 3 (2009) 54e68 www.elsevier.com/locate/jher

Research paper

Particleeturbulence interaction and local particle concentration in sediment-laden open-channel flows Kazunori Noguchi*, Iehisa Nezu Department of Civil Engineering, Kyoto University, Kyoto 615-8540, Japan Received 5 March 2009; revised 8 June 2009; accepted 13 July 2009

Abstract The present study describes an experimental investigation on the effects of ejection and sweep motions to the local sediment concentration and turbulence modulation in suspended sediment-laden open-channel flows by using a combination between a discriminator particle tracking velocimetry (D-PTV) for sediment particles and a discriminator particle image velocimetry (D-PIV) for fluid tracers. Fluid tracers and sediment particles were discriminated by their occupied particle sizes, and the particle velocity and the fluid velocity were determined simultaneously. It is necessary to investigate coherent structure and particleeturbulence interaction in suspended sediment-laden open-channel flows for predicting the transport of suspended sediment in rivers. There are a lot of previous studies on velocity measurements and numerical simulations in these suspended sediment flows. However, there are little investigation on simultaneous measurements between particles and fluid in bursting phenomena of open-channel flow. So, this study focuses the particleefluid interaction in the ejection and sweep events by using the discriminator PIV/PTV. The present study found that the turbulence in sediment-laden flows is enhanced or suppressed as compared with that of sediment-free (clearwater) flow. These enhancement and suppression of turbulence are determined by the critical particle diameter, which is correlated with the Kolmogoroff microscale rather than the macroscale of turbulence. The strength of the ejections and sweeps was changed by suspended sediment. The local sediment concentration became about 20e40% larger when the ejection motion occurred, whereas it became about 10e30% smaller when the sweep motion occurred. Ó 2009 International Association for Hydraulic Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved. Keywords: Sediment-laden flow; Turbulence modulation; Particleefluid interaction; Bursting phenomena; Sediment concentration

1. Introduction In suspended sediment-laden flows, it has been suggested that turbulence characteristics are changed by the existence of particles in water. Many researchers in various engineering communities have highlighted the fundamental and applied studies about particle-laden turbulent flows, because these flows are involved in a lot of phenomena of multiphase processes. Gore and Crowe (1989) have first reviewed the earlier research on particleefluid interaction, i.e., the two-way coupling, in particle-laden air jets and pipe flows, and

* Corresponding author. E-mail address: [email protected] (K. Noguchi).

proposed a noticeable criterion that smaller size particles than the scale of energy-containing eddies suppress the turbulence, whereas larger size particles enhance it. Further, Hetsroni (1989) re-examined the particleeturbulence interaction on the basis of available experimental data of gasesolid, liquidesolid and gaseliquid flows (however, almost gasesolid flows were examined) including data of Gore and Crowe (1989) and found that the presence of smaller particles with a low particle Reynolds number tended to suppress the turbulence of the carrier fluid. In contrast, he concluded that larger particles with high particle Reynolds number (based on relative velocity and particle size), larger than about 400, tended to enhance the turbulence most likely due to vortex shedding by particles. Lyn (1991) has first conducted the simultaneous measurements of particle phase and fluid phase in sediment-laden open-

1570-6443/$ - see front matter Ó 2009 International Association for Hydraulic Engineering and Research, Asia Pacific Division. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jher.2009.07.001

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

Notation a C ~cðtÞ CH cv dc dp H hp Lx Ne, Ns Su ( f ) Te, Ts

reference point for Rouse equation (h0.05 hp) volume-averaged sediment (particle) concentration instantaneous particle concentration threshold-value-averaged particle concentration in ejections and sweeps sediment flux critical particle diameter of turbulence modulation particle diameter threshold value in instantaneous Reynolds stress maximum elevation of the lifted-up particles integral scale or length scale of the energy-containing eddies counted number of ejections and sweeps, respectively energy spectrum of u(t) ejection period and sweep period, respectively

channel flows by laser Doppler anemometer (LDA), and pointed out that the fluid velocity of sediment-laden flow became slower than that of sediment-free flow (i.e., clear-water flow) as the particle concentration increased. Lyn (1992) also found that turbulence characteristics in sediment-laden open-channel flows might be changed significantly by particleeturbulence interaction as compared with those in clear-water flows. Furthermore, Song et al. (1994) measured the bed-load flow in the near-bed region by acoustic Doppler velocimetry (ADV), and pointed out that the turbulence intensity and Reynolds stress became weaker than those of the fixed-bed clear-water flow due to the existence of bed-load materials. These earlier experimental results of turbulence modulation in sediment-laden open-channel flows might be similar to those of gasesolid twophase flows, and thus it is further necessary to investigate the mechanism of such particleeturbulence interaction on the basis of recent turbulence theory. It is well known that the coherent structure of ejections and sweeps occurs intermittently and periodically near the wall in boundary layers and open-channel flows. This is so-called the bursting phenomenon, which is quite important in particle entrainment and transport mechanism, as pointed out by Rashidi et al. (1990), Nin~ o and Garcia (1996), and others. They suggested that the ejections and sweeps in the near-wall region might govern the interaction between particles and fluid. The transport mechanism of suspended sediment is also one of the most important and challenging topics in river engineering, because it has a complicated interaction among turbulent flow, particle motion and bed configuration. Therefore, a lot of efforts have been devoted to understandings and predictive capability of the closely coupled phenomena of sediment-laden flow and sediment transport in open-channel flows. Rashidi et al. (1990) and Nin~ o and Garcia (1996) have measured the suspended particle motion in sediment-laden flows by flow-visualization techniques, and pointed out that the fluid velocities are faster

55

TH

duration time between the neighboring threshold range values H streamwise mean velocity of clear-water flow Ucw fluid mean velocity of sediment-laden flow Uf particle mean velocity of sediment-laden flow Up friction velocity of clear-water flow U*0 u0 f, v0 f streamwise and vertical turbulence intensities of fluid phase, respectively u0 cw,v0 cw streamwise and vertical turbulence intensities of clear-water flow, respectively x, y streamwise and vertical coordinates, respectively yþ hy U0 =n normalized by the inner variables Rouse-fitted value of diffusivity to eddy viscosity bR measured value of diffusivity to eddy viscosity bExp d boundary-layer thickness k von Karman constant h Kolmogoroff microscale particle specific density rp

than those of particles in the outer layer of open-channel flow. However, the velocities of particles and fluid were not measured simultaneously in their researches. Recently, simultaneous measurements of both fluid velocity and particle velocity in sediment-laden open-channel flows have been feasible with non-intrusive measurement techniques. Best et al. (1997) and Righetti and Romano (2004) have conducted simultaneous velocity measurements of water and glass beads using a phase Doppler anemometer (PDA). PDA is an epoch-making system for the simultaneous measurements of particle-laden flows although particles must be exact sphere. Two of them suggested that the enhancement and suppression of turbulence intensity due to particles were distinguished by the Stokes number of particle-laden flow. Muste and Patel (1997) have developed LDA system incorporated with a unit for particle-size discrimination and measured the particle velocity Up and fluid velocity Uf simultaneously in the outer layer of open-channel flow. Kulick et al. (1994) conducted the similar measurements in duct flow and pointed out an existence of the relative velocity between particles and fluid. That is to say, the values of (Up  Uf) did not become equal to zero, and thus the particle Reynolds number had a finite value, which inferred an occurrence of turbulence modulation on the basis of Hetsroni’s (1989) criterion. To reveal the momentum exchanges between particles and fluid, Kaftori et al. (1995) have measured the relative velocity by using LDA even in the near-wall region although the particle specific density rpwas near-neutrally buoyant solid, i.e., rp ¼ 1.05. They pointed out that the averaged velocity of particles was larger than that of carrier fluid in the near-wall region. This result of the relative velocity contradicted to that of the outer region. They explained then that the result of Up > Uf very near the wall might be caused by the following two factors, i.e., one is the deceleration of fluid velocity due to viscous effect and the other is due to the high-

