THE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE

Transcription

1 Bulletin of the Transilvania University of Braşov Series II: Forestry Wood Industry Agricultural Food Engineering Vol. 5 (54) No. 1-1 THE EFFECT OF SOLID PARTICLE SIZE UPON TIME AND SEDIMENTATION RATE M. MARINUC 1 F. RUS 1 Abstract: In any application, the sizes of the particles to be reoved fro the ixtures heterogeneous deterine, to a large extent, the ethod to be used for their separation. The literature reveals that the cyclone efficiency and iplicitly the sedientation rate is dependent on the particle size fro the ass of heterogeneous solid-fluid ixtures. The objective of this paper is to theoretically deonstrate the influence of the solid particle diensions on the sedientation rate in centrifugal field, inside the cyclone and the tie influence on sedientation in the two sedientary regies. Key words: particles size, sedientation rate, cyclone. 1. Introduction There are any cases during the processing and handling of particulate solids when particles are required to be separated fro suspension in a gas. In any application, the size of the particles to be reoved fro the gas deterines, to a large extent, the ethod to be used for their separation. Generally speaking, particles larger than about 1 µ can be separated easily by gravity settling. For particles less than 1 µ ore energy intensive ethods such as filtration, wet scrubbing and electrostatic precipitation ust be used. The principle of separation in a cyclone is to increase the effect of sedientation by centrifugal force, which is achieved by introducing tangential suspension in a device. The efficiency of separation cyclones is uch higher than dusting roos because in a centrifugal force field, the effect of separation is axiized. In the case of cyclones, the effect of centrifugal force anifests itself differently fro particles and gas. Due to centrifugal force the solid particles are thrown to the wall where they lose energy and fall oving under the action of gravity at the botto of the device where it is discharged (particle ass > gas ass). So, gas is oving in a downward spiral, solid particles being driven to the top of the gas and then gas (air) is discharged through the central tube of the cyclone due to the circulation effect [1]. The ost coon type of cyclone is known as the reverse flow type (Figure 1). Inlet gas is brought tangentially into the cylindrical section and a strong vortex is thus created inside the cyclone body. Particles in the gas are subjected to centrifugal forces which ove the radially outwards, against the inward flow of gas and towards the inside surface of the cyclone on which the solids separate. The direction of flow of the vortex reverses near 1 Dept. of Engineering and Manageent in Food and Touris, Transilvania University of Braşov.

2 16 Bulletin of the Transilvania University of Braşov Series II Vol. 5 (54) No. 1-1 in ters of speed v, speed at which the heterogeneous ixture enters the cyclone through the inlet: a c = w R = v / R, (1) where R is the radius of the circular path described by the particles when entering inside the cyclone body through the inlet feed, []; w - angular velocity; v - peripheral velocity of a particle in suspension in the cyclone inlet, [/s] (Figure ). Fig. 1. Scheatic diagra of a reverse flow cyclone separator the botto of the cylindrical section and the gas leaves the cyclone via the outlet in the top (the solids outlet is sealed to gas). The solids at the wall of the cyclone are pushed downwards by the outer vortex and out of the solids exit. Gravity has been shown to have little effect on the operation of the cyclone [3]. One of the deterinants of separation of heterogeneous systes by the action of gravity is the sedientation rate.. Sedientation Rate Once the forces acting on a particle are balanced, the particle otion becoes a unifor oveent (particle falls into the ediu at a constant speed), the speed of the particle being called sedientation rate. Sedientation rate in the centrifugal force field in the cyclone is deterined by the sae reasoning as in the centrifugal sedientation field, of devices with rotating eleents. To be applied to the cyclone, centrifugal acceleration in these relations is expressed Fig.. Horizontal section through the cyclone If in the relations used to deterine sedientation rate, for the case of flow characteristic regies, the centrifugal acceleration forula is introduced, expressed in ters of peripheral speed, we obtain relations for the calculation of the sedientation rate: lainar regie of sedientation, when Ar Fr < 36: v scl 1 d ρ p ρ v =, () 18 υ ρ R where: d is the diaeter of the particle, []; ν - cineatic viscosity, [ /s]; ρ p, ρ - particle density and environent density, [kg/ 3 ]; v - peripheral velocity of a particle in suspension in the cyclone inlet, [/s]; interediate regie of sedientation, when 36 <Ar Fr < 845: v sci w =.15 ρ p ρ ρ 1.48 υ, R ;.714 d (3)

3 Marinuc, M., et al.: The Effect of Solid Particle Size upon Tie and Sedientation Rate 163 turbulent regie of sedientation, when Ar Fr > 845: v sct d ρ p ρ = 1.74 v. (4) R ρ To deterine the tie of sedientation one ust apply the reasoning used and consider that the sedientation rate is space derivative with respect to tie and that the oving particles to the place of sedientation is carried out on radial directions: d R v sc =. (5) dt If we separate variables and if sedientation rate is replaced by one of the relations derived for the characteristic regies of sedientation, differential equations are obtained and by integrating the resulting expressions which calculate the sedientation tie for each of these characteristic regies. Based on this reasoning we obtain: for the lainar regie of sedientation, the sedientation tie expression is: 9 υ ρ ts = ( R R1 ) ; (6) d v ρ ρ p for the turbulent regie of sedientation, sedientation tie is: t s = R.55 v 1.5 R d ρ p ρ ρ. (7) In the above relations R 1 is the surface radius of separation, which is considered equal to the outlet orifice radius of solid phase; R - inner radius of the cylindrical part of cyclone. The analysis of relation (6) and (7) shows that sedientation rate is even greater as the radius R of cyclone is bigger and as the velocity input of the heterogeneous ixture is lower. To deterine the transit tie inside the cyclone, it is considered that the path length traveled by the particle fro the oent of entry into the cyclone and until total sedientation, can be calculated by: L = φ R, (8) where φ is the angle at the center corresponding to the spiral trajectory described by particles fro the oent of their entry into cyclone until sedientation; R - average radius of the trajectory: R = (R 1 + R ) /. The angle φ is deterined by the relationship: φ = π n, (9) where n is the nuber of rotations around the axis of syetry of the cyclone. Experiental investigations revealed that fro the entry into the cyclone and until sedientation the particles perfor 4 to 5 coplete rotations around the axis of syetry of the cyclone, (n = 1.5 5). Nubers of turns that particles had perfored inside the cyclone until sedientation were deterined fro traces left by the on the inner walls of the cyclone. If replaceents are ade in (8), the path length traveled by the particles is: L = π (R 1 + R ) n. (1) Considering that at the entry into the cyclone inlet the heterogeneous ixture has linear velocity v and particles retain this velocity along the path length L, the transit tie of particles in the cyclone is:

4 164 Bulletin of the Transilvania University of Braşov Series II Vol. 5 (54) No. 1-1 L π( R1 + R) n t1 = =. (11) v v To achieve sedientation, the condition that the sedientation tie is less than the transit tie of particles in the cyclone ust be fulfilled, i.e.: t s > t 1, and if in this relationship the analytical expressions that deterine the duration of sedientation and transit in cyclone for the characteristic regies are replaced, we obtain atheatical relationships which deterine the critical diaeter (iniu) of particles that are separated during the flow regies [4]. 3. Material and Method For the theoretical investigation regarding the influence of particle size over the sedientation rate in centrifugal field inside the cyclone, the diensions of the interediate products resulting fro the grist were used []. To calculate the sedientation rates in the centrifugal field the following relationship were used: (), (4); and for calculating the sedientation tie corresponding for the two sedientation regies we used the relations (6) and (7). In Table 1 the values obtained by sedientation rate calculation for the two regies of sedientation for five values of particle diaeters are recorded: d 1 =.4 ; d =.45 ; d 3 =.56 ; d 4 =.66 and d 5 =.9. In Table 1, d there is the diaeter of flour particles, in []; ρ p - flour solids density, in [kg/ 3 ]; ρ f - air density, in [kg/ 3 ]; v - heterogeneous ixture inlet velocity in the cyclone inlet, in [/s]; η - dynaic viscosity of air, in [N s/ ]; υ - cineatic viscosity of air, in [ /s]; R 1 - surface radius of separation, which is considered equal to the outlet orifice radius of solid phase, in []; R - inner radius of the cylindrical part of cyclone, in []; v st - sedientation rate in the turbulent regie, in [/s]; v sl - sedientation rate in the lainar regie, in [/s]. In Table the values obtained by sedientation tie calculation for the two regies of sedientation for the five values of particle diaeters entioned above are recorded. In this table, with t sl we note the sedientation tie in the lainar regie and with t st we denoinate the sedientation tie in the turbulent regie. Sedientation rates values Table 1 d [] ρ p [kg/ 3 ] ρ f [kg/ 3 ] v [/s] η [Pa s] υ [ /s] R 1 [] R [] v st [/s] v sl [/s] Sedientation tie values Table d [] t sl [s] t st [s]

5 Marinuc, M., et al.: The Effect of Solid Particle Size upon Tie and Sedientation Rate Results and Discussions To highlight the influence of particle size on sedientation for the two regies of sedientation, data obtained fro calculations were processed and graphs were drawn in Figures 3 and 4 using the coputer progra Microsoft Office Excel 3. The chart fro Figure 3 showed the influence of solid particle diensions over the sedientation rate in centrifugal field in the turbulent regie inside the cyclone separator. It can be observed that the lowest sedientation rate in the turbulent regie was obtained for the sallest diaeter.4 and the highest sedientation rate was obtained for the bigger diaeter.9. The chart fro Figure 4 showed the influence of solid particle diensions over the sedientation rate in centrifugal field in the lainar regie inside the cyclone separator. It can be observed that for a diaeter of.4, a sedientation rate of 7.17 /s was obtained, and for a diaeter.9 a sedientation rate of /s was obtained. Influence of particle diaeter on sedientation rate in the turbulent regie Sedientation rate in turbulent regie, /s ,343 1,9 1,97 14,469 15,78,4,45,56,66,9 Particle diaeter, Fig. 3. Influence of particle diaeter on sedientation in the turbulent regie Influence of particle diaeter on sedientation rate in the lainar regie Sedientation rate in lainar regie, /s ,537 19,649 14,146 9,134 7,17,4,45,56,66,9 Particle diaeter, Fig. 4. Influence of particle diaeter on sedientation in the lainar regie Fig. 5. Influence of particle size over the sedientation tie in the two regies of sedientation

6 166 Bulletin of the Transilvania University of Braşov Series II Vol. 5 (54) No. 1-1 The chart fro Figure 5 showed the influence of particle diension on the sedientation tie inside the cyclone in both sedientation regies, either lainar or turbulent. It can be seen that sedientation tie in the turbulent regie is greater than the sedientation tie in the lainar regie of sedientation in the centrifugal field. 5. Conclusions In the case of turbulent sedientation regie, sedientation tie is even greater as the solid particle diaeter is greater, while in the case of the lainar sedientation regie, sedientation tie is greater when the solid particle size is saller. Sedientation rate in the lainar and turbulent sedientation regie is directly proportional to the solid particle size that is separated inside the cyclone separator. In the case of influence of solid particle size over the sedientation rate, it can be observed that for the sae diaeter of.4, a value of sedientation rate in the turbulent sedientation regie of 1.9 /s was obtained and for the lainar sedientation regie, a value of sedientation rate of only 7.17 /s was obtained. Great differences can be observed in the case of diaeter.9, for which, a value of sedientation rate in the lainar regie of /s was obtained, a rather high value in coparison with the sedientation rate in the turbulent regie which was of /s. Acknowledgeents This paper is supported by the Sectoral Operational Prograe Huan Resources Developent (SOP HRD), financed fro the European Social Fund and by the Roanian Governent under the contract nuber POS-DRU: ID References 1. Ivan, E., Craiu, I.: Operations and Equipent in Food Industry. Tiişoara. Publisher Mirton, 3.. Lupea, A.: Technologies in Food Industry. Tiişoara. Technical University, Martin, R.: Introduction to Particle Technology. Second Edition. Australia. John Wiley & Sons Ltd, Rus, F.: Separation Operations in the Food Industry. Braşov. Transilvania University Press, 1.