Particle collision behavior and heat transfer performance in a Na2SO4 circulating fluidized bed evaporator

Feng Jiang *,Di Xu ,Ruijia Li ,Guopeng Qi ,Xiulun Li

1 School of Chemical Engineering and Technology,Tianjin University,Tianjin 300350,China

2 Tianjin Key Laboratory of Chemical Process Safety and Equipment Technology,Tianjin University,Tianjin 300350,China

3 School of Biological and Environmental Engineering,Tianjin Vocational Institute,Tianjin 300410,China

Keywords: Heat transfer enhancement Particle collision behavior Circulating fluidized bed Evaporation Na2SO4 Standard deviation

ABSTRACT The particle collision behavior and heat transfer performance are investigated to reveal the heat transfer enhancement and fouling prevention mechanism in a Na2SO4 circulating fluidized bed evaporator.The particle collision signals are analyzed with standard deviation by varying the amount of added particles ε(1% –3%),circulation flow velocity u(0.37–1.78 m?s-1),and heat flux q(7.29–12.14 kW?m-2).The results show that the enhancement factor reach up to 14.6% by adding polytetrafluoroethylene particles at ε=3% , u=1.78 m?s-1,and q=7.29 kW?m-2.Both the standard deviation of the particle collision signal and enhancement factor increase with the increase in the amount of added particles.The standard deviation increases with the increase in circulation flow velocity;however,the enhancement factor initially decreases and then increases.The standard deviation slightly decreases with the increase in heat flux at low circulation flow velocity,but initially increases and then decreases at high circulation flow velocity.The enhancement factor decreases with the increase in heat flux.The enhancement factor in Na2SO4 solution is superior to that in water at high amount of added particles.The empirical correlation for heat transfer is established,and the model results agree well with the experimental data.

1.Introduction

Heat exchanger is one of the important equipment in industrial production.It has been widely used in various fields such as petroleum [1],electric power [2],and chemical industry [3] and so on.However,the fouling problem commonly exists in the application of heat exchangers.The accumulation of fouling deposition on the heating wall may lead to many operational and safety problems such as reducing heat transfer efficiency,increasing flow resistance,corroding heating wall,and shortening the service life of heat exchanger [4–7].

The fluidized bed heat transfer and fouling prevention technology (FBHFT) can effectively online enhance heat transfer and prevent fouling by combining the fluidized bed technology with heat transfer process [8–10].The circulating fluidized bed heat exchanger(CFBHE)have been widely used in many industries such as inorganic salt[11],waste heat recovery[12],electric power[13],food[14],catalytic cracking[15],boiler[16,17]and so on due to its high heat transfer efficiency,wide operation range,and easy manufacturing [18].Many studies on the CFBHE have been also conducted [19–26].

Wenet al.[19] constructed a three-phase circulating fluidized bed evaporator to investigate the heat transfer and anti-fouling performance.They found that the fluidized solid particles could prevent and remove fouling deposits by shearing the heating wall.A mathematical model was established to predict the three-phase flow boiling heat transfer coefficient.The pressure drop and energy consumption were also analyzed.Junet al.[20] built a multi-riser CFBHE to evaluate the heat transfer performance and fouling reduction characteristics.They found that a small amount of circulating particles contributed not only to the fouling reduction,but also to the heat transfer enhancement.Songet al.[21]investigated the flow and heat transfer characteristics of a pumpkin juice circulating fluidized bed evaporator.The results showed that the heat transfer efficiency was increased by 35% by adding the inert particles in the two-phase evaporation process.Guoet al.[22] investigated the heat transfer performance and pressure drop of the green tea extract circulating fluidized bed evaporator.The evaporator showed a good performance of heat transfer enhancement and fouling prevention when the volume fraction of the solid particles ranged from 6% –12% .A dimensionless correlation is built to depict the relationship between the heat transfer coefficient and the pressure drop.Liuet al.[23] established a multi-tube naturalcirculation fluidized bed evaporator to investigate the characteristics of the heat transfer enhancement and fouling prevention in the concentration of Gengnian’an extract.They observed that the three-phase evaporator had obvious antiscaling and descaling performance.Blaszczuket al.[24]investigated the influence of particle size on the local heat transfer coefficient in a large circulating fluidized bed reactor.They found that the heat transfer coefficient was related to the hydrodynamic conditions,and increased with the increase in particle size.Jianget al.[25,26] investigated the effect of the flow direction on the flow boiling heat transfer in a circulating fluidized bed evaporator by varying the amount of added particles,circulation flow velocity and heat flux.The results showed that the heat transfer enhancement factor of the horizontal bed was significantly greater than those of the up-flow and downflow beds at low heat flux.

