Experimental and mathematical modeling of metal spray forming process

Baosteel Technical ResearchVolume 5 ,Number 3，September 2011 ,Page 9Experimental and mathematical modeling of metal spray forming processZHANG Yin':2) , FAN Junfei") and REN Sanbin?)1) Inner Mongolia Key Laboratory for Uilization of Bayan Obo Multi-Metallic Resources , Inner Mongolia University ofScience and Technology, Baotou 014010, Inner Mongolia, China;2) School of Rare Earth, Inner Mongolia University of Science and Technology, Baotou 014010, Inner Mongolia, China3) Advanced Technology Division, Research Instiute, Baoshan lron & Steel Co, Ltd, Shanghai 201900, ChinaAbstract: The metal spray forming process was examined using mathematical simulation and verified through theprototyping evaluation at Baosteel ' s test and development facilities. The mathematical model comprised of four sections ,including jet gas flow in the deposition chamber ;single droplet behavior along its trajectory path ;probability and statisticalanalysis of droplet mass behavior , and forecast of the shape and temperature distribution of the billet during the sprayforming process.Key words: spray forming; droplets; simulation; statistical method; billetdoi: 10. 3969/j. issn. 1674 - 3458.2011.03.002degrees. The substrate and the delivery tube could beadjusted to move upward or downward. The distance to1 Introductionthe substrate varied from 320 mm to 400 mm.The metal spray forming technology is used forcomposite materials and surface engineering. Itgeneral, the process is based on the inert gasatomization of a liquid metal stream into various sizeddroplets which are propelled away from the regionatomized by the jets gas. The droplet trajectories areinterrupted by the substrate which collects andsolidifies the droplets into a coherent and fully densebillet.The spray forming process is very complicated. Itwas divided into four sections to simulate the process.四The four sections included the jets gas flow in thedeposition chamber, the trajectory and temperature(a) Front view(b) Side viewchange in one droplet along its trajectory path,Fig. 1 Scheme of the spray forming of Baosteelstatistically analysis and forecast of mass droplets ofdifferent sizes ,location and initial velocity deposited on2.2 The velocity distribution in the chamberthe substrate, and forming of the billet' s shape. TheThe numerical simulation software that was developedoverall temperature distribution in the billet was alsoat Baosteel makes forecasts of the velocity distribution ascalculated with time1s5.illustrated in Fig. 2. The gas flow without the substrateresults in a typical jet flow pattem where the momentum2 Mathematical modeling of the jet gas flowof gas decreases sharply in the very beginning, as theambient gas is mixed into the jet. A comparison of theThe jets gas flow can be simply described by thevelocity distribution along the center line between thegoverming equations for three-dimensional compressibleexperiment results measured by the Pitot tube and thegas flow which include the continuity , the momentum,theoretical prediction are in good agreement as shown inthe turbulent viscosity of k-E two-model equations andFig. 2( b). In comparison,Fig. 3 provides the gas velocitythe ideal gas state equation.distribution with the substrate in different sections of thechamber. The substrate divided the flow current into two2.1 The schematic of the prototyping experimentbig recycle zones. The upward recycle zone is the mainconducted at Baosteelreason for the bonding of the fine droplets which couldThe spray forming chamber was conjoined by twoblock中国煤化工been observed. Thecylinders (Fig. 1). The jet nozzle restrictions were I mmgas flfrfluences the shapein diameter with 18 jet nozzles located evenly around theof theHCNMHGeafetstheyieldmetal delivery tube. The angle of the jets was set at 45rate of the metal. .Corresponding author: ZHANG Yin; E mail: zhangyin, 69@ 163. com10Baosteel Technical Research, Vol. 5, No.3, Sep. 2011Y(3)=0.10210 m/sSimulation resultl250-1- Experimental resultE200: 15100500.0.60.8(a) Velocity distribution in the chamber(b) Comparison of the detected andwith no deposition systemcalculated velocity in the axisFig.2 Velocity distribution in the 5 kg spray forming equipmentThe size distribution was determined by the Rozin-3 The trajectory and temperature change inRammler empirical equation.one droplet(2) The trajectory of the droplets was determined byeither the gravity force or the drag force only.3.1 Modeling assumptions(3) The temperature distribution in radius was(1) The droplet formed by the jets was a spheroid.neglected.