Extending homogeneous fluidization flow regime of Geldart-A particles by exerting axial uniform and steady magnetic field

Qiang Zhang,Wankun Liu,Hengjun Gai,Quanhong Zhu,*

1 College of Chemical Engineering,Qingdao University of Science and Technology,Qingdao 266042,China

2 School of Chemical &Environmental Engineering,China University of Mining &Technology-Beijing,Beijing 100083,China

Keywords: Fluidized-bed Fluidization Geldart-A particles Flow regimes Extend Magnetic stabilization

ABSTRACT The homogeneous/particulate fluidization flow regime is particularly suitable for handling the various gas–solid contact processes encountered in the chemical and energy industry.This work aimed to extend such a regime of Geldart-A particles by exerting the axial uniform and steady magnetic field.Under the action of the magnetic field,the overall homogeneous fluidization regime of Geldart-A magnetizable particles became composed of two parts: inherent homogeneous fluidization and newly-created magnetic stabilization.Since the former remained almost unchanged whereas the latter became broader as the magnetic field intensity increased,the overall homogeneous fluidization regime could be extended remarkably.As for Geldart-A nonmagnetizable particles,certain amount of magnetizable particles had to be premixed to transmit the magnetic stabilization.Among others,the mere addition of magnetizable particles could broaden the homogeneous fluidization regime.The added content of magnetizable particles had an optimal value with smaller/lighter ones working better.The added magnetizable particles might raise the ratio between the interparticle force and the particle gravity.After the magnetic field was exerted,the homogeneous fluidization regime was further expanded due to the formation of magnetic stabilization flow regime.The more the added magnetizable particles,the better the magnetic performance and the broader the overall homogeneous fluidization regime.Smaller/lighter magnetizable particles were preferred to maximize the magnetic performance and extend the overall homogeneous fluidization regime.This phenomenon could be ascribed to that the added magnetizable particles themselves became more Geldart-A than -B type as their density or size decreased.

1.Introduction

Gas–solid heterogeneous reactions which consist of five consecutive steps are frequently encountered in the chemical and energy industry.To reduce the resistance of internal diffusion steps and promote the overall reaction rate,the solid phase is generally broken or prepared into small particles.Consequently,most gas–solid heterogeneous reactions turn into ones between gas and solid particles.The fluidized bed reactor was born exactly to deal with such reactions.The fluidization behavior of particles could be anticipated to affect the gas–solid contact performance therein.

Early in 1973,Geldart [1] classified the various particles into four basic types as per their fluidization behavior: A,B,C,and D.The Geldart-A particles exhibit a unique homogeneous/particu late/uniform fluidization flow regime as the gas velocity (Ug)increases beyondUmf0(minimum fluidization velocity in the absence of the magnetic field).Due to the absence of gas bubbles,the gas–solid contact performance therein can be as excellent as that in the fixed-bed flow regime [2,3].Meanwhile,the pressure drop of gas flow therein could be much lower owing to the uniform bed expansion.To conclude,the homogeneous fluidization regime is particularly suitable for handling the various gas–solid contact processes met in the chemical and energy industry.It is always desirable to extend this flow regime for Geldart-A particles so that a higher gas throughput could be achieved without negligible loss in its single-pass conversion and negligible increase in power consumption for driving the gas flow.

As for Geldart-B particles,there is no such homogeneous fluidization regime atUg>Umf0.It is generally reckoned that bubbles form immediately onceUgexceedsUmf0.However,as for Geldart-B magnetizable particles,the magnetic field has been successfully employed to suppress/delay such bubble formation and creat a similar homogeneous fluidization regime,which is well known as magnetic stabilization[4–8].As illustrated in Fig.1(a),the applied magnetic field caused the minimum bubbling velocity (Umb) to become greater than the minimum fluidization velocity (Umf).The interval confined byUmfandUmbwas exactly the magnetic stabilization regime.Note additionally from Fig.1(a)that as the magnetic field intensity(H)increased,Umfremained virtually invariant atUmf0whereasUmbincreased apparently,indicating that the stronger the applied magnetic field,the wider the as-obtained magnetic stabilization regime.