56

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

speed particles which inrush into the viscous sublayer. These surprising results of Kaftori et al. (1995) that the particle velocity might become larger than the carrier water velocity very near the wall have recently been verified using innovative PIV/PTV measurements by Nezu and Azuma (2004a), Muste et al. (2009) and others, who all pointed out the importance of simultaneous measurements of particles and fluid in openchannel flows. Such simultaneous measurements of particles and fluid have first been conducted by LDA and PDA as mentioned above, although these measurement systems have some difficult limitations. For example, smaller sizes of suspended particles have to be used in order to avoid the blocking of laser beams due to particles. Only spherical particles are feasible in PDA measurements. Moreover, because LDA and PDA are the pointmeasurement systems, it is fairly difficult to examine the relation among the coherent structure, particleefluid interaction and particle concentration in sediment-laden open-channel flows. To overcome such difficulties, Nezu and Azuma (2004a) have measured both the fluid and particle velocities simultaneously in sediment-laden open-channel flows by using a discriminator Particle Tracking Velocimetry (D-PTV), in which sediment particles were separated from fluid tracers by the occupied area of particles in camera images. With this technique of PTV, the relative velocity between particles and fluid was examined in the inner layer as well as in the outer layer. Recently, Bigillon et al. (2006), Breugem and Uijttewaal (2006), Le Louvetel-Poilly et al. (2007), Noguchi et al. (2008) and Muste et al. (2009) have conducted simultaneous measurements of particles and fluid velocities in sediment-laden open-channel flows by using a combination of PTV and PIV, the techniques of which are almost similar to those developed by Nezu and Azuma (2004a). All of them found an essential importance of particleeturbulence interaction as well as significant contributions of ejection and sweep motions to suspended sediment transport. However, all of above-mentioned researchers have used natural sands and glass particles (specific density rp ¼ 2.6) as well as polystyrene particles (rp ¼ 1.05) as suspended sediment particles in their experiments. These kinds of particles may be not necessarily suitable to reveal the hydrodynamic mechanism of particleefluid interaction and the effects of bursting motions on sediment transport experimentally. When glass particles are used, the number of suspended particles is too poor to examine the effects of particle concentration except for the near-wall region. If particles are as heavy as and more than glass beads (rp ¼ 2.6), high speed and supercritical flow condition may be needed to conduct suspended sediment experiments throughout the whole flow depth from the bed to free surface. However, it may be fairly difficult to conduct discriminator visualizations of particles and fluid by PIV/PTV in such a high-speed open-channel flow. On the other hand, if near-neutrally buoyant particles like polystyrene (rp ¼ 1.05) are used, it may be fairly difficult to evaluate the effects of specific density on particleefluid interaction because of their good traceability to the carrier fluid flow. Fortunately, ‘‘Polyplus’’ (rp ¼ 1.5) and ‘‘Polyextra’’ (rp ¼ 1.2) particles are available commercially, and are suitable to conduct

suspended sediment experiments in subcritical open-channel flows. Polyplus and Polyextra particles are the unsaturated polyester. In the present study, we conducted simultaneous measurements of fluid velocity and particle velocity as well as local particle concentration by using a combination of discriminator PIV and PTV in sediment-laden open-channel flows, in which the particles of specific density rp ¼ 1.2 and 1.5 were used. We examined the relative velocity and turbulence modulation due to particles in the inner and outer layers of open-channel flow, and then revealed the relations between coherent structure and particle concentration. 2. Experimental techniques and hydraulic conditions 2.1. Experimental techniques The present experiments were conducted in a 4.0 m long, 5.0 cm wide and 10.0 cm deep tilting flume, as shown in Fig. 1. x, y, and z are the coordinates in the streamwise, vertical and spanwise directions, respectively. U, V, and W denote the time-averaged components of velocity vector in each direction, and u, v, and w are the corresponding turbulent fluctuations. The test section was located 3.0 m downstream of the flume entrance. 2 W Ar-ion laser light sheet (LLS) with 4 mm thickness was set to illuminate the centerline of the flume from the free surface (Fig. 1). Illuminated particle images were taken by a high-speed CMOS camera of 12801024 pixels, which was placed near the sidewall of the flume. The time interval between two images for PIV and PTV measurements was set 0.002 s, that is to say, the PIV/PTV pair rate was set 500 Hz. The sampling rate of these pair images was set 100 Hz. Polyextra particles (specific density rp ¼ 1.2) and Polyplus particles (rp ¼ 1.5) were used as suspended sediment, and four kinds of particle diameter dp were selected, i.e., dp ¼ 0.25, 0.37, 0.5, and 1.0 mm for each specific density. The occupied area of a particle dp was projected about 100 times larger than that of the fluid tracer (Nylon-12 spheres of rp ¼ 1.02 and dp ¼ 0.025 mm) on CMOS images, and consequently the discrimination between fluid and particles was easily conducted by using D-PTV, which was developed by Nezu and Azuma (2004a). Consequently, simultaneous measurements of particles and fluid were conducted reasonably. That is to say, particles were analyzed by PTV, whereas fluid velocity was analyzed by standard PIV. Three kinds of the volume-averaged sediment concentration C were chosen for each particle experiment run, as shown in Table 1. The subscripts cw, f, and p are attached to various amounts to distinguish the clear-water (particle-free) data, fluid data, and particle data, respectively. For example, Uf denotes the timeaveraged mean velocity of fluid. 2.2. Hydraulic conditions The hydraulic condition is indicated in Table 1.pUffiffiffiffiffi m is the bulk mean velocity, h is the flow depth, FrhUm = gh is the Froude number, and U* is the friction velocity. Two kinds of experiments were conducted, i.e., the particle specific density rp ¼ 1.2 (Polyextra) and 1.5 (Polyplus), in which the particle

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

Fluid tracer

Particles

h

57

Laser Light Sheet

High Spee d CMOS Camera

centerline of flume

y ,v Monitor

z ,w

x,u

B

Fig. 1. Experimental setup.

diameter dp was changed from 0.25 to 1.0 mm. dpþ hdp U =n is the dimensionless particle diameter normalized by the inner variables of U* and the kinematic viscosity n. By setting subcritical flow Fr ¼ 0.43, it was possible to form fully Table 1 Hydraulic conditions. Polyextra (rp ¼ 1.2)

Um (cm/s)

h (cm)

Fr

U* (cm/s)

dp (mm)

dpþ

C (104)

Clear water

30.0

5.0

0.43

1.41

e

e

e

PE25-A PE25-B PE25-C

30.0

5.0

0.43

1.34 1.28 1.23

0.25

3.11 2.97 2.86

3.04 10.2 31.6

PE37-A PE37-B PE37-C

30.0

5.0

0.43

1.39 1.36 1.34

0.37

4.76 4.66 4.59

2.94 10.5 30.8

PE50-A PE50-B PE50-C

30.0

5.0

0.43

1.46 1.50 1.53

0.5

6.48 6.66 6.79

2.83 9.87 30.3

PE100-A PE100-B PE100-C

30.0

5.0

0.43

1.52 1.59 1.64

1.0

13.83 14.47 14.92

3.07 10.1 29.4

Polyplus (rp ¼ 1.5)

Um (cm/s)

h (cm)

Fr

U* (cm/s)

d (mm)

dpþ

C (103)

