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2 17 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe Zongming LIU, Guangbin DUAN and Kun WANG Univerity of JINAN China P.R 1. Introduction Computational Fluid Dynamic i now a new ramification of the numerical dicretization method baed on high-performance electronic computer, which focue on fluid mechanic imulation. Fluid mechanic ha two main brache that one i theoretical analyi and another i experimental reearch. Therefore, theoretical and experimental fluid mechanic were created a mot important contituent in early day. Although the theoretical method could give the quantum reult of the olving problem, it wa till little ued for it complicated olution procedure. Computational fluid mechanic ha developed rapidly to cover the hortage of theoretical method. It ha been involved each fluid field though it development hitory i hort. Many numerical olution method were formed according to different imulation purpoe. Finite difference calculu and finite element method were mainly involved. In the application, Finite difference calculu wa uually ued in reolving fluid problem, while finite element method wa exploited to reearch olid mechanic theme. Ga-olid two phae flow mean olid particle are conveyed by compreed ga phae. The particle trace are irregular, which caued by the diperion action and coupling force between ga and olid phae. The interaction proce lead to the irregular motion of ga olid two phae flow and the flow characteritic parameter altering greatly. Nowaday, the recognization and analyi of ga olid two phae flow wa not enough with limitation of tet technique, which retricted the application development and ytem optimization of ga olid flow. So ome freh technique mut be appeared to uit the application ituation. Until now, the reearch technique in ga olid two phae flow focu on experiment cae becaue of the complexity of ga olid flow. Te ga olid two phae flow theory became more and more ophiticated with the development of particle dynamic and aerodynamic. Both had ome deficiency. For example, in experimental reearch, calculation of ome conveying parameter motly depend on empirical equation baed on experiment which lead to the limitation, and which are the ame with it experimental condition commonly and generalized hardly. Theoretical tudie are motly hort of accuracy becaue of lot of hypothei in the proce of deduction. Therefore, in thi thei, imulation tudy on the proce of dene-phae ga-olid two phae flow wa carried on baed on experimental and theoretical invetigation in order to cover the hortage of experimental and theoretical invetigation.

3 374 Computational Simulation and Application Numerical imulation technique improve rapidly with the advance of computer hardware. And it play more and more important role in the reearch of dene-phae ga olid flow. Thi article gave the numerical imulation concluion baed on the experimental and theoretical reearch. By aociating with experimental condition and the applicability of experimental equation, tranport equation of Reynold wa deduced by uing time averaged method baed on intantaneou equation of ga and olid. The control equation of turbulent energy and turbulent diipative ratio were formed, which conidered reciprocity between ga and olid, colliion of particle and interaction between particle and wall. The model included continuity equation, momentum equation, turbulent kinetic energy equation and turbulent kinetic energy ratio equation. Phyical meaning of primary item of control equation wa dicued too. Two-fluid model of ga-olid turbulence in proce of dene-phae ga olid two phae flow wa founded, o did the correponding numerical olution and calculating flow. The model could mention reciprocity between ga and olid, colliion of particle and interaction between particle and wall. The proce of dene phae ga olid two phae flow in pipeline under experimental condition wa imulated with FLUENT oftware by founded model and correponding arithmetic. Preure ditribution diagram, denity ditribution diagram and velocity vectogram etc. were given which diplayed the flow alternation of dene-phae pneumatic conveying. And comparion between imulated reult and experimental cae howed good uitable which illuminated the model had good accuracy and forecating capacity. In all, in thi tudy, fluid mechanic characteritic of dene-phae ga olid two phae flow in pipeline were dicued by computational fluid dynamic method baed on flow theory of ga-olid, and a erie of ignificative reult were obtained. The reearch howed that the numerical imulation of dene-phae pneumatic conveying can complement experimental and theoretical tudie which had promoted effect on the application and development of dene-phae ga olid flow in pipeline technique. 2. Experiment The technique of dene-phae pneumatic conveying ha been widepread applied in indutry. Invetigation on dene-phae pneumatic conveying uually include experimental reearch and theoretical reearch becaue of the complexity of flow in pneumatic conveying. But, both of the method have limitation. In experimental reearch, calculation of ome conveying parameter motly depend on empirical equation baed on experiment which lead to the limitation, and which are the ame with it experimental condition commonly and generalized hardly. Experimental reearch were carried on by changing feeding preure on the poitive preure tyle pneumatic conveying pilot-cale experiment table. The conveying characteritic along pipeline were tudied primarily. Pneumatic conveying ytem in thi paper wa a circulating experiment ytem with longditance pipeline, which conited of an air compreor, a feeder, a conveying pipeline, and a et of meaurement/control ytem, a hown in Fig.1. The pipeline wa made of eamle teel pipe with a length of 203 m and pipe diameter of 80 mm. Weight balance wa intalled to meaure the fly ah dicharge rate of the feeding bin. Ga ma flow meter wa adopted to meaure the ma flow ratio of the compreed air.

