Numerical simulation of mould filling process for pressure plate and valve handle in LFC

Research & DevelopmentNovember 2010Numerical simulation of mould fillingprocess for pressure plate and valvehandle in LFC* Jiang Junxia', Li Qinliang 1, Wu Zhichao2 and Chen Liliang'(I. Department of Information Control and Manufacturing, Shenzhen Institute of Information Technology, Shenzhen, China; 2. HuazhongUniversity of Science and Technology, Wuhan, China)Abstract: In lost foam casting (LFC), the distribution of polymer beads during the bead fling process is notuniform, and the collision between polymer beads determines the distribution of two-phase flow of gas and solid.The interaction between the gas and solid phases reveals as coupling effect of the force that gas exerts onparticles or vice versa, or that among particles. The gas-solid flow in fling process is nonlinearity, which makes thecoupling effect an essential point to carry out a simulation properly. Therefore, information of each particle s motionis important for acquiring the law of filing process. In bead filing process, compressed air is pressed into moldcavity, and discharged from gas vent, creating a pressure difference between outer and inner space near the gasvent. This pressure difference directly changes the spatial distribution and motion trace of gas and solid phases. Inthis paper, Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) are employed to simulatethe fluid dynamic character based on Newton's Third L aw of Motion. The simulation results of some castingproducts such as pressure plate and valve handle are compared with the result obtained from practical experimentin order to test the feasibility of DEM. The comparison shows that this DEM method can be a very promising tool inthe mould flling simulation of beads' movement.Key words: lost foam casting; bead flling process; two-phase flow; numerical simulationCLC number: TG249.6/TP391.9Document code: AArticle ID: 1672-6421(2010)04-367-06he flling process of polymer beads in lost foam casting as Discrete Particle Model (or DPM) when it was applied to(LFC) is complex due to the fact that it is a typicalparticle system". In DEM-CFD model, the Eulerian method isprocess of two-phase flow involving the high-speed gas phaseand the polymer bead phase. Gas solid two-phase flow occursfor tracing discrete particle in the particle field. The key ofwidely in engineering field, and it has been investigated andDEM model is discretely processing particle phase. Since theexperimented for many years (14. However, some of the :particle-collision models as well as the computation methodmechanisms are still not clear, and the influential factors are are different, the particle discrete simulation usually uses threerather complicated, which limited the related analysis andmodels/ methods, including hard sphere model, soft sphereresearch of the experiment-based traditional approach.model and Monte Carlo method. In this approach, particleWith the development of computer technology and collision can be described by the hard sphere model and the softintroduction of hydrodynamic theory, numerical simulation sphere model, while particle movement can be calculated by thecombined with mathematics and fuid mechanics has becomeMonte Carlo method. These three models/methods are differentan important tool in simulation of beads-filling process in in calculation efficiency, and they are used in different fields.casting industry 15-6. Discrete Element Method (DEM) modelHard sphere model and soft sphere model are different in theis established in this paper to research the dynamic property offollowing four aspects:gas -solid flow in bead-iling process of LFC.(1) Static propertyDEM model was raised by Cundall and Sreack, knownFor usual gas-solid dynamic system, under conditionthat particle movement is frequent enough and void ratio*Jiang Junxiais adequate, the calculated speed of simulating hard sphereMale, borm in 1976, Ph.D, a lecturer on information control andis faster than that of soft sphere. However, when some partmanufacturing. He obtained his doctor's degree from Huazhongof field appears de-fluidized, particles will be pushed intoUniversity of Science and Technology in 2009, and his researchtogether tightly, and中国煤化工which willinterest is mainly focused on casticess simulation.，By now histhen increase the amo10 papers has been published in jourmals at home and abroad.(2) Elastic stiffnessHCNM HGE-mail: xiaijno1 @163.comReceived: 2009-07-28; Accepted: 2010-05-10Soft sphere model is able to calculate all elastic stiffness367CHINA FOUNDRYVol.7 No.4principle, it can predict the time of particle collision, which flling process. The equations of gas phase momentum areis very important for study on the process coupled with heatlisted below:transmission and mass transfer. But meanwhile, if the elasticstiffness value is too small, it will not make any sense of(P&Eu2)+V.(EgRu,"z)=-VP-Sp_ -(V.tg)+ε。Pg (2)calculation.rg= u4[Vu。g +Vu[]-气4V.u。