Self-excited pneumatic conveying of granular particles in various horizontal curved 90° bends

Experimental Thermal and Fluid Science 63 (2015) 9–19

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Self-excited pneumatic conveying of granular particles in various horizontal curved 90° bends 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 9 April 2014 Received in revised form 8 January 2015 Accepted 8 January 2015 Available online 14 January 2015 Keywords: High-speed PIV Soft fin Particle velocity Particle fluctuating energy Pneumatic conveying Pressure drop

a b s t r a c t The effect of using the soft fins on a horizontal pneumatic conveying of granular particles in various curved 90° bends was studied in this paper, in order to reduce pressure drop and conveying air velocity. Experimental measurements were performed in terms of the pressure drop, conveying air velocity, power consumption and additional pressure drop. The distributions of particle velocity near and in the curved 90° bend were measured by high-speed PIV. The test pipeline consisted of a 4.5 m-long horizontal straight acrylic tube, a curved 90° acrylic bend and a 1.5 m-long horizontal straight acrylic tube, having an inside diameter of 80 mm. The polyethylene particles with diameter of 2.3 mm were used as conveying materials. The superficial air velocity was varied from 10 to 14 m/s, and the solid mass flow rate was fixed at 0.45 kg/s. Comparing with the dilute phase pneumatic conveying, the pressure drop, the minimum pressure drop (MPD) velocity, power consumption and additional pressure drop can be reduced by using soft fins for various bends in lower air velocity range. The reduction becomes more evident with increasing the radius ratio of bend. The maximum reduction rates of the MPD velocity and power consumption by using soft fins is about 8.2% and 11.7%, respectively. At the upstream of bend, the particle velocity of the soft fins is evidently higher than that of the dilute phase in the bottom part of pipe for all bends. The effect of soft fins on the particle velocity and its fluctuating energy still remains in the bend and the downstream of bend, and the fluctuating energy of particle velocity gradually decreases through the bend. At the downstream of bend, the fluctuating energy of particle velocity decreases with increasing the radius ratio of bend. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction The bends are one of the major critical devices in a pneumatic conveying pipeline, and the most contributes to the pressure drop or power consumption come from the bends. Furthermore they cause blockage, a great damage to the particles and bend erosion. When a gas–solid suspension flows through a bend, particles are first decelerated due to particle–wall and particle–particle impacts and friction with pipe, which results in large pressure loss, a great damage to the particles and bend erosion. Then the particles are reaccelerated by air velocity in the downstream of bend. Therefore in order to reduce particle degradation and bend erosion it is important to reduce the conveying air velocity as low as possible. However, the conveyed particles are easily deposited at the bottom of the pipe or the bends due to the force of gravity, which may result in large pressure loss, high fluctuation of pressure, and blockage of the transport line. Therefore the conveying of the ⇑ Tel./fax: +81 238 26 3225. E-mail address: [email protected] http://dx.doi.org/10.1016/j.expthermflusci.2015.01.003 0894-1777/Ó 2015 Elsevier Inc. All rights reserved.

safety operation and saving energy should be controlled at a low air velocity without the appearance of material sediments. Some investigations and experimental measurements on the pneumatic conveying bends [1,3,4,5,17,18] were carried out. However, few particle dynamics has been previously investigated in the bends near the minimum conveying velocity, thus motivating the present work. One the another hand, some energy-saving pneumatic conveying techniques, such as spiral tube [19] and swirling flow [6,7,8], were applied to the straight and bend conveying pipeline and result in the reduction of conveying velocity and pressure drop as compared to the equivalent experimental rigs employing dilute phase axial flow pneumatic conveying. Recently author proposed two methods of using dune model [10] and soft fins [16,13] to accelerate and suspend particles near the particle feeder in a horizontal straight pipeline. These techniques have successfully reduced the conveying velocity and power consumption in the straight pipeline. However, the important questions to be asked are whether the soft fins are also efficiency in the case of conveying pipeline involving the curved 90°

