Particle fluctuation velocity of a horizontal self-excited pneumatic conveying near the minimum pressure drop

Powder Technology 241 (2013) 115–125

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Particle fluctuation velocity of a horizontal self-excited pneumatic conveying near the minimum pressure drop Fei Yan, Akira Rinoshika ⁎ Department of Mechanical Systems Engineering, Graduate School of Science and Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa-shi, Yamagata 992-8510, Japan

a r t i c l e

i n f o

Article history: Received 25 September 2012 Received in revised form 23 February 2013 Accepted 2 March 2013 Available online 13 March 2013 Keywords: High-speed PIV MPD air velocity Power spectrum Intensity of particle fluctuating velocity Skewness Probability density function

a b s t r a c t In order to reveal the mechanism of the steady transport at the low conveying velocity by using soft fins, the high-speed particle image velocimetry (PIV) is used to measure and analyze particle fluctuation velocity near air conveying velocity of the minimum pressure drop (MPD) in a horizontal self-excited pneumatic conveying. The study focuses on the effect of the different fin's lengths on the horizontal pneumatic conveying in terms of the time-averaged particle concentration and velocity, power spectrum, auto-correlation coefficients, two-point correlation coefficients, fluctuation intensity of particle velocity, skewness factor and probability density function. It is found that the power spectra peaks of fins, especially the longer fins, are larger than that of non-fin even at lower air velocity, suggesting the accelerating efficiency of fins' vibration. Meanwhile, the profiles of particle fluctuation velocity intensity indicate that the fins' oscillation generates large particle fluctuating energy even at lower air velocity so that the particles are more easily accelerated and suspended. This is one of the important reasons why the fins' oscillation results in the low pressure drop and low MPD air velocity. From the distribution of the skewness factor and the probability density function, it is found that the particle fluctuation velocities of all cases follow the Gaussian distribution in the lower and middle parts of pipe, and departure from the Gaussian distribution in the upper part of the pipe. The particle fluctuation velocity of the most efficient Fin320 more obeys the Gaussian-type fluctuation. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The pneumatic conveying of granular materials has been widely applied in a number of industrial processes, for example power generation, steel making, chemical, pharmaceutical, food processing, agricultural granular processing and commodity transfer processes. This conveying technique has many merits such as low power consumption, high efficiency, flexibility of layout, ease of automation, security, low maintenance, ease of installation and environmental friend and so on. However, the high power consumption, pipe erosion and particle degradation are often caused when the pneumatic conveying is operated in the dilute-phase regime or in the high air velocity region. As an important design standard of the pneumatic conveying, the pressure drop and conveying velocity should be kept as low as possible. In order to realize this target, some saving-energy techniques, such as spiral tube [1], swirling flow [2,3], spiral flow [4], venturi feeder [5] and dune model [6], have been developed. Recently, Yan and Rinoshika [7,8] further reduced the conveying velocity and power consumption by using the soft fins in the inlet of the conveying pipeline to excite air flow. However, the mechanism of the steady transport at the low conveying velocity due to the oscillation of soft fins is not completely understood, even the profiles of time-averaged particle velocity and concentration ⁎ Corresponding author. Tel./fax: +81 238 26 3225. E-mail address: [email protected] (A. Rinoshika). 0032-5910/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.powtec.2013.03.009

were measured and analyzed by high-speed particle image velocimetry (PIV) [9,10]. It is necessary to investigate the behaviors of particle fluctuation velocity in the range of low conveying velocity. This is of fundamental significance and, thus becoming an objective of this study. Since Tsuji and Morikawa [11] measured air and particle fluctuation velocities in a dilute-phase gas-particle suspension flow of a horizontal pipe by use of Laser Doppler anemometry, also known as Laser Doppler velocimetry (LDV), the investigations on the particle fluctuating velocity have the strong theoretical interest in explaining the complicated phenomena presented in the gas–solid two-phase flows. However, the LDV technique is mostly limited to dilute-phase particulate flows and higher air velocity or suspension flows. Recently, Yan and Rinoshika [12] applied the high-speed PIV to measure the profiles of particle velocity in a horizontal pneumatic conveying and proved the applicability and validity of PIV measurement in the relatively dense gas–solid two-phase flow. Rinoshika et al. [13] analyzed the particle fluctuation velocity of the high-speed PIV near the minimum conveying velocity in the relatively dense-phase pneumatic conveying. Further, the continuous wavelet transform and orthogonal wavelet multi-resolution technique were employed to analyze the fluctuating particle velocities of the high-speed PIV for providing both quantitative and qualitative information on the particle fluctuation velocity of various frequencies [14,15]. In this study, the high-speed PIV is first used to measure the distribution of particle fluctuation velocity near the air conveying velocity

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Fig. 1. Schematic diagram of the experimental apparatus.

a)

of the minimum pressure drop (MPD) at a pipe section of the acceleration and the fully developed regimes in a horizontal self-excited pneumatic conveying. The effects of the different fin's lengths on the particle fluctuation velocity are evaluated in terms of the power spectrum, auto-correlation coefficients, two-point correlation coefficients, fluctuation intensity of particle velocity, skewness factor and probability density function. 2. Experimental apparatus and procedure 2.1. Experimental setup

b)

