Characterization of multiphase gas-solid flow and accuracy of turbulence models for lower stage cyclones used in suspension preheaters

Marek Wasilewski ,Stanis?aw Anweiler ,Maciej Masiukiewicz

1 Faculty of Production Engineering and Logistics,Opole University of Technology,76 Proszkowska St.,45-758 Opole,Poland

2 Faculty of Mechanical Engineering,Opole University of Technology,76 Proszkowska St.,45-758 Opole,Poland

ABSTRACT This study involved the analysis and characterization of the multiphase flow phenomenon inside the lower stage cyclone separator used in the clinker burning process.The analysis was performed using both CFD and experimental research methods.Very few studies are devoted to such types of cyclone separators,which in addition to their basic functions are also responsible for the technological process.Due to the atypical working conditions of these cyclone separators,they are characterized with a complex geometry,which significantly differs from that of the traditional separators.Furthermore,the evaluation of the accuracy and level of reliability of the two models of turbulence closure—k-ε RNG and RSM(RANS),and the LES.The results obtained led to the conclusion that for the lower stage cyclone separators,the LES model proved to be the most accurate (both in the case of forecasting the separation efficiency and pressure drop).The performance parameter (in particular the separation efficiency) values obtained for the RSM model were also characterized by high accuracy.The k-ε RNG model was characterized by significantly larger deviations.

Keywords:Cyclone separators Separation Multiphase flow CFD Pressure drop Clinker burning

1.Introduction

Since the introduction of the dry method,which implemented an external heat exchanger,cyclone-based systems have become an inseparable part of the thermal processing of the raw meal in the cement clinker burning process [1-3].Cyclone separators with a series of supply lines constitute an external heat exchanger—a heat exchanger tower.The total height of the tower is usually between 80 m and 120 m[4-6]and is determined by the cyclone separators’geometry,the length of the vertical conductors,and the location of the calciner.In the heat exchanger tower,exhaust gases from the combustion processes are used to heat the raw material and the heat exchange is of the suspension countercurrent nature.The heating process is done in three to five stages and each stage increases the temperature of the particles by 150-250 K [7,8].The temperature of the heated particles ranges from 1000 K to 1100 K [2,3,8].

The overall separation efficiency of cyclone separators used in the cement clinker burning process ranges from 70% to 95% [1-3].Variable conditions prevail inside the exchanger tower depending on the stage,and accordingly require different cyclone separator designs.The highest values of separation efficiency are achieved in the first-stage cyclone separators[1-3,8-10].First-stage cyclone separators are characterized by smaller dimensions,which maximize the separation efficiency (reduce raw material losses),and a cone-shaped vortex finder is often used instead of a cylindrical one.However,in the cyclone separators at the lower stages,the ratio of the length of the cylindrical part to the conical part decreases—smaller lengths of the vortex finder are used to reduce the pressure drop(negative effect is the decrease in the separation efficiency:70%-85%).The lower stage (low-pressure—LP) cyclones used today are originally developed by FLSmidth in the 1980s.In comparison to the previous designs of lower cyclone separators,they allow the pressure drop to reduce by 40%-50% [1,11].LP cyclone separators have an inlet at an angle of 270°as well as larger gas inlet and outlet surfaces [11,12].The dimensions of the vortex finder have also undergone changes—the length has decreased and the width has increased.Because the separation efficiency is less than 100%,the internal recirculation of the raw material takes place in the exchanger tower.At lower stages,the internal particle stream is at least 40%larger than the mass stream at the inlet to the first-stage cyclone separators.This phenomenon is undesirable because it leads to an increase in the pressure drop(additional friction)and disturbs the heat balance(the heated raw material moves in an undesirable direction (upward),which reduces the thermal efficiency of the system).