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bend and how the soft fins affect particle motions in the bend. These are important for designing the saving-energy pneumatic conveying and also motivate the present investigation. In order to reveal the mechanism of the steady transport in a horizontal straight pipeline at the low conveying velocity due to the oscillation of soft fins, Yan and Rinoshika [12,14,15] applied the high-speed PIV to measure the profiles of time-averaged particle velocity and concentration. It was revealed that particle fluctuation velocity intensity of using soft fins were higher than that of the dilute phase pneumatic conveying even at lower air conveying velocity, so that the particles are more easily accelerated and suspended. This study is to verify whether the soft fins are also efficient in the case of conveying pipeline involving the various curved 90° bends and to reveal the particle dynamics near or in the bend. The experimental study focuses on the effect of using the soft fins on a horizontal pneumatic conveying involving the various curved 90° bends in terms of the pressure drop, conveying velocity and additional pressure drop. The distributions of fluctuating particle velocity near and in the curved 90° bend are measured by highspeed PIV.

Fig. 2. Bends with different radius.

2. Experimental apparatus and procedure 2.1. Experimental setup 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 a conveying smooth acrylic pipeline with an inside diameter of D = 80 mm ± 6.3% and the particles are separated by the separator at the pipeline exit. The conveying pipeline consists of a 4.5 m-long horizontal straight tube, a curved 90° bend and a 1.5 m-long horizontal straight tube. The straight sections of the pipe were matched very accurately to the curved section. Three bends of mean curvature radius R = 150, 250 and 350 mm, corresponding to the radius ratios of Rr = R/D = 1.9, 3.2 and 4.4, respectively, were used as the curved section and were shown in Fig. 2. The airflow rate and the solids mass flow rate were respectively measured by the orifice meter and load cell. The pressures loss of the conveying pipeline was measured by a differential pressure sensor between two pressure gauge positions in Fig. 1.

Fig. 3. Test solid particles.

The polyethylene non-spherical particles with a volume equivalent diameter of dp = 2.3 ± 4.1% mm, aspect ratio of 2.06 and solid density of 978 kg/m3, as shown in Fig. 3, were used as conveying materials. Here the terminal velocity of the particle is 7.5 m/s. The superficial air velocity Ua was varied from 10 to 14 m/s, the mass flow rate of solids Gs was fixed at 0.45 kg/s.

Fig. 1. Experimental setup.

A. Rinoshika / Experimental Thermal and Fluid Science 63 (2015) 9–19

11

Fig. 4. Soft fins and their location in a conveying pipe.

The statistical uncertainty of the superficial mean air velocity, the pressure loss and the solids mass flow rate are respectively ±4.3%, ±1.2% and ±2.4% at the 95% confidence level. The flapping fins, mounted in horizontal plane of the inlet through the pipe axis, have been used to increase turbulence levels or flow oscillation, resulting in accelerating solid particles in the horizontal straight pneumatic conveying. Tour pieces of the soft fins made of polyethylene, as shown in Fig. 4, were used. The upstream side of the fins was secured at the location 0.25 m from the particle inlet, as shown in Fig. 1, and the downstream side is allowed to freely motion. Each piece of soft fin has a lengths of 300 mm, width of 20 mm, thickness of 0.2 mm and density of 789 kg/m3, corresponding to piece mass of 0.95 g. Since the location of the upstream side of the fins is secured, the soft fins can directly touch particle streams that are fed from the feed tank at the inlet of the conveying pipeline. This case was efficient to save potential energy in pneumatic conveying systems by low pressure loss and low conveying velocity to convey particles in the horizontal straight pipeline [16,13]. 2.2. PIV measurement of particle velocity The PIV measurements, as shown in Fig. 1, were carried out at three different locations: the 0.15 m upstream of bend (4.3 m from