Fig.1.Creation of magnetic stabilization regime for (a) Geldart-B magnetizable particles by applying axial uniform and steady magnetic field and (b) Geldart-B nonmagnetizable particles by simultaneously introducing magnetizable particles and applying the magnetic field.

As for Geldart-B nonmagnetizable particles,the magnetic field could also creat the magnetic stabilization regime.Nevertheless,certain amount of magnetizable particlesmust be premixed so as to transmit the magnetic stabilization [9–13].As illustrated in Fig.1(b),after the magnetic field was applied to the binary admixture of Geldart-B nonmagnetizable and magnetizable particles,Umbalso became greater thanUmf.The interval confined byUmfandUmbwas the so-called magnetic stabilization regime.Note again from Fig.1(b) thatUmfremained almost invariant atUmf0whereasUmbincreased remarkably with increasingH,indicating that the stronger the magnetic field,the broader the as-obtained magnetic stabilization regime.It was further reported that at a givenH,the magnetic stabilization regime became broader as the added content of magnetizable particles increased [9,14].

To the best of our knowledge,most of previous research concerning magnetized fluidized bed focused on Geldart-B particles with the purpose of suppressing/delaying the bubble formation[15,16].The remaining research focused mainly on Geldart-C particles;the original intention was to achieve their normal fluidization by destroying slugging/channeling or reducing agglomerate size [17].In contrast,little attention has been paid to Geldart-A particles given that they were generally reckoned to have an excellent fluidization quality.

Inspired by the above findings on Geldart-B particles,this work aimed to extend the homogeneous fluidization regime of Geldart-A particles by applying the axial uniform and steady magnetic field.The performance of such a magnetic field in extending homogeneous fluidization regime for Geldart-A magnetizable particles was first explored.As for Geldart-A nonmagnetizable particles,some magnetizable particles had to be premixed to transmit the effect of magnetic field.In this case,the performance of merely adding magnetizable particles in extending homogeneous fluidization regime was first investigated.Then the performance of subsequently-applied magnetic field was studied and analyzed.

2.Experimental

2.1.Experimental setup

The experimental setup used throughout this work was similar to that employed in our previous work [18,19].As illustrated in Fig.2,the fluidization column had an inner diameter of 30 mm and a height of 350 mm.To ease visual observation,it was constructed from transparent Plexiglas.A sintered metal plate (nonmagnetic) with a thickness of 4 mm and an equivalent pore size of 20 μm served as the gas distributor.Four identical Helmholtz coils with an inner diameter of 200 mm,outer diameter of 260 mm,and height of 58 mm were employed to excite the axial uniform and steady magnetic field.The distances between two adjacent coils were carefully refined to ensure that the generated magnetic field was as uniform as possible in space.Additionally,the height of the gas distributor relative to the lowest coil was carefully assigned(Fig.2(b))so that particles were always fluidized in the uniform magnetic field.The settled height of particles was set as 60 mm,which was twice the inner diameter of the fluidization column.Note particularly that the uniform magnetic field only induced magnetic forces among the magnetizable particles whereas exerted no net body force on the magnetizable particles taken as a whole [8,20].

Fig.2.(a) Experimental setup and (b) relative position of gas distributor to lowest coil (unit:mm)

2.2.Materials

Air at ambient temperature and pressure served as the fluidizing agent whose flow rate into the wind box was adjusted using a mass flow meter(CS200,Sevenstar,China).The magnetite-I particles with an average diameter of 61.7 μm served as Geldart-A magnetizable particles[21,22]whereas the alumina particles with an average diameter of 60.1 μm served as Geldart-A nonmagnetizable particles.For the alumina particles,some magnetizable particles should be premixed to transmit the magnetic stabilization.In this case,both magnetite and iron particles were employed (more details about selecting these two types of particles will be introduced in Section 3.4.3).Physical properties of these particles are summarized in Table 1.The average particle size(dp)listed therein denoted the Sauter mean diameter which was calculated from the particle size distribution(Fig.3,BT-9300ST,Bettersize,China).The particle density (ρp) was measuredviathe well-known drainage method.Umf0andUmb0(minimum bubbling velocity in the absence of the magnetic field) were determined from analyzing the ΔPb–Ug↑and σP–Ug↑curves,respectively.More details about their identification will be specified in Section 3.1.

