Rashmi Dhurandhar,Sumit H.Dhawane,Jyoti Prakash Sarkar,Bimal Das

1 Department of Chemical Engineering,National Institute of Technology,Durgapur 713209,West Bengal,India

2 Department of Chemical Engineering,Maulana Azad National Institute of Technology,Bhopal 462003,Madhya Pradesh,India

Keywords:Pneumatic conveying Pressure drop Converging riser Gas-solid dynamics

ABSTRACT The understanding of the flow characteristics and effect of gas-solid interactions in pneumatic risers is fundamental to investigate to ensure effective design cost-effective operation.Thus,to understand the effect of gas-solid interactions on the hydrodynamics of newly proposed conversing risers,this study mainly focused on predicting pressure drop in the dilute phase pneumatic conveying system.The experiments were conducted in a converging riser having a convergence angle of 0.2693°.Various solid particles such as sago,black mustard,and alumina have been considered to study the effect of particle sizes and density on the pressure drop.The experimental outcomes indicate that the total pressure drop increases with an increase in the solid density and gas mass flow rate.Moreover,smaller particle sizes are also increased the pressure drop.An empirical correlation is developed for the prediction of total pressure drop ΔPT in converging pneumatic riser via dimensional analysis.All dependent variables such as particle and air density,drag force,acceleration due to gravity,the mass flow rate of air and particle,the diameter of particle and converging riser,the height of converging riser were considered to develop the empirical correlation.The established relationship is tested,and experimental data have been fitted for its validation.The estimated relative error of less than 0.05 proved the significance of the developed correlation.Hence,it can be stated that the established relationship is useful in studying the effects of various parameters on the pressure drop across the length of the conversing riser.

1.Introduction

Pneumatic conveyingsystems comprise of a small diameter pipe used to transport the solidsviagas or air as a transporting medium.Pneumatic conveyors are widely used across many industries for solid transportation from the past few decades.Besides,the higher gas-particle interaction under pneumatic conditions encouraged to extend such a mechanism towards many industrial gas-particle heat and mass transfer equipments,including gassolid reaction.Numerous investigations have been conducted on its hydrodynamics.A brief report on studies on hydrodynamics by earlier researches needs to be mentioned in connection with present work.

Pneumatic conveying mostly refers to the concurrent flow of gas and solid,where the gas velocity is higher than the particle terminal velocity [1].Pneumatic conveying systems are categorized into two categories,i.e.,dilute phase and dense phase.In the dilute phase,the gas velocity is very high(greater than 20 m per second),and air supply pressure is low (less than 5 mbar per metre,1 bar=105Pa) while in the dense phase the pressure is very high(greater than 20 mbar per metre) and velocity is low (1-5 m per second).In the dilute phase pneumatic system,the solid to gas loading ratio is less than 1% by volume.But in the dense phase,the solid to gas loading ratio is very high(greater than 30%by volume),resulting in high solid-solid interaction [2].The fast fluidized bed and the dense phase vertical pneumatic conveying are quite similar.The fast fluidized bed is classified into a fixed bed,bubbling regime,slugging regime,turbulent regime,fast fluidization,and dilute phase pneumatic conveying [3].If the pipe size is large and particle size is small,his classification can be applied as it is.If the pipe size is small and the particle size is large,the bubbling regime is not observed.There are possibilities of two different dense flows on the basis of particle size and tube diameter.Wherein,particles can be transported as slug or bubble which can be termed as slugging dense transport [4],and in other,the solids are transported by means of recirculation near the wall that can be termed as fast fluidization [5].Among the various conveying systems,the simple construction,flexibility in layout,and easy maintenance make it meritorious [6].

The pneumatic system is extensively used in the cement industry,food and pharmaceutical industries,coal combustion,pollutants scattering,ceramic industries,and in fluid catalytic cracking units,etc.[7].Among the other types of the dryer,the flash dryer(pneumatic dryer) is having the highest moisture removal rate from the solid particle within very less residence time [8].The pressure drop is an essential parameter for the design of a pneumatic conveying system since the power consumption for the operation of such a conveying system is of utmost importance.Hence an accurate prediction of this parameter is necessary for trouble-free,smooth,and optimized working of pneumatic systems.A semi-empirical pressure drop model is proposed to streamline the process.This optimization is mainly applied to the reduction of power consumption [9].

