- Email: [email protected]
Heat and Mass Transfer in U-Bend of a Pneumatic Conveying Dryer
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER M. Hidayat1,2 and A. Rasmuson1, 1
Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers University of Technology, Go¨teborg, Sweden. 2 Chemical Engineering Department, Engineering faculty, Gadjan Mada University, JL Gratika No 2, Yogyakarta, Indonesia.
Abstract: Computational fluid dynamics (CFD) modelling with the Eularian –Eularian formulation is used to describe the drying phenomena occurring in pneumatic conveying drying particularly in the U-bend. Two user defined scalar equations (UDSs) are inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The drying kinetics cover the two periods of drying: the constant drying rate and the falling drying rate. The investigation emphasized influences of the parameters (solid loading ratio, gas velocity, bend radius ratio, feed moisture content and geometry arrangement of a U-bend) on the drying rate and moisture content. A validation of the drying model is accomplished by comparing calculation results with experimental data. In general, the drying rate decreases along the axial direction of pipe due to the decrease in driving force (the air humidity increases). The mass-weighted average drying rate shows a slight decrease in and just after the U-bend, which is mainly due to the high accumulation of solid particles at the outer U-bend wall. Solid particles disperse and the slip velocities are high in the area after the U-bend. This causes the mass-weighted average drying rate to slightly increase. Keywords: pneumatic conveying drying; U-bend; computational fluid dynamics (CFD).
Correspondence to: Dr A. Rasmuson, Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-41296. Go¨teborg, Sweden. E-mail: rasmuson@ chemeng.chalmers.se DOI: 10.1205/chered06162 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, March 2007 # 2007 Institution of Chemical Engineers
INTRODUCTION
drying gas, solid particles and walls. The gas and particles exchange heat and mass through drying, and momentum is exchanged in order to convey particles. The gas and particles interact with the walls through wall friction and heat convection (radiation). The drying times are typically short, in order of seconds, due to limited conveying distances (Stoess, 1983) and the fact that the drying gas becomes saturated. For this reason, many of these dryers are utilized as predryers ahead of longer residence time fluid bed and rotary dryers, for example, in polymer drying operations (Kirk-Othmer, 1993). However, some pneumatic conveying dryers are also applied as main dryers, for instance, for drying fibres in the pulp and paper industry. A comprehensive study concerning fluid dynamics, heat and mass transfer between gas and solid particles in the pneumatic drying system is necessarily needed to obtain better knowledge for the design of a pneumatic dryer. Studies of the fluid dynamics of gas and solid particles through a bend have been accomplished by several authors, for example, Huber and Sommerfeld (1994),
Pneumatic conveying dryers are widely used in industry. In such a dryer, the external (temperature, humidity, mass/heat transfer coefficients) conditions for particles vary along the flow path. A typical dryer is depicted in Figure 1. It consists of erect sections with uprisers and downcomers connected with U-bends. In a study by Fyhr and Rasmuson (1997) it is found that U-bends significantly influence drying behaviour since they enhance velocity differences (slip) between suspended material and the drying medium. This slip will increase external heat and mass transfer rates, thereby enhancing drying conditions. In contrast, the bend will increase the pressure drop of the system. Thus, choosing the appropriate bend shape can be utilized in the overall optimization of a pneumatic conveying dryer. The U-bends may cause problems for sticky materials or if the material is very wet in combination with too low drying rates, our experience though is that this mainly gives problems in the feeding section of the dryer. Pneumatic drying involves simultaneous momentum, heat and mass transfer between 307
Vol 85 (A3) 307–319
308
HIDAYAT and RASMUSON Influences of important parameters (gas velocity, solid loading ratio, bend radius ratio and moisture content of solid particles entering the system) on heat and mass transfer coefficients and the drying rate are studied numerically. The commercial software package Fluent 6.1 is used in the calculations. The Eularian –Eularian modelling approach is applied to predict flow behaviour. A drying model is added using two user defined scalar equations (USDs) to take into account the gas humidity and moisture content of the solid particles. This is necessary since the standard multiphase feature of Fluent 6.1 is not able to handle this complex system. Source terms for both UDSs and the energy equation for the solid particles are also introduced. The results obtained from the simulations are compared with experimental data from a pilot dryer.
Figure 1. Schematic drawing of the pneumatic conveying dryer developed at Chalmers University of Technology (Fyhr and Rasmuson, 1997).
Levy and Mason (1998), Yilmaz and Levy (2001), Akilli et al. (2001) and Tu and Fletcher (1995). Huber and Sommerfeld (1994) have investigated the role of centrifugal forces in segregating solid particles from a carrier gas and they have found the presence of particle size segregation due to centrifugal forces at a 908-bend. The phenomena of secondary flows and of the formation and dispersion of ropes are usually studied simultaneously. Huber and Sommerfeld (1994), Levy and Mason (1998) and Yilmaz and Levy (2001) have studied the distribution of particles in a pipe cross-section affected by a 908-bend. Levy and Mason (1998) have concluded that the paths taken by the particles after the bend are strongly dependent on the diameter of the particles. The ropes are dispersed due to secondary flow and flow turbulence (Akilli et al., 2001). In previous papers by the authors (Hidayat and Rasmuson, 2004, 2005, 2007), the influence of a Ubend on particle velocity, slip velocity, particle concentration distribution, pressure profile and heat transfer phenomena between gas and solid particles have been studied. Kemp et al. (1991) carried out drying experiments to find particle velocities, heat transfer and drying rates in a vertical unit. They have reviewed models for pneumatic conveying dryers and have concluded that none have been entirely successful. They also noticed that effective drying occurs in the inlet zone. Levy and Borde (1999) and Skuratovsky et al. (2005) have simulated vertical pneumatic conveying dryers in one- and two-dimensional models, respectively. In the drying modelling, they have considered that solid particles experience two drying stages. During the first stage, heat transfer controls the evaporation process from the saturated outer surface of a particle to the surrounding gas (a constant drying rate period). During the second stage, diffusion of moisture through the particle crust and convection into the gas medium control the evaporation process. Fyhr and Rasmuson (1997) have presented a model for a pneumatic conveying dryer employing a one-dimensional hydrodynamic plug flow model coupled to a comprehensive twodimensional model for drying single wood chips. In this study it is found that U-bends significantly influence drying behavior since they enhance velocity differences (slip) between suspended material and the drying medium. The present study examines heat and mass transfer (i.e., drying) between gas and solid particles in a U-bend.
MATHEMATICAL MODEL The Eulerian–Eularian model is presented in this section. The model expands the definition of continuum assumption to the dispersed phase and employs the Navier –Stokes equation to both continuous (gas) and dispersed (solid particles) phases. Both phases are assumed to be incompressible. The condition is steady-state and involves heat and mass transfer between phases. However, in order to avoid divergence problems, the numerical solution is iterated at unsteady-state conditions. In the momentum equation the gas and solid are linked using a drag force. The drag force model employs the correlation proposed by Gidaspow et al. (1992). This correlation combines the Wen and Yu model (Wen and Yu, 1966) for the dilute system and the Ergun equations (Ergun, 1952) for the dense system. The heat and mass transfer coefficients between gas and solid use the correlation developed by Gunn (1978). He proposes Nusselt and Sherwood correlations which are valid for a system having the porosity range of 0.35–1.0 and a Reynolds number up to 105. Two UDSs are inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The moisture evaporation rate of solid particles and the humidification rate of gas are treated in the source terms of the corresponding UDS equations. The evaporation energy of moisture is treated in the source term of the solid energy equation. More details about heat and mass transfer are given in the heat and mass transfer model formulation section. The realizable k –1 epsilon model is used to capture turbulence phenomena in both phases. The granular theory for the gas–solid flow of the Eulerian model is introduced (Ding and Gidaspow, 1990). The set of governing equations was solved by using the commercial Fluent 6.1 software package. The discretised equations, along with the initial condition and boundary conditions, were solved using the segregated solution method. Using the segregated solver, the conservation of mass and momentum were solved iteratively and a pressure –correction equation was used to ensure consistency of the conservation of momentum and the conservation of mass (continuity equation). To assist in obtaining a convergent solution, Fluent allows one to solve the discretized equations using a step-by-step solution by activating and deactivating the discretised equations in the numerical solution window.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER Governing Equations The conservation equation of the mass of phase i (i ¼ gas or solid) is @ (ai ri ) þ r (ai ri ui ) ¼ 0 @t X ai ¼ 1: with the constraint
(1) (2)
Constitutive equations play the role of closing governing equations. The following section describes the constitutive equations for the heat and mass transfer between gas and solid in the conservation equation of the energy of the solid phase and the transport equation of the UDSs of both phases. Additional constitutive equations are given in the previous paper (Hidayat and Rasmuson, 2005).
The conservation equation of the momentum of phase i (i ¼ gas or solid) is @ (ai ri ui ) þ r (ai ri ui ui ) ¼ rpi @t þ r ti r (ai ri u0i u0i ) þ ai ri g þ Kji (uj ui )
ð3Þ
where the index j is a pair of the index i (if the index i represents the gas phase then the index j represents the solid phase, and vice versa). The pressure gradients of gas and solid phase are rpi ¼ ag rp and rpi ¼ as rp rps , respectively. The Kji ¼ Kij in the drag force term represents the inter-phase gas– solid momentum exchange coefficient which uses correlations derived by Gidaspow et al. (1992). The Reynolds stresses of phase i, ri u0 i u0i employ the Boussinesq hypothesis (Hinze, 1975) to relate the Reynolds stresses to the mean velocity gradients. The turbulence kinetic energy and turbulence dissipation rate employ the realizable k –1 model proposed by Shih et al. (1995). Equation (3) needs additional information for the solid phase (i ¼ s) which is mainly obtained from the granular temperature equation: 3@ (as rs us ) þ r (as rs us us ) ¼ ( ps I þ ts ):rus 2 @t þ r (kus rus ) gus þ fgs
(4)
The conservation equation of the energy of phase i (i ¼ gas or solid) is @ @pi (ai ri Hi ) þ r (ai ri ui Hi ) ¼ ai þ ti :rui þ Qji þ Sh,i @t @t
where Qji is the intensity of heat exchange between gas and solid phases and Sh,i is the source term of the conservation equation of the energy of phase i. The intensity of heat exchange (Qji) employs the Nusselt correlation developed by Gunn (1978) to calculate the heat transfer coefficient between gas and solid phases. The source term for gas phase (Sh,i ) is zero and the source term for the solid phase (Sh,i ) is due to moisture evaporation from solid phase to gas phase. More details regarding the source term of the solid phase are given in the heat and mass transfer model formulation section. The transport equation of the UDS of phase i (i ¼ gas or solid) is @ai ri ci þ r (ai ri ui ci ) ¼ r (ai Gi rci ) þ Sc,i @t
Heat and Mass Transfer Drying involves coupled heat and mass transfer. The inlet gas, which is the drying medium, is hotter than the inlet solid. The energy transfer is mainly governed by external convection from gas to solid phase. The internal energy transport (mainly conduction) is usually rapid. This energy is used to increase solid temperature and to evaporate the moisture from the solid material. The moisture transport occurs mainly by means of external convection at higher moisture contents and internal transport (capillary flow, diffusion) at lower moisture contents. Due to the complexity of the multiphase flow problem, the drying model has to be simple but comprehensive, which means that it must include a constant drying rate and a falling drying rate as the general characteristics of the drying process. The standard multiphase flow feature of Fluent 6.1 is not able to solve these phenomena. The continuous and the dispersed phases represent only the gas and solid phases, respectively. The mass fraction of water in the gas phase and the moisture content of the solid phase have to be modeled in two additional UDSs. For the convective heat and mass transfer between gas and solid we use the correlations proposed by Gunn (1978), here written for heat transfer: 1=3 Nus ¼ (7 10ag þ 5a2g )(1 þ 0:7Re0:2 ) s Pr 1=3 þ (1:33 2:4ag þ 1:2a2g )Re0:7 s Pr
hsg (5)
(6)
where c is the scalar variable which represents the mass fraction of water in the gas or in the solid particles. The mass fraction of water in the solid particles is the moisture content itself.