Fig.3.Size distributions of magnetizable and nonmagnetizable particles.

2.3.Operation procedure

The magnetic field was first applied to the “settled bed”;then the fluidizing gas was introduced and gradually increased.In short,the magnetization-FIRST operation mode was adopted [16].The bed pressure drop (ΔPb) as well as its fluctuation with time was measured during the step-wise increase ofUgfrom zero to complete fluidization and during its subsequent decrease to zero.As for purely Geldart-A magnetizable particles,the initial “settled bed” before applying the magnetic field was always obtainedviadecreasingUggradually from high values to zero [23].As for Geldart-A nonmagnetizable particles,some magnetizable particles should be premixed to transmit the magnetic stabilization.In this case,the initial “settled bed” before applying the magnetic field was always obtainedviadecreasingUgquickly (but not abruptly)from high values to zero [24].The special requirement on the decrease rate ofUgwas to ensure that the two types of particles in the as-obtained settled bed could have excellent mixing and meanwhile,the so-called wedging effect [25,26] could be eliminated to some extent.More details about acquiring the initial“settled bed” will be specified in Sections 3.1 and 3.3.1.

2.4.Measurement of ΔPb and its fluctuation

Variations of ΔPband its fluctuation with increasing and decreasingUgwere usually analyzed to determineUmf0andUmb0.They were also frequently used to identify the lower and upper limits of magnetic stabilization regime (i.e.,UmfandUmb).At a givenUg,the gauge pressure (Pw) at the wind box was recorded directly for 10 min using a pressure transducer (CGTL-300B,Skysen,China).The time-averaged value was then used to calculate ΔPbby deducting the pressure drop over the gas distributor,which equaledPwin an empty bed and could be previously measured.The standard deviation (σP) ofPwwas used to quantify the fluctuation of ΔPbwith time.

3.Results and Discussion

3.1.Conventional fluidization behavior of Geldart-A particles

This work focused on extending homogeneous fluidization regime of Geldart-A particles by exerting the axial uniform and steady magnetic field.As a prerequisite,their conventional fluidization behavior had to be first investigated.To be precise,the homogeneous fluidization regime in the absence of the magneticfield should be first quantified,which was confined byUmf0andUmb0.Umf0demarcates the state transition of particles from packed/fixed to fluidized.According to previous researches from others[27,28]and ourselves[23,24,29],it could be identified from analyzing the ΔPb–Ug↑curve,which is exemplified in Fig.4.The values ofUmf0for the magnetite-I and alumina particles were 0.0088 and 0.0038 m?s-1,respectively.On the other hand,Umb0denotes theUgat which macro gas bubbles (diameter >5 mm[1]) begin to rise continuously in the bed.It could be determined from analyzing the σP–Ug↑curve since the rising of gas bubbles was the root cause for the fluctuation of ΔPb[5,14,30].An example of this method is also illustrated in Fig.4.The values ofUmb0for the magnetite-I and alumina particles were 0.0148 and 0.0074 m?s-1,respectively.

Fig.4.Conventional fluidization behavior of (a) magnetite-I and (b) alumina particles.

Either for the magnetite-I or alumina particles,Umb0was much greater thanUmf0,confirming that both belonged to Geldart-A group.In the absence of the magnetic field,the operating range(Umb0–Umf0) of homogeneous fluidization regime for the magnetite-I particles was 0.0060 m?s-1whereas that for the alumina particles was 0.0036 m?s-1.The existence of such a flow regime for Geldart-A particles was generally ascribed to the appropriate ratio between the interparticle force and the particle gravity[31,32].

During the identification ofUmb0from the σP–Ug↑curve,the occasional and slight increases of σPabove the environment noise level atUg>Umf0should be ignored carefully.Coarsely speaking,they resulted from the random loosening of particles to keep a constant resistance to the gas flow rather than from the formation/-movement of macro gas bubbles.To be deeper,the homogeneous fluidization regime of Geldart-A particles has been demonstrated to consist of two sub-regimes:solid-like homogeneous fluidization and fluid-like homogeneous fluidization [33–36].The fluid-like homogeneous fluidization sub-regime is characterized by continuous formation of micro gas bubbles or cavities whose diameter is smaller than 5 mm.It is the movement of these micro gas bubbles that drives the particles to loosen their structure (i.e.,expand uniformly in height).From this perspective,the occasional and insignificant increases of σPabove the noise level atUg>Umf0could be attributed to the formation and rising of micro gas bubbles or cavities in the fluid-like homogeneous fluidization regime.OnceUgexceededUmb0and macro gas bubbles formed in the bed,σPwould increase monotonously with increasingUguntil the onset of turbulent fluidization regime.

