Effect of inlet area on the performance of a two-stage cyclone separator

Jihe Chen,Zhongan Jiang,,Bin Yang,Yapeng Wang,Fabin Zeng

1 School of Civil and Resource Engineering,University of Science and Technology Beijing,Beijing 100083,China

2 China Academy of Safety Science and Technology,Beijing 100029,China

Keywords:Two-stage cyclone Mass separation efficiency Pressure drop Taguchi method Particle concentration

ABSTRACT The cyclone separator is an important separation device.This paper presents a new type of embedded two-stage cyclone,which includes a 2nd-stage cyclone(internal traditional cyclone)with multiple inlets and a 1st-stage cyclone (outer cylinder) that unifies the 2nd-stage cyclone inlets into one inlet.The Taguchi experimental method was used to study the two-stage cyclone separator’s inlet area on its performance.Studies have shown that the increase of the 1st-stage cyclone inlet area and the increase in the number of 2nd-stage cyclone inlets(N)positively affect reducing the pressure drop and a negative effect on efficiency.It is recommended to use 2S (the original 1st-stage cyclone inlet area) of the 1st-stage cyclone inlet area and 2N of the 2nd-stage cyclone inlets when separating fine particles.Compared with a traditional cyclone,the pressure drop is reduced by 1303 Pa,the mass separation efficiency (Eq) is increased by 0.56%,and the number separation efficiency(En)is increased by 2.05%.When separating larger particles,it is recommended to use 2S of the 1st-stage cyclone inlet area and 4N of the 2nd-stage cyclone inlets.Compared with a traditional cyclone,although En decreases slightly,the pressure drop is reduced by 3055 Pa,and the Eq is increased by 0.56%.The research results provide new insight into the design of the cyclone.

1.Introduction

As a critical component of many equipment systems,the cyclone has been widely used in various industries [1–6].Lappleet al.[7,8] and Stairmand [9] conducted systematic experimental research on single-stage cyclones and obtained the influence of cyclone structural parameters and operating parameters on their performance.Finally,two optimally configured cyclone parameters were obtained,named the Lapple cyclone and the Stairmand cyclone,which provided theoretical guidance for subsequent cyclone design.To improve the cyclone performance,the scientists applied new technologies and methods based on the Lappleet al.and Stairmand cyclones to make various structural improvements.

The structural improvement mainly includes the optimization of each part of the cyclone’s parameters and accessories.Other scientists have connected several cyclones in parallel and series to increase the processing capacity and improve the cyclone performance.Although these improvements have achieved good results,they are more or less concerned with one thing but not the other.Either the efficiency is sacrificed to reduce the pressure drop,or the pressure drop is sacrificed to improve the efficiency.Yuet al.[10]proposed a new type of cyclone separator which nests an inner cyclone with a double-spiral inlet in an outer cyclone.Compared with the conventional Lapple cyclone,it has higher separation efficiency and a better symmetric flow field.The new cyclone’s pressure drop was only slightly elevated because of the low velocity in the outer cyclone.Chenet al.[11,12] also proposed a new two-stage cyclone separator with a simplified 1st-stage cyclone.Compared with the conventional Lapple cyclone,both the pressure drop and the separation efficiency were improved.Moreover,this two-stage cyclone can be used for particle classification.

There are large and small particles that need cyclone separation,large ones such as various seeds,and small ones such as PM2.5(particles smaller than 2.5 μm) [13–16].For large particles,a lowpressure drop can achieve high separation efficiency and save energy.For small particles,an improved cyclone separator is needed to improve the separation efficiency.For different particles,we have to optimize the two-stage cyclone.Adjusting the cyclone inlet size and structure can change the inlet airflow velocity,the particles’ centrifugal force,and the pressure drop and separation efficiency.Weiet al.[17] studied the effect of inlet size on axial velocity stagnation and separation efficiency.Gaoet al.[18] used the Reynolds stress model and Doppler particle analyzer to study the effect of inlet structure on cyclone separation performance.Wang and Leet al.[19,20] studied the effect of two cyclone inlets and four cyclone inlets on cyclone performance and obtained the same conclusion as Gaoet al.[18].The cyclone with symmetric inlets has better performance.However,none of them optimized the cyclone for particles of different particle sizes.

