Physical and chemical processes in shaft furnaces proceeds in counter – current system. Reacting gas carrying powders flows up in packed bed of descending metallurgical materials. In this system the problem of bed particles hanging up appears. That is why the author undertook the investigations of gas – powder flow in descending bed. Physical model with glass bed and glass powders was constructed. The experiments were carried out and the influences of gas velocity, type and size of powders, type and size of bed particles and powder concentration in gas were established. The conditions, in which bed hanging up appears were defined. Mathematical model of two phase (gas + powder) flow in moving bed was developed.Fizikalni i kemijski procesi u metalurškim pećima odvijaju se po protustrujnom sustavu. Reakcijski plin koji prenosi prašak utječe u “packed bed” opadajućeg metalurškog materijala. Kod ovog sustava javlja se problem zaostajanja čestica u sloju. Zbog toga je autor proveo istraživanje protoka plin-prašak u opadajućem sloju. Izrađen je fizički model sa staklemim slojem i staklenim praškom. Provedeni su eksperimenti i određeni su utjecaj brzine plina, tipa i veličine praška, tipa i veličine čestica sloja (bed particles) i koncentracije praška u plinu. Definirani su uvjeti u kojima se javlja zaostajanje u sloju. Razvijen je matematički model toka dvije faze (plin+prašak) u “moving bed”

B. Panic

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B. PANICPHYSICAL AND MATHEMATICAL MODELINGOF PHENOMENA PROCEEDING WITH GAS– POWDER TWO PHASE FLOW THROUGH MOVINGPACKED BED IN METALLURGICAL SHAFT FURNACESReceived – Prispjelo: 2010-06-21Accepted – Prihva}eno: 2010-11-30Preliminary Note – Prethodno priop}enjeINTRODUCTIONA lot of metallurgical processes take places in shaftfurnaces, where reacting gas carrying powders flows upin packed bed of descending metallurgical materials.Gas + powder two phase flow in fixed packed bed hasbeen investigated by author for many years 1. At pres-ent author undertakes the investigations with movingbed. Physical model with glass bed and glass powderswas constructed. The experiments were carried out andthe influences of gas velocity, type and size of powders,type and size of bed particles and powder concentrationin gas were established. The conditions, in which bedhanging up appears were defined.EXPERIMENTAL INSTALLATIONAND PROCEDUREPhysical model has been constructed to find princi-pal dependences for gas + powder flow in moving bed asa basis for mathematical model. Experimental columnmade of plexi has inner diameter of 114 mm and heightof 400 mm. Moving down of the bed particles is gener-ated by the extraction of particles at the bottom, usingscrew feeder. The gas–air feeds an installation with con-stant volume rate of flow, checked by rotameter. Pres-sure drops along the column are measured by using ofdifferential manometer system. The powder transportedby gas is injected into the lower part of packed bed. Thefeed rate of powder is controlled by screw feeder, dosingthe powder to gas. Gas with powder leaves the column atthe top, flowing to the cyclone.The hold up of powder in bed and gas pressure dropwere measured as a results of experiments. Powder holdup in bed was defined stopping powder feed and bedmoving. Powder leaves the bed and it is measured in cy-clone. Schematic diagram of model installation and thetable containing gas flow conditions, bed rates andphysical properties of materials used in model were pre-sented earlier 2. Similarity of author installation condi-tions with conditions in blast furnace shaft and reductionshaft of Corex were showed.As materials for bed particles, glass spheres (8 and10 mm), alumina spheres (7 mm), blast furnace pelletsMETALURGIJA 50 (2011) 3, 183-187 183Physical and chemical processes in shaft furnaces proceeds in counter – current system. Reacting gas carryingpowders flows up in packed bed of descending metallurgical materials. In this system the problem of bed parti-cles hanging up appears. That is why the author undertook