After analyzing the available literature and patent resources,it can be concluded that research on the subject of cyclone separators that is applicable to the clinker burning process is limited.In particular,there are no exact geometrical data for cyclone separators at individual stages.This is most likely because companies producing such separators protect information about their projects.A few researchers have provided geometrical dimensions used in their studies.For example,Bernardo et al.[13]reported the geometric proportions of the cyclone separators they tested.Similar proportions,except for the size of the inlet,were reported by Bhatty[7].Zhang et al.[14]referred to the body diameter of the cyclone without defining specific dimensions.Mikulcic et al.[15]defined the characteristic dimensions of the cyclone separator being tested.In addition to the analysis of the basic parameters (pressure drop and separation efficiency),they took into account the chemical reactions taking place in the clinker burning process.Mariani et al.[16]presented an instance of optimization of the lower stage cyclone separators.They presented several optimization methods.In addition,based on CFD research,they took into account the heat exchange process.Kashani et al.[17]used CFD research and the method of genetic algorithms to optimize the Hurriclon separator geometry.These types of separators are often used in first-stage cyclones of the heat exchangers used in the dry method used for clinker burning.Wasilewski and Duda [3]proposed structural guidelines for first-stage cyclone separators.Based on these guidelines,Wasilewski and Brar [18]analyzed a case study.Analyzing the available geometric data,they concluded that these cyclones diverge significantly from the Stairmand standard cyclones.Often,the geometrical dimensions of a cyclone separator depend to a large extent on the individual parameters of the cement clinker installation.The performance characteristics and efficiency of cyclones used in the cement industry are in many respects similar to those used in CFB;several research groups have conducted research on this topic [7,19-21].To illustrate the geometrical differences between traditional cyclone separators and constructions used in the clinker burning process,the data available in the specialist literature on the geometrical relationships existing between individual structural elements are shown in Appendix A.Significant differences in values of these parameters can be noticed.There is also a noticeable difference between the first-stage and lower stage separators (e.g.,in the lower stages,the length of the cylindrical part has been limited—compared to traditional and first-stages separators).This is due to the fact that,among others,cyclones not only play the role of separators but also are locations for conducting the technological process.Therefore,the design of the cyclones directly affects the production capacity.Moreover,the flow rate of a solid phase(raw material)directly translates into the production capacity.Therefore,it is reasonable to increase the proportion of the solid phase depending on the thermal efficiency of the rotary kiln.Currently,in the cement-manufacturing plants worldwide,the proportion of solid phase ranges from 300 to 700 g·m-3of the gas phase.However,in the conventional highperformance cyclones,the share of the solid phase is much smaller(the vast majority of studies have reported the use of 100 g·m-3solid phase—usually it does not exceed 50 g·m-3in traditional cyclones).This high proportion of solid phase can lead to the phenomenon of excessive agglomeration of particles and accumulation in the lower region of the conical part of the separators in the lower stages [22].Because of this,a two-step conical part is often used (a solution not used in traditional cyclone separators).

Due to the rapid advancement in computer technology as well as access to increasingly efficient computing equipment and software,research based on the Computational Fluid Dynamics (CFD)method is finding wider application.Since the 1990s,CFD has been used in the optimization of cyclone separator geometry.Research concerned with the analysis of the flow inside the cyclone separator is linked with the necessity of mapping the turbulent flow,which is characterized by irregularity,vorticity,diffusion,and discontinuity.After analyzing the existing work in this field,it can be concluded that in the case of research on these devices,two methods were used:Reynolds average Navier-Stokes—RANS(k-ε RNG,Reynolds Stress Model — RSM) and Large-Eddy Simulation (LES).Choosing the right method of mapping the phenomenon of turbulent flow to a specific research process is a key stage in defining numerical research strategies.

The aim of this study was to analyze the flow phenomenon(characterized by high share of solid phase) in the lower stage cyclone separators used in the clinker burning process and to assess the accuracy and level of reliability of the CFD numerical models.This research was conducted using numerical flow modeling of the Reynolds average Navier-Stokes (RANS) model and the LES model.In case of the RANS model,two closure models were used:the k-ε RNG and RSM.The verification was conducted (in the range of values of pressure drop and separation efficiency of solid particles) based on experimental research.In addition,the following flow parameters were compared:mean tangential velocity,mean axial velocity,and mean static pressure for the tested models.