I(3(3) Energy conservationHard sphere model has the advantage of being able toV = (OxAyOz)'3(4analyze energy conservation in collision model, that is, oncethe speeds before and after collision are assigned, energywhere τg is stress tensor of gas, Hg is gas dynamical viscositycoefficient, Spg is interactive force between particle phasecan never do this because its precision determines on the timeand gas phase acquired by calculating particle phase, P is gasstep of numerical integral, which is assumed arifially.pressure, g is gravity acceleration, I is unit tensor, and Or, Oy,(4) Multi-spheres collisionOz are mesh sizes.The most obvious disadvantage of hard sphere model is thatParticle movement pushed by external force conformsit cean only deal with two spheres cllision, not cllision of to Newton s second law. Considering that the particle onlythree spheres or more. As to the particle flow in high density,receives gravity and the drag force from gas, the particlethe calculation may make mistakes on particles collision movement equation is as fllowsdynamics. But all of these cases can be dealt with by softdv,3p。Csphere model.4ρ,d,|",。-,(u_-v,)(5method has the advantage of fast enough calculation. where vp is particle velocity, Ca is drag force cofficient, ρpis .Besides, it is based on particle dynamic theory, and particlethe particle density, and dp is the diameter of the particle. Tospeed distribution function generated by random samplingsimplify the calculation, those cases that the particle Reynoldscan be done by computer conveniently. These two main number is less than 0.4 are disregarded. The drag coefficientadvantages make the Monte Carlo method more suitable Cs refers to the formula given by Richardson and Rowe shownfor calculating speed distribution function than by dynamicbelow:24 (theory directly. These three methods are complementary but(1+0.15(Re,)98 ) Re, < 1000 .not interchangeable, and they are all important to research theCg=(6particle flow mechanism and to resolve some relevant practical.0.44Re,≥1,000problems.Re, is particle Reynolds number defined as:DEM presents a method to research macro mechanicsproperties from micro structure, and gives some fundamentalEg p|lu。-v,d,(7laws about particle flow and dynamics. With the developmentof computer calculation capability, simulation system becomesmore feasible for practical applications, though DEM focusesWhen Hoomans et al. dealt with phase coupling, theyon a small amount of particles, which is quite different fromadopted an empirical relation to calculate force on particlespractical conditions.phase by gas phase, and another to counterforce on gas phaseAccordingly, considering that the polymer beads are of by particles phase. But this treatment results in imbalance ofsmall density and the time of collision among them is short,the interaction force between the two phases, and goes againstthe flling process of gas. -solid flow will be simulated by hardNewton's third law of motion. To maintain the conservationsphere model in this paper.of interaction force, the counterforce on gas phase by particlesphase is supposed to equal with the force on paticles by gas.1 Governing equationsThen, according to Newton's Third Law of Motion, volumeforce on gas by particles is:The theory of gas- solid flow in flling process and the relatively28Fimportant technology, such as force model of polymer beads,Spg =-AV(8coupling between phases, confirmation of parameters etc, arediscussed based on Newton's Third Law of Motion combinedwhere FJ is drag force on particle phase by gas phase, OVwith DEM and CFD.is volume of calculating mesh, OV=OxOyOz, and ke is theThe gas phase continuous equation is as follows:number of beads in meshes.(Pgεg)+V.(PgEqug)=0(12 Results中国煤化工The common me.MHCNMHG.where uy is velocity of gas,pg is density of gas, and8g is void. w 5u10 w...near equationsin the model include SIMPLE, MAC, SMAC and SOLA. Dr.368Research & DevelopmentNovember 2010Clutch pressure plate as well as valve handle is a kind oftime by making a comparison among SIMPLE, SMAC andring-shaped plate castings, with rib or cross gate connectingSOLA methods, and concluded that SOLA method is the bestthe centre part. To simplify the simulation process, theone because of higher iteration efficiency and shorter CPUparts and their flling process are simplified as demonstratedcalculating time. Therefore, SOLA is adopted in this researchin Fig.2. Due to the application of hexahedral mesh, thereto calculate the movement of the gas flow.will be too many faces in the stiffening rib of the originalClutch is an important part of automotive tansmission usedpart during meshing. Since the increased faces in numericalto maintain automobiles to start smoothly, to transmit shift simulation will increase collision of bead onto the surfaceimmediately and not to be overload. Pressure plate, the main of the stiffening rib which actually does not occur, thepart of clutch which connects clutch to engine tightly, is thestiffening rib is therefore simplfied to be a straight one andcarry out numerical simulation on the condition of havinga casting of round plate, with supporting lugs at fringe, and 3 orlittle affect on simulation result. The beads are assumed to4 load transfer lugs on outer sphere, as shown in Fig.1 (a). Itsbe the same mono-sized particles with diameter of 1 mm,overall diameter is 180 mm, and the foam patterm is producedand density of 20 kg.m°. Uniform grid is adopted, and thewith gating system.mesh is set at dx = 2 mm in dimension, giving the totalValve handle is usually a ring plate casting, contains number of meshes at 14,400. Gas density is 1.205 kgm-,turntable frame, ftting pad in the center of turntable, stiffeninggas viscosity is 1.79 X 10° Pa.s, and gravity acceleration isrib to connect turntable and fiting pad, as shown Fig.l (b). 