the investigations of gas – powder flow in descen-ding bed. Physical model with glass bed and glass powders was constructed. The experiments were carried outand the influences of gas velocity, type and size of powders, type and size of bed particles and powder concen-tration in gas were established. The conditions, in which bed hanging up appears were defined. Mathematicalmodel of two phase (gas + powder) flow in moving bed was developed.Key words: modeling, blast furnace, gas – powder flow, powder hold upFizikalno i matemati~ko modeliranje fenomena procedure s dvofaznim tokom plin-pra{ak krozpokretni “packed bed” u metalur{kim pe}ima. Fizikalni i kemijski procesi u metalur{kim pe}ima odvijajuse po protustrujnom sustavu. Reakcijski plin koji prenosi pra{ak utje~e u “packed bed” opadaju}eg metalur{kogmaterijala. Kod ovog sustava javlja se problem zaostajanja ~estica u sloju. Zbog toga je autor proveo istra`ivan-je protoka plin-pra{ak u opadaju}em sloju. Izra|en je fizi~ki model sa staklemim slojem i staklenim pra{kom.Provedeni su eksperimenti i odre|eni su utjecaj brzine plina, tipa i veli~ine pra{ka, tipa i veli~ine ~estica sloja(bed particles) i koncentracije pra{ka u plinu. Definirani su uvjeti u kojima se javlja zaostajanje u sloju. Razvijenje matemati~ki model toka dvije faze (plin+pra{ak) u “moving bed”.Klju~ne rije~i: modeliranje, metalur{ka pe}, tok plin-pra{ak, zadr`avanje pra{kaISSN 0543-5846METABK 50(3) 183-187 (2011)UDC – UDK 62.001.57:669.041:669.162.2:544.4:621.762=111B. Panic, Department of Metallurgy, Silesian University of Technology,Katowice, Poland(10 mm) were used. Powders were of glass (110-130µm, 90-110 µm), and iron sinters (90-130 µm).RESULTSThe influences of powder concentration in gas, bedparticle size, powder particle size on hold ups of powderand gas pressure drop in moving packed bed were de-fined and described earlier 2, 3. In this paper the influ-ence of bed type and powder hold ups in bed (Figure 1)and gas pressure drops in moving packed bed (Figure 2)are presented.The results were the basis for mathematical model oftwo phase (gas +powder) flow in moving packed bed de-veloped by author.MATHEMATICAL MODELThe results 2,3 were the basis for mathematicalmodel of two phase (gas +powder) flow in movingpacked bed developed by author. In the experiment itwas observed that the total powder is the sum of staticpowder (powder particles settled on the packed parti-cles) and the dynamic powder (powder particles movingin the packed bed void). Hence it appears that:g+pd+z+ps=1, (1),Vs=(z+ps)Vk , (2).The fundamental equations of continuity and mo-mentum for gas, powder and bed are presented below.Gas phaseContinuity equation:d U dxg g g( ) /’  0, (3).Momentum equation:d U U dx d p dx F Fg g g g g g z g p( ) / ( ) / ( )’ ’         (4).Powder phaseContinuity equation:d U dx Rs Rdpd p p( ) /’   , (5).Momentum equation:d U U dx F Fpd p p p g p p z( ) /’ ’       , (6).Packed bed phaseContinuity equation:d U dx Rd Rsz ps zps z(( ) ) /’    , (7).Momentum equation:d U U dx F F Fz ps zps z z g z p z z z(( ) ) /’ ’           ,(8).where z=1-0 (9);p=ps+pd (10).The drag caused by the forces interacting betweengas and pieces of the bed surrounded by the static pow-der is described, similar to the papers 1,4,5, by themodified Ergun equation:FdUUg zz pspd g e eggz( ) (	 	1502    	 175,     gz pspd g e eggzdUU	 UUggz(11),whered de zz psz 3 (12).The drag caused by the forces interacting betweengas and dynamic powder particles was formulated bas-ing on the Darcy-Weisbach’s equations, where the over-all drag force is the sum of drag forces of single particles(conception similar to 1, 4-8)F CdUUUUg p mg pdp pggpdggpd( )   	34   (13)where Cm is the modified drag coefficient of powdercaused by the gas-powder interaction. It is usually as-sumed 1, 4, 8, 9 that Cm can be expressed in terms ofdrag coefficient for a single particle CdC F Cm g d 0 ( ) (14);F g g04 65( ) ( ) ,   (15),where F0(g) is Richardson – Zaki’s voidage function10.184 METALURGIJA 50 (2011) 3, 183-187B. PANIC: PHYSICAL AND MATHEMATICAL MODELING OF PHENOMENA PROCEEDING WITH GAS...Figure 1 The influence of bed and powder type on pow-der hold ups in bed.Figure 2 The influence of bed and powder type on gaspressure drops in moving packed bed.The drag coefficient Cd is function of Reynold’snumber and it is formulated by. Stokes, Allen and New-ton 11:Cdp24 0,Rewhen Re ,p  0 4 (16),Cd p p 24 0 10 1150 69, ( , , Re ) / Re( , )when 0 4 103, Re p (17),Cd  0 44, when Re p 103 (18),where Rep is expressed with consideration of „slip”:Re pp p g ggggpdd UU 	   (19).The drag Fp-z, caused by the interaction forces be-tween dynamic powder particles and bed particles sur-rounded by static powder can be formulated on basis ofthe gravity force of spherical particles in fluid and theFanning’s equation   F FU U U Udp z pd p kpd z pd zh( )( )   2(20),whereFFfkgprkk		212(21).The coefficient Fk includes the Froude’s number:FU Ud grpd zh( ) (22).The drag caused by the interaction forces betweenmoving bed particles surrounded by static powder wasdescribed by equation F Uz z z ps zz z   ( )  2 (23).The expression zz2Uz considers friction forces be-tween bed particles as for fluid particles.Developed model assumes that the powder and gasvelocity is constant in the longitudinal direction, equa-tions (3) to (4) can be transformed as follows: F d p dx Fg p g g z  ( ( )) / (24).The procedure of calculating values of the ps and pdindicators, coefficient Fk and Froude’s number was be-gun by introducing of experimentally obtained values ofthe p indicator into equation (10) and pressure loss intoequation (24). Relations between indicators ps and pd,and coefficient Fk for different model system are ex-pressed by equations (25)(26)(27)(28). For model sys-tem – bed of glass spheres or high alumina spheres +glass powders:ps=25 808pd2+40,689pd +0,0011 (25),Fk = -2,4565ln(Fr) + 14,009 (26);For model system – bed of high alumina spheres orblast furnace pellets + iron sinter powders:ps=-25 006pd2+56,558pd +0,002 (27).Fk=15,12(Fr-0,13 )exp (-0,01Fr) (28).Figures 3 and 4 show relations ps=f(pd) andFk=f(Fr). For explanation of the most frequently usedsymbols, see List of symbols.METALURGIJA 50 (2011) 3, 183-187 185B. PANIC: PHYSICAL AND MATHEMATICAL MODELING OF PHENOMENA PROCEEDING WITH GAS...Figure 3 Relations between indicators ps and pdTable 1 List of frequently used marksdz / m 0 - dp / m p - G / kg/m2s 0,01 0,38 110-130 0,88 0,45 0,01 0,38 110-130 0,88 0,35 0,01 0,38 90-110 0,82 0,45• 0,008 0,36 110-130 0,88 0,45 0,007 0,36 110-130 0,88 0,45 0,007 0,36 90-130 0,76 0,45 0,01 0,39 90-130 0,76 0,45 bed: glass spheres, powder: glass • bed: high alumina spheres, powder: glass bed: high alumina spheres, powder: iron sinter dust bed: blast furnace pellets, powder: iron sinter dustFigure 4 Relations between Froude number and additio-nal pressure loss coefficientDISCUSSION OF EXPERIMENTALAND MODEL RESULTSExchanging the bed of glass spheres for the bed ofalumina spheres, considerable increase of powder holdup and gas pressure drop in moving packed bed were no-ticed. Surface properties of bed particles changed andbetter conditions for powder hold up occurred. True gasvelocity in bed increased because of void friction de-crease. The exchange glass powder for sinter powdercaused change of powder particle shapes. Increase ofpowder hold up and gas pressure drop in moving bedwere observed. Comparing the system “alumina particlebed – sinter powder” and “blast furnace pellet bed –sinter powder”, it was noted that surface properties ofbed particles as well as void friction of bed changed. Thevoid friction was 0,36 for alumina bed and 0,39 for blastfurnace pellet bed. That is why in blast furnace pelletbed in which void friction is higher, powder hold up in-creases but gas pressure drop decreases. For investi-gated system- packed bed of coke + blast furnace pow-der, at maximal applied gas velocities and feed rate ofpowder 0,45 kg/m2s bed hanging up appeared.The mathematical model was developed. For eachexperimental point, using the mathematical model, thepressure loss and