In the application of the CFBHE,the fluidized inert solid particles destroy and thin the flow and heat transfer boundary layers,and increase the nucleate sites,thereby reducing the heat transfer resistance and enhancing the heat transfer.Meanwhile,the particle–wall action also can inhibit the fouling materials from adhering to the heating wall,thereby preventing fouling.Therefore,the particle collision behavior has an important influence on the heat transfer enhancement and fouling prevention.It is necessary to investigate the effect of particle collision behavior on the performance of the CFBHE.

Pronket al.[27]investigated the particle impact on the heating wall in both the stationary and circulating fluidized beds by piezoelectric measurement.The results showed that the fluidized particles could remove the sediments from the heating wall and prevent scaling or fouling.The fouling prevention performance depended strongly on the frequency and intensity of particle–wall collision.Anet al.[28] measured the vibration acceleration signal in a circulating fluidized bed evaporator with brittle graphite tube bundle.The vibration characteristics at different axial positions caused by the vapor–liquid–solid flow boiling were investigated under different vapor pressures,solid holdups,and particle sizes.Xuet al.[29]investigated the multi-value phenomenon of the correlation dimension in the multi-scale flow behavior of a vapor–li quid–solid circulating fluidized bed evaporator by the chaotic analysis on the vibration acceleration and pressure drop signals.The characteristics of low and medium frequency signals were determined by wavelet decomposition and signal reconstruction.Maet al.[30] developed a signal acquisition and processing system to measure and analyze the vibration acceleration signals of a graphite tube circulating fluidized bed evaporator.They investigated the effect of steam pressure,solid holdup and particle size,and obtained meaningful results for the vibration risk assessment and heat transfer enhancement.

Na2SO4is an important chemical raw material,which can be used in the production of sodium silicate,pulp,detergent and so on [31,32].Fouling problem is also serious and still not solved in the evaporation of Na2SO4solution,which greatly restricts the production.However,few studies are reported on solving this problem.The preliminary investigation [33,34] was conducted by combining the FBHFT with the evaporation of Na2SO4solution in our previous study.The results showed that the FBHFT has a promising prospect in solving the fouling problem in the evaporation of Na2SO4solution.Therefore,this study focuses on the particle collision behavior and heat transfer performance in Na2SO4CFBHE in order to further reveal the heat transfer enhancement and fouling prevention mechanism,which is still not fully investigated and analyzed so far.The particle collision behaviors are measured by the accelerometer sensors and analyzed by the signal processing of time and frequency domains.Polytetrafluoroethylene (PTFE) particles are selected as the inert solid particles due to its good physical and chemical properties.The effect of operating parameters,such as the amount of added particles,circulation flow velocity,and heat flux are also discussed.The findings are helpful for promoting the industrial application of the FBHFT.

Fig.1.Schematic diagram of the Na2SO4 circulating fluidized bed evaporator.

Fig.2.Distribution of the RTDs and accelerometer sensors on the heating tube(unit:mm).

2.Experimental

2.1.Experimental apparatuses and procedure

A Na2SO4circulating fluidized bed evaporator is designed and built.The evaporator mainly consists of a heating tube,an evaporation chamber,a centrifugal pump,a particle collector,and a data collection system(Fig.1).The apparatus is made of 316 L stainless steel.The heating tube has a dimension ofΦ38 mm×3 mm and a length of 1500 mm.The resistance wire with a nominal power of 3 kW is wrapped around the heating tube to supply heat.The whole apparatus is covered with insulation cotton to minimize the heat loss.