事二t lE中国煤化工FYHCNMHG1---一一「ZHANG Yin, et al. Experimental and mathematical modeling of metal spray forming process11学Fig.3 Gas velocity distribution in difTerent planes3.2 Mathematical modelwhere ur。 and σ, are the expected value and the(1) Size distribution:variance of radius velocity distribution ,respectively.Circumferential even distribution:(1)u。=0R(d) = 0(/门]where R (dk) stands for the percentage of particles(4) Droplets move along the z direction:dwdnwith radius larger than dh occupying the whole particle'dr2“drgroup. Here n and d' are the experimental constants.(2) Position distribution function: .gpwQu c:C.(w)(6)Assume the liquid droplets are created in the samehorizontal plane.where Au= /(u-u) +(v-v])*+(w-w.)rAxis direction:(5) Temperature change and solidifcation model inz =Zoa droplet with the lumped heat capacity method:where z is the height of the created liquid droplets.d7Radial direction:pC"Vk =a(Tg -T)A. +F(r) = λe~"(2)where λ is the parameter describing the congregatingσse(ζ -T)A +pH,°πV. (7)degree of the created liquid droplets.Circumferential direction:where V="&,A =d,a= NF(0) =-(3)N。=2.0+0.6R时，二=一+-1(3) Initial velocity distribution:Solidification rate f;:F(u2) =一exp -(u-un)2(4)p0T>T2o;f, ={f(T) Ts≤T≤π (8)where un and σ: are the expected value and theTRdroplets within the whole particle group. The particleTake random value ηsize from 30 μm to 150 μm represents such mainη=A(1-e~*),thenξ=-→n(1-2,一=-,fractions that the percentage of particles with too largesize or too fine size is very small. About 2.5% of theRRRtotal particles have a diameter of 30 μm. The paricles2A'3'3A”smaller than 30 μm are the dust created in the sprayforming process.3.3 Results1.0The droplet moves under either the force of thegravity or that of the drag. In Fig. 4, the curves which.8-represent the velocities of the gas and the droplets withdifferent sizes have an intersection point. That means0.6 tthe droplet is accelerated by the jets gas in thebeginning. After both the velocities of the gas and thedroplet become equal , the velocity of the droplet isdecreased with the drag force being dominant.0.2-6005000.0.2 0.0.4 0.Pellet diamneter 1 mm心400- OasFig.5 The size distribution of atomizing droplets2.5 [/200 .304m2.010300 um0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Flight distance /m.1.0Fig.4 Velocity of gas and droplets4 Statistical model of liquid droplets andtheir massIt is necessary to leam the deposition velocity of中国煤化工04 0.5atomized droplets in order to model and adjust theshape of the billet. The mass of liquid dropletsDYH. CNMH Gmes ofr dple ;depositing on the substrate has a great influence on theshape and temperature distribution of the billet. In this4.3 The position distribution of dropletsstudy. ,a statistical model for droplet mass was used toBased on the function which provides the positionZHANG Yin, et aL. Experimental and mathematical modeling of metal spray forming process13distribution of the droplets ，one can determine the dataconvenience purposes, the assumption was adopted ofand spread of droplets created in different locations. Itmean thickness and mean temperature of the layeris assumed that the droplets are created in the samedeposited on the billet.plane and evenly distributed over the circumference,The mean thickness H, deposited by the droplets inbut vary in the radial direction. In Fig. 7 ,the amount of0.03 second interval can be calculated by the followingthe droplets created in one radius occupies the wholeequation.number of droplets. The majority of the droplets are2 (dP(d))created at the center and the droplet fraction decreasesH。