2.Experimental Studies

To perform this research,it was necessary to design an experimental system (Fig.1).The main element of this station was a cyclone separator model (Fig.2a) based on the geometry of the lower cyclone separator used in the clinker burning process.The model was made of acrylic glass (PMMA was the main component).Dimensions of the cyclone separator are presented in Fig.2b.The experimental system was additionally equipped with a gas pipe system (gas pipe,air exhaust fan with frequency converter),particle transport (particle feeder with a frequency converter,particle bin,filter),and measuring equipment (flow meter,pressure sensors+a differential pressure gauge).The study was performed for three gas volume flow rates (Qi=0.244 m3·s-1,u=12 m·s-1;Qi=0.295 m3·s-1,u=14.5 m·s-1;Qi=0.345 m3·s-1,u=17 m·s-1;ρ=1.168 kg·m-3) and solid mass stream of particles(Gi=0.129 kg·s-1;ρp=2750 kg·m-3).The particle size distribution,as measured using a Mastersizer 2000 laser particle size analyzer,is shown in Table 1.The pressure drop was determined by measuring the pressure difference between the inlet and outlet of the cyclone separator.Separation efficiency was determined as the difference between the mass of solid particles delivered to the system and the mass of separated particles (after each measurement series,the particles collected in the dustbin were subjected to granulometric analysis).Each experiment was repeated at least three times to ensure a relative error of less than 5%.Average values were considered for the analysis (each measurement series was performed three times).

3.CFD Studies

3.1.Governing equations for the continuous phase

3.1.1.RANS

The classical Navier-Stokes equation of the averaged flow,supplemented by the element containing the fluctuation components(the so-called Reynolds stress) can be presented in the following form [25]:

Fig.1.Schematic diagram of the experimental system:1—Gas inlet pipe,2—Flow meter,3—Particle feeder(frequency converter),4—Pressure sensors,5—Differential pressure gauge,6—Cyclone separator,7—Particle bin,8—Filter,9—Air exhaust fan (+frequency converter),10—Gas outlet pipe.

Fig.2.Schematic diagram of cyclone separator (a) and its geometrical dimensions [mm](b).

Table 1 Particle size distribution

The Reynolds stress tensor can be defined as follows [25]:

According to the Boussinesq hypothesis(used,among others,in the k-ε model),the notion of the coefficient of turbulent viscosity(μT) is introduced and it can be presented in the following form[25]:

Reynolds stress tensor introduces further unknowns,resulting in the use of the so-called closing turbulence models that bind turbulent stresses with other fluid properties.One of the most popular models,in this case,is the k-ε model,which uses the concept of the so-called turbulent viscosity.This model has several variations.One of the most popular is the k-ε RNG model.The changes concern the modification of,among others,the nature of the description of rotational flows and low Reynolds’ numbers.

The most developed model,binding the Reynolds turbulence stress tensor with the flow parameters based on the RANS equation,is the RSM model.It is based on the full equations of Reynolds stress balance [25-29].

Detailed information on the models presented above can be found in several published papers [28,30,31].

3.1.2.LES

The LES model is another approach to the issue of turbulent flow.It is a method of approximation of subscale turbulence properties.It enables the elimination of subscale whirls from the solution of the Navier-Stokes equation by means of “filtering”equations [32].

For the subgrid stress tensor,the appropriate (subgrid) model must be used.In properly modeled subgrid stresses,approx.20%of the energy of turbulent fluctuations may be included [33].One of the basic models is the model based on the use of turbulent viscosity.

A detailed description of the LES model and subgrid models can be found in a study [32].

3.1.3.RANS versus LES

All presented models have been successfully used in research studies on cyclone separators.There are several examples of studies using the k-ε and k-ε RNG models [34-36].Wilcox et al.[37]and Menter [38]have indicated that the k-ε turbulence model and its variants do not simulate a sufficiently strong rotating turbulent flow in cyclone separators due to the assumption of an isotropic turbulence structure.As a result,they cannot satisfactorily reproduce the flow and fully predict the functioning of cyclone separators [28,39-42].The RSM model (e.g.,[16-18,28,29,31,42]),which abandons the isotropic hypothesis,can reproduce the flow field much more accurately and determine the cyclone separators’efficiency,at a reasonable calculation time [43-47].Investigations are also increasingly being undertaken using the LES model[15,48-51].The LES model allows similar and even better quantitative compatibility (compared to RSM) with experimental data[52,53]to be obtained.