In this paper,based on the two-stage cyclone separator proposed by Chenet al.[11,12],we first applied the experimental analysis method to study the effects of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets on the performance of the two-stage cyclone when loaded with particles smaller than 10 μm.Then the Taguchi method was applied to find the optimal results of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets for different particle sizes.

2.Experimental

2.1.Materials

The common talc and coal powder are non-spherical particles and are more viscous.As the experiment proceeds,they will be deposited on the cyclone’s inner wall,causing the particle clustering phenomenon [12,16,21–25].The grinding particles are hightemperature molten spherical particles with small viscosity [26].We made some grinding particles in the lab.Fig.1 shows the SEM image of the grinding particles.Low viscosity and high sphericity of the particles can effectively reduce the phenomenon of particle deposition on the inner wall of the cyclone and improve the accuracy of the experiment.A homemade dust generator dispersed grinding particles.In our study,the inlet grinding particle mass concentration was (300 ± 15) mg?m-3.

The particle size distribution(PSD)of the polished particles was measured with an AeroTrakTM TSI 9306-V laser particle counter(TSI,USA).The measurements are the results of the number PSD,as shown in Fig.2.The total number of inlet particles is 799,332,000.The number of particles per particle size distribution can be calculated from Fig.2.It can be seen from Fig.2 that PM1(particles smaller than 1 μm)account for 82.17%of the total particles.This paper defines particles with a particle size of less than 1 μm as small particles.It shows that small particles account for a large proportion,consistent with the observation results in Fig.1(a).99.69% of the particles have a diameter below 10 μm(PM10).

Fig.1.SEM images of grinding particles:(a) molten spherical particles less than 2.5 μm,(b) molten spherical particles larger than 2.5 μm.

Fig.2.Grinding particles PSD.

2.2.Experimental equipment and parameters

The experimental setup is shown in Fig.3(a).The blower generates negative pressure,and airflow enters the two-stage cyclone from the inlet pipe.The PSD,concentration,and gas flow were measured inside the inlet pipe.Similarly,PSD and particle concentration were measured at the 2nd-stage cyclone inlets and outlet.Although the inlet pressure of the 2nd-stage cyclone is different,the default gas flow rate is unchanged according to the law of mass conservation.Therefore,it is not necessary to measure the gas flow at the 2nd-stage cyclone inlets and outlet.

Experimental research shows that the number of inlets affects the pressure drop and separation efficiency of the cyclone [4,27–29].The number of inlets directly affects the inlet area and thus the inlet air velocity.Fig.3(b) is a structural diagram of a twostage cyclone.The 1st-stage cyclone is an external cylinder,and the 2nd-stage cyclone is an internal small Lapple cyclone [7,8].When the 2nd-stage cyclone has multiple inlets,multiple interfaces are required,which is inconvenient to use.The two-stage cyclone with this structure can unify multiple inlets of the 2ndstage cyclone and reduce the pressure drop.Due to the large volume of the 1st-stage cyclone,the internal gas velocity is low,and only particles with a larger size can settle to the bottom of the 1st-stage cyclone when subjected to centrifugal force.Because of this,the 1st-stage cyclone can handle most of the larger particles.The smaller particles rise inwardly into the 2nd-stage cyclone with airflow.The 2nd-stage cyclone has a smaller volume.According to the law of conservation of mass,the airflow velocity is much larger than that of the 1st-stage cyclone.Even small particles can be subjected to large centrifugal forces,enhancing the particles’ separation effect.

Fig.3.Structural parameters of the experimental device and the two-stage cyclone:(a)experimental setup,(b)two-stage cyclone structure,(c)two-stage cyclone parameters and dimensions,(d) 2nd-stage cyclone and inlet number.