4 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 375 GP/DP tranmitter were ued to meaure preure of the feeder, etting point along pipeline and preure drop of tet egment. Fly ah wa tranported from the feeder veel into the receiver in dene phae. The material propertie were hown in Table GP 9 DP 8 GP 9 DP 8 GP GP 8 DP 9 8 GP GP 8 DP A/ D Fig. 1. Schematic diagram of experimental ytem. 1. air compreor 2. ga torage pot 3.oilwater egregator and air drier 4. ga adapter 5. ga inlet valve 6. ga flow meter 7. feeder 8. tatic preure gauge 9. differential preure gauge 10 dut catcher 11. collecting bin 12. weighing-appliance 13 data acquiition equipment 14. micro-computer 15. bleeder valve. After being put into the feeder, fly ah wa fluidized by compreed air. Then at a preet tranporting preure in the feeder, fly ah paed through the conveying pipeline and reached the collecting bin finally. Five tet egment along horizontal pipeline were employed averagely to analyze the tendency of preure drop along the pipeline. A differential preure tranmitter and a gauge preure tranmitter were aembled in the egment of m, m, m, m. Gauge preure tranmitter were alo intalled at the terminal of pipeline (6) a well a the vent of feeder. In thi experiment, operating condition wa mainly controlled by changing the preure of feeder The experiment under different operating condition and each with everal repetition were carried out in total. Equivalent pherical Bulk denity Material Sphericity diameter (μm) (kg m -3 ) Fly ah Table 1. Experimental material propertie. 3. Experimental reult 3.1 Ga velocity along the pipe The ga velocity along the pipe i an important parameter, and it can be expreed by the following equation. u g Mg Mg RT A A p (1) g

5 376 Computational Simulation and Application Where, M g i the ga ma flow ratio. A i the cro ection of pipeline. T tand for Kelvin temperature. P i tatic preure in the pipe. i poroity, and it can be achieved by the following equation. k g (2) In thi equation, i olid denity. i ga denity. k i olid loading ratio, the ratio of g olid ma veru ga ma in total. Fig. 2 how the trend of ga velocity along the pipeline under different feeder preure. Ga velocity increae gradually with the increae of feed preure. While under the ame feed preure, ga velocity increae gradually along pipeline, which i caued by ga volume expanion. Ga velocity(m/) MPa 0.32MPa 0.36MPa 0.40MPa Ditance along pipe(m) Fig. 2. Experimental value of ga velocity along pipeline. 3.2 Solid velocity along the pipe In thi paper, the olid velocity along the pipe can be given by the following equation. u ij Lij (3) t ij Where Lij mean the ditance between the tranmitter of NO. i and NO. j. and tij tand for the time interval of the preure ignal appearance between NO. i and NO. j tranmitter. The relationhip between preure drop and tranport ditance along pipeline in different feed preure wa obtained baed on the meaured data from the four differential preure tranmitter in the experiment proce, a hown in Fig. 3.

6 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 377 Fig. 3. Variable curve of tatic preure with the feed preure 0.32Mpa. Fig. 4 how the trend of olid velocity along the pipeline under different feeder preure. olid velocity increaed gradually with the increae of feed preure. And under the ame feed preure, olid velocity increae gradually along pipeline, which i caued by the increaing of ga velocity. 12 Solid velocity(m/ MPa 0.32MPa 0.36MPa 0.40MPa Ditance along pipe(m) Fig. 4. Experimental value of olid velocity along pipeline.