3.2.Governing equations for the dispersed phase

The Euler-Lagrange model(E-L)has been used to map the flow of the disperse phase;this has been performed in the ANSYS Fluent program as the Discrete Phase Model (DPM).The fluid phase is treated as a continuity by solving Navier-Stokes equations,while the dispersed phase is solved by tracing certain particle numbers(representative sample)[25,54,55].According to the E-L approach,the particle motion equation can be written as [18,25,54,56]:

The drag force (Fd) per unit particle mass is given as [52,58]:

The drag coefficient (CD) is described using the Schiller-Naumann drag model,which assumes the following values depending on the value of Reynolds number (Re) [57]:

For a particle with a straight shape immersed in Newton’s fluid,the drag coefficient depends on the Reynolds number of the particles,which is defined as [52,58]

The solid phase comprised particles with a diameter between 2.5 and 30 μm (Table 2).The trajectories of the particles that accounted for the gas turbulence caused dispersion through the Discrete Random Walk (DRW) [25,58].The one-way coupling(stochastic tracking;max.number of steps: 500000;step length factor:5) method was used to describe the dispersed phase.

3.3.Characteristics of CFD studies

In this study,the simulation was carried out using the commercial software ANSYS Fluent 18.2.The pressure-based coupled algorithm [25,58]was used to solve the finite volume method-based continuity and momentum-governing equations.The secondorder upwind scheme was applied to discretize the Reynolds stress transport equation,momentum,turbulent kinetic energy,and turbulent dissipation rate equations.Differential equations were solved using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm to accurately determine the coupling ofthe pressure and velocity fields while maintaining the continuity equation for the momentum [25,28,59].The Pressure Staggering Option (PRESTO) scheme was used to interpolate the pressure at the mesh faces [25,42,54].For the cyclone separator wall,a noslip assumption was adopted and the standard wall function was used to account for the fluid-wall interaction [25,46,54,60].The particle-wall collision was assumed to be fully elastic or partially elastic [61,62].The term of convergence was set at 10-6for the continuity equation and 10-3for the other equations.In CFD studies,the same flow conditions were used for both phases as in the case of experimental research.The unsteady solver was used with a time step of 0.0001 s.The research was carried out for two RANS models (k-ε RNG,RSM) and LES.This research was carried out using a computing cluster equipped with Intel E5-2697 v3 processors(the amount of memory in the node:128 GB).Table 2 provides detailed information about the established conditions for the CFD modeling.

Table 2 Details of CFD settings

Fig.3.Discretization of the computational area for RANS model (a) and LES model(b).

Discretization of the computational domain was based on the hexagonal mesh structure.Before choosing the density of the mesh,the analysis of the mesh sensitivity for five densities( 360436; 438777; 513142; 590915;and 666967) of the elements with the use of the RSM model was conducted.The maximum discrepancy for separation efficiency between the rarest and the densest mesh was 0.5% (86.4%;86.3%;86.5%;86.7%;and 86.7%,respectively) and 5% for pressure drop (682 Pa;690 Pa;700 Pa;714 Pa;and 720 Pa,respectively).A separate analysis was conducted for the LES model.Due to the fact that for this model,the computational domain required higher density,four mesh densities of the elements were proposed:( 962431;1 258358;1 513428;and 1666967).In this instance,for the pressure drop,the maximum discrepancy was 4% and the separation efficiency was 1%.These tests were performed for the inlet velocity u=14.5 m·s-1.Bearing in mind the small discrepancies in the results obtained among the various configurations of test meshes,a mesh with a density of 590915 was used for the RSM and k-ε RNG models (Fig.3a),whereas a mesh with a density of 1513428 was selected for the LES model (Fig.3b).These mesh densities guaranteed the convergence and reliability of the results while maintaining rational calculation efficiency.

4.Results and Discussion

4.1.Characteristics of performance parameters of cyclone separators

The values obtained by using the two research methods(experimental and CFD studies) were subjected to comparative analysis.The characterization was performed within the scope of the twoparameters that define the efficiency of cyclone separators:pressure drop and separation efficiency.The analysis took into account the influence of the inlet velocity (u=12 m·s-1;u=14.5 m·s-1;u=17 m·s-1) of the gas phase on the discussed parameters.