309
kg Nus ¼ ds
(7) (8)
The mass transfer analogue is obtained by substituting Sh for Nu and Sc for Pr. The transition between the constant and the falling drying rate periods occurs when the solid particle surface becomes unsaturated and internal mass transfer resistance becomes significant. Due to the fact that the studied particle diameter is small and a simple drying model is desired, the drying rate in the falling drying rate period is assumed to decrease in a linear fashion. This assumption was also utilized by Szafran and Kmiec (2004) in their CFD modelling of a spouted bed dryer. The transition point in their case is defined by comparing values of the mass flux calculated using the external mass transfer equation and the internal mass transfer equation. The equilibrium moisture content is taken as a constant value using the value at the inlet. In the present study, the transition point and the equilibrium moisture content is taken locally, considering the influence of gas and solid phase local conditions. In our case we use wood as a model material. The moisture equilibrium is obtained by doing a polynomial regression on the experimental data of the sorption isotherm of wood at different temperatures and humidities of gas as given by
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
310
HIDAYAT and RASMUSON I II where Nc,s represents to Nc,s and Nc,s in the constant and falling drying rate, respectively. Heat transfer:
Table 1. The polynomial coefficients for equation (9) as function of the solid temperature. Polynomial coeff.
Equations 20.010688 þ 2.7619 1025 Ts 1.1709 2 2.6459 1023 Ts 22.2111 þ 4.9748 1023 Ts 1.7714 2 3.7579 1023 Ts
A B C D
Qsg ¼
6as ag hsg (Ts Tg ) ds
(14)
The source term for the conservation equation of the energy for solid phase is Sh,s ¼ Nc,s Hvap,c
(15)
Siau (1984). Xc ¼ A þ BHc þ CHc2 þ DHc3
(9a)
2 3 Xme ¼ A þ BHme þ CHme þ DHme
(9b)
where Hvap,c is the evaporation energy of water obtained by doing a polynomial regression from available steam tables (Hellsten, 1992). Hvap,c ¼ 3 006 300 1428:1Ts 1:5534Ts2
where Hc and Hme are the saturated humidity of gas (Hc ¼ 1) and the local gas humidity, respectively and A, B, C and D are polynomial coefficients as function of the solid temperature and given in Table 1. The mass flux of moisture evaporated from the solid material during the constant drying rate is I Nc,s
kg,c Mc ¼ (Pc,s Pc,g ) RTs
NUMERICAL SOLUTION Geometry Calculations are conducted for U-bend pipes with the same length, i.e., 5 m, regardless of different bend radius ratios. The calculation domain is constructed of three parts, i.e., the upstream pipe, the U-bend and the downstream pipe. The length of the upstream pipe is 0.5 m for all variations. The different lengths of pipe in the bend due to different bend radius ratios are compensated for by adapting the length of the downstream pipe (Table 2). Figure 2 shows a sketch of the geometry of the calculation domain of the U-bend. The pipe diameter is 0.1 m. The dimensions of the experimental equipment are given in the experimental setup section. The computational grids are approximately 48 000 cells (Figure 3). This number was generated by applying the same cross-sectional meshes of pipe obtained from the optimum cross-sectional meshes of pipe in the single-phase flow case (Hidayat and Rasmuson, 2004). The grid was generated using Gambit 2.0, which is compatible with Fluent 6.1. A boundary layer, which contains four cells with a distance of the cell adjacent to the wall at 2% of the diameter of the pipe and a growth factor of 1.2, was employed at the wall to improve the performance of the wall function and to fulfill the requirement of y þ, the dimensionless wall distance, for
(10)
where R is the gas constant The mass flux of moisture evaporated from the solid material during the falling drying rate is modelled as II Nc,s ¼
X Xme I N Xc Xme c,s
(11)
where Xme X Xc. The two UDSs take into account the mass transfer of water between the solid and gas phases. The drying rate of solid particles and the humidification rate of gas are treated in the source terms of their respective UDS equations. Mass transfer: 6as Nc,s ds ¼ Sc,s
Sc,s ¼
(12)
Sc,g
(13)
(16)
Table 2. Summary of parameter values for calculations. Parameter Bend variation SLR, kg kg21 0.1 0.25 0.5 1.5 7.5
ug, m s21
BR, m m21
L1, m
B, m
L2, m
10 15 20 25 30
3 4 6 8 10 12
0.5 0.5 0.5 0.5 0.5 0.5
0.4712 0.6283 0.9425 1.2566 1.5708 1.8850
4.0288 3.8717 3.5575 3.2434 2.9292 2.6150
The feed moisture content, kg water/kg sawdust 0.175 0.200 0.225 0.250 0.275 0.300 0.325 1.41
Base case. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
311
not shown in the paper. A flat profile of each parameter was introduced at the inlet of this pipe and they resulted in a fully developed flow at the outlet. The fully developed flow obtained at the outlet was used as the inlet boundary condition for the actual calculation domain, as depicted in Figure 2. The gravitation direction is downward or in the opposite direction of the inlet velocity. The outlet boundary condition of the latter was set up as a pressure outlet boundary instead of as an outflow boundary to avoid difficulties with backflow. No slip was used to model gas velocity at the wall and wall functions were used as described in the previous paper (Hidayat and Rasmuson, 2005). The solid phase used a generalized Eularian solid surface boundary condition model developed by Tu and Fletcher (1995). The derivation of this model is similar to the Lagrangian treatment of wall-particles interaction. The generalized wall boundary condition for the particulate phase can be written in a generic form. @w T aw þ b ¼ c; where w ¼ ½uN s , us , @h w a ¼ ½aN ,aT , b ¼ ½bN ,bT and c ¼ ½cN ,cT
Figure 2. Sketch of the geometry of the calculation domain.
the cell adjacent to the wall. The y þ is defined by yþ ¼
rut yp m
(18)
The detailed derivation and the coefficient values are given by Tu and Fletcher (1995).
Solution Strategy and Convergence (17)
Further considerations regarding this meshing system are given in the previous paper (Hidayat and Rasmuson, 2004).
Boundary Conditions The calculation domain (Figure 2) contains three boundaries: the inlet boundary, the wall boundary and the outlet boundary. A fully developed flow was introduced at the inlet boundary of the calculation domain (Figure 2). The fully developed flow was obtained from the separate calculation domain of a straight vertical pipe with a length of 40 times the pipe diameter. This straight pipe calculation domain is
To enhance convergence, a calculation of a multiphase flow in a complex geometry situation (like a U-bend) using a two-fluid model needs an appropriate numerical strategy. Instead of using a steady-state solution strategy for this problem, a transient solution with quite small time steps was used and gave convergent solutions and reasonable results. Initiating a solution from a simple case and then step-by-step increasing the complexity of the solution is a good strategy to break-down the complexness of the problem. This strategy can be accomplished by activating and deactivating the discretised equations in the numerical solution window. Reducing the values of the under relaxation factor of the sensitive variables often assists in reducing a jumping fluctuation of their residual values. When the solution advances smoothly, the values are turned back to the previous ones.
Figure 3. (a) Mesh system for the cross-sectional area of circular pipe; (b) mesh system for the longitudinal plane of the U-bend. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
312
HIDAYAT and RASMUSON
A good initial guess of each variable is, of course, important to promote convergence. A second order upwind discretization scheme was used for the momentum equation while a first order upwind discretization was used for volume fraction, energy, turbulence kinetic energy and turbulence dissipation rate. These schemes ensured, in general, satisfactory accuracy, stability and convergence. The convergence criterion is based on the residual value of the calculated variables, i.e., mass, velocity component, energy, turbulence kinetic energy, turbulence dissipation rate and volume fraction. In the present calculations, the threshold values were set to a ten thousandth of the initial residual value of each variable except the residual value of energy which was a millionth. The residual value of energy requires a very small value to ensure accuracy of the solution (Fluent, 2001). In pressure–velocity coupling, the phasecoupled SIMPLE algorithm (Vasquez and Ivanov, 2000) was used, which is an extension of the SIMPLE algorithm (Patankar, 1980) to multiphase flows.
pressure drop indicator (TI-2). The detailed positions of the pressure drop and temperature indicators are given in Figure 4.
Experimental Method Heat loss determination In order to determine the performance of the system insulation, a heat loss test was performed by flowing air through the system and turning the heater on. This test was done at steady-state conditions: before and after feeding particles into the system. The steady-state condition was obtained in about 30 min. Heat loss can be determined from the air temperature difference between the TI-3 and the TI-4. Heat loss data was used to estimate the heat flux through the wall in the simulations with the assumption that there is no significant change in heat loss in air flow only, as compared to air –solid particle flow.
Air mass flow rate measurement EXPERIMENTAL SETUP AND VALIDATION Experimental Apparatus A schematic diagram of the pilot dryer is shown in Figure 4. The dryer consists of five basic components: a pipeline including bends; a manual solid feeder; a cyclone; a heater; and a fan which is positioned after the cyclone to produce negative pressure on the system. The pipeline is insulated and the total length of pipe is 25.7 m and the pipe diameter is 0.072 m. A pressure drop indicator (PI), which is engaged on the pipe before the heater, utilizes the dryer to determine the gas flow rate entering into the system. Dry temperature indicators are located at three positions: at the inlet near the pressure drop indicator (TI-1), after the heater (TI-3) and at the outlet after the cyclone (TI-4). A wet bulb temperature indicator is located at one position only, at the inlet near the
The air mass flow rate is indirectly determined by using the values indicated by the PI and the temperature indicators (TI01 and TI-02). The PI is used to predict the air velocity flowing through the pipe and TI-01 and TI-02 are used to predict the density of air. The air mass flow rate can be easily calculated when the air velocity, the pipe diameter and the density of air are available.
Solid particles preparation Sawdust was used as the solid particles to be dried. For simulation purposes, the sawdust particles were assumed to be spherical with an average diameter of 0.00075 m. This size was obtained from measurements using SEM. Raw material sawdust taken from a storage room was weighed. The moisture content of the raw material was measured in order to determine how much water should be added to obtain the stipulated initial moisture content. The raw material was fed into a rotary mixer and after that water was poured slowly into the rotary mixer to obtain better mixing. When the raw material sawdust and water were well mixed, after about 15 min, several samples from different positions were analysed for the initial moisture content of the feed. The moisture content of the feed was 1.41 kg water kg21 dry wood and the total wet weight of the feed was 10 kg.