powder hold up were calculated. Cal-culated values are not different than measured onesmore than 20 % (Figure 5 and Figure 6).CONCLUSION1. Developed model allows satisfactory evaluatepressure loss of gas with powder flow and powder holdup in descending bed. The steady flow perturbation ofgas + powder two phase flow in moving bed is possibleto predict.2. It was stated, that the hanging hazard of descend-ing appears when the powder concentration in gas andgas velocity increase. The conditions of hanging can bedefined with the ratio of bed material column pressureon experimental column cross-section to gas phase pres-sure at the level of gas with powder injection. When thisratio is more than 1, the bed hanging appears.3. In further investigations the influence of gas veloc-ity, type and concentration of powder in gas, size andshape of powder particles on hold ups of powder and gaspressure drop in packed bed as a function of experimentalradius and with participation of liquid phase will be de-fined.LIST OF SYMBOLSCdCmdedhdpdzfkkF0(gFg-pFg-zFp-zFz-zFkFrGLpRepRddrag coefficient of a single particlemodified drag coefficient of powders due togas in packed bedequivalent diameter for packed bed particlesand static powderhydraulic diameterpowder diameterdiameter of a packed particleinteraction coefficient between powders andpacked particlesRichardson- Zaki’s functioninteraction force between gas and pieces ofdynamic powderinteraction force between gas and pieces ofbed surrounded by staticpowder interaction force between dynamicpowder particles and bed particles surroun-ded by static powderinteraction force between bed particlesadditional pressure loss coefficientFroude numberpowder feed ratelength of packed column under considerationpressureReynolds numberdetaching rate of powder from particle surfa-ce--mmmm--N/m3N/m3N/m3N/m3--kg/m2smPa-kg/m3s186 METALURGIJA 50 (2011) 3, 183-187B. PANIC: PHYSICAL AND MATHEMATICAL MODELING OF PHENOMENA PROCEEDING WITH GAS...Figure 5 Comparison of experimental data with calculatedvalues for powder hold up.Figure 6 Comparison of experimental data with calculatedvalues for pressure loss.RsUgUpUpdUzp0pgpdzpsepgzzgpzsticking rate of powder to particle surfacesuperficial gas velocitypowder velocitydynamic powder velocitybed particles velocitypressure differencevoid fraction in packed bedvolume fraction of total (dynamic and sta-tic) hold up of powdersvolume fraction of gasvolume fraction of the dynamic hold up ofpowdersvolume fraction of bedvolume fraction of the static hold up ofpowdersshape factor of equivalent bed piecesshape factor of a powderviscosity of gascoefficient of friction between bed particlesdensity of gasdensity of a powderdensity of packed bedkg/m3sm/sm/sm/sm/sPa--------Pa sPa skg/m3kg/m3kg/m3REFERENCES1 B. Panic, L. Król, J. Dankmeyer-£¹czny: Steel Research,(2000) 8, 271-276.2 B. Panic, J. Dankmeyer-£¹czny: Hutnik – WiadomoœciHutnicze, (2006) 5, 201-204.3 B. Panic, J. Dankmeyer-£¹czny: Hutnik – WiadomoœciHutnicze, (2007) 5, 236-238.4 J. Chen, T. Akiyama, H. Nogami, J-I. Yagi: ISIJ Internatio-nal, 34 (1994) 2, 133-139.5 X.F. Dong, S.J. Zhang, D. Pinson, A.B. Yu, P. Zulli: Pow-der Technology, 149 (2004), 10-22.6 H. Yamaoka: ISIJ International, 31 (1991), 939-949.7 T.S. Pham, D. Pinson, A.B. Yu, P. Zulli: Chemical Enginee-ring Science, 54 (1999), 5339-5345.8 J.-I. Yagi: ISIJ International, 33 (1993) 619-639.9 K. Shibata, M. Shimizu, S. Inaba, R. Takahaski, J. Yagi:ISIJ International, 31 (1991), 434-439.10 J.F. Richardson, W.N. Zaki: Trans. Inst.Chem.Eng., 32(1954), 35-53.11 L. Schiller, A. Neumann: Zeits. Ver. Deut. Ing., (1933), 318.Note: The responsible translator for English language is the lecturer fromSilesian University of Technology Katowice, Poland.METALURGIJA 50 (2011) 3, 183-187 187B. PANIC: PHYSICAL AND MATHEMATICAL MODELING OF PHENOMENA PROCEEDING WITH GAS...

Fizikalno i matematičko modeliranje fenomena procedure s dvofaznim tokom plin-prašak kroz pokretni “packed bed” u metalurškim pećima

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