The experimental facility of the positive pressure conveying system, as shown in Fig. 1, is used in the present study. Air from a blower flows through the orifice meter, and picks up the solid materials fed by gravity from the feed tank at the inlet of the conveying pipeline. Then, the gas-particle mixture enters the test pipe and the particles are separated at the pipe exit by the separator. The conveying pipe consists of a horizontal smooth acrylic tube with an inside diameter of D = 80 mm and total length of about L = 5 m. The airflow rate and the solids mass flow rate are respectively measured by the orifice meter and load cell. The gauge pressures along the pipe are measured by two pressure sensors. The polyethylene particle with mean diameter of 2.3 mm and density of 978 kg/m3 is used as conveying material in this experiment. The particle size distribution is between 1.65 and 2.95 mm with a standard deviation of 0.34. The floating velocity of a particle, which is defined as

Fig. 2. (a). Soft fins. (b). Mounted soft fins in a test pipe.

Light sheet Light sheet

Particles

Particles Flo

wd

irec

tion

High-speed Camera

Fig. 3. Schematic of the high-speed PIV measurement system.

Pipeline

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

A

117

A-A b

Measurement volume

Sub volume 10

y

9 8 7

D

6 5 4

y

3 2

x

1

L

A

Fig. 4. Measurement volume of particle concentration.

the air velocity required for a particle to suspend in a vertical air stream, is 7.5 m/s. The superficial air velocity Ua is varied from 10 to 17 m/s, the mass flow rate of solids Gs is fixed at 0.45 kg/s. The statistical uncertainty of the superficial mean air velocity, the solids mass flow rate and the gauge pressure are respectively ±3.79%, ±1.25% and ±1.52% at the 95% confidence level.

2.3. High-speed PIV imaging setup and procedure Fig. 3 shows an experimental setup of high-speed PIV. A high-speed camera (Photron FASTCAM-SA3) with a resolution of 1024 × 1024 pixels was used to capture the 2000 successive digital particle images

2.2. Soft fins

a) x/D = 25 1.0 Fin's type Ua (m/s)

0.8

Non-fin Fin200 Fin250 Fin320

0.6

y/D

In order to excite flow oscillation, four pieces of the soft fins made of polyethylene, as shown in Fig. 2, are mounted in a horizontal center plane through the pipe axis in front of the particle inlet. Each piece of soft fin has a width of 20 mm, thickness of 0.2 mm and density of 789 kg/m 3. Three kinds of soft fins having lengths of 200, 250 and 320 mm (corresponding to piece mass of 0.63, 0.79 and 1.01 g), called Fin200, Fin250 and Fin320 respectively, are used. Because the upstream side of the fins is fixed at the location of 0.25 m from the particle inlet, as shown in Fig. 1, the downstream side of fins oscillates up and down as the air flows over them and the oscillating fins of Fin320 directly touch particles that are fed from the feed tank at the inlet of the conveying pipeline. The other soft fins (Fin200 and Fin250) are just oscillated from up to down due to the air flow.

13.45 12.6 12.1 11.8

0.4 0.2 0.0 0

1

ρpi /ρpo

2

3

2

3

b) x/D = 44

1.8

1.6

0.8 0.6

1.4

y/D

Pressure drop Δp(kPa)

1.0

0.4 1.2

Non-fin Fin200 Fin250 Fin320 PIV measurement points

0.2

1.0

0.0 10

11

12

13

14

15

16

17

Superficial air velocity Ua(m/s) Fig. 5. Relation between pressure drop and air velocity for different lengths of fins and non-fin.

0

1

ρpi /ρpo

Fig. 6. Profiles of time-averaged particle concentration at different locations for different lengths of fin and non-fin at their air velocities Ua.

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at a time interval of 1 ms (i.e. 1000 frames/s) between two consecutive images and the shutter speed of each frame is set at 0.1 ms. A fixed focal-length Nikkor lens (manual focus 50 mm f/1.2) set at the maximum f-stop 1.2 was used to capture images. A thin light-sheet of thickness b = 5 mm produced by a high-intensity continuous light source (Fig. 3) is used to illuminate the objective particulate flow on the vertical center plane of the pipe. The distance from the camera's focal plane mark to the light-sheet plane was fixed at about 0.5 m. The measurements are performed at two different locations: x = 2 m (x/D = 25, location A) and 3.5 m (x/D = 44, location B) from the particle inlet (Fig. 1). The PIV View software based on spatial cross-correlation method is applied to measure the particle group velocities in the gas-particle two-phase flow. The large PIV interrogation areas that contain several particles are adopted since the size of particle is relatively large. The image of size 80 mm × 111 mm is divided into 18 × 25 interrogation areas and the size of each interrogation area is about 4.4 mm × 4.4 mm. The velocity of each interrogation area or particle group is defined as local particle velocity (Yan and Rinoshika 2012a), which has two components of up (horizontal direction x) and vp (vertical direction y). Fluctuating velocities of particles, u′ p in the x-direction and v′ p in y-direction, are computed by subtracting the mean. In order to cross-validate the PIV measurement results, the particle velocities are also manually measured by analyzing particle tracks in the successive high-speed images using SigmaScan Pro 5 software,

