VELOCITY PROFILE OF ENTRAINED AIR IN FREE FALLING PARTICLE PLUMES

Transcription

1 VELOCITY PROFILE OF ENTRAINED AIR IN FREE FALLING PARTICLE PLUMES ZQ Liu 1,*, XJ Li 1, PQ Lu 1, TH Zou 1, BY Lu 1 1 Faculty of Mechanical Engineering, Tianjin University of Commerce, Tianjin, , China ABSTRACT This aer describes an exerimental investigation of the velocity distribution within entrained air to move by free falling articles (article lume). The toic is of relevance to the design of dust control systems involving free falling bulk solids (eg conveyor belt transfers, filling silos, etc). Exeriments on corvic vinyl have indicated that for the laboratory scale aaratus used to date a Gaussian distribution rovides a good descrition of the velocity rofile within the induced air flow as a function of distance from the centreline of the lume. Plume radius and velocity of entrained air increase with both increasing dro height and increasing bulk solid mass flow rate. The comarison of the velocity rofiles between the article lume, Boussinesq miscible lume and the non-boussinesq miscible lume is highlighted in the discussion. The entrainment caability of the article lume is less than miscible lumes. INDEX TERMS velocity rofile, entrained air velocity, entrained air, article lume, free falling articles INTRODUCTION Bulk material handling oerations involving a falling stream of articles are very common in industry throughout the world. In the rocess of bulk material transfer, fugitive dust may be generated and the surrounding air is entrained into the article stream during free fall conditions in Figure 1. Dust generation are involved in many bulk solids rocesses when the material is under free-fall conditions. Understanding of how air entrainment by articles in free fall can assist in the design of effective dust control systems. Much work has been done in the study of the methods of dust control in industrial rocesses. A well-designed ventilation system may offer a solution to caturing dust emitted from the working rocess, and maintaining the oeration environment at the required health and safety standards. Figure 1. Photos of article stream during free fall conditions (refer DSH Systems LTD) However, at the commencement of this roject, research in the field of air entrainment in a free falling article * Corresonding author liuzq@tjcu.edu.cn 1567

2 stream was limited due to the shortage of theoretical analysis and exerimental data reorted in the literature. Therefore, it is necessary to understand the velocity rofile of entrained air in the study of air entrainment in free falling articles. In the rocess of articles free falling, the ambient air is induced to article stream flow as the bulk solid accelerates and exands. Some articles, articularly smaller articles located on the surface of the article stream, mix with the entrained air to form a dusty boundary layer (or lume) around the falling "core" of bulk material. The radius of this article lume grows with increasing dro height. Previous fundamental research into air entrainment during the rocess of bulk material free falling has been quite limited in the article research field. The exerimental investigation of the velocity distribution within entrained air in free falling article lumes also did not declare in the research field. In the rocess of free fulling articles, the dust concentration in this induced air flow should be moved by the dust control system. The aer resented in here will concern with the characteristics of the velocity rofile of the entrained air in the free falling article lume in the theoretical work of the volume flux of the air entrainment. The lume of entrained air has similarities with other buoyancy-driven air flow such as "thermal lumes". It is useful to comare velocity rofiles for different tyes of lumes, so as to facilitate understanding of the behaviour of article lumes in different situations. The Gaussian distribution can be used to describe the velocity rofiles of the miscible lume and the bubble lume. The velocity rofile in miscible lumes may be resented by Gaussian distribution as: 2 r v ( r) = v0ex 2 (1) b where, v is the local velocity within the stream flow, r is the radius within the stream, v 0 is the maximum velocity of the lume at the centreline, and b is the radius of the lume (i.e. the oint where the local velocity has decayed to 1/e of the centreline velocity). To date there has been no ublished research into the velocity distribution of entrained air that occurs in a falling stream of bulk material. In some ways this is not surrising since it very difficult to measure the velocity of the induced air flow directly for many reasons including: The very high article densities within the core of the stream revent otics-based velocity measurement techniques (eg Laser Doler Anemometry) Particles damage or render inaccurate techniques such as hot wire or hot film. A great deal of work has been reorted on ordinary miscible lume theory over the ast six decades. The first major study on a ure lume was resented by Schmidt in He found that turbulent hot air rising from a small oint source tended to be confined within a conical region. Batchelor (1953) and Morton et al. (1956) carried out the first theoretical studies of Boussinesq miscible lume on a oint source in both uniform and stratified environments. In addition, Rooney and Linden (1996) investigated the characteristics of non-boussinesq miscible lume. Moreover, many ublished aers resented the research of bubble lume, such as Haberman and Morton (1954), Cederwall and Ditmars (1970), Wilkinson (1979), McDougall (1978), Leitch and Baines (1989). These researches are beneficial to the general understanding of the rocesses at hand but not of direct assistance in the modelling and rediction of entrained air flow rates and the velocity rofile of the entrained air. Thus, the urose of the resent aer is to describe recent exerimental research into the motion of bulk materials under free fall. The exeriments have been carried out so at to determine the entrained air velocity rofile in a article stream and to describe the variations in the radius of the article stream as a function of various rocess arameters. EXPERIMENTAL METHOD AND RESULTS The exerimental method used in our testing was based on that the mass flow rate of bulk materials was maintained aroximately constant for each test by means of the double-hoer arrangement, the lower hoer being flooded by the uer. The entire hoer system was susended from a frame so that the mass flow rate of material could be measured directly by means of load cells attached to the susension cables. Induced air was extracted from the underside of the shelf in the bottom of the observation chamber until there was no static ressure difference between the chamber and the ambient air. Pressure equilibrium between the ambient air and the inside of the testing chamber was determined by smoke visualization at the ressure observation ort. To maintain a constant height of stockile during each exeriment, the collection bin was installed to receive the excess articles from the stockile falling through an annular slot. The rig frame could be lifted u to adjust dro heights for various tests. The determination of the diameter of the 1568

3 outlet of the discharging hoer was varied to match the measurement caacity of the test rig. Corvic vinyl owder was selected as the bulk material for testing with median article diameter d 50 = 116 µm, article density = 1487 kg/m 3 ; and loose-oured bulk density = 512 kg/m 3, resectively. As mentioned above it is difficult to measure directly the velocity of the air as a function of radius and dro height in testing. Instead the velocity distribution in the induced air was inferred by measuring the volumetric flow rate through a series of circular aertures of different radius laced in the shelf. The inherent assumtion behind this methodology is that the resence of the shelf around the aerture does not significantly influence the quantity of air and bulk solid flowing in the lume within a radius equal to the aerture in the shelf, though clearly any air flowing in the lume beyond this radius must be deflected by the shelf and revented from entering the region under the shelf. The exerimental data of the entrained air velocity rofile in free falling articles may be obtained by using the method of the falling article lume assed through an aerture in Figure 2. The aerture size can be changed to gain the mean air velocity within each annulus of the aertures. The obtained testing data were used to fit a Gaussian distribution using least squares method to minimize the sum of the squares of the deviations, Montgomery (1994). Figure 2. Schematic of the aerture in the shelf used to infer the volumetric flow rate of induced air as a function of radius from the stream centreline. v a, (m/s) Gaussian best z=720 mm Gaussian best z=400 mm Gaussian best z=300 mm Ext. z=720 mm Ext. z=400 mm Ext. z=300 mm r a, (mm). Figure 3. Velocity of entrained air against radius of stream at different dro heights for same nominal material mass flow m& = 287 kg/s, corvic vinyl An examle of tyical variations in the velocity of the entrained air against the radius of the article lume at different dro heights under the same nominal mass flow rate is resented in Figure 3, where z is the dro height. 1569

4 The velocity rofile is seen to be modelled reasonably well by a Gaussian distribution. However, in the exerimental testing, we found that changes in environmental conditions and samles of bulk material caused slight differences in mass flow rate between exeriments. The exerimental data for each dro height were then fitted to a Gaussian rofile using least squares method. Velocities clearly increase with dro height as one might intuitively exect. The fact that the velocity rofiles of the entrained air are described adequately by the Gaussian model suggests that the flow is self-similar at the dro heights investigated. Figure 4 illustrates the influence of mass flow rate on the velocity rofiles at a given dro height. Increasing the mass flow rate results in an increase in both the velocity at a given location (and hence overall volumetric flow rate) and also results in an increase in the radius, b, of the Gaussian rofile. Gaussian best m =287 kg/s Gaussian best m =144 kg/s Ext. m =287 kg/s Ext. m =144 kg/s v a, (m/s) r a, (mm) Figure 4. Velocity rofile of entrained air as a function of bulk solid mass flow rate z = 720 mm, corvic vinyl DISCUSSION m& for articles dro height Velocity of entrained flow, v (m/s) Gaussian best fit to ext. data Exerimental data of artilce lume Boussinesq miscible lume Non-Boussinesq miscible lume Plume radius, r (mm) Figure 5. Comarison of velocity rofiles on same nominal buoyancy flux B = m 4 /s 3 of entrained air in article lume, z = 720 mm, m& = 287 kg/s, d = 116 µm, ρ b = 512 kg/m3, ρ = 1487 kg/m 3, (corvic vinyl) 1570

5 The determination of the entrained air velocity rofile can assist in understanding the characteristics of air entrainment in free falling bulk solids. The exerimental data indicated that the Gaussian distribution could be used to describe the entrained air velocity rofile in the rocess of free falling articles. To comrehend the characteristics of lume velocity rofile, it is necessary to comare the velocity rofiles of the article lume (resented in above), the Boussinesq miscible lume and the non-boussinesq miscible lume (refer above introduction) for the same nominal buoyancy flux in Figure 5. The results are interesting in that the article lume velocity rofile is significantly different from the revious miscible lumes. The entrained air velocity of the article lume near the centreline is considerably faster than both the Boussinesq lume and the non-boussinesq lume in Figure 5. The radiuses of the miscible lumes are significantly larger than the article lume. These comarisons indicate that the entrained caability of the article lume is less than those ordinary miscible lumes. CONCLUSION To the knowledge of the authors this is the first data to have been shown on the velocity distribution in a article lume generated by a stream of free-falling bulk material. This aer has resented results of an exerimental study of the velocity distribution of entrained air in the rocess of articles free falling. The major findings of this work are as follows. The velocity within the lume at a given elevation and as a function of distance from the lume centreline aroximates a Gaussian rofile. Volumetric flow rate, lume radius and velocity of entrained air increase with both increasing dro height and increasing bulk solid mass flow rate. The entrained caability of the article lume in surrounding air is less than both the Boussinesq lume and the non-boussinesq lume. These findings are useful to exlore the characteristics of air entrainment in the rocess of free falling articles in the research field of air entrainment in falling article lumes, thereby to understand of how air entrainment by articles in free fall can assist in the design of effective dust control systems. They also rovided imortant information to aid the study in the fundamental of entrained flow in article lumes. REFERENCES Batchelor GK The Theory of Homogenous Turbulence. Cambridge University Press, London. Cederwall K. and Ditmars JD Analysis of Air-Bubble Plumes, W. M. Keck Laboratory of Hydraulics and Water Resources Reort No. KH R 24, California Institute of Technology, Pasadena, California. Haberman WL. and Morton RK An Exerimental Study of Bubbles Moving in Liquids, Proc. American Soc., Civil Engineers, Vol 80, New York, Leitch AM. and Baines WD Liquid Volume Flux in a Weak Bubble Plume, Journal of Fluid Mechanics, Vol 205, McDougall TJ Bubble Plumes in Stratified Environments, Journal of Fluid Mechanics, Vol. 85, Part 4, Montgomery DC. and Runger GC Alied Statistics and Probability for Engineers. John Wiley and Sons, New York. Morton B., Taylor GI. and Turner JS Turbulent gravitational convection from maintained and instantaneous sources, Proc. Royal Soc. London, Series A, Vol 234A, Rooney GG. and Linden PF Similarity Considerations for Non-Boussinesq Plumes in an Unstratified Environment, Journal of Fluid Mechanics, Vol 318, Wilkinson DL Two-Dimensional Bubble Plumes, Journal of the Hydraulics Division, ASCE, Vol. 105, No. HY2,