Effect of the inlet duct angle on the performance of cyclone separators

Accepted Manuscript Effect of the inlet duct angle on the performance of cyclone separators Marek Wasilewski, Lakhbir Singh Brar PII: DOI: Reference:

S1383-5866(18)33354-9 https://doi.org/10.1016/j.seppur.2018.12.023 SEPPUR 15165

To appear in:

Separation and Purification Technology

Received Date: Revised Date: Accepted Date:

4 October 2018 7 December 2018 11 December 2018

Please cite this article as: M. Wasilewski, L. Singh Brar, Effect of the inlet duct angle on the performance of cyclone separators, Separation and Purification Technology (2018), doi: https://doi.org/10.1016/j.seppur.2018.12.023

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Effect of the inlet duct angle on the performance of cyclone separators Marek Wasilewski Faculty of Production Engineering and Logistics, Opole University of Technology, 76 Proszkowska St., 45-758 Opole, Poland, Tel. 48 693 28 62 61, E-mail: [email protected] Lakhbir Singh Brar Mechanical Engineering Department, Birla Institute of Technology, Mesra, Ranchi 835215, India E-mail: [email protected]

Abstract: This study analyzed the effect of the angle of the inlet duct bend on the separation efficiency and pressure drop in cyclone separators. The design of the inlet to the cyclone chamber is a significant parameter that has been analyzed to date only in a few research studies. Following the literature review of this subject, 20 bend angles (10 in the vertical plane and 10 in the horizontal plane) were proposed and analyzed by means of the computational fluid dynamics code Fluent V18.2. As a closure model to the Reynolds-averaged Navier– Stokes equation, the Reynolds stress model was used, as it solves the transport equations for Reynold’s stresses and the dissipation rate ‒ this model is capable of accounting highly curved streamlines prevailing inside the cyclone separators. The discrete phase model with one-way coupling was used, in which the trajectory of solid particles was calculated based on Lagrangian formulation. Conclusive results indicate that the bend angle (in both planes) marginally affects the collection efficiency (the maximum difference being 3.1%), whereas its effect on Eu is highly significant (the difference being 5,700%) ‒ all the comparisons were made with respect to the base variant at 0° angle. Keywords: Cyclone separator; Inlet duct angle, Separation efficiency; Pressure drop; CFD

Nomenclature a - height of the gas inlet

RANS - Reynolds average Navier–Stokes

b - width of the gas inlet

RSM - Reynolds stress model

B - diameter of the cyclone lower (dust) outlet

s – the source term

CD - drag coefficient

S - height of the outlet duct in the interior of the

CFD - computational fluid dynamics

cyclone

dp - diameter of a particle

SIMPLE - semi-implicit method pressure-linked

D - cyclone body diameter

equations

De - diameter of the cyclone gas outlet

t - time

De1 - upper diameter of the cyclone gas outlet

v - gas velocity

De2 - lower diameter of the cyclone gas outlet

vin - inlet gas velocity

DPM - discrete phase model

vi (j, k) - gas velocity to direction i (j, k)

Dij - the stress diffusion term

v’i (j, k) - fluctuating velocity to direction i (j, k)

F - area of cyclone inlet

vp - particle velocity

Fd - drag force g - acceleration of gravity

α – angle of the inlet duct contained in a vertical plane

Gi - inlet particle mass flow rate

β - angle of the inlet duct contained in a horizontal

Gij - equals Buoyancy Production

plane

h - height of the cyclone cylindrical section

γ - angle of the cyclone inlet head

H - height of the cyclone

ΔP - pressure drop in a cyclone separator

k - turbulence kinetic energy

δ - Kronecker factor

P – pressure

εij - the dissipation term

Pij – the shear production term

µ - viscosity of gas

PRESTO - Pressure Staggering Option

Πij - the pressure-strain correlation term

p' – dispersion pressure

ρ – density of gas

Qi – inlet gas volumetric flow rate

ρp – density of a particle

Re - Reynolds number

τij - the Reynolds stress tensor

1. Introduction Cyclone separators are commonly used in many industrial processes to separate solid particles from the transporting fluid (e.g., dust separation, recovery of raw materials). These devices are structurally simple, cost-effective in terms of manufacturing and operation, have a wide range of operating conditions (high temperature, high pressure, and corrosive environments), and are also nearly maintenance-free. Cyclone separators are used in many industrial sectors, including energy, fuel, chemicals, production, forestry, and cement. They can be applied in typical dust separation processes related to air protection as well as in technological processes (pneumatic conveyance, drying, calcination, or heating). Cyclonic flows constitute a double vortex: the outer (free) vortex where fluid swirls down till the bottom and the inner (forced) vortex where the fluid is directed upward toward the cyclone exit—this resembles the Rankine vortex. The inner vortex exhibits a complicated flow pattern, and it is well known to precess at a small average distance from the cyclone axis. Such a 3D time-dependent motion of the vortex center leads to enhanced levels of velocity fluctuations in the core region [1] that affect the performance parameters of cyclone separators. Despite their simple structure, cyclone separators exhibit extremely complex fluid dynamics and flow patterns. The strongly rotational, turbulent flow of the two-phase mixture inside the devices is highly anisotropic. Consequently, even a carefully performed research on the subject may be burdened with some errors. The most popular research methods for cyclone separators include experimental studies [e.g., 2–4], computational methods based on analytic models (classical cyclone design) [e.g., 5–11], and the numeric modeling of flows (computational fluid dynamics, CFD) [e.g., 12–20]. The literature on this subject also features studies that apply genetic algorithms [e.g., 21–24] and neural networks [e.g., 23–27]. A