Eight resistance temperature detectors(RTDs,Pt100,Xuri Thermal Control Equipment Co.,Ltd.,China) are uniformly installed on the outer wall of the heating tube along the axial direction with an interval of 200 mm to measure the outer wall temperature.The entrance and exit temperatures of the fluid are also measured by the RTDs inserted into the center of the heating tube.Two pressure transducers are used to measure the inlet and outlet pressures of the heating tube.Three accelerometer sensors are installed on the outer wall of the heating tube along the axial direction to mea-sure the collision acceleration signals.The distribution of the RTDs and accelerometer sensors are illustrated in Fig.2.

A certain amount of particles and liquid are initially added to the evaporator.Then,the frequency modulator is regulated to adjust to the specified circulation flow rate,and the heating tube is electrically heated.When the temperature of the liquid reaches its boiling point,boiling begins.The vapor is separated from the liquid and particles in the evaporation chamber.The vapor is condensed in the condenser and the condensate flows into the collecting tank.The liquid–solid two phases are circulated to the heating tube.The steady state is achieved when the temperature fluctuation of each RTD within 5 min is less than 0.1 ℃.Then,the temperature and collision acceleration signal are automatically collected by the“Kingview”(Ver 6.60 SP3,Beijing Yakong Technology Development Co.,Ltd.,China) and“Weekend Dynamic”(Ver 9.4,Tianjin Weekend Measurement and Control Equipment Technology Co.,Ltd.,China)software,respectively.Each run is repeated three times to check the reproductivity.The specifications of the relevant apparatuses are listed in Table 1.

Table 1 Specifications of the relevant apparatuses

Table 2 Physical properties of the Na2SO4 solution

2.2.Experimental materials and parameters

The Na2SO4solution with mass fraction of 20% and tap water are used as the liquid working media in this experiment,respectively.Polytetrafluoroethylene (PTFE) particles are used as the inert solid particles.The relevant properties of the Na2SO4solution and the PTFE particles are listed in Tables 2 and 3,respectively.

Table 3 Relevant properties of the PTFE particles

The effects of the amount of added particles,circulation flow velocity and heat flux on the particle collision behavior and heat transfer performance are investigated in this study.The amount of added particles ε refers to the ratio of the bulk volume of added particles to that of the liquid phase working medium.ε is set as 1% ,1.5% ,2% ,and 3% within the experimental range.The circulation flow velocity of the liquiduis set to 0.37,0.72,1.06,1.41,and 1.78 m?s-1.The input heating powerQ0is 1200,1600,and 2000 W.The corresponding heat fluxqis 7.29,9.72,and 12.14 kW?m-2.

2.3.Data processing

2.3.1.Processing of the collision acceleration signal

The time series of the collision acceleration signal collected can be transformed into the power spectral density (PSD) by discrete Fourier transform [35].The calculation is as follows:

wherex(n) andw(n) are the time series and window function,respectively.fis the frequency.The Welch method is selected to modify the estimate of PSD,which is described as follows [36]:

where window is the window function,overlap is the overlap ratio,nfft is the sample length,fsis the sampling frequency.

Hamming window is selected as the window function.The overlap ratio,sample length and sampling frequency are set as 0.75,32,768 and 64 kHz,respectively [37].The analysis process of the collision acceleration signal can be completed by Tianjin Weekend Dynamic Software Ver 9.4.

The standard deviation σ of the collision acceleration signal represents the collision intensity [38].The standard deviation can be calculated as follows:

whereNis the number of the points measured for the time series.Xiandare the instantaneous and average accelerations,respectively.

2.3.2.Data processing of heat transfer

The flow boiling heat transfer coefficient is calculated as follows:

whereQis the actual heating power,which is equal to the input powerQ0minus the heat lossQL.Siis the internal surface area of the heating tube.twiandtwoare the mean inner and outer wall temperatures of the heating tube,respectively.tfis the mean temperature of the fluid.doanddiare the outer and inner diameters of the heating tube,respectively.lis the length of the heating tube.λ is the thermal conductivity of the heating wall.The heat lossQLcan be approximately determined by the following equations:

where αTis the joint heat transfer coefficient of convection and radiation.dcis the outer diameter of the insulation cotton.andtare the mean outer wall temperature of the insulation cotton and the ambient temperature,respectively.

The heat transfer enhancement effect is expressed by the enhancement factorE,which can be calculated as follows:

where αvlsand αvlare the vapor–liquid–solid three-phase and vapor–liquid two-phase flow boiling heat transfer coefficients,respectively.