Table 3 Relative CPU time of the transient simulations for CFD models (for u=12 m·s-1)

When assessing the accuracy and level of reliability of CFD numerical models,the time of the computational process should be considered.Table 3 presents examples of calculation times(for inlet velocity u=12 m·s-1) for the three models tested.The presented data indicate that the LES model requires a much larger(about five times compared to the k-ε RNG model) computational effort.This is mainly because this model requires a more refined computational mesh.

4.1.1.Pressure drop

Considering the role of the structure of the tested cyclone separator(lower stage cyclones)in the heat exchanger tower,the pressure drop,in this case,plays a key role;it is a function of the cyclone geometry and its working conditions.It is designated as the pressure differences between the inlet and outlet of the cyclone.Part of the resulting pressure losses is related to losses inside the apparatus due to energy dissipation caused by turbulent stresses associated with the rotational motion.The remaining losses are caused by the constriction of the fluid flow at the outlet and the expansion at the inlet [63].When characterizing the pressure drop,it is reasonable to present the results obtained in the form of a dimensionless pressure drop,the Euler number(Eu)(Eq.(14)).Fig.4 presents the Euler number (and pressure drop)values obtained,from the test method,the turbulence model used,and the inlet velocity.Increase in the inlet velocity leads to an increase in the value of the Eu number,which is largely due to the intensification of the friction phenomenon around the walls of the cyclone separator thereby generating an increased pressure drop.Comparing the Eu curves obtained,we can see that they have a similar trend.Only for the LES model,an increase in the inlet velocity of up to the maximum value caused an increase in the deviation value.The resulting discrepancy is probably because the standard wall function used in the simulation does not adequately describe the interaction between the gas phase and the separator walls.Due to the varied turbulence of flow in the various areas of the separator(inlet walls,body walls,and vortex finder walls),actual gas-wall interactions at different locations inside the cyclone may not be represented well with one standard wall function.However,taking the computational efficiency and the obtained high compliance with measurements of experimental research into account,a single standard wall function was used in this study.

In order to determine the accuracy of the numerical models relative to the experimental investigations in terms of the Euler number,it was necessary to determine deviations;according to the equation:

Fig.4.Euler number (a) and pressure drop (b) for experimental and CFD studies.

The LES model showed the lowest deviation values.For velocity u=12 m·s-1,14.5 m·s-1,and the highest velocity 17 m·s-1,the deviations were 1.3%,1.2%,and 3.5%,respectively.In the case of the RSM model,the deviations were 3.9%,3.9%,and 4.4%,respectively.The k-ε RNG model was the least accurate (deviations 4.5%,4.9%,and 4.0%,respectively).The k-ε RNG model lowered the obtained values in contrast to the LES and RSM models,which were overstated.A detailed analysis of the pressure drop based on the mean pressure drops in the selected areas of the cyclone separator has been conducted in Section 4.2.

4.1.2.Overall separation efficiency

Another parameter that characterizes the performance of cyclone separators is the separation efficiency.Fig.5 shows the values obtained for overall separation efficiency and cut-off size diameter (d50),which determines the size of solid particles for which the separation efficiency is 50%.The shape of the obtained curves for all CFD models is similar to the curve obtained from experimental research.In the case of the d50parameters,the largest deviation values were shown on using the k-ε RNG model(u=12 m·s-1,8.6%;u=14.5 m·s-1,7.5%;u=17 m·s-1,7.1%).On the other hand,the LES model was the most accurate;the deviations were 1.7%,0.9%,and 1.0%,respectively.The RSM model also showed a high compatibility with the experimental method(3.4%,3.8%,and 3.0%,respectively).The LES and k-ε RNG models overestimated the overall separation efficiency,whereas the RSM model underestimated these parameters in comparison with the experimental studies.The deviation values were calculated based on Eq.(15) (the Eu parameter was replaced by d50).