combination of several methods is also frequently used for studies on cyclone separators [e.g., 22–33], as it provides more precise and reliable results. Most studies on this topic have addressed the improvement in cyclone performance over the baseline models based on the geometrical parameters, including the geometry of the inlet [e.g., 34–38], the size and the shape of the vortex finder [e.g., 39–45], the configuration of the cylindrical and conical parts [e.g., 46–49] and the use of additional elements inside cyclone separators [e.g., 50–51]. The design of the inlet to the cyclone chamber is a significant parameter that has been addressed in only a few earlier studies. Bernardo et al. [35] performed numerical simulations on a cyclone suspension preheater with a scroll inlet that was installed in a cement plant. They assessed four inlet angles of the feeding duct, namely 0°, 30°, 45°, and 60°, and they reported an improvement in both collection efficiency and pressure drop. Furthermore, at the inlet angle of 60°, the separation efficiency increased by approximately 14% with almost 51% reduction in pressure drop as compared to those for the baseline model. In another study [52] on the traditional cyclone structure, the authors reported the critical inlet angle as 45°. Qian and Wu [53] conducted a study based on three inlet angles, namely 0°, 30°, and 45° and concluded that altering the inlet angle affected the flow fields and yielded better cyclone performance. It was further reported that the best results were obtained at 45° inlet angle where the total separation efficiency increased by approximately 3% and pressure drop reduced by 15% as compared to those for the conventional design. Yoshida et al. [54] conducted an experimental and theoretical study on the effect of the shape of the inlet duct on separation efficiency of solid particles and concluded that feeding the two-phase mixture into a cyclone separator at an angle improved separation efficiency as compared to that for a straight inlet. Sy [55] studied 12 different cyclone inlet angles and concluded that the configuration of the inlet had a considerable effect on the collection efficiencies.

Piemjaiswang et al. [56] assessed three angles of the inlet section, namely −45°, 0°, and 45°, and the obtained results indicated that the 45° angle showed the highest separation efficiency and the lowest pressure drop. Misiulia et al. [57, 58] studied the effect of the inlet angle on cyclone separators with a helical-roof inlet. In one of their studies [57], they evaluated 10 different inlet configurations and concluded that increasing the inlet angle reduced the tangent velocity and pressure drop. In their another study [58], they assessed five different inlet angles, namely 7°, 11°, 15°, 20°, and 25°, and reported that collection efficiencies increased with increasing inlet angles. They further recommended that the optimal inlet angle was 10°– 15° (for cyclone separators with a helical-roof inlet) for higher separation efficiencies with moderate pressure drop. In a different study, Su et al. [37] addressed alterations made to the inlet duct angle contained in a (horizontal) plane perpendicular to the cyclone axis. They compared three different geometries of an inlet in a square cyclone separator: a single inlet, a double inlet at 0° angle, and a double inlet at 45° angle. The obtained results indicated that for the double inlets, the 0° angle provided the highest separation efficiency and similar pressure drop as compared to those for the 45° inlet angle. In most industries, the ducts carrying the process gas stream from the plant to the cyclone chamber may not be a straight one; rather—depending on the location of the cyclone—it may encounter bends at several locations. Flowing fluids are known to experience pressure losses at bends—such bends also affect the flow pattern of the two-phase mixture. Furthermore, the turbulence created may cause momentum exchange between the two phases, which may influence particle dispersion. Second, it remains unclear how the mean flow and particle separation capability of a cyclone are affected by such bends. Abrahamson et al. [59] conducted a study on cyclone separators both with real installations and under laboratory conditions for upflow to horizontal bends, downflow to

horizontal bends, and bending toward the barrel and away from it. They concluded that an appropriate angle of the inlet duct bend may considerably improve separation efficiency. In particular, a downflow bend leading to a horizontal entry yields a higher separation efficiency than an upflow bend. Given an existing upflow bend, a similar improvement in efficiency can be made by installing a deflector plate from the top of the inlet duct. They recommended the use of a deflector plate mounted on the roof of the inlet pipe to force solids downward and away from the cyclone roof. They also suggested avoiding the use of upward bends leading into the cyclone. In addition, pipe bends that imparted a spin opposite to the rotation of the cyclone vortex also decreased separation efficiency. Consequently, the ideal inlet piping layout leading into a cyclone consists of a downward section slanting away from the cyclone axis, followed by a long horizontal section. The changes in separation efficiency were caused by a stronger or weaker radial penetration of the cyclone vortex by the incoming stream of coherent solid particles. The same idea—after allowing for the properties of the strand conveying in the inlet duct—could also give a new explanation for the commonly occurring rise in separation efficiency with solid loading and other cyclone phenomena. Zenz [60] stated that the only important factor regarding the layout of upstream piping was to have all pipe bends positioned far before the cyclone to achieve a uniform distribution of particles. Gauthier [61] observed an increase in separation efficiency with the length of a straight duct section leading to a uniflow cyclone; this finding was consistent with Zenz’s recommendation. With regard to the effect of downstream piping, Horvath et al., [62] observed that the flow of exiting gas around relatively large outlets of gas was more strongly affected by downstream piping than in the case of outlet pipes with a small diameter. In the present study, among several possible ways to connect the ducts and cyclone chamber, we consider the bends close to the cyclone inlet at a fixed location. Two aspects of bending of the ducts—based on the planes containing them—are accounted here: one along

the horizontal plane and the other along the vertical plane. In either case, apart from the baseline model that corresponds to the 0° angle, 10 different cases of bending of inlet duct on each plane are studied. For this purpose, we conducted a numerical study to investigate the effect of bend angle on the performance of cyclone separators. It is worth mentioning here that investigating different methods to reduce pressure drop inside the duct due to bends is not a part of the present study; instead, we focus on the counterintuitive effects of such bends on the overall performance of cyclone separators. The present work is summarized as follows: first, we define the flow systems that elucidate the details of cyclone geometry, followed by the number of design variables considered. Second, we perform validation of the simulation methodology and determine the dependency of the grid density on numerical predictions. Finally, we present the effects of duct bends on the collection efficiency and pressure drop in cyclone separators.