which is also called PTV. It is found that the particle velocity distribution of PIV is quite in agreement with that of PTV, and the average relative error is less than 1.19%. This result proves the validation of PIV measurement. In this study, the statistical uncertainty of the time-averaged particle velocity in the high-speed PIV measurement is ±4.3% at the 95% confidence level. 2.4. Measurement method of particle concentration Profiles of time-averaged particle concentration with soft fins and without soft fins are measured by using the high-speed digital images of gas-solid two-phase flow. Fig. 4 presents the measurement region of particle concentration. A rectangular volume with a size of length L × height D × thickness b (=5 mm, the thickness of light-sheet) is vertically set through the pipe axis. This measurement volume is divided into ten sub volumes from the bottom to top of the pipe, and each sub volume has a size of length L × height Δy × thickness b (Fig. 4). The coordinates of the particles are first measured in the measurement volume by SigmaScan Pro5 software. Then the number of particles in each sub volume is counted based on the coordinates of the particles. The particle concentration of each sub volume is calculated by

ρpi ¼

mp ⋅N Δy⋅L⋅b i

ð1Þ

a) y/D = 0.24

a) x/D = 25

0.30 Fin's type U a (m/s)

1.0 Fin's type Ua (m/s) 13.45 12.6 12.1 11.8

0.4 0.2 0.0 0.1

Non-fin Fin200 Fin250 Fin320

0.20

y/D

0.6

Non-fin Fin200 Fin250 Fin320

P/u'2p(s)

0.8

0.25

13.45 12.6 12.1 11.8

0.15 0.10 0.05 0.00

0.2

0.3

0.4

0.5

0.6

1

0.7

10

100

f(Hz)

up/Ua

b) y/D = 0.48

b) x/D = 44

0.30

1.0

0.25

0.8

0.20

y/D

P/u'2p(s)

0.6 0.4

0.15 0.10

0.2 0.0 0.1

0.05 0.2

0.3

0.4

0.5

0.6

0.7

up/Ua Fig. 7. Profiles of time-averaged particle velocity measured by PIV at different locations for different lengths of fin and non-fin at their air velocities Ua.

0.00 1

10

100

f(Hz) Fig. 8. Power spectra of particle fluctuation velocity u′ p at the location of x/D = 25 for different lengths of fin and non-fin at their air velocities Ua.

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

where mp is mass of a particle, Ni is the number of particles in sub volume i. The particle concentration of the measurement volume is calculated by ρp0 ¼

10 mp X N D⋅L⋅b i¼1 i

ð2Þ

In this study, the normalized local particle concentration ρpi/ρpo of sub volume i is defined as ρpi 1 Ni Ni ¼ ¼ 10 10 10 ρp0 Δy X X Ni Ni D i¼1

ð3Þ

i¼1

It is evident that ρpi/ρpo is independent on the length L and the thickness b of the measurement volume. 3. Experimental results and discussions 3.1. Pressure drop and particle concentration To compare with the pneumatic conveying of non-fins, the pressure loss due to the presence of soft fins should be considered. Therefore, the pressure drop Δp of pneumatic conveying is measured by the difference between the first pressure sensor and second pressure

sensor (i.e. between the inlet of air flow and exit of the conveying pipe in Fig. 1) in this study, where the fin-induced pressure loss is included. The air velocity at the MPD is referred to as the MPD velocity, which is the lowest air velocity used to safely convey particles without choking occurring. Fig. 5 shows the pressure drop Δp versus the air velocity Ua with different lengths of soft fins and non-fin. As the air velocity decreases, the pressure drops of all cases first decrease and then increase after the MPD velocity. Making a comparison among the different lengths of fins and no-fin, the pressure drops with fins are higher than that of non-fin in the range of high air velocity. In the range of low air velocity, however, the pressure drops with fins become lower than that of non-fin. In addition, comparing with the MPD velocity of non-fin (Ua_min = 13.45 m/s), the minimum air velocity is largely decreased by using fins at Ua-min = 12.6 (Fin200), 12.1 (Fin250) and 11.8 m/s (Fin320). The reduction rates of the pressure drop and minimum velocity become apparently large when increasing the length of fins. This is because the fins' vibration causes the air flow of the self-excited oscillation and so that the particles are easily suspended and accelerated. Among the three kinds of fins, the longest fin (Fin320) shows the lowest pressure drop and the MPD velocity. The maximum reduction rates of the pressure drop and MPD velocity reach about 11.2% and 12.2%, respectively. The above results indicate that the soft fins are efficient for reducing the pressure drop and the MPD velocity. In order to study the mechanism of the steady transport in the range of low air velocity due to the

a) y/D = 0.24

a) y/D = 0.24

0.14

0.40

Fin's type U a (m/s)

0.12

Non-fin Fin200 Fin250 Fin320

0.10 0.08

13.45 12.6 12.1 11.8

0.06

Fin's type Ua (m/s)

0.35

Non-fin Fin200 Fin250 Fin320

0.30

P/u'2p(s)

P/v'2p(s)

119

0.04

0.25

13.45 12.6 12.1 11.8

0.20 0.15 0.10

0.02

0.05 0.00 1

10

0.00

100

1

f(Hz)

100

f(Hz)

b) y/D = 0.48

b) y/D = 0.48

0.14

0.40

0.12

0.35 0.30

P/u'2p(s)

0.10

P/v'2p(s)

10

0.08 0.06

0.25 0.20 0.15

0.04

0.10

0.02

0.05 0.00

0.00 1

10

100

f(Hz) Fig. 9. Power spectra of particle fluctuation velocity v′ p at the location of x/D = 25 for different lengths of fin and non-fin at their air velocities Ua.