Drying the sawdust feed
Figure 4. Schematic diagram of the pilot dryer for validation purposes.
Feeding the sawdust into the pilot dryer was carried out at a steady-state air flow condition. To achieve this condition, initially the TI recorder and printer were turned on and permitted to work properly for few minutes. Then, the fan was turned on. It is recommended to start the fan at a low rpm and increase the flow-rate gradually. If there was no problem with the air flow, the heater was activated. The steady-state air flow condition was normally achieved within 30 min. Ten kilograms of wet sawdust was fed constantly into the pilot dryer. The time needed to feed all the wet sawdust was 52 min and 22 s. The temperatures of feed and product were measured frequently and were 20 and 348C, respectively. The air mass flow rate entering to the system was 0.041 kg s21 and the inlet dry air temperature before and after entering the heater was 20 and 1258C, respectively.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER The humidity of inlet air before entering the heater was 45% or 0.007 of water content in air (kg water kg21 air). The moisture content of the feed was 1.41 kg water kg21 dry wood. The process continued to perform the heat loss determination. The moisture content of the samples was analyzed by using the Mellter LP16 electronic moisture analyser.
Validation A simulation using the data of drying process in the pilot dryer was conducted in the calculation domain, as shown in Figure 5. The pilot dryer was divided into six parts. The inlet condition for the first part was obtained from the experimental data. The outlet of the previous part was used as the inlet for the next one. The drying process in the cyclone was not simulated. Table 3 summarizes the values of several variables obtained from the experiment and the simulation. Simulation results show that the moisture content is somewhat slightly overpredicted. A major reason for this may be due to the absence of a cyclone in the simulation. Another reason may be the lack of detailed modelling of sawdust properties. The uniform solid particles assumption in terms of size, structure and physical properties could not be avoided because of the limitation of the code itself. Over-estimated moisture content of sawdust influences the sawdust temperature as well. Due to less water evaporated from the sawdust, less energy is needed. The evaporating energy of water is taken from the sawdust. This causes the temperature estimation of the sawdust to be higher than the temperature
313
Table 3. The summary of the value of several variables obtained from the experiment and the simulation. Variable
Experiment
Simulation
11.4 7.5 1024
11.4 7.5 1024
7.86 1022
7.86 1022
1.41
1.41
0.94
1.04
7 1023
7 1023
2.2 1022
1.9 1022
125 75 20 34
125 73 20 43
21
Gas flow velocity, m s The averaged effective sawdust diameter, m Solid loading ratio at inlet, kg sawdust/kg air Moisture content of sawdust at inlet, kg water/kg dry sawdust Moisture content of sawdust at outlet, kg water/kg dry sawdust Water content of air at inlet, kg water/kg air Water content of air at outlet, kg water/kg air Air temperature at inlet, 8C Air temperature at outlet, 8C Sawdust temperature at inlet, 8C Sawdust temperature at outlet, 8C
of the sawdust obtained from the experimental data. However, the calculation of air temperature shows very good agreement with experimental data.
RESULTS AND DISCUSSION This study simulates the mechanisms of pneumatic conveying drying in a U-bend. Several important parameters: solid loading ratio (SLR); inlet gas velocity; bend radius ratio (BR); feed moisture content and geometry arrangement; are investigated and the effect of each parameter on drying rate behaviour and particle moisture content is studied. Validation of the model used is given in the validation section and in the previous papers (Hidayat and Rasmuson, 2005, 2007).
General
Figure 5. Sketch of the calculation domain geometry of the pilot dryer pipe for validation purposes.
In a drying process, the drying rate and particle moisture content are the two most relevant parameters. Other relevant parameters are pressure and the temperature of the drying medium and the temperature of the dried material. For detailed discussions of the latter see the previous papers by Hidayat and Rasmuson (2005, 2007). A general overview of the drying rate and solid moisture content through the U-bend is given in Figures 6 and 7. Figure 6 shows the local drying rate and the local moisture content parameters in the longitudinal plane [Figure 3(b)]. The longitudinal plane is acquired at the symmetry plane of the system. Figure 7 gives the mass-weighted and areaweighted average values of the drying rate and moisture content calculated at several cross-sectional planes along the axial direction. The cross-sectional planes were acquired at several positions (including eight positions in the 4 m of the vertical straight pipe not shown in this paper), i.e., in the upstream pipe at LD ¼ 25; in the U-bend at u8 ¼ 0, 45, 90, 135 and 180; and in the downstream pipe at LD ¼ 0.575 to 35.575 with an interval of 5. Figure 6(a) shows that the local drying rate slightly decreases along the upstream pipe. However, a drastic increase in the local drying rate occurs in the U-bend and in the downstream near the U-bend outlet. After this, the local drying rate decreases gradually along the downstream
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
314
HIDAYAT and RASMUSON
Figure 6. (a) The local drying rate and (b) the local moisture content on the longitudinal plane of the base case. This figure is available in colour online via www.icheme.org/cherd
pipe. This behaviour apparently indicates that the U-bend increases the drying rate. However, it should be noted that solid particle distribution is also of importance. When solid particles flow through a curvature, i.e., a U-bend, they experience centrifugal forces which cause solid particles to accumulate at the outer bend wall (Hidayat and Rasmuson, 2005). In fact, the high drying rate takes place at locations where the solid volume fraction is low. In the area where the solid particles accumulate, the local drying rate tends to be slightly lower than the area where solid particles do not accumulate. An accumulation of particles around the outer bend causes much more energy to be transferred from the gas to solid particles. This causes the solid temperature in this area to be slightly lower than in areas where the solid volume fraction is lower. A lower temperature of solid and a more humid surrounding air decrease the driving force of the drying rate and of course the drying rate decreases as well. As a result, the mass-weight average drying rate slightly decreases in the U-bend and just after the U-bend. This behaviour is clearly shown in Figure 7(a). The behaviour of moisture content is presented in Figures 6(b) and 7(b). The moisture content decreases gradually in the upstream pipe, the U-bend and in the downstream pipe. In the U-bend and just after the U-bend, the decrease of moisture content is slightly slower than in the upstream and in the downstream directions, located far from the U-bend exit. This is understandable since the drying rate in that area is slightly lower. A higher drying rate, of course, causes a faster decrease in the moisture content.
Influence of Studied Parameters Solid loading ratio The solid loading ratio influences the flow regime occurring in the system. In the present study, the solid loading ratio was varied from 0.1 to 7.5 kg s21 of solid particles flow per kg s21 of air flow (Table 2). In this range the flow is considered to be dilute (Crowe et al., 1998) which is suitable for a pneumatic system. Figures 8(a) and (b) show the effect of varying solid loading ratios on the mass-weighted average values of the drying rate and moisture content, respectively. As seen in Figure 8(a), the drying rate decreases with increased solid loading ratio. The decrease is clearly seen at solid loading above 1.5. A major reason for this is a strong decrease in the driving force. For the higher solid loading ratio, the increase in solid temperature is less than the lower solid loading ratio. As a result, the water vapor pressure at the surface of solid particles is lower. Also, for the higher solid loading ratio, the drying air becomes more humid. This means that the driving force of the drying rate decreases. In the axial direction, the drying rate tends to decrease slowly due to mainly the increase in air humidity. Figure 8(b) shows that an increase in the solid loading ratio causes a lower reduction of the moisture content. At the highest solid loading ratio 7.5, the reduction in moisture content occurs only in the inlet area where the air is still at low humidity. As soon as the solid particles come in contact with air, the air humidity increases drastically since its capacity is limited.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
Figure 7. (a) The mass-weighted and area-weighted average values of the drying rate and (b) the mass-weighted average values of moisture content behaviors along the axial direction of the base case.
Later along the axial pipe, the drying rate is very low and the moisture content remains almost constant throughout the rest of the pipe. A sign of limited air appears already at the solid loading ratio of 1.5. It shows up as a slower decrease in the moisture content. In pneumatic conveying drying, dilute conditions are necessary since the process is limited by the humidity of the drying medium. A higher solid loading ratio causes a faster saturated drying medium. Based on the current results, a solid loading ratio of 0.5 seems to give better operating conditions in terms of drying rate and even operating capacity.
Gas velocity The gas velocity and solid loading ratio are major factors dictating the flow characteristic and the flow regime of the system. In the present study, gas velocity was varied from 10 to 30 m s21, normally the operating velocity of pneumatic conveying. The effect of varying gas velocity on the massweighted average values of the drying rate and the moisture content is shown in Figures 9(a) and (b), respectively. The role of gas velocity in changing the drying rate is mainly due to the presence of the mass transfer coefficient in equation (10). The mass transfer coefficient was calculated from the mass transfer analogue of equations (7) and (8). The Sherwood number (Sh) increases with increased Reynolds number (slip velocity indirectly). It is obvious that an increase in the gas velocity will increase the slip velocity; so that the
315
Figure 8. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different solid loading ratios.
drying rate increases with increased gas velocity, as clearly depicted in Figure 9(a). In contrast, an increase in gas velocity will give a shorter residence time for drying. This is seen in Figure 9(b) where an increase in gas velocity gives less reduction in moisture content.
Bend radius ratio To study the influence of the bend radius ratio (BR) on the mass-weighted average values of the drying rate and the moisture content, calculations were performed for variations in the bend radius ratio from 4 to 12 m m21. The effect of varying bend radius ratios on the mass-weighted average values of the drying rate and the moisture content is shown in Figures 10(a) and (b), respectively. As can be seen, the mass-weighted average values of the drying rate and moisture content are the same for all variations before entering the U-bend, since the flow properties are the same. In the general section, above, it was explained that the mass-weighted average drying rates slightly decrease in the U-bend and just after the U-bend. The bend radius ratio plays a role in altering the distribution of solid particles around the U-bend and the dispersion of solid particles after the U-bend. Due to improved dispersal of solid particles after the U-bend and the fact that slip velocities are high in this area, the mass-weighted average drying rate slightly increases.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
316
HIDAYAT and RASMUSON
Figure 9. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different gas velocities.
The different bend radius ratios slightly alter the massweighted average values of the drying rate and moisture content in and after the U-bend. At higher bend radius ratios, solid particles experience higher centrifugal forces and thus the accumulation of solid particles at the outer bend wall and just after the bend exit will be higher. This causes the massweighted average drying rate for the higher bend radius to be slightly lower. As a result, the reduction in the mass-weighted average moisture at higher bend radius ratios is also lower than the reduction at lower bend radius ratios. A minor discrepancy occurs at the low bend radius ratios (at BR ¼ 3, 4 and 6). At BR ¼ 6, the mass-weighted average drying rate in the U-bend and after the U-bend is slightly higher than the mass-weighted average drying rate of BR 3 and 4.
Figure 10. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different bend radius ratios.
moisture content was varied from 0.175 to 0.325 kg water per kg solid particles. This interval covers the range of critical or transition point between the constant and falling drying rate that is 0.245 to 0.285 kg water per kg solid particles. Figures 11(a) and (b) show the effect of the feed moisture content on the mass-weighted average values of the drying rate and the moisture content. As seen in Figure 11(a), the mass-weighted average drying rate slightly decreases with a decrease in feed moisture content, and also gives a lower reduction in moisture content [Figure 11(b)]. If the moisture content reaches the critical point, the drying mechanism shifts from the constant drying rate to the falling drying rate mechanism.