Fig.5 shows that at a velocity of u=14.5 m·s-1,the obtained curves slightly change their profile.A similar trend can be observed in the case of the Eu curve and the pressure drop(Fig.4).This may be because cyclone separators,depending on their geometry and operating conditions,have an optimal range of inlet velocities.In case of cyclone separators of the lower stages used in the clinker burning process,the final geometry of the separator and the inlet velocity is adapted to the planned installation performance(should consider for example thermal efficiency of the rotary kiln,raw material humidity,and solid phase flow rate).In the case of the analyzed cyclone separator’s construction,the inlet velocity in the actual installation was found to be approximately 15 m·s-1.An increase in the inlet velocity above this value resulted in a less intensive increase in the separation efficiency than for velocities below 15 m·s-1.

4.1.3.Fractional separation efficiency

Fig.5.Overall separation efficiency (a) and cut-off size diameter (b).

The fractional separation efficiency is the measure of the efficiency in separating particular diameters of solid particles.It is often presented using the grade efficiency curve(GEC).It is a curve that describes the separation efficiency depending on the size of the particles.The GEC curve and the cut-off size diameter make it possible to determine the internal separation potential of a given cyclone construction in strictly defined conditions [36].Fig.6 shows the GEC for individual inlet velocities.All curves have the shape of a flattened S.The data presented confirm the tendencies observed for the overall separation efficiency.The smallest values of separation efficiency were recorded for particles with a diameter of 2.5 μm.Regardless of the research method as well as the inlet velocity,their separation efficiency was lower than 18%(minimum for 12RSM—9.6%;maximum for 17RNG—17.9%).This confirms the theory that particles of this type are not significantly separated in this type of mechanical separators.However,for particles with diameters of 15 μm,20 μm,and 30 μm,a separation efficiency of 100% was achieved.In the case of cyclone separators used in the clinker burning process,the GEC curve can be helpful for the process of raw material preparation before delivery to the exchanger tower.Proper preparation for the milling process (e.g.,optimization of the mill curve of the raw material) may lead to limiting the percentage of fine particles,and thus increase the separation efficiency in the entire cyclone suspension preheater system.

Fig.6.The GEC:(a) u=12 m·s-1;(b) u=14.5 m·s-1;(c) u=17 m·s-1.

Table 4 presents the deviation values (based on Eq.(15),Eu value was replaced with the obtained values of separation efficiency for individual particle diameters)in the range of separation efficiency for individual CFD models (including inlet velocities).Additionally,the LES and k-ε RNG models overstated the obtained values,while the RSM model decreased them.For particles with adiameter of 2.5 μm,an increase in velocity for all cases led to a significant increase in deviations.This tendency has not been recorded for larger particle diameters.In turn,in almost all cases,the increase in particle diameter led to a decrease in deviations.

Table 4 Values of deviations [%]for particular diameters and CFD models

4.2.Analysis of the flow phenomenon

For proper interpretation of the performance parameter values obtained for individual CFD models,it may be helpful to analyze the phenomenon of flow inside the cyclone separator.A uniform scale for individual parameters was used for the analysis.In addition,the values in the scale are expressed in the nondimensional form(the velocities are normalized by the inlet velocity,pressures are normalized by ρ·).

Fig.7.Contour plots of mean static pressure (a),mean tangential velocity (b) and mean axial velocity (c).

Fig.8.Example(u=17 m·s-1 LES)vortex core representation based on λ2 criteria at level 0.3 (a) and contours of mean turbulent kinetic energy (T.K.E.) (b).

The analyzed construction of the cyclone separator is characterized by an atypical geometry due to its functions.The limited length of the cylindrical part is designed to minimize the pressure drop in the cyclone separators of the lower stages of the exchanger tower.In addition,the use of a cylindrical vortex finder allows limited turbulence in this region (Figs.7,8b).The two-step conical part results from the high share of the solid phase,which may lead to the risk of excessive agglomeration and the occurrence of the socalled accretions and “avalanches”in the area of the walls of the separator(that is particularly important considering the high temperature inside the real installations).The geometry of the cyclone separator formed this way translates into the unstable shape of the internal vortex (Figs.7a,b,8a).An important fact is that these changes did not cause a sudden increase in the negative pressure(i.e.,below the atmospheric pressure),which developed in the core region(Fig.8a);hence,the chances of entrapment of separated out particles is reduced.The use a cyclone separator with cut roof did not lead to an increase in the turbulence in this region(Figs.7,8b),but it might have positively affected the limitation of reverse flow of solid particles.The role of the nonstandard inlet surface is to reduce the formation of the so-called accretions in this area.This configuration did not adversely affect the pressure distribution in the separator (Fig.7a).The only modification that can negatively affect the value of the pressure drop is the large angle of the inlet head(270°).Its task is to discharge more solid particles to the outer wall of the cyclone.This change increases the friction of the surface,which in turn leads to an increase in the pressure drop.