An equation for the pneumatic conveying system is firstly proposed for estimating the pressure drop with an assumption of negligible particle-wall friction[10].A correlation for the prediction of the pressure drop is suggested[11],which is demonstrated by the subsequent equations:

whereG1andG2are dependent on the empirical function of the dimensionless group,DtandDpis the riser and particle diameter,ρgand ρsare the density of gas and particle,ΔPTis the total pressure drop and ΔPgis the pressure drop due to gas only,θ is the mass ratio of solid to gas,andReis the gas Reynolds number.

A correlation is suggested for pressure drop as a function of five dimensionless groups in a vertical pneumatic transport system[12].The pressure drop is a function of the system dynamic parameters as follows:

where ΔPTandLare the pressure and length.Ugis the nominal gas velocity,Vgis the actual gas velocity,Vsis the slip velocity,Ws,andWgare the particle and gas mass velocities.fis the friction factor,ρsis the particle density,DTis the tube diameter.

The pressure loss could be estimated by summing up the contribution of the particle acceleration,the static heads due to air and particles,gas wall friction and particle friction [13].The summary of the correlation available for the prediction of pressure drop in the dilute phase vertical pneumatic conveying system has been reported [14].A similar equation for prediction of total pressure drop in the dilute phase vertical pneumatic conveying system has been used [15].

The influence of solid particle size,shape,Reynolds number,and solid mass loading on the pressure drop of the vertical pneumatic transport system has been reported [16].

The pressure drop is predicted with the help of computational fluid dynamics[17].In another work,the pressure drop prediction in the vertical and horizontal pneumatic transport system is carried out with the help of the hydrodynamic model [18].Most of the similar correlations used for the prediction of pressure drop in the pneumatic conveying system have been summarized [19].

The pressure drop for the acceleration section is estimated with the help of a uniform flow model [20].The influence of particle dynamics on pressure drop has been experimentally investigated[21].The pressure drop is predicted with the help of a onedimensional steady-state two-fluid model in a gas-solid vertical pneumatic conveying system [22].The acceleration pressure drop is predicted based on the momentum change concept [23].The effect of riser geometry on gas-solid hydrodynamics and heat transfer have been reported and they found that converging risers are more efficient in terms of gas-solid heat transfer [24].However,the studies on pressure drop estimation for pneumatic conveying in converging riser is lacking in the literature as most of the reported literature covers heat and mass transfer aspects.

The present work focuses on investigating the influence of various operational parameters on gas-particle pressure drop in a converging pneumatic conveying system.A converging riser having a riser convergence angle of 0.2693 deg is used for the present study.The effect of continuous change in the cross-section of the riser along the riser height on the gas-solid hydrodynamic behavior was taken into account.As the cross-sectional continuously decreases,the gas velocity and particle velocity increases,resulting in an increase in slip velocity and particle Reynolds number.The particle Reynolds number is directly proportional to the convective heat and mass transfer so that the heat and mass transfer is higher for converging riser.The pressure drop increases with increasing gas velocity,but at the same time,the particle Reynolds number increases and resulting in an increase in gas-solid heat and mass transfer,which overcome the pressure loss.

The experimental data is also generated on the total pressure drop using different particles having different density and size for the converging pneumatic conveying system.An empirical correlation has been developed for the estimation of the overall pressure drop as a function of the physical and dynamic variables of the system in the converging riser.

2.Experimental

The experimental set-up has been fabricated to conduct experiments on hydrodynamic behavior of gas-solid flow in vertical converging pneumatic risers.The schematic diagram and pictorial view of the experimental set-up are revealed in Fig.1(a) and (b).The set-up consists of a converging pneumatic conveying riser,blower,storage bin,and cyclone separator.The vertical transport riser,cyclone,and return leg are made of acrylic plastic.The converging vertical riser is having a length of 2.7 m,bottom diameter of 0.0762 m,and it vertically converges to 0.0508 m with an angle of convergence 0.2693 deg.The air is used as a conveying medium,and it is supplied by a blower.The flow rate and velocity of the conveying air are measured using an orifice meter connected to a U-riser manometer.The airflow rate is controlled by the globe valve V3fitted between the blower and the orifice meter.Solid feeding is done by the brass riser,having a diameter of 2.05 cm and controlled by valve V2fitted at the bottom of the hopper.Pressure taps are provided along with the vertical height of the transport riser at a distance of every 11 cm,which is connected to a common pressure tap connector to measure the differential pressures with the help of the U riser manometer.The common pressure tap-connector drum is made of acrylic riser and sheets.All the pressure taps of the vertical transport riser are connected to the common connector through the brass valves.A single riser from the center of the common connector is connected with one end of a U riser water manometer.By opening the individual valves of the pressure taps,the differential pressure reading is measured by connecting the other end of the manometer with the bottommost pressure tap (P1) of the transport riser.

