CFD Simulation of an Industrial Dust Cyclone Separator: A Comparison with Empirical Models: The Influence of the Inlet Velocity and the Particle Size on Performance Factors in Situation of High Concentration of Particles

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Introduction
Te industry is currently subject to environmental and hygiene requirements (international regulations limit the dust content of workplaces to 5 mg/m 3 of air for respirable dust) [1].It turns out that cyclones do a good job of removing dust from exhaust gas.In addition, they can satisfy the need to separate the components of a mixture for individual component operation [2][3][4][5][6].Tese advantages have enabled this technique to be extended to a number of industrial felds, including the food industry, the hydrocarbon industry, the cement industry, the mechanical industry, foundry (air fltration, iron trapping, etc.), the waste treatment industry, soil decontamination, combustion (burner and combustion chamber), heat exchangers, the biomass, and biotechnology [2,4,7,8].
Te proper defnition of the work of a cyclone is defned by the product of the centrifugal forces acting on the particles suspended in an air stream [4,7].As the particles have a higher density than the gas, they are forced toward the wall of the cyclone, where, once deposited, they are transported down the cone, to the outlet where they are collected [4,9].Te clean gas, now free of some of its dust load, rises through the center of the cyclone, escaping through the outlet tube, which passes through the roof [10].Imagine that the gas enters through the inlet at the top of the cyclone (tangentially), then spirals downward (frst vortex) until it reaches the point where the diameter of the cone is equal to the diameter of the outlet in the roof (vortex fnder) (Figure 1).Finally, the gas rises through the center, creating a second vortex in the opposite direction to the frst, and then escapes through the hole through the roof [4,9,11,12].
Te cyclone separator, which has many advantages such as simple structure, high separation efciency, low energy consumption, and easy operation, has been widely used in engineering processes to separate dispersed solid particles from suspension by centrifugal and vortex action [4].However, the common cyclone shows a low efciency for fne particles [13].Many attempts have been conducted to improve the separation performance of cyclone separators by optimizing the structure dimension, such as vortex length [14,15], vortex fnder shape and diameter [16][17][18], inlet type, including single, double inlet and more than two inlets [19][20][21], tangential, and spiral inlet [20], inlet dimension [22], diferent inlet section angles in relation to the cyclone body [23][24][25], symmetrical inlet and a volute scroll outlet [26], cone tip diameter [27,28], cyclone height [29], conical length [18,30,31], diameter and length of vortex fnder [32,33] and hopper length [9].Tere are also various kinds of cyclone separators developed to improve the separation efciency, such as Lee type [34], semispherical cyclone [35], dynamic cyclone [36], square cyclone [37], CFC cyclone [38], and the new generation of cyclone separators presented as multichannel cyclone separators [39][40][41][42][43]. Te multichannel cyclone separator's structure has some essential external and internal elements, including upgraded curved elements with openings cut with their plates bent outwards to make curvilinear channels for the continuous movement of the peripheral and transitional gas fows from the infow opening to the central axis [39].In contrast to the study of the conventional cyclone separator, where the modeling is studied in particular detail, the operating principle and design of this new generation equipment is not well understood [39,43].However, although the improvements have been observed, these techniques cannot signifcantly improve the collection efciency for microsized particles.In the word, many attempts have been conducted to improve the separating capacity of fne particles from the exhaust gas.However, the design of a high efciency, low-energy consumption, and low-maintenance separation system with a simple structure for fne particle is still a challenge.
Te study of cyclones is motivated by their use in many industrial sectors (mentioned above) because of the multiple advantages they ofer, notably their simplicity, compactness (10% of the surface can be occupied by other industrial equipment) [3,11,[44][45][46], low manufacturing and maintenance costs, very short residence time (1 to 2 seconds), insensitivity to orientation due to the intense rotational feld (of the order of thousands of times the gravitational feld), and the absence of moving parts [4,47].
However, the fow within these devices is very complex.Te fow is highly turbulent with a three-dimensional, sometimes unsteady behavior.Tis complexity is compounded by the presence of several phases with diferent characteristics and trajectories [2,9].
During the past decades, experimental studies have shown their limitations, especially in the measurement of the parameters afecting the performance factors, due to the complexity of the cyclone geometry (its closed space) [2].
Numerical studies, in particular CFD, appear to be the best means of studying and analysing the indicators (velocity felds, pressure felds, and temperature felds) that afect the performance factors (efciency and pressure drop) [9,48,49].Among the most widely used codes, the FLUENT code is the most widely used code in the CFD analysis of cyclone separators.
Te main objective of this work is the treatment by numerical simulation of the turbulent three-dimensional fow of a Newtonian incompressible two-phase fuid (gaseous and solid phase) in a cyclone dust separator.Te CFD will be preceded by a theoretical evaluation which will include the choice of the type of cyclone (type of entry), the calculation of its dimensions, the analysis of empirical models of comparison and the choice of numerical simulation models.2 Journal of Engineering An analysis will be made on diferent felds (velocity and pressure) infuencing the efciency of the separator.Te infuence of inlet velocity and particle size in the gas phase will be the main factors of comparison.
1.1.Cyclone Separator Geometry.Te cyclone model chosen for the numerical calculation is the Stairmand model [8,[49][50][51].It is a cyclone with single tangential inlet.Te geometry is given in Figure 2 and the ratios of dimensions with respect to D are presented in Table 1.We have chosen an industrial application cyclone with a body diameter of D � 300 mm, with a cone base diameter extension and discharge hopper [9].

