A CORRELATION EQUATION FOR CALCULATING INCLINED JET PENETRATION LENGTH IN A GAS-SOLID FLUIDIZED BED

CHINA PARTICUOLOGY Vol. 3, No. 5, 279- 285, 2005A CORRELATION EQUATION FOR CALCULATING INCLINEDJET PENETRATION LENGTH IN A GAS-SOLID FLUIDIZED BEDRuoyu Hong'", Haibing Li, Jianmin Ding* and Hongzhong Li2'Department of Chemistry and Chemical Engineering, Soochow University, Suzhou 215006, P. A. China2Institute of Process Engineering, Chinese Academy of Sciences, Bejing 100080, P. A. China"Laboratory of Solid Waste Energy, Guangzhou Institute of Energy Conversion,Chinese Academy of Sciences, Guangzhou 510640, P. A. China*IBM, HYDA/050-3 C202, 3605 Highway 52 North, Rochester, MN 55901, USA*Author to whom correspondence should be adressed. E-mail: rhong@ suda.edu.cnAbstract Numerical simulation of gas-solid flow in a two-dimensional fuidized bed with an inclined jet was per-formed. The numerical model is based on the two-fluid model of gas and solids phase in which the solids constitutiveequations are based on the kinetic theory of granular flow. The improved ICE algorithm, which can be used for both lowand high-velocity fluid flow, were used to solve the model equations. The mechanism of jet formation was analyzed usingboth numerical simultions and experiments. The emergence and movement of gas bubbles were captured numericallyand experimentally. The influences of jet velocity, nozzle diameter, nozzle inclination and jet postion on jet penetrationlength were obtained. A semi-empirical expression was derived and the parameters were correlated from experimentaldata. The correlation equation, which can be easily used to obtain the inclined jet penetration length, was compared withour experimental data and published correlation equations.Keywords fluidized bed, jet, penetration length, two fluid model1. Introduction2. ExperimentalThe ash-agglomerating fluidized-bed coal gasification2.1 Experimental apparatus and bed materialstechnology is being developed for utilizing pulverized coalOur previous experimental apparatus (Hong et al., 1996)in an eficient and environmentally acceptable manner. For with only a vertical jet was modified to include an inclinedthis purpose, many problems related to multiphase hydro- jet, as shown in Fig. 1. The thickness of the two-dimensionaldynamics should be resolved. The inclined jet will be used fluidized bed is 25 mm and its width 314 mm. The width ofin the coal gasifier to reduce slag formation on the the central jet tube is 20 mm. In the separating zone, theV-shaped gas distributor. Among all the important hydro- angle between the tube surtace and the vertical direction isdynamic phenomena of the fluidized-bed gasifir, the jet 9 degree. At the bottom of the fuidized bed, there is a 45penetration lengh is the crux (Hong et al, 1996; Hong&L, degree angled dstributor with an aperture density of 1%.1996; Hong & Li, 1997; Hong et al., 2003; Hong et al., 2005;AlBlake et al, 1990; Merry, 1971). While our previous atten-tion was focused on vertical jet (Hong et al, 1996), doublejets (Hong et al, 2003) and downward jet (Hong et al,R|2005), inclined jet penetration will be scrutinized in thepresent investigation since the inclined jet has not been asmuch investigated as the other jets.0Our previous two-luid model (Hong et al, 2003; 2005),which has fewer model parameters, is used here in simu-lating the inclined jet in a gasifier. Because the jet velocityis high, the model equations are solved by the improvedICE (implicit continuum Eulerian) method at instantaneoustime steps. The motions of gas and solids were demon-strated from the simulations. The infuence of jet velocity,Fig. 1 Flow diagram of the 2-D experimental setup. (1 rotameters; 2V-shaped gas distributor; 3 2-D fluidized bed; 4 inclined gas jetnozzle diameter, inclination angle, and nozzle location on! camera; 7 gas com-the inclined jet penetration length was analyzed. Based on中国煤化工numerical simulation, a semi-empirical expression wasderived. The parameters of the expression were obtainedMillet,TYHCNMHGwereusedasfuby correlating experimental data and ilustrated with idization material respectively in the experiments. Theirmeasured data under various conditions.physical properties are shown in Table 1.280CHINA PARTICUOLOGY Vol. 3, No.5, 2005Table 1 Physical properties of bed materialswhere p.