Fig.3(c)shows the specific dimensions of the structural parameters of the two-stage cyclone.Since the 2nd-stage cycloneDis 64 mm,while the widthband heightLeof the 2nd-stage cyclone inlets are 16,32 mm,respectively,the 2nd-stage cyclone can have a maximum of 6 inlets.The area of each inlet of the 2nd-stage cyclone is 512 mm2.All inlets have a width-to-height ratio of 1/2.For the convenience of subsequent expressions,the original 1st-stage cyclone inlet area is represented byS,in which the width is 16 mm,and the height is 32 mm.The number of the 2nd-stage cyclone inlets is represented byN.For example,when the 1ststage cyclone inlet area is 4 times the area of the 2nd-stage cyclone inlet,and it is recorded as 4S.At this time,the width and height of the 1st-stage cyclone inlet are 32,64 mm,respectively.The 2ndstage cyclone has two inlets,designated 2N.Fig.3(d)is the physical picture of the 2nd-stage cyclone and the inlet number.The same direction as the inlet pipe in Fig.3(a) isinlet.Looking down and clockwise,the inlets are ②,③,④,⑤and ⑥.The number of the 2nd-stage cyclone inlets can be reduced by blocking the 2ndstage cyclone inlets.

Adjust the blower parameters so that the entire experiment is performed at a gas flow rate of 128 m3?h-1.When the gas flow rate is 128 m3?h-1,even if the 1st-stage cyclone inlet area is 6Sor the number of 2nd-stage cyclone inlets is 6N,the airflow velocity entering the cyclone separator is 11.6 m?s-1,between the recommended 8–18 m?s-1[30].This will not only save energy but also ensure the efficiency of the cyclone.

2.3.Taguchi experimental design

Taguchi in Japan proposed the Taguchi method [25].The basic idea is to design product robustness into the product and manufacturing process by controlling the quality at the source to counteract the interference of a large number of downstream production or uncontrollable factors in customer use.Taguchi methods have been widely used in industrial process design.It is mainly used in development experiments to establish optimal conditions for a specific process using the minimum number of experiments possible [31–34].In this study,the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets were the influencing factors.The Taguchi method was used to find the optimal parameters for the 1st-stage cyclone inlet area and the number of the 2ndstage cyclone inlets for optimization.According to the previous analysis,the 2nd-stage cyclone has a maximum of 6 inlets.If the 1st-stage cyclone inlet area is too large,the separation efficiency of the 1st-stage cyclone would be greatly reduced,so the maximum area of the 1st-stage cyclone inlet would be set to 6S.To better predict the experimental results,four levels were selected for each factor,as shown in Table 1.Table 2 shows the variation of the 1st-stage cyclone inlet size with inlet area.The height and width of each 2nd-stage cyclone inlet are 32 and 16 mm,respectively,and do not vary with the number of the 2nd-stage cyclone inlets.

Table 1 Levels of the factors used in the experiment

Table 2 Variations of 1st-stage cyclone inlet size with inlet area

Pressure drop and separation efficiency are two important indicators of cyclone separators [12].They can be used to evaluate cyclone performance.The expression of the pressure drop is:

There are two kinds of separation efficiency:mass separation efficiency (Eq) and number separation efficiency (En).According to the formula for calculating the mass of spherical particles,the mass of particles with a particle diameter of 10 μm is 1000 times that of particles with a particle diameter of 1 μm.Large particles contribute much more to mass than to numbers [35].Therefore,when the PSD is broad and the number of small particles is large,theEqis not very descriptive of small particle separation.Eqdoes not represent the separation performance of a cyclone well.When the PSD is narrow,or the number of small particles is small,Enis not very descriptive of large particle separation,and it does not represent the performance of cyclones well.Based on the particles’actual situation,EqandEnshould be used to indicate the separation performance of the cyclone.Because the volume flow of the air passing through the cyclone is constant,Eqcan be expressed in particle mass concentration.DustTrak II Aerosol Monitor 8530 can measure PM1,PM2.5,Respirable dust,and PM10concentrations in the gas.Therefore,theEqof PM1,PM2.5,Respirable dust,and PM10can be calculated.The expressions forEqandEnare:

3.Results and Discussion

3.1.Influence of inlet area on the overall performance of a two-stage cyclone

When the volume flow is constant,the inlet area’s change directly affects the tangential velocity of the particles entering the cyclone.Tangential velocity plays a dominant role in particle separation.The particles settle by centrifugation from inside to outside according to the action of tangential velocity [36].Fig.4 shows the effect of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets onEqandEnof the two-stage cyclone.

