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

  • 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), © IAEME191PREDICTION OF SLIP VELOCITY IN THE PNEUMATICCONVEYANCE OF SOLIDS IN THE HORIZONTAL CONDUITSatya Narayan*and Om Prakash**Deptt. of Chemical Engg., B.I.T. Sindri, DhanbadABSTRACTIn designing the pneumatic conveying system, estimation of pressure variation alongthe 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 particlevelocity (up) from the fluid velocity (uf). A correlation for us/uf has been developed. Thecoefficient of correlation for which has been found to be 0.9041 and the standard error ofestimate (Syx) is 0.0487. The correlated and experimental values are in good agreement.INTRODUCTIONPneumatic 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 asone of the most efficient methods for transporting materials like grains, coal, sand, cement,ash, dust, minerals, fertilizers, catalysts, etc. The pneumatic conveyance is a complexphenomenon 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 andtheir interactions. For designing a pneumatic conveyor, a prior estimation of pressuredifferential and velocities of the fluid required to keep the suspension flowing is necessary. Itis well known that the solid particles are introduced at almost zero axial velocities in thepassage of the horizontally flowing fluid. The particles are accelerated before a steadyvelocity is reached. Thus the entire conveying length is divided into two zones namelyaccelerating zone and established flow zone. The flow pattern of particles in the two zonesare different and so the conventional methods of correlating the pressure drop in the twozones together, are not with the actual phenomenon. Therefore, it is necessary to predict thepressure drops generated in the length of the pipe in which acceleration occurs and in thelength in which flow is established.INTERNATIONAL JOURNAL OF ADVANCED RESEARCH INENGINEERING AND TECHNOLOGY (IJARET)ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online)Volume 4, Issue 2 March – April 2013, pp. 191-196© IAEME: www.iaeme.com/ijaret.aspJournal Impact Factor (2013): 5.8376 (Calculated by GISI)www.jifactor.comIJARET© I A E M E
  • 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), © IAEME192CORRELATION OF SLIP VELOCITYMany 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 onslip velocity. While estimating the slip velocity, the particle velocity, up has beencalculated by using different correlations proposed by Hinkle(5), Wen(6), Hitchcockand Jones(7), Hariu and Molsted(8), Rose and Duckworth(9), Reddy and Pei(10)andYang(11)and a comparative study has been made and seen that there are widedeviations in some cases. Only the equations of Hinkle(5)and Wen(6)gave identicalvalues. In estimating the up values using Wen(6)and other correlations, an iterativeprocedure was followed. In view of this difficulty, the equation proposed by Hinkle(5)has finally been chosen and calculations made accordingly. Also Hinkle(5)developedthe equation by observing the particle velocities photographically and empiricallycorrelating 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 theformulaus = uf - up …………………………………………….(1)The prediction of slip velocity is a complex phenomenon which depends onvarious parameters such as physical properties of solids, fluid and the characteristicsof the duct. A dimensionless relation of the following form has been proposedus / uf = A[(ρs/ ρf )a(Gs/Gf)b(dp3ρf2g / 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). Thecoefficient A and the overall exponent B have been estimated by the least squaremethod using computational technique and are found to be equal to 6.0 x 10-3and 1.0respectively. It is also evident from the exponent of the group Gs/Gf that slip ratio isalmost independent of solid loading ratio for the dilute phase employed and so, thegroup Gs/Gf is insignificant. Consequently, the final correlation for the prediction ofslip velocity may be written asus / uf = 6.0 x 10-3[(ρs/ ρf )0.5(dp3ρf2g / µf2)0.1]1.0……. …(4)
  • 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), © IAEME193EXPERIMENTAL TECHNIQUEFig.1. Experimental Set-upThe experimental set-up (Fig.1) consists of a horizontal conveying duct made ofgalvanized iron pipe of 5 cm internal diameter and 14 m long. A flow control valve fitted inthe conveyance before the solids feeding point has been used to measure the air flow rate. Amixture nozzle has been employed for inducing suction necessary for feeding the solids intothe duct. The other accessories include a blower driven by a 10 H.P. induction motor, the feedhopper made of 20 gauge galvanized iron sheet, a cyclone separator and a manometer panelto measure the pressure drop at 40 different points.To start with the experiment, the blower is put on and the control valve regulated soas to get the desired flow rate of air. All manometers readings are noted so that pressure dropsfor the flow of air alone can be known. The feed control valve is then opened partly to allowlow flow rates of solids. Various feed rates have been used for each run and pressure readingswere recorded. Data are taken for various air flow rates and solid feed rates. The particularsof systems investigated are given in Table – 1.11.Blower22.By pass valve3Air control valve344.Orifice meter55.Ejector66.Solid control valve77.Hopper88.Test pipe99.Diffuser1010.Cyclone separator1111.Discharge ControlValve1212.Collector25 cm100cm30cm1400cm
  • 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), © IAEME194Table 1: Physical properties of materials usedSl. No Materials Shape Diameter Sp.Gravity Shericity1. Mustard seed Spherical 2.2240 1.157 1.02. Mustard seed Spherical 1.6760 1.157 1.03. Sago Spherical 1.6760 1.320 1.04. Sago Spherical 0.6970 1.320 1.05. Sand Spherical 1.6760 2.680 1.06. Sand Spherical 0.4255 2.680 1.07. Wheat Ellipsoidal 3.4265 1.412 0.8RESULT AND DISCUSSIONFor slip velocity Equ. 2 has been developed. The group Gs/Gf is insignificant so the finalequation has been obtained in the form of Equ.4. The correlation coefficient r and thestandard error of estimates Syx are found to be 0.9041 and 0.0487 respectively. Fig. 2 showsthe us/uf values plotted with respect to the system variables and found to be in very goodagreement. Also the slip ratio with respect to solid density and solid dia. almost increases asshown in Table No. 2 and Table No.3.Thus it follows from Tables (2 and 3) that physical property of solids play a very importantrole in predicting the slip ratio.Table No. 2: Variation of Slip ratio with solid densityParticle Particle density us /ufKg / m3Mustard seed 1.157x1030.313Sago 1.32x1030.378Sand 2.68x1030.366Wheat 1.412x1030.428
  • 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), © IAEME195Table No.3: Variation of Slip ratio with solid diaParticle Particle dia. Us /ufMMustard seed 1.676x10-30.3132.224x10-30.341Sago 1.676x10-30.3342.614x10-30.378Sand 6.97x10-40.366Wheat 2.426x10-30.428[(Gs/Gf) 0.0006(ρs/ ρf) 0.50(dp3ρf2 g / µf2)0.1]Fig. 2 Correlation for the prediction of slip velocity0.1110 100us/uf
  • 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), © IAEME196NOMENCLATURESA, correlation constantB, overall exponenta empirical constantb empirical constantc empirical constantdp diameter of the solid particle , mGf mass velocity of fluid (air), kg/m2sGs mass velocity of solids, kg/m2sg acceleration due to gravity, m/s2Gs/Gf Solids loading ratio, dimensionlessr correlation coefficientSyx standard error of estimateuf Velocity of fluid, m/sup Velocity of solid particles, m/sus Slip velocity, (uf – up), m/sus/uf Slip ratio, dimensionlessGREEK NOMENCLATUREρf fluid density, kg/m3ρs solid particle density, kg/m3µf viscosity of fluid, kg/m sREFERENCES1. Matsumoto, S., Hara, M., Saito, S., and Maeda, S., Minimum Transport Velocity ForHorizontal 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 Dprediction of air – solid flow in 180ocurved 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 andHarrison, 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)