Numerical Simulation
2.1.Numerical Procedure 2.1.1.Computation of the Grid.Te study of the mesh is essential in the numerical simulation, as the accuracy of the solution depends on the grid used (Figure 3).Geometry and the mesh have been developed in Fluent.We have chosen a tetrahedral mesh as shown in Figure 3 with 134 642 elements; 25 125 nodes.Te simulation with a tetrahedral mesh gives good results for the case of a cyclone, according to Slack [52].Te mesh can be suitably refned in Fluent to properly control the results.

Solver.
Te numerical simulation of the fuid fow in the cyclone separator having complex geometry and a closed space was performed with the solver FLUENT, version R19.2.FLUENT is a coupled implicit numerical solver, which incorporates fnite volume methods to discretise the equations that govern fuid dynamics in a spatial domain [53].Te simulations were conducted on an HP computer with an INTEL(R) Core i3-4005U CPU@1.70GHz; a 8 GHz RAM memory; and a 64 bit operating system.

Boundary Conditions.
Boundary conditions, in this case, surface conditions, are conditions that completely defne the fow characteristics in the cyclone separator.Tese surfaces here are the "inlet" (Figure 4(a)) or entry surface which is the section at which the exhaust gas enters the separator; the "outlet" (Figure 4(b)) or exit section which is the face through which the clean gases escape with the fnest particles, the collection or "Collection bin" (Figure 4(c)) which represents the collection section of the particles of the solid phase of the mixture; the "WALL" which represents the body of the separator.Te temperature of the gas (air with density ρ g � 1.225 kg/m 3 ) used as the continuous phase for the general study was fxed at 300 K, and the steel particles (sizes : 5μ m ; density: 8030 kg/m 3 ) as the solid transport particles (dispersed phase).We assumed spherical particles with a loading of C o � 500g dust per m 3 of air (sectors such as metal refning, blast furnaces, the iron and steel industry, metal machining, etc.).Atmospheric pressure was used as the reference pressure.

Fluid Flow Modeling.
We know in advance that the fow behavior is turbulent in nature in most (or all) industrial cyclones.Turbulent fow is described by the Navier-Stokes equations.But in a general framework, it is impossible to solve these equations directly [53].Te Navier-Stokes equations can be put in tensor form as follows [46,54]: In this study, we used three numerical simulation models to solve the fuid fow problem of the cyclone.
(1) Reynolds Stress Models (RSM).Tis model was used to analyse the behavior of the diferent parameters that afect the pressure drop and the efciency of the separator, namely: the velocity feld and the pressure feld.Te RSM model presents the best behavior of the fuid in the separator [9,33]; it predicts well the two vortices as well as the fuid fow feld in the separator, and fnally the tangential velocity [46,55].Te form of the fnal equation is Te numerical discretisation scheme for general study case with Te RSM model is presented in Table 2, and Boundary conditions in Table 3.
(2) Te Standard k-Epsilon Model.Te numerical turbulence model used for the analysis of the efect of inlet velocity on pressure drop and separator efciency is the standard kepsilon (k − ε) turbulence model; because, it not only allows fows to be modeled with fully turbulent fow [57], but also assumes that the fuid has the same physical properties in all directions.Te Navier-Stokes system coupled to the kepsilon model is written as [54] Te numerical discretisation scheme for general study case with the standard k-epsilon model is presented in Table 4, and Boundary conditions in Table 5.
(3) Te RNG k − ε Model.Te numerical turbulence model used for the analysis of the efect of particle size on the efciency of the separator is the RNG k-epsilon (k − ε) turbulence model, as this closure model takes into account vortex efects in the turbulence and the velocity of the forced Journal of Engineering fow, but also has the ability to be used to resolve low Reynolds number fow efects in the vicinity of boundary layer walls [2,58].
where α k and α ε are inverses of the efective Prandtl numbers for the kinetic energy  k and the mean dissipation  ε, respectively.Te normalisation group term for the dissipation ε is where ≊Sk/ε ; η 0 � 4.38; et β � 0.012.G k represents the generation of turbulence kinetic energy due to velocity variation; G b represents the generation of turbulence kinetic energy due to buoyancy; Y m represents the contribution of the fuctuating expansion of compressible turbulence to the overall dissipation rate; S k et S ε represent the source terms; C ε1 , C ε2 , and C ε1 are constants.
Te numerical discretisation scheme for general study case with the RNG k-epsilon model is presented in Table 6, and Boundary conditions in Table 7.
(4) Equations Governing the Solid Phase.Te equations of motion of the particles with the Euler-Lagrange approach are given by [3,48,49]: where x pi is the ith coordinate of the particle; g i is the acceleration of gravity in i direction; ρ p and ρ are the densities of the particle and the gas, respectively.Generally, the diference between the particles velocity and the fuid velocity result from the imbalance of the pressure distribution and the viscous tensions on the particle surfaces.Tis gives rise to the drag force forces F d which can be calculated by where τ P , the relaxation time of the particle is given by Te drag coefcient C d is a function of the particle Reynolds number defned by Morsi and Alexender [59] defne the drag coefcient for spherical particles as F x is the additional acceleration (force per unit mass of particle); it was defned by Safman [3] as where d ij is the deformation tensor and K � 2.594.
2.1.5.Centrifugal Force.Centrifugal force plays an important role in the separation of particles.Centrifugal force is usually presented as a pseudoforce that arises directly from the transport of the inertia of a body when another force sets it in motion in a curved region.If the particle moves in a curved region with a radius r and velocity V c along the region, then it has angular velocity: And the centrifugal force For cyclone analysis, the centrifugal force is commonly expressed as its ratio to the force of gravity [47]:

Numerical Inlet Data of Studies
(i) To analyse the infuence of inlet velocity on performance factors, we based our analysis in the literature [50] on the experimental work of Stairmand (1969); Swift (1969); and Lapple (1951) (Table 8), who determined the ratio of fow rate to cyclone cylinder .Ten, we calculated the diferent efciencies as a function of the particle diameters, for those any three velocities as Table 8.Te efciency formula is given in (15) "number of particle tracked" represents the number of particle injected by the inlet and "number of particle trapped", the number of particle that hit the collection bin as mentioned above.If, when numerically performing steady DPM trajectory in Fluent, the calculation converges (or the maximum number of steps is reached) and a given particle still does not reach the outlet or collection bin (or escape/ trap), that particle fat is reported as "incomplete".In such a case, it is probable that particle is kept churning in the re-circulation region and is not coming out the domain, thus being reported incomplete.As these particles cannot be considered as either escaped or collected, they must be subtracted from the number of particle injected when calculating the cyclone efciency, as shown in the following formula: 2.1.7.Convergence Criterion.Te calculation is considered to converge when the residual stabilises [61].Depending on the number of iterations imposed, this can happen before (fast convergence) or exactly after the number of iterations imposed.
Due to the computation time and the improvement of the results, a residual of 10 − 5 seems to be the most appropriate for a good estimation of the convergence accuracy for the diferent unknowns of the Navier-Stokes equations.Since for residuals of 10 − 6 and 10 − 7 , the computation is rather time consuming and leads to little improvement in the results.
Te simulations were performed on an HP laptop with an INTEL(R) Core i3-4005U CPU@1.70GHz; a 6 GHz RAM memory, and a 64 bit operating system.

Collection Criterion.
In reality, particles are deposited on cyclone walls just after entering, and the rest are suspended in the fow and separated by the centrifugal action accomplished with particle agglomeration, while some may leave without collecting [9].However, this reality is difcult to model in CFD, as there is no evidence on whether, when, or where a particle is collected.Particles that touched the cyclone hopper bottom were counted as collected by Ke ˛pa [62], Wan et al. [63], and Qiu et al. [64].Ma et al. [65] assumed that particles that touched the cyclone wall were collected, while Grifths et al. [66] considered particles that touched the conical part and the bottom walls to be collected.Te assumption based on studies by Yoshida et al. [67], Gimbun et al. [27], Chuah et al. [68], and Bhaskar et al. [69] was that the particles that escaped from the cyclone bottom were collected.Te number and mass of particles that escaped from the cyclone during the simulation period are also considered as collected in the literature [58,70,71].In summary, the conclusions derived for the selection of particle deposition zones in cyclone separators in CFD simulations are unclear.
Another study by de Souza et al. [72] considered two particle collection criteria: particles escaped from the outlet and those that escape through the lower diameter of the cone section.Te second criterion is reasonable and fts well with the experimental results of Bohnet [73], Lim et al. [74], and Yoshida et al. [75] but can overpredict fne particle collection as there is no re-entrainment from the cone bottom.However, the authors found that the grade efciency curves do not converge after the cyclone residence time, and thus particles may bounce back and escape from the outlet, leading to an underprediction of collection efciencies assuming particles escaping from the outlet [9].Terefore, assuming particles that touched the hopper bottom were assumed to be collected in this study.
2.1.9.Analysis Sections.Te analysis sections are the 2D sections of the model on which we will plot the profles of the diferent parameters that infuence the efciency of the separator in order to analyse them.Tese are as follows: Journal of Engineering (i) Section A-A: An output section in the vortex fnder (x � 0; y � 1.300; z � 0) (ii) Section B-B: A section of the cylinder (x � 0 ; y � 1.125 ; z � 0) (iii) Section C-C: A section of the cone (x � 0; y � 0.500; z � 0) (iv) Section D-D: A section of the extension of the base diameter of the cone (x � 0; y � − 0.100; z � 0) (v) Section E-E: A section of the collector (x � 0; y � − 0.300; z � 0) For the diferent contours, we used the planes (0; y; 0); the plane (x � 0; y � 1.125; z � 0) and the plane (x � 0; y � 1; z � 0) on which we represented the smooth and/or scratched profles to better observe the contour lines.
Tose are show at Figure 5.

Teoretical Approach.
Te pressure drop in a cyclone separator plays a vital role in the performance evaluation.It is generally caused by the frictional interactions between the fowing fuid and the solid wall.Te total pressure losses in a cyclone separator mainly comprise the losses at inlet, cyclone chamber and outlet.So, the proper cyclone design is very essential as it is directly related to the pressure drop.Te maximum amount of total pressure drop take place over the cylindrical and conical chamber in a cyclone separator, due to energy dissipation loss by the strong swirling turbulent fow.Demir et al. [76], introduced the standard pressure drop equation for a cyclone separator, which is generally given as: where ∆P is cyclone pressure drop, ρ g is the gas density, V in is the gas velocity at inlet and ξ C is an important pressure drop parameter, which mainly contains some dimensional correlations.Tere are various models are available in the literature, but in this present study, six models have been selected to predict the pressure drop including model based on estimating the dissipative loss such as Stairmand [51], and fve purely empirical models such as Casal and Martinez-Benet [77], Coker [78], Dirgo [79], Shepherd and Lapple [80], and First, as shown in Table 9. Te pressure drop between the inlet and outlet of a cyclone separator is the quantity of work, which is important to operate the static device for given conditions [81].Te operational cost, energy consumption and collection efciency are directly associated with the pressured drop.Te pressure drop in cyclone is directly proportional to velocity head and gas density.In these analytical models some includes the efect of cyclone body diameter, conical heights, friction factor, cross-section of inlet, gas viscosity, vortex fnder diameter, and height as well.In the present work, the static pressure drop under diferent operating condition is predicted numerically and also validated with theoretical models and experimental model of the Stairmand 1D2D design cyclones found by Lingjuan W. [60].
To improve the efciency, we used three models: Iozia and Leith and Dirgo and Leith model [4,82] have an excellent record to calculate the cyclone efciency as function of particle size at fxed velocity (V in � 10 m/s).Te mathematical expression is given in Table 10.Te model basically assumes that a particle carried out by the vortex encounter two forces mainly the centrifugal force and the fow resistance.Te logistic model named Iozia and Leith [82,83] shows a good investigation with experimental data for the large cyclone size Dc � 0.25-0.4m [83,84].We also used the Licht [4] model based to exponential and logarithm functions Table 10.Tose three empirical models were combined with the Barth model of cut-size [4], Table 10, and the design of separator.So, these models can be used for the efciency calculation in the cyclone separator and can be validated with numerical result for the present geometry and experimental data found by Yangyang et al. [85] with 1D2D Stairmand design cyclone.Journal of Engineering

Results and Analysis
Te collection efciency and pressure drop of a cyclone separator are a direct result of the fow pattern of the gas and solid phase, as well as the pressure feld within the cyclone.Based on the meantime, the dominant fow character in the cyclone is a vortical and can be described as the "Rankine vortex".It is a combination of a quasi-free outer vortex and a quasi-forced inner vortex.Apart from the gas inlet velocity and geometrical parameters, wall friction and solid particle loading also infuence the strength of the vortex.Empirical models often neglect the latter two and are therefore limited in their applications.Numerical modeling is therefore necessary to understand velocity and pressure felds [12].

Pressure Field Analysis
3.1.1.Static Pressure.Te static pressure variation has a relatively identical profle in all the sections of the separator (Figure 6).Te maximum value of the static pressure is found in the body of the cyclone (dress), more precisely in the region of the quasi-free vortex; its intensity drops drastically from the walls to the center (region of the quasiforced vortex) (Figure 7), due to a strong vortex velocity; then many particles can be re-entrained and escape if they enter this zone.Although the static pressure drops drastically in the radial centripetal direction, its axial variation remains small (Figure 7).
Te pressure feld has a stronger gradient in the radial direction because a greatly intensifed forced vortex exists, while in the axial direction it remains weak.Tis results in the existence of two helical motions, one heading towards the base of the cyclone and the other towards the vortex fnder.Tese two vortices are clearly visible in the axial and tangential velocity felds (Figures 8 and 9).Tus, a long region of negative static pressure exists at the center of the cyclone (Figure 6).

Dynamic Pressure.
Te dynamic pressure is highest at the cyclone inlet at the interface between the quasi-free vortex and the quasi-forced vortex (Figure 10).Te dynamic pressure curve is asymmetric (Figure 11), due to the nonsymmetry of the tangential velocity profle (because the cyclone has only one inlet, and therefore the axis of the vortex cannot coincide with its geometric axis).
Te dynamic pressure is high in the quasi-free vortex region and cancels out in the quasi-forced vortex region on the central axis of the cyclone (Figure 10).Te same behavior is visible in the extension of the base diameter of the cone and even in the collector.

Models Numerical values
Grade efciency functions Cut-size of Barth-Muschelknautz: x 50 � 2.05 μm With the extension of the base diameter of the cyclone cone, the pressure drops decrease along the vertical axis; meanwhile, with the efects of velocity nonsymmetry and especially the tangential velocity, which dominates the vortex fow feld, the dynamic pressure remains nonaxisymmetric [9].
Te dynamic pressure profle is closely related to that of the tangential component of the mean velocity: the higher the mean velocity, the higher the dynamic pressure.

Flow Field Analysis
3.2.1.Average Speed Intensity.Te contour of average speed intensity is presented on Figure 12.Of the three velocity components in the vortex fow inside the cyclone, the tangential component is the largest which governs the fow pattern and separates particles by centrifugal force [86].
Te axial fow is also important for the transport of particles collected from the walls to the base collector.In cyclone aerodynamics, the radial velocity is the weakest component [9], although it contributes to the transport of the collected particles from the walls to the collector with the efect of the centripetal force and also contributes largely to the return of the quasi-forced central vortex [2].

Axial Velocity.
Te axial velocity is of major infuence in the transport of solid particles towards the collection device.Te empirical model based on the double vortex structure postulates constant values for the downward fow in the outer vortex (quasi-free) and the upward fow in the inner vortex (quasi-forced) [12,64].Tese values cancel at the axial position where the vortices end.
In fact, the numerical analysis shows us that the axial velocity contour has a positive downward fow and a negative upward fow (Figure 8).Tese fows are helical in the cone and its extension and even in the collector, allowing a rapid transport of solid particles towards the collector.But these helical fows can also allow a re-drainage of the particles towards the vortex fnder, thus contributing to a decrease in the efciency of the cyclone.Also, the contour is not fat (uniform) (Figure 13), but has maxima and minima.Typically, the outer fow shows maxima in the vicinity of the edges, while the inner fow chows a minimum in the vicinity of the cyclone geometry axis.
Te diameter of the quasi-forced inner vortex of the gas entering the vortex fnder is larger than that of the vortex fnder; as a result, the gas velocity drops drastically in the vortex fnder at the center, at the exit of the separator.Tis can contribute to increase pressure drops [2].
Te axial velocity component is not axisymmetric and is directed upward out of the cyclone walls and downward inside the cyclone core (Figure 13).Te upward and downward maxima are always less than the inlet velocity for any study [7].

Tangential Velocity.
Te typical tangential velocity contour is shown in Figure 9.
Te distribution of tangential velocity is similar to that of the dynamic pressure (Figure 10).Tis shows that the tangential velocity is the most dominant velocity component in the cyclone separator [87].For the same reasons, the magnitude contour of the average velocity is almost similar to that of the tangential velocity (Figure 12).Consequently, the tangential velocity dominates the fow, and the intense shear in the radial direction.Tis results in a centrifugal force, which determines the separation of the particles.
It was observed that the inlet velocity is accelerated due to the geometry of the cyclone and its value increases from its initial value, and then decreases as the gas swirls towards the base along the cyclone separator and reaches its minimum in the center of the cyclone (Figure 9).At the certain cross-section within the cone (diameter less than or equal to that of the vortex fnder), there is a reversal of fow and the  12 Journal of Engineering gas fows opposite direction.Before entering the vortex fnder, the gas in the quasi-forced return vortex collides with the continuous fow; this result in a chaotic fow just below the vortex fnder, and the speed drops sharply (Figure 9).Tis causes energy losses and pressure drops.Te tangential velocity is highly dependent on the geometry of the cyclone, the frictions and the particle loading [12].
Te tangential velocity contour (Figure 9) shows the socalled "Rankine vortex" which consists of two parts: an intense or quasi-free outer vortex and an inner or quasi-forced vortex.Te tangential velocity profle [88] (Figure 14) is relatively similar at diferent sections within the same cyclone separator; these profles show that the velocity is zero at the cyclone walls, refecting the removal of solid particles from the downward vortex fow (Figure 14).It can be also be seen that in the outer region of the quasi-free vortex, due to a rapid decrease in the tangential velocity intensity (almost zero) in the vicinity of the walls, the distribution is diferent at each section and the change in the value of the maximum tangential velocity is relatively limited [7,88].
Generally, the tangential velocity distribution varies only slightly with the axial position in the cyclone (Figure 14) [57].Tis means that if the tangential velocity increases in one section of the cyclone, it will also increase in all other sections.

Radial Velocity.
Te radial velocity afects the defection of particle.Tis is an important factor in the analysis of particle collection and cyclone efciency.Analytically, the radial velocity is considered to be the average velocity component with the lowest value [64].However, this is only valid for the inner or quasi-forced vortex, and especially in the vicinity of the vortex fnder, where it grows rapidly towards the core of the vortex [12,89].
Te radial velocity contour is given in Figure 15.Tis contour is helical.Te axis of the vortex is slightly curved and not aligned with the geometric axis of the cyclone.It can be seen from Figure 16 that the radial velocity contour is positive on one side and negative on the other, alternating along the separator.Tis is due to the fact that the cyclone separator with a single tangential inlet is nonaxisymmetric.It is also observed that the radial velocity increases sharply towards the core of the vortex at the inlet of the separator.Alekseenko [12] suggested that this phenomenon is the result of the helical rotation of the vortex along the fow around the geometric axis of the cyclone (Figure 15).Journal of Engineering It is also observed that as the distance from the base of the separator increases, so does the radial velocity intensity in the quasi-forced vortex, which accelerates the helical rotation of the inner vortex (Figures 15 and 16).Tese two factors contribute to a re-entrainment of some (fnest) particles and therefore to the decrease of the cyclone separator efciency.
Te radial velocity contour shows that it is negative in the gas at the inlet to the separator and quickly becomes zero.Ten, it becomes positive due to the centrifugal force and the acceleration of the mean velocity (due to the geometry of the separator) around the vortex fnder.
Finally, the radial velocity profle in the vortex fnder (parabolic pointing upwards) (Figure 16 section A-A) shows that it is largely the mean velocity component responsible for the backfow.

Infuence of the Flow Rate (Inlet Velocity) on the Pressure
Drops and Efciency of a Cyclone Separator.Te curve of pressure drops and efciency as a function of the inlet velocity are presented in Figure 17.Tey present parabolic profles.Te pressure drop and collection efciency in the cyclone separator are related to each other (Table 11).
Te pressure drops and efciency across the cyclone separator increases closely with the inlet velocity of the separator.It is therefore higher for higher inlet velocity and lower for lower ones.
Te particle collection efciency is the most signifcant index by which the cyclone performance can be evaluated.Te collection efciency of a cyclone separator is known as the particle capture rate, which is the ability to separate the solid inert particles from the gas stream.Tere are many important factors, that afects the overall collection efciency such as density of solid particle, particle diameter, gas velocity (in this study), gas temperature, cyclone dimensions, and pressure drop.
In the cyclone separator, high-speed fow enters from the inlet, and particles are subjected to an inwardly directed drag as well as an outwardly directed centrifugal force in barrel section.Particles directly attack on the cylindrical wall and create a swirling motion around the gas outlet inside the cyclone chamber (tangential velocity).So, the gas starts following an outer vortex shaped pathway and particles falls down in the collection bin, in a helical manner (axial velocity).Finally, the light gas moves upward or discharged through the outlet tube with fne particles, following an inner vortex (radial velocity).Te centrifugal force is directly proportional to the mass of the particle.It is assumed that the particle velocity is same as that of gas fow.When the particles are suspended in a fuid fow, the phenomenon can be characterised by a dimensionless number named Stokes number, which is the ratio of the characteristic time of a particle to the fuid fow.Te mathematical expression is written as where t 0 is the relaxation time of the particle, V θw is the fow velocity and D is the cyclone diameter [90].Te characteristic time of the particle is given as where ρ p is the particle density, d p is the diameter of particle and μ g is the fuid viscosity.For the accurate tracing, the response time of particle should be faster compared to the smallest time scale of the fuid fow.So, smaller the value of stokes number, produce acceptable tracing accuracy.When

Journal of Engineering
Stk ≫ 1, the particles are detached from the fuid fow and for Stk ≪ 1, particles follow the fuid fow properly.But for Stk < 0.1, the tracing accuracy is high with less than 1% error [83].So, we can conclude that, when the inlet velocity increases, the fow velocity increases, and so does the Stokes number, which helps to improve efciency.Te pressure drop in a cyclone can be described as the amount of energy required to operate the system by moving the fowing gas through the inlet and outlet of the static device.So, the separation efciency is associated with the pressure drop, which helps to estimate the operating cost of a cyclone separator.
Te main part of the pressure drop, i.e., about 80%, is considered to be pressure losses inside the cyclone due to the energy dissipation by the viscous stress of the turbulent rotational fow [81,83].Te remaining 20% of the pressure drop are caused by the contraction of the fuid fow at the outlet, expansion at the inlet and by fuid friction on the  16 Journal of Engineering cyclone wall surface.Pressure drop or fow resistance is strongly dependent on fow velocity.As the velocity increases, Reynold's number also increases, resulting in intense turbulence and shocks between particles in fow.Te result is an increase in efciency, but also an increase in pressure drop, as shown in Table 11 and Figure 17.
In conclusion, efciency and pressure drops increase with inlet velocity into the cyclone dust separator, one being positive impact and other negative.A balance therefore needs to be struck at the design stage in terms of available energy and the desired efciency range, in order to choose the best inlet velocity for an application.In order to better understand the behavior of the pressure drops as a function of the gas inlet velocity in the separator, we will plot the curve of the natural logarithm of the pressure drops ln(∆ P ).Table 12 presents the values of ln(∆ P ) as a function of ln(v).
Te profle of the curve of the logarithm of pressure drops ln(∆ P ) is a straight line (Figure 18), proof that the pressure drops in the cyclone are exponent functions of the speed.
We can then obtain by calculating the slope of the line: ln(∆ P ) � 2.0007 ln(v).
It can then be concluded that the variation of the pressure drops as a function of the inlet velocity can correspond to the frst order theoretical formulation which is in the form: where A is constants and v the speed; we can therefore validate the agreement with the theoretical expression: where ξ C is an Euler number, ρ g is density and is inlet velocity.

Infuence of Particle Size on the Efciency of a Cyclone
Separator.Te curves obtained are shown in Figure 19.Te summary of the diferent efciencies as a function of the diameters for any three speeds v 1 � 8.02 m/s(Efficiency E1); v 2 � 10 m/s (Efficiency E2) and v 3 � 15 m/s (Efficiency E3) is presented in Table 13.

Interpretation 1.
Te efciency curve of a cyclone dust collector separator (for a given inlet velocity) as a function of particle size is strictly increasing and shows three main zones (Figure 19): (i) A light growth zone for particles between 0 and 2 μm, corresponding to ultrafne particles.For these particles, the efciency is very low (less than 25%), and the cut-of diameter is large.For particle sizes in this zone, it would be wise to combine the cyclone separator with other fltering devices, in particular bag flters, even if there are expensive to maintain, but it is also possible to combine several cyclones in series to increase the separation efciency, in order to reach the required rejection threshold.(ii) A steep growth zone corresponding to fne particles of a size between 2 and 10 μm: the efciency of a separator in this zone can be between 25% and close to 95% for a fxed speed, depending on the average size of the particles.Te cut diameter is also average there.(iii) Tis is a zone that ofers a signifcant advantage in the analysis of the efciency of a cyclone separator and hence its design, as it can allow the desired efciency to be obtained just by changing (incrementing or decrementing) the inlet velocity, which may include costs on the fow generator (fan or any other mechanical device).Most of the particles discharged by industries have sizes within this range, making the cyclone separator one of the most requested elements in industry for this purpose.Journal of Engineering (iv) A constant zone or convergence zone; this corresponds to particles of size greater than or equal to 10 μm.All particles in this zone have efciency greater than 95%.Terefore, almost all particles larger than 10 μm are collected by the cyclone separator if they are in the exhaust gas stream.

Interpretation 2.
It is also observed in Figure 19 that the efciency of a cyclone separator dust collector varies in increasingly with the particle inlet velocity for any fxed diameter.Tus, the higher the inlet velocity, the more particles contained in a waste air stream are likely to be captured in the separator.Tese phenomena can be explained physically by centrifugal force: Tus, for a given particle of diameter D � 2r, increasing V c amounts to increasing ω 2 � V c /r and therefore also increasing F c , hence the increase in efciency as a function of inlet velocity.
On the other hand, increasing the size of the particles means to increasing their mass, which also leads to an increase in efciency for a given fxed inlet velocity.
It can be observed that the experimental profle is similar to that obtained in our study.In terms of particle size, these models predict a convergence from 10 μm and an abrupt growth of around 1 μm which also coincides with our simulation results.

Comparison of the Tree Numerical Models in terms of
Contours, Efciency, and Pressure Drops 3.6.1.Te Infuence of Inlet Velocity.It (Figure [20][21][22] shows that the RSM turbulent model has a higher pressure drop than K-epsilon turbulence models (standard and RNG).It also should be noted that this model has a higher efciency at constant inlet velocity than the last two models.As for RNG model, it efciency and pressure drop are higher than those of the standard model at constant velocity (Figure 21).At high inlet speeds (V in > 10 m/s), all tree models are perfectly efcient.
Tose observations can be justifed by the fact that, the Reynolds stress model (RSM) is the most classical turbulence model in which the individual stress tensors are computed directly.Te directional efects and the complicated turbulence fow interactions are strongly taken into account in the RSM model.However, the standard k-epsilon and RNG

Journal of Engineering 21
k-epsilon models are not suitable for swirling fows, which has anisotropic turbulence, and these models underpredicts the performance [81,83].
Ten, the RSM model constitutes a closed N-S equation in three-dimensional fow, which can more accurately simulate the strong cyclone fow in the internal fow feld of the cyclone separator.
It is shown that good agreement of the CFD numerical calculation when compared with experimental data and predictions from empirical correlation.Te results show that the CFD prediction by using the Fluent code can be used for pressure drop evaluation in cyclone design.Te Fluent code with the RSM turbulence model, predict very well the pressure drop in cyclones and can be used in cyclone design for any operational conditions (Figures 21-24).In the CFD numerical calculations, a small pressure drop deviation was observed, with less than 30% of deviation at diferent inlet velocity which probably in the same magnitude of the experimental error of Lingjuan W. [60].Te CFD simulations with RNG k-epsilon turbulence model still yield a reasonably good prediction (Figures 20,21,23,24) at lower velocity with the deviation about 35-38% of an experimental data.It considerably tolerable since the RNG k-model is much less on computational time required compared to the complicated RSM turbulence model.In all cases of the simulation, the RNG k-epsilon model considerably underestimates the cyclone pressure drop as revealed by Grifths and Boysan [66].
Te cyclone pressure drop can be rewritten as a function of inlet velocity head.Te empirical model used for the

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Journal of Engineering prediction of pressure drop is much depends on the cyclone operating condition.Stairmand [51], Casal and Martine-Benet [77], and Dirgo [79] models show a good prediction on cyclone pressure drop under diferent operational inlet velocity (Figure 24), the prediction within 6-20% of the measured value.Te deviation between RNG K-epsilon and the First model is less than 3% (Figures 24 and 25), so this empirical model can be use at its place if one does not want to compute.

Te Infuence of Particle Size
. Te RSM turbulence model has higher efciency than that given by the K-epsilon models for a given particle size (Figure 26); this is undoubtedly due to the reasons mentioned above.On the other hand, there is a gap (max value 50%) between this model and the experimental data of Yangyang et al. [85] (this could be the maximum margin error found by Yangyang T. et al. in their experiment) for fne particle (≤3μm) (Figure 26).Te RNG model presents a curve almost similar to that of the RSM model, in the second zone of the curve (steep growth zone) (Figure 26).Te curves of the empirical models are in perfect agreement with each other and show very good agreement with experimental model (Figures 27 and 28), but show a high gape with the numerical models (Figure 28).Te numerical model that best approximates the empirical models at low particles size is once again, the RSM model.Tis can therefore be used when analysing efciency as function of the particle size.Te RNG model, whose calculation time is more reasonable than one of the RSM model can also be used in the case of law machines resources.

Te Contours.
Observation of the diferent contours of mean velocity and pressure felds (Table 14) shows us that, the Reynolds stress turbulence model (RSM) proves to be relatively successful in detecting the diferent aspects of rotational fow inside the cyclone separators such as anisotropy of the turbulence, presence of quasi-free and quasiforced vortices, and the behavior of the core formed at the central region, with respect to the RNG k-ε model.Tis model better predicts the law of the walls.On the other hand, the RNG model predicts greater maximum value of dynamic and static pressure (ofset of 3.75% for static pressure and 4.68% for dynamic pressure), but the measurement of the value of static pressure between inlet and the outlet (pressure drop) remains lower than that given by the RSM model.It is the same observation for tangential velocity (ofset of 3.06 % ).Tis could be explained by the fact that the RNG model does a better job of calculating the turbulent kinetic energy and its dissipation (Tables 14 and 15), whereas the Reynolds stress model requires the solution of transport equations for each of the Reynolds stress components as well as for dissipation transport without the necessity to calculate an isotropic turbulent viscosity feld (Tables 14 and 15).Tis is in perfect harmony with the numerical studies carried out by Fredriksson [91] which reveal that the RNG k-epsilon model underestimates the variation of the axial velocity profle across the radial direction and also overestimates the magnitude of the tangential velocity and the cyclone pressure feld.Te Reynolds stress turbulence model yields an accurate prediction of swirl fow pattern, axial velocity, tangential velocity, and pressure drop on cyclone simulations [33,46,91,92].

Trajectory of a
Particle inside the Separator.Te trajectory of a particle inside the cyclone separator is shown in Figure 29.It can be seen that a particle takes on average 7 s to be captured in the collector; note a region of very strong vorticity at the extension of the lower diameter of the cone.Tis strong vorticity is intended to prevent the particle from entering the quasi-forced vortex and being re-entrained.

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Journal of Engineering

Conclusion and Perspectives
Te aim of the present study is to numerically simulate the turbulent and three-dimensional aerodynamic multiphase fow inside conventional industrial cyclone dust collector with a single tangential inlet.Te numerical simulation tool Fluent R19.2 was our means, thanks to its simple and attractive interface; it allowed us to go from the generation of the 3D schematic of the separator to the results, through the meshing and the implementation of the various simulation parameters.Tis software allowed us to obtain with clarity the phenomena that govern the turbulent fow inside the cyclone separator.Some of the results obtained are in good agreement with the experimental and numerical results.Te conclusions drawn from this work are as follows.
Te mean velocity feld is made up of three components, each with a very specifc role in the turbulent fow inside the cyclone separator: the tangential velocity, which has the highest value, is responsible for separating the particles (discrete phase) from the gas that constitutes the continuous phase in the quasi-free outer vortex; then the axial velocity is responsible for transporting these particles toward the base of the collector in a helical fashion, still in the quasi-free vortex; and fnally, the radial component is responsible to returning the fow with the fnest particles, but this time in the quasi-forced inner vortex.
Efciency and pressure drop are performance indicators that increase with inlet speed.Te former is an advantage, but the latter a disadvantage; so it is up to the engineer to fnd the right balance between the energy resources available and the efciency margin to be achieved.Efciency also increases with particle size for given inlet velocity.But efciency can also be varied for a given particle size by varying the inlet velocity.
Of the three numerical models used, the RSM model proved to be the most suitable for studying the turbulent fow inside the cyclone, but it is characterised by a very long calculation time and requires large machine resources.An alternative to this model is the RNG K-epsilon model, which ofers a reasonable calculation time with acceptable results.
Analysis of the empirical and semiempirical models shows that they can be used to calculate efciency and pressure drops.Te Stairmand model correlates well with experimental data, probably because the geometry of the separator we have chosen is the high-efciency Stairmand model.Te Casal and Martine-Benet and Dirgo models can also be used.In terms of efciency, the Iozia and Leith model proved to be the most suitable.Te frst pressure drops model correlate perfectly with the RNG K-epsilon numerical model, so it can be an alternative.
Finally, it should be said that the new generation of separators for which no results have been presented in this work, has a higher efciency gap of between 3 and 12% for particle smaller than 10 μm and high pressure drops compared with the simple cyclone separator.Tis is due to the progressive friction experienced by the multiphase vortex fow between the channels inside the cyclone.Te result is an increase in pressure drop and also an increase in efciency.However, it should also be noted that this new generation of cyclone requires meticulous design in terms of the arrangement and orientation of the channels in the separation chamber (cylinder).Once again, it should be remembered that in order to choose the right type of separator for a specifc application, it is up to the engineer to fnd the right balance between the energy resources available and the efciency margin to be achieved.

Figure 13 :
Figure 13: Axial velocity curves depending on the analysis section.

Figure 14 :
Figure 14: Curves of tangential speed according to the section of analysis.

Figure 18 :
Figure18: Curve of the natural logarithm of the pressure drop ln(∆ P ) as a function of ln(v).

Figure 19 :
Figure 19: Efciency curve as a function of particle size.

Figure 21 :Figure 20 :Figure 22 :
Figure 21: Comparison of the three numerical models in terms of pressure drop and efciency as function of inlet velocity.

Figure 23 :Figure 24 :Figure 25 :
Figure 23: Comparison of the three numerical models and experimental data in terms of pressure drop as function of inlet velocity.

Figure 26 :Figure 27 :Figure 28 :
Figure 26: Comparison of the three numerical models and experimental data in terms of efciency as function of particle size at 10 m/s.

Figure 29 :
Figure 29: Trajectory of a particle inside the separator.

NomenclatureD:
Body diameter, m a: Inlet tube length, m b: Inlet tube width, m D e : Vortex fnder diameter, m S: Vortex fnder height, m B c : Cone base diameter, m H: Cyclone height, m h: Body height, m L e : External extension of the vortex fnder, m L i : Extension of the inlet, m H t : Cone tip length, m H k : Collector height, m D k : Collector diameter, m g: Gravitational acceleration, m/s 2 F c : centrifugal Force, N m: Mass, kg V c : centrifugal velocity, m/s ω: Rotational velocity, rad/s r: Radius, m

Table 1 :
Geometrical parameters of the cyclone dust separator.

Table 3 :
Boundary conditions for study general study case.

Table 5 :
Boundary conditions for study the efect of inlet velocity.

Table 7 :
Boundary conditions for the study the efect of particle size.To analyse the Infuence of particle size on the effciency of a cyclone separator, we fxed three values of inlet velocity: v 1 � 8.02 m/s ; v 2 � 10 m/s and v 3 � 15 m/s, and for each velocity value, we chose ten diferent particle diameters, from fnest to the least fne (0.01, 0.1, 1, 2, 3, 4, 7, 10, 15, and 20 μm)

Table 9 :
Empirical models of pressure drops.

Table 11 :
Efciencies and pressure drops as a function of speeds.

Table 12 :
Values of ln(∆ P ) as a function of ln(v).

Table 13 :
Grade efciency as function of particle size.

Table 14 :
Comparison of the three numerical models in terms of pressure and velocity contours at V �

Table 15 :
Comparison of the three numerical models in terms of turbulent kinetic energy and turbulent dissipation rate at V � ∆ P : Pressure drop, pa F g : force of gravity, N F d : resisting forces, N ρ: densities of the gas, kg/m 3 ρ p : densities of the particle, kg/m 3 x pi : Te ith coordinate of the particle position, m u pi : Te ith coordinate of the particle velocity, m/s F x : Safman force, N g i : the acceleration due to gravity in i direction m/s 2 C d : coefcient of resistance for spherical particles τ P : relaxation time of the particle, s R ep : Reynolds number μ: Dynamic viscosity d p : Particle diameter, m d ij : Strain tensor τ: Shear stress components (τ l