1

10

100

f(Hz) Fig. 10. Power spectra of particle fluctuation velocity u′ p at the location of x/D = 44 for different lengths of fin and non-fin at their air velocities Ua.

120

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

soft fins, high-speed PIV is used to measure the particle fluctuation velocity near the MPD velocities for different lengths of fins and non-fin that are indicated by the solid symbols in Fig. 5. To quantify the effect of the soft fins on the distribution of particle concentration, the profiles of particle concentration at the locations of x/D = 25 and 44 are measured by analyzing PIV images described in Section 2.4. Fig. 6 shows the normalized local particle concentration ρpi/ρpo versus y/D (y is the ordinate from bottom to top of pipe, as shown in Fig. 4) at different locations with fins and non-fin. The statistical uncertainty of the particle concentration is ± 6.3% at the 95% confidence level. At the upstream region of x/D = 25, as shown in Fig. 6(a), the particle concentrations with fins and non-fin display the maximum value around y/D = 0.15. The particle concentrations of using the fins are slightly lower than that of non-fin near the bottom of pipe and are higher than that of non-fin in the middle part of pipe, although the air velocities of the fins are lower than that of non-fin. This is because the air flow of the inlet is oscillating due to the fins' vibration and generates the vertical component of air velocity so that the particles are easily suspended. Although the Fin320 has the lowest minimum air velocity (Ua_min = 11.8 m/s) among these fins, its particle concentration is still lower than that of non-fin (Ua_min = 13.1 m/s) near the bottom of pipe. It is because that Fin320 can not only cause the larger oscillation of air flow than that of other fins, but also touch particles that are fed from the feed tank at the inlet of the test pipeline, so that particles are easily dispersed and suspended for accelerating and the deposition of particles on the bottom of the pipe can be avoided even at low air velocity.

At the downstream region of x/D = 44, as shown in Fig. 6(b), the distributions of particle concentration for different lengths of fins and non-fin decrease near the bottom of pipe and increase in the top part of pipe comparing to the location of x/D = 25. It indicates that particles have been accelerated and suspended at downstream. The difference of particle concentration between fins and non-fin is hardly observed, suggesting that the effect of fins on the particle concentration disappears.

3.2. Profiles of time-averaged particle velocity Fig. 7 shows normalized profiles of time-averaged particle axial velocity component u p =U a , measured by the high-speed PIV, for different lengths of fins and non-fin at locations of x/D = 25 and 44. The maximum and minimum axial particle velocities are respectively observed near the top and bottom of pipe. It is due to the low particle concentration in the top of pipe and the high particle concentration on the bottom of pipe (Fig. 6). At the upstream region of x/D = 25, as shown in Fig. 7(a), the axial particle velocities u p =U a of Fin200 and Fin250 are almost same as non-fin near the top of pipe, and Fin320 exhibits the highest axial particle velocity although it has the lowest air conveying velocity. However, the axial particle velocities u p =U a of fins become lower than that of non-fin in the middle and low parts of pipe, suggesting the steady pneumatic conveying at the low air velocity by using the fins. This is because the air flow of the inlet is oscillating due to the fins' vibration and generates the vertical component of air velocity so that the particles are easily suspended and accelerated; especially for Fin320 which can not only cause the oscillation of air

a) y/D = 0.24 0.18 Fin's type Ua (m/s)

0.16

Non-fin Fin200 Fin250 Fin320

0.14

Fin's type Ua (m/s)

0.06

Non-fin Fin200 Fin250 Fin320

0.6

0.10 0.08

1.0 0.8

Rup(τ)

P/v'2p(s)

0.12

a

13.45 12.6 12.1 11.8

13.45 12.6 12.1 11.8

0.4 0.2

0.04 0.0

0.02

-0.2

0.00 1

10

100

-0.4 0.0

f(Hz)

b) y/D = 0.48

b

0.18 0.16

0.2

0.4

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

1.0 0.8

0.14 0.6

Rvp(τ)

P/v'2p(s)

0.12 0.10 0.08

0.4 0.2

0.06 0.04

0.0

0.02 -0.2

0.00

1

10

100

f(Hz) Fig. 11. Power spectra of particle fluctuation velocity v′ p at the location of x/D = 44 for different lengths of fin and non-fin at their air velocities Ua.

0.0

τ(s) Fig. 12. Auto-correlation coefficients of particle fluctuation velocity at the location of x/D = 25 and y/D = 0.24 for different lengths of fin and non-fin at their air velocities Ua.