particle inlet), bend and the 0.6 m downstream of bend. A laser light-sheet of thickness b = 2 mm is used to illuminate the objective particulate flow. A high-speed camera (Photron FASTCAMSA3) with a resolution of 1024  1024 pixels is adopted to capture the successive digital particle images at a frame rate of 1000 fps (frame per second) and the shutter speed of each frame is set at 0.1 ms. The distributions of particle velocity, as shown in Fig. 5, are respectively measured in a vertical center plane (x–y plane) through the pipe axis for the upstream and downstream of bend (Fig. 5a) and in a horizontal center plane (x–z plane) through the pipe axis for the bend (Fig. 5b). The particle velocity of the inside bend is measured in a horizontal plane ((x, z)-plane) through the pipe axis, as shown in Figs. 1 and 5(b). The polar coordinate system (r, h), as indicated in Fig. 5(c), is adopted to describe the particle motion in the bend. Here the radii of the inner and outer walls are ri = R  D/2 and ro = R + D/2, respectively. Fig. 6 shows PIV images of three locations. Spatial cross-correlation PIV is used to measure the particle group velocities in the relatively dense-phase gas–solid two-phase flows. In this method the particle image is first divided by many large interrogation areas since the size of conveyed particle is relatively large. Each interrogation area should contain several particles as a particle group to obtain reliable measurements. The high-speed PIV images were analyzed by PIV View software. The

(a) Upstream and downstream of bend

(b) Bend

x θ

(c) Measurement coordinate system in the bend Fig. 5. Schematic of the high-speed PIV measurement.

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A. Rinoshika / Experimental Thermal and Fluid Science 63 (2015) 9–19

(a) Upstream of bend

(b) Downstream of bend

(c) Bend Fig. 6. High-speed PIV images.

3. Results and discussion 3.1. Pressure drop and power consumption The pressure drop Dp of gas–solid phase and Dpa of a singlephase flow (air only) in this experiment, as shown in Fig. 1, are measured by a differential pressure sensor between the inlet of air flow and exit of the conveying pipe, in which the pressure loss produced by the equipment of soft fins as included. Fig. 7 shows the pressure drop Dpa of a single-phase flow (air only) versus air velocity Ua by using fins and non-fins in the cases of three bends. Here the pressure drop generated by the equipment of soft fins is also included in Dpa. It is observed that the pressure drops of all cases increase as increasing air velocity. However, the pressure drops of using soft fins are higher than those of non-fin because the fins’ vibration and the oscillation of air flow causing by soft fins result in the higher pressure drop. No evident difference of Dpa among three bends can be observed in the case of either fins or non-fin, implying the change of radius ratios R/D (=1.9–4.4) has no evident effect on the pressure drop of bend in a single-phase flow (air only). Fig. 8 presents the pressure drop Dp versus the air velocity Ua for the dilute phase and using soft fins at Gs = 0.45 kg/s when using different bend. As the air velocity decreases, the pressure drops of the dilute phase and soft fins first decrease and then increase after the minimum pressure drop (MPD). Comparing with the dilute

0.6

Pressure drop Δpa (kPa)

velocity of each interrogation area or particle group is defined as local instantaneous particle velocity. The detail measurement method of high-speed PIV was described in the previous study [11]. The statistical uncertainty of the time-averaged particle velocity is ±4.5% at the 95% confidence level. The variation of the time-averaged particle velocity along the straight pipeline was measured by the previous study [11] and indicated that the location of 3.5 m (x/D = 44) belongs to the fully developed regime. Therefore, the curved 90° bend of this study is set up in the fully developed regime (4.5 m from particle inlet) without loss of generality.

0.5

Non-fin Fin300 R/D=1.9 R/D=3.2 R/D=4.4

0.4

0.3

0.2

0.1 12

13

14

15

16

Superficial air velocity U a (m/s) Fig. 7. Pressure drop of a single-phase flow (air only) versus air velocity for different radius ratios of bend.

phase pneumatic conveying, as shown in Fig. 8, the pressure drops of the soft fins are higher than that of dilute phase in the range of high air velocity. However, the pressure drops with the soft fins become lower than that of dilute phase in the range of low air velocity, and this difference becomes more evident as increasing R/D. When the pneumatic conveying operates in very low air velocity, the particle sediments easily appear in the neighborhood of the particles inlet, which cause a high pressure loss. Because the flapping fins directly touch particles that are fed from the feed tank at the inlet of the pipeline and make the particles to generate the dispersion and easily suspend, the deposition of particles at the bottom of the pipe can be avoided by using the soft fins even at low air velocity and the lower pressure loss is realized. The air velocity of the minimum pressure drop, as indicated in Fig. 8, is referred as the MPD velocity in this study. The MPD velocity is the lowest air velocity that can be used to transport particles without the particles settling at the bottom of the pipe, which belongs to the dense-phase regime. It is one of important factor