Clear water

30.0

5.0

0.43

1.41

e

e

e

PE25-a PE25-b PE25-c

30.0

5.0

0.43

1.24 1.19 1.15

0.25

PE37-a PE37-b PE37-c

30.0

5.0

0.43

1.36 1.33 1.31

PE50-a PE50-b PE50-c

30.0

5.0

0.43

PE100-a PE100-b PE100-c

30.0

5.0

0.43

developed turbulent flows without significant water waves, which enabled us to project the laser light sheet from the free surface for PIV/PTV measurements (see Fig. 1). The properties of these sediment particles and fluid tracer are summarized in Table 2. Three kinds of the volume-averaged particle concentration C were changed in a range of 0.3  103 to 3.0  103 for each diameter dp. Because these concentrations are relatively dilute, it is expected that only the two-way coupling, i.e., particleefluid interaction occurs except for very near the bed, as pointed out experimentally by Nezu and Azuma (2004a) and Muste et al. (2009) as well as numerically by Pan and Banerjee (1996). In the present experiments, any deposit of particles and visible streaks on the bed were not observed, i.e., starved-bed flow condition. It is of course preferable to use a wide flume of large aspect ratio, i.e., the wide channel category (B/h is larger than 5. B is the channel width), in order to verify 2-D open-channel flow, as pointed out by Nezu and Nakagawa (1993). However, enormous suspended sediment particles are transported in a wide channel, and thus will interrupt the images of the laser light sheet in the measuring centerline section. To overcome these difficulties, the flume width had to be set narrower in

3.06 2.94 2.84

0.5 1.04 1.73

Table 2 Particle properties. Particle kind

Diameter (mm)

Specific density

0.37

5.03 4.93 4.85

0.49 0.98 1.64

Polyextra

1.2

1.50 1.53 1.54

0.5

7.51 7.66 7.71

0.48 0.96 1.59

0.25 0.37 0.5 1.0

Polyplus

1.5

1.52 1.55 1.57

1.0

15.41 15.44 15.64

0.39 0.79 1.31

0.25 0.37 0.5 1.0

Nylon-12

0.025

1.02

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

58

order to obtain CMOS images more clearly. In this study, B ¼ 5 cm was arranged and B/h became 1.0. Consequently, the maximum velocity point appeared below the free surface, i.e., evidently, the velocity-dip phenomena occurred. Correspondingly, the Reynolds stress uv became negative near the free surface because of secondary currents, as shown in Fig. 2. The height at which uv ¼ 0, is defined as the boundarylayer thickness d. Then, d ¼ 3.2 cm was obtained in all cases. If the boundary layer of y  d corresponds to 2-D turbulent flow, the Reynolds stress uv is described theoretically in the followings, e.g. see Nezu and Nakagawa (1993). 

uv  y vU þ ¼ 1   þ vy U2 d

ð1Þ

in which, Uþ h U/U* and yþ h yU*/n. The theoretical curve of Eq. (1) is also shown in Fig. 2. The measured data are in good agreement with Eq. (1) in the boundary layer of y/d  1. Nezu and Azuma (2004b) examined the effect of sidewall on the particleefluid interaction in the same flume as used in the present study and found that the secondary currents were negligibly small in the region of y  d. From all these results, it is considered that 2-D turbulent openchannel flow is almost fully developed in the region of y  d. The friction velocity U* is one of the most important variables to predict turbulence characteristics and sediment transport, and the value of U* in the present study was evaluated reasonably from the linear distribution of Eq. (1) in the outer layer, where the viscous term is neglected as seen in Fig. 2. 3. Results 3.1. Velocity profile of fluid and particles Fig. 3 shows the mean velocity Ucw of clear-water flow and the fluid velocity Uf of sediment-laden flows against the vertical coordinate yþ hyU0 =n, in which U*0 is the friction velocity of the corresponding clear-water flow. The data were y δ 1.2

case

d p (mm)

PE25-C

0.25 0.37 0.50 1.0

PE37-C PE50-C

1

PE100-C

chosen in the highest sediment concentration case as a function of four particle sizes dp ¼ 0.25, 0.37, 0.5 and 1.0 mm. Two kinds of particle density rp are 1.2 and 1.5. These data are shifted by 10 units in Fig. 3 to avoid confusion. Ucw and Uf are normalized by the friction velocity U*0, which was evaluated from the Reynolds stress (Fig. 2). The theoretical velocity profiles in clear-water flow are as follows, e.g., see Nezu and Nakagawa (1993).   Uf ¼ y þ yþ  5 U0

ð2Þ

  Uf 1 yU0 þ A yþ  30 ¼ ln U0 k n

ð3Þ

in which, the von Karman constant k and the integral constant A are used here as k ¼ 0.41 and A ¼ 5.3, which were obtained in 2-D open-channel flows over smooth bed by Nezu and Rodi (1986). The curves of Eqs. (2) and (3) are included in Fig. 3. However, the velocity curve of the buffer layer (5 < yþ < 30) is not shown in Fig. 3 because it is not obtained analytically. The values of the clear-water flow are in good agreement with Eqs. (2) and (3) in the inner layer of yþ < 200. These confirm the validity of 2-D fully developed open-channel flow over smooth bed. Very near the bed, on the contrary, the velocities of sediment-laden flows were faster than those of clear-water flow, i.e., Uf  Ucw. These tendencies are in good agreement with recent data of Muste et al. (2009) who used natural sands of rp ¼ 2.65 and dp ¼ 0.21e0.25 mm as suspended particles. From these results, it is considered that the existence of particles cannot be disregarded in the viscous layer of yþ  10. Therefore, the values of the particle velocity Up obtained by PTV are plotted in Fig. 4 to compare with the fluid velocity Uf. Fig. 4 shows the relative velocity of (Up  Uf) against yþ hyU0 =n. The experimental data of Kaftori et al. (1995) are also plotted for comparison. The present data are in good agreement with Kaftori et al.’s data, although the particle density rp is different from each other. The same characteristics were obtained by Muste et al. (2009) for natural sands although their data cannot be unfortunately included in Fig. 4

Uf U* 0

C = (1.3 ~ 1.7 )×10−3 ρ p = 1 .5

25

0.8

20

0.6

log-law distribution

15 0.4 0.2

y ∂U + − uv U *2 = 1 − − + ∂y δ

10

U + = y+

C ≈ 3 .0 × 10 − 3 ρ p = 1 .2

5 0 -0.2

0

0.2

0.4

0.6

0.8

Fig. 2. Reynolds stress distribution uv.

− uv

2

U*

0 1

d p(mm) clear-water 0.25 0.37 0.5 1.0

10

+

100 y ≡ yU *0 ν 1,000

Fig. 3. Distribution of Ucw and Uf.

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

U

2.0

(mm)

PE25-C PE37-C PE50-C PE100-C PP25-c PP37-c PP50-c PP100-c

U *0 Present data

1.0 Kaftori et al . (1995)

ρp

dp

Case

−U f

p

Lx ¼

0.25 0.37 0.50 1.0 0.25 0.37 0.50 1.0 0.28 0.90

1.2

1.5

1.05

0.0

-1.0

(ii) Inner

(i) Viscous

-2.0 1

(iii) Outer

10

100

y

+

≡ yU* 0

1,000

ν

Fig. 4. Relative velocities between Up and Uf.

because they showed the plots of Up, but the experimental curves of Uf. In the near-wall region of yþ  15, the particle velocity Up is faster than the fluid velocity Uf (i.e., Up  Uf), whereas in the region of 15  yþ  100, the particles are transported slower than the carrier fluid (i.e., Up < Uf). In the outer region of yþ  100, the value of Up approaches to the Uf distribution because of the good followness of suspended particles to the carrier flow. From these tendencies of Up  Uf, the sediment-laden turbulence structure can be classified into three subregions as indicated in Fig. 4. That is to say, (i) the viscous region of yþ  15, (ii) the inner region of 15  yþ  100, and (iii) the outer region of yþ  100. To evaluate the entrainment and transport of particles, it is very important to clarify the coherent structure of carrier flow in these three subregions, as suggested by Nin~ o and Garcia (1996) and Nezu and Azuma (2004a). Firstly, we examined the length scale Lx of mean eddies in turbulence structure, which is defined as follows:

Lx

(cm)