7 378 Computational Simulation and Application 4. Numerical imulation of ga olid flow in pipe 4.1 Mathematical model A we all know, the phyical apect of fluid flow are governed by three fundamental principle (1) ma i conerved; (2) Newton econd law; (3) energy i conerved. So N-S equation are formed. To thi paper, the uitable mathematical model were elected according to experimental concluion. A we all know, the Reynold Number value of ga and granule in dene phae ga olid flow are both high than that of lean phae, which lead to more turbulent motion. Therefore, the addition of olid particle greatly changed ga phae turbulent contruction and meanwhile ga fluctuation affect particle motion. So the interaction between the two phae lead to the ma, momentum and energy tranmiion. When the olid concentration i high enough, interaction among particle affect olid flow characteritic greatly. Conequently, the interaction among particle hould be given in imulation proce in addition to ga olid interaction and turbulent a the ga olid two phae flow turbulent model being et up. Two-fluid model which baed on granule dynamic theory wa adapted in the tudy. Flow parameter uch a macrocopic granule tranport equation, olid preure, vicou coefficient, diffuion coefficient, heat conductivity coefficient, granule temperature etc can be obtained through the model. Thi model wa ued comprehenively in everal field becaue it mentioned interation action of ga olid flow, granule turbulent vicoity and particle colliion roundly. In thi tudy, by uing k-ε two phae model, granule dynamic model and ga olid two phae coupled, the ga olid two phae turbulent model were built up. Some reaonable aumption about the flow proce mut be given a following. 1. The particle were compoed of mooth rigid phere with the ame diameter. And during the flow proce, two phere colliion were mentioned while colliion among lot of olid particle mut be ignored. 2. Ga olid two phae exited in the flow pipe homogeneouly with defined phyical parameter. Each phae wa continuou while the time averaged velocity and volume ratio wa different. 3. The acting force of olid phae involved gravity and reitance force. Other kind of force uch a buoyancy, fale-ma-force, Baet force, thermophoretic force etc wa ignored according to experimental cae. 4. The turbulent impule of ga olid two phae wa iotropy. Diffuion and Brownian movement effect could be neglected. The change of ga phae turbulent energy howed the influence of particle to ga phae Intantaneou equation etup of ga olid flow According to ma conervation and momentum conervation law, ga and olid phae intantaneou volume averaged conervation equation can be given a following. Ga continuity equation: Solid continuity equation: gg ggugj t x j 0 (4)

8 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 379 t Ga momentum equation: Solid momentum equation: uj x j 0 u u u p g g gi g g gi gj ij cd g gggi Fi t xj xi xj u uu p i i j ij cd gi Fi t xj xi xj (5) (6) (7) Where, g, are ga, olid volume rate, g 1 ; g, are ga denity and olid denity repectively ; u gi, u gj, u i, u j are intantaneou velocity component of ga, olid in i, j direction. p g p are preure of ga, olid; g i i component of gravitation in i cd direction; Fi i interaction between ga and olid, which include the inter-phae reitance, fale ma force, and preure gradient force. In horizontal pipe, drag force i the dominant factor. So here cd i gi pi Where i drag force coefficient between the two phae. F u u (8) A α g 0.8, according to experiment reult, the expreion of can be given a below. u u 0.75C (9) g 2.65 D g g dp C D i ingle particle drag force coefficient, the calculation equation are given a following. Re 1000 p 1000 Re 1 Re 1 p p C C C D D D 0.44 Re 24 (1 0.15Re 0.68 p ) p 24 Re p (10) Re p i defined a particle Reynold number, Here, D Re p C (11) Re p