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13.5

Non-fin Fin300 R/D=1.9

MPD conveying velocity (m/s)

Pressure drop Δp (kPa)

2.2

2.0

1.8

Non-fin Fin300 13.0

12.5

12.0

11.5

12.2 m/s 12.8 m/s 1.6

11.0 1

2

2.2

3

4

5

Radius ratio of bend Fig. 9. Variation of MPD conveying velocity with radius ratio of bend.

Fin300 R/D=3.2 2.0

Minimum power consumption coefficient

Pressure drop Δp (kPa)

Non-fin

1.8

11.55m/s

12.44m/s

1.6 2.2

Pressure drop Δp (kPa)

Non-fin Fin300 R/D=4.4

Non-fin Fin300 4.2

4.0

3.8

3.6

3.4 1

2.0

2

3

4

5

Radius ratio of bend Fig. 10. Variation of minimum power consumption coefficient with radius ratio of bend.

1.8

11.25 m/s

12.25 m/s

1.6 10

11

12

13

14

Superficial air velocity Ua (m/s) Fig. 8. Pressure drop versus air velocity for different radius ratios at Gs = 0.45 kg/s.

in the design of a pneumatic conveying system. The variation of MPD velocities of the non-fin and using the soft fins with R/D is shown in Fig. 9. As increasing R/D, the MPD velocity decreases. Compared with the dilute phase pneumatic conveying, the MPD velocity of using fins is evidently decreased, and the maximum reduction rate of the MPD velocity by using soft fins is 8.2%. It indicates that using the soft fins largely reduce the MPD velocity in the bend. To evaluate the power consumption of pneumatic conveying systems, the power consumption coefficient E, which is calculated from the pressure drop Dp, solids flow rate Gs and the air flow rate Qa, is used according to the following equation [6]:

E¼

4.4

DpQ a gGs L

ð1Þ

where g is the gravity acceleration and L is the total length of conveying pipeline. Fig. 10 illustrates the minimum power consumption coefficient Emin versus R/D with the dilute phase and fins. Emin decreases with increasing R/D for both of fins and non-fins. Although E of using the soft fins is larger than that of the dilute phase in the range of high air velocity, E of using the soft fins becomes smaller than that of the dilute phase below the air velocity of the dilute phase Emin (not shown here). Comparing with the dilute phase pneumatic conveying, as shown in Fig. 10, Emin of using fins is largely decreased for various radius ratios of bend, and the maximum reduction rate of Emin by using the soft fins is about 11.7% at R/D = 4.4. The above results clarify that the soft fins are more efficient for reducing the pressure drop, power consumption and the conveying velocity in the pneumatic conveying with a horizontal bend. The efficiency of the soft fins becomes quite evident for large radius ratio of bend in the dense phase region. For long conveying distance, i.e. relatively high pressure drop, the air velocity increases downstream because of air expansion and the air kinetic energy increases along conveying pipe. Therefore, if the deposition of particles on the bottom of the pipeline is solved avoided in the acceleration region by using the soft fins, the particles are conveying without deposits at downstream as

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the air velocity is lower, and may result in lower pressure drop than that of non-fin.