Geometry arrangement Feed moisture content As mentioned before pneumatic conveying dryers have short drying times so many of these dryers are utilized as pre-dryers ahead of main dryers. However, some pneumatic conveying dryers are also applied as main dryers. The previous variations were calculated at high feed moisture content (1.41 kg water per kg solid particles) where the external convection mainly controls the drying. When the moisture content is low enough (reaching the critical point between the constant and falling drying rates), both the external convection and the internal transport become important. To study the drying mechanism at low moisture contents, the feed
A pneumatic dryer usually consists of uprisers and downcomers connected with U-bends. The effect of geometry arrangement of a U-bend on drying behavior is thus of interest. The study of geometry arrangement of a U-bend was conducted using base case geometry by simply changing the sign of the gravitational force. In this way, the inlet position becomes located in the downcomer and the outlet position is located in the upriser. For purposes of simplification, the current case is called down-case and the usual case is called up-case. The effect of changing the geometry arrangement of a U-bend on the mass-weighted average values of the drying rate and moisture content is shown in Figure 12.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
317
Figure 11. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different feed moisture content ratios.
As can be seen, the drying rate for the up-case tends to be higher than the drying rate for the down-case in the region before U-bend. In the U-bend, the drying rates for both cases show almost the same values, and in the region after the U-bend, the drying rate for the up-case tends to be lower than the drying rate for the down-case. These different results are due to the effect of the gravitational force direction. When the gas-solid flows through the upriser section, the flow direction is opposite to the gravitational force. This, of course, creates higher slip velocity and eventually increases the drying rate. In the U-bend, the centrifugal force still seems to dominate. High accumulation of particles at the outer U-bend wall is the main reason for having almost the same drying rate. The up-case shows a slightly better performance than the down-case. The solid particles coming out of the outlet of the up-case are slightly drier than at the outlet of the down-case. Different lengths of upriser and downcomer can be the reason for the difference in performance. The up-case has upriser and downcomer lengths of 4.50 and 3.56 m, and the down-case has upriser and downcomer lengths of 3.56 and 4.50 m. Another reason for this could be the fact that the initial drying process gives the highest drying rate. For the down-case, the initial drying process occurs in the downcomer where the drying rate is less than in the upriser.
CONCLUSIONS The phenomena of pneumatic conveying drying were studied numerically by using the extended Fluent 6.1. The investigation emphasized influences of the parameters (solid loading ratio, gas velocity, bend radius ratio, feed
Figure 12. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for the up-case and down-case.
moisture content and geometry arrangement of a U-bend) on two variables: drying rate and moisture content. Incompressible, Eularian –Eularian gas –solid phase model, nonisothermal and steady-state conditions were considered. Two UDSs were inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The moisture evaporation rate of solid particles and the humidification rate of gas were treated in the source terms of the corresponding UDS equations. The evaporation energy of moisture was treated in the source term of the solid energy equation. The drying model was validated by drying sawdust using the pilot pneumatic conveying dryer. Simulation results showed that the moisture content is slightly overpredicted. A major reason for this may be due to the absence of a cyclone in the simulation and another reason may be the lack of detailed modelling of sawdust properties. The estimated temperature of the sawdust was higher than the temperature of sawdust obtained from experimental data. However, the calculation of air temperature showed very good agreement with experimental data. The mass-weighted average drying rate occurring in the U-bend showed slightly undesired results. The slight decrease in the mass-weighted average drying rate occurred in the U-bend and just after the U-bend, which was mainly due to the high accumulation of solid particles at the outer U-bend wall. In the area after the U-bend, the solid particles dispersed and the slip velocities were high, causing the
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
318
HIDAYAT and RASMUSON
mass-weighted average drying rate to slightly increase. An increase in the solid loading ratio caused a decrease in the drying rate. A major reason for this was a strong decrease in the driving force. An increase in gas velocity basically augments the drying rate, since the mass transfer coefficient in equation (10) increased due to the increased Reynolds number (slip velocity indirectly). Different bend radius ratios slightly altered the mass-weighted average values of the drying rate and moisture content in and after the U-bend. The feed moisture content was varied to evaluate the performance of the drying model. Lower feed moisture content caused a lower drying rate. Changing the U-bend position had small effect on drying behaviour.
NOMENCLATURE BR D ds g H h Hvap,c I K k ku kg,c LD Mc Nc Nu p Pr ps Pc Q R Re Sc Sh Sh Sc SLR T t u u´ ut X yp
a bend radius ratio (a bend radius divided by a pipe radius), m m21 pipe diameter, m diameter of solid particle, m the acceleration due to gravity, m s22 the specific enthalpy, m2 s22 in equation (5) or humidity in equation (9) the heat transfer coefficient, kg s23 K21 the evaporation energy of moist or water, m2 s22 the tensor unit inter-phase momentum exchange coefficient, kg m23 s21 the thermal conductivity, kg m s23 K21 the solid diffusion coefficient, kg m23 s21 the mass transfer coefficient of moisture, m s21 the normalized axial direction, m m21 the molecular weight of moisture, kg mole21 the drying rate, kg m22 s21 the Nusselt number the static pressure, Pa the Prandtl number the solid pressure, Pa the moist or water vapour pressure, kg ms22 the intensity of heat exchange, kg ms23 bend radius, m the Reynolds number the Schmidt number the Sherwood number the source term of the conservation equation of the energy, kg ms23 the source term of the transport equation of the UDS, kg ms23 the solid loading ratio, kg solid particles kg21 air the temperature, K the time unit, s the mean velocity, m s21 the fluctuating velocity, m s21 the shear velocity, m s21 the moisture content of sawdust the wall distance of the first cell, m
Greek symbols a the volume fraction, volume of particles, m3 / volume of gas, m3 f the energy exchange, kg ms23 gu the collisional energy dissipation, kg ms23 m the shear viscosity, kg ms21 t the stress-strain tensor, kg ms22 u the granular temperature, m2 s22 r density, kg m23 h the normal direction in general coordinate, kg ms22 (Tu and Fletcher, 1995) c the scalar variable which is the mass fraction of water in the gas or in the solid particles G the diffusion coefficient of scalar variable, kg ms21
Superscripts N the normal direction in equation (16) T the transpose sign in equation (12) or the tangential direction in equation (16) Subscripts c critical g the gas phase i the subscript i represents either the gas phase (subscript g) or the solid phase (subscript s) j the pair of the index i (if the index i represents the gas phase then the index j represents the solid phase, vice versa) me moisture equilibrium s the solid phase w the position at a wall
REFERENCES Akilli, H., Levy, E.K. and Sahin, B., 2001, Gas-solid flow behavior in a horizontal pipe after a 908 vertical-to-horizontal elbow, Powder Technol, 116(1): 43–52. Crowe, C., Sommerfeld, M. and Tsuji, Y., 1998, Multiphase Flows with Droplets and Particles, (CRC Press, Boca Raton, Boston, New York, Washington and London). Ding, J. and Gidaspow, D., 1990, A bubbling fluidization model using kinetic theory of granular flow, AIChE J, 36(4): 523–538. Ergun, S., 1952, Fluid flow through packed columns, Chem. Eng. Prog, 48(2): 89–94. Fluent, 2001, User’s Guide, Fluent 6.1, (Fluent Incorporation New Hampshire Company, USA) Lebanon. Fluent, FLUENT Flow Modeling Software, http://www.fluent.com/ software/fluent/index.htm, accessed September 2006. Fyhr, C. and Rasmuson, A., 1997, Mathematical model of a pneumatic conveying dryer, AIChE J 43: 2889–2902. Gidaspow, D., Bezburuah, R. and Ding, J., 1992, Hydrodynamics of circulating fluidized beds, kinetic theory approach, in Fluidization VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization. Gunn, D.J., 1978, Transfer of heat or mass to particles in fixed and fludized beds, Int J Heat Mass Transfer, 21: 467– 476. Hellsten, G., 1992, Tabeller och diagram, energi och kemiteknik, (Almqvist&Wiksell, Stockholm, Sweden). Hidayat, M. and Rasmuson, A., 2004, Numerical assessment of gassolid flow in a U-bend, Chem Eng Res Des, 82(A3): 332–343. Hidayat, M. and Rasmuson, A., 2005a, Some aspects on gas-solid flow in a U-bend: numerical investigation, Powder Technol, 153(1): 1– 12. Hidayat, M. and Rasmuson, A., 2007, A computational investigation of non-isothermal gas-solid flow in a U-bend, in press Powder Technol, Hinze, J.O., 1975, Turbulence, (McGraw-Hill Publishing Co, New York, USA). Huber, H. and Sommerfeld, M., 1994, Characrerization of the crosssectional particle concentration distribution in pneumatic conveying systems, Powder Technol, 79(3): 191– 210. Kemp, I.C., Bahu, R.E. and Oakley, D.E., 1991, Computational fluid dynamics modelling of vertical pneumatic conveying dryers, Powder Technol, 65: 477– 484. Kirk-Othmer, 1993, Encyclopedia of Chemical Technology (John Wiley & Sons, Inc., New York, USA) (access year 2000). Levy, A. and Borde, I., 1999, Steady state one dimensional flow model for a pneumatic dryer, Chemical Engineering and Processing, 38: 121– 130. Levy, A. and Mason, D.J., 1998, The effect of a bend on the particle cross-section concentration and segregation in pneumatic conveying systems, Powder Technol, 98(2): 95– 103. Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, (McGraw-Hill, New York, USA). Shih, T.H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J., 1995, A new k-1 eddy-viscosity model for high Reynolds number turbulent flows, Computers & Fluids, 24(3): 227 –238. Siau, J.F., 1984, Transport Process in Wood, (Springer-Verlag, Berlin, Heidelberg, New York and Tokyo).
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER Skuratovsky, I., Levy, A. and Borde, I., 2005, Two-dimensional numerical simulation of the pneumatic drying in vertical pipes, Chemical Engineering Processing, 44: 187– 192. Stoess, H.A., 1983, Pneumatic Conveying (John Wiley & Sons, New York, Chichester, Brisbane, Toronto and Singapore). Szafran, R.G. and Kmiec, A., 2004, CFD modeling of heat and mass transfer in a spouted bed dryer, Ind Eng Chem Res, 43: 1113– 1124. Tu, J.Y. and Fletcher, C.A.J., 1995, Numerical computation of turbulent gas-solid particle flow in a 90 degree bend, AIChE J, 41(10): 2187–2197.
319
Vasquez, S.A. and Ivanov, V.A., 2000, A phase coupled method for solving multiphase problem on unstructured meshes, Fluids Engineering Division Summer Meeting, Boston, USA, ASME. Wen, C.Y. and Yu, Y.H., 1966, Mechanics of fluidization, Chem Eng Prog Symp Series. Yilmaz, A. and Levy, E.K., 2001, Formation and dispersion of ropes in pneumatic conveying, Powder Technol, 114: 168– 185. The manuscript was received 7 July 2005 and was accepted for publication after revision 6 November 2006.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers University of Technology, Go¨teborg, Sweden. 2 Chemical Engineering Department, Engineering faculty, Gadjan Mada University, JL Gratika No 2, Yogyakarta, Indonesia.
