Prediction of slip velocity in the pneumatic conveyance of solids in the

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME
191
PREDICTION OF SLIP VELOCITY IN THE PNEUMATIC
CONVEYANCE OF SOLIDS IN THE HORIZONTAL CONDUIT
Satya Narayan*
and Om Prakash*
*Deptt. of Chemical Engg., B.I.T. Sindri, Dhanbad
ABSTRACT
In designing the pneumatic conveying system, estimation of pressure variation along
the length of the conduit is essential which is again greatly influenced by the slip velocity (us)
in the line, which in a multiphase flow system is defined as the variation in the solid particle
velocity (up) from the fluid velocity (uf). A correlation for us/uf has been developed. The
coefficient of correlation for which has been found to be 0.9041 and the standard error of
estimate (Syx) is 0.0487. The correlated and experimental values are in good agreement.
INTRODUCTION
Pneumatic conveyance system is used for transporting granular materials in pipe lines.
It has been used for transporting catalysts in continuous flow process(1)
. It is considered as
one of the most efficient methods for transporting materials like grains, coal, sand, cement,
ash, dust, minerals, fertilizers, catalysts, etc. The pneumatic conveyance is a complex
phenomenon and its flow behavior depends on the dimensions and the nature of the conduit,
characteristics of the materials to be conveyed, such as, size, shape, density, concentration,
surface roughness and properties of the fluid like density, viscosity, pressure, temperature and
their interactions. For designing a pneumatic conveyor, a prior estimation of pressure
differential and velocities of the fluid required to keep the suspension flowing is necessary. It
is well known that the solid particles are introduced at almost zero axial velocities in the
passage of the horizontally flowing fluid. The particles are accelerated before a steady
velocity is reached. Thus the entire conveying length is divided into two zones namely
accelerating zone and established flow zone. The flow pattern of particles in the two zones
are different and so the conventional methods of correlating the pressure drop in the two
zones together, are not with the actual phenomenon. Therefore, it is necessary to predict the
pressure drops generated in the length of the pipe in which acceleration occurs and in the
length in which flow is established.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 2 March – April 2013, pp. 191-196
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192
CORRELATION OF SLIP VELOCITY
Many workers like, Gil, A.(2)
, Sany M. El. – Behry, Mofresh H. Hamed, M.A.
El. – Vadi, K.A. Ibrahim(3)
, Iyer, P.V.R., Mani, B.P. and Rao, D.S(4)
have worked on
slip velocity. While estimating the slip velocity, the particle velocity, up has been
calculated by using different correlations proposed by Hinkle(5)
, Wen(6)
, Hitchcock
and Jones(7)
, Hariu and Molsted(8)
, Rose and Duckworth(9)
, Reddy and Pei(10)
and
Yang(11)
and a comparative study has been made and seen that there are wide
deviations in some cases. Only the equations of Hinkle(5)
and Wen(6)
gave identical
values. In estimating the up values using Wen(6)
and other correlations, an iterative
procedure was followed. In view of this difficulty, the equation proposed by Hinkle(5)
has finally been chosen and calculations made accordingly. Also Hinkle(5)
developed
the equation by observing the particle velocities photographically and empirically
correlating them for conveyance of solids in horizontal ducts. The slip velocities (us)
for different systems and for different air flow rates have been estimated by using the
formula
us = uf - up …………………………………………….(1)
The prediction of slip velocity is a complex phenomenon which depends on
various parameters such as physical properties of solids, fluid and the characteristics
of the duct. A dimensionless relation of the following form has been proposed
us / uf = A[(ρs/ ρf )a
(Gs/Gf)b
(dp
3
ρf
2
g / µf
2
)c
]B
……………. ……… (2)
us / uf = A[Product]B
…………………… (3)
The exponents a, b and c have been determined and found to be equal to 0.5,
0.0006 and 0.1 respectively by computational technique (curve fitting). The
coefficient A and the overall exponent B have been estimated by the least square
method using computational technique and are found to be equal to 6.0 x 10-3
and 1.0
respectively. It is also evident from the exponent of the group Gs/Gf that slip ratio is
almost independent of solid loading ratio for the dilute phase employed and so, the
group Gs/Gf is insignificant. Consequently, the final correlation for the prediction of
slip velocity may be written as
us / uf = 6.0 x 10-3
[(ρs/ ρf )0.5
(dp
3
ρf
2
g / µf
2
)0.1
]1.0
……. …(4)