: CW

: 0.25

: 0.37

: 0.5

dp = 1.0 mm

1.0

ZN

ð4Þ

RðrÞdr 0

RðrÞ ¼ uðx0 þ rÞ  uðx0 Þ=u02

ð5Þ

in which, R(r) is the space correlation between u(x0 þ r) and u(x0). x0 is the reference point and r is the lag distance. pffiffiffiffiffi u0h u2 is the turbulence intensity. Fig. 5 shows the distributions of Lx in all cases, which were calculated from Eq. (4) using PIV data. The values of Lx are in almost proportion to ðyþ Þ1=2 , the relation of which was proposed in sediment-free open-channel flow by Nezu and Nakagawa (1993). It is found that Lx is not changed significantly by the existence of suspended sediment. This implies that the coherent motion is not changed drastically by dilute suspended sediment, say C ¼ in order of 103. The same results were obtained numerically by Pan and Banerjee (1996) and also experimentally by Muste et al. (2009). Fig. 6 shows the zone-averaged absolute values of jUp  Ufj against the relative particle diameter dp/Lx in all experimental cases. The zone-average was conducted in each subregion. The particle diameter dp was normalized by the mean-eddy scale Lx. It is found that the absolute values jUp  Ufj of the relative velocity become larger as the relative particle diameter dp/Lx becomes larger. It is interesting that the zone-averaged values of jUp  Ufj in the viscous region of (i) overlap well with those in the inner region of (ii), although these signs are of course opposite (see Fig. 4). The plotted data of the outer region of (iii) deviate from those of (i) and (ii) regions. This suggests that the particleefluid interaction in the inner region should be distinguished from that in the outer region. In the inner region, the particle concentration is much larger than the volume-averaged one (see Fig. 7). Therefore, the particleefluid interaction (twoway coupling) would be also influenced by the particleeparticle interaction (four-way coupling) in the inner region. On the other hand, in the outer region, the particle concentration is much smaller than the volume-averaged one, and consequently, the

Up

: 1.0

59

− Uf U*0

0.1

dp = 0.5 mm

~ 1.0 ~

1

0.1

(ii)

dp = 0.37 mm

~ 1.0 ~

(i)

0.1

dp = 0.25 mm

~ 1.0 ~

ρp

0.1

open symbols 1.2 closed symbols 1.5

0.1

~ 1.0 ~

Clear Water

(iii)

0.1

1

d p Lx

2

0.01

1

10

100

Fig. 5. Integral length scale Lx.

y

+

1,000

0.01 0.01

0.1

1

10

100

Fig. 6. Zone-averaged relative velocity between particles and fluid.

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

60

In this study, the value of bExp h 3s/3m was calculated from the measured particle diffusivity 3s and the measured fluid eddy viscosity 3m, which were defined as follows:    uf v f  3m ¼  ð7Þ vUf =vy

1

y h y = hp ρp 0.1

= 1 .2

C ≈ 3 . 0 × 10

   up v p  3s ¼  vUp =vy

−3

d p (mm)

βR

β Exp

0.25 0.37 0.5 1.0

1.00 1.02 1.06 1.32

1.03 1.03 1.05 1.13

ð8Þ

four-way coupling effects may be negligibly small. It is also found that the heavier particles of rp ¼ 1.5 have slightly larger relative velocity than the light particles of rp ¼ 1.2, which infers an effect of particle inertia.

These were evaluated directly by using PIV/PTV data. Fig. 7 shows the measured values of C( y) in the logelog plot. The calculated curves of Rouse formula of Eq. (6) are also shown, in which the value of b was best-fitted and then bR ¼ b is described in the legend of Fig. 7 to avoid confusion. The observed values of C( y) are in good agreement with the Rouse formula of Eq. (6) in the whole suspended layer. The experimental value of bExp coincides well with the Rouse value of bR in the smaller particle sizes, say dp  0.5 mm, irrespective of the particle density rp and the mean concentration C. However, of particular significance is that the Rouse value of bR for Eq. (6) had to be selected fairly larger than the value evaluated from Eqs. (7) and (8), that is to say, bR > bExp in the case of dp ¼ 1.0 mm. Especially, bR was 2.94 in the case of dp ¼ 1.0 mm and rp ¼ 1.5, whereas the experimental value of bExp was 1.15. These differences between bExp and bR are considered to be due to the responsibility of particles to the carrier flow. The value of bR deviates more significantly from the experimental value bExp as the particle size dp is larger for high specific density rp. This implies the necessity of twophase flow approach for larger sizes of particle, instead of the Rouse formula of Eq. (6) that was derived from a diffusion theory of single-phase flow. These necessities have also been pointed out by Muste (2002) and Nezu and Azuma (2004a). To sum up, it is concluded that the present evaluation method of particle concentration by counting the number of particles in PTV images is reasonable and accurate for sediment-laden flows.

3.2. Particle concentration

3.3. Turbulence modulation and critical diameter

In this study, the concentration of the particles was obtained by counting the number of particles in PTV images. These data were evaluated only in the section of the laser light sheet, and thus, it is necessary to verify the accuracy in such an evaluation of particle concentration. The distribution of the particle concentration C( y) is described by the Rouse formula, as follows, e.g. see Yalin (1977):   z C hp  y a ws ¼ ; Zh ð6Þ bkU0 Ca hp  a y

Fig. 8 shows the streamwise and vertical components of turbulence intensity for the clear-water and sediment-laden fluids, i.e., (u0 cw and u0 f) and (v0 cw and v0 f), respectively. These data were normalized by the friction velocity U*0 of the clearwater flow. The curves in these figures are the semi-theoretical formulae proposed by Nezu and Nakagawa (1993) in 2-D sediment-free open-channel flows.

0.01 -6 10 1

10

-5

10

-4

y

ρp

0.1

-3

C

10

-2

Curves are Rouse formula

y = hp

h

10

= 1.5

C = (1.3~1.7) × 10−3

0.01 -6 10

d p (mm)

βR

β Exp

0.25 0.37 0.5 1.0

1.02 1.07 1.19 2.94

1.05 1.09 1.12 1.15

10

-5

10

-4

10

-3

C

10

-2

Fig. 7. Particle concentration C( y) and the Rouse formula.

in which, hp is the maximum elevation of the lifted-up particles, Ca is the particle concentration at the reference point, i.e., a ¼ 0.05 hp. ws is the settling velocity of particles, and it was measured from experiments in still water. k is the von Karman constant, and k ¼ 0.41 was used as well as in Eq. (3).

u0f ¼ 2:3 expðy=dÞ U0

ð9Þ

v0f ¼ 1:27 expðy=dÞ U0

ð10Þ

In the clear-water flow, the present experimental values are in good agreement with the universal functions of Eqs. (9) and (10). In the sediment-laden flow, however, they are divided

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

u f′ U* 0

C

2.5

≈ 3 .0 × 10− 3

d p (mm)

×

Clear-water 0.25 0.37 0.5 1.0

2

1.5

1

u ′f U *0 = 2 . 3 exp( − y δ ) 0.5 0.0

0.2

0.4

0.6

y

δ

0.8

1.0

vf′ U*0

C

1.5

≈ 3 .0 × 10− 3

d p (mm)

v ′f U *0 = 1 .27 exp( − y δ )

×

Clear-water 0.25 0.37 0.5 1.0

1

0.5

0 0.0

0.2

0.4

0.6

y δ

0.8

1.0

Fig. 8. Turbulence intensities u0 f/U*0 and v0 f/U*0 against the vertical coordinate y/d.

into two categories by their particle sizes. That is to say, one category is to enhance turbulence intensities, and the other suppresses them from the clear-water condition. In the case of larger particle sizes of dp ¼ 0.5 and 1.0 mm, the turbulence intensities are enhanced significantly. Similarly, such turbulence enhancements were also observed for larger particle sizes by Kaftori et al. (1998) who used polystyrene particles of rp ¼ 1.05 and dp ¼ 0.9 mm, and also by Nezu and Azuma (2004a) who used particles of rp ¼ 1.05 and 1.15, and dp ¼ 0.5e1.3 mm. In contrast, the present turbulence intensities are suppressed significantly for smaller particle sizes of dp ¼ 0.25 and 0.37 mm. This tendency coincides well with the observed data of Muste et al. (2009) who used natural sands of rp ¼ 2.65 and dp ¼ 0.21e0.25 mm. All of these experimental data in particle-laden openchannel flows suggest strongly that the turbulence enhancement and suppression by particles in water flows might depend on the particle size dp rather than the particle density rp. Such a turbulence modulation has been investigated intensively in gasesolid two-phase flows. Gore and Crowe (1989) reviewed previous existing experimental data of jets and pipe flows and proposed that turbulence intensity of fluid might be enhanced