Abstract: Computational fluid dynamics (CFD) modelling with the Eularian –Eularian formulation is used to describe the drying phenomena occurring in pneumatic conveying drying particularly in the U-bend. Two user defined scalar equations (UDSs) are inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The drying kinetics cover the two periods of drying: the constant drying rate and the falling drying rate. The investigation emphasized influences of the parameters (solid loading ratio, gas velocity, bend radius ratio, feed moisture content and geometry arrangement of a U-bend) on the drying rate and moisture content. A validation of the drying model is accomplished by comparing calculation results with experimental data. In general, the drying rate decreases along the axial direction of pipe due to the decrease in driving force (the air humidity increases). The mass-weighted average drying rate shows a slight decrease in and just after the U-bend, which is mainly due to the high accumulation of solid particles at the outer U-bend wall. Solid particles disperse and the slip velocities are high in the area after the U-bend. This causes the mass-weighted average drying rate to slightly increase. Keywords: pneumatic conveying drying; U-bend; computational fluid dynamics (CFD).
Correspondence to: Dr A. Rasmuson, Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-41296. Go¨teborg, Sweden. E-mail: rasmuson@ chemeng.chalmers.se DOI: 10.1205/chered06162 0263–8762/07/ $30.00 þ 0.00 Chemical Engineering Research and Design Trans IChemE, Part A, March 2007 # 2007 Institution of Chemical Engineers
INTRODUCTION
drying gas, solid particles and walls. The gas and particles exchange heat and mass through drying, and momentum is exchanged in order to convey particles. The gas and particles interact with the walls through wall friction and heat convection (radiation). The drying times are typically short, in order of seconds, due to limited conveying distances (Stoess, 1983) and the fact that the drying gas becomes saturated. For this reason, many of these dryers are utilized as predryers ahead of longer residence time fluid bed and rotary dryers, for example, in polymer drying operations (Kirk-Othmer, 1993). However, some pneumatic conveying dryers are also applied as main dryers, for instance, for drying fibres in the pulp and paper industry. A comprehensive study concerning fluid dynamics, heat and mass transfer between gas and solid particles in the pneumatic drying system is necessarily needed to obtain better knowledge for the design of a pneumatic dryer. Studies of the fluid dynamics of gas and solid particles through a bend have been accomplished by several authors, for example, Huber and Sommerfeld (1994),
Pneumatic conveying dryers are widely used in industry. In such a dryer, the external (temperature, humidity, mass/heat transfer coefficients) conditions for particles vary along the flow path. A typical dryer is depicted in Figure 1. It consists of erect sections with uprisers and downcomers connected with U-bends. In a study by Fyhr and Rasmuson (1997) it is found that U-bends significantly influence drying behaviour since they enhance velocity differences (slip) between suspended material and the drying medium. This slip will increase external heat and mass transfer rates, thereby enhancing drying conditions. In contrast, the bend will increase the pressure drop of the system. Thus, choosing the appropriate bend shape can be utilized in the overall optimization of a pneumatic conveying dryer. The U-bends may cause problems for sticky materials or if the material is very wet in combination with too low drying rates, our experience though is that this mainly gives problems in the feeding section of the dryer. Pneumatic drying involves simultaneous momentum, heat and mass transfer between 307
Vol 85 (A3) 307–319
308
HIDAYAT and RASMUSON Influences of important parameters (gas velocity, solid loading ratio, bend radius ratio and moisture content of solid particles entering the system) on heat and mass transfer coefficients and the drying rate are studied numerically. The commercial software package Fluent 6.1 is used in the calculations. The Eularian –Eularian modelling approach is applied to predict flow behaviour. A drying model is added using two user defined scalar equations (USDs) to take into account the gas humidity and moisture content of the solid particles. This is necessary since the standard multiphase feature of Fluent 6.1 is not able to handle this complex system. Source terms for both UDSs and the energy equation for the solid particles are also introduced. The results obtained from the simulations are compared with experimental data from a pilot dryer.
Figure 1. Schematic drawing of the pneumatic conveying dryer developed at Chalmers University of Technology (Fyhr and Rasmuson, 1997).
Levy and Mason (1998), Yilmaz and Levy (2001), Akilli et al. (2001) and Tu and Fletcher (1995). Huber and Sommerfeld (1994) have investigated the role of centrifugal forces in segregating solid particles from a carrier gas and they have found the presence of particle size segregation due to centrifugal forces at a 908-bend. The phenomena of secondary flows and of the formation and dispersion of ropes are usually studied simultaneously. Huber and Sommerfeld (1994), Levy and Mason (1998) and Yilmaz and Levy (2001) have studied the distribution of particles in a pipe cross-section affected by a 908-bend. Levy and Mason (1998) have concluded that the paths taken by the particles after the bend are strongly dependent on the diameter of the particles. The ropes are dispersed due to secondary flow and flow turbulence (Akilli et al., 2001). In previous papers by the authors (Hidayat and Rasmuson, 2004, 2005, 2007), the influence of a Ubend on particle velocity, slip velocity, particle concentration distribution, pressure profile and heat transfer phenomena between gas and solid particles have been studied. Kemp et al. (1991) carried out drying experiments to find particle velocities, heat transfer and drying rates in a vertical unit. They have reviewed models for pneumatic conveying dryers and have concluded that none have been entirely successful. They also noticed that effective drying occurs in the inlet zone. Levy and Borde (1999) and Skuratovsky et al. (2005) have simulated vertical pneumatic conveying dryers in one- and two-dimensional models, respectively. In the drying modelling, they have considered that solid particles experience two drying stages. During the first stage, heat transfer controls the evaporation process from the saturated outer surface of a particle to the surrounding gas (a constant drying rate period). During the second stage, diffusion of moisture through the particle crust and convection into the gas medium control the evaporation process. Fyhr and Rasmuson (1997) have presented a model for a pneumatic conveying dryer employing a one-dimensional hydrodynamic plug flow model coupled to a comprehensive twodimensional model for drying single wood chips. In this study it is found that U-bends significantly influence drying behavior since they enhance velocity differences (slip) between suspended material and the drying medium. The present study examines heat and mass transfer (i.e., drying) between gas and solid particles in a U-bend.
MATHEMATICAL MODEL The Eulerian–Eularian model is presented in this section. The model expands the definition of continuum assumption to the dispersed phase and employs the Navier –Stokes equation to both continuous (gas) and dispersed (solid particles) phases. Both phases are assumed to be incompressible. The condition is steady-state and involves heat and mass transfer between phases. However, in order to avoid divergence problems, the numerical solution is iterated at unsteady-state conditions. In the momentum equation the gas and solid are linked using a drag force. The drag force model employs the correlation proposed by Gidaspow et al. (1992). This correlation combines the Wen and Yu model (Wen and Yu, 1966) for the dilute system and the Ergun equations (Ergun, 1952) for the dense system. The heat and mass transfer coefficients between gas and solid use the correlation developed by Gunn (1978). He proposes Nusselt and Sherwood correlations which are valid for a system having the porosity range of 0.35–1.0 and a Reynolds number up to 105. Two UDSs are inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The moisture evaporation rate of solid particles and the humidification rate of gas are treated in the source terms of the corresponding UDS equations. The evaporation energy of moisture is treated in the source term of the solid energy equation. More details about heat and mass transfer are given in the heat and mass transfer model formulation section. The realizable k –1 epsilon model is used to capture turbulence phenomena in both phases. The granular theory for the gas–solid flow of the Eulerian model is introduced (Ding and Gidaspow, 1990). The set of governing equations was solved by using the commercial Fluent 6.1 software package. The discretised equations, along with the initial condition and boundary conditions, were solved using the segregated solution method. Using the segregated solver, the conservation of mass and momentum were solved iteratively and a pressure –correction equation was used to ensure consistency of the conservation of momentum and the conservation of mass (continuity equation). To assist in obtaining a convergent solution, Fluent allows one to solve the discretized equations using a step-by-step solution by activating and deactivating the discretised equations in the numerical solution window.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER Governing Equations The conservation equation of the mass of phase i (i ¼ gas or solid) is @ (ai ri ) þ r (ai ri ui ) ¼ 0 @t X ai ¼ 1: with the constraint
(1) (2)
Constitutive equations play the role of closing governing equations. The following section describes the constitutive equations for the heat and mass transfer between gas and solid in the conservation equation of the energy of the solid phase and the transport equation of the UDSs of both phases. Additional constitutive equations are given in the previous paper (Hidayat and Rasmuson, 2005).
The conservation equation of the momentum of phase i (i ¼ gas or solid) is @ (ai ri ui ) þ r (ai ri ui ui ) ¼ rpi @t þ r ti r (ai ri u0i u0i ) þ ai ri g þ Kji (uj ui )
ð3Þ
where the index j is a pair of the index i (if the index i represents the gas phase then the index j represents the solid phase, and vice versa). The pressure gradients of gas and solid phase are rpi ¼ ag rp and rpi ¼ as rp rps , respectively. The Kji ¼ Kij in the drag force term represents the inter-phase gas– solid momentum exchange coefficient which uses correlations derived by Gidaspow et al. (1992). The Reynolds stresses of phase i, ri u0 i u0i employ the Boussinesq hypothesis (Hinze, 1975) to relate the Reynolds stresses to the mean velocity gradients. The turbulence kinetic energy and turbulence dissipation rate employ the realizable k –1 model proposed by Shih et al. (1995). Equation (3) needs additional information for the solid phase (i ¼ s) which is mainly obtained from the granular temperature equation: 3@ (as rs us ) þ r (as rs us us ) ¼ ( ps I þ ts ):rus 2 @t þ r (kus rus ) gus þ fgs
(4)
The conservation equation of the energy of phase i (i ¼ gas or solid) is @ @pi (ai ri Hi ) þ r (ai ri ui Hi ) ¼ ai þ ti :rui þ Qji þ Sh,i @t @t
where Qji is the intensity of heat exchange between gas and solid phases and Sh,i is the source term of the conservation equation of the energy of phase i. The intensity of heat exchange (Qji) employs the Nusselt correlation developed by Gunn (1978) to calculate the heat transfer coefficient between gas and solid phases. The source term for gas phase (Sh,i ) is zero and the source term for the solid phase (Sh,i ) is due to moisture evaporation from solid phase to gas phase. More details regarding the source term of the solid phase are given in the heat and mass transfer model formulation section. The transport equation of the UDS of phase i (i ¼ gas or solid) is @ai ri ci þ r (ai ri ui ci ) ¼ r (ai Gi rci ) þ Sc,i @t
Heat and Mass Transfer Drying involves coupled heat and mass transfer. The inlet gas, which is the drying medium, is hotter than the inlet solid. The energy transfer is mainly governed by external convection from gas to solid phase. The internal energy transport (mainly conduction) is usually rapid. This energy is used to increase solid temperature and to evaporate the moisture from the solid material. The moisture transport occurs mainly by means of external convection at higher moisture contents and internal transport (capillary flow, diffusion) at lower moisture contents. Due to the complexity of the multiphase flow problem, the drying model has to be simple but comprehensive, which means that it must include a constant drying rate and a falling drying rate as the general characteristics of the drying process. The standard multiphase flow feature of Fluent 6.1 is not able to solve these phenomena. The continuous and the dispersed phases represent only the gas and solid phases, respectively. The mass fraction of water in the gas phase and the moisture content of the solid phase have to be modeled in two additional UDSs. For the convective heat and mass transfer between gas and solid we use the correlations proposed by Gunn (1978), here written for heat transfer: 1=3 Nus ¼ (7 10ag þ 5a2g )(1 þ 0:7Re0:2 ) s Pr 1=3 þ (1:33 2:4ag þ 1:2a2g )Re0:7 s Pr
hsg (5)
(6)
where c is the scalar variable which represents the mass fraction of water in the gas or in the solid particles. The mass fraction of water in the solid particles is the moisture content itself.