Fig.1.(a)Schematic diagram of the experimental set-up(b)Pictorial view of complete set-up with converging riser and common connector for pressure measurement used in hydrodynamic experiments.

One storage hopper(S)is used for solid storage from which the solid is fed to a solid feeding line by a rotary feeder driven by a motor.In the case of the non-working of a rotary feeder,there is a provision to replace the rotary feeder by a small vertical riser fitted with a gate valve.The measured solid discharged from the storage hopper is normally flowing through the feeding riser by gravity.It is also forced to flow through the solid feeding riser to distribute the particulate solids throughout the cross-section of the feeding point of the riser by a small amount of compressed air by opening the valve,V5.Then the flow rate of this additional air is also measured by using a digital flow meter,which is added to the main air entering through the bottom of the riser.This additional airflow will help to balance the pressure between the solid feeding section and the converging riser,and a water manometer maintains the compressed airline.As a result,the main air through the riser will not be bypass through the solid feeding riser.

The upper portion of the converging riser is connected with the cyclone separator to separate a solid particle from conveying gas.One acrylic plastic quick closing on-off valve (V1) is installed on the return leg of the cyclone separator for intermittent estimation of the solid hold-up in the system.The return leg is graduated,starting from the top of the valve V1.During the steady operation of the experimental run,the total hold-up in the circulating system is measured by suddenly closing the valve V1in the cyclone return leg for a short time interval,and deposited bed height is measured.The volume of solids deposited in the return leg of cyclone above the valve V1is evaluated by multiplying the height of the deposited solid by the cross-sectional area of the return leg.The masscirculation rate is determined by multiplying the solid volume with solid bulk density and dividing by the time of duration for which the valve is kept closed.Another globe valve V4is fitted at the bottom-most of the converging vertical riser,which is used to empty the riser during two consecutive experimental runs.

During operation in the experimental set-up,the particles have been discharged after a few cycles of operation.The screening of the solid particles has been performed with the help of appropriate meshes.The particles are again reloaded.So that the percentage of crust particles in the fresh feed will be as minimum as possible.

The different types of particulate solids like small sago,large sago,alumina,and black mustard are used for obtaining experimental data,and their physical properties are provided in Table 1.The range of air mass flow rate used for sago,black mustard,and alumina was 0.02-0.09 kg·s-1.At the outlet of the converging section,the velocity was 2.25 times greater than the inlet velocity of the converging riser.

Table 1Physical properties of materials

3.Results and Discussion

The pressure drop is a crucial parameter for conveyor design.The pressure drop of the system is directly related to power consumption.It is directly associated with the economy of the process.The system’s total pressure drop is strongly influenced by solid physical properties,gas flow rate,and pipe geometry.The experimental outcomes obtained at different parametric conditions were analyzed to check the influence of individual parameters on the total pressure drop.

The effect of the riser dimension on overall pressure drop has studied by Dhurandharet al.[24].They found that with decreasing the riser diameter,the total pressure drop increases.Also with decreasing riser diameter the slip velocity increasing result in an increase in particle Reynolds numbers (Rep)，which enhances the heat and mass transport coefficients.Using a converging riser instead of a uniform riser improves the heat transfer between gas-solid.So that the experimental studies carried out in a converging riser are presented with their subsequent discussions.

3.1.Estimation of pressure drop contribution of solid in total pressure drop

Fig.2 represents the pressure drop due to solid,air,and airsolid mixture.The pressure drop due to solid is experimentally measured by subtracting the pressure drop occurred by particlefree airflow from the total pressure drop due to gas-solid flow.The sago particle of size 3.75 mm with a mass flow rate of 0.0396 kg·s-1is used for this study.

