The impact of temperature and particle size on minimumfluidizing velocity was studied and analyzed in a small pilot scale of bubbling fluidized bed reactor.This study was devoted to providing some data about fluidizat...The impact of temperature and particle size on minimumfluidizing velocity was studied and analyzed in a small pilot scale of bubbling fluidized bed reactor.This study was devoted to providing some data about fluidization to the literature under high temperature conditions.The experiments were carried out to evaluate the minimum fluidizing velocity over a vast range of temperature levels from 20℃ to 850℃ using silica sand with a particle size of 300-425μm,425-500μm,500-600μm,and 600-710μm.Furthermore,the variation in the minimumfluidized voidage was determined experimentally at the same conditions.The experimental data revealed that the Umf directly varied with particle size and inversely with temperature,whileεmf increases slightly with temperature based on the measurements of height at incipient fluidization.However,for all particle sizes used in this test,temperatures above 700℃ has a marginal effect on Umf.The results were compared with many empirical equations,and it was found that the experimental result is still in an acceptable range of empirical equations used.In which,our findings are not well predicted by the widely accepted correlations reported in the literature.Therefore,a new predicted equation has been developed that also accounts for the affecting of mean particle size in addition to other parameters.A good mean relative deviation of 5.473% between the experimental data and the predicted values was estimated from the correlation of the effective dimensionless group.Furthermore,the experimental work revealed that the minimum fluidizing velocity was not affected by the height of the bed even at high temperature.展开更多
Minimum spouting velocity (Ums) is one of the most important flow characteristics for proper design and operation of spouted bed reactors. Many correlations for Ums have been published since spouted bed technology w...Minimum spouting velocity (Ums) is one of the most important flow characteristics for proper design and operation of spouted bed reactors. Many correlations for Ums have been published since spouted bed technology was initiated in 1955. In this paper, a new correlation is developed for Ums based on 767 published experimental data covering both high pressure and high temperature conditions. The calculated and the measured results of Ums are in better agreement than other published correlations.展开更多
Fluidized-bed reactors are widely employed in various high-temperature industrial processes.Thus,it is crucial to understand the temperature effect on various fluidization phenomena,specifically the minimum fluidizati...Fluidized-bed reactors are widely employed in various high-temperature industrial processes.Thus,it is crucial to understand the temperature effect on various fluidization phenomena,specifically the minimum fluidization velocity(U_(mf))that governs various aspects of fluidized bed behavior.In this study,we comprehensively analyze U_(mf) data from the literature to unravel the complexity and underlying mechanisms of temperature influence on this critical velocity.The research examines experimental data encompassing a wide range of temperatures,pressures,and solid particles.The analysis reveals that the influence of temperature on U_(mf) is fundamentally determined by the relative importance of hydrodynamic forces and interparticle forces within fluidized beds and is realized by three distinctive temperature-induced changes:gas properties,bed voidage,and physiochemical characteristics of particles.On this basis,an equation is derived to enable predictions of temperature influences on the minimum fluidization velocity under broad temperature conditions.展开更多
In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The est...In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.展开更多
The minimum fluidization velocity of a fluid-solid particle fluidized bed is the primary focus of this paper.The computationally economic Eulerian Granular model has been used to analyze fluidization for both gas-soli...The minimum fluidization velocity of a fluid-solid particle fluidized bed is the primary focus of this paper.The computationally economic Eulerian Granular model has been used to analyze fluidization for both gas-solid particle and liquid-solid particle fluidized beds.The conventional approach of finding minimum fluidization velocity(umf)is either with a pressure drop across the particle bed or the change in bed height.However,these parameters are often unstable and cannot be used to generalize the degree of fluidization accurately.In this paper,the dominant factor of unstable pressure drop estimation in the 2D Two-Fluid Model(TFM)and a key non-dimensional Euler number has been