309
kg Nus ¼ ds
(7) (8)
The mass transfer analogue is obtained by substituting Sh for Nu and Sc for Pr. The transition between the constant and the falling drying rate periods occurs when the solid particle surface becomes unsaturated and internal mass transfer resistance becomes significant. Due to the fact that the studied particle diameter is small and a simple drying model is desired, the drying rate in the falling drying rate period is assumed to decrease in a linear fashion. This assumption was also utilized by Szafran and Kmiec (2004) in their CFD modelling of a spouted bed dryer. The transition point in their case is defined by comparing values of the mass flux calculated using the external mass transfer equation and the internal mass transfer equation. The equilibrium moisture content is taken as a constant value using the value at the inlet. In the present study, the transition point and the equilibrium moisture content is taken locally, considering the influence of gas and solid phase local conditions. In our case we use wood as a model material. The moisture equilibrium is obtained by doing a polynomial regression on the experimental data of the sorption isotherm of wood at different temperatures and humidities of gas as given by
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
310
HIDAYAT and RASMUSON I II where Nc,s represents to Nc,s and Nc,s in the constant and falling drying rate, respectively. Heat transfer:
Table 1. The polynomial coefficients for equation (9) as function of the solid temperature. Polynomial coeff.
Equations 20.010688 þ 2.7619 1025 Ts 1.1709 2 2.6459 1023 Ts 22.2111 þ 4.9748 1023 Ts 1.7714 2 3.7579 1023 Ts
A B C D
Qsg ¼
6as ag hsg (Ts Tg ) ds
(14)
The source term for the conservation equation of the energy for solid phase is Sh,s ¼ Nc,s Hvap,c
(15)
Siau (1984). Xc ¼ A þ BHc þ CHc2 þ DHc3
(9a)
2 3 Xme ¼ A þ BHme þ CHme þ DHme
(9b)
where Hvap,c is the evaporation energy of water obtained by doing a polynomial regression from available steam tables (Hellsten, 1992). Hvap,c ¼ 3 006 300 1428:1Ts 1:5534Ts2
where Hc and Hme are the saturated humidity of gas (Hc ¼ 1) and the local gas humidity, respectively and A, B, C and D are polynomial coefficients as function of the solid temperature and given in Table 1. The mass flux of moisture evaporated from the solid material during the constant drying rate is I Nc,s
kg,c Mc ¼ (Pc,s Pc,g ) RTs
NUMERICAL SOLUTION Geometry Calculations are conducted for U-bend pipes with the same length, i.e., 5 m, regardless of different bend radius ratios. The calculation domain is constructed of three parts, i.e., the upstream pipe, the U-bend and the downstream pipe. The length of the upstream pipe is 0.5 m for all variations. The different lengths of pipe in the bend due to different bend radius ratios are compensated for by adapting the length of the downstream pipe (Table 2). Figure 2 shows a sketch of the geometry of the calculation domain of the U-bend. The pipe diameter is 0.1 m. The dimensions of the experimental equipment are given in the experimental setup section. The computational grids are approximately 48 000 cells (Figure 3). This number was generated by applying the same cross-sectional meshes of pipe obtained from the optimum cross-sectional meshes of pipe in the single-phase flow case (Hidayat and Rasmuson, 2004). The grid was generated using Gambit 2.0, which is compatible with Fluent 6.1. A boundary layer, which contains four cells with a distance of the cell adjacent to the wall at 2% of the diameter of the pipe and a growth factor of 1.2, was employed at the wall to improve the performance of the wall function and to fulfill the requirement of y þ, the dimensionless wall distance, for
(10)
where R is the gas constant The mass flux of moisture evaporated from the solid material during the falling drying rate is modelled as II Nc,s ¼
X Xme I N Xc Xme c,s
(11)
where Xme X Xc. The two UDSs take into account the mass transfer of water between the solid and gas phases. The drying rate of solid particles and the humidification rate of gas are treated in the source terms of their respective UDS equations. Mass transfer: 6as Nc,s ds ¼ Sc,s
Sc,s ¼
(12)
Sc,g
(13)
(16)
Table 2. Summary of parameter values for calculations. Parameter Bend variation SLR, kg kg21 0.1 0.25 0.5 1.5 7.5
ug, m s21
BR, m m21
L1, m
B, m
L2, m
10 15 20 25 30
3 4 6 8 10 12
0.5 0.5 0.5 0.5 0.5 0.5
0.4712 0.6283 0.9425 1.2566 1.5708 1.8850
4.0288 3.8717 3.5575 3.2434 2.9292 2.6150
The feed moisture content, kg water/kg sawdust 0.175 0.200 0.225 0.250 0.275 0.300 0.325 1.41
Base case. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
311
not shown in the paper. A flat profile of each parameter was introduced at the inlet of this pipe and they resulted in a fully developed flow at the outlet. The fully developed flow obtained at the outlet was used as the inlet boundary condition for the actual calculation domain, as depicted in Figure 2. The gravitation direction is downward or in the opposite direction of the inlet velocity. The outlet boundary condition of the latter was set up as a pressure outlet boundary instead of as an outflow boundary to avoid difficulties with backflow. No slip was used to model gas velocity at the wall and wall functions were used as described in the previous paper (Hidayat and Rasmuson, 2005). The solid phase used a generalized Eularian solid surface boundary condition model developed by Tu and Fletcher (1995). The derivation of this model is similar to the Lagrangian treatment of wall-particles interaction. The generalized wall boundary condition for the particulate phase can be written in a generic form. @w T aw þ b ¼ c; where w ¼ ½uN s , us , @h w a ¼ ½aN ,aT , b ¼ ½bN ,bT and c ¼ ½cN ,cT
Figure 2. Sketch of the geometry of the calculation domain.
the cell adjacent to the wall. The y þ is defined by yþ ¼
rut yp m
(18)
The detailed derivation and the coefficient values are given by Tu and Fletcher (1995).
Solution Strategy and Convergence (17)
Further considerations regarding this meshing system are given in the previous paper (Hidayat and Rasmuson, 2004).
Boundary Conditions The calculation domain (Figure 2) contains three boundaries: the inlet boundary, the wall boundary and the outlet boundary. A fully developed flow was introduced at the inlet boundary of the calculation domain (Figure 2). The fully developed flow was obtained from the separate calculation domain of a straight vertical pipe with a length of 40 times the pipe diameter. This straight pipe calculation domain is
To enhance convergence, a calculation of a multiphase flow in a complex geometry situation (like a U-bend) using a two-fluid model needs an appropriate numerical strategy. Instead of using a steady-state solution strategy for this problem, a transient solution with quite small time steps was used and gave convergent solutions and reasonable results. Initiating a solution from a simple case and then step-by-step increasing the complexity of the solution is a good strategy to break-down the complexness of the problem. This strategy can be accomplished by activating and deactivating the discretised equations in the numerical solution window. Reducing the values of the under relaxation factor of the sensitive variables often assists in reducing a jumping fluctuation of their residual values. When the solution advances smoothly, the values are turned back to the previous ones.
Figure 3. (a) Mesh system for the cross-sectional area of circular pipe; (b) mesh system for the longitudinal plane of the U-bend. Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
312
HIDAYAT and RASMUSON
A good initial guess of each variable is, of course, important to promote convergence. A second order upwind discretization scheme was used for the momentum equation while a first order upwind discretization was used for volume fraction, energy, turbulence kinetic energy and turbulence dissipation rate. These schemes ensured, in general, satisfactory accuracy, stability and convergence. The convergence criterion is based on the residual value of the calculated variables, i.e., mass, velocity component, energy, turbulence kinetic energy, turbulence dissipation rate and volume fraction. In the present calculations, the threshold values were set to a ten thousandth of the initial residual value of each variable except the residual value of energy which was a millionth. The residual value of energy requires a very small value to ensure accuracy of the solution (Fluent, 2001). In pressure–velocity coupling, the phasecoupled SIMPLE algorithm (Vasquez and Ivanov, 2000) was used, which is an extension of the SIMPLE algorithm (Patankar, 1980) to multiphase flows.
pressure drop indicator (TI-2). The detailed positions of the pressure drop and temperature indicators are given in Figure 4.
Experimental Method Heat loss determination In order to determine the performance of the system insulation, a heat loss test was performed by flowing air through the system and turning the heater on. This test was done at steady-state conditions: before and after feeding particles into the system. The steady-state condition was obtained in about 30 min. Heat loss can be determined from the air temperature difference between the TI-3 and the TI-4. Heat loss data was used to estimate the heat flux through the wall in the simulations with the assumption that there is no significant change in heat loss in air flow only, as compared to air –solid particle flow.
Air mass flow rate measurement EXPERIMENTAL SETUP AND VALIDATION Experimental Apparatus A schematic diagram of the pilot dryer is shown in Figure 4. The dryer consists of five basic components: a pipeline including bends; a manual solid feeder; a cyclone; a heater; and a fan which is positioned after the cyclone to produce negative pressure on the system. The pipeline is insulated and the total length of pipe is 25.7 m and the pipe diameter is 0.072 m. A pressure drop indicator (PI), which is engaged on the pipe before the heater, utilizes the dryer to determine the gas flow rate entering into the system. Dry temperature indicators are located at three positions: at the inlet near the pressure drop indicator (TI-1), after the heater (TI-3) and at the outlet after the cyclone (TI-4). A wet bulb temperature indicator is located at one position only, at the inlet near the
The air mass flow rate is indirectly determined by using the values indicated by the PI and the temperature indicators (TI01 and TI-02). The PI is used to predict the air velocity flowing through the pipe and TI-01 and TI-02 are used to predict the density of air. The air mass flow rate can be easily calculated when the air velocity, the pipe diameter and the density of air are available.
Solid particles preparation Sawdust was used as the solid particles to be dried. For simulation purposes, the sawdust particles were assumed to be spherical with an average diameter of 0.00075 m. This size was obtained from measurements using SEM. Raw material sawdust taken from a storage room was weighed. The moisture content of the raw material was measured in order to determine how much water should be added to obtain the stipulated initial moisture content. The raw material was fed into a rotary mixer and after that water was poured slowly into the rotary mixer to obtain better mixing. When the raw material sawdust and water were well mixed, after about 15 min, several samples from different positions were analysed for the initial moisture content of the feed. The moisture content of the feed was 1.41 kg water kg21 dry wood and the total wet weight of the feed was 10 kg.
Drying the sawdust feed
Figure 4. Schematic diagram of the pilot dryer for validation purposes.