2. Materials and methods The aim of this study is to assess the effect of the inlet duct angle on the separation efficiency and pressure drop of cyclone separators. The study is based on the geometry of a cyclone separator used for clinker burning. This allowed for the modeling of real operating conditions of the device, which in turn, helped to minimize discrepancies between the results of numerical studies and data collected from industrial installations. Thus, the inlet ducts with 20 different angles—10 each for the bends in vertical and horizontal planes that feed the twophase mixture into the inlet of a cyclone—are proposed (apart from the conventional design). By using this real installation cyclone geometry, conducting a study on the effects of different duct angles is practically relevant, and the complete analysis is performed using the CFD approach.

2.1. The details of cyclone geometry and inlet duct angles The study is based on the geometry of a cyclone separator that formed a part of the cyclone suspension preheater used for clinker burning. Figure 1 and Table 1 show the geometry of the cyclone separator and its dimensions, respectively. In addition, Figure 1 shows the variations in the angle of the inlet duct contained in the vertical plane (α) and the horizontal plane (β), and all the details of the analyzed variants are presented in Table 2 wherein the former is addressed as v-variant and the latter as h-variant cyclone models. The obtained values of the separation efficiency and pressure drop for the inlet duct angle of the real installation (α=−38°; β=0°) formed the basis for the validation of the numerical model. The inlet gas volumetric flow rate was 36.1 m3/s, and the inlet particle mass flow rate was 16.7 kg/s. Table 3 summarizes the complete details of the real installation, and the particle size distribution is presented in Table 4. The proposed angles are based on the observations from the real industrial installations and on the comments of industry practitioners. For all test models, it was important to maintain constant values of the volumetric flow of the gas phase (Qi) and the mass flow of the solid phase (Gi); this enables a reliable comparative analysis and allows practical conclusions to be drawn from the study. Furthermore, this is especially important in cases where cyclones not only function as separators but also regulate technological processes (e.g., clinker burning, a process in which the flows of each phase affect the performance of an installation).

2.2. CFD studies 2.2.1. Gas flow governing equations For steady and incompressible fluid flow in cyclone separators, the Reynolds-averaged Navier–Stokes (RANS) equation is expressed as follows [14, 18, 31, 63]: (1)

(2) where i, j = 1, 2, 3 indicate the components in the Cartesian coordinate system, and the Reynolds stress tensor is given as follows: (3) In this study, the Reynolds stress model (RSM) is used as a closure model to solve the Reynolds stress tensor. Among all closure models for RANS, the RSM is currently the most popular and widely used turbulence model for flows involving high streamlined curvatures, such as that in cyclone separators. The transport equations for the RSM can be written as follows [18, 31, 64]: Π

(4) (5) (6)

Π

(7)

(8) 2.2.2. Particle motion governing equations In this study, solid particles are treated as a discrete phase and are tracked using the Lagrangian approach, whereas the fluid is treated as a continuous phase for which we use the Eulerian approach. Therefore, the cyclonic flows are better modeled using the Euler– Lagrange (E–L) approach. For the dispersed phase, the trajectory of each group of particles is predicted by adding the forces that affect it. In the E‒L approach, the equation for particle motion is given by [49] (9)

The difference between fluid velocity (v) and the particle velocity (vp), i.e. (v-vp), represents the slip-velocity. This difference in velocity leads to an unbalanced pressure distribution as well as viscous stresses on the surface of particles and forms the basis of drag force. The drag force per unit particle mass is given as follows [14, 17, 49, 65, 66]: ρ

(10)

The drag coefficient is described using the Schiller–Naumann drag model, which assumes the following values depending on the value of the Reynolds number (Re) [65]:

(11)

The Re for a particle is given by the following equation [33, 49]: (12) The DPM with a one-way coupling (stochastic tracking; maximum number of steps: 50,000; step length factor: 5) was used for the description of the dispersed phase and the solid phase comprising the particles with a diameter in the range between 2.5 µm and 500 µm. We account for 10 fractions of solid particles that corresponded to the real distribution of particles (the total number of particles for all fractions was about 1,850,000). Collisions between particles and the walls of the cyclone were assumed to be perfectly elastic (with the coefficient of restitution equal to 1) [40, 68]. The particles that reached the dust bin were considered as separated, and those leaving the cyclone through the vortex finder were considered as escaped [69]. The applied DPM model does not take into account e.g. particle agglomeration. The agglomeration of small particles may play an especially important role here. The mapping of these phenomena in the case of CFD study is difficult. It requires the use of additional models, which contributes to a significant increase in the load of calculation units.

2.2.3. Method of resolution The present study uses the finite volume method based on the CFD code Fluent V18.2 to model the flow field and to predict the performance parameters. The pressure—velocity coupling was performed with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm [33, 44, 65, 70], with the PRESTO pressure discretization scheme [16, 44, 45, 49, 70, 71]. The second-order upwind interpolation method was used to determine the representative samples of the constituent values on the surface of the control volumes. The unsteady solver was used with a time step of 0.000551 Tin (where Tin=D/vin is the integral time scale; D is the main body diameter of cyclone; and vin is the velocity prescribed at the cyclone inlet). The convergence criteria were set to 10-6 for the continuity equation and 10-3 for the other equations. The inlet velocity was 19 m/s with turbulence intensity set to 5% (a turbulence intensity of 1% or less is generally considered low and turbulence intensities greater than 10% are considered high [72, 73) and hydraulic diameter (Dh=(2∙a∙b)/(a+b)) of 1.31 m [72, 73]. The standard wall function was used to model the turbulent flow in the wall regions [49, 72]; the no-slip boundary condition was used for the walls [72]. 2.2.4. Analysis of computational mesh sensitivity The discretization of the computational domain into tiny control volumes is an important step in CFD as it greatly affects both the precision of results and physical runtime of the numerical calculations. In this study, the sensitivity of the computational mesh on performance parameters was analyzed with respect to the base variant. For this purpose, five different configurations of the computational mesh were proposed, and all the configurations with the nonorthogonal hexahedral mesh aligned well with the flow streamlines to reduce numerical diffusion (cf. Figure 2a). Figure 2b elucidates the comparison of tangential velocity for different grid resolutions at section Z2 of the base variant. The difference in the tangential velocity profiles

at level 1 and 2 mesh is larger, whereas beyond level 2 mesh, no appreciable differences are noted. The obtained values of separation efficiency, i.e., the Stokes number based on the cutsize (Stk50=((d50)2∙ρp∙vin)/(18∙μ∙D) [74] with d50 as the cut-off particle size, ρp as the density of the solid particles, vin as the inlet velocity, μ as the dynamic viscosity of the fluid, and D as the main body diameter of cyclone) and the Euler number (Eu=ΔP/(0.5∙ρ∙v2in) [74] with ΔP as the pressure drop based on static pressure measured across the inlet and outlet, ρ as the density of the fluid, and vin the inlet velocity), were compared to those collected from industrial installation. Table 5 presents the difference between the numerical predictions and the experimental data. Beyond the first and second levels of the mesh, there was no appreciable difference in the performance indicators. Mesh levels 3–5 yielded similar results for separation efficiency (η), Stk50, and Eu (cf. Table 5). The research process was carried out on the computing cluster equipped with Intel E5–2697 v3 processors (the amount of memory in the node: 128 GB). The range of total CPU running time for individual variants was as follows: (1 − 1.45)∙106 Tin; (2 − 1.67)∙106 Tin; (3 − 1.84)∙106 Tin; (4 − 1.98∙)106 Tin; and (5 − 2.36)∙106 Tin, respectively. With increasing mesh density, the changes in the values of the analyzed parameters were insignificant, while this translated into a significant increase in the calculation time. Thus, considering the accuracy and computational load, the mesh topology adopted for level 4 mesh (Figure 2a) was selected as a reference for the rest of the models.

3. Results and discussion The present study analyzed the obtained results for two parameters describing the effectiveness of a cyclone separator, i.e., the separation capability and Eu. To properly interpret the obtained values of these parameters by using CFD, it is necessary to analyze flow inside the cyclone separator. Thus, the following flow parameters were analyzed: mean tangential velocity, mean axial velocity, mean static pressure, mean turbulent kinetic energy

(TKE), and vortex core shape. This would facilitate to understand and estimate the effects of geometrical changes (for each angle of the inlet duct bend) near the cyclone inlet on the flow field inside the cyclone separator.

3.1. The performance of the cyclone separator 3.1.1. Separation efficiency 3.1.1.1. Overall separation efficiency The separation efficiency is a key parameter that describes the effectiveness of a cyclone separator. Figure 3 shows the obtained values of η (to the left) and Stk50 (to the right) for different bending angles of the inlet duct. The results indicate that the angle of the inlet duct bend affects the separation efficiency, with the maximum difference being 3.9% for the inlet duct bending on the vertical plane. For the bends confined to the vertical planes (vvariants), feeding solid particles from the top yielded higher values of separation efficiency. Feeding a two-phase mixture from the top directs both phases downward inside the cyclone (limiting flow in the upper areas of the inlet and the roof of the cyclone separator), thus providing a better downward penetration. In the range −90°≤α≤90°, η decreases with the increase in the angle from −90° to −45° and, thereafter, it increases with the increase in the angle from −45° to 30°. A mild reduction in η was noted with the angle ranging from 30° to 45°, and thereafter, it increases with the increase in the angle from 45° to 90°. In general, for −90°≤α≤0° and 0°≤α≤90°, a local minimum in η was observed at α=±45°, which is an interesting observation. In turn, for changes in the bend angles confined to the horizontal plane (h-variants), feeding the particles along the direction of the rotation of the particles inside the cyclone separator was found to be a better solution for angles greater than 0°. This allowed for a larger stream of solid particles to be directed into the area of the cyclone walls, and thus provided a

better penetration of particles in that direction. We observed higher values of η for all bend angles α, β > 0° than for the angles α, β < 0°; the only exception was β = −90° angle, and this was more likely due to the side wall of the inlet duct reflecting clusters of solid particles, thus changing the direction of the flow. In the h-variant, the maximal difference between the obtained values was 2.8%. 3.1.1.2. Partial collection efficiency To fully analyze separation efficiency according to the inlet bend angle, fractional separation efficiency for particles of a given diameter should also be considered. The fractional separation efficiency provides detailed information on the collection efficiency as a function of particle size and is commonly referred to as the grade efficiency curve (GEC). Figure 4 presents the GEC for each variant, wherein all curves have the shape of a flattened S. For the smaller particles with Stk = 0.00028, the obtained values of separation efficiency were the least and were not affected by the angle of inlet duct (with an exception at β = −90°). For Stk = 0.00028, the highest values in the v-variants were obtained for the bend angles of α = 15° and 30°. The highest values in the h-variants were obtained at β = −45° and −30°. A similar trend was observed for particles with Stk = 0.00256; the maximal value of separation efficiency was obtained for the h3 model (9.5% and 33.7%, respectively). Similar values were noted for the v8 model (8.2% and 33.2%, respectively). The subsequent size of solid particles showed a similar trend as that for the total value of separation efficiency: an increase in the duct bend angle—regardless of the plane—led to a marginal increase in the fractional separation efficiency. For the v-variant cyclones, feeding particles from the top yielded better values of separation efficiency; for the h-variant models, feeding solid particles along the direction of rotation in the cyclone also improved separation efficiency. Furthermore, it can be elucidated from Figure 4 that for α = ±90° and β = ±90°, the large-sized particles (i.e., with size above Stk50) undergo better separation.

3.1.2. Pressure drops The other parameter describing the effectiveness of a cyclone separator is pressure drop that is highly sensitive to the cyclone geometry and its working conditions. Part of the resulting pressure losses are due to energy dissipation and the turbulent stresses associated with the rotational motion; moreover, these losses are also caused by the constriction and expansion of the fluid flow at the outlet and inlet, respectively [75]. An analysis of the obtained results indicates that the angle of the inlet duct significantly affects Eu. It was observed that Eu increased with an increase in the angle (both for the v- and h-variants). Figure 5 indicates that Eu number increases once a critical value of the angle is reached, which is α = −30° for vvariants and β = −45° for h-variants. For the v-variants, the behavior of Eu—though not symmetrical—is comparable at α = ±90°. On the other hand, for h-variant models, Eu increases significantly with the increase in angle β, particularly at β = 90°. To analyze the effect of inlet angles on the obtained values of pressure drop in greater detail, we consider two additional zones inside the cyclone separator (as elucidated in Figure 6). Eu1 signifies the pressure loss inside the inlet duct due to the bend, and Eu2 elucidates the pressure loss inside the vortex finder (due to high swirl intensity). The analysis is complemented by Table 6, which presents the percentage changes in relative Eu (Eq. 13) for individual variants in the inlet region (Eu1) and the gas phase outlet zone (Eu2) with respect to the 0° angle. (13) Eur is the relative value of Euler number of all models with respect to the standard cyclone variant. Here, x represents the cyclone variant and n represents the model number. For instance, x = v and n = 2 indicate the v-variant cyclone model v2 and x = h and n = 2 indicate the cyclone model h2.

In the inlet duct, dimensionless pressure drop (Eu1) increased with an increase in the inlet angle of duct (regardless of the cyclone variant) because of increasing flow resistance. The greater the change in the fluid flow direction (relative to the 0° angle), the more intense is the increase in Eu1. Unambiguously lowest values of pressure drop were observed for angles close to 0°; this angle also showed the lowest pressure drop in the vortex finder area (Eu2). It was observed that the difference in Eu1 is the largest in h-variant for β = 90°, where it increases by more than 5,700%. For v-variants, at α = 90°, Eu1 increases by more than 4,200%. It is worth noting that the increase in Eu1 is highly significant for the negative values of angle (β<0°) than for the corresponding positive values of angle (β>0°). The presented values of Eu1 parameter confirm that the inlet region of the cyclone separator is of key importance with regard to the pressure drop. Differences in the obtained values of the Eu2 parameter were much smaller (maximum 24%) than Eu1. 3.1.3. Summary of the performance of cyclone separators Table 7 presents the percentage change in the performance parameters of the cyclone separator, namely Eu, η, and Stk50, for different angles of bend in the inlet duct. From the presented data, the following conclusions can be drawn on the basis of comparison with the standard cyclone model vh6: 

With increasing angle of bend (α, β > 0°), a. Eu increases significantly. The increment is more than 62% in cyclone v11, and it reaches up to 111% in cyclone h11. b. η increases marginally. This difference is nearly 3% in both cyclone v11 and h11. c. Stk50 decreases moderately. The value decreases by 28.8% in cyclone v11 and by 20.5% in h11.



With decreasing angle of bend (α, β < 0°),

a. Eu varies dramatically. It decreases first from α = 0° to −30°, then increases slightly in v3, and thereafter increases by up to 57.7% for v1. For h-variant cyclones, Eu decreases from β = 0° to 60° nonmonotonically, and an abrupt increase in this value is observed at β = −90°. b. η decreases from α = 0° to 60°, and a slight increase in this value is observed at α = −90°. A similar trend is observed for β = 0° to −60° and also at β = −90° c. Stk50 increases from α = 0° to −60° and decreases by 4.5% for v1 (α = −90°). In contrast, for h-variant cyclones, Stk50 increases from β = 0° to −15° and then decreases monotonically from β = 30° to −90°

3.2. Analysis of the flow field The performance parameters of cyclones have already been discussed. We now present the flow field details to further elaborate our understanding and relate it to the obtained values of performance parameters of the analyzed variants. Therefore, in this section, we present the contour plots (on the Y = 0 plane) as well as radial profiles of the mean static pressure, mean tangential velocity, mean axial velocity, and TKE. 3.2.1. Mean static pressure The first two rows of Figure 7a present the contour plots of mean static pressure normalized with density multiplied with the square of velocity at the inlet. The figure shows that the low—pressure zone in each variant is located near the forced vortex region (central area). In contrast to the forced vortex region, the free vortex region seems to be more affected by the bends provided near the inlet duct. Figure 8a presents the x-y plots of mean static pressure at axial locations Z/D = 1.0 and 2.0 for all cyclone variants. In all cyclone models, the static pressure decreases radially from the wall to the center due to the high-intensity swirling field induced by the swirl flow. Over a wide range of angles (α = −90° to 90°), the wall static

pressure is the maximum at α = ±60° and ±90°, whereas, for all other angles, a slight variation is observed. On the other hand, with β ranging from −90° to 90°, the wall static pressure is the maximum at α = ±45°, ±60°, and ±90° angles. In particular, in comparison with the baseline model, the wall static pressure is increased for all inlet duct bends. Second, at α = ±90° and β = −90°, the wall static pressure is comparable quantitatively, whereas for β = 90°, the difference is quite large (this also holds for β = 60°). Further, with positive increment in the angle β, the low—pressure region confined to the vortex core shows a marginal shift in the upward direction. In general, with bending of the inlet duct, the outer vortex region experiences a much larger variation in static pressure than the forced vortex region. 3.2.2. Mean tangential velocity Tangential velocity is one of the key parameters characterizing the performance of cyclone separators. This is because it significantly affects the centrifugal force and, consequently, the separation efficiency. On the one hand, a higher tangential velocity magnitude aids in better separation efficiency due to a strong centrifugal force field; however, on the other hand, the high-intensity swirl results in higher pressure losses—the latter being highly sensitive to the tangential velocity than the former. The contour plots of mean tangential velocity presented in Figure 7b are similar for all considered cyclone variants. Figure 8b shows two regions: an external region resembling free vortex flow and the core region resembling the forced vortex flow; both these regions together constitute the Rankine vortex. At Z/D = 1.0, the slope of tangential velocity in the core region is nearly the same for all values of α and β; the only difference was observed in the peak values of the local maxima or minima of tangential velocity. However, at Z/D = 2.0, a slight difference was observed for different angles of the duct bend in the forced vortex region. Compared with the forced vortex region, the outer vortex region undergoes noticeable changes at all angles. With increasing angles, for both α and β, the magnitude of tangential velocity increases significantly, thus

justifying the variations in pressure drop for different angles of the bend. The reason for marginal decrease in η (or increase in Stk50) from α = 30° to 45° is a slight decrease in the tangential velocity peak. Thus, it can be stated that the angle of bend significantly affects the tangential velocity distribution inside the cyclone separation space. 3.2.3. Mean axial velocity Axial velocity in cyclone separators the solid particles down in the near wall region. The axial velocity in the outer vortex is directed downward, whereas it is directed upward toward the vortex finder tube in the core region. The contour plots of mean axial velocity are presented in Figure 7c. Differences in the structure were noted especially in the region confined to the diameter of the vortex finder and in the conical part of the separator. The effect of the change in the angle of bend on the axial velocity is shown in Figure 8c. The shapes of profiles for all bend angles at both axial locations resemble an inverted W profile (which is the typical pattern observed in most of the cyclone separators). The axial velocity in the external vortex area is negative (downward flow), and it increases in the radially inward direction until it reaches the maximum value corresponding to the diameter of the vortex finder. At a small average distance, near the axis of the cyclone separator, the area of zero axial velocity is located. At Z/D = 1.0 and 2.0, the axial velocity values at the cyclone axis are negative. The obtained profiles in the axial location Z/D = 1.0 are more “flattened,” and the differences for individual bend angles are not remarkable. Marginal changes in the profiles were recorded for α = 60° and 90°. It is worth noting that for the abovementioned four variants, no negative values were noted in the vortex core region at Z/D = 1.0. However, significant differences for individual bend angles in axial velocity profiles were noted for the axial location Z/D = 2.0 (located in the region confined to the vortex finder). Changes in the bend angles not only led to changes in the location of the minimum and maximum values, but these changes also influenced the shape of the profiles. The largest differences in profiles were recorded for α, β

= ±60°, and ±90°. The maximum values of axial velocities were obtained at α, β = ±45°. In turn, for the highest values of the bend angles α, β = ±90°, the minimum (negative) value in the free vortex region clearly increased. 3.2.4. Mean TKE The intensity of turbulence is, in general, expressed in terms of TKE, and it represents the strength of the turbulence in any flow. Thus, it is an important parameter, and it could affect the mixing (and hence the dispersion) of the discrete phase matter near the duct bends as well as the separation space inside cyclone separators. Figure 9 shows the contours of mean TKE for the studied variants. The maximum intensity of turbulence for all cases exists in the regions both upstream and downstream of the vortex finder lower lip. This could be typical due to the sudden contraction in the path of flow, which causes greater variations in the velocity field. Increase in TKE is more pronounced in h-variant cyclones (it is largest for β = 90°). As a common observation, the TKE in the separation space, upstream of the vortex finder, does not exhibit noticeable difference and, consequently, variations in collection efficiencies are also not large enough. The behavior of TKE is dramatic; for α = −90°, the TKE decreases, whereas in the upper region, i.e., Z/D = 2.0, it is maximum (cf. Figure 10). The same observation holds for α = −60°. In contrast, at β = 90°, a slight increase in TKE in the outer vortex region at Z/D = 1.0 is observed, whereas in the upper region, it is least in the core region and maximum in the outer vortex region. In general, the relative variations in TKE in the lower part of the cyclone are comparatively much smaller than those in the upper region. The TKE decreases in the core region and aggravates slightly in the free vortex region (with exceptions at α = −60° and −90°) in comparison with the baseline model. The radial profile analyzes of mean TKE reveal that changes in bend angles do not affect profiles in the lower region of the cyclone separator (axial location Z/D = 1.0), although

slight changes were noted for β = −90° and α = 90° (Figure 10a). In turn, significant changes can be seen in the case of profiles located in the axial location Z/D = 2.0 (located near the vortex finder). With inlet duct angles α, β = ±90°, the intensity of TKE in the free vortex region increased significantly. For all angles of inlet duct bend, TKE in the free vortex region is also affected as does in the forced vortex region. 3.2.5. Investigation of the flow field inside the inlet duct Because the largest changes in pressure drop values for individual variants were noted in the inlet region of the cyclone separator, it becomes important to analyze profiles of mean static pressure (Figure 11) and mean TKE (Figure 12) at locations Zin1 and Zin2 (cf. Figure 6). In general, changing the duct angle from 0° over a range of −90°≤α, β≤90° significantly influences the flow variables inside the inlet duct. The following observations were noted: 

In v-variants, the dimensionless static pressure profiles (cf. first two columns of Figure 11) show the lowest pressure in the baseline model, and for the other models, this value increases with the increase in the duct angle on either side. In particular, at α = ±60° and ±90°, this difference is significant. A similar explanation holds for h-variants (cf. third and fourth row of Figure 11).



In v-variants, the normalized TKE profiles (cf. first two columns of Figure 12) does not reflect noticeable variations along the location Zin1. This variation is significant along Zin2, especially at α = ±60° and ±90° due to increased velocity in the crosssectional area above and below Zin2. A similar explanation holds for h-variants (cf. third and fourth row of Figure 12).

3.2.6. Vortex core One of the methods for presenting the vortex core is to use the λ2 criterion—a method that allows the vortex core to be presented through a 3D iso-surface. The method is based on the hessian of pressure, which constitutes the negative values of the second eigen value of the

symmetry square of the velocity gradient tensor. A vortex core is given by a region that relates to these negative λ2 values. Because a strong vortical structure is associated with lowpressure, the absolute value of λ2 is related to vortex intensity [74, 76]. Figures 13 and 14 show the vortex core region based on the λ2 criterion (level set to 0.165 and colored with velocity magnitude) for the v- and h-variants, respectively. The vortex core shape and spatial location do not reflect significant differences as there is no noticeable change in the tangential velocity profiles confined to the forced vortex region. However, for the extreme bend angles, a twisted rope-like structure started to develop. One observable difference is the shape of the inner vortex near the cyclone bottom, especially in cyclone variants v1, v11, h1, and h11.

4. Conclusion This study analyzed the effect of the angle of the inlet duct bend on separation efficiency and pressure drop in cyclone separators. Following a literature review of the subject, 20 bend angles (10 in the vertical plane and 10 in the horizontal plane of the bend) were proposed and analyzed by CFD. The obtained results were compared to those of the base variant at 0° angle. The angle of the inlet duct bend was found to significantly affect the Euler number, with marginal effects on the Stokes number.

The obtained results led to the following conclusions:

 The maximum difference noted in the overall separation efficiency was 3.1% for the vvariants and 2.8% for the h-variants with respect to the baseline model. The analysis indicated that bend near the inlet duct increased the chances for the particles to come closer to the cyclone walls.

 For bends in the vertical plane, feeding solid particles from the top provided higher values of separation efficiency (ensuring a better penetration of both phases into the lower areas of the cyclone separator). Separation efficiency increased with an increase in the angle, with the exception at α = 45°. The optimal angle was α = 90° (η increased by 3.1% and Stk50 decreased by 28.8% compared to the 0° angle). On the other hand, when the particles were fed from the bottom, the critical angle equaled α = −45°, as this value provided the lowest separation efficiency (η decreased by 1.2 % and Stk50 increased by 18.6%).  For changes in bend angles in the horizontal plane, feeding the particles along the direction in which the particles rotated inside the cyclone separator was a better solution for angles higher than 0°. This allowed a larger flux of solid particles to be directed toward the walls of the cyclone, thus ensuring a better penetration of the particles in that direction. In this case, the optimal angle also equaled α = 90° (η increased by 2.8% and Stk50 decreased by 20.5%). The only exception was at α = −90°; this is most likely due to the clusters of solid particles reflected from the side wall of the cyclone inlet duct that possibly change the direction of the flow.  In general, an increase in the bend angle (in both planes) led to an increase in the Eu number. The Eu number was found to increase after the angle reached a critical value, i.e., α = −30° for v-variants and β = −45° for h-variants. For the v-variants, the trend of the Eu number is comparable (albeit not symmetrically in both directions); the maximal increase in Eu, by 62%, was observed for α = 90°. On the other hand, for models with h-variants, Eu increased significantly with an increase in the β angle (maximal increase in Eu, by 111%, was observed for β = 90°).  The inlet area of a cyclone separator is the key factor for the value of pressure drop inside the inlet duct. The highest difference in the values of Eu (across the cross-sectional areas

attributed to the inlet and the bend) was an increase by 5,700% at β = 90° (compared to the 0° angle). For α = 90°, Eu increased by over 4,200%.

This research was carried out with the support of the Interdisciplinary Centre for Mathematical and Computational Modelling (ICM) University of Warsaw under grant no G71-5.

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List of Figures Fig. 1. Geometry of the cyclone separator. Fig. 2. Discretization of the computational area for the base variant - mesh 4 (a) and radial profiles of mean tangential velocity for the base variant of cyclone separator at axial locations - Z/D=2.0 (b). Fig. 3. Overall separation efficiency η (a) and Stokes number at cut-off size Stk50 (b) for each variant. Fig. 4. The grade efficiency curves for varying α (a) and β (b). Fig. 5. Euler number for each variant.

Fig. 6. Areas of the cyclone inlet and vortex finder with the lines Zn1 and Zin2. Fig. 7. Contour plots of mean static pressure (a), mean tangential velocity (b), and mean axial velocity (c) for the studied variants. Fig. 8. Radial profiles of mean static pressure (a), mean tangential velocity (b) and mean axial velocity (c) for the studied variants, at locations Z/D=1.0 and Z/D=2.0, respectively. Fig. 9. Contours of mean turbulent kinetic energy for the studied variants (a - for varying α; b - for varying β) of cyclone separators. Fig. 10. Radial profiles of mean turbulent kinetic energy at axial locations Z/D=1.0 (a) and Z/D=2.0 (b). Fig. 11. Radial profiles of mean static pressure at locations Zin1 (a) and Zin2 (b). Fig. 12. Radial profiles of turbulent kinetic energy at locations Zin1 (a) and Zin2 (b). Fig. 13. The vortex core representation based on λ2 criteria at level 0.165 in cyclone separators for varying α. Fig. 14. The vortex core representation based on λ2 criteria at level 0.165 in cyclone separators for varying β.

List of Tables Table 1. Geometrical dimensions of base variant cyclone separator. Table 2. Variants of the applied modifications. Table 3. Euler number, overall separation efficiency and flow parameters included in the CFD study. Table 4. Particle size distribution. Table 5. Characteristics of the CFD meshes. Table 6. Characteristics of the local values of the Euler number in relation to variant vh6. Table 7. Variations in the Euler number, overall separation efficiency and Stokes number w.r.t. the standard inlet configuration.

Table 1. Geometrical dimensions of base variant cyclone separator.

Dimensions*

α a/D

b/D

S/D B/D De1/D De2/D H/D

h/D

L/D

L1/D

γ

L2/D

[-] Values

β

[°] [°] [°] 0.58 0.284 0.58 0.16 0.507 0.58 2.71 1.71

0.58 0.725 0.725 -38 0 180

*

All geometrical parameters are normalized with cyclone diameter, D=3.45m

Table 2. Variants of the applied modifications.

Symbol Vertical angle α [°]

v1

v2

v3 v4 v5 vh6 v7 v8

-90 -60 -45 -30 -15

0

15 30

v9

v10 v11

45

60

h9

h10 h11

45

60

90

Symbol Horizontal h1

h2

h3 h4 h5 vh6 h7 h8

angle β [°] -90 -60 -45 -30 -15

0

15 30

90

Table 3. Euler number, overall separation efficiency and flow parameters included in the CFD study.

Eu

5.38

Overall separation efficiency, η

90.01 %

Flow parameters Gaseous phase

Solid phase

Qi

36.1 m3/s

Gi

16.7 kg/s

ρ

1.225 kg/m3

ρp

2750 kg/m3

Table 4. Particle size distribution.

Stk [-]

0.00028 0.0026 0.010 0.018 0.041

0.073 0.164 0.454

1.82

11.4

5.49

26.15

11.47

Volume fraction

0.05

1.10

5.09 16.54 8.90

9.39

15.81

[%]

Table 5. Characteristics of the CFD meshes.

Industrial Mesh 1

Mesh 2

Mesh 3

Mesh 4

Mesh 5

install. result

Total number of elements

306050

384602

483211

522426

620107

Overall separation efficiency [%]

87.8

88.0

88.2

88.4

88.5

The difference between the industrial installation result [%]

2.5

2.2

2.0

1.8

1.7

Stk50

0.0139

0.0138

0.0133

0.0130

0.0128

The difference between the industrial installation result [%]

9.7

8.4

4.7

2.3

1.1

Euler number (Eu)

4.88

4.97

5.02

5.15

5.27

90.01

0.0127

5.38

The difference between the industrial installation result [%]

9.2

7.7

6.7

4.3

2.0

CPU running time 1.45∙106∙Tin 1.67∙106∙Tin 1.84∙106∙Tin 1.98∙106∙Tin 2.36∙106∙Tin (Tin=D/vin) = 0.1816 sec

Table 6. Characteristics of the local values of the Euler number in relation to variant vh6.

Cyclone

% difference in

% difference in

variants

Eu1*

Eu2*

v1

4250

16

v2

1700

7

v3

383

7

c4

83

5

v5

33

7

vh6

-

-

v7

33

9

v8

117

1

v9

450

3

v10

1817

3

v11

4283

10

h1

5550

20

h2

2150

14

h3

433

7

h4

117

1

h5

17

12

vh6

-

-

h7

50

10

h8

217

8

h9

717

9

h10

2317

14

h11

5733

24

* % changes in all parameters are calculated based on the base variant vh6.

Table 7. Variations in the Euler number, overall separation efficiency and Stokes number w.r.t. the standard inlet configuration. Changes in parameters* (%) Eu η Stk50

Variants of the applied modifications v1 57.7 0.3 4.5

v2 15.9 -0.6 14.5

v3 -1.0 -1.2 18.6

v4 -3.3 -0.6 12.5

v5 -0.3 -0.4 7.8

vh6 -

v7 2.3 0.4 -5.0

v8 6.2 1.7 -19.3

v9 14.6 0.9 -6.3

v10 32.9 2.0 -19.3

v11 61.9 3.1 -28.8

h9 26.2 1.8 -18.2

h10 66.3 2.0 -13.5

h11 111.2 2.8 -20.5

Variants of the applied modifications Eu η Stk50 *

h1 53.3 1.7 -18.8

h2 8.4 -0.2 -6.9

h3 -6.6 0.3 -21.6

h4 -2.5 -0.3 -0.6

h5 -1.3 -0.2 1.3

vh6 -

h7 0.8 0.4 -6.3

h8 7.9 1.0 -10.5

% changes in all parameters are calculated based on the base variant vh6. Negative values indicate decrease in the performance indicators and vice versa.

Highlights: 

A large (20) number of bend angles of the inlet duct of cyclone separators were studied.



The angle of the inlet duct bend significantly affects pressure drop and separation efficiency.



Feeding solid particles from the top yielded higher values of separation efficiency.



The maximal difference in the overall separation efficiency between the proposed angles was 3.9%.



The pressure drop increased as the bending angle increased.

Graphical abstract