PREDICTION OF SLIP VELOCITY IN THE PNEUMATIC CONVEYANCE OF SOLIDS IN THE by iaemedu

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									  International Journal of Advanced Research in OF ADVANCED (IJARET), ISSN 0976 –
  INTERNATIONAL JOURNALEngineering and TechnologyRESEARCH IN
  6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME
             ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)                                                 IJARET
Volume 4, Issue 2 March – April 2013, pp. 191-196
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          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.

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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

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 (dp3 ρf 2g / µf2)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 (dp3 ρf 2g / µf2)0.1]1.0   ……. …(4)




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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


EXPERIMENTAL TECHNIQUE


                                    25 cm
                                                        1.Blower                8.Test pipe
                                                        2.By pass valve         9.Diffuser
                                                        3 Air control valve     10.Cyclone separator
                                                        4.Orifice meter            11.Discharge Control
                        7                               5.Ejector                          Valve
                                                                                 12.Collector
                                                100cm   6.Solid control valve
                                                        7.Hopper




                                                30cm




                                            6
                                                                                         9
                                5
                3                                           8


     2                                                                                                         10
                                                                1400cm
                            4




                    1
                                                                                                          11

                                                                                                                    12



                                        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.



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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

                           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




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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


                             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




                   1
       us / u f




                  0.1
                        10                                                                   100



                                [(Gs/Gf) 0.0006 (ρs/ ρf) 0.50(dp3 ρf2 g / µf2)0.1]
                                Fig. 2 Correlation for the prediction of slip velocity




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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


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/m2s
Gs      mass velocity of solids, kg/m2s
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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