solidification of impinging molten metal …€¦ · · 2017-10-19486 int. j. mech. eng. &...

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Int. J. Mech. Eng. & Rob. Res. 2014 Amitesh Kumar, 2014

SOLIDIFICATION OF IMPINGING MOLTENMETAL DROPLET ON A COLD SUBSTRATE

Amitesh Kumar1*

*Corresponding Author: Amitesh Kumar,[email protected]

The phenomenon of impingement and solidification of a molten metal droplet on a substrateoccurs in processes like thermal spray coating and spray casting. Molten metal droplet afterimpingement over a substrate becomes a splat after spreading and solidification. Thephenomenon of spreading and solidification of a droplet can be understood by mathematicalmodeling. In the present work, the spreading and solidification phenomenon of an impingingliquid metal droplet over a cold substrate are studied numerically using computational fluiddynamics software Fluent and validated experimentally. A model for heat transfer and solidificationduring impingement of a falling liquid Al-33wt%Cu droplet on a 304 stainless steel substrate hasbeen developed. Al-33wt%Cu was selected so that Jackson-Hunt theory can be utilized for thevalidation of the impingement model.

Keywords: Metal droplet impingement, Solidification, Microstructure, Simulation

INTRODUCTIONThe process of impingement of molten metalis complex and involves heat transfer, fluid flowand solidification. Droplet spreading is a freesurface problem with large domaindeformation in the presence of surface tension.The associated transient heat transferprocesses involve convection with largetemperature gradient in a deforming domain,liquid spread constrained by the multi-dimensional advancement of solidificationinterface, as well as the extraction of heat froma diminishing liquid region that is coupled with

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1 Assistant Professor, National Institute of Foundry and Forge Technology, Hatia, Ranchi, India 834003.

conduction in the substrate. The couplingbetween solidification and fluid dynamics canlead to non instinctive shapes (Waldvogel andPoulikakos, 1997). Experimentalinvestigations of droplet solidification are quitechallenging too, due to rapid change in shapeand temperature as well as the small size ofthe droplet.

Most researchers in the 1960s and early1970s focused on metallurgical aspects of theprocess, as evidenced in the review byAnantharaman and Suryanarayana (1971),Jones (1973), Jones (1982) and many of the

Research Paper

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existing heat transfer investigations of dropletimpact ignore the fluid dynamics aspect of theprocess altogether.

Nichols et al. (1980) developed analternative algorithm for solving completeNavier-Stokes equation in transient flow withmultiple free surface. The method is called“Volume Of Fluid (VOF) method”. Trapaga andSzekely (1991) used FLOW 3D, acommercially available code whichimplements the VOF methods to model threedimensional unsteady free surface flows, tostudy the isothermal impingement of liquiddroplet in spraying process. Liu et al. (1993)studied the impingement of tungsten dropletby solving axisymmetric Navier-Stokesequations and the VOF equation. They useda RIPPLE code (Kothe et al., 1991).

Bennett and Poulikakos (1994) and Kanget al. (1994) studied droplet depositionassuming that solidification starts only afterdroplet spreading is complete and the splat isin the form of a disc. Theoretical andexperimental studies done by Bennett andPoulikakos (1994) showed that the thermalconductivity of the substrate significantlyaffects the cooling rate of the splat. They didnot incorporate the convection.

Using numerical models and experiments,Zhao et al. (1996a and 1996b) studied heattransfer and fluid dynamics during collision ofa liquid droplet on a substrate. They extendedthe earlier model of Fukai et al. (1993) toaccount for the relevant convection andconduction heat transfer phenomena, both inthe droplet and in the substrate, in the case,when there is no solidification. Their results,therefore, are applicable to the pre-solidification stage of the impact process. Liu

et al. (1993) used a one-dimensionalsolidification model in conjunction with a two-phase flow continuum technique to track themoving liquid-solid boundary. The model,however, does not account for the convectionin the liquid and conduction in the substrate.

Trapaga et al. (1992) used a commerciallyavailable code, FLOW-3DTM (Sicilian et al.,1988), to study the heat transfer andsolidification phenomena during droplet-impact. They assumed that the substrate wasisothermal, and neglected any thermal contactresistance at the liquid-solid interface.Bertagnolli et al. (1997) used a finite elementapproach with an adaptive discretizationtechnique to model the deformation of thedroplet as well as the evolution of thermal fieldwithin the splat. Their model, however, doesnot take into account the solidification and heattransfer to the substrate. Liu et al. (1995)measured the temperature variation on theupper surface of an impacting metal dropletusing a pyrometer, and used these results toestimate the thermal contact resistance underthe drop. Wang and Matthys (1996)investigated the contact resistance effectsexperimentally and numerically for the dropletdeposition. They described some newexperimental results for copper splat coolingand estimated the interfacial thermalconductance between the molten copper andvarious cold substrates, and also thedifference in conductance between liquid/solidcontact and solid/solid contact. Chung andRangel (2000) investigated numerically thecontact resistance between the substrate andthe splat and the undercooling effect at the two-dimensional phase change interface. Kamnisand Gu (2005) studied the case of droplet

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impingement, when a powder particle isprojected on substrate from a thermal spraygun to provide protective coatings. In this studythey proved that the thermal contact resistanceis the key parameter in characterizing thesubstrate surface roughness for impingementmodeling and finally concluded that spreading,solidification and air entrapment are closelyrelated to surface roughness. They validatedtheir model using the experimental data ofcontact resistance between tin droplets andsteel substrate. Shakeri and Chandra (2002)studied the splashing of molten tin droplet ona rough steel surface.