The uncertainties of the experimental results are determined by the deviations of the measured values of the different parameters involved in the experiment [39].The calculation equations are as follows:

Fig.3.Effects of the PTFE particles on the heat transfer performance of the Na2SO4 circulating fluidized bed evaporator:(a)ε=1% ;(b)ε=3% .

Fig.4.PSD of the collision acceleration signals (measuring point A1,PTFE particles):(a) ε=0,u=0, q=0;(b) ε=0,u=1.78 m?s-1,q=0;(c) ε=3% ,u=1.78 m?s-1,q=0;(d) ε=0,u=1.78 m?s-1,q=12.14 kW?m-2;(e) ε=3% ,u=1.78 m?s-1,q=12.14 kW?m-2.

The maximum uncertainties of the heat transfer coefficient α and the enhancement factorEare 2.46% and 3.3% within the experimental range,respectively,which meet the requirements of engineering calculation.

3.Results and Discussion

3.1.Heat transfer performance of the Na2SO4 circulating fluidized bed evaporator

Fig.5.Comparison of the standard deviation of the collision acceleration signals between the solid phase and liquid phase: q=9.72 kW?m-2, u=1.06 m?s-1.

Fig.3 illustrates the effect of the addition of the PTFE particles on the heat transfer performance of the Na2SO4solution.The PTFE particles can enhance the heat transfer in most cases.The enhancement factor reaches up to 14.6% at ε=3% ,u=1.78 m?s-1,andq=7.29 kW?m-2.The enhancement factor obviously increases with the increase in the amount of added particles.

3.2.Characteristic frequency range of the multiphase flow

Fig.4 shows the PSD of the different signals in the Na2SO4circulating fluidized bed evaporator.The PSD can be used to analyze and determine the characteristics frequency range of the multiphase flow system.

The PSD of the equipment background noise is very small(Fig.4(a)),which can be ignored in this study.Fig.4(b)–(e) depict the characteristics frequency ranges of the liquid phase,liquid–solid two-phases,vapor–liquid two-phases,and vapor–liquid–solid three-phases,respectively.The frequency range of the liquid is 0–1000 Hz (Fig.4(b)) [28].The characteristics peaks in the range of 1000–6000 Hz reflect the effect of the equipment vibration caused by the centrifugal pump.

The new characteristic peaks can be clearly observed at 6000–17,000 Hz by comparing the Fig.4(b) and (c).These peaks are caused by the particle collision on the heating wall.Therefore,the characteristic frequency range of the particle collision is 6000–17,000 Hz.Meanwhile,Fig.4(c) also illustrates that the peaks of the equipment vibration are obviously enhanced.This phenomenon is attributed to the strengthened vibration caused by the collision of the particles on the shell and impeller of the centrifugal pump.

No new peaks exist with the generation of vapor by comparing Fig.4(b)and(d),(c)and(e).However,the original peaks are significantly strengthened.This phenomenon is attributed to the formation,growth,detachment and coalescence of the bubbles that intensify the turbulence of the fluid,thereby enhancing the collision of the fluid and particles on the heating wall.This result is different from that of Anet al.[28],which showed the frequency range of the characteristic peaks representing the bubbles is 500–3000 Hz.

Fig.5 further compares the standard deviations of the collision acceleration signals between the solid phase and liquid phase in the Na2SO4circulating fluidized bed evaporator.The standard deviation of the solid particles is greater than that of the liquid phase,which is consistent with the study of Jiang and Wanget al.[40].Moreover,the difference in standard deviation increases with the increase in the amount of added particles,which shows that the particle collision on the heating wall may have a great influence on the heat transfer performance of the Na2SO4circulating fluidized bed evaporator.Therefore,the effect of different operating parameters on particle collision behaviors and heat transfer performance in the Na2SO4evaporator is discussed in detail in the following part.

3.3.Effects of the operating parameters on the particle collision behavior and heat transfer performance in the Na2SO4 evaporator

Fig.6 illustrates the effect of the amount of added particles on the standard deviation and enhancement factor.Both the standard deviation and the enhancement factor generally increase with the increase in the amount of added particles,which is similar to the conclusion confirmed by Zhanget al.[41].The standard deviation slightly increases at low circulation flow velocity but sharply increases at high circulation velocity.

The increase in the amount of added particles increases the solid holdup in the heating tube,which is beneficial to increasing the frequency and intensity of the particle collision on the heating wall,thereby resulting in the increase in standard deviation.The turbulent extent of the fluid is weak at low circulation flow velocity,which is not conducive to the radial movement of the particles[42].Meanwhile,the kinetic energy of a single particle is low.Therefore,the standard deviation slightly increases with the increase in the amount of added particles.The added PTFE particles have a large size,and a moderate density and settling velocity,which is beneficial to the fluidization and radial movement with a high collision kinetic energy.The increase in circulation flow velocity intensifies the turbulent extent of the fluid,which promotes the radial movement of the particles and elevates the collision kinetic energy of the particles.Therefore,both the collision frequency and the collision intensity of a single particle on the heating wall obviously increase with the increase in the amount of added particles,which results in a sharp increase in standard deviation.

The particle collision on the heating wall is strengthened with the increase in the amount of added particles,which intensifies the shear and destruction to the flow and heat transfer boundary layers,thereby reducing the heat resistance and enhancing the forced convection heat transfer.Meanwhile,the poor wettability performance of the PTFE particles may reduce the wall superheat and the critical radius of bubble required for the boiling on the PTFE surface [19].Therefore,the strengthened particle collision is also conductive to increasing the nucleate sites,breaking the large bubbles into small ones,and promoting the detachment of bubbles from the heating wall.As a result,the enhancement factor increases with the increase in the amount of added particles.

Fig.7 depicts the effect of the circulation flow velocity on the standard deviation and enhancement factor.The standard deviation increases with the increase in circulation velocity;the enhancement factor initially decreases and then increases.

As previously mentioned,the turbulent extent of the fluid is intensified with the increase in circulation flow velocity,which promotes the radial movement of the particles and elevates the collision kinetic energy of the particles,thereby increasing the intensity and frequency of the particle–wall collision.Thus,the standard deviation of the collision acceleration signal increases with the increase in circulation flow velocity.

Fig.6.Effects of the amount of added particles on the standard deviation and enhancement factor in the Na2SO4 evaporator:(a) q=7.29 kW?m-2, u=0.37 m?s-1;(b)q=7.29 kW?m-2, u=1.41 m?s-1;(c) q=12.14 kW?m-2, u=0.37 m?s-1;(d) q=12.14 kW?m-2, u=1.41 m?s-1.

Fig.7.Effects of the circulation flow velocity on the standard deviation and enhancement factor in the Na2SO4 solution:(a) q=7.29 kW?m-2,ε=1% ;(b) q=7.29 kW?m-2,ε=3% ;(c) q=12.14 kW?m-2,ε=1% ;(d) q=12.14 kW?m-2,ε=3% .

On the one hand,the amplitude of the radial movement and the kinetic energy of the particles increase with the increase in circulation flow velocity,which is conducive to the particle–wall collision and the destruction to the flow and heat transfer boundary layers,thereby enhancing the heat transfer.On the other hand,the particles tend to flow upwards near the wall of the heating tube in the up-flow bed at low circulation flow velocity due to the higher density compared with the fluid.The increase in circulation flow velocity increases the turbulent extent of the fluid,which is beneficial to the uniform distribution of the particles at the cross section of the heating tube.This phenomenon results in the decrease in the solid holdup near the heating wall,which may reduce the interaction between the particles and the heating wall.Therefore,the enhancement factor initially decreases and then increases with the increase in circulation flow velocity under the joint action of the above-mentioned factors.

Fig.8 illustrates the effect of the heat flux on the standard deviation and enhancement factor in Na2SO4evaporator.The standard deviation slightly decreases with the increase in heat flux at low circulation flow velocity,but initially increases and then decreases with heat flux at high circulation flow velocity.The enhancement factor decreases with the increase in heat flux.