Last but not least,to improve reproducibility of ΔPb–Ug↑and σP–Ug↑curves during repeated measurements,the so-called wedging effect[25,26,37]in the initial fixed/packed bed should be minimized/eliminated as much as possible.Herein,the initial fixed/packed bed that served as the starting point for measuring these two curves was obtainedviadecreasing the gas flow gradually from high velocities to zero [23,24].Therefore,“settled bed”was used in Section 2.3 to denote the starting point.Furthermore,to quantify the gradual decrease of gas flow,the concept of decrease rate (α=(–dUg/dt)) ofUgwas proposed and utilized.It was found that provided α was smaller than 0.025 m?s-2,the obtained settled bed as well as ΔPb–Ug↑and σP–Ug↑curves measured subsequently could remain invariant.

3.2.Performance of magnetic field in extending homogeneous fluidization regime of Geldart-A magnetizable particles

After the axial uniform and steady magnetic field was exerted on the “settled bed” with magnetite-I particles,ΔPb–Ug↑and σP–Ug↑curves measured subsequently could also give two characteristic gas velocities,which were termedUmfandUmbto distinguish those obtained in the absence of the magnetic field.The interval confined by them was the homogeneous fluidization regime acquired in the presence of the magnetic field.It was observed that asUgincreased fromUmftoUmb,the bed expanded uniformly in height without formation of macro gas bubbles.

During magnetized fluidization of Geldart-B magnetizable particles,Umbwas generally determined from analyzing the ΔPb–Ug↓curve[31,38–42].As for the fluidization of Geldart-A magnetizable particles in the axial uniform and steady magnetic field,the determinations ofUmbfrom the ΔPb–Ug↓and σP–Ug↑curves are compared in Fig.5.Apparently,values ofUmbidentifiedviathese two methods were close to each other,indicating that both methods were feasible.

Fig.5.Comparing determination of Umb from(a)ΔPb–Ug↓and(b)σP–Ug↑curves for magnetite-I particles.

At a givenH,Umfwas found to approximately equalUmf0=0.0 088 m?s-1whereasUmbbecame much greater thanUmb0=0.014 8 m?s-1,indicating that the homogeneous fluidization regime of Geldart-A magnetizable particles was successfully enlarged by the magnetic field.Moreover,as illustrated in Fig.6,the stronger the magnetic field,the wider the operating range (Umb–Umf) of homogeneous fluidization regime.To be specific,Umbincreased apparently whereasUmfremained invariant with increasingH,which was consistent with that found during magnetized fluidization of Geldart-B magnetizable particles [4,5,43].

Fig.6.Expansion of homogeneous fluidization regime for magnetite-I particles by applying the magnetic field.

Under the influence of the magnetic field,the overall homogeneous fluidization regime of Geldart-A magnetizable particles became composed of two parts.The part confined byUmfandUmb0was that inherent to Geldart-A particles.On the other hand,the interval confined byUmb0andUmbwas that newly-created by the magnetic field,which was well knowns as magnetic stabilization regime [4].As illustrated in Fig.6,the magnetic stabilization regime could be much broader than the inherent homogeneous fluidization regime.To conclude,the mechanism how the magnetic field extended the homogeneous fluidization regime for Geldart-A magnetizable particles lay in that it created an additional magnetic stabilization regime.Although as illustrated in Fig.6,the stronger the magnetic field,the wider the overall homogeneous fluidization regime,Hcould not be increased beyond 8 kA?m-1.Otherwise,the magnetizable particles would become magnetically frozen [44].Under such circumstances,there was no concept of homogeneous fluidization at all.The magnetizable particles taken as a whole would be lifted like a piston above the gas distributor afterUgexceededUmf0.