=(9)as the radius increases. When the radius is larger than2 p(a)2.0 mm, the fraction is lower than0. 1%.The mean temperature T, of the layer deposited in0. 03 second interval is:0.9E [T(d)dP(d)]T。=(10)0.8[dP(d)]g 0.7直0.64.5 The motion course of droplets巨0.5The initial conditions of droplets are generated三0.4randomly. However, the motion and temperature喜0.3change are determined by Newton's laws of motion0.2-( Equation (7 )) and Fourier' s heat transfer law( Equation (8)). In Fig. 9, it can be found the0~ 0.5 1015 2.02.5 3.03.54.04.5 5.0tendency of motion and course of the droplets underNozzle radius 1 mmdifferent conditions is the same. The traces of fineparticles are curved , with even some flow returming asFig.7 Amount of droplets created in one radius occupiedoccurred near the top of the chamber. This explains4.4 The initial velocity distribution of dropletswhy the delivery tube sometimes is blocked. TheThe mean initial velocity ditribution can be definedparticles of a diameter less than 3 μm are easy to returnin Fig. 8. For droplets of different sizes , the initialto the delivery tube. The groups of other sizes do notvelocity of the droplets varies as an inverse ratio to itsdemonstrate this backflow phenomenon and thediameter, because the momentum given to different-particles with a size larger than I5 μm do not appear tosized particles by the jets is the same. That means theexhibit any curvature on the trace. The large particlesinitial velocity of big particles is lower than that ofmaintain the motion of a straight line. The particleswith a size less than 6 μm flow always exhibitsmaller ones.curvature, whereas the particles with a size between9 μm and 12 μum show the bending phenomenon only0.40 rin some traces. This highlights the importance of being0.35able to control or limit the production of very fineparticles ( <3 μm) in the atomization region.0.300.255 Conclusions0.20 t(1) The gas in the atomizing chamber can be号0.15-represented by a compressible flow characteristic. Thehigh-speed gas sprays into the chamber from some0.10 tdefinite angles , converges at the focal point, and thenextends outwards.(2) The substrate divides the flow curent into two-400-300-200-100 0 100 200 300 400 500big recycle zones. The upward recycle zone is the mainu/(ms')reason for leading to the bending of the droplet pathsand potential backflow , causing blockage of the metalFig.8 Initial velocity distribution of dropletsdelivery tube.With the distribution of the position and initial(3) The gas flow influences the shape of the billetvelocity of the droplets obtained through using theand "中国煤化工the yield rale ofrandom method， combining the motion modelthe mconsistent between( Equation (7)), we can calculate the location ofthe exHCNMHG_different-sized particle groups reaching the substrate.(4) 1 ne patn or mouon races Ior fine particles ( lessMoreover，through the statistical regularity of the massthan 6 μm) exhibits curvature or bending , whereas bigdroplets , the shape of the billet can be figured out. Forparticles ( larger than 15 μm) move in straight lines.Baosteel Technical Research, Vol.5, No. 3, Sep. 20113-6(a)3 pm(b)6 um33-1833-60 .(C) 9-12 um(d)15 umFig.9 Flow trajectory of diferent sizes of liquid particlesdimensions[ J]. Materials Science Forum,2005 ,475-479:2799. 2802.5] Mi J,Shi Z,and Grant P s. Modeling shape evolution andReferencesheat flow of spray-formed ring performs [ J]. Materials[1] Mathur P,Applain D and Lawley A. Analysis of the sprayscience forum ,2005 ,475-479 :2807-2810.deposition process[ J]. Acta Metallurgy, 1989, 37 (2):429-443.[2] Lawrynowicz A，Liang X, Srivatsan T s, et al.Processing, microstructure and fracture behavior of aspray-atomized and deposited nickel aluminidespray-aiomernintermtallice [ J]. Journal of Materials Science, 1998 , 33(2):1661-1675.[3] Gutierez E,Lavernia E J and Grant N J. A mathematicalmodel of spray deposition[ J]. Metallurgical Transactions[4] Chen Z,Teng J, Yan H,et al. 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