The number of the nucleate sites formed on the heating wall increases with the increase in heat flux,which results in a high generation frequency of the bubbles.The generating rate of the bubbles is greater than the detaching rate from the heating wall.Some bubbles converge and form a vapor film on the heating wall,which greatly increases the heat transfer resistance due to the low conductivity of the vapor phase.The surface covered by the vapor film increases with the increase in heat flux.Therefore,the enhancement factor decreases with the increase in heat flux,which is similar to the findings in literature [9,26,33].

The turbulent extent of the fluid is weak and the radial movement of the particles is not intense at low circulation flow velocity.Therefore,the generated vapor film is easy to attach to the heating wall and prevent the particles from contacting the heating wall,which inhibits the particle collision on the heating wall,thereby reducing the standard deviation.This has been proved by Arumemi-Ikhideet al.[9].

The increase in circulation flow velocity intensifies the turbulent extent of the fluid,which promotes the radial movement of the particles and elevates the collision kinetic energy of the particles,thereby increasing the particle collision intensity and intensifying the destruction to the vapor film.The vapor film is easier to be separated from the heating wall compared with low circulation flow velocity.On the one hand,the vapor film grows and covers more heating surface,which is not conducive to the particle–wall collision.On the other hand,the detachment,breakup and coalescence of the vapor phase further intensify the disturbance to the fluid,which is beneficial to the radial movement of the particles,thereby strengthening the particle–wall collision.Under the joint action of the above-mentioned factors,the standard deviation initially increases and then decreases with the increase in heat flux at high circulation flow velocity.

3D diagrams are established to illustrate the effect of the operating parameters on the standard deviation and enhancement factor in the Na2SO4circulating fluidized bed evaporator (Fig.9).The diagrams depict the heat transfer performance and the corresponding particle collision characteristics,which is beneficial to analyzing and revealing the heat transfer enhancement mechanism and finding the suitable operation range.

Fig.8.Effects of the heat flux on the standard deviation and enhancement factor in the Na2SO4 evaporator:(a) u=0.37 m?s-1,ε=1% ;(b) u=1.78 m?s-1,ε=1% ;(c)u=0.37 m?s-1,ε=3% ;(d) u=1.78 m?s-1,ε=3% .

The standard deviation increases with the increase in circulation flow velocity and the amount of added particles.The enhancement factor initially decreases and then increases with the increase in circulation flow velocity,but increases with the increase in the amount of added particles.Large amount of added particles can achieve good heat transfer enhancement effect at low and high circulation flow velocity (u<0?6 m ?s-1andu>1?2 m ?s-1) when the heat flux is low.However,low circulation flow velocity and large amount of added particles are beneficial to the heat transfer enhancement when the heat flux is high.Therefore,combined with the standard deviation of the particles collision signal,large amount of added particles and low circulation flow velocity are recommended based on the consideration of good heat transfer enhancement effect and low equipment vibration and abrasion.

3.4.Comparison of the particle collision between the Na2SO4 solution and water and the heat transfer performance

The particle collision behavior and heat transfer performance are compared between the Na2SO4solution and water in order to better understand the heat transfer enhancement mechanism of the FBHFT.Fig.10 compares the vapor–liquid two-phase flow boiling heat transfer coefficients of the Na2SO4solution and water.The heat transfer coefficients of the Na2SO4solution and water generally both increase with the increase in circulation flow velocity and decrease with the increase in heat flux.The heat transfer coefficient of the Na2SO4solution is obviously lower than that of water.

The viscosity of the Na2SO4solution is higher than water,but the thermal conductivity and specific heat is smaller than water,which are not beneficial to the turbulence of the fluid and convective heat transfer.Therefore,the vapor–liquid two-phase flow boiling heat transfer coefficient of the Na2SO4solution is smaller than water,which was also proved by Jianget al.[33].

Fig.11 compares the standard deviations of the particle collision signals between the Na2SO4solution and water.The standard deviation in water is higher than that in the Na2SO4solution at low amount of added particles.However,the difference of the standard deviation decreases with the increase in the amount of added particles.

The increase in the amount of added particles increases the particle collision frequency on the heating wall,which weakens the effect of the physical properties of the fluid on the particle collision,thereby reducing the difference in standard deviation between the Na2SO4solution and water.This phenomenon is especially obvious at high heat flux.It is due to the fact that the temperature of the fluid near the heating wall rises at high heat flux,which reduces the difference in viscosity and surface tension between the Na2SO4solution and water.Meanwhile,the increase in nucleate site enhances the boiling heat transfer.The generation,grow,and detachment of the bubbles intensify the disturbance to fluid near the heating wall,thereby further reducing the effect of the physical properties of the fluid on the particle–wall action.

Fig.9.Effects of the operating parameters on the standard deviation and enhancement factor in the Na2SO4 evaporator.

Fig.10.Comparisons of the vapor–liquid two-phase flow boiling heat-transfer coefficients between the Na2SO4 solution and water.

Fig.12 compares the flow boiling heat transfer coefficients of the Na2SO4solution and water with the addition of the PTFE particles.The particle addition can enhance the heat transfer of both the Na2SO4solution and water.The enhancement factors ranged from–2.14% to 14.6% and–0.48% to 14.4% for the Na2SO4solution and water,respectively,as illustrated in Fig.13.

The vapor–liquid–solid three-phase flow boiling heat transfer coefficient of water is greater than that of the Na2SO4solution at low amount of added particles,which is consistent with the results of the vapor–liquid two-phase flow system.However,the difference in heat transfer coefficient decreases with the increase in the amount of added particles,especially at high circulation flow velocity.At this time,the heat transfer coefficient of the Na2SO4solution is almost equal to that of water(Fig.12(c)and(d)),which shows the heat transfer enhancement effect of the PTFE particles in the Na2SO4solution is superior to that in water at high amount of added particles (Fig.13(c) and (d)).

The solid holdup is small in the heating tube at low amount of added particles,which results in a low particle–wall contact frequency.The viscosity of water is small.Therefore,the turbulent extent of water is more intense than the Na2SO4solution at the same circulation flow velocity,which is beneficial to promoting the radial movement of the particles and increasing the collision kinetic energy of the particles,thereby intensifying the particle–wall collision(Fig.11(a)and(b)).Meanwhile,the surface tension of water is smaller than Na2SO4solution,the bubbles is easier to generate and detach from the heating wall,which intensifies the turbulent extent of the fluid,thereby further promoting the particle–wall contact and enhancing the heat transfer(Figs.11(a)and 13(a)).

Fig.11.Comparisons of the standard deviations of the particle collision signals between the Na2SO4 solution and water:(a) q=7.29 kW?m-2,ε=1% ;(b)q=12.14 kW?m-2,ε=1% ;(c) q=7.29 kW?m-2,ε=3% ;(d) q=12.14 kW?m-2,ε=3% .

The increase in heat flux increases the nucleate sites on the heating wall,which enhances the boiling heat transfer of the liquid phase,thereby weakening the heat transfer enhancement effect of the particles.Thus,the enhancement factors of both the Na2SO4solution and water decrease with the increase in heat flux(Fig.13(b)).

The increase in the amount of added particles increases the solid holdup in the heating tube,thereby increasing the particle–wall collision frequency.Thus,the effect of the difference in physical properties of the fluid,such as the density and viscosity,on the particle collision frequency is weakened (Fig.11(c) and (d)).The heat transfer resistance in the thermal boundary layer of the Na2-SO4solution is greater compared with water due to the high viscosity and low thermal conductivity of the Na2SO4solution.Therefore,the destruction of the particle collision to the thermal boundary layer results in a superior heat transfer enhancement effect in the Na2SO4solution compared with water (Fig.13(c)and (d)).

3.5.Empirical correlation for heat transfer in Na2SO4 CFBHE

The empirical correlation for heat transfer is established to reflect the effect of the operating parameters,such as the amount of added particles,circulation flow velocity and heat flux,on the flow boiling heat transfer coefficient in Na2SO4CFBHE,which is helpful for the design of Na2SO4CFBHE.

R2=0.9751

The model results agree well with the experimental data,and the relative error is within the range of±5% ,as illustrated in Fig.14.

4.Conclusions

The particle collision behavior and heat transfer performance of a Na2SO4circulating fluidized bed evaporator with the PTFE particles as the inert solid particles is investigated by varying the operating parameters.The main conclusions are as follows:

The addition of the PTFE particles can enhance the heat transfer of the Na2SO4solution.The enhancement factor reach up to 14.6% at ε=3% ,u=1.78 m?s-1,andq=7.29 kW?m-2.The characteristic frequency range of the liquid and solid phases is 0–1000 Hz and 6000–17,000 Hz,respectively.No new peaks exist with the generation of the vapor phase.However,the generation of the vapor phase significantly strengthens the other peaks.

Fig.12.Comparisons of the vapor–liquid–solid three-phase flow boiling heat transfer coefficients between the Na2SO4 solution and water:(a) q=7.29 kW?m-2,ε=1% ;(b)q=12.14 kW?m-2,ε=1% ;(c) q=7.29 kW?m-2,ε=3% ;(d) q=12.14 kW?m-2,ε=3% .

Both the standard deviation and enhancement factor increase with the increase in the amount of added particles.The standard deviation increases with the increase in circulation flow velocity;however,the enhancement factor initially decreases and then increases.The standard deviation slightly decreases with the increase in heat flux at low circulation flow velocity,but initially increases and then decreases with heat flux at high circulation flow velocity.The enhancement factor decreases with the increase in heat flux.In general,the amount of added particles and circulation flow velocity has a more obvious influence on the particle collision behaviors.

The physical properties of the liquid working medium influence the particle collision behavior and heat transfer performance of the circulating fluidized bed evaporator.The two-phase and threephase flow boiling heat transfer coefficients of water is higher than those of the Na2SO4solution.The standard deviation of the particle collision in water is slightly higher than that in the Na2SO4solution in most cases.However,the heat transfer enhancement effect of the PTFE particles in Na2SO4solution is superior to that of water at high amount of added particles which reduces the difference in heat transfer performance between the Na2SO4solution and water.

Three-dimensional diagrams are established to reflect the relationship between the particle collision behavior and heat transfer enhancement effect in the Na2SO4circulating fluidized bed evaporator,which is beneficial to revealing the heat transfer enhancement mechanism and promoting the industrial application of the fluidized bed heat transfer and fouling prevention technology.In the following study,the effect of operating parameters,such as the particle type and size,will be further investigated.Meanwhile,the relevant numerical simulation of the vapor–liquid–solid threephase flow boiling heat transfer will also be conducted.

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 is supported by the open foundation of State Key Laboratory of Chemical Engineering (SKL-ChE-18B03) and by the Municipal Science and Technology Commission of Tianjin,China under Contract No.2009ZCKFGX01900.

Nomenclature

dcouter diameter of the insulation cotton,m

diinner diameter of the heating tube,m

doouter diameter of the heating tube,m

Eenhancement factor

ffrequency,Hz

fssampling frequency of acceleration signal,Hz

llength of the heating tube,m

Ntotal counter

Fig.13.Comparisons of the enhancement factors between the Na2SO4 solution and water:(a) q=7.29 kW?m-2,ε=1% ;(b) q=12.14 kW?m-2,ε=1% ;(c) q=7.29 kW?m-2,ε=3% ;(d) q=12.14 kW?m-2,ε=3% .

Fig.14.Comparison between the calculated and experimental values of the threephase boiling heat transfer coefficient in the Na2SO4 evaporator.

P(f)power spectral density function of collision acceleration signal,m2?s-4?Hz-1

Qactual heating power,W

Q0input power,W

QLheat loss,W

qheat flux,kW?m-2

Siinternal surface area of the heating tube,m2

tmean outer wall temperature of the insulation cotton,°C

tfmean temperature of the fluid,°C

tfientrance temperature of the fluid,°C

tfoexit temperature of the fluid,°C

twimean inner wall temperature of the heating tube,°C

twomean outer wall temperature of the heating tub,°C

ucirculation flow velocity,m?s-1

w(n) window function

x(n) acceleration time series,m?s-2

α flow boiling heat transfer coefficient,W?m-2?°C-1

αTjoint heat transfer coefficient of convection and radiation,W?m-2?°C-1

αvlvapor–liquid two-phase flow boiling heat transfer coefficient,W?m-2?°C-1

αvlsvapor–liquid–solid three-phase flow boiling heat transfer coefficient,W?m-2?°C-1

ε amount of added particles,%

λ thermal conductivity of the heating wall,W?m-1?°C-1

σ standard deviation,m?s-2