Furthermore,the mechanism by which the magnetic field created the magnetic stabilization regime for Geldart-A magnetizable particles was identical to that for Geldart-B magnetizable particles.First,the magnetic field induced additional forces among the magnetizable particles,thus increasing “surface tension” of the solid phase which could be treated as a pseudo-fluid as per the discipline of fluidization [45].Most intuitively,the motion of particles was observed to become more viscous.According to Gibbs function in physical chemistry [46],this would eventually make the increase of interfacial area (caused either by the bubble formation or by its size increase)become more difficult.Second,the magnetic field induced magnetizable particles to form the so-called magnetic chains which tended to align in the direction of magnetic field lines [47].The network structure woven by these magnetic chains could expand uniformly like a sponge rather than form macro gas bubbles to let more gas pass through without increasing the resistance.Third,some magnetic chains suspending in the bed could work like “floating internals”,splitting the macro gas bubbles already formed in the bed from the top [47].Fourth,there were also magnetic forces among the magnetic chains,thus squeezing the macro gas bubbles already formed in the bed and suppressing their growth in the lateral direction.Eventually,the bubble formation was suppressed and postponed to higher gas velocities.

3.3.Performance of merely adding magnetizable particles in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles

As illustrated in Fig.4(b),the homogeneous fluidization regime of Geldart-A alumina particles ranged from 0.0038 to 0.0074 m?s-1.The axial uniform and steady magnetic field was also explored to broaden this flow regime.Under such circumstances,certain amount of magnetizable particles had to be introduced and premixed so as to transmit magnetic stabilization to the alumina particles.To derive the performance of applying magnetic field in extending homogeneous fluidization regime for Geldart-A alumina particles,the performance of merely adding magnetizable particles had to be known as a prerequisite.

3.3.1.Effect of added content

After magnetite-I particles were premixed into the alumina particles,Umf0andUmb0of the resulting binary admixture could also be determined from analyzing the ΔPb–Ug↑and σP–Ug↑curves.The interval confined byUmf0andUmb0was the homogeneous fluidization regime inherent to the binary admixture.Variations ofUmf0andUmb0withxM(volume fraction of added magnetite-I particles)are plotted in Fig.7.The inherent homogeneous fluidization regime of the binary admixtures was always broader than that of purely alumina particles (height of shaded area in Fig.7),indicating that the mere introduction of magnetite-I particles could enlarge homogeneous fluidization regime for the alumina particles.This phenomenon might be ascribed to that the added magnetite-I particles offered certain degrees of lubrication,enhanced the interparticle force,and raised the ratio between the interparticle force and the particle gravity.This ratio was believed to determine the fluidization behavior of various particles [31].

Fig.7.Variations of Umf0, Umb0, Umf,and Umb for binary admixture of alumina and magnetite-I particles with xM at H=2.425 kA?m-1;height of shaded area denotes inherent homogeneous fluidization regime of purely alumina particles.

Furthermore,sinceUmf0of magnetite-I particles was greater than that of the alumina particles (see Table 1),Umf0of the binary admixture increased monotonically asxMincreased.On the other hand,Umb0first increased and then declined slightly with increasingxM.Eventually,the inherent homogeneous fluidization regime of the binary admixture first increased and then decreased slightly with the increase ofxM.Apparently,the added content of magnetite-I particles had an optimal value so as to maximize their performance in expanding homogeneous fluidization regime for the alumina particles.Although the introduction of some magnetite-I particles into the alumina particles could enhance the interparticle force,the excessive addition weakened such a performance.Under those circumstances,the interparticle force between the magnetite-I and alumina particles exceeded that among the alumina particles and played the dominant role in deciding the fluidization behavior of the binary admixture.

Note additionally that to improve reproducibility of ΔPb–Ug↑and σP–Ug↑ curves during repeated measurements,particular attention should be given to the starting point for measuring these two curves.Herein,the initial fixed/packed bed was always acquiredviadecreasingUgquickly (rather than abruptly) from complete fluidization with no segregation to zero[24].To be specific,the gas flow was decreased from 4UmfJ(UmfJdenoting the minimum fluidization velocity of jetsam[48])to zero within 10 s[49].Only in this case could the obtained fixed/packed bed have excellent mixing between the two types of particles.Meanwhile,the so-called wedging effect therein could be minimized to some extent.The fixed/packed bed acquiredviathe above method was also termed “settled bed” in Section 2.3.