3.2.Factor influencing the total pressure drop

Since the particle physical properties and gas mass flow rate affects the overall pressure drop of the system.The following graphical plots with subsequent discussions are furnished below.

3.2.1.Effect of gas flow rate on pressure drop

The pressure drops along the riser height of the converging riser have experimentally studied by using the particle of a single size(1.61 mm) at approximately the same particle feed rate(0.0056 kg·s-1) at a different gas flow rate (0.06-0.09 kg·s-1).The effect is represented in the following Fig.3(a).

Fig.3(a) represents the total pressure drop with varying gas flow rates.With an increase in gas volumetric flow rate,the gas velocity also increases,resulting in higher slip velocity between conveying air and particles and thereby higher drag force acting on the particles.So,at the high gas flow rate,particle acceleration is more as compared to the lower gas flow rate.Thereby,the acceleration pressure drop component is comparatively larger in case of higher gas flowrate and contributing more to the total pressure drop.The gas frictional pressure drop is increasing with an increase in gas velocity as the friction pressure drop is proportional to square of the gas velocity.Therefore for the high conveying air velocity,the frictional pressure drop is also very high.These two pressure drop component contribution increases the total pressure drop.

3.2.2.Effect of particle size on pressure drop

The particle size plays an essential role in increasing or reducing the pressure drop.Thus,the influence of particle size has been experimentally studied for the same solid loading ratio,i.e.,the proportion of solid to gas mass flow rate and its effect is represented in the following Fig.3(b).

Fig.2.Pressure drop in a mixture of air-solid flow and individual pressure drop due to air and solid for converging riser.

Fig.3.(a)Variation of total pressure drop with a gas flow rate for converging riser.(b) Variation of total pressure drop with particle size for converging riser.(c)Variation of total pressure drop with particle density for converging riser.

With constant gas mass flow rate and solid loading,the total pressure drop decreases with an increase in particle size.For the same solid loading ratio,the number of particles increases with decreasing the particle size.Resulting there is an increase in smaller size particle’s surface area than that of bigger size particles,and more surfaces are exposed to the flowing gas.Therefore the total drag force increases with decreasing the particle size.The particles of smaller sizes are having comparatively much lesser gravity than the bigger size particles and thereby accelerated more rapidly than the bigger size particles.As a result,the pressure drop component due to particle acceleration in case of smaller particles per unit mass is comparatively much higher than that of bigger particles.Due to this,the acceleration pressure drop component contributes more to the total pressure drop leading to a higher total pressure drop in case of smaller size particles.

3.2.3.Effect of particle density on pressure drop

The effect of particle density on pressure drop has experimentally studied for the same operating condition,and its effect is shown in Fig.3(c).The alumina and mustard particle having a density of 2480 and 1020 kg·m-3is used for this study.The pressure drop for heavier particles(Alumina)is more than that of the lighter particle (Mustard),and the pressure differences between the profiles are observed to increase slightly with the height of the converging riser.The lighter particle is accelerated more than the heavier particles,and the acceleration pressured drop is also more for the lighter particle.It can also be concluded that for the heavier density particle,the voidage is less,density is more,and the particle velocity is also less.The drag force is dependent on size,are the same for both the particles.Consequently,the net upward force on the heavier particle will be less than lighter resulting in lower particle velocity of the high-density particle.The heavier particle will be more sluggish in the riser and increases particle volume fraction in the riser,and voidage(ε)or void fraction for higher density particle would less.Due to this the static pressure drop component for heavier particles is having the higher value as compared to lighter density particle resulting increases in the total pressure drop.

3.3.The empirical correlation for prediction of pressure drop in converging riser

The pressure drop (ΔP) in a gas-solid pneumatic system is a function of the physical and dynamic variables of the system.Pressure drop (ΔP) depends on the following variables:FD(the drag force on the particles by the fluids,kg·m·s-2),ρg(the density of a gas,kg·m-3),ρp(the density of solid particles,kg·m-3),g(acceleration due to gravity,m·s-2),dp(diameter of the solid particle,m),DT(diameter of the converging riser,m),RL(height of the riser,m),qs(solid mass flow rate,kg·s-1),qG(gas mass flow rate,kg·s-1).

The above variables are having an impact on ΔPT.Drag force results in higher acceleration of the particles,which implies a higher acceleration pressure drop component leading to elevated total pressure drop.The gas frictional pressure drop component is directly proportional to the gas density.The solid static pressure drop component is directly proportional to the solid density.For the denser solid particle,the solid static pressure drop will be higher.Acceleration due to gravity implies the mass of the particle due to which the static pressure drop component will depend.The drag force acting on the particle depends on the surface area per unit volume of the particle.Thereby it increases with increasing particle size.The frictional pressure drop depends on the riser diameter.For large diameter risers,the frictional pressure drop is more,but the gas velocity is less,which will have an impact on the pressure component and thereby on the total pressure drop.The pressure drop component depends on the riser length.More will be the riser length more will be the pressure drop component.The solid frictional pressure drop component and static pressure drop component depend on the solid flow rate.For high solid flow rate,solid frictional pressure drop component and static pressure drop component will be more.The gas frictional pressure drop component is directly proportional to the square of the gas velocity.

The Buckingham’s π theorem for estimation of empirical correlation has been used.The dependent variable is mathematically expressed as a function of independent variables.Hence the pressure drop can be expressed as a function of the above variables,

The above equation is dimensionally homogeneous,which containsnvariables.If the number of fundamental dimensions ism,then the above equations can be written in terms of the dimensionless group.

So,in this case,the repeating variables aredp，gand(ρP-ρg)and each term can be written as

So each π term is dimensionless and is independent of the system.Each equation is solved by the principle of dimensionless homogeneity,and values ofa1,b1,c1,etc.are obtained.Then the final results are written as

By Eq.(4),the regression analysis is carried out with the help of FORTRAN software in Microsoft developer studio-95 using the experimental data of pressure drop yielded the following correlation.

The experimental results obtained are utilized for the estimation of the correlation coefficient (R2),and their impeccable fit is confirmed by the accomplished value ofR2as 0.9783.The unity value of the correlation coefficient signifies the linear and ideal fit of the developed equation.The standard deviation is the square root of the variance,and for the present study,it was 0.1565.The lower value of standard deviation demonstrates that the developed equation can predict the best condition with high accuracy.The degree of freedom,probability level,and confidence range is 73%,0.05%,and 95%.

Fig.4.Comparison between Experimental and Predicted value of total pressure drop for converging riser.

A comparative plot of the experimental and predicted pressure drops is shown in Fig.4,which signifies the overall validity of empirical Eq.(5)for all the solid particles having different physical properties and hydrodynamic conditions.The pressure drops have measured at different riser heights ranging from the solid feed point to 2.7 m.Almost all the points are observed to lie nearby the 45° diagonal lines except some minor deviations near the exit of the riser,indicating that the experimental pressure drops are lower than predicted values.This may be due to an error in measurement for partial clogging of the pressure taps near the exit.However,the overall trend confirms the accuracy of the estimation of pressure drops using the proposed empirical equation.

4.Conclusions

In the present investigation,the influence of particle physical parameters like particle size and density and gas flow rate on total pressure drop are studied.It is observed that the total pressure drop increases with an increase in gas mass flow rate and particle density.However,it decreases with an increase in particle size.The correlation which has developed for the prediction of pressure drop can predict the pressure drop in a converging pneumatic riser with a reasonable accuracy having an overall correlation coefficient of 0.9783,less than 0.05 relative error,and Willmottdindex greater than 0.9871.

Nomenclature

DTconverging tube diameter,m

dhheight of an elemental section,m

dpsolid diameter,m

dTiinlet diameter of converging riser,m

dTooutlet diameter of converging riser,m

FDparticle drag force,kg·m·s-2

gacceleration due to gravity,m·s-2

ΔPpressure drop,N·m-2

qGgas mass flow rate,kg·s-1

qssolid mass flow rate,kg·s-1

RLriser height,m

ρggas density,kg·m-3

ρpparticle density,kg·m-3

φssolid loading ratio

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

The authors would like to thank the Ministry of Human Resource and Development Government of India for funding this research work.The authors also express their thanks to Gajanand Suryawanshi,for their immense support during the execution of the work.