0.050

3.2. Additional pressure drop

λz

0.045

The measured pressure drop Dp (Fig. 8) conveying solid particles in this study may be decomposed into the following two components:

Dp ¼ Dpa þ Dpz

0.035

0.030 0.050

Dpz qa U 2a

Non-fin Fin300 R/D=3.2

ð3Þ

2

0.045

0.040

0.035

0.030 0.050

Non-fin Fin300 R/D=4.4

0.045

λz

where Ga is the air flow rate and kz is the air density that is calculated based on the temperature measured at the orifice meter. Fig. 11 plots a comparison of the additional pffiffiffiffiffiffi pressure drop coefficient kz versus Froude number Fr (¼ U a = gD) between the dilute phase and soft fins for three radius ratios of bend. It can be clearly seen that kz decreases with increasing Fr. kz of using soft fins is lower than that of the dilute phase. The difference of kz between the soft fins and dilute phase increases as decreasing Froude number Fr or the radius ratio of bend. kz of soft fins exhibits large reduction especially in range of lower Fr since the particle sediments appear and result in a high additional pressure loss. For higher Fr numbers, the additional pressure drop is mainly caused by the particle motions that exhibit almost same suspension flow pattern for using either fins or non-fin, therefore kz of using fins closes to that of the dilute phase. Although the additional pressure drop coefficient of the bend is not measured in this study, the bend makes the most contribution to the additional pressure drop, accounting for about 75%, comparing with the results of the straight pipe [9].

λz

Gs L Ga D

0.040

ð2Þ

where Dpa, indicated in Fig. 7, is the pressure drop of air alone including the pressure loss due to the equipment of the soft fins. Dpz is the additional pressure drop due to the presence of particle motions, which is calculated based on the data from Figs. 7 and 8. The additional pressure drop coefficient kz [2] is defined as:

kz ¼

Non-fin Fin300 R/D=1.9

0.040

3.3. Characterstics of particle velocity at the upstream and downstream of the bend 0.035

3.3.1. Profiles of time-averaged particle velocity To compare the distribution of time-averaged axial particle velocity up among the dilute phase and soft fins, the profiles of up in a vertical plane ((x, y)-plane) through the pipe axis at the upstream of bend (4.3 m from the particle feed) and 0.6 m downstream of bend, as shown in Figs. 1 and 5(a), were measured by the high-speed PIV at the MPD velocities (Ua = 12.8 m/s for R/ D = 1.9, Ua = 12.44 m/s for R/D = 3.2 and Ua = 12.25 m/s for R/ D = 4.4) of dilute phase pneumatic conveying at Gs = 0.45 kg/s. The profiles of normalized local axial particle velocity up/Ua versus y/D are plotted in Fig. 12. At the upstream of the bend, as indicated in Fig. 12(a), the maximum and minimum axial particle velocities are respectively observed near the top and bottom of pipe for all bends due to the low particle concentration on the top part of the pipe and the high particle concentration in the bottom part of pipe. This location (x/D = 54) belongs to the fully developed regime [11]. up/Ua of the soft fins is almost same as the dilute phase pneumatic conveying on the top part of the pipe, but it becomes clearly higher than that of the dilute phase in the bottom part of pipe for all bends. It is because that the flapping soft fins directly touch particles and particles are more easily dispersed and accelerated, and this effect exists at the downstream. Since the high particle velocities of the soft fins at the inlet of the bend cause the particle–wall

0.030 12

13

14

15

16

Fr Fig. 11. Comparison of additional pressure drop coefficient between non-fin and soft fins for different radius ratios of bend.

strong impact when flowing through the bend, the pressure drops of the soft fins, as shown in Fig. 8, become higher than that of the dilute phase pneumatic conveying at the MPD velocity of the dilute phase. However, these high particle velocities can maintain the steady pneumatic conveying by using the soft fins in the range of low air velocity, and can realize lower MPD velocity. At the downstream of bend (0.6 m from bend outlet), as indicated in Fig. 12(b), up/Ua of all cases is largely reduced comparing to the upstream of the bend (Fig. 12a), due to the particle–wall and particle–particle impacts and the friction with pipe in the bend. Especially up/Ua of the large R/D (=4.4) exhibits the smallest value because of the low air velocity Ua. Furthermore, the small R/D (=1.9) causes strong particle–wall impacts and results in the large reduction of particle velocity. Therefore, up/Ua of R/D = 3.2 is larger than that of small R/D (=1.9) on the top part of the pipe. The almost