Feeding the sawdust into the pilot dryer was carried out at a steady-state air flow condition. To achieve this condition, initially the TI recorder and printer were turned on and permitted to work properly for few minutes. Then, the fan was turned on. It is recommended to start the fan at a low rpm and increase the flow-rate gradually. If there was no problem with the air flow, the heater was activated. The steady-state air flow condition was normally achieved within 30 min. Ten kilograms of wet sawdust was fed constantly into the pilot dryer. The time needed to feed all the wet sawdust was 52 min and 22 s. The temperatures of feed and product were measured frequently and were 20 and 348C, respectively. The air mass flow rate entering to the system was 0.041 kg s21 and the inlet dry air temperature before and after entering the heater was 20 and 1258C, respectively.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER The humidity of inlet air before entering the heater was 45% or 0.007 of water content in air (kg water kg21 air). The moisture content of the feed was 1.41 kg water kg21 dry wood. The process continued to perform the heat loss determination. The moisture content of the samples was analyzed by using the Mellter LP16 electronic moisture analyser.
Validation A simulation using the data of drying process in the pilot dryer was conducted in the calculation domain, as shown in Figure 5. The pilot dryer was divided into six parts. The inlet condition for the first part was obtained from the experimental data. The outlet of the previous part was used as the inlet for the next one. The drying process in the cyclone was not simulated. Table 3 summarizes the values of several variables obtained from the experiment and the simulation. Simulation results show that the moisture content is somewhat slightly overpredicted. A major reason for this may be due to the absence of a cyclone in the simulation. Another reason may be the lack of detailed modelling of sawdust properties. The uniform solid particles assumption in terms of size, structure and physical properties could not be avoided because of the limitation of the code itself. Over-estimated moisture content of sawdust influences the sawdust temperature as well. Due to less water evaporated from the sawdust, less energy is needed. The evaporating energy of water is taken from the sawdust. This causes the temperature estimation of the sawdust to be higher than the temperature
313
Table 3. The summary of the value of several variables obtained from the experiment and the simulation. Variable
Experiment
Simulation
11.4 7.5 1024
11.4 7.5 1024
7.86 1022
7.86 1022
1.41
1.41
0.94
1.04
7 1023
7 1023
2.2 1022
1.9 1022
125 75 20 34
125 73 20 43
21
Gas flow velocity, m s The averaged effective sawdust diameter, m Solid loading ratio at inlet, kg sawdust/kg air Moisture content of sawdust at inlet, kg water/kg dry sawdust Moisture content of sawdust at outlet, kg water/kg dry sawdust Water content of air at inlet, kg water/kg air Water content of air at outlet, kg water/kg air Air temperature at inlet, 8C Air temperature at outlet, 8C Sawdust temperature at inlet, 8C Sawdust temperature at outlet, 8C
of the sawdust obtained from the experimental data. However, the calculation of air temperature shows very good agreement with experimental data.
RESULTS AND DISCUSSION This study simulates the mechanisms of pneumatic conveying drying in a U-bend. Several important parameters: solid loading ratio (SLR); inlet gas velocity; bend radius ratio (BR); feed moisture content and geometry arrangement; are investigated and the effect of each parameter on drying rate behaviour and particle moisture content is studied. Validation of the model used is given in the validation section and in the previous papers (Hidayat and Rasmuson, 2005, 2007).
General
Figure 5. Sketch of the calculation domain geometry of the pilot dryer pipe for validation purposes.
In a drying process, the drying rate and particle moisture content are the two most relevant parameters. Other relevant parameters are pressure and the temperature of the drying medium and the temperature of the dried material. For detailed discussions of the latter see the previous papers by Hidayat and Rasmuson (2005, 2007). A general overview of the drying rate and solid moisture content through the U-bend is given in Figures 6 and 7. Figure 6 shows the local drying rate and the local moisture content parameters in the longitudinal plane [Figure 3(b)]. The longitudinal plane is acquired at the symmetry plane of the system. Figure 7 gives the mass-weighted and areaweighted average values of the drying rate and moisture content calculated at several cross-sectional planes along the axial direction. The cross-sectional planes were acquired at several positions (including eight positions in the 4 m of the vertical straight pipe not shown in this paper), i.e., in the upstream pipe at LD ¼ 25; in the U-bend at u8 ¼ 0, 45, 90, 135 and 180; and in the downstream pipe at LD ¼ 0.575 to 35.575 with an interval of 5. Figure 6(a) shows that the local drying rate slightly decreases along the upstream pipe. However, a drastic increase in the local drying rate occurs in the U-bend and in the downstream near the U-bend outlet. After this, the local drying rate decreases gradually along the downstream
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
314
HIDAYAT and RASMUSON
Figure 6. (a) The local drying rate and (b) the local moisture content on the longitudinal plane of the base case. This figure is available in colour online via www.icheme.org/cherd
pipe. This behaviour apparently indicates that the U-bend increases the drying rate. However, it should be noted that solid particle distribution is also of importance. When solid particles flow through a curvature, i.e., a U-bend, they experience centrifugal forces which cause solid particles to accumulate at the outer bend wall (Hidayat and Rasmuson, 2005). In fact, the high drying rate takes place at locations where the solid volume fraction is low. In the area where the solid particles accumulate, the local drying rate tends to be slightly lower than the area where solid particles do not accumulate. An accumulation of particles around the outer bend causes much more energy to be transferred from the gas to solid particles. This causes the solid temperature in this area to be slightly lower than in areas where the solid volume fraction is lower. A lower temperature of solid and a more humid surrounding air decrease the driving force of the drying rate and of course the drying rate decreases as well. As a result, the mass-weight average drying rate slightly decreases in the U-bend and just after the U-bend. This behaviour is clearly shown in Figure 7(a). The behaviour of moisture content is presented in Figures 6(b) and 7(b). The moisture content decreases gradually in the upstream pipe, the U-bend and in the downstream pipe. In the U-bend and just after the U-bend, the decrease of moisture content is slightly slower than in the upstream and in the downstream directions, located far from the U-bend exit. This is understandable since the drying rate in that area is slightly lower. A higher drying rate, of course, causes a faster decrease in the moisture content.
Influence of Studied Parameters Solid loading ratio The solid loading ratio influences the flow regime occurring in the system. In the present study, the solid loading ratio was varied from 0.1 to 7.5 kg s21 of solid particles flow per kg s21 of air flow (Table 2). In this range the flow is considered to be dilute (Crowe et al., 1998) which is suitable for a pneumatic system. Figures 8(a) and (b) show the effect of varying solid loading ratios on the mass-weighted average values of the drying rate and moisture content, respectively. As seen in Figure 8(a), the drying rate decreases with increased solid loading ratio. The decrease is clearly seen at solid loading above 1.5. A major reason for this is a strong decrease in the driving force. For the higher solid loading ratio, the increase in solid temperature is less than the lower solid loading ratio. As a result, the water vapor pressure at the surface of solid particles is lower. Also, for the higher solid loading ratio, the drying air becomes more humid. This means that the driving force of the drying rate decreases. In the axial direction, the drying rate tends to decrease slowly due to mainly the increase in air humidity. Figure 8(b) shows that an increase in the solid loading ratio causes a lower reduction of the moisture content. At the highest solid loading ratio 7.5, the reduction in moisture content occurs only in the inlet area where the air is still at low humidity. As soon as the solid particles come in contact with air, the air humidity increases drastically since its capacity is limited.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
Figure 7. (a) The mass-weighted and area-weighted average values of the drying rate and (b) the mass-weighted average values of moisture content behaviors along the axial direction of the base case.
Later along the axial pipe, the drying rate is very low and the moisture content remains almost constant throughout the rest of the pipe. A sign of limited air appears already at the solid loading ratio of 1.5. It shows up as a slower decrease in the moisture content. In pneumatic conveying drying, dilute conditions are necessary since the process is limited by the humidity of the drying medium. A higher solid loading ratio causes a faster saturated drying medium. Based on the current results, a solid loading ratio of 0.5 seems to give better operating conditions in terms of drying rate and even operating capacity.
Gas velocity The gas velocity and solid loading ratio are major factors dictating the flow characteristic and the flow regime of the system. In the present study, gas velocity was varied from 10 to 30 m s21, normally the operating velocity of pneumatic conveying. The effect of varying gas velocity on the massweighted average values of the drying rate and the moisture content is shown in Figures 9(a) and (b), respectively. The role of gas velocity in changing the drying rate is mainly due to the presence of the mass transfer coefficient in equation (10). The mass transfer coefficient was calculated from the mass transfer analogue of equations (7) and (8). The Sherwood number (Sh) increases with increased Reynolds number (slip velocity indirectly). It is obvious that an increase in the gas velocity will increase the slip velocity; so that the
315
Figure 8. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different solid loading ratios.
drying rate increases with increased gas velocity, as clearly depicted in Figure 9(a). In contrast, an increase in gas velocity will give a shorter residence time for drying. This is seen in Figure 9(b) where an increase in gas velocity gives less reduction in moisture content.
Bend radius ratio To study the influence of the bend radius ratio (BR) on the mass-weighted average values of the drying rate and the moisture content, calculations were performed for variations in the bend radius ratio from 4 to 12 m m21. The effect of varying bend radius ratios on the mass-weighted average values of the drying rate and the moisture content is shown in Figures 10(a) and (b), respectively. As can be seen, the mass-weighted average values of the drying rate and moisture content are the same for all variations before entering the U-bend, since the flow properties are the same. In the general section, above, it was explained that the mass-weighted average drying rates slightly decrease in the U-bend and just after the U-bend. The bend radius ratio plays a role in altering the distribution of solid particles around the U-bend and the dispersion of solid particles after the U-bend. Due to improved dispersal of solid particles after the U-bend and the fact that slip velocities are high in this area, the mass-weighted average drying rate slightly increases.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
316
HIDAYAT and RASMUSON
Figure 9. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different gas velocities.
The different bend radius ratios slightly alter the massweighted average values of the drying rate and moisture content in and after the U-bend. At higher bend radius ratios, solid particles experience higher centrifugal forces and thus the accumulation of solid particles at the outer bend wall and just after the bend exit will be higher. This causes the massweighted average drying rate for the higher bend radius to be slightly lower. As a result, the reduction in the mass-weighted average moisture at higher bend radius ratios is also lower than the reduction at lower bend radius ratios. A minor discrepancy occurs at the low bend radius ratios (at BR ¼ 3, 4 and 6). At BR ¼ 6, the mass-weighted average drying rate in the U-bend and after the U-bend is slightly higher than the mass-weighted average drying rate of BR 3 and 4.
Figure 10. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different bend radius ratios.
moisture content was varied from 0.175 to 0.325 kg water per kg solid particles. This interval covers the range of critical or transition point between the constant and falling drying rate that is 0.245 to 0.285 kg water per kg solid particles. Figures 11(a) and (b) show the effect of the feed moisture content on the mass-weighted average values of the drying rate and the moisture content. As seen in Figure 11(a), the mass-weighted average drying rate slightly decreases with a decrease in feed moisture content, and also gives a lower reduction in moisture content [Figure 11(b)]. If the moisture content reaches the critical point, the drying mechanism shifts from the constant drying rate to the falling drying rate mechanism.