In the present work the development of acomprehensive mathematical model (thattakes into account of impingement andsolidification of molten droplet over asubstrate) for the impingement of liquid Al-33Cu alloy droplet on a grade 304 stainlesssteel substrate has been attempted onFLUENT 6.3.16 platform. The present studyalso aims to validate the comprehensivemodel using Jackson and Hunt theory (1966)which relates the interlamellar spacing insolidified eutectic alloy with the solidificationfront velocity.

MODELINGPresent study aims at developing amathematical model of flow and heat transferin a liquid metal which falls freely throughgaseous medium and impinges on a coldsubstrate. Modeling of the phenomena iscomplex because it involves interactionsamong three phases, viz., liquid metal, solidsubstrate and gaseous medium. Further, asthe droplet falls under the action of gravity andimpinges on the substrate, its shape changes

rapidly with time and its cooling isaccompanied by solidification.

Figure 1 is a schematic sketch of theimpingement phenomenon. With a symmetricboundary in the middle only half of the domain(ABFCDEA) was actually computed and avery fine grid was used for the regions whereimpact, spreading and solidification occur.

A droplet of Al-33wt%Cu, which is initiallyspherical, falls through the gaseous mediumand impinges on a grade 304 stainless steelsubstrate. At the droplet/substrate interface agap was created. This gap was used to modelthe interfacial contact resistance by prescribingan effective thermal conductivity to the gap.The thickness of the substrate was assumedto be 1 mm. Since the initial shape of thedroplet is assumed to be spherical, the fluidflow and the heat transfer are axisymmetric(r-z direction).

The following assumptions have been madein the mathematical model:

• Spherical geometry Droplet is assumed upto just before the impingement.

• The problem is axi-symmetric about the axisshown in Figure 1.

• Impinge velocity of the droplet isperpendicular to the plane of the substrate.

• No rotation of droplet occurs along the axis.

• The flow of metal (droplet) and gas islaminar and incompressible. The velocity ofgaseous media at domain walls is zero.

• Walls of the domain (Figure 1) are assumedto be at ambient temperature.

• The radiation from the droplet surface to thesurroundings is ignored.

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• To take into account the thermal contactresistance due to air gap a solid layer hasbeen defined. The conductivity of the solidlayer is estimated experimentally.

• Initial velocity of droplet (when it forms) iszero. It acquires velocity during the free fall.The velocity just before the impingementwas gH2 , where H is the distancebetween the orifice of crucible andsubstrate.

Numerical simulations of the axis-symmetricdroplet impingement processes wereconducted by solving the 2-dimensional (r-z)continuity, Navier-Stokes and energyequations. The Volume Of Fluid (VOF)approach (Waldvogel and Poulikakos, 1997)was coupled with Navier-Stokes and energyequations to track the surface of the impingingdroplet on a fixed eulerian structured mesh.

Solidif ication results in latent heatgeneration and a modified form of the energy

equation, incorporating latent heat havebeen used. The modified energy equationis given by

hSTkuHHt

...(1)

where H is the enthalpy per unit volume, k isthermal conductivity and Sh is the rate ofenergy generation per unit volume. Theenthalpy of the material was computed as thesum of the sensible enthalpy, h, and the latentheat, H. It is expressed as

H = h + H ...(2)

where,

dTchhT

TPref

ref

...(3)

In Equation (3) href is the sensible enthalpyat the reference temperature and CP is thespecific heat at constant pressure.

The liquid fraction, , is defined as:

= 0 if T < Tsolidus

= 1 if T > Tliquidus, ...(4)

solidusliquidus

solidus

TTTT

if Tsolidus < T < Tliquidus.

The latent heat content can be written interms of the latent heat of freezing, L:

H = L ...(5)

The source term appearing on the right-hand side of Equation (1) is given by

( ) ( )hHS u

t

...(6)

Due to high temperature difference betweenthe droplet and substrate and the relatively lowdroplet velocity, viscous dissipation of heat

Figure 1: Schematic Representationof the Mathematical Model of Droplet

Impingement

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was negligible and thus not included in thesource term.

Solidification results in phase change.Instead of tracking the interface, Al-33 wt%Cuwas assumed to be a single phase pseudo-porous medium whose porosity was taken asproportional to the liquid fraction. Thus theporosity of this single phase pseudo-porousmedium varied from zero in the solidified regionto one in the completely liquid region. However,Al-33wt%Cu is a eutectic alloy and thus asudden transition in the porosity is expectedat the solidification front. To avoid numericaldifficulties associated with this suddentransition the solidification front was assumedto be a narrow band and the porosity wasvaried from zero one over this band. The effectof porosity was incorporated in the momentumequations through a momentum source terms.