A. Rinoshika / Experimental Thermal and Fluid Science 63 (2015) 9–19

1.0

Non-fin Fin300 R/D=1.9 0.8 R/D=3.2

R/D=4.4

y/D

0.6

0.4

0.2

0.0 0.3

0.4

0.5

0.6

u p /U a

15

2 bend. But v 02 p =U a of the dilute phase and soft fins exhibits almost the same profiles of the fluctuating energy, except for R/D = 1.9 on the top part of the pipe, indicating the weak effect of soft fins 2 on v 02 p =U a at this location. At the downstream of bend (0.6 m from bend outlet), as shown 2 in Fig. 13(b), u02 p =U a exhibits symmetric profiles with respect to the pipe axis and the higher fluctuating energy of axial particle velocity 2 appears near the wall. The lower u02 p =U a is observed at the large 2 radius ratio of bend (R/D = 4.4). Near the centerline u02 p =U a of the small radius ratio of bend (R/D = 1.9) exhibits the largest value 2 among the bends. The large difference of v 02 p =U a can be found on the top part of the pipe. As decreasing the radius ratio of bend, v 02p =U 2a increases rapidly. However, no evident difference of u02p =U 2a 2 and v 02 p =U a can be found between the dilute phase and soft fins, except for R/D = 1.9 near the central part of pipe. As compared to the upstream of bend, the fluctuating energy of particle velocity decreases due to the decrease of particle velocity after the bend.

(a) At upstream of bend (4.3m from particle feed) 3.4. Profiles of time-averaged particle velocity in the bends

1.0

0.8

y/D

0.6

0.4

Non-fin Fin300 0.2

R/D=1.9 R/D=3.2 R/D=4.4

0.0 0.2

0.3

0.4

0.5

u p /U a

(b) At 0.6m downstream of bend Fig. 12. Profiles of time-averaged axial particle velocity for different radius ratios of bend.

same profile of up/Ua is observed at the large R/D (=4.4), however, up/Ua of the soft fins is higher than that of the dilute phase pneumatic conveying at the small R/D (=1.9). At the bend of R/D = 3.2, up/Ua of the soft fins is also higher than that of the dilute phase on the top part of the pipe. It indicates that the effect of soft fins on up/Ua still remains at the downstream of bend in the (x, y)-plane, and it is a reason that the soft fins can generate the low MPD velocity. 3.3.2. Intensity of particle fluctuation velocity In this study the mean-squared particle fluctuation velocities u02 p and v 02 p are used to evaluate the fluctuating energy of particle 02 velocity. The statistical uncertainty of u02 p and v p are respectively ±4.7% and ±0.56% at the 95% confidence level. 2 2 02 Fig. 13(a) shows the normalized profiles of u02 p =U a and v p =U a at the upstream of bend (4.3 m from the particle feed) for the dilute 2 phase and soft fins in the three bends. u02 p =U a appears the maximum value near the top of the pipe, which is agreeable with Rinoshika’s et al. report (2012), suggesting a large fluctuating energy of particle velocity in the suspension flows. No evident dif2 ference of u02 p =U a can be found between the dilute phase and soft 2 fins or among the bends. v 02 p =U a increases with y/D and reaches peaks around y/D  0.8, and then decreases near the top of the 2 pipe. v 02 p =U a of R/D = 1.9 is smaller than that other bends in the range of y/D > 0.7, implying that the small radius ratio of bend suppresses the vertical particle fluctuating velocity before the

The time-averaged particle velocity of the inside bend in a horizontal plane ((x, z)-plane) through the pipe axis, as shown in Figs. 1 and 5(b), is measured by the high-speed PIV at the MPD velocity of dilute phase pneumatic conveying. The polar coordinate system (r, h) (Fig. 5c) is used in the bend. Figs. 14–16 show the comparison of the time-averaged particle velocity vectors in the bend between the dilute phase and soft fins for different radius ratio of bend. Particles are gradually concentrated along the outer wall of the bend due to the centrifugal forces and are decelerated due to the particle–wall and particle–particle impacts and the friction along the pipe wall. At downstream of 30°, the particles gradually move towards the outer wall from the inner wall, and this flow pattern becomes more evident as increasing the radius ratio of bend. At the bend exit the most particles move along the outer wall, especially in the case of large radius ratio of bend (R/D = 4.4). Comparing the dilute phase with soft fins, the almost similar distribution of particle velocity vectors is observed, implying less effect of soft fins on particle motion in the bend of the (x, z)-plane. To reveal the variation of particle velocity along the axial and radial directions, the profiles of the time-averaged particle velocity 1=2