investigated in deter-mining minimum fluidization velocity for different quasi-2D fluidized beds for different bed sizes,par-ticle sizes,and particle numbers.Averaging assumptions and limitations of these numerical models are discussed in detail for four different fluidized bed cases.A comparative study of the drag model shows little to no influence in unstable pressure drop estimation near fluidization velocity,and all drag models perform similarly.It is observed that particle-particle collision is not the dominant reason for unstable pressure drop near minimum fluidization.Instead,wall effects on the particle bed including frictional losses and wall-particle collision play a key role in unstable pressure drop calculation for the quasi-2D fluidized beds.Pressure drop characteristics alone do not suffice to obtain minimum fluidization ve-locity with 2D TFM using existing models.Thus,a different approach has been proposed to investigate minimum fluidization involving the Euler number,which has shown promising performance in deter-mining minimum fluidization velocity and characterizing fluidization with 2D TFM.Results show con-sistency in Euler number characteristics for all different fluidized bed cases considered in this paper.This can revitalize computationally economic 2D Eulerian simulations,increase the range of possible appli-cations,and provide guidance to the future development of computationally efficient and more accurate numerical models,and empirical correlations for minimum fluidization velocity.展开更多
Experiments were performed on spout characteristics of a cylindrical spout-fluidized bed (I.D. = 10 cm) with different static heights and two materials (A1203 and high density polyethylene). Results of minimum spo...Experiments were performed on spout characteristics of a cylindrical spout-fluidized bed (I.D. = 10 cm) with different static heights and two materials (A1203 and high density polyethylene). Results of minimum spouting velocity obtained in this study were compared with reported correlations for both spouted and spout-fluidized beds. Considerable discrepancies were found between the values obtained using different model equations as well as with respect to experimental results. Based on the Mathur-Gishler correlation, a new correlation is proposed for calculating the minimum spouting velocity that introduces the ratio U/Umf. It was found that the minimum spouting velocity decreases with increasing fluidizing gas velocity (U/Umf). The pressure drop at the point of minimum spouting velocity is also correlated using this dimensionless group and is presented in this work. This investigation demonstrates that the use of correlations reported in the literature that focus primarily on conical bottom spouted beds are not applicable to fiat-bottom spouted and spout-fluidized beds.展开更多
Single orbit bistatic space-based radar (SBR) is composed of two radars in the same orbit. The characteristics of the clutter Doppler-angle spectrum of a single orbit bistatic SBR show that the slope of the mainbeam...Single orbit bistatic space-based radar (SBR) is composed of two radars in the same orbit. The characteristics of the clutter Doppler-angle spectrum of a single orbit bistatic SBR show that the slope of the mainbeam clutter spectrum is highly sensitive to the cone angles. Therefore, the minimum detectable velocity of the bistatic system is dependent on the cone angle. Then a new combined working mode of singleorbit bistatic SBR system was developed in which one radar will act as the transmitter and another as the receiver to improve detection performance for all angles. Simulation results by space-time adaptive processing verify the improved detection performance. The new design also reduces the average power of each radar system and the size and weight of the on-board solar array-battery system.展开更多
The minimum fluidization velocity(U_(mf))is a key parameter for the scale-up of inverse liquid-solid flu-idized beds.Theoretical predictions using common correlations were compared against experimental minimum fluidiz...The minimum fluidization velocity(U_(mf))is a key parameter for the scale-up of inverse liquid-solid flu-idized beds.Theoretical predictions using common correlations were compared against experimental minimum fluidization velocity measurements of low density(28-638 kg/m^(3)),0.80-1.13 mm Styrofoam particles in a fluidized bed with a height of 4.5 m and 0.2 m diameter.The average absolute relative deviation for the predicted minimum fluidization velocity for particles below 300 kg/m^(3) was above 40%using the studied common correlations.A modified Wen and Yu correlation was thus proposed based on novel and past measurements with low-density and small-diameter particles,expanding the range for predicting U_(mf).The new correlation predicted U_(mf) with deviations below 15%for ST028,ST122 and ST300.This modified correlation also improved U_(mf) predictions for comparable particles from a previous study,demonstrating its validity for a larger range of low-density particles.展开更多