Geometry arrangement Feed moisture content As mentioned before pneumatic conveying dryers have short drying times so many of these dryers are utilized as pre-dryers ahead of main dryers. However, some pneumatic conveying dryers are also applied as main dryers. The previous variations were calculated at high feed moisture content (1.41 kg water per kg solid particles) where the external convection mainly controls the drying. When the moisture content is low enough (reaching the critical point between the constant and falling drying rates), both the external convection and the internal transport become important. To study the drying mechanism at low moisture contents, the feed
A pneumatic dryer usually consists of uprisers and downcomers connected with U-bends. The effect of geometry arrangement of a U-bend on drying behavior is thus of interest. The study of geometry arrangement of a U-bend was conducted using base case geometry by simply changing the sign of the gravitational force. In this way, the inlet position becomes located in the downcomer and the outlet position is located in the upriser. For purposes of simplification, the current case is called down-case and the usual case is called up-case. The effect of changing the geometry arrangement of a U-bend on the mass-weighted average values of the drying rate and moisture content is shown in Figure 12.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER
317
Figure 11. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for different feed moisture content ratios.
As can be seen, the drying rate for the up-case tends to be higher than the drying rate for the down-case in the region before U-bend. In the U-bend, the drying rates for both cases show almost the same values, and in the region after the U-bend, the drying rate for the up-case tends to be lower than the drying rate for the down-case. These different results are due to the effect of the gravitational force direction. When the gas-solid flows through the upriser section, the flow direction is opposite to the gravitational force. This, of course, creates higher slip velocity and eventually increases the drying rate. In the U-bend, the centrifugal force still seems to dominate. High accumulation of particles at the outer U-bend wall is the main reason for having almost the same drying rate. The up-case shows a slightly better performance than the down-case. The solid particles coming out of the outlet of the up-case are slightly drier than at the outlet of the down-case. Different lengths of upriser and downcomer can be the reason for the difference in performance. The up-case has upriser and downcomer lengths of 4.50 and 3.56 m, and the down-case has upriser and downcomer lengths of 3.56 and 4.50 m. Another reason for this could be the fact that the initial drying process gives the highest drying rate. For the down-case, the initial drying process occurs in the downcomer where the drying rate is less than in the upriser.
CONCLUSIONS The phenomena of pneumatic conveying drying were studied numerically by using the extended Fluent 6.1. The investigation emphasized influences of the parameters (solid loading ratio, gas velocity, bend radius ratio, feed
Figure 12. (a) The mass-weighted average drying rate and (b) the mass-weighted average moisture content of sawdust along the axial direction of pipe for the up-case and down-case.
moisture content and geometry arrangement of a U-bend) on two variables: drying rate and moisture content. Incompressible, Eularian –Eularian gas –solid phase model, nonisothermal and steady-state conditions were considered. Two UDSs were inserted into the solution to take into account the solid particle moisture content and the mass fraction of water in the gas phase, respectively. The moisture evaporation rate of solid particles and the humidification rate of gas were treated in the source terms of the corresponding UDS equations. The evaporation energy of moisture was treated in the source term of the solid energy equation. The drying model was validated by drying sawdust using the pilot pneumatic conveying dryer. Simulation results showed that the moisture content is slightly overpredicted. A major reason for this may be due to the absence of a cyclone in the simulation and another reason may be the lack of detailed modelling of sawdust properties. The estimated temperature of the sawdust was higher than the temperature of sawdust obtained from experimental data. However, the calculation of air temperature showed very good agreement with experimental data. The mass-weighted average drying rate occurring in the U-bend showed slightly undesired results. The slight decrease in the mass-weighted average drying rate occurred in the U-bend and just after the U-bend, which was mainly due to the high accumulation of solid particles at the outer U-bend wall. In the area after the U-bend, the solid particles dispersed and the slip velocities were high, causing the
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319
318
HIDAYAT and RASMUSON
mass-weighted average drying rate to slightly increase. An increase in the solid loading ratio caused a decrease in the drying rate. A major reason for this was a strong decrease in the driving force. An increase in gas velocity basically augments the drying rate, since the mass transfer coefficient in equation (10) increased due to the increased Reynolds number (slip velocity indirectly). Different bend radius ratios slightly altered the mass-weighted average values of the drying rate and moisture content in and after the U-bend. The feed moisture content was varied to evaluate the performance of the drying model. Lower feed moisture content caused a lower drying rate. Changing the U-bend position had small effect on drying behaviour.
NOMENCLATURE BR D ds g H h Hvap,c I K k ku kg,c LD Mc Nc Nu p Pr ps Pc Q R Re Sc Sh Sh Sc SLR T t u u´ ut X yp
a bend radius ratio (a bend radius divided by a pipe radius), m m21 pipe diameter, m diameter of solid particle, m the acceleration due to gravity, m s22 the specific enthalpy, m2 s22 in equation (5) or humidity in equation (9) the heat transfer coefficient, kg s23 K21 the evaporation energy of moist or water, m2 s22 the tensor unit inter-phase momentum exchange coefficient, kg m23 s21 the thermal conductivity, kg m s23 K21 the solid diffusion coefficient, kg m23 s21 the mass transfer coefficient of moisture, m s21 the normalized axial direction, m m21 the molecular weight of moisture, kg mole21 the drying rate, kg m22 s21 the Nusselt number the static pressure, Pa the Prandtl number the solid pressure, Pa the moist or water vapour pressure, kg ms22 the intensity of heat exchange, kg ms23 bend radius, m the Reynolds number the Schmidt number the Sherwood number the source term of the conservation equation of the energy, kg ms23 the source term of the transport equation of the UDS, kg ms23 the solid loading ratio, kg solid particles kg21 air the temperature, K the time unit, s the mean velocity, m s21 the fluctuating velocity, m s21 the shear velocity, m s21 the moisture content of sawdust the wall distance of the first cell, m
Greek symbols a the volume fraction, volume of particles, m3 / volume of gas, m3 f the energy exchange, kg ms23 gu the collisional energy dissipation, kg ms23 m the shear viscosity, kg ms21 t the stress-strain tensor, kg ms22 u the granular temperature, m2 s22 r density, kg m23 h the normal direction in general coordinate, kg ms22 (Tu and Fletcher, 1995) c the scalar variable which is the mass fraction of water in the gas or in the solid particles G the diffusion coefficient of scalar variable, kg ms21
Superscripts N the normal direction in equation (16) T the transpose sign in equation (12) or the tangential direction in equation (16) Subscripts c critical g the gas phase i the subscript i represents either the gas phase (subscript g) or the solid phase (subscript s) j the pair of the index i (if the index i represents the gas phase then the index j represents the solid phase, vice versa) me moisture equilibrium s the solid phase w the position at a wall
REFERENCES Akilli, H., Levy, E.K. and Sahin, B., 2001, Gas-solid flow behavior in a horizontal pipe after a 908 vertical-to-horizontal elbow, Powder Technol, 116(1): 43–52. Crowe, C., Sommerfeld, M. and Tsuji, Y., 1998, Multiphase Flows with Droplets and Particles, (CRC Press, Boca Raton, Boston, New York, Washington and London). Ding, J. and Gidaspow, D., 1990, A bubbling fluidization model using kinetic theory of granular flow, AIChE J, 36(4): 523–538. Ergun, S., 1952, Fluid flow through packed columns, Chem. Eng. Prog, 48(2): 89–94. Fluent, 2001, User’s Guide, Fluent 6.1, (Fluent Incorporation New Hampshire Company, USA) Lebanon. Fluent, FLUENT Flow Modeling Software, http://www.fluent.com/ software/fluent/index.htm, accessed September 2006. Fyhr, C. and Rasmuson, A., 1997, Mathematical model of a pneumatic conveying dryer, AIChE J 43: 2889–2902. Gidaspow, D., Bezburuah, R. and Ding, J., 1992, Hydrodynamics of circulating fluidized beds, kinetic theory approach, in Fluidization VII, Proceedings of the 7th Engineering Foundation Conference on Fluidization. Gunn, D.J., 1978, Transfer of heat or mass to particles in fixed and fludized beds, Int J Heat Mass Transfer, 21: 467– 476. Hellsten, G., 1992, Tabeller och diagram, energi och kemiteknik, (Almqvist&Wiksell, Stockholm, Sweden). Hidayat, M. and Rasmuson, A., 2004, Numerical assessment of gassolid flow in a U-bend, Chem Eng Res Des, 82(A3): 332–343. Hidayat, M. and Rasmuson, A., 2005a, Some aspects on gas-solid flow in a U-bend: numerical investigation, Powder Technol, 153(1): 1– 12. Hidayat, M. and Rasmuson, A., 2007, A computational investigation of non-isothermal gas-solid flow in a U-bend, in press Powder Technol, Hinze, J.O., 1975, Turbulence, (McGraw-Hill Publishing Co, New York, USA). Huber, H. and Sommerfeld, M., 1994, Characrerization of the crosssectional particle concentration distribution in pneumatic conveying systems, Powder Technol, 79(3): 191– 210. Kemp, I.C., Bahu, R.E. and Oakley, D.E., 1991, Computational fluid dynamics modelling of vertical pneumatic conveying dryers, Powder Technol, 65: 477– 484. Kirk-Othmer, 1993, Encyclopedia of Chemical Technology (John Wiley & Sons, Inc., New York, USA) (access year 2000). Levy, A. and Borde, I., 1999, Steady state one dimensional flow model for a pneumatic dryer, Chemical Engineering and Processing, 38: 121– 130. Levy, A. and Mason, D.J., 1998, The effect of a bend on the particle cross-section concentration and segregation in pneumatic conveying systems, Powder Technol, 98(2): 95– 103. Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, (McGraw-Hill, New York, USA). Shih, T.H., Liou, W.W., Shabbir, A., Yang, Z. and Zhu, J., 1995, A new k-1 eddy-viscosity model for high Reynolds number turbulent flows, Computers & Fluids, 24(3): 227 –238. Siau, J.F., 1984, Transport Process in Wood, (Springer-Verlag, Berlin, Heidelberg, New York and Tokyo).
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307– 319
HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER Skuratovsky, I., Levy, A. and Borde, I., 2005, Two-dimensional numerical simulation of the pneumatic drying in vertical pipes, Chemical Engineering Processing, 44: 187– 192. Stoess, H.A., 1983, Pneumatic Conveying (John Wiley & Sons, New York, Chichester, Brisbane, Toronto and Singapore). Szafran, R.G. and Kmiec, A., 2004, CFD modeling of heat and mass transfer in a spouted bed dryer, Ind Eng Chem Res, 43: 1113– 1124. Tu, J.Y. and Fletcher, C.A.J., 1995, Numerical computation of turbulent gas-solid particle flow in a 90 degree bend, AIChE J, 41(10): 2187–2197.
319
Vasquez, S.A. and Ivanov, V.A., 2000, A phase coupled method for solving multiphase problem on unstructured meshes, Fluids Engineering Division Summer Meeting, Boston, USA, ASME. Wen, C.Y. and Yu, Y.H., 1966, Mechanics of fluidization, Chem Eng Prog Symp Series. Yilmaz, A. and Levy, E.K., 2001, Formation and dispersion of ropes in pneumatic conveying, Powder Technol, 114: 168– 185. The manuscript was received 7 July 2005 and was accepted for publication after revision 6 November 2006.
Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319