=P,ar and Ea=1.MaterialsMiletSilica sand 1# Silica sand 2#Momentum equations for phase k(k=g ors; 1=g or s; 1*k),T。/(mm)1.432.25(,0,)+.(,0.O,)= -&,Vp。+ B(0,-0,)+V.G+p.g.A% /(kgm3)878808817(2p.(kg.m-9)1 0421582The derivation of the two-phase model equations, thU(m-s~).611.78.determination of the model parameters and the solution ofUm/(m-s~)0.520.640.45these equations are given in detail by Hong & Li, (1996). Itwas also found that these equations could be simplified toThe incipient fuidization velocity (Um) in Table 1 was those of Davidson's (Hong et al, 1996). The model equa-obtained from measuring the bed pressure drop (△p) as a tions were solved previously by the improved IPSA methodfunction of fluidization velocity (U) when Op became in- (Hong et al., 1996). A computer program with this modeldependent of U.has been used to calculate the vertical jet penetrationlength (Hong et al, 1996). In the present study, the pro-2.2 Experimental operation rangegram was modified using the improved ICE method toThe central jet velocity (4) should be higher than the simulate the inclined jet penetration in a fluidized bed.particle terminal velocity (U), but not too high to cause3.2 Constitutional equationschanneling in the bed. The gas velocity above the gasdistributor should be high enough to ensure the incipient Gas-phase stress tensorfluidization of particles. The gas flow rate of the central jetand the two V-shaped distributors in the present experi-者。= 2a,4S。,(3ments are given in Table 2.where(4Table 2 Experimental parameters for measuring 4 (Un=1.5 ms-1 ,h0=270 mm)Solid-phase stress tensorParametersMilletSicasand1# Silia sand2#τ=[-P,+e5V U.j+2a,uS,.(5Nozzle diameter/mm 5,7,8,10 5,7,8,10 5, 8, 10Inclination angle10°, 0%, -10Jet position (m)0.043, 0.103, 0.163, 0.223s.-+10.+(0.]-+v0,i，(6Q/m2.h*1)Q2=Q2+Q2/(m.h)10-2412- 2412-24is the unit matrix.Q/(m?.h~")7.9-21.97.4-17.47.9-17.9U/(m-s~)26.2-189.726.2 -218.035.0-196.7Drag constant between the two phasesNo. of frames312288The drag model of Syamlal et al. (1993) was employed,(1-ε)ep。|0。-0[2.3 Experimental measurementρ=zG'V,d,(7To observe the development of the jet clearly andmeasure the jet penetration length accurately, the devel- where C=| 0.63+ 4.8、N Rewas recommended byopment of a jet was recorded with a video camera in theexperiments. Under the same experimental condition, the Dalla Valle (1948) and V, was devised by Garside andjet was recorded five times. The video was then replayed Al-Dibouni (1977).on a TV frame by frame. Thus the jet penetration length3.3 Boundary conditionswas obtained from the five values recorded.For the boundary conditions used in this investigation:3. Two-Fluid Model(1) at the inlet, all the variable are known; (2) at the exit,the flow is assumed to be fully developed; (3) at walls, the3.1 Governing equationsThe equations of the two-fluid model (Hong et al., 1996;gas velocities were taken to be zero, while partial slip wasused for the solids (Ding & Gidaspow, 1990) as shownHong & Li, 1997; Hong et al, 2003; 2005; Ding & Gi-bel中国煤化工daspow, 1990; Gidaspow, 1994)， describing gas-solidmacroscopic flow in fluidized beds, are given as follows:*YYHCNMHG(8Continuity equations for phase K(k=g or s),where 4p is the mean free path of particles (Ding & Gi-apV (p20,)=0,(1)daspow, 1990).atHong, u, Ding& L: A Crrelation Equation for Calculating lnlined Jet Penetration Length281and particles entrainment by the jet due to the high gas3.4 Numerical methodvelocity and the low gas pressuretheeck of the jet.To obtain instantaneous jet penetration details, the ICETherefore, the jet neck is compressed by the entranmentalgorithm (Harlow & Amsden, 1975) is used. The method process, and to some extent, further compression leads toimproves the numerical computation in such a way that,if ththe detachment of the jet from the nozzle. When the gas isU。 aV au。 dV de。and。 are evaluatedfirst introduced through the nozzle, there is no jet, and thefirst process predominates, leading to the formation ofa jet.dp’ap’ap' p’papfrom the unconverged solutin, then the pressure correC-At this instant, the gas velocity at the base of the jetis verylarge, the second process predominates, and the jet be-tion (p) iscomes unstable and detaches. Therefore, the jet emergese, e,near the nozzle and detaches from the nozzle, altema-p'=-P。 P。(9)tively.de, de,4.3 Factors affecting inclined jet penetrationdp. dplength (4)PP。4.3.1 Influence of jet velocity (V)The crrection for U2. Vg, U% and Vs can be obtained to0.Hong et al. (1996) found that the vertical jet penetrationDetais about the numerical algorthm and solution proce- length (4) increased with increasing jet velocity (V) until itdure can be found in reference (Harlow & Amsden, 1975).reached a plateau at high jet vlocity For the iclined jet, itNumerical computations were conducted using a DECwas found by numerical simulation that the jet velocityis aAlpha workstation, and the numerical results in this inves- major factor in determining the inclined jet penetrationtigation were post- processed using the Tecplot (version 7.5)length, which increases obviously with increasing jet ve-(Amtec Engineering Inc., 1999) on a personal computer.locity even at relatively high jet velocity (Fig. 3).4. Results and Discussion4.1 Definition of jet penetration length (4)The inclined jet penetration lengh (4) is defined as themaximum length from the farthest point of the jet to the jetnozzle when the jet is detached from the nozzle (Hong etal, 1996) (see Fig. 2). In the numerical computation, thefirst-order upwind diference scheme is used in discretizingthe solid continuity equation to obtain the solid volume10fraction. The voidage of the jet surface is defined as theJet vlocity /(m.s~7)voidage value of 0.8 (Hong et al, 1996), which is consis-Fig.3Influence of jet velocity (N) on dimensionless jet penetrationtent with Yang's definition (Yang & Keaims, 1980).length (4d); bed material, mllt.ell4.3.2 Influence of jet diameter (d)Flee boardIt is found from numerical simulation that the inclined jetDease phaspenetration length (4q) can be increased (Fig.4) by e-ducing the cross -sectional area of the nozzle when the flowrate of the jet is fixed at Q3=15m.h~'. This is due to theincrease of the jet velocity (V9), leading to increase of jetNozzlemomentum of unit cross section area (A: Vi).ITAxisFluidizing AirFig.2 Askelch of horizontal jet penetration length (4).4.2 The mechanism of the jet中国煤化工、It is found by numerical simulation that there are twoprocesses taking place above the nozzle. One is theMHCNMHG-。1movement of particles under the drag force exerted by theNozle diameter d/mmgas of high velocity This movement will result in aFig.4 Inftuence of jet diameter (4) on dimensionless jet penetationtorch-ike vacant space due to the jet. The other is the gaslength (4d) ; bed material, mllt282CHINA PARTICUOLOGY Vol. 3, No.5, 2005When the inclined jet velocity (V) is maintained at the periments showed that, placing the jet nozzle at the heightsame value, by enlarging the nozzle diameter, the inclinedof 0.2h, 0.4ho, 0.6h, and 0.8ho above the bed bottom re-penetration length (4) is also increased.sulted in ltte difference in jet length, as can be seen in4.3.3 Influence of jet inclination angle (3)Fig. 7.To the author's knowledge, no researchers studied theinfluence of jet inclination angle (2) on jet penetrationlength (4). The present study showed that jet inclinationangle has definite influence on jet penetration, as shown inFigs. 5 and 6. In particular, when other conditions maintain了the same, horizontal jet penetration length is less than that。ffor vertical jet for jet velocities in the range, as shown inFig. 5.Dimensionless height hhoFig. 7 Influence of horizontal jet position (h) on jet penetration length享“(L/G) (O: V=102.8m.s~'; 0: V=161.4 m.s~I)4.4 Derivation of a correlation equationA semi-empirical expression for calculating the inclinedjet penetration length (4) is derived in this section, to ac-count for the infuence on inclined jet penetration length (4)Jet velocity V/(ms~I)by jet velocity (V), nozzle diameter (d), jet inclination angleFig.5 Infuence of jet angle (a) on dimensionless jet penetration(2) and jet position (h).length (4d) (s: -10°; o: horizontal;●: +10%) with upward in.Consider a horizontal gas jet penetrating into a station-clining as position.ary medium, as shown in Fig. 8. The horizontal gas velocity(V of a given cross-section can be expressed as (Merry,1971):平.1.0-点,(10)where Vm is the velocity on the jet axis and 5 =x/b , whereb is the cross-sectional radius of the jet.Boundary of间rogion .V/(m-s~)Fig. 6 Comparison of vertical with horizontal jet penetration length(o: horizontal; 0: vertcal).Evidently the jet is pushed upward by the fluidizing gasas well as by buoyancy, as shown in Fig. 2. The force act-Fig. 8 Ahorizontal gas jet penetrating into a fluidized bed.ing on the jet is in the same direction for the vertical jet,thus elongating the jet. At higher jet velocity, the vertical jetpenetration length (4) increases slowly with jet velocity (V)The fllowing equation can be obtained by using mo-(Hong et al, 1996), while for horizontal jet, its penetrationmentum balance:length increases more notably with jet velocity. In Yang'spdV= pbBV,(11)correlation equation (Yang & Keairns, 1980), the vertical jetwhere P and V are respectively the mean density andpenetration length (4) is directly proportional to themean velocity of the cross section. In turbulent flow, the0.374-power of jet velocity (V), while in Merry's correlationequation, the inclined jet penetration length (4) to the rel中国煤化Iermy, 1971)0.80-power of jet velocity (V).TYHCNMHG(12)4.3.4 Influence of jet position (h)/mHong et al. (1996) found that bed depth had ltte infu-ence on vertical jet penetration length.' The present ex- Combination of Eqs. (10), (11) and (12) yieldsHong, Li, Ding & Li: A Correlation Equation for Calculating Inclined Jet Penetration Length283BV21_ d,travels until the relatve velocity (Vg-V,) flls to 1/e of its(13)VAV~ Ay+y(10个“initial value, then h can be calculated aswhere A= 0.26tanθ = 0.26b/(y+y), y being the distance1=22Pd(24)from the nozzle to the cross-section.Assume constant density of the gas, and the aboveAs a matter of fact, n characterizes the momentum trans-equation can be rewritten asfer between the gas and the particle phase (Merry, 1971). .(14)Taking account of this momentum transfer, Eq. (22) shouldA步y+y((10号be multiplied by (21L)*.The entrainment velocity (Vo) at the boundary layer canConsidering the infuences of the nozzle inclination an-be expressed as (Merry, 1971)gle (a) and the nozzle position (川) on the inclined jet pene-tration length (4), and assuming the jet half angle constant,必品(1.0-(15)Eq. (22) is modified to be_PVPWhen 5=0， y+y=4, and the inclined jet penetration[(号(=叮(%]呵length (4) can be given as4114.5 Correlating the experimental data(16)dAV。By inserting experimental data into the parameters ofSimilar to gas penetrating into a stationary medium,Eq. (25), it can be expressed as the fllowing empiricalwhen gas penetrates into a fluidized bed, the penetrationexpression for jet penetration:length may be expressed as (Merry, 1971)5+3.80=4_1「_ ρV_乍(17)d“A(1-e)p。VE1.64x10*1l (1-)p.gd,..0”(影)”()("[()广where V is velocity at the jet boundary. When V is fixed,the inclined jet penetration length can then be calculated.In a fluidized bed, there are two forces exerting on theComparison of above equation with experimental data isilustrated in Fig. 9, showing a maximum diference of lessparticle phase: drag force exerted by the horizontal jet:than 25%.(18)and gravitational force:5tF=RGpg.(19)For a particle at the boundary of the jet (Merry, 1971),tanφ=5_ 4 p.gd.(20)20↑F。~ 3p。GVETherefore, the gas velocity at the jet boundary, V%, is de-termined as6, =p。9d(21)4d1 pedictledby Eq. (26)3C。tanp P。,Substitution of Eq. (21) into Eq. (17) yieldsFig. 9 Comparison of experimental data for jet penetration length withEq. (26).「3C。tanp.pBp。下(22)dl 4A2 (1-e)P.gd。 P._4.6 Comparison of simulated data with ex-For a spherical particle with diameter (d6) at high Rey-per中国煤化工。nolds number flow, the equation for steady motion of theFor milE0 mm, h=0.223 m,particle is assumed to beand a=1:TYHC N M H Gtration length pre-(23)dicted by numerical simulation with experimental meas-urements is shown in Fig. 10. The two curves are veryIf名is defined as the distance through which the particleclose.284CHINA PARTICUOLOGY Vol. 3, No.5, 2005based on a two-fluid model. The predicted results are1sin accordance with the experimental data.(3) A semi-empirical expression was obtained to deter-mine the inclined jet penetration length. The equationis in good agreement with experimental data.AcknowledgmentThe project was supported by the National Natural Science00 110 120Foundation of China (NNSFC, No. 20476065), the Scientific Re-search Foundation for Returned Overseas Chinese Scholars ofJet velocity V/(m.s~)State Education Ministry (SRF for ROCS, SEM) and theig. 10 Comparison of simulated results with experimental dataMulti-Phase Reaction Laboratory of the Chinese Academy of(O: Experimental; o: Numerical).Sciences (No. 2003-5).4.7 Comparison with Merry's correlationSubstuting the experimental conditions of jet velocity,Nomenclaturenozzle diameter and particle diameter, etc. into Eq. (26) agas or sld volume fractionand Mery's crrelation equation (Blake et al, 1990) re- dbubble size, mnozzle diameter, mspectively, the horizontal jet penetration lengths at variousparticle diameter, mconditions can be obtained, as shown in Fig. 11. Comparedbed width, mto Fig. 9, which compares Eq. (26) with measured data, iterror of gas or solid phase continuity equation,can be concluded that our empirical equation yields better eg.skg-m"3.s"'agreement with experimental data than Merry's. The ad- sgravitational acceleration, m.s2vantage of our correlation is that it can be used for either Hthe fluidized bed height, mhorizontal or inclined jets.jet position, mturbulent fluctuation kinetic energy, m?.m2jet penetration length, m35gas axial momentum, kgm"s?temperature, Kgas phase pressure, P、25solids phase pressure, Papressure correction, Pa是20gas flow rate of separation column, m'.s-1Qgas flow rate of V- shaped gas distributor, m'.s-'10gas flow rate of inclined jet, m'.s~Rayparticle Reynolds numbertime, s5 10152025303540Sdeformation rate tensor, s-'yd predicted by Eq (26)bubble ascending velocity, m-s~'Ucentral jet velocity, ms~Fig. 11 Comparison of Merny's correlation for horizontal jet penetra-=(U% VI), velocity vector of phase k, mstion length with Eq. (26).superficial gas velocity in bed, ms~'Unincipient fluidization velocity, ms~'5. Conclusionsinclined jet velocity, ms"bed superficial gas velocity, m.s-'The fllowing conclusions can be drawn from the pre- Vmaximum gas velocity of cross-section as defined insent investigations:Fig. 6, ms~"'(1) From numerical simulations for inclined jets in a 2-Dlength defined in Fig. 6, mfluidized bed using a two-fluid model, it was found thatGreek lettersthe inclined jet penetration length (4) was affected byjet inclination anglegas density (P。), bed structure (), particle properties(P, d), jet characeristics (p, U), jet diameter (d) e中国煤化工kinetic energy, m2 m~3kgm-.s"'and jet inclination angle (a), and lttle by jet positionHog, IMYHCN M H Gsity, kgm's"μsgas viscosity, kg-m^ 's'gas density, kg.m~(2) The inclined jet penetration lengths (4) under varioussolids density, kg.m-3conditions were obtained from numerical simulations 1Hong, Li, Ding & Li: A Correlation Equation for Calculating Inclined Jet Penetration Length285Agas density at nozzle, kg-m~3reltionship for fluidization and sedimentation. 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London: Pitman.gas entrainment into a gas- solid two-phase jet in a fluidizedDing, J. & Gidaspow, D. (1990). A bubbling fluidization modelbed. In Grace, J. R. & Matsen, J. M. (Eds.), Fluidization (p.305).using kinetic theory of granular flow. AIChE J, 36(4), 523- -538.New York: Plenum Press.Garside, J. & Al-Dibouni, M. R. (1977). Velocity-voidageManuscript received November 19, 2004 and acceptod May 19, 2005.中国煤化工MYHCNMHG