It can be seen from Fig.4 that theEqof the 1st-stage cyclone,the 2nd-stage cyclone,and the two-stage cyclone is generally greater than theEn.Most grinding particles have a smaller particle size,and the cyclone has a higher efficiency in separating large particles than small particles.Large particles contribute much more toEqthan small particles.

Except for the 1st-stage cyclone inlet area of 1Sand the number of the 2nd-stage cyclone inlets of 6N,the experimental errors were within 5%.These belong to experimental measurement errors.When the 1st-stage cyclone inlet area of 1Sand the number of the 2nd-stage cyclone inlets of 6Ncause the 1st-stage cyclone inlet velocity to be larger.Some particles may enter the 2nd-stage cyclone directly from theandinlets due to inertia.It causes unstable experimental results and relatively large errors.

With the increase of the 1st-stage cyclone inlet area,the difference ofEnbetween the 1st-stage cyclone and 2nd-stage cyclone gradually increased.For example,when the number of the 2ndstage cyclone inlets is 4N,as the 1st-stage cyclone inlet area increases,the differences ofEnbetween the 1st-stage cyclone and 2nd-stage cyclone are-2.2%,9.0%,18.3%,and 19.4%,as shown in Fig.4(a),(b),(c),and (d),respectively (The negative sign indicates that the 2nd-stage cycloneEnis smaller than the 1st-stage cyclone).As the area of the inlet increases,the velocity of the airflow entering the 1st-stage cyclone decreases.The centrifugal force on the particles will be reduced,resulting in a reduction in cyclone separation efficiency.And as the 1st-stage cyclone inlet area increases,the width and height of the 1st-stage cyclone inlet increase.The increase in the cyclone’s height and width leads to a decrease in the separation efficiency of the particles away from the wall and the top of the cyclone inlet [37,38].Thus,the 1ststage cyclone separation efficiency is reduced.These are not conducive to the separation of particles by the 1st-stage cyclone.

As the number of the 2nd-stage cyclone inlet increased,theEnof the 1st-stage cyclone and 2nd-stage cyclone gradually decreased.When the number of the 2nd-stage cyclone inlets is greater than 2N,En’s decline becomes larger.The effect of the 2nd-stage cyclone inlets onEqappears to be less regular.As shown in Fig.4(d),when the 1st-stage cyclone inlet area is 6S,as the number of the 2nd-stage cyclone inlets increases,Eqof the 1st-stage cyclone shows an inverted ‘‘V”shape,andEqof the 2nd-stage cyclone shows a ‘‘V”shape.No matter how the number of the 2nd-stage cyclone inlets changes,the two-stage cyclone’sEqalways stays high.Therefore,the number of 2nd-stage cyclone inlets has little effect on theEqof the two-stage cyclone.

Although increasing the 1st-stage cyclone inlet area and increasing the number of the second-stage cyclone inlets will reduce the performance of the two-stage cyclone separation,it can greatly reduce the pressure drop of the two-stage cyclone.The energy cost of the cyclone is directly proportional to the pressure drop.The greater the pressure drop,the greater the energy consumption [30].Fig.5 shows the effect of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets on the pressure drop of the two-stage cyclone.