9 380 Computational Simulation and Application Re p ggdp ug u (12) g ij i ga vicoity tre. u u 2 u ij gg ij x x 3 x Where, g i ga phae kinetic vicoity coefficient. ij i Kronecker delta, gi gi gk j i k (13) ij 1 0 i j i j, Time averaged equation etup of ga olid flow Ga continuity equation: gg ggugj g gugj 0 t x x j j (14) Solid continuity equation: uj uj 0 t x x j j (15) Ga momentum equation: ' 2 ugk u p ' gk ggugi ggugiugj g gg gg t xj xi 3 xj xk xk (16) x x x x x ' ' ug i ugj u ' gi ugj ' ' ' g g g g gggi ui ugi ui ugi j j i j i j x ' ' ' ' ' ' ' ' g gugiugj gugi gugj gugj gugi g gugiugj

10 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 381 Solid momentum equation: p ' ui uiuj gi ij dij ugi ui t x x x j i j ugi ui uu i j ui uj uj ui uu i j ' ' ' ' ' ' ' ' ' ' ' x j (17) From equation above, time averaged equation etup provided everal unknown quantity. Above all factor, turbulent tre played a dominant role to the governing equation. So ome aumption or new turbulent model equation mut be introduced to accomplih the equation et. Nowaday, Reynold tre model and vortex model were often employed to agree with different uitable cae. In the tudy, by contrat to all occaion, Reynold tre model wa elected Turbulent kinetic energy and turbulent diipation rate equation 1. Reynold tre tranport equation According to Bouine aumption and ome mathematical operation, Reynold tre tranport equation can be given a below. uu u uu uu uu t x x x x x x ' ' ' ' ' ' ' ' uu i j uu i j u t ' ' j u ' ' j i j k i j i k j k k k k k k k k t ' ' 2 gi gj C1 uu i j kij Pr t xj x i k 3 u ' ' j ' ' u i 1 32 ' ' ' 2 ' ' k C2 uu i k ujuk Pkkij xk x C1 ukumnknmij uu i knn i k k 3 k 3 Cld 32 ' 3 3 k 2 2 km,2 k mij ik,2 j k ik,2 i k ij 2 2 l 3 C n n n n nn C d (18) To thi tudy, the buoyant force and revolution effect were neglected. So the equation above can be rewritten a below. uu u uu uu uu t x x x x x x ' ' ' ' ' ' ' ' uu i j uu i j u t ' ' j u ' ' j i j k i j i j j k k k k k k k k 2 u u 1 2 C uu k C uu u u P ' ' ' ' j ' ' i 1 i j ij 2 i k j k kk ij ij k 3 xk x k Ga Turbulent Kinetic Energy Equation and Turbulent Diipation Rate Equation By analogy ingle flow theory and Bouineq vortex aumption, the relationhip of ga Reynold tre and averaged velocity gradient wa hown a below. (19) g 1 / 0,max 1/3 1 (20)

11 382 Computational Simulation and Application Where pt i addition preure which i caued by puled velocity. k i turbulent kinetic energy. 2 Pt ggk (21) 3 gt i turbulent vicoity, which depend on flowage. Then, turbulent diipation rate i introduced. ' i ' j uu 1 '2 '2 '2 k ugi ugj ugk (22) 2 2 ' ' gt u i u i g x k x k The tranport expreion of k and can be given when the addition drag ource caued by adding the olid phae. Therefore, the ga turbulent kinetic energy and turbulent diipation rate in the ga olid flow can be given. Ga phae turbulent kinetic energy equation: ggk ggugjk e k Gkg Gg g g t xj x j k x j Ga phae turbulent diipation rate equation: u gg gg gj e C G G C t xj x j x j k G kg i the generation of ga turbulent kinetic energy. 1 kg g 2 g g (23) (24) (25) G ugj ugj ugj ugi ugk 2 ugk x i xi x j xi xk 3 x k kg gt gt ij e G g i additional ource caued by granule adding to ga phae turbulent kinetic energy. 2 (26) G 2 k k (27) g Where C 1 =1.44,C 2 =1.92, k =0.82, = Solid turbulent kinetic energy equation and turbulent diipation rate equation By uing the ame proceing method, Solid turbulent kinetic energy equation can be given a following. k u k j p k Gk Gg t xj x j k x j (28)