Fig.7a shows contour plots of mean static pressure.In all cases,the vortex core was found to be slightly helical with the pressure increasing radially outward.The contour shape of the mean static pressure for RSM and LES models is very similar;slightly higher values were obtained for the RSM model.The difference is most likely associated with higher mean tangential velocity values(Fig.7b).The 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.The higher the value of the radially directed centrifugal force,the more are the particles that are discharged into the vicinity of the wall boundary area of cyclone separator(and less entrained into the vortex finder).The contour distribution of tangent velocities is similar to the dynamic pressure distribution to a large extent.This is confirmed by the fact that this parameter is of great importance when considering the flow inside the cyclone separator.In turn,the contours of mean pressure,mean tangent,and axial velocities (Fig.7c) obtained for the k-ε RNG model differed from those obtained for the other two models;the values for the k-ε RNG model were much lower (particularly the mean static pressure).In this instance,the core of the internal vortex was much wider,especially in the vortex core region.The only zone in which higher values were recorded for this model(the mean axial velocity) was the lower vortex finder area (on the inlet side to the cyclone separator).

The presented contours of mean static pressure and mean tangential and axial velocities have the same distribution shape for different inlet velocities.They differ only slightly in values.This indicates that the changes in inlet velocity do not have a significant impact on the shape of the velocity distribution profile (only on values);indeed,the shape of the velocity profile is determined by the geometry of the cyclone separators.

To better illustrate the distributions of the analyzed flow parameters,Fig.9 presents radial profiles of mean static pressure,mean tangential velocity,and mean axial velocity at locations Z1/D and Z2/D.Based on the curves shown in Fig.9a,it can be concluded that the static pressure decreases radially from the wall to the center of the cyclone separator,regardless of the model used.The lowpressure zone appears in the forced vortex region (central region)due to intense vortex motion.The pressure gradient is greatest along the radial direction,while the gradient in the axial direction is limited.Comparing the profiles of mean static pressure for all cases,the overall shape of the profile is the same at different cross-sections,and the only difference is the numerical value of static pressure at various points.

For the RSM and LES models,very similar characteristics were obtained for both mean static pressure and mean tangential velocity.In the case of the LES model,slightly lower values of mean static pressure were observed.This model was also characterized by a minimal milder transition of the mean tangential velocity curve from the minimum to the maximum values in the area of the internal vortex core.This is the result of a smaller minimum and maximum values obtained for the LES model.As the distance from the axis of the cyclone separator increased,the curves for both models became almost identical.Analyzing the next parameter,the mean axial velocity(Fig.9c),one can notice significant differences in the values obtained for the RSM and LES models.The difference between the profiles obtained may be related to the phenomenon of unsteady oscillating flow by a precessing vortex core (PVC) in the central region.Derksen et al.[64]found that extrinsic flow phenomena,such as PVC,can be more accurately reproduced using the LES model.The axial velocity influences the movement of solid particles down the cyclone separator.Under the influence of the tangential velocity resulting from the cyclic structure of the cyclone,the solid particles are driven by the gas flow to rotate in the wall boundary area.At the same time,the axial velocity of the external vortex is also affected by this effect on the particles,moving them down.In the analyzed cases,the axial velocity in the external vortex area is negative (downward flow),while in the inner vortex regions the axial velocity is pointing upward to the vortex finder.