From Fig.5,it can be seen that the 1st-stage cyclone inlet area has a greater effect on the pressure drop of the 1st-stage cyclone but has little effect on the pressure drop of the 2nd-stage cyclone.As the 1st-stage cyclone inlet area increases,the velocity of the airflow entering the 1st-stage cyclone decreases.The cyclone pressure drop is proportional to the square of the inlet velocity,and the pressure drop of the1st-stage cyclone is more likely to decrease.Regardless of how the area of the 1st-stage cyclone increases,the airflow velocity entering the 2nd-stage cyclone is constant,so the 1st-stage cyclone inlet area will no longer affect the pressure drop of the 2nd-stage cyclone.With the increase of the 1st-stage cyclone inlet area,the pressure drop of the 1ststage cyclone decreased rapidly.The proportion of the 2nd-stage cyclone pressure drop to the two-stage cyclone pressure drop gradually increases.As shown in Fig.5(d),where the 1st-stage cyclone inlet area is 6S,and the number of the 2nd-stage cyclone inlets is 4N,the pressure drops of the 1st-stage cyclone,2nd-stage cyclone,and two-stage cyclone are 295,2601,and 2896 Pa,respectively.The 2nd-stage cyclone accounted for 89.8% of the pressure drop in the two-stage cyclone.When the 1st-stage cyclone inlet area is 1S,and the number of the 2nd-stage cyclone inlets is 4N,the 2nd-stage cyclone accounts for only 37.8%of the pressure drop of the two-stage cyclone,as shown in Fig.5(a).

Fig.4.Effects of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets on the two-stage cyclone Eq and En:(a) 1S,(b) 2S,(c) 4S,(d) 6S.

Fig.5.Effects of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets on the pressure drop of the two-stage cyclone:(a) 1S,(b) 2S,(c) 4S,(d) 6S.

With the increase in the number of 2nd-stage cyclone inlets,the pressure drop of the 1st-stage cyclone,2nd-stage cyclone,and twostage cyclone decrease.When the number of inlets is increased from 1Nto 2N,the pressure drop of the two-stage cyclone separator is reduced by about half.As shown in Fig.5(d),when the 1ststage cyclone inlet area is 6S,and the number of the 2nd-stage cyclone is increased from 1Nto 2N,the pressure drop of the twostage cyclone separator is reduced from 9495 to 4313 Pa,and the pressure drop is reduced by 54.6%.The increase in the number of 2nd-stage cyclone inlets will greatly reduce the airflow velocity entering the 2nd-stage cyclone.When the number of 2nd-stage cyclone inlets is increased from 1Nto 2N,the average air velocity entering the 2nd-stage cyclone decreases from 69.4 to 34.7 m?s-1.As a result,the 2nd-stage cyclone pressure drop will be rapidly reduced.

3.2.Influence of inlet area on mass classification efficiency and number classification efficiency

BothEqandEnare unified statistics of all particles and cannot represent the particle separation efficiency within a certain PSD interval.The classification efficiency can make up for this shortcoming.We also divide the classification efficiency into mass classification efficiency and number classification efficiency to better analyze the two-stage cyclone separator’s separation performance.Figs.6 and 7 show the mass classification efficiency and number classification efficiency of the two-stage cyclone.The horizontal direction is the change law of the classification efficiency with the area of the 1st-stage cyclone inlet.The vertical direction is the change law of the classification efficiency with the number of the 2nd-stage cyclone inlets.The ‘‘Channel”in Fig.6 refers to the instrument’s classification of measurement results into several channels according to different indicators.For example,PM1channel for particles smaller than 1 μm,PM2.5channel for particles smaller than 2.5 μm.RESP refers to respiratory particles with a particle size of fewer than 7.07 μm.

It can be seen from Fig.6 that the area of the 1st-stage cyclone inlet greatly influences the mass classification efficiency of the 1ststage cyclone.With the increase in the area of the 1st-stage cyclone inlet,the mass classification efficiency of the 1st-stage cyclone rapidly decreases.It has been analyzed earlier that an increase in the area of the 1st-stage cyclone inlet will cause an increase in the width and height of the inlet.Regardless of the particle size,the separation efficiency will decrease.As shown by the blue arrow in Fig.6,when the number of 2nd-stage cyclones is 2N,as the area of the 1st-stage cyclone increases,the mass classification efficiency of the 1st-stage cyclone to PM2.5is 73.6%,43.1%,18.8%,and 7.7%,respectively.

The area of the 1st-stage cyclone inlet has almost no effect on the pressure drop of the 2nd-stage cyclone,but it does have a certain effect on the mass classification efficiency of the 2nd-stage cyclone.With the increase of the 1st-stage cyclone inlet area,the mass classification efficiency of the 1st-stage cyclone rapidly decreased.The number of particles entering the 2nd-stage cyclone increased,and more particles were deposited at the bottom of the 2nd-stage cyclone.With the increase of the running time,the particles will be re-entrained with the vortex and discharged from the cyclone,causing secondary pollution and reducing the 2nd-stage cyclone classification efficiency [12,39,40].However,an increase in the number of particles entering the 2nd-stage cyclone will increase the inlet particle concentration.As the particle concentration at the inlet increases,the cyclone separation efficiency increases [41,42].In summary,with the increase in the area of the 1st-stage cyclone inlet,the classification efficiency of the 2nd-stage cyclone changes irregularly.

The number of 2nd-stage cyclone inlets has a relatively small effect on the mass classification efficiency of the 1st-stage cyclone.Still,it has a large effect on the mass classification efficiency of the 2nd-stage cyclone.As the number of 2nd-stage cyclone inlets increases,the 2nd-stage cyclone inlet airflow velocity decreases,reducing theEqof the 2nd-stage cyclone.As shown by the pink arrow in Fig.6,when the area of the 1st-stage cyclone inlet is 1S,as the number of the 2nd-stage cyclone increases,the mass classification efficiency of the 2nd-stage cyclone for PM2.5is 77.5%,60.0%,47.6%,and 35.0%,respectively.

It can be seen from Fig.7 that no matter how the area of the 1ststage cyclone inlet and the number of 2nd-stage cyclone change,the number classification efficiency of the 1st-stage cyclone and the 2nd-stage cyclone will always present a fishhook effect [43].The 1st-stage cyclone has the lowest separation efficiency for 1.5–2.5 μm particles.The 2nd-stage cyclone has the lowest separation efficiency for 1.0–1.5 μm particles.Because the particle diameters of the lowest point of the 1st-stage cyclone and the 2nd-stage cyclone are different,the two-stage cyclone can improve the separation efficiency of all PSD.

The area of the 1st-stage cyclone inlet has little effect on the number classification efficiency of the 2nd-stage cyclone but has a greater impact on the number classification efficiency of the 1st-stage cyclone.As the area of the 1st-stage cyclone increases,the number classification efficiency of the 1st-stage cyclone gradually decreases.And the effect on particles below 5.0 μm is more obvious.This situation indicates that the area of the 1st-stage cyclone inlet has a greater effect on the separation efficiency of PM2.5,which corresponds to the mass classification efficiency of PM2.5mentioned above.

The effect of the number of the 2nd-stage cyclone on theEnof the 2nd-stage cyclone is much greater than that of the 1st-stage cyclone.When the 1st-stage cyclone inlet area is 1S,the number separation efficiency of small particles by the 1st-stage cyclone is higher than that of the 2nd-stage cyclone.With the increase in the number of the 2nd-stage cyclone inlets,the differences inEnof 1st-stage cyclone and 2nd-stage cyclone for 1.0–2.5 μm particles are -21.7%,-17.4%,15.7%,and 33.7%,respectively (Negative sign indicates that the number separation efficiency of the 1st-stage cyclone is less than that of the 2nd-stage cyclone).

The increase in the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets have a negative effect on the classification efficiency of the two-stage cyclone.When the area of the 1st-stage cyclone inlet and the number of the 2nd-stage cyclone are 1S–1N,2S–2N,4S–4N,and 6S–6N,the separation efficiency of the two-stage cyclone for 1.0–1.5 μm particles is 88.3%,77.3%,53.0%,and 24.5%.The decline is as high as 72.3%.

3.3.Taguchi orthogonal array results and analysis of variance

Design-Expert is a widely used experimental design and data analysis software [43–46].Design-Expert makes it easy to see what,if anything,emerges as statistically significant and how to model the results most precisely.Data were input into Design-Expert software for analysis of variance and optimization.The experimental results are shown in Table 3.

Earlier studies have shown that the increase in the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets positively affect the reduction of the pressure drop and a negative effect on the separation efficiency of the two-stage cyclone.There is no interaction between the two factors,so the main effect mathematical model was chosen to analyze variance.

Fig.6.Effects of inlet area on mass classification efficiency.

Fig.7.Effects of inlet area on number classification efficiency.

TheFtest’s principle is that the larger theFvalue of a specific factor,the greater the impact of changes in the factor on the response value.R2and Adj.R2are parameters that measure the relationship between the observed value and the predicted value.The closer it is to 1,the more agreement between the observed value and the predicted value.The Adeq Precision is a measure of signal-to-noise ratio,and ratios greater than 4 are desirable.Tables 4–6 show the analysis of the variance of pressure drop,Eq,andEn,respectively.

It can be seen from Table 4 that theFvalues of the influence of the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets on the pressure drop are 303.51 and 882.75 Pa,respectively.The 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets greatly influence the pressure drop of the two-stage cyclone.And the effect of the number of the 2nd-stage cyclone inlets on pressure drop is greater than the area of the 1st-stage cyclone inlet.This is consistent with our previous analysis.BothR2and Adj.R2approached 1,indicating that the pressure drop observations have a high degree of agreement with the predicted values.

It can be seen from Table 5 that the 1st-stage cyclone inlet area greatly influences theEqof the two-stage cyclone.The number of 2nd-stage cyclone inlets has almost no effect on theEqof the two-stage cyclone.The Adeq Precision is 6.834,indicating that expectations are reliable.

It can be seen from Table 6 that the 1st-stage cyclone inlet area and the number of the 2nd-stage cyclone inlets greatly affect theEnof the two-stage cyclone.And the number of the 2nd-stage cyclone inlets affects the number classification efficiency of the two-stage cyclone greater than the 1st-stage cyclone inlet area.

Table 3 Taguchi experimental results

Table 4 ANOVA analysis of pressure drop

Table 5 ANOVA analysis of Eq

Table 6 ANOVA analysis of En

The variance analysis can only reflect whether the overall regression model is significant,so it is necessary to diagnose the observed and predicted values.Fig.8 shows the linear relationship between the observed value and the predicted value.However,if observations are excluded,how will the predicted values change?So we introduce DFFITS as shown.DFFITS indicates the effect of deleting each observation on the model’s predicted value.The more test points in the ± 2 range,the better the regression.

Fig.8(a)and(c)show that the observed and predicted values of pressure drop andEnpresent a strong linear relationship.Fig.8(b)shows that the linear relationship between the observed and predicted values ofEqis not ideal.This is because the number of 2nd-stage cyclone inlets has a small effect on theEqof the twostage cyclone.

It can be seen from Fig.8(d),(e),and(f)that basically all DFFITS values are between±2,and only a few tests are out of range.A larger DFFITS value is ‘‘pull the regression up,”such as Run No.7 in Fig.8(d).A larger negative value of DFFITS ‘‘pull the regression down,”such as Run No.4 in Fig.8(f).Fig.8(d) shows that the DFFITS values are larger for experiments Run No.2 and Run No.7.This is consistent with the results observed in our experiments in Section 3.1.It is caused by experimental errors.Fig.8(e) and(f) show that the DFFITS values ofEqandEnfor experiment Run No.4 are larger.We have also analyzed in Section 3.1 that this is due to the larger inlet velocity when the area of the 1st-stage cyclone inlet is small.It has a greater effect oninlet of the 2ndstage cyclone,which affects efficiency.

Fig.8.Diagnosis analysis of regression model:(a)observed and predicted values of pressure drop,(b)observed and predicted values of Eq,(c)observed and predicted values of En,(d) DFFITS values of pressure drop,(e) DFFITS values of Eq,(f) DFFITS values of En.

3.4.Optimization analysis and verification

There are two criteria for determining a response value:importance and goal.There are five levels of importance.The larger the value,the greater the weight.The default value is 3,which can be modified as needed.If the particle size is small,to improve the separation efficiency of small particles,we can set the value ofEnto 5 andEqto 1.

Similarly,if the particle size is large,we can set the importance ofEnto 1 and the importance ofEqto 5.The smaller the pressure drop,the better.The higher the efficiency,the better.Therefore,we set the pressure drop goal to minimize and a goal of efficiency to maximize.Based on the settings’ value,we get two optimal results,as shown in Table 7.To compare the optimal solution with a traditional Lapple cyclone performance,the 2nd-stage cyclone was removed from the two-stage cyclone,leaving only one inlet for testing.The test results and the comparison of the optimal solutions are shown in Fig.9.

It can be seen from Table 7 that the error between the predicted value and the observed value is quite small and can be almost ignored.It shows that the prediction model is quite reliable.When the size of the required separation particles is small,to improve the separation efficiency of small particles,it is recommended to adopt a design of 2Sof the 1st-stage cyclone inlet area and 2Nof the number of the 2nd-stage cyclone inlets.When the size of the particles to be separated is large,it is recommended to use a design of 2Sof the 1st-stage cyclone inlet area and 4Nof the number of the 2nd-stage cyclone inlets.This can reduce pressure drop and save energy.

Table 7 Predicted and observed values of the optimal solutions

As shown in Fig.9,compared with the Lapple single-stage cyclone,the pressure drop of the 2S–2Ntwo-stage cyclone is reduced by 1303 Pa,Eqis increased by 0.56%,andEnis increased by 2.05%.Achieved the goal of reducing pressure drop while increasing efficiency.Compared with the Lapple single-stagecyclone,the pressure drop of the 2S–4Ntwo-stage cyclone is reduced by 3055 Pa,Eqis increased by 0.56%,andEnis reduced by 0.37%.AlthoughEndecreased slightly,the pressure drop was greatly reduced (41% reduction),andEqwas increased.

Fig.9.Performance comparison between the optimal two-stage cyclone and traditional Lapple cyclone.

4.Conclusions

This paper presents a new two-stage cyclone separator.The 2nd-stage cyclone has multiple inlets to reduce pressure drop.The 1st-stage cyclone can unify multiple inlets of the 2nd-stage cyclone,making it more convenient for connecting pipes.The Taguchi method was used to study the influence of the inlet area on the two-stage cyclone separator’s performance,and an optimization analysis was performed.The main conclusions are as follows:

(1) Increasing the area of the 1st-stage cyclone inlet and the number of 2nd-stage cyclone inlets can effectively reduce the two-stage cyclone’s pressure drop.The effect of the number of the 2nd-stage cyclone inlets on the pressure drop of the two-stage cyclone is significantly greater than the area of the 1st-stage cyclone inlet.

(2) The increase in the area of the 1st-stage cyclone inlet and the number of the 2nd-stage cyclone inlets have a negative effect on the separation efficiency of the two-stage cyclone.Increasing the area of the 1st-stage cyclone inlet,theEqof PM2.5decreases rapidly.With the increase of the area of the 1st-stage cyclone inlet and the number of the 2ndstage cyclone inlets,theEnof the two-stage cyclone to 1.0–1.5 μm particles decreased by up to 72.3%.

(3) The Taguchi method can effectively analyze and predict the performance of the two-stage cyclone.When the particles being separated are small,the 2S–2Ndesign is recommended.Compared with the traditional Lapple cyclone,the pressure drop is reduced by 1303 Pa,Eqis increased by 0.56%,andEnis increased by 2.05%.When the required separation particles are large,the 2S–4Ndesign is recommended.Compared with the traditional Lapple cyclone,under the premise of a small reduction inEn,the pressure drop is reduced by 41%,and theEqis increased by 0.56%.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was financially supported by the National Key Research and Development Program of China (2016YFC0801700),the Project of the National Natural Science Foundation of China(51604018),the Basic Research Funding of the China Academy of Safety Science and Technology (2019JBKY11 and 2019JBKY04).