12 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 383 Solid Turbulent Diipation Rate Equation u i p C1Gk GgC2 t xi x j x j k G k i the generation of olid turbulent kinetic energy. G u j uj u j uj uk 2 u k x i xi x j xi xk 3 xk k t t ij p G g i additional ource caued by granule adding to ga phae. 2 (29) (30) Thereinto, c 1/ 110 /,max / TL Lagrangian time cale of ga turbulent can be written a below. Particle relaxation time, / G 2 ck k (31) g T 0165 k/ L When the mathematical model i built up, the key tep of the imulation i how to identify turbulent vicoity t. In thi paper, by comparing to the pure flow, ga and granule phae turbulent vicoity gt, t can be achieved a following equation repectively. gt C gg 2 k (32) 2 k t C pp (33) The expreion of ga effective vicoity coefficient i given a below. e gg gt (34) The granule effective vicoity coefficient i the following equation. p t (35) The granule phae hear vicoity can be gained by the next equation. 5 d 4 4 g d 1e 1 g 1e eg0 5 2 (36) Where g 0 tand for granule radial ditribution function, which can reflect the effect of olid concentration

13 384 Computational Simulation and Application g 1 / 0,max The expreion of granule phae preure i given a below. 1/3 1 (37) 0 The total vicoity of granule phae i the below equation. p 12 1e g (38) 4 2 dg p 0 1 e (39) 3 It mut be noted that, in the equation above, the ymbol of e tand for granule colliion recovery coefficient. And it obey the following rule. e 0 e 1 0 e 1 When e= 1, it mean elatic colliion, which i in cae of no energy lo. When e=0, it mean complete inelatic colliion. When 0 e 1, it mean energy will diffue in form of elatic colliion. (40) 4.2 Simulation condition Geometric model and grid A we all know, in numerical imulation proce, the grid tructure ha a greatly effect on the calculation preciion. Meh with bad tructure may lead to the enlargement of relative error and tability degradation or even imulation procedure divergent. Fig. 5. Diagram of grid for geometric model.

14 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 385 Meanwhile, the grid formation technique ha become a critical part in modern computational fluid dynamic. The meh formation method can be divided two way. One i algebraic method and the other i differential method. Thereinto, differential method can be ued to produce mooth grid to uit complex flow domain. Of coure, we can adjut the meh degree of cloene by changing the control function. And if more accurate olution needed, mah mut be thicker. In thi tudy, horizontal pipe ection with 1 meter length, 0.08 meter diameter and range from to 128.7m were choen a reearch object. In thi pipe ection, fly ah wa conveyed by compreed ga. Fig.5 gave the pipe geometric model with full grid Boundary condition 1. Boundary condition for ga phae Inlet boundary for ga There are the aumption that the ga axial velocity cro-ection of the entrance with the fully developed turbulent flow of mooth pipe, radial velocity i zero, given the preure of the entrance, turbulent kinetic energy expreion i Turbulent diipation rate can be expreed by 3 2 k ugig (41) k C (42) l Where Ig i ga turbulent intenity, to the fully arien turbulent flow, then, 1/8 gd Ig 0.16 Re H (43) To the equation, D H i hydraulic diameter. From the equation above, it can be concluded, the Reynold number in the ga turbulent intenity equation i regard hydraulic diameter a characteritic length. L i length dimenion, to circle pipe, l 0.07L, L i pipe diameter. The ga velocity of inlet i et 9.9m/. Outlet boundary for ga The aumption that the fully developed condition of the pipe flow, namely the normal derivative of the variable olved i zero, given the export preure. 0 x i ( u, k, ) (44) g gi Pipe wall urface In the tudy, no-lip condition wa adapted. Each parameter near the pipe wall wa conidered a zero. And wall function method wa applied. So