This paper investigated the effect of Gaussian distribution width,average particle diameter,particle loading,and the tapered angle on minimum fluidization velocity(U_(mf))by conducting extensive experiments in tapered...This paper investigated the effect of Gaussian distribution width,average particle diameter,particle loading,and the tapered angle on minimum fluidization velocity(U_(mf))by conducting extensive experiments in tapered fluidized beds.Three powders with Gaussian size distribution and different distribution widths were used in the experiments.An increase in U_(mf)with increasing the average particle diameter,particle loading,and the tapered angle was observed.There was also a nonmonotonic behavior of Umf as the Gaussian distribution width increased.An empirical correlation including dimensionless groups for predicting Umf in tapered beds was developed in which the effect of distribution width was considered.The proposed correlation predictions were in good agreement with the experimental data,with a maximum deviation of 16.5%and average and standard deviations of,respectively,6.4%and 7.4%.The proposed correlation was also compared with three earlier models,and their accuracy was discussed.展开更多
文摘The impact of temperature and particle size on minimumfluidizing velocity was studied and analyzed in a small pilot scale of bubbling fluidized bed reactor.This study was devoted to providing some data about fluidization to the literature under high temperature conditions.The experiments were carried out to evaluate the minimum fluidizing velocity over a vast range of temperature levels from 20℃ to 850℃ using silica sand with a particle size of 300-425μm,425-500μm,500-600μm,and 600-710μm.Furthermore,the variation in the minimumfluidized voidage was determined experimentally at the same conditions.The experimental data revealed that the Umf directly varied with particle size and inversely with temperature,whileεmf increases slightly with temperature based on the measurements of height at incipient fluidization.However,for all particle sizes used in this test,temperatures above 700℃ has a marginal effect on Umf.The results were compared with many empirical equations,and it was found that the experimental result is still in an acceptable range of empirical equations used.In which,our findings are not well predicted by the widely accepted correlations reported in the literature.Therefore,a new predicted equation has been developed that also accounts for the affecting of mean particle size in addition to other parameters.A good mean relative deviation of 5.473% between the experimental data and the predicted values was estimated from the correlation of the effective dimensionless group.Furthermore,the experimental work revealed that the minimum fluidizing velocity was not affected by the height of the bed even at high temperature.
基金the National Natural Science Foundation of China through the program "Time and Spatial Multi-Scale Interactions in Chemical Engineering and Their Effects" (Grant No. 20490201).
文摘Minimum spouting velocity (Ums) is one of the most important flow characteristics for proper design and operation of spouted bed reactors. Many correlations for Ums have been published since spouted bed technology was initiated in 1955. In this paper, a new correlation is developed for Ums based on 767 published experimental data covering both high pressure and high temperature conditions. The calculated and the measured results of Ums are in better agreement than other published correlations.
基金supported by the National Natural Science Foundation of China(grant No.U22A20410).
文摘Fluidized-bed reactors are widely employed in various high-temperature industrial processes.Thus,it is crucial to understand the temperature effect on various fluidization phenomena,specifically the minimum fluidization velocity(U_(mf))that governs various aspects of fluidized bed behavior.In this study,we comprehensively analyze U_(mf) data from the literature to unravel the complexity and underlying mechanisms of temperature influence on this critical velocity.The research examines experimental data encompassing a wide range of temperatures,pressures,and solid particles.The analysis reveals that the influence of temperature on U_(mf) is fundamentally determined by the relative importance of hydrodynamic forces and interparticle forces within fluidized beds and is realized by three distinctive temperature-induced changes:gas properties,bed voidage,and physiochemical characteristics of particles.On this basis,an equation is derived to enable predictions of temperature influences on the minimum fluidization velocity under broad temperature conditions.
文摘In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.