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

flow, but also touch particles that are fed from the feed tank at the inlet of the test pipeline, particles are more easily accelerated. At the downstream region of x/D = 44, as shown in Fig. 7(b), the distributions of axial particle velocities u p =U a are almost same as the location of x/D = 25 for all cases in the top part of pipeline. However, u p =U a becomes larger than the location of x/D = 25 for the fins (except Fin320) and non-fin near the bottom of pipeline. Although u p =U a of Fin320 is obviously lower than that of other cases and the location of x/D = 25 on the bottom part of pipeline, the pneumatic conveying can be still safely operated, suggesting the efficiency of long fins even though at the low air velocity. 3.3. Spectral characteristics of particle fluctuating velocity To study the behaviors of particle velocity in a horizontal self-excited pneumatic conveying of using soft fins, the fluctuation velocities of particle u′ p and v′ p , which are respectively calculated by subtracting the time-averaged particle velocity from instantaneous particle velocity in x- and y-direction, are analyzed by Fourier transform at vertical positions of y/D = 0.24 and 0.48. The power spectral density functions ∞

2

2

2

2

P, defined as ∫−∞ Pdf ¼u′ p or v′ p , are normalized by u′ p and v′ p for indicating the normalized energy distribution with frequency f. The normalized power spectra of locations x/D = 25 and 44 are presented in Figs. 8–11. Fig. 8 shows the power spectra of u′p at the upstream region of x/D = 25 for different lengths of fins and non-fin. It is found that the spectra of u′p in the bottom part of pipe (y/D = 0.24), as shown in Fig. 8(a), exhibit pronounced peaks in the range of lower frequency

a

for all cases, and decrease as increasing f. This is because the high particle concentration for the bottom of the pipe (Fig. 6a) causes the low frequency component of u′p . The peaks of power spectra of fins are larger than that of non-fin even at lower air velocity of fins, suggesting the accelerating efficiency of fins' vibration. Especially Fin320 exhibits the largest spectrum peak around f = 2 Hz. As increasing y/D, as shown in Fig. 8 (b), the power spectra of u′p decrease due to the particle suspension flow in the upper part of pipe. The power spectra of v′p at the upstream region of x/D = 25 for different lengths of fins and non-fin are shown in Fig. 9. It is clearly seen that the power spectra distribution of v′p are similar to u′p (Fig. 8). The peaks of power spectra of fins are also larger than that of non-fin, especially Fin320 exhibits the largest spectrum peak around f = 4 Hz in the bottom part of pipe. It exhibits the suspended efficiency due to fins' vibration. At the downstream of x/D = 44, as shown in Figs. 10 and 11, the evident peaks of power spectrum for u′p and v′p are still observed in the range of low frequency and become larger than that of x/D = 25. The power spectrum u′p of Fin320 exhibits the largest peaks of spectrum around f = 3 Hz, implying the effect of fins on the particle fluctuation velocity at the downstream. Figs. 12 and 13 present the auto-correlation coefficients of particle fluctuation velocity near the bottom of pipe (y/D = 0.24) at the locations of x/D = 25 and 44 for different lengths of fin and non-fin. It is clearly seen that Rup and Rvp of Fin320 respectively display a quasi-periodical wave as time-lag τ increases among all cases, especially at the downstream of x/D = 44. It suggests a quasi-periodical particle flow of the high concentration near the bottom of pipe and in accordance with the largest peak of spectrum.

1.0 1.0 Fin's type Ua (m/s) Non-fin Fin200 Fin250 Fin320

Rup(τ)

0.6

0.8

13.45 12.6 12.1 11.8

0.6

y/D

0.8

0.4

0.4 Fin's type Ua (m/s) Non-fin 13.45 Fin200 12.6 Fin250 12.1 Fin320 11.8

0.2 0.0

0.2

-0.2

0.0 0.0

b

121

-0.4 0.0

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

1.0

0.8

1.0

Rup0up

1.0

1.0

1.0

0.8 0.8 0.6

0.4

y/D

Rvp(τ)

0.6

0.2

0.4

0.0 0.2 -0.2 -0.4 0.0

0.0 0.2

0.4

0.6

0.8

1.0

τ(s) Fig. 13. Auto-correlation coefficients of particle fluctuation velocity at the location of x/D = 44 and y/D = 0.24 for different lengths of fin and non-fin at their air velocities U a.

0.0

0.2

0.4

0.6

Rvp0vp Fig. 14. Lateral two-point correlation coefficients of particle fluctuation velocity at the location of x/D = 25 for different lengths of fin and non-fin at their air velocities Ua (the reference velocity is at y/D ≈ 0.5).

122

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

3.4. Two-point fluctuation velocity correlation In order to assess the two-point correlation coefficient of the particle fluctuation velocity, Rαp0αp, in the measurement plane is defined as α p0 α p Rα p0 α p ¼  1=2 α 2p0 α 2p

ð4Þ ′

′

where αp represents particle fluctuation velocities of u p or v p , and αp0 is the reference particle fluctuation velocity selected at y/D ≈ 0.5. Fig. 14 shows the profiles of Rαp0αp at location of x/D = 25 for different lengths of fin and non-fin. It is found that the values of Rup0up for the long fins (Fin250 and Fin320) are larger than that of non-fin, and especially in the lower part of pipeline they show a high correlation because of the high particle concentration. And Rup0up of Fin320 exhibits a largest correlation value near the bottom of pipe. However, the little difference of Rvp0vp between fins and non-fin is observed, and is almost independent on the fins' length. Meanwhile, it is clearly seen that the value of Rvp0vp is almost close to zero near the bottom of pipe, indicating less space correlation of v′p for all cases.