magnitude ðu2p þ w2p Þ at the downstream of h = 45° in the bend is extracted from Figs. 14–16. Fig. 17 shows the profiles of  1=2 normalized by the air velocity Ua against a dimenu2p þ w2p sionless inner wall distance r⁄ = (r  ri)/D for the dilute phase and soft fins in the different bends. It is observed that the peaks of particle velocity appear around r⁄ = 0.8 near the outer wall for all bends, but almost no particle motion can be observed in range of r⁄ < 0.3. The almost same profile of particle velocity is observed for the dilute phase and soft fins in the bend of R/D = 4.4, but the particle velocities of the soft fins are slightly higher than that of the dilute phase near the peak in the bends of R/D = 1.9 and 3.2. The particle velocity decreases in the part of the inner wall since the inner wall airflow slows down more abruptly towards the downstream. Comparing to the inlet of the bend (Fig. 12a), the particle velocity decreases and is concentrated on the range of the outer wall of the bend. The decrease of particle velocity is more evident in the case of small radius ratio of bend (R/D = 1.9). Fig. 18 plotted the distribution of fluctuating energy of particle   2 02 velocity u02 p þ wp =U a at the location of h = 45° in the bend.   2 02 Although u02 p þ wp =U a of various bends have almost same maximum values, the position of maximum value gradually moves towards the outer wall of the bend with decreasing radius ratio

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1.0

0.8

0.8

0.6

0.6

y/D

y/D

1.0

0.4

0.4

Non-fin Fin300 0.2

Non-fin Fin300 0.2

R/D=1.9 R/D=3.2 R/D=4.4

R/D=1.9 R/D=3.2 R/D=4.4

0.0

0.0 0.0

5.0x10

-3

1.0x10

-2

2

2

1.5x10

-2

2.0x10

-2

0.0

2.0x10-4

4.0x10-4

6.0x10-4 2

8.0x10-4

1.0x10-3

2

u'p/Ua

u'p /Ua

1.0

0.8

0.8

0.6

0.6

y/D

y/D

1.0

0.4

0.4

Non-fin Fin300 0.2

Non-fin Fin300 0.2

R/D=1.9 R/D=3.2 R/D=4.4

R/D=1.9 R/D=3.2 R/D=4.4

0.0

0.0 -4

0.0

2.0x10

-4

-4

4.0x10

6.0x10 2

-4

8.0x10

-3

0.0

1.0x10

-4

1.0x10

-4

-4

2.0x10

3.0x10 2

2

-4

4.0x10

2

v'p/Ua

v'p /Ua

(a) At upstream of bend (4.3m from particle feed)

(b) At 0.6m downstream of bend

Fig. 13. Profiles of mean-squared particle fluctuating velocity for different radius ratios of bend.

0o

0o

5 m/s

5 m/s

45o

45o

90o

90o

(a) Non-fin

(b) Fins

Fig. 14. Distribution of time-averaged particle velocity vectors in the bend of R/D = 1.9 (Ua = 12.8 m/s, Gs = 0.45 kg/s).

-4

5.0x10

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A. Rinoshika / Experimental Thermal and Fluid Science 63 (2015) 9–19

0o

0o

5 m/s

5 m/s

45o

45o

90o

90o

(a) Non-fin

(b) Fins

Fig. 15. Distribution of time-averaged particle velocity vectors in the bend of R/D = 3.2 (Ua = 12.44 m/s, Gs = 0.45 kg/s).