文摘The minimum fluidization velocity of a fluid-solid particle fluidized bed is the primary focus of this paper.The computationally economic Eulerian Granular model has been used to analyze fluidization for both gas-solid particle and liquid-solid particle fluidized beds.The conventional approach of finding minimum fluidization velocity(umf)is either with a pressure drop across the particle bed or the change in bed height.However,these parameters are often unstable and cannot be used to generalize the degree of fluidization accurately.In this paper,the dominant factor of unstable pressure drop estimation in the 2D Two-Fluid Model(TFM)and a key non-dimensional Euler number has been investigated in deter-mining minimum fluidization velocity for different quasi-2D fluidized beds for different bed sizes,par-ticle sizes,and particle numbers.Averaging assumptions and limitations of these numerical models are discussed in detail for four different fluidized bed cases.A comparative study of the drag model shows little to no influence in unstable pressure drop estimation near fluidization velocity,and all drag models perform similarly.It is observed that particle-particle collision is not the dominant reason for unstable pressure drop near minimum fluidization.Instead,wall effects on the particle bed including frictional losses and wall-particle collision play a key role in unstable pressure drop calculation for the quasi-2D fluidized beds.Pressure drop characteristics alone do not suffice to obtain minimum fluidization ve-locity with 2D TFM using existing models.Thus,a different approach has been proposed to investigate minimum fluidization involving the Euler number,which has shown promising performance in deter-mining minimum fluidization velocity and characterizing fluidization with 2D TFM.Results show con-sistency in Euler number characteristics for all different fluidized bed cases considered in this paper.This can revitalize computationally economic 2D Eulerian simulations,increase the range of possible appli-cations,and provide guidance to the future development of computationally efficient and more accurate numerical models,and empirical correlations for minimum fluidization velocity.
文摘Experiments were performed on spout characteristics of a cylindrical spout-fluidized bed (I.D. = 10 cm) with different static heights and two materials (A1203 and high density polyethylene). Results of minimum spouting velocity obtained in this study were compared with reported correlations for both spouted and spout-fluidized beds. Considerable discrepancies were found between the values obtained using different model equations as well as with respect to experimental results. Based on the Mathur-Gishler correlation, a new correlation is proposed for calculating the minimum spouting velocity that introduces the ratio U/Umf. It was found that the minimum spouting velocity decreases with increasing fluidizing gas velocity (U/Umf). The pressure drop at the point of minimum spouting velocity is also correlated using this dimensionless group and is presented in this work. This investigation demonstrates that the use of correlations reported in the literature that focus primarily on conical bottom spouted beds are not applicable to fiat-bottom spouted and spout-fluidized beds.
文摘Single orbit bistatic space-based radar (SBR) is composed of two radars in the same orbit. The characteristics of the clutter Doppler-angle spectrum of a single orbit bistatic SBR show that the slope of the mainbeam clutter spectrum is highly sensitive to the cone angles. Therefore, the minimum detectable velocity of the bistatic system is dependent on the cone angle. Then a new combined working mode of singleorbit bistatic SBR system was developed in which one radar will act as the transmitter and another as the receiver to improve detection performance for all angles. Simulation results by space-time adaptive processing verify the improved detection performance. The new design also reduces the average power of each radar system and the size and weight of the on-board solar array-battery system.
文摘The minimum fluidization velocity(U_(mf))is a key parameter for the scale-up of inverse liquid-solid flu-idized beds.Theoretical predictions using common correlations were compared against experimental minimum fluidization velocity measurements of low density(28-638 kg/m^(3)),0.80-1.13 mm Styrofoam particles in a fluidized bed with a height of 4.5 m and 0.2 m diameter.The average absolute relative deviation for the predicted minimum fluidization velocity for particles below 300 kg/m^(3) was above 40%using the studied common correlations.A modified Wen and Yu correlation was thus proposed based on novel and past measurements with low-density and small-diameter particles,expanding the range for predicting U_(mf).The new correlation predicted U_(mf) with deviations below 15%for ST028,ST122 and ST300.This modified correlation also improved U_(mf) predictions for comparable particles from a previous study,demonstrating its validity for a larger range of low-density particles.
文摘This paper investigated the effect of Gaussian distribution width,average particle diameter,particle loading,and the tapered angle on minimum fluidization velocity(U_(mf))by conducting extensive experiments in tapered fluidized beds.Three powders with Gaussian size distribution and different distribution widths were used in the experiments.An increase in U_(mf)with increasing the average particle diameter,particle loading,and the tapered angle was observed.There was also a nonmonotonic behavior of Umf as the Gaussian distribution width increased.An empirical correlation including dimensionless groups for predicting Umf in tapered beds was developed in which the effect of distribution width was considered.The proposed correlation predictions were in good agreement with the experimental data,with a maximum deviation of 16.5%and average and standard deviations of,respectively,6.4%and 7.4%.The proposed correlation was also compared with three earlier models,and their accuracy was discussed.