3.3.2.Size effect of added magnetizable particles

The above section demonstrated that the mere introduction of magnetizable particles could broaden the homogeneous fluidization regime for Geldart-A nonmagnetizable particles.It could be anticipated that aside fromxM,the diameter (dpM) and density(ρpM) of added magnetizable particles would also affect their performance.This section concentrated on the effect ofdpM.Variations ofUmf0andUmb0for the binary admixture withdpMare illustrated in Fig.8.Umf0increased gradually whereasUmb0first increased slightly and then decreased with increasingdpM,resulting in that the inherent homogeneous fluidization regime of the binary admixture shrunk slightly with the increase ofdpM.Smaller magnetite particles were preferable to maximize their performance in extending homogeneous fluidization regime for the alumina particles.This phenomenon was not difficult to understand given that asdpMincreased from 61.7 to 177.8 μm,the homogeneous fluidization regime of magnetite particles shrunk sharply (Table 1) and their fluidization behavior became more Geldart-B than -A type.

Fig.8.Variations of Umf0, Umb0, Umf,and Umb for binary admixture of alumina and magnetite particles with dpM at H=2.425 kA?m-1 and xM=0.30;height of shaded area denotes inherent homogeneous fluidization regime of purely alumina particles.

3.3.3.Density effect of added magnetizable particles

This section focused on how ρpMaffected the performance of added magnetizable particles in expanding homogeneous fluidization regime for Geldart-A nonmagnetizable particles.Variations ofUmf0andUmb0for the binary admixture with ρpMare summarized in Table 2.Umf0increased whereasUmb0decreased with increasing ρpM,leading to that the inherent homogeneous fluidization regime of the binary admixture decreased apparently with the increase of ρpM.Lighter magnetizable particles worked better in broadening homogeneous fluidization regime for the alumina particles.This phenomenon was not beyond expectation given that the denser iron particles were more Geldart-B type than the lighter magnetite particles: the homogeneous fluidization regime of the former was narrower than that of the latter (Table 1).Note that due to the complexity of particle system and difficulty in accurately adjusting its size distribution,the slight difference (<5%) in average size between the magnetite and iron particles was acceptable from the perspective of single-variable experimental design.

To conclude,the mere introduction of some magnetizable particles could broaden the homogeneous fluidization regime for Geldart-A nonmagnetizable particles to some extent.For given magnetizable particles,there existed an optimal value of the added content to maximize their performance.On the other hand,smaller/lighter magnetizable particles had a better performance.

3.4.Performance of subsequently-applied magnetic field in further extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles

After the axial uniform and steady magnetic field was applied to the “settled bed” with the alumina and magnetite-I particles(xM=0.30),UmfandUmbof the binary admixture could also be determined from analyzing the ΔPb–Ug↑and σP–Ug↑curves.Their variations with increasingHare shown in Fig.9.Umfremained almost invariant atUmf0of the binary admixture whereasUmbincreased significantly beyondUmb0of the binary admixture.A new flow regime confined byUmb0andUmbappeared.On the one hand,this regime could be reckoned as the magnetic stabilization regime created for the binary admixture by the magnetic field.On the other hand,it could be reckoned as another homogeneous fluidization regime newly-created for the alumina particles by the magnetic field.To conclude,the homogeneous fluidization regime of the alumina particles could be further extended by the subsequently-applied magnetic field.Note again that although the stronger the applied magnetic field,the broader the overall homogeneous fluidization regime,Hcould not be increased beyond the magnetically-frozen value.

Fig.9.Variations of Umf0, Umb0, Umf,and Umb for binary admixture of alumina and magnetite-I particles with H, xM=0.30;height of shaded area denotes inherent homogeneous fluidization regime of purely alumina particles.