61

by larger size particles when dp was larger than 0.1 Lx, whereas it might be suppressed by particles when dp/Lx < 0.1. In contrast, Hetsroni (1989) proposed that turbulence modulation might depend on the particle Reynolds number Rp hjUp  Uf jdp =n rather than the relative particle size dp/Lx and that the particles with high Rp larger than about 400 tended to enhance the turbulence most likely due to vortex shedding, which infers that the relative velocity between particles and fluid might induce the particleefluid interaction and thus turbulence modulation. It is very important and challenging topics to clarify whether such a criterion of turbulence modulation in gasesolid twophase flows may be applied to or modified to sediment-laden open-channel flows and also to examine the particleeturbulence interaction because the relative velocity occurs evidently near the bed (see Fig. 4). Righetti and Romano (2004) and Nezu and Azuma (2004a) found that the turbulence modulation due to particles depended on the scale of energy-containing eddies which is the same order of magnitude as the macroscale Lx. However, all of the present experiments were that dp/Lx > 0.1 (see Fig. 6), and consequently, the criterion of dp/Lx ¼ 0.1 by Gore and Crowe (1989) is not applicable to the present flume experiments. In fact, Nezu and Azuma (2004a) modified this criterion and suggested the following relation from the Stokesnumber criterion, e.g., see Elghobashi (1994):   dp 9 rf for turbulence enhancement ð11Þ  Lx dpþ rp in which, dpþ hdp U =n is the dimensionless particle diameter. Because dpþ ¼ 3e15 in the present experiments (see Table 1), it is suggested from Eq. (11) that when dp/Lx  (0.4e2.0), the turbulence will be enhanced by particles. This value of dp/Lx is really in a range of the inner layer of y/d < 0.2, as seen in Fig. 6, which infers an occurrence of turbulence modulation. However, the particle Reynolds number Rp in the present study was below 30 at most, which suggests that the enhancement of turbulence due to vortex shedding by particles will not occur at all on the basis of Hetsroni’s (1989) criterion. In contrast, Best et al. (1997) and Muste et al. (2009) found that the turbulence modulation depended on the Taylor microscale l rather than the macroscale such as Lx, on the basis of the Stokes number by Elghobashi (1994). However, Tennekes and Lumley (1972) and others have pointed out that the Kolmogoroff microscale h is more universal length scale than l in the cascade theory of turbulent energy. Therefore, the present study examines whether or not the turbulence modulation depends on Kolmogoroff microscale, in the followings. The turbulence modulation defines here that the turbulence intensities of sediment-laden flow are normalized by those of the corresponding clear-water flow, i.e., u0 f/u0 cw and v0 f/v0 cw. Firstly, we examined the relation between the turbulence modulation and the particle diameter dp, and focused on the inner-layer characteristics because the particleefluid interaction seems to be much stronger in the inner layer as suggested from Fig. 6. The values of turbulence intensities were zoneaveraged, i.e., the streamwise component hu0 f/u0 cwi and the

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

62

vertical component hv0 f/v0 cwi, in the inner layer of 0.05 < y/ d < 0.2. Fig. 9a and b show the zone-averaged values hu0 f/u0 cwi and hv0 f/v0 cwi against the dimensionless particle diameter dpþ, respectively. Evidently, these turbulence modulations depend on the particle diameter dpþ and the volume-averaged particle concentration C. The turbulence intensity is enhanced for larger particle sizes, whereas it is suppressed for smaller particle sizes. The critical diameter dc of turbulence modulation, at which hu0 f/u0 cwi becomes equal to unity, was estimated from Fig. 9a. That is to say, the streamwise turbulence intensity is suppressed for dp < dc, whereas it is enhanced for dp > dc. Of particular significance is that the critical diameter dcþ did not depend on the particle concentration C, as seen clearly in Fig. 9a. In this study, it was obtained that the critical diameter dcþ ¼ 5:7 for the turbulence modulation of the streamwise component. The turbulence modulation of the vertical component v0 f was similar to that of u0 f, and then the critical diameter dcþ ¼ 6:0 was obtained, the value of which is nearly equal to dcþ ¼ 5:7 for the streamwise component.

u ′f

a

u ′cw

streamwise component

1.1 1.05

enhanced

1

suppressed 0.95

+

d c ≈ 5 .7

0.9

−3

C ≈ 0 . 3 × 10

−3

C ≈ 1 . 0 × 10

0.85

C ≈ 3 . 0 × 10

−3

0.8 2

v ′f

4

6

b

v cw ′

8

10

12

14

+

dp

vertical component

1.1 1.05

enhanced

1

suppressed 0.95

+

d c ≈ 6 .0

−3

C ≈ 0 .3 × 10

0.9

−3

C ≈ 1 .0 × 10

0.85

C ≈ 3 .0 × 10

−3

0.8 2

4

6

8

10

12

14

+

dp

Fig. 9. Turbulence modulation hu0 f/u0 cwi and hv0 f/v0 cwi of inner layer against the particle diameter (the critical diameter dc of modulation is indicated for each component).

On the other hand, the Kolmogoroff microscale h is defined as, h¼

 3 1=4 n 3

ð12Þ

in which, 3 is the dissipation rate of turbulent energy. The value of 3 is evaluated from the Kolmogoroff 5/3 power law, as follows: 3¼

 3=2 2p 1 5=3 f Su ðf Þ U C

ð13Þ

in which, Su( f ) is the energy spectrum of u(t) and f is the frequency. C ¼ 0.5 is the Kolmogoroff constant (e.g. see Nezu and Nakagawa, 1993). The value of 3 was evaluated from Eq. (12) using PIV data and then it was zone-averaged in the inner layer. As the results, the zone-averaged value hhi was obtained as hhþi ¼ 5.4. Consequently, it should be noticed that the critical particle diameter dc is nearly equal to the Kolmogoroff microscale hhi. It is considered at present that the turbulence modulation depends on the Kolmogoroff microscale rather than the macroscale Lx. Pan and Banerjee (1996) have conducted direct numerical simulation (DNS) of particleefluid interaction in the inner layer of open-channel flow, and concluded that particles smaller than the Kolmogoroff microscale in the near-wall region tend to suppress turbulence, whereas particles larger than this microscale tend to enhance turbulence. This conclusion is in good agreement with the present results of Fig. 9, although Pan and Banerjee (1996) calculated dpþ ¼ 1, 2 and 4 for particles of rp ¼ 1.05. They examined numerically the mechanism of particle effects on turbulence and explained the turbulence modulation on the basis of turbulent energy budget. In their DNS results, the larger particles ðdpþ ¼ 4Þ enhanced the turbulence production more largely than the dissipation, and the smaller particles ðdpþ ¼ 1Þ enhanced the dissipation more largely than the production. The particles of dpþ ¼ 2 did not modulate turbulence significantly, and this critical diameter coincided well with the Kolmogoroff microscale. It is further necessary to verify the mechanism of particleefluid interaction and turbulence modulation numerically by changing the specific density rp, hopefully rp ¼ 1.2 and 1.5 (present experiments) and 2.6 (natural sand). Fig. 10 shows the relation between the turbulence modulation of hu0 f/u0 cwi and the particle concentration C, as a function of the particle density rp and the particle diameter dp. The recent data of Muste et al. (2009) are also included in Fig. 10 for comparison. As the particle concentration C increases, the turbulence modulation of enhancement/suppression is observed more significantly. As the particle density rp increases, the modulation also becomes slightly larger. Such effects of particle concentration have been predicted numerically by Pan and Banerjee (1996). When hu0 f/u0 cwi vs. C were plotted in a semi-log description (Fig. 10), the former seems to obey the linear lines of log C in both enhancement and suppression of

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68 diameter d p (mm) 0.25 0.37 Present data 0.5 1.0 Muste et al.(2009) 0.21~0.25

u ′f u ′cw

p =1.2

63

a

p =1.5

−uv clear water 20

(

p =1.02)

10

1.1

0

1.05

-10

enhanced

1

-20 0

0.2

0.4

0.6

0.8

suppressed

t ( sec )

b

0.95

−uv ejection

0.9

clear water

20

0.85 10

0.8 -4 10

-3

10

C

10

-2

Fig. 10. Relation between turbulence modulation and concentration.

0 -10

sweep

turbulence. These findings may be very interesting and further necessary to be clarified. 3.4. Instantaneous Reynolds stress for ejections and sweeps The lifted-up phenomena of suspended particles are examined in the instantaneous motions of ejections, as pointed out by Nin~ o and Garcia (1996) and others. It is well known that the instantaneous Reynolds stress wf ðtÞh  uf ðtÞvf ðtÞ becomes large positive value in the ejection and sweep motions. Fig. 11a shows an example of the time series of the instantaneous Reynolds stress wf (t) at yþ ¼ 50. To distinguish the ejections (vf > 0) and the sweeps (vf < 0) in the distribution of wf (t), the signals are replotted in the following manner in Fig. 11b. wf ðtÞ for vf > 0 ðejection-likeÞ wðtÞh ð14Þ wf ðtÞ for vf < 0 ðsweep-likeÞ With this simple operation, the Reynolds stress becomes large negative value when the sweep event occurs. On the basis of this figure, the intermittent ejection period Te and the sweep period Ts were evaluated. To remove the inwardeoutward interactions and some noises in PIV data, the threshold hole value H was set here as H ¼ 1.0, in the same manner as conducted by Nezu and Azuma (2004a). Only when the Reynolds stress jw(t)j was greater than H  u0 v0 , the ejections/sweeps were counted as coherent motions. These observed values of the ejection period Te and the sweep period Ts are shown in Fig. 12. The horizontal axis indicates the ejection period and sweep period, and the vertical axis indicates the counted number of ejections and sweeps.

-20 0

0.2

0.4

0.6

0.8

t ( sec )

Fig. 11. (a) Time series of instantaneous Reynolds stress at yþ ¼ 50. (b) Examples of ejections and sweeps in instantaneous Reynolds stress.

The effects of suspended sediment on the ejection period Te and the sweep period Ts are not observed significantly. The averaged values in all sediment-laden flows were obtained as follows: Te Umax =h ¼ 1:83 and Ts Umax =h ¼ 1:85

ð15Þ

in which, Umax is the maximum mainflow velocity. These results of Eq. (15) are in good agreement with the formula of the bursting period in sediment-free open-channel flows, which was given by Nezu and Nakagawa (1993) as follows: Te Umax Ts Umax z ¼ ð1:5  3:0Þ ð16Þ h h The histogram of the ejection period and sweep period was also in good agreement with the log-normal distribution, as shown in Fig. 12. Such an applicability of log-normal distribution has been pointed out by Nezu and Nakagawa (1993). These results suggest strongly that the particleefluid interaction does not influence the coherent structure of turbulence significantly. 3.5. Instantaneous Reynolds stress distribution and local particle concentration Nin~o and Garcia (1996), Nezu and Azuma (2004a), Breugem and Uijttewaal (2006), Le Louvetel-Poilly et al. (2007)

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

64

Ne

Counted number of ejections clear-water

80

dp =0.25mm

Ns

Counted number of sweeps clear-water

80

dp =0.25mm

dp =0.37mm dp =0.5mm

60

dp =0.37mm dp =0.5mm

60

dp =1.0mm

dp=1.0mm 40

40

log-normal distribution

log-normal distribution 20

20

0

0 0

0.1

0.2

0.3

0.4

0.5

0.6 T (sec) e

0

0.1

0.2

0.3

0.4

0.5

0.6 Ts (sec)

Fig. 12. Period of ejections and sweeps.

and Nezu et al. (2008) and others found that the suspended particles are lifted up by ejections. From the operation of Eq. (14), the Reynolds stress fluctuations w(t) become large positive values in ejections, and large negative ones in sweeps (Fig. 11b). In the left-hand side of Fig. 13a, the Reynolds stress distribution wðx; y; tÞ=U2 is shown in color contours for particles of rp ¼ 1.2. A typical ejection motion occurs at t ¼ 0.0 s near the bed region (indicated by white circle). This area of the positive values is convected downstream with a rise toward the free surface. After the ejection motion at t ¼ 0.12, a typical sweep motion with negative values of w(t) inrushes into the inner layer of yþ < 100. In addition, at the right-hand side of Fig. 13a, the corresponding instantaneous particle concentration ~cðx; tÞ is shown in the case of rp ¼ 1.2 and dp ¼ 0.25 mm. Similarly, Fig. 13b shows the results in the case of rp ¼ 1.5 and dp ¼ 0.25 mm. The plotted data of ~cðx; tÞ is the zone-averaged concentration in the region of 20 < yþ < 80 (indicated by white lines in Fig. 13) for each x-position. When the ejection motion occurred at t ¼ 0.0 s as shown in Fig. 13, the particle concentration ~cðtÞ became larger (indicated by red circle) in the region of the ejection. Evidently, this implies that the high-concentration area is transported by the ejection motion. In the case of sweeps after t ¼ 0.12 s, the particle concentration was not changed significantly in the case of rp ¼ 1.2 (Fig. 13a). In contrast, the particle concentration in the sweep motions became 20e30% smaller in the case of rp ¼ 1.5 (Fig. 13b). These data of the local particle concentration are some examples of typical motions of the ejections and sweeps. It is further necessary to examine the correlation between the particle concentration and turbulence structure and also to conduct relevant conditional analysis of velocity and concentration fluctuations, which are investigated in the followings.

3.6. Quadrant conditional averaging of particle concentration To examine a relation between the strength of ejections/ sweeps and the local particle concentration, a conditional averaging of particle concentration, i.e., the zone-averaged concentration CH, was conducted in the following way. CH ¼

1 TH

Z

~cðtÞdt

ð17Þ

TH

in which, ~cðtÞ is the instantaneous concentration. TH is the duration time between the neighboring threshold range values H, i.e., the hole value of ejections/sweeps mentioned before. In this study, the value of H was changed by 0.5 units. Fig. 14 indicated the values of CH =C by column for dp ¼ 0.25 mm particles, together with the counted numbers of ejections (Ne) and sweeps (Ns) shown by symbols. Of particular significance is that the stronger ejections (i.e., the larger H ) increase the local particle concentration CH, whereas the stronger sweeps decrease it. As the threshold value H increases, the counted numbers of ejections and sweeps become significantly smaller. This means that only the stronger ejection/sweep motions can be selected by tuning the value of H, as pointed out by Nezu and Nakagawa (1993). It is found from Fig. 14 that the stronger ejection motions contribute to sediment transport more significantly, which is in good agreement with recent measurements by Breugem and Uijttewaal (2006). Fig. 14 also shows some differences due to particle diameters dp in the probability samples of ejections and sweeps. In the case of dp ¼ 0.25 mm, the number Ne of ejections with H ¼ 1e2 is enhanced as compared with that of clear-water

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

a

y+ ≡ yU* ν 200

-1.0

1.0

w(t ) U

y δ = 0.2

150

b

ρp =1.2 and d p=0.25mm

Particles of

200

ρp =1.5 and d p=0.25mm

Particles of

y+ ≡ yU* ν

c~(t) (×10−3 ) 60

2 *

-1.0

1.0

w(t ) U*2

y δ = 0.2

150

20

100 20

50

0.0 (s)

0

0

200

0.5

1

1.5

2

2.5

y + = 50

0 0

3

0.5

1

1.5

2

2.5

3

60

150

40

100 20 50

0.024 (s)

0

0

0.5

1

1.5

2

2.5

y = 50 0

200

60

150

40 20

50

0.048 (s)

0

0

200

0.5

1

1.5

2

2.5

3

150

0.024 (s)

0

3

100

+

0.5

1

1.5

2

+

y = 50 0.5

1

1.5

2

2.5

0.0 (s)

0

0

200

3

1

1.5

2

2.5

3

30 20

0.024 (s)

0

0

0.5

1

1.5

2

2.5

3

40

150

30

100

20

20

50

0.072 (s)

0

0

0.5

1

1.5

2

2.5

3

y = 50

0 0

200

60

150

40

100

+

20

50

0.096 (s)

0

0 200

0.5

1

1.5

2

2.5

1

1.5

2

y + = 50

0 0

3

0.5

0.072 (s)

0

0.5

1

1.5

2

2.5

3

0.5

2.5

3

0.096 (s) 1

1.5

2

2.5

3

60

150

40

100 20

50

0.12 (s)

30 20

0 200

0

0.5

1

1.5

2

2.5

0

3

0.5

0.12 (s) 1

1.5

2

2.5

3

60

150

40

100 20

50

0.144 (s)

0 200

0

0.5

1

1.5

2

2.5

0

3

0.5

0.144 (s) 1

1.5

2

2.5

3

60

150

0.5

1

1.5

2

2.5

3

20

50

0.168 (s)

0

30 20

0.096 (s)

0

0 200

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

0

3

0.5

0.168 (s) 1

1.5

2

2.5

3

30 20

0

0.5

1

1.5

2

2.5

150

40

100 20

50 0 0

0.5

1

1.5

2

0.192 (s) 2.5 x (cm)

y + = 50

0

0

0.5

1

1.5

2

0.192 (s) 2.5 x (cm)

0

3 30

100

20

1

1.5

2

1

1.5

2

1

1.5

2

1

1.5

2

1

1.5

2

1

1.5

2

1

1.5

2

0.024 (s)

0

0.5

2.5

3

0.048 (s)

y + = 50 0

0.5

2.5

3

0.072 (s) 2.5

3

+

y = 50 0.096 (s) 0

0.5

2.5

3

+

y = 50 0.12 (s) 0

0.5

2.5

3

+

y = 50

10

0.144 (s) 0

0.5

1

1.5

2

2.5

0

3

0.144 (s) 0

0.5

2.5

3

40

150

30

100

20

0.168 (s) 0

0.5

1

1.5

2

2.5

+

y = 50

10 0

3

0.168 (s) 0

40

150

30

100

20

0.5

0.192 (s) 0

0.5

1

1.5

2

2.5

x (cm)

0

2.5

3

+

y = 50

10

50 0

2

3

40

150

0

1.5

10

0.12 (s)

200

200

1

2.5

40

100

200

60

0

3

150

0

0.5

10

50

0

2

40

100

50

y + = 50

0

0

150

40

100

200

0

50

y + = 50

0

200

0.072 (s)

1.5

y + = 50

10

50

0.0 (s) 1

40

100

50

y + = 50

0

0

150

0

0

10

0.048 (s)

40

100

0

200

50

0.5

y + = 50

10

50

0

0

40

100

200

60

0.5

0

150

3

0.048 (s)

0 0

2.5

y + = 50

10

50

0.0 (s)

c~(t ) (×10−3 ) 40 30

40

100

65

0

0.5

0.192 (s) 2.5 x (cm)

Fig. 13. Instantaneous Reynolds stress wðtÞh  uf ðtÞvf ðtÞ and local particle concentration when ejection and sweep occur.

flow. In the case of dp ¼ 1.0 mm, on the other hand, the number Ne of ejections with larger H is also enhanced. The strength distribution of the sweeps seems to be similar to that of the ejections. The sweeps with low H is increased in the case of dp ¼ 0.25 mm, whereas the sweeps with larger H is increased in the case of dp ¼ 1.0 mm. This tendency suggests that the strength of ejection and sweep motions may be influenced by sediment diameter dp although these motion periods are not so significantly influenced (Fig. 12). 3.7. Quadrant conditional analysis of sediment flux To examine interactions between the local sediment concentration and the ejection/sweep motion, the conditional

analysis of the sediment flux, cv, was conducted by using the quadrant theory, in which v is the vertical component of turbulent fluctuations and c is the corresponding concentration fluctuations. Fig. 15 shows the results when the hole value H ¼ 0. As seen in Fig. 15, the largest contribution to the sediment flux cv is the ejection events (Q2). The second largest contribution is the sweeps (Q4). The outward (Q1) and the inward (Q3) interactions are negligibly small, i.e., cv ¼ 0. These tendencies are in good agreement with Cellino and Lemmin (2004). This means that the ejection and sweep events play an important role on sediment transport. The deviation of the sediment concentration from the time-averaged non-conditional concentration is larger in the ejection motion than the sweep one. Consequently, the sediment flux of Q2 became larger than that of Q4.

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

66

Q2 event (ejection)

Q4 event (sweep)

CH

Ne

Ns

C

60

1.5

40

1.0

clear-water

CH C

60

1.5

40

1.0

20

0.5

d p=0.25 d p =0.37

20

d p =0.5

0.5

d p =1.0 CH

CH C

0

C

0 1

1.5

2

2.5

3

3.5 ~ H

1

1.5

2

2.5

3

3.5

~H

Fig. 14. Zone-averaged particle concentration CH and counted numbers of ejections (Ne) and sweeps (Ns).

To compare the sediment flux of ejection/sweep events in two kinds of particle series (rp ¼ 1.2 and 1.5) from dp ¼ 0.25 to 1.0 mm, the sediment flux was normalized by the volumeaveraged sediment concentration C and the friction velocity U*. Fig. 16a shows the normalized sediment flux cvðyÞQ2 =CU for the ejection events. The case of dp ¼ 0.25 mm (PE25-C and PP25-c) has the largest correlation between the sediment liftup and ejections. The smallest correlation was observed for dp ¼ 1.0 mm. The differences between two series of specific density (rp ¼ 1.2 and 1.5) were not observed significantly. This means that the particle size dp has much larger influence on the particle response than its specific density rp in ejection events. In the same manner as ejections, Fig. 16b shows the normalized sediment flux cvðyÞQ4 =CU in the sweep events. The tendency of the particle-size effect is similar to the ejection events. However, the effect of the specific density is observed more clearly for sweeps than for ejections. The larger specific density, i.e., heavier particles may cause the

drop-down phenomena in flow structure due to gravity. Therefore, the negative value of vp became larger than vf. As a results, the sediment flux of rp ¼ 1.5 for sweeps became slightly larger than that of rp ¼ 1.2.

ay

δ

0.8

0.6 1.5

0.4

Q1

0 0.1

0.2

0.3

δ

0.4

ρp

Case

0.8

Q2

0.8

1.2

Q3 0.6

0.6

Q4

1.5

Ejection

0.25 0.37 0.50 1.0 0.25 0.37 0.50 1.0

0.2

by

δ

dp

1.2

0

y

ρp

Case

0.4

cvQ 2 CU*

dp

0.25 0.37 0.50 1.0 0.25 0.37 0.50 1.0

0.4 0.2

0.2

Sweep 0 -0.0004

0 0

0

0.0004

0.0008

0.0012

Fig. 15. Conditional sediment flux when H ¼ 0.

0.1

0.2

0.3

0.4

cv Q 4 CU *

cv Fig. 16. (a) Normalized conditional sediment flux in ejection motion. (b) Normalized conditional sediment flux in sweep motion.

K. Noguchi, I. Nezu / Journal of Hydro-environment Research 3 (2009) 54e68

4. Conclusions In this study, the particle and fluid velocities were measured simultaneously by the D-PIV/PTV, and the turbulence modulation and also the relations between coherent structure and local particle concentration were examined intensively. The main findings obtained in this study are as follows: (1) In the region of yþ  15, the particle velocity is faster than the carrier fluid one, i.e., Up  Uf. This suggests that the particles inrushed into the viscous layer have comparatively high speed at the elevation of yþ ¼ 15. Whereas in the region of yþ  15, the fluid velocity is faster than the particle one, i.e., Uf  Up. These tendencies of the relative velocity between fluid and particles were enhanced in the case of larger size particles. This indicates that the particle response to the carrier fluid becomes smaller with an increase of particle size dp. (2) The absolute values of the relative velocity, jUp  Ufj, become larger as the relative particle diameter dp/Lx becomes larger. The values of jUp  Ufj in the viscous layer overlap well with those of the inner layer. The plotted data of the outer layer deviated from those of the inner layer. This suggests that the particleefluid interaction in the inner layer should be distinguished from that in the outer layer. (3) The turbulence modulations hu0 f/u0 cwi and hv0 f/v0 cwi, which were zone-averaged in 0.05  y/d  0.2, became smaller than unity in the case of smaller size particle (dp ¼ 0.25 and 0.37 mm), whereas they became larger than unity in the case of larger size particles (dp ¼ 0.5 and 1.0 mm). From these tendencies, the critical diameter dc of turbulence modulation, in which turbulence is enhanced at dp > dc, whereas it is suppressed at dp < dc, was evaluated as dc ¼ 0.44 mm. This value of dc was in good agreement with the zone-averaged Kolmogoroff microscale hhi. These results show that the turbulence modulation, i.e., particleefluid interaction is governed by the Kolmogoroff microscale rather than the macroscale such as the integral scale Lx in sediment-laden open-channel flows. This significant criterion of turbulence modulation was also predicted numerically by Pan and Banerjee (1996). (4) The values of the ejection period Te and the sweep period Ts were evaluated from the instantaneous Reynolds stress. The counted number of ejections and sweeps are not changed significantly by the existence of suspended sediment. The local particle concentration increased when the ejections occurred, whereas it decreased when the sweeps occurred. Such significant changes were observed in the ejection motions, in which the particle concentration became about 20e40% larger in comparison with the time-averaged particle concentration. This tendency was seen more significantly in the case of heavier particles of rp ¼ 1.5. (5) To examine a relation between the strength of ejections/ sweeps and the local particle concentration, the conditional averaging of particle concentration, CH, was evaluated. Of particular significance is that the stronger

67

ejections increase the local particle concentration CH, whereas the stronger sweeps decrease it. This suggests that the stronger and more violent ejections contribute to sediment transport more significantly. (6) The conditional analysis of the sediment flux, cv, was conducted in the quadrant theory. The largest contribution to the sediment flux cv is the ejection events (Q2), and the second largest contribution is the sweeps (Q4). The largest intensity of sediment flux at ejections and sweeps was observed in the case of smallest particle size dp ¼ 0.25 mm. Acknowledgements The present study was carried out under the financial support of the Research Project Grant-In-Aid for Scientific Research of Japanese Government (Kakenhi No. (B) 20360218, Principal Investigator ¼ I. Nezu). The authors gratefully acknowledge this support. References Best, J., Bennett, S., Bridge, J., Leeder, M., 1997. Turbulence modulation and particle velocities over flat sand beds at low transport rates. J. Hydraulic Eng., ASCE 123, 1118e1129. Bigillon, F., Nin~o, Y., Garcia, M.H., 2006. Measurements of turbulence characteristics in an open-channel flow over a transitionally-rough bed using particle image. Exp. Fluids 41, 857e867. Breugem, W.A., Uijttewaal, W.S.J., 2006. A PIV/PTV experiment on sediment transport in a horizontal open channel flow. River Flow 2006, Balkema, pp. 789e798. Cellino, M., Lemmin, U., 2004. Influence of coherent flow structures on the dynamics of suspended sediment transport in open-channel flow. J. Hydraulic Eng., ASCE 130, 1077e1088. Elghobashi, S., 1994. On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309e329. Gore, R.A., Crowe, C.T., 1989. The effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow 15, 279e285. Hetsroni, G., 1989. Particle-turbulence interaction. Int. J. Multiphase Flow 15, 735e746. Kaftori, G., Hetsroni, G., Banerjee, S., 1995. Particle behavior in the turbulent boundary layer. II. Velocity and distribution profiles. Phys. Fluids 7, 1107e1127. Kaftori, G., Hetsroni, G., Banerjee, S., 1998. The effect of particles on wall turbulence. Int. J. Multiphase Flow 24, 359e386. Kulick, J.D., Fessler, J.R., Eaton, J.K., 1994. Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 177, 133e166. Le Louvetel-Poilly, J., Bigillon, F., Champagne, J.Y., 2007. Experimental investigation of the turbulent structures involved in particle motion. Proc. of 32nd IAHR Congress of Venice, No. 1091(8 pages on CD-ROM). Lyn, D.A., 1991. Resistance in flat-bed sediment-laden flows. J. Hydraulic Eng., ASCE 117, 94e114. Lyn, D.A., 1992. Turbulence characteristics of sediment-laden flows in open channels. J. Hydraulic Eng., ASCE 118, 971e988. Muste, M., 2002. Source of bias errors in flume experiments on suspendedsediment transport. J. Hydraulic Res. 40, 695e708. Muste, M., Patel, V.C., 1997. Velocity profiles for particles and liquid in open-channel flow with suspended sediment. J. Hydraulic Eng., ASCE 123, 742e751. Muste, M., Yu, K., Fujita, I., Ettema, R., 2009. Two-phase flow insights into open-channel flows with suspended particles of different densities. J. Environ. Fluid Mech. 9, 161e186. Nezu, I., Azuma, R., 2004a. Turbulence characteristics and interaction between particles and fluid in particle-laden open-channel flows. J. Hydraulic Eng., ASCE 130, 988e1001.

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Nezu, I., Azuma, R., 2004b. Effect of side wall on particle-fluid motions in particle-laden open-channel flow. Ann. J. Hydraulic Eng., JSCE 48, 487e 492 (in Japanese). Nezu, I., Nakagawa, H., 1993. Turbulence in open channel flows. IAHR Monograph. Balkema, Rotterdam, The Netherlands. Nezu, I., Noguchi, K., Sanjou, M., 2008. Effects of particle size and concentration on turbulent structure in sediment-laden open-channel flow. River Flow 2008, Kubaba, 91e98. Nezu, I., Rodi, W., 1986. Open-channel flow measurements with a laser Doppler anemometer. J. Hydraulic Eng., ASCE 112, 335e355. Nin~ o, Y., Garcia, M.H., 1996. Experiments on particle-turbulence interactions in the near-wall region of an open channel flow: implications for sediment transport. J. Fluid Mech. 326, 285e319.

Noguchi, K., Nezu, I., Sanjou, M., 2008. Turbulence structure and fluidparticle interaction in sdiment-laden flows over developing sand dunes. J. Environ. Fluid Mech. 8, 569e578. Pan, Y., Banerjee, S., 1996. Numerical simulation of particle interactions with wall turbulence. Phys. Fluids 8, 2733e2755. Rashidi, M., Hetsroni, G., Banerjee, S., 1990. Particle-turbulence interaction in a boundary layer. Int. J. Multiphase Flow 16, 935e949. Righetti, M., Romano, G.P., 2004. Particle-fluid interactions in a plane nearwall turbulent flow. J. Fluid Mech. 505, 93e121. Song, T., Graf, W.H., Lemmin, U., 1994. Uniform flow in open channels with movable gravel bed. J. Hydraulic Res. IAHR 29, 387e401. Tennekes, H., Lumley, J.L., 1972. A First Course in Turbulence. MIT Press. Yalin, M.S., 1977. Mechanism of Sediment Transport. Pergamon Press, Elmsford, N.Y.