9.81 m-s2 with the same direction as flling process.. SprueCross gate(a) Clutch pressure plat(b) Valve handleFig. 1: 3D drawing of the partsVent■let(a) The simplified part(b) The fling processFig. 2: the simplified product and flling processThe particles are numbered to track their movement.because of the narrow mould cavity in shooting direction, and isDifferent colors are used to mark particles of different rangesrebounded radially outward. When polymer beads are shot intoof numbers, for example, the green standing for numbers 1 tothe four channels from the centre inlet by compressed air, the5,000, and red for those 5,001 to 30,000. Thus, the particles'pressure in the ring part reduces and that at walls of connectingdistribution can be shown obviously.channels increases. After that, beads move into the circum andThe numerical simulation result of the flling process is showncollide with the wall. The rebounded beads will converge at thein Fig.3, and pressure profiles of gas phase in Fig.4 In initial stage middle of one fourth circum when spreading around. and then pileof fling process, the pressure in the ring part is higher than that in by the gravity and coll中国煤化工y fled, andthe four channels. The pressure in the centre inlet, which appearsthen the neighboring foCNMHGlsaretallyas a thombus, is the highest and spreads from centre to periphery.filled with beads, these particles will fill the inlet in model' s centerThe flow of beads rapidly ollides with the bottom of the mouldpart. Then the flling process is finished.369CHINA FOUNDRYVol.7 No.4(a)0.12s(b) 0.25 s(C)0.61s(d)0.84s(e) 1.10 s()1.67sFig. 3: The numerical simulation result of fling process(b) 0.25s(c)0.61 s(d) 0.84 s(e) 1.10s(f) 1.67 sFig. 4: The numerical simulation of the pressure profilesInlet/Vent, Gland strip中国煤化工(a) Simplified partIYHCNMHGFig. 5: Mould structure70Research & DevelopmentNovember 2010black also for convenience of observation on the contrary ofwill be compared with that of practical experiment to test the the white color of polymer beads.feasibility of DEM. Clutch pressure plate and valve handleThe comparisons between the simulation result andare simplfied based on their same structure, and the commonexperiment result are shown in Fig.6 and Fig.7. It can be seenmould for experiment is designed as shown in Fig.5. In that the simulation result mainly accords with the experiment,the front of the aluminum mould a synthetic glass is fixedwhich is evident the feasibility of the method to simulatinghermetically for observation. The mould cavity is paintedfllig process in LFC.(a) 0.32 s(b) 1.77s(C) 3.16s(d)4.52 sFig. 6: The experiment result(a)0.12s(b) 0.32s十十(c) 0.68 s(d) 1.29s(e) 1.77s(f) 2.25s(g) 3.16s(h)4.52 sFig. 7: The simulation resultIn Fig.7, green color represents those particles with the3 Summaryfrom 8,001 to 40,000. Figure 8 shows that, during the initialThe numerical simulation was carried out to study the fluidstage, the pressure at outer circum is the lowest, next atdynamical character during bead flling process in LFC basedinner circum and the pressure at centre inlet is the highest.on DEM. The motion of polymer beads is related to gasPolymer beads firstly fill the outer circum, and as the fllingpressure distribution closely, because the pressure differenceprocess continues, the pressure at outer circum increases,between outer and i中国煤化工the drivingand then beads fill the inner circum. When the beads pile up,force of flling procesCNMHGThe simulation of t.... privwoure plate andthe pressure increases gradually from outer to inner until thevalve handle parts based on DEM is compared with the result offlling process finishes.371CHINA FOUNDRYVol.7 No.4G(a)0.12s(b)0.32s(c) 0.68 s(d) 1.29 s(e) 1.77s(f) 2.25s(9) 3.16s(h) 4.52 sFig. 8: The numerical simulation of the pressure profilesvisible experiment. It can be found that the simulation matches [4] Pan Y, Tanaka T and Tsuji Y. Turbulence modulation bythe experimental results reasonably well, suggesting that thisdispersed solid particles in rotating channel flows. Int. J.Multiphase Flow, 2002, 28(4): 527-552.method for beads flling process is quite eficient and adequate.5] Arastoopour H. Numerical simulation and experiment analysisof gas/solid flow systems. Powder Technology, 2001, 119(2):References59-67.6] Castro J, Nogami H and Yagi J Y. Numerical investigation of[1] Hudson J, Harris D. A high resolution scheme for Euleriansimultaneous injection of pulverized coal and natural gas withgas- solid two phase isentropic flow. Journal of Computationaloxygen enrichment to the blast furnace. ISIJ Int, 2002, 42(11):Physics, 2006, 216(2): 49- -525.1203- -1211.[2] Campbell C S, Brennen C E. Chute flows of granular material:[7] Hoomans B P B, Kuipers J A M. Granular dynamics simulationsome computer simulation. J. Appl. Mech., 1985, 52(1): 172- -178.of segregation phenomena in bubbling gas-fluidized beds.[3] Elghobashi S E, Truesdell G C. On the two-way interactionPowder Technology, 2000,109(1-3): 41-48.between homogeneous turbulence and dispersed solid8] Wang Junqing. Mold fling process modeling and numericalparticles: turbulence modulation. Phys. Fluids, 2003, A(5):simulation of flow field. Foundry, 1987, 36(12):20-22. (in1790-1796.Chinese)This research is financially supported by The Second Doctor Innovative Projects of Shenzhen Institute ofInformation Technology (BC2009013).中国煤化工MHCNM HG72