are normalized by Ua2) are compared between different lengths of fin and non-fin. 2 Fig. 15 shows the profiles of u′ p =U 2a at the locations of x/D = 25 and 44 for different lengths of fin and non-fin. At the upstream loca2

tion of x/D = 25, as shown in Fig. 15(a), the u′ p =U 2a of fins are slightly larger than that of non-fin in the lower part of pipe although the air 2

velocity of fins are lower than that of non-fin, especially u′ p =U 2a of Fin320 having a minimum air velocity exhibits the largest value near the bottom of pipe and in the middle part of pipe. It is because Fin320 not only causes the more intense oscillation of air flow, but also directly touch particles makes the particles to generate larger fluctuating energy 2

so that the particles are more easily accelerated. The higher u′ p =U 2a is one of the important reasons why Fin320 exhibits the low pressure drop and low MPD air velocity among all cases. However, at the down2

stream of x/D = 44, as shown in Fig. 15(b), u′ p =U 2a becomes larger than that of the upstream region of x/D = 25 in the lower part of pipe for all 2

cases. u′ p =U 2a of fins are almost larger than that of non-fin, implying that 2

fins' oscillations cause larger u′ p =U 2a and steady conveying. Especially 2

3.5. Intensities of particle fluctuation velocity In order to reveal the effect of fins on the particle fluctuation energy, 2

2

the intensities of particle fluctuation velocity u′ p , v′ p and u′p v′p (which

u′ p =U 2a of Fin320 keeps the largest value in the range of y/D > 0.6, although its air velocity is lowest among all cases, proving the efficiency of long fins. 2 Fig. 16 presents the profiles of v′ p =U 2a at the locations of x/D = 25 and 44 for different lengths of fin and non-fin. At the upstream

a) x/D = 25

1.0

1.0

0.8

0.8

0.6

0.6

y/D

y/D

a) x/D = 25

0.4

0.4

Fin's type Ua (m/s)

Non-fin Fin200 Fin250 Fin320

0.2 0.0 0

1x10-3

3x10-3

2x10-3

13.45 12.6 12.1 11.8

4x10-3

Fin's type Ua (m/s)

Non-fin 13.45 Fin200 12.6 Fin250 12.1 Fin320 11.8

0.2 0.0 0

5x10-3

1x10-4

3x10-4

2 v'p

2

2

2x10-4

u' p /Ua

4x10-4

5x10-4

2

/U a

b) x/D = 44

b) x/D = 44

1.0

0.8

0.8

0.6

0.6

y/D

y/D

1.0

0.4

0.4

0.2

0.2 0.0

0.0 0

1x10-3

2x10-3

3x10-3 2

4x10-3

5x10-3

2

u' p /Ua

2

Fig. 15. Intensity of particle fluctuation velocity u′ p =U 2a at different locations for different lengths of fin and non-fin at their air velocities Ua.

0

1x10-4

2x10-4

3x10-4 2

4x10-4

5x10-4

2

v'p /Ua 2

Fig. 16. Intensity of particle fluctuation velocity v′ p =U 2a at different locations for different lengths of fin and non-fin at their air velocities Ua.

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125 2

location of x/D = 25, as shown in Fig. 16(a), v′ p =U 2a increases with y/D and exhibits almost the same profiles of fluctuating energy for all cases in the range of y/D b 0.25.

2 v′ p =U 2a

of long fins (Fin250 and Fin320) are 2 v′ p =U 2a

larger than that of non-fin in the range of y/D > 0.5, especially of Fin320 keeps the maximum value in the range of 0.2 ≤ y/D ≤ 0.85 al2

though its air velocity is the lowest among all cases. The large v′ p =U 2a of long fins causes the larger suspending force so that the particles are more easily suspended, proving the fins' efficiency. At the downstream 2 v′ p =U 2a

of x/D = 44, as shown in Fig. 16(b), of fins are evidently larger than that of non-fin in the lower part of pipe even their air velocities are lower than that of non-fin, especially Fin320 exhibits a largest 2

value of v′ p =U 2a around y/D = 0.8. Fig. 17 shows the profiles of u′p v′p =U 2a at the locations of x/D = 25 and 44 for different lengths of fin and non-fin. At the upstream of x/D = 25, as shown in Fig. 17(a), u′p v′p =U 2a exhibits almost the same distributions in the lower part of pipe. The maximum value of u′p v′p =U 2a or large correlation between u′p and v′p is observed in the middle part of pipe and u′p v′p =U 2a of long fins (Fin250 and Fin320) is larger than that of non-fin. u′p v′p =U 2a of Fin320 exhibits the largest value around y/D = 0.6 among all cases, where is the interface between suspension flow (upper part) and particle sliding strands (lower part). It implies that the large correlation between u′p and v′p results in low pressure drop and low MPD air velocity due to the fins' oscillation. At the

123

downstream of x/D = 44, as shown in Fig. 17(b), the distributions of u′p v′p =U 2a are similar as x/D = 25 (Fig. 17a). u′p v′p =U 2a increases in the upper part of pipe and decreases in the lower part of pipe. u′p v′p =U 2a of Fin320 also exhibits a maximum value around y/D = 0.8 among all cases. 3.6. Skewness factor of particle fluctuation velocity The skewness factor is one of the signal processing tools used to identify whether a signal follows the Gaussian probability distribution. To study the statistical properties of particle fluctuation velocity further, the skewness factor S that is defined as  3=2 S ¼ u′ 3p = u′ 2p

ð5Þ

is used. When a fluctuation component follows the Gaussian probability distribution, the skewness factor has the value of zero. Fig. 18 shows the profiles of S at the locations of x/D = 25 and 44 for different lengths of fin and non-fin. In the upper part of pipeline, S appears no-zero distributions for all cases, indicating that the particle fluctuation velocity of suspension flow deviates from the Gaussian-type fluctuation. However, S gradually closes to zero in lower part of pipeline for all cases; here particle flow exhibits the high concentration flow. Especially S of Fin320 is nearest to the value of zero, suggesting that u′p of the most efficient Fin320

a) x/D = 25

a) x/D = 25

1.0

1.0 0.8 0.8

y/D

0.6 0.4

Fin's type Ua (m/s)

y/D

0.6 0.4

Non-fin 13.45 Fin200 12.6 Fin250 12.1 Fin320 11.8

0.2

Fin's type Ua (m/s)

Non-fin 13.45 Fin200 12.6 Fin250 12.1 Fin320 11.8

0.2

0.0

0

1x10-4

2x10-4

3x10-4

4x10-4

5x10-4

0.0

2

-6

u' p v'p /Ua

-5

-4

b) x/D = 44 1.0

0.8

0.8

0.6

0.6

y/D

y/D

b) x/D = 44

-1

0

1

2

3

4

5

6

0.4

0.2 0.0 -2x10-4 -1x10-4 0

-2

S

1.0

0.4

-3

0.2 1x10-4 2x10-4 3x10-4 4x10-4 5x10-4 2

u' p v'p /Ua

Fig. 17. Intensity of particle fluctuation velocity u′ p v′ p =U 2a at different locations for different lengths of fin and non-fin at their air velocities Ua.

0.0 -3

-2

-1

0

1

2

3

S Fig. 18. Skewness factor of particle fluctuation velocity u′ p at different locations for different lengths of fin and non-fin at their air velocities Ua.

124

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

obeys more to the Gaussian-type fluctuation. It implies that the particle fluctuation velocity of particle sliding strands follows the Gaussian probability distribution and results in the low pressure drop of the pneumatic conveying [13].

a) y/D = 0.24 0.8 Fin's type Ua (m/s)

0.7

Non-fin Fin200 Fin250 Fin320

0.6 0.5

P

3.7. Probability density function of particle fluctuation velocity Figs. 19 and 20 show the probability density functions, P, of particle fluctuation velocity u′p =u′p rms at y/D = 0.24, 0.48 and 0.78 of two

13.45 12.6 12.1 11.8

0.4 0.3 0.2 0.1

a) y/D = 0.24

0.0 -4

0.8 0.7

Non-fin Fin200 Fin250 Fin320

0.6 0.5

P

-3

-2

-1

Fin's type Ua (m/s) 13.45 12.6 12.1 11.8

1

2

3

4

2

3

4

2

3

4

b) y/D = 0.48 0.8 0.7

0.4

0.6

0.3

0.5

P

0.2 0.1

0.4 0.3

0.0 -4

-3

-2

-1

0

1

2

3

4

0.2

u'p/u'p-rms

0.1 0.0

b) y/D = 0.48

-4

-3

-2

-1

0

1

u'p/u'p-rms

0.8 0.7

c) y/D = 0.78

0.6

0.8

0.5

0.7

0.4

0.6

0.3

0.5

0.2

0.4

P

P

0

u'p/u'p-rms

0.3

0.1

0.2

0.0 -4

-3

-2

-1

0

1

2

3

4

u'p/u'p-rms

0.1 0.0 -4

c) y/D = 0.78

-3

-2

-1

0

1

u'p/u'p-rms

0.8

Fig. 20. Probability density function of particle fluctuation velocity u′ p at the location of x/D = 44 for different lengths of fin and non-fin at their air velocities Ua.

0.7 0.6

P

0.5

locations of x/D = 25 and 44 for different lengths of fin and non-fin. qffiffiffiffiffiffiffi 2 Here u′p rms ¼ u′ p .

0.4 0.3 0.2 0.1 0.0 -4

-3

-2

-1

0

1

2

3

4

u'p/u'p-rms Fig. 19. Probability density function of particle fluctuation velocity u′ p at the location of x/D = 25 for different lengths of fin and non-fin at their air velocities Ua.

P of y/D = 0.24 and 0.48 (Figs. 19ab and 20ab) exhibits almost symmetrical with respect to u′p =u′p rms ¼ 0 and considerable spread, ranging from −3 to 3. All cases display almost the same distribution, except for Fin320 of y/D = 0.48 at x/D = 25. It implies that u′p of the lower and middle parts of pipe follows the Gaussian distribution, corresponding to the skewness factor (Fig. 18). At y/D = 0.78 (Figs. 19c and 20c), however, P is significantly less asymmetrical with respect to u′p =u′p rms ¼ 0 for all cases, and especially Fins show obvious departure from the Gaussian distribution. This is because the low particle concentration and suspension flow in the upper

F. Yan, A. Rinoshika / Powder Technology 241 (2013) 115–125

part of the pipeline, and these results correspond to the skewness factor (Fig. 18). 4. Conclusions

125

most efficient Fin320 more obeys the Gaussian-type fluctuation resulting in the low pressure drop and low MPD air velocity.

Acknowledgement

The characteristics of particle fluctuation velocity near MPD air velocity of a horizontal self-excited pneumatic conveying are analyzed based on the high-speed PIV measurement. The important results are summarized as follows. (1) The power spectra peaks of fins are larger than that of non-fin even at lower air velocity, suggesting the accelerating efficiency of fins' vibration. Especially the longest fin exhibits the largest spectrum peak. (2) Rup0up of Fin250 and Fin320 are larger than that of non-fin, especially in the lower part of pipe showing a high correlation. However, the little difference of Rvp0vp between fins and non-fin is observed. 2 (3) In the acceleration region, u′ p =U 2a of fins is slightly larger than that 2

of non-fin in the low part of pipe. u′ p =U 2a of the longest fin exhibits the largest value near the bottom of pipe and in the middle part of pipe, and keeps the largest value in the range of y/D > 0.6 in the fully-developed region. 2

(4) In the acceleration region, v′ p =U 2a increasing with y/D exhibits almost the same profiles for all cases in the lower part of pipe. 2

However, v′ p =U 2a of fins becomes larger than that of non-fin in the fully-developed region. Fin320 exhibits the largest value of 2

v′ p =U 2a in the upper part of pipe. (5) The fins' oscillation generates large particle fluctuating energy so that the particles are more easily accelerated and suspended. This is one of the important reasons why the fins' oscillation results in the low pressure drop and low MPD air velocity. (6) u′p v′p =U 2a shows almost the same distributions in the lower part of pipe. The maximum value of u′p v′p =U 2a appears in the middle part of pipe, where u′p v′p =U 2a of long fins is larger than that of non-fin. The fins' oscillation causes large correlation between u′p and v′p resulting in low pressure drop and low MPD air velocity. (7) The distribution of the skewness factor and the probability density function indicate that the particle fluctuation velocities of all cases follow the Gaussian distribution in the lower and middle parts of pipe, and departure from the Gaussian distribution in the upper part of the pipe. The particle fluctuation velocity of the

The second author (AR) wishes to acknowledge support given to him by Grant-in-Aid for Scientific Research (C) (no. 23560186) from the Japanese Society for the Promotion of Science. The present affiliation of the first author is School of Mechanical Engineering, Jiangsu University of Science and Technology, China. References [1] K. Watanabe, Transport of solids by pipelines with spiral tube, ASME FED 234 (1995) 57–64. [2] H. Li, Y. Tomita, An experimental study of swirling flow pneumatic conveying system in a horizontal pipeline, Trans. ASME, Journal of Fluids Engineering 118 (1996) 526–530. [3] H. Li, Y. Tomita, Particle velocity and concentration characteristics in a horizontal dilute swirling flow pneumatic conveying, Powder Technology 107 (2000) 144–152. [4] H. Ueda, M. Sakai, K. Horii, K. Funatsu, Y. Tomita, Study of swirling pneumatic transport of granule in a horizontal pipe (in Japanese), Transactions of the JSME B-67 (2001) 3011–3017. [5] D. Mills, Pneumatic Conveying Design Guide, Butterworth-Heinemann, 2004. [6] A. Rinoshika, M. Suzuki, An experimental study of energy-saving pneumatic conveying system in a horizontal pipeline with dune model, Powder Technology 198 (2010) 49–55. [7] F. Yan, A. Rinoshika, An experimental study on a horizontal energy-saving pneumatic conveying system with soft fins, Powder Technology 217 (2012) 516–522. [8] F. Yan, A. Rinoshika, An experimental study of a horizontal self-excited pneumatic conveying, ASME, Journal of Fluids Engineering 134 (2012) 04302–1 7. [9] F. Yan, A. Rinoshika, Characteristics of particle velocity and concentration in a horizontal self-excited gas–solid two-phase pipe flow of using soft fins, International Journal of Multiphase Flow 41 (2012) 68–76. [10] F. Yan, A. Rinoshika, High-speed PIV measurement of particle velocity near the minimum air velocity in a horizontal self-excited pneumatic conveying of using soft fins, Experimental Thermal and Fluid Science 44 (2013) 534–543. [11] Y. Tsuji, Y. Morikawa, LDV Measurements of an air-solid two-phase flow in a horizontal pipe, Journal of Fluid Mechanics 120 (1982) 385–409. [12] F. Yan, A. Rinoshika, Application of high-speed PIV and image processing to measuring particle velocity and concentration in a horizontal pneumatic conveying with dune model, Powder Technology 208 (2011) 158–165. [13] A. Rinoshika, F. Yan, M. Kikuchi, Experimental study on particle fluctuation velocity of a horizontal pneumatic conveying near the minimum conveying velocity, International Journal of Multiphase Flow 40 (2012) 126–135. [14] A. Rinoshika, Y. Zheng, F. Yan, Wavelet analysis on particle dynamics in a horizontal air-solid two-phase pipe flow at low air velocity, Experiments in Fluids 52 (1) (2012) 137–149. [15] Y. Zheng, F. Yan, A. Rinoshika, Multi-scale analysis on particle fluctuation velocity near the minimum pressure drop in a horizontal pneumatic conveying, Chemical Engineering Science 72 (2012) 94–107.