All zones were initialized with thetemperature of 300 K, except the droplets. Thedroplets were set to a predetermined highertemperature. The initial velocities at every pointinside the domain were zero, except within thedroplets.

Since problem is axis-symmetric only halfof the domain shown in Figure 1 wasconsidered in the computation domain. Axisof symmetry was like a free-slip wall. Thenormal velocity was zero. Tangential velocitydid not have normal gradient. Thus along theaxis of axis-symmetry u = 0 and v/r = 0. Atthe other boundaries u = 0 and v = 0. Sincethese boundaries are far away from the droplet,the temperatures at these boundaries were setequal to the ambient temperature, i.e., 300 K.The above described model was simulatedusing FLUENT 6.3.16 plat form.

Thermo-physical properties of Al-33wt%Cuthat have been used for simulation are givenin Table 1. Table 2 provides the thermo-physical properties of the grade 304 stainlesssteel.

Thermal conductivity (Wm-1 K-1) Ks = 155

Kl = 71

Density (kg m-3) s = 3410

l = 3240

Solidus Temperature (K) 821

Liquidus Temperature (K) 821

Melting Heat (J Kg-1) 350000

Specific Heat (J Kg K-1) Cs =1070

Cl = 895

Viscosity* (kg m-1 s-1) at 943 K = 1.001 X 10-3

(Korol’kov, 1960)

at 973 K = 8.624 X 10-4

(Korol’kov, 1960)

at 1023 K = 5.65 X 10-4

(Korol’kov, 1960)

Surface Tension (N m-1) 0.868 (Lang, 1974)

Table 1: Thermo-Physical Propertiesof Al-33Cu Alloy

Properties of Al-33wt%CuUsed in Model Value

Note: s = solid; l = liquid;

*Value of viscosity of Al33wt%Cu has been calculated using

Arrhenius equation: )exp(0 RTE

up to the solidus

temperature.

Properties of Grade 304 Stainless Steel Value

Thermal Conductivity (Wm-1 K-1) 15

Density (kg m-3) 7900

Specific Heat (J Kg-1 K-1) 477

Table 2: Thermo-Physical Propertiesof 304 Stainless Steel Alloy

Contact resistance was estimated using theinverse modeling approach and its value wasestimated to be 7 x 10-4 m3-K/w. The details of

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this are given in the paper by Kumar et al.(2010).

EXPERIMENTS FORVALIDATION OF MODELA droplet impingement set up to validate themodel was fabricated. Figure 2 shows theschematic sketch of the set-up.

A vertical resistance furnace was used formelting. The furnace has a cylindrical shapehaving a height of 8 inch, an outer diameter of4 inch and an inner diameter of 1 inch. Thetemperature of the melt could be controlledwithin ±5 °C. It was placed at the top of thedroplet impingement chamber as shown inFigure 2. A quartz tube with an inner diameterof 17 mm was used as a crucible. At thebottom of the crucible there was a melt deliverynozzle. The diameter of the melt delivery nozzlewas 2 mm. Substrate was made of grade 304stainless steel. The substrate was circular inshape having a diameter of 20 cm and

thickness of 20 mm. It was placed inside thespray chamber. Pieces of master alloy Al-33Cu were melted in the quartz crucible. Thetemperature of the melt was maintained at~150 °C above the melting point. Byapplication of air pressure droplets werepushed out of the 2 mm diameter melt deliverynozzle. These droplets impacted on thesubstrate, deformed and finally solidified onit. For deposited splats, the size of the dropletwas estimated by measuring the weight ofsplats. The microstructural characterizationsof the deposited droplets were carried outusing standard metallographic procedures.

JEOL JSM-5800 Scanning Microscope andField Emission Scanning Electron Microscope(Model: Carl Zeiss SMT Ltd.) were used fortaking the microstructure at highermagnifications. The interlamellar spacing ()of the eutectic structure of Al-33Cu wasmeasured by drawing perpendicular line usingOptical Image Analyzer Leica DMLM.

RESULTS AND DISCUSSIONSimulation of Droplet ImpingementIn the present study simulations were carriedout for the droplets of diameter 5.39 mm fallingthrough a height of 50 cm on a grade 304stainless steel substrate. The substratethickness was taken as low as 1mm in orderto reduce the computational time. This will notaffect the accuracy of the prediction of thethermal field because during the short durationof droplet spreading and solidification thetemperature rise in the substrate did not takeplace beyond a distance of 0.2 mm.

The computed velocity, temperature, liquidfraction and phase (Al-33Cu and air) fieldswere plotted at different time intervals by

Figure 2: Schematic Sketch of DropletImpingement Set Up

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simulation of the impingement model onFLUENT 6.3.16 platform. Figure 3 shows thephase contour of Al-33Cu droplet having adiameter of 5.39 mm in air. In this case thevelocity of impingement was 3.13 ms -1.Therefore the Weber number was 207. Thespread of the droplet occurred within a shorttime frame of 5.0 ms and no disintegration dueