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Computational Fluid Dynamics Techniques for Flows in Lapple Cyclone Separator

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Computational Fluid Dynamics Techniques for Flows in Lapple Cyclone Separator COMPUTATIONAL FLUID DYNAMICS TECHNIQUES FOR FLOWS IN LAPPLE CYCLONE SEPARATOR A. F. Lacerda, L. G. M.Vieira, A. M. Nascimento, S. D. Nascimento, J. J. R. Damasceno and M. A. S. Barrozo. Federal University of Uberlândia, Faculty of Chemical Engineering -FEQUI, Block K, Campus Santa Mônica, Uberlândia-MG - Brazil. ZIP: 38400-902 – Fax: 55-034-32394188 E-mail: [email protected] Keywords: Separation; Lapple; Cyclones; Computational Fluid Dynamics; Fluent Abstract A two-dimensional fluidynamics model for turbulent flow of gas in cyclones is used for available the importance of the anisotropic of the Reynolds stress components. This study presents consisted in to simulate through computational fluid dynamics (CFD) package the operation of the Lapple cyclone. Yields of velocity obtained starting from a model anisotropic of the Reynolds stress are compared with experimental data of the literature, as form of validating the results obtained through the use of the Computational fluid dynamics (Fluent). The experimental data of the axial and swirl velocities validate numeric results obtained by the model. 1 - Introduction Cyclones are equipment used for the separation and suspended solid collection in gaseous chains. Its popularity if must mainly to the its simplicity of construction, absence of mobile parts, what it guarantees a low necessity of maintenance. Cyclones are among the oldest of industrial particulate control equipment and air sampling device. The primary advantages of cyclones are economy and simplicity in construction and designs. By using suitable materials and methods of construction, cyclones may be adapted for use in extreme operating conditions: high temperature, high pressure, and corrosive gases. Therefore, cyclones have found increasing utility in the field of air pollution [1]. A more accurate method of determining cyclone performance is the use of fractional efficiency curves. Evaluations of cyclone performance have long been studied to better understand and improve cyclone design theory. Lapple (1951) developed the Classical Cyclone Design process (the CCD process) for designing cyclones and predicting their performance (emission concentrations and pressure drop). This model incorporated the number of effective turns, cut-point diameter, and a “generalized” fractional efficiency curve. For many situations, the Lapple model has been considered acceptable [2]. The developments in software and computer hardware have created an increase in the use of plausible computer modeling research in recent years. If numerical simulations are conducted the immediate need for validation arises if the results are to be of practical use [3]. Computational fluid dynamics (CFD) is a computer-based tool for the solution of the fundamental equations of fluid dynamics - the basic principles of conserving mass, momentum and energy for a fluid flow. CFD is often perceived as a virtual fluids laboratory where experiments can be performed on the computer, but numerical simullation actually holds many advantages over its traditional counterpart, including: speed, cost, completeness of information, and simulation of all operating conditions. The objective of this work is simulate through use of the Fluent fluidynamic program, the operation of the Lapple cyclone separator and to compare the simulation reults with experimental datas of the literature. 2 - Modelling Mathematics In Reynolds averaging, the solution variables in the instantaneous Navier-Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged ) and fluctuating components. For the velocity components: ui = ui + u'j (1) Where ui and u' j , are the mean and fluctuating velocity components ( i = 1, 2, 3). Likewise, for pressure and other scalar quantities: φ = φ + φ' (2) Where φ denotes a scalar such as pressure, energy, or species concentration. Substituting expressions of this form for the flow variables into the instantaneous continuity and momentum equations and taking a time ( or ensemble) average ( and dropping the overbar on the mean velocity, u ) yields the ensemble-averaged momentum equations. They can be written in Cartesian tensor form as: ∂ρ ∂ + ()ρui = 0 (3) ∂t ∂xi ∂u ∂ ∂ ∂Ρ ∂ ∂ui j 2 ∂uil ∂ ' ' ()ρui + ()ρuuu j = − + µ + − δij + (− ρui u j ) (4) ∂t ∂x ∂x ∂x ∂x ∂x 3 ∂xl ∂x j i j j i j Eq.3 and Eq.4 are called Reynolds-averaged Navier-Stokes (RANS) equations. They have the same general form as the instantaneous Navier-Stokes equations, with the velocities and other solution variables now representing ensemble-averaged (or time-averaged) values. Additional terms now appear ' ' that represent the effects of turbulence. These Reynolds stresses, ρu i u j , must be modeled in order to close Eq.4. For variable-density flows, Eq.3 and Eq.4 can be interpreted as Favre-averaged Navier-Stokes equations, with the velocities representing mass-averaged values. As such, Eq.3 and Eq.4 can be applied to density-varying flows. ' ' The exact transport equations for the transport of the Reynolds stresses, ρu iu j , may be written as follows: ∂ ∂ ∂ ∂ ∂ ρu' u' + ρu u' u' = − ρu' u' u' + Ρ δ u' + δ u' + µ u' u' i j K i j i j K ()Kj iK j i j ∂ ∂x K ∂xK ∂x K ∂x K ∂u ' ' ∂u ' ' j ' ' ∂ui ' ' ∂ui ∂u j ∂u i j Ρu iu K + + u ju K − ρβ g u jθ + u iθ + Ρ + − 2µ i ∂x K ∂xK ∂x j ∂xi ∂x K ∂x K ' ' ' ' 2ρΩ u ju m ∈ +u iu m ∈ + S (5) K iKm jkm user Of the various terms in these exact equations, Cij , DL,ij , Ρij , and Fij do not require any modeling. However, DT,ij , Gij , φij , and ∈ij need to be modeled to close the equations. DT,ij can be modeled by the generalized gradient-diffusion model of Daly and Harlow [4]: ' ' ' ' ∂ Ku Ku l ∂u iu j D = C ρ (6) T,ij S ∂x ∈ ∂x K l However, this equation can result in numerical instabilities, so it has been simplified in FLUENT to use a scalar turbulent diffusivity as follows [5]: ' ' ∂ µ ∂u iu j D = t (7) T,ij ∂K σ ∂x K K The turbulent viscosity, µt , is computed similarly to the κ− ∈models: κ2 µ = ρC (8) t µ ∈ Where Cµ = 0,09 . Lien and Leschziner [6] derivared a value of σK = 0,82 by applying the generalized gradient- diffusion model, Eq.6, to the case of a planar homogeneuous shear flow. Note that this value of σK is different from that in the standard and realizable κ− ∈ models, in wich σK = 1,0 . In general, when the turbulence kinetic energy is needed for modeling a specific term, it is obtained by taking the trace of the Reynolds stress tensor: 1 ' ' κ = u iu j (9) 2 ∂ ∂ ∂ µ ∂Κ 1 t 2 ()ρΚ + ()ρκui = µ + + ()Ρii + Gii − ρ∈ (1 + 2M t )+ SK (10) ∂t ∂xi ∂x j σK ∂x j 2 where σK = 0,82 and SK is a user-defined source term. Eq.10 is obtainable by contracting the modeled equation for the Reynolds stresses (Eq. 5). As one might expect, it is essentially identical to Eq. 10 used in the standard κ− ∈ model. Although Eq. 10 is solved globally throughout the flow domain, the values of κ obtained are used only for boundary conditions. In every other case, Κ is obtained from Eq. 9. This is a minor point, however, since the values of Κ obtained with either method should be very similar. The dissipation tensor, ∈ij , is modeled as: 2 ∈ = δ (ρ∈ +Y ) (11) ij 3 ij M 2 where YM = 2ρ ∈ M t is an additional “ dilatation dissipation” term according to the model by Sarkar [7]. The turbulent Mach number in this term is defined as : Κ Mt = (12) a 2 where a( γRT ) is the speed of sound. This compressibility modification always takes effect when the compressible form of the ideal gas law is used. The scalar dissipation rate, ∈, is computed with a model transport equation similar to that used in the standard κ− ∈ model: ∂ ∂ ∂ µ ∂ ∈ 1 ∈ ∈2 t ()ρ∈ + ()ρ∈ ui = µ + + C∈l []Ρii + C∈3Gii − C∈2ρ + S∈ (13) ∂t ∂xi ∂x j σ∈ ∂x j 2 Κ Κ where σ∈ = 1,0 , C∈1 = 1,44 , C∈2 = 1,92 , C∈3 is evaluated as a function of the local flow direction relative to the gravitational vector, and S∈ is a user-defined source term. 4 - Results and Discussion For the estimation of CFD of this work, it was chosen the Lapple cyclone, whose main geometric characteristic, it is shown in the Fig.1 and Table 1. Table 1: Dimensions of the Lapple Cyclone Cyclone Design Configuration Term Lapple Ds(m) 0.0508 Dc(m) 0.1020 Dl(m) 0.0254 Db(m) 0.1020 Le(m) 0.0508 Ls(m) 0.1080 Lc(m) 0.0950 Lco(m) 0.2030 Lb(m) 0.1520 Fig.1: Cyclone Design The discretization methods of the transport equations are shown in the Table 2. Table2: The parameters utilized in the study. Particle type Inert Created material Calcium Carbonate Swirl Velocity (m/s) 0 Tangency Velocity (m/s) 15.08 Radial Velocity (m/s) -1.2001 Pressure PRESTO Pressure-Velocity Coupling SIMPLE Momentum First order Swirl Velocity First order Turbulence Kinetic Energy First order Turbulence dissipation rate First order Turbulence model Reynolds Stress The data obtained in the simulation were compared with the experimental data of Patterson and Munz [8], collected in a located axial position in the cylindrical section of the cyclone, in z=0.1900 m. A numerical mesh was used with approximately 144269 cells. The Fig.2 and Fig.3 presents graphs with the lines representing the Yields of Swirl Velocity and Axial Velocity, respectively, and points representing the experimental data. It is verified in both a good agreement of the numeric solutions with the experimental data. Fig.2: Swirl Velocity Fig.3: Axial Velocity The Fig.4, Fig.5 and Fig.6 presents the Yields of Swirl, Axial Velocities and pressure, respectively: Fig.4: Swirl Velocity (m/s) Fig.5: Axial Velocity (m/s) Fig.6: Pressure Profile (Pa) In the Fig.4 is observed a region of the high spin near the inlet of the vortex-finder.
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