0o

0o

5 m/s

5 m/s

45o

45o

90o

90o

(a) Non-fin

(b) Fins

Fig. 16. Distribution of time-averaged particle velocity vectors in the bend of R/D = 4.4 (Ua = 12.25 m/s, Gs = 0.45 kg/s).

of bend. It is because the collisions between particles and between particle and bend outer wall increases as decreasing radius ratio of   2 02 bend. No evident difference of u02 p þ wp =U a is observed between the dilute phase and soft fins in the bends of R/D = 1.9 and 3.2 since the particle collision and particle–wall impact dominate fluctuating energy of particle velocity in the small radius ratio of bend.   2 02 However, u02 p þ wp =U a of the soft fins is higher than that of the dilute phase in the bend of R/D = 4.4, indicating that the effect of the soft fins on the particle fluctuating velocity still remains in the large radius ratio of bend. The distribution range of   2 02 u02 p þ wp =U a decreases in the radius direction of bend as increasing with the radius ratio of bend. It implies that particle collision and particle–wall increase the fluctuation of particle velocity and result in extending the range of particle motion when flowing through the small radius ratio of the bend.

4. Conclusion Comparing the dilute phase pneumatic conveying with the usage of soft fins in various horizontal bends, the following conclusions can be drawn. (1) Due to the oscillation of air flow caused by soft fins, the reductions of pressure drop and additional pressure drop can be realized for various bends in the range of low air velocity. Furthermore, this efficiency of the soft fins becomes more evident with increasing the radius ratio of bend. (2) The maximum reduction rates of the MPD velocity and power consumption by using soft fins is about 8.2% and 11.7%, respectively. The reduction of MPD velocity and power consumption also increases with increasing the radius ratio of bend.

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A. Rinoshika / Experimental Thermal and Fluid Science 63 (2015) 9–19

1.0

0.8

0.8

0.6

0.6

r*

r*

1.0

0.4

0.4

Non-fin Fin300 o R/D=1.9, θ=45

0.2

Non-fin Fin300 o R/D=1.9, θ=45

0.2

0.0

1.0

1.0

0.8

0.8

0.6

0.6

r*

r*

0.0

0.4

0.4

Non-fin Fin300 o R/D=3.2, θ=45

0.2

Non-fin Fin300 o R/D=3.2, θ=45

0.2

0.0

0.0

1.0

1.0

0.8

0.8

0.6

r*

r*

0.6 0.4 0.4

Non-fin Fin300 o R/D=4.4, θ=45

0.2

0.0 0.0

0.1

0.2

0.3 2

0.4

Non-fin Fin300 o R/D=4.4, θ=45

0.2

0.5

2 1/2

(up+wp) /Ua Fig. 17. Profiles of time-averaged particle velocity at the location of h = 45° in the different bends.

(3) At the upstream of bend, the particle velocity of the soft fins is evidently higher than that of the dilute phase in the bottom part of pipe for all bends. The effect of soft fins on the particle velocity also remains at the downstream of the bend. (4) The fluctuating energy of particle velocity decreases through the bend and, however, the fluctuating energy of particle velocity increases with decreasing the radius ratio of bend at the bend exit. (5) At the location of h = 45° in the bend, the particle velocities of the soft fins are slightly higher than that of the dilute phase near the peak in the bends of R/D = 1.9 and 3.2, and the fluctuating energy of particle velocity of the soft fins is higher than that of the dilute phase in the bend of R/D = 4.4, indicating the effect of the soft fins in the large radius ratio of bend.

0.0 0.00

0.01

0.02

0.03 '2

'2

0.04

0.05

2

(up +wp )/Ua Fig. 18. Profiles of particle fluctuating energy at the location of h = 45° in the different bends.

Acknowledgements The author 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, and would like to thank Kenji Satoh for their assistance with experiments. References [1] H. Akilli, E.K. Levy, B. Sahin, Gas–solid flow behavior in a horizontal pipe after a 90° vertical-to-horizontal elbow, Powder Technol. 116 (2001) 43–52. [2] W. Barth, Stromungsvorgange beim transport von festteilchen und flussigkeitsteilchen in gasen, Chem. Ing Technol. 30 (1958) 171–180.

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