193
EXPERIMENTAL TECHNIQUE
Fig.1. Experimental Set-up
The experimental set-up (Fig.1) consists of a horizontal conveying duct made of
galvanized iron pipe of 5 cm internal diameter and 14 m long. A flow control valve fitted in
the conveyance before the solids feeding point has been used to measure the air flow rate. A
mixture nozzle has been employed for inducing suction necessary for feeding the solids into
the duct. The other accessories include a blower driven by a 10 H.P. induction motor, the feed
hopper made of 20 gauge galvanized iron sheet, a cyclone separator and a manometer panel
to measure the pressure drop at 40 different points.
To start with the experiment, the blower is put on and the control valve regulated so
as to get the desired flow rate of air. All manometers readings are noted so that pressure drops
for the flow of air alone can be known. The feed control valve is then opened partly to allow
low flow rates of solids. Various feed rates have been used for each run and pressure readings
were recorded. Data are taken for various air flow rates and solid feed rates. The particulars
of systems investigated are given in Table – 1.
1
1.Blower
2
2.By pass valve
3
Air control valve3
4
4.Orifice meter
5
5.Ejector
6
6.Solid control valve
7
7.Hopper
8
8.Test pipe
9
9.Diffuser
10
10.Cyclone separator
11
11.Discharge Control
Valve
12
12.Collector
25 cm
100cm
30cm
1400cm

194
Table 1: Physical properties of materials used
Sl. No Materials Shape Diameter Sp.Gravity Shericity
1. Mustard seed Spherical 2.2240 1.157 1.0
2. Mustard seed Spherical 1.6760 1.157 1.0
3. Sago Spherical 1.6760 1.320 1.0
4. Sago Spherical 0.6970 1.320 1.0
5. Sand Spherical 1.6760 2.680 1.0
6. Sand Spherical 0.4255 2.680 1.0
7. Wheat Ellipsoidal 3.4265 1.412 0.8
RESULT AND DISCUSSION
For slip velocity Equ. 2 has been developed. The group Gs/Gf is insignificant so the final
equation has been obtained in the form of Equ.4. The correlation coefficient r and the
standard error of estimates Syx are found to be 0.9041 and 0.0487 respectively. Fig. 2 shows
the us/uf values plotted with respect to the system variables and found to be in very good
agreement. Also the slip ratio with respect to solid density and solid dia. almost increases as
shown in Table No. 2 and Table No.3.
Thus it follows from Tables (2 and 3) that physical property of solids play a very important
role in predicting the slip ratio.
Table No. 2: Variation of Slip ratio with solid density
Particle Particle density us /uf
Kg / m3
Mustard seed 1.157x103
0.313
Sago 1.32x103
0.378
Sand 2.68x103
0.366
Wheat 1.412x103
0.428

195
Table No.3: Variation of Slip ratio with solid dia
Particle Particle dia. Us /uf
M
Mustard seed 1.676x10-3
0.313
2.224x10-3
0.341
Sago 1.676x10-3
0.334
2.614x10-3
0.378
Sand 6.97x10-4
0.366
Wheat 2.426x10-3
0.428
[(Gs/Gf) 0.0006
(ρs/ ρf) 0.50
(dp
3
ρf2 g / µf
2
)0.1
]
Fig. 2 Correlation for the prediction of slip velocity
0.1
1
10 100
us/uf

196
NOMENCLATURES
A, correlation constant
B, overall exponent
a empirical constant
b empirical constant
c empirical constant
dp diameter of the solid particle , m
Gf mass velocity of fluid (air), kg/m2
s
Gs mass velocity of solids, kg/m2
s
g acceleration due to gravity, m/s2
Gs/Gf Solids loading ratio, dimensionless
r correlation coefficient
Syx standard error of estimate
uf Velocity of fluid, m/s
up Velocity of solid particles, m/s
us Slip velocity, (uf – up), m/s
us/uf Slip ratio, dimensionless
GREEK NOMENCLATURE
ρf fluid density, kg/m3
ρs solid particle density, kg/m3
µf viscosity of fluid, kg/m s
REFERENCES
1. Matsumoto, S., Hara, M., Saito, S., and Maeda, S., Minimum Transport Velocity For
Horizontal Pneumatic Conveying, Jr. of Chem. Engg. of Japan, 7,6,(1974),425.
2. Gil, A., et. al.,“Gas-particle flow inside cyclone diplegs with pneumatic extraction”,
Powder Technology 128 (2002) 78-91.
3. Sany M. El. – Behry, Mofresh H. Hamed, M.A. El. – Vadi, K.A. Ibrahim; C F D
prediction of air – solid flow in 180o
curved duct, Powder Technology, 2008.
4. Iyer, P.V.R., Mani, B.P. and Rao, D.S., Ind. Inst. Chem. Engrs.(1980),77.
5. Hinkle, B.L., Ph.D. Thesis, Georgia Institute of Technology (1953).
6. Wen, C.Y. and Galli, A.F., ‘Dilute Phase System’ “Fluidzation” Davidson and
Harrison, Acd. Press, N.Y. (1971).
7. Hitchcock, J.A. and Jones, C., Brit. Jn. of Appl. Physics, 9,218-212 (1958).
8. Hariu, O. H. and Molsted, M. C., Ind. Eng. Chem., 41, 1148 (1949).
9. Rose, H.E. and Duckworth, R.A., The Eng. 227(5903)(1969), 392: 227(5904)(1969),
430: 227(5905)(1969),478.
10. Reddy, K.V.S. and Pei, D.C.T., Ind. Engg. Chem. (Fundamental), 8,490 (1969).
11. Yang, W.C., A.I.Ch.E., J., 20 (3), 605 (1974)

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