The homogeneous fluidization regime of the alumina particles has been expanded from 0.0036 to 0.0070 m?s-1by the addition of magnetite-I particles (xM=0.30).After the magnetic field was subsequently applied,the newly-created magnetic stabilization regime could be 0.0205 m?s-1atH=4.071 kA?m-1.Finally,due to the simultaneous introduction of magnetite-I particles and application of the magnetic field,the homogeneous fluidization regime of the alumina particles was extended from 0.0036 to 0.0275 m?s-1(more than seven times).

When the axial uniform and steady magnetic field was exerted on the binary admixture of alumina and magnetite-I particles,the magnetite-I particles also formed magnetic chains that had a strong tendency to align in the axial direction.These magnetic chains could entrap alumina particles among them[50–52],forming a bacon-like network structure [13].AsUgincreased withinUmb0andUmb,such a network structure could expand uniformly in height instead of form macro gas bubbles to accommodate the excess gas flow beyondUmb0.Although the distance among magnetic chains would increase gradually withUgincreasing fromUmb0toUmb,it was still smaller than the diameter of alumina particles.Under such circumstances,the alumina particles could not escape from the siege of magnetic chains and segregate towards the upper part of the bed.The alumina and magnetite-I particles still maintained good mixing during the uniform bed expansion.

In summary,as for Geldart-A nonmagnetizable particles,the homogeneous fluidization regime could be extended significantly by simultaneously introducing magnetizable particles and applying the magnetic field.For one thing,the first premixing of magnetizable particles could enlarge the inherent homogeneous fluidization regime.For another,the subsequent application of the magnetic field could create an additional magnetic stabilization regime.

3.4.1.Influence of xM on magnetic performance

Given that the magnetic stabilization was transmitted to Geldart-A nonmagnetizable particles by the added magnetizable particles,the added content could be anticipated to affect the performance of magnetic field in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles.This section focused exactly on such an issue.

As for the binary admixture of alumina and magnetite-I particles,variations ofUmfandUmbwithxMatH=2.425 kA?m-1are plotted in Fig.7.Apparently,the magnetic stabilization regime became broader with the increase ofxM,indicating that the magnetic performance in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles became better as the added content of magnetizable particles increased.This phenomenon was not beyond anticipation since the more magnetite-I particles added to the alumina particles,the more magnetic chains would form at a givenH,and the stronger the capability of these chains to entrap the alumina particles.In this case,the network structure had greater potential to expand uniformly in height with no alumina particles segregating to the upper part of the fluidization column.Eventually,more excess gas flow beyondUmb0could be accommodated by the bed expansion and the formation of macro gas bubbles could be postponed to higher values ofUg.

After the simultaneous introduction of magnetizable particles and application of the magnetic field,the overall homogeneous fluidization regime of the alumina particles (including inherent homogeneous fluidization and magnetic stabilization regimes of the binary admixture)increased with the increase ofxM,indicating that higher added contents of magnetizable particles favored the extension of homogeneous fluidization regime for Geldart-A nonmagnetizable particles.

3.4.2.Influence of dpM on magnetic performance

As for the binary admixture of alumina and magnetite particles,variations ofUmfandUmbwithdpMatH=2.425 kA?m-1andxM=0.30 are plotted in Fig.8.The magnetic stabilization flow regime remained almost invariant with increasingdpM,indicating that the magnetic performance in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles was hardly affected by the size of added magnetizable particles.Although the magnetic chains formed by larger magnetite particles were less in number,the space confined by them might not decrease significantly and their capability to entrap the alumina particles remained almost unchanged.

After the simultaneous introduction of magnetizable particles and application of the magnetic field,the overall homogeneous fluidization regime of the alumina particles decreased slightly with the increase ofdpM,indicating that smaller magnetizable particles worked better in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles.Nevertheless,dpMcould not be decreased without restriction.Otherwise,the magnetizable particles would enter Geldart-C group.As per our experimental observation,the optimum size of magnetite particles was about 61.7 μm.

3.4.3.Influence ofρpM on magnetic performance

This section focused on the impact of ρpMon the magnetic performance in extending homogeneous fluidization regime.In this case,various magnetizable particles with distinct densities should be employed.Ideally,these magnetizable particles should have identical magnetic properties so that the single-variable principle of experimental design could be obeyed.To be specific,the selected magnetizable particles with different densities should have a close magnetic susceptibility.However,it was a tough task to find such magnetizable particles.In this work,only two types of magnetizable particles (magnetite and iron) were used.As illustrated in Fig.10,within the range ofHcovered in this work,the deviation of magnetization curves between them was always less than 10%.We could reckon that they had identical magnetic properties and the only difference between them lay in their density.

Fig.10.Magnetization curves for magnetite and iron particles.

Variations ofUmfandUmbfor the binary admixture with ρpMatH=2.425 kA?m-1andxM=0.30 are summarized in Table 2.The operating range (Umb–Umb0) of magnetic stabilization regime also decreased with the increase of ρpM,indicating that the performance of magnetic field in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles was weakened as the density of added magnetizable particles increased.This happened because the magnetic chains formed by the denser iron particles also had a greater density.The larger density difference between the alumina particles and the iron-chains meant that it was easier for the alumina particles to escape from the siege of magnetic chains.Eventually,the network structure constituted by the denser iron-chains had weaker potential to expand uniformly in height and macro gas bubbles formed at a smaller gas velocity.

After the simultaneous introduction of magnetizable particles and application of the magnetic field,the overall homogeneous fluidization regime of the alumina particles shrunk to some extent with the increase of ρpM,indicating that lighter magnetizable particles were preferred in extending homogeneous fluidization regime for Geldart-A nonmagnetizable particles.

4.Conclusions

This work aimed to expand the operating range of homogeneous fluidization regime for Geldart-A particles by exerting the axial uniform and steady magnetic field.Both Geldart-A magnetizable and nonmagnetizable particles were explored.For these two types of particles,the homogeneous fluidization regime could be extended remarkably by the magnetic field.Under the action of the magnetic field,the overall homogeneous fluidization regime became comprised of two parts.The part confined byUmb0andUmfwas the homogeneous fluidization regime inherent to Geldart-A particles.The interval betweenUmbandUmb0was the magnetic stabilization regime newly created by the magnetic field.Although the inherent homogeneous fluidization regime was hardly affected by the magnetic field,the magnetic stabilization regime became broader asHincreased.

Particularly for Geldart-A nonmagnetizable particles,certain amount of magnetizable particles had to be premixed to transmit the magnetic stabilization.It was found that the mere introduction of magnetizable particles could expand the homogeneous fluidization regime.This was probably because the added magnetizable particles raised the ratio between the interparticle force and the particle weight.There existed an optimal content for the added magnetizable particles to maximize their performance.With the same content,smaller and lighter ones worked better in expanding homogeneous fluidization regime for Geldart-A nonmagnetizable particles.

The performance of magnetic field in expanding homogeneous fluidization regime for Geldart-A nonmagnetizable particles was also affected by the added content and physical properties of magnetizable particles.For one thing,the more the added magnetizable particles,the better the magnetic performance.For another,smaller and lighter magnetizable particles were preferable to maximize the magnetic performance.

Data Availability

Data will be made available on request.

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 supported by Shandong Provincial Natural Science Foundation (ZR2023MB038) and National Natural Science Foundation of China (21808232 and 21978143).Financial support from the Qingdao University of Science and Technology was also appreciated.

Nomenclature

dpSauter mean diameter of particles,μm

dpMaverage diameter of magnetizable particles,μm

Hmagnetic field intensity,kA?m-1

Pwgauge pressure in wind box,kPa

ΔPbbed pressure drop,kPa

ΔPdpressure drop through the gas distributor,kPa

Ugsuperficial gas velocity,m?s-1

Umbminimum bubbling velocity in presence of magnetic field,m?s-1

Umb0minimum bubbling velocity in absence of magnetic field,m?s-1

Umfminimum fluidization velocity in presence of magnetic field,m?s-1

Umf0minimum fluidization velocity in absence of magnetic field,m?s-1

UmfJminimum fluidization velocity of jetsam,m?s-1

W/Aapparent particle mass per bed cross section area,kPa

xMvolume fraction of magnetizable particles

α decreasing rate ofUg,m?s-2

ρpparticle density,kg?m-3

ρpMdensity of magnetizable particles,kg?m-3

σPstandard deviation of ΔPb-fluctuation,kPa