Regarding the static pressure contour,in this case,the curve for the k-ε RNG model also differs significantly those of the remaining two models.Considering the mean tangential velocities (Fig.9b)and mean axial velocities (Fig.9c),the k-ε RNG model (even with a“swirl dominated flow”)is unable to map a strong swirl flow field inside the cyclone separators.On comparing the shape of the curves for this model to other models,it is observed that it cannot predict the location of the maximum tangential velocity and downflow in the external flow region.In addition,it cannot reproduce the axial velocity in all areas of the apparatus.The conducted simulations show that the axial velocities are uniform in the internal flow region,while other models show that the axial velocity profile is characterized by a significant decrease in the central part,creating a profile that resembles a flattened letter“M”(defined as a pattern of axial velocity curve in cyclone separators).

5.Conclusions

The analysis of the multiphase gas-solid flow phenomenon in lower stage cyclones used in suspension preheaters showed that the nonstandard construction solutions applied,primarily led to limiting the pressure drop.This was because the exchanger towers of the clinker burning installation consisted of this type of cyclones in several stages (often also working in a dual system).This allowed a reduction in the electricity consumption by the tower fans.In addition,the applied modifications were designed to limit the negative effects of the technological process such as excessive agglomeration of particles and the formation of the so-called accretions in the region of the separator’s walls.

Fig.9.Radial profiles of mean static pressure (a),mean tangential velocity (b) and mean axial velocity (c) at locations Z1/D and Z2/D.

The comparative analysis confirms the effectiveness of the CFD method as a tool,which enables a proper characterization of multiphase flow occurring in atypical cyclone separators of lower stages used in the clinker burning process.Each of the applied numerical models made it possible to obtain consistency of results for parameters describing the efficiency of cyclone separators at a satisfactory level (deviations were within the limit of 10%).The results obtained allowed to state that in the case of lower stage cyclones,the LES model is the most accurate (in the case of forecasting,both the separation efficiency and pressure drop).The values obtained for the performance parameters (in particular the separation efficiency) considered for the RSM model were also characterized by high accuracy.Based on the analysis of factors characterizing the flow,the profiles obtained for these models were very similar.The RSM model slightly overestimated the maximum values of the mean static pressure and the mean axial velocity.The only significant difference was recorded for the mean axial velocity.This is most likely due to the phenomenon of unsteady oscillating flow by a PVC in the central region.The literature sources indicate that the LES model allows for more accurate mapping of this phenomenon.Both these models can be effectively used to estimate the performance and simulation of the main flow parameters.The k-ε RNG model is characterized by significantly larger deviations.

A separate aspect that should be considered before undertaking CFD research is the purpose and scope of the tests (including the time range)and available hardware resources(computing capacity of computer units).In the case of industrial research (aimed at optimizing a given performance parameter),when a shorter calculation time is required (and qualitative results are sufficient),the choice of the RSM model seems more reasonable.However,in the case of scientific research,with access to high-performance computing equipment,it is reasonable to use the LES model(especially in the case when the optimization of the computational mesh is additionally important).This allows valuable qualitative and quantitative results to be obtained.

Nomenclature

Dijthe stress diffusion term

DL,ijthe molecular diffusion term

dpdiameter of a particle

F area of cyclone inlet

Fddrag force

Fijwork done by the rotational motion of the system

Gbcoefficient the generation of turbulence kinetic energy due to buoyancy

Gijequals Buoyancy Production

Gkcoefficient the generation of turbulence kinetic energy due to the mean velocity gradients

g acceleration of gravity

k turbulence kinetic energy

P pressure

Pijthe shear production term

p’ dispersion pressure

ΔP pressure drop in a cyclone separator

S source component,defined by the user

s the source term

t time

ui(j,k)gas velocity to direction i (j,k)

u’i(j,k)fluctuating velocity to direction i (j,k)

upparticle velocity

YMcontribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate

αkreciprocals of the Prandtl number for k

δ Kronecker factor

εijthe dissipation term

μ viscosity of gas

μeffreciprocals of the Prandtl number for ∈

∏ijthe pressure-strain correlation term

Acknowledgements

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.

Appendix A

Geometric relations for various cyclone designs(D-cyclone body diameter;De-diameter of the cyclone gas outlet;De1-upper diameter of the cyclone gas outlet;De2-lower diameter of the cyclone gas outlet;h -height of the cyclone cylindrical section;H -height of the cyclone;Hc-height of the cyclone conical section;αg-angle of the cyclone inlet head,degree).