15 386 Computational Simulation and Application ugikc ln w u gi y g gk EY Y Y (45) Where u gi tand for the ga velocity which i parallel to the pipe axi near the pipe wall Y C 0.5 k / g y, y i the ditance between calculated node and pipe wall. E= Boundary condition for olid phae Inlet boundary for olid Homogeneou inlet condition are et and the volume fraction of particle i given. The expreion of turbulent kinetic energy and turbulent diipation rate are et a following. Where 3/ /4 k k ui, C (46) 2 l 1/8 D I 0.16 Re H (47) The olid velocity i et 4.3 m/ baed on experiment data. Outlet boundary for olid The aumption that the olid phae wa the fully developed condition of the pipe flow, namely the normal derivative of the variable olved i zero. x i 0 u, k, i (48) Pipe wall urface To granule phae, the velocity doen t agree with no-lip condition, thu the velocity value can t be equal to zero. According to particle colliion near pipe wall reearch, the granule phae normal velocity can be given a following. u u i 1 2 i 1hKn 0 w xi w (49) where, 2 e 1/2 e1 e 1/2 1 1, e h mean the ditance between the center point of the firt control bulk and the pipe wall. Kn i Knuden number, which can be given a following. Kn u u u (50) gi i i w w

16 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 387 It mut be noted that, in thi paper, the turbulent kinetic energy and turbulent diipation rate near the pipe wall were defined zero Baic parameter in proce of imulation Table 2 gave the baic parameter in proce of numerical imulation Solid phae ga phae pipe ρ =770kg m -3 ρ g =2.03kg m -3 D=0.08m d =60μm μ g = L=1m Table 2. Baic parameter ued for imulation. 4.3 Numerical imulation proce Equation dicretization In thi paper, Finite Volume Method wa utilized to dicrete the governing equation above. The elected pipe ection wa divided into many non-concurrent domain which wa called calculating grid. And then, each nodal point of tationary divided domain and it controlled volume were confirmed. In the proce of dicretization, the phyical quantity of thi controlled volume were defined and tored in the determined nodal point Numerical calculation method In thi tudy, we ued SIMPLE method to carry out two phae flow imulation. And the ga olid two phae flow were coupled each other. Firt of all, on the bai of initial condition and boundary condition, pure ga phae governing equation can be olved. And then, we can reolve granule phae governing equation which are baed on ga flow characteritic. The lat tep wa to gain the ga and olid flow field repectively by combining with thi two ingle flow and coupling effect between two phae Numerical calculation circuitry The numerical calculation circuitry i hown a below.

17 388 Computational Simulation and Application Relaxation factor Becaue of the exitence of inter phae coupled and nonlinear, the governing equation of ga olid two phae flow became more complex. So ometime, low relaxation interation may be adopted to enure the table contriction during the imulation proce. The relaxation factor of thi tudy can be given a the following table. Preure, p Turbulent kinetic energy k Turbulent diipation rate, ε Ga velocity, u g Solid velocity u Granule volume ratio,α Table 3. Relaxation factor. 4.4 Simulation reult and analyi On the bai of imulation analyi above, high concentration ga olid flow in horizontal pipe ufficient development wa imulated. Flow information uch a preure, olid concentration, ga and granule velocity can be achieved Preure ditribution along the pipe Fig.6 give the tatic preure ditribution along the pipe. From thi figure, it can be een that the tatic preure and differential preure gradient decreae along the pipe. That i to ay, the differential preure reduce with the decreaing of tatic preure. It i becaue, with the ga olid flow moving in pipeline, more tatic preure tranit to dynamic power to impel and accelerate particle. Thi concluion agree with experimental reult well. Fig. 6. Ditribution diagram of tatic preure.

18 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 389 Fig. 7. Ditribution diagram of dynamic preure. Fig.7 how dynamic preure ditribution along the pipe. From the diagram, we can know that the dynamic preure decreaed gradually in the upper of the pipe, while at the bottom of pipe the dynamic preure increaed on the contrary. The reaon for the phenomenon i the increaing of particle concentration at the bottom of pipe Solid concentration ditribution along the pipe Solid concentration can reflect the olid motion tyle directly in proce of pneumatic conveying. But in the experiment reearch, it hard to meaure thi parameter accurately. In thi tudy, we ue numerical imulation method to gain the olid concentration in pipeline, a hown in Fig.8. Fig. 8. Graph of concentration ditribution.

19 390 Computational Simulation and Application Fig.9 how that the particle i accelerated by ga phae along the axial direction, o the concentration become lower. But at the ame time, the turbulent kinetic energy of two phae flow increae at the tube center, which lead to more preure difference. The particle near pipe center diffue to upper or bottom of pipeline under high preure gradient. Meanwhile, with the action of gravity force, the olid particle continue moving to the bottom of pipe, which reult in the concentration increaing of pipe bottom. A in all, particle concentration decreaed in the upper of the pipe, while at the bottom of the pipe the particle concentration wa growing. Thi illuminated that particle were not homogeneou upenion in conveying proce, but the ettlement of particle, o particle concentration at the bottom of the pipe wa greater than that of the upper part Velocity ditribution along the pipe In the pneumatic conveying of horizontal pipe, the original pure ga flow tyle doen t exit any more. The larget ga velocity value poition will deviate from the pipe centre and rie to upper part of the pipe. By contrarie, the ga velocity reduce under the pipe centre. Fig. 9. Vector graph of ga velocity. Fig. 10. Vector graph of particle velocity.

20 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 391 In all, the ga velocity ditribution i more untable, and the value i much higher near pipe center, while lower near the pipe boundary, which i chiefly becaue no lip of ga phae. Fig.9 and 10 how ga and particle velocity vector along pipe repectively. A can be een from the diagram, ga and particle velocity increaed gradually along pipe, a expected, near the pipeline wall velocity i le, and the velocity upper part i larger than the velocity of the bottom. The particle velocity at the inlet i 4.3 m/, and which at the outlet i 4.6 m/. The ga velocity of inlet i et a 9.9 m/, while the velocity at the outlet i 10.3 m/. then all thi i approximately conitent 4.5 Comparion of experimental data and imulation reult Comparion of ga velocity Fig.11 give the contrat of experiment data and imulation reult for ga velocity in the elected pipe ection under a et conveying preure. From the figure, the trend of the two reult i imilar. And it relative error i le Ga velocity(m/) Experiment data Simuation data Ditance along pipe(m) Fig. 11. Relationhip of ga velocity between imulated and experimental value. Solid velocity(m/) Experiment data Simuation data Ditance along pipe(m) Fig. 12. Relationhip of olid velocity between imulated and experimental value.

21 392 Computational Simulation and Application Comparion of olid velocity Actually, the experimental olid velocity in elected pipe ection concentrate a point velocity which tand for the average velocity in thi egment. Fig 12 give the contrat of experiment data and imulation reult for olid velocity in the elected pipe ection under a tationary preure. From the figure, we can conclude that the imulation data i approximately equal to the average value of experiment value. So, numerical imulation can be ued to predict the ga olid flow parameter preciely Comparion of preure drop Similar to the olid velocity ditribution, the experimental value of preure drop i to be regarded a the average value along the pipe. 1.4 Preure drop(kpa/m) Experiment data Simuation data Ditance along pipe(m) Fig. 13. Relationhip of preure drop between imulated and experimental value. 2 Simulation reult(kpa/m) Experiment data(kpa/m) Fig. 14. Relationhip between experiment data and imulation reult.

22 Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe 393 Fig.13 give the contrat cae of experiment data and imulation reult for preure drop. From the figure, we can gain that the experiment data point lie in the imulation average value dot. In thi work, we alo et another everal et of boundary condition to imulate correponding experiment cae in the elected pipe ection. Figure 14 how the comparion of the experimental data and imulation reult. From thi figure, we can know, the relative error between the experiment and imulation range from -8.48% to 4.70%, which illutrate good agreement and accuracy. 5. Concluion In thi paper, dene phae pneumatic conveying i carried out. The trend of flow characteritic along the pipe i given in different cae. And baed the experimental reult, the k-ε-kp-εp two-fluid model wa etablihed with the conideration of ga-olid turbulent flow and taking into account the iue of ga-olid two-way coupling. Numerical imulation of fly ah flow for dene-phae pneumatic conveying wa carried out by uing Fluent oftware. The numerical imulation and experimental reult were compared. The imulated concluion are given a below. 1. Along pipe axial direction, preure and preure gradient decreaed, dynamic preure increaed gently. Meanwhile the dynamic preure in the upper part of pipe decreaed, while at the bottom of pipe dynamic preure enlarged gradually. It can be een that ga and particle velocity increae along the pipeline, the velocity in the upper pipe part wa larger than that of the bottom of pipe. Particle concentration i different along pipe radial direction. The olid conitency i larger at the bottom of pipe. 2. The reult of numerical imulation were compared with experimental reult. The imulation reult were validated by the experimental data, which indicate that the model and the correponding algorithm have higher accuracy and better prediction. So it can reveal the baic characteritic of dene phae pneumatic conveying in horizontal pipe. 6. Acknowledgment The author gratefully acknowledgement the financial upport from the National Natural Science Foundation of China (No ) and Shandong Provincial.Education Department of China (No. J10LD05) 7. Reference Example of fluid engineering and application of computer imulation. (Han zhan-zhong, 2005). Modeling of the Ga Solid Turbulent Flow in a Rier Reactor. (ZHENG Yu, WAN Xiao-tao, WEI Fei, etl., 2001). Numerical tudy on the I nfluence of variou phyical parameter over the ga-olid twophae flow in the 2D rier of a circulating fluidized bed.( Luben Cabeza-Gomez, Fernando Eduardo Milioli. 2003). Numerical imulation of the ga-particle turbulent flow in rier reactor baed on k-ε-k p -ε p -Θ two-fluid model. ( Zheng Y, Wan X T, Qian Z, et al., 2001).

23 394 Computational Simulation and Application Velocity Analyi of Fly Ah Solid Particle Conveyed by Dene-phae Pneumatic Force. (YI Hua,LIU Zong-ming,DU Bin, et al., 2007). Effect of an electrotatic field in pneumatic conveying of granular material through inclined and vertical pipe. ( EldinWee Chuan Lim, Yan Zhang, Chi-HwaWang, 2006). Evaluation of model and correlation for preure drop etimation in dene phae pneumatic conveying and an experimental analyi. ( Lui Sancheza, Netor A. Vaqueza, George E. Klinzinga, et al, 2005). Dilute ga olid two-phae flow in a curved 90 duct bend: CFD imulation with experimental validation( B. Kuan, W.Yang, M.P. Schwarz., 2007). Analytical prediction of preure lo through a udden-expanion in two-phae pneumatic conveying line. (Mehmet Yaar Gundogdu, Ahmet Ihan Kutlar, Haan Duz, 2009) Numerical imulation on dene phae pneumatic conveying of pulverized coal in horizontal pipe at high preure. (Wenhao Pu,Changui Zhao,Yuanquan Xiong,et al., 2010).

24 Computational Simulation and Application Edited by Dr. Jianping Zhu ISBN Hard cover, 560 page Publiher InTech Publihed online 26, October, 2011 Publihed in print edition October, 2011 The purpoe of thi book i to introduce reearcher and graduate tudent to a broad range of application of computational imulation, with a particular emphai on thoe involving computational fluid dynamic (CFD) imulation. The book i divided into three part: Part I cover ome baic reearch topic and development in numerical algorithm for CFD imulation, including Reynold tre tranport modeling, central difference cheme for convection-diffuion equation, and flow imulation involving imple geometrie uch a a flat plate or a vertical channel. Part II cover a variety of important application in which CFD imulation play a crucial role, including combution proce and automobile engine deign, fluid heat exchange, airborne contaminant diperion over building and atmopheric flow around a re-entry capule, ga-olid two phae flow in long pipe, free urface flow around a hip hull, and hydrodynamic analyi of electrochemical cell. Part III cover application of non-cfd baed computational imulation, including atmopheric optical communication, climate ytem imulation, porou media flow, combution, olidification, and ound field imulation for optimal acoutic effect. How to reference In order to correctly reference thi cholarly work, feel free to copy and pate the following: Zongming Liu, Guangbin Duan and Kun Wang (2011). Numerical Simulation of Dene Phae Pneumatic Conveying in Long-Ditance Pipe, Computational Simulation and Application, Dr. Jianping Zhu (Ed.), ISBN: , InTech, Available from: InTech Europe Univerity Campu STeP Ri Slavka Krautzeka 83/A Rijeka, Croatia Phone: +385 (51) Fax: +385 (51) InTech China Unit 405, Office Block, Hotel Equatorial Shanghai No.65, Yan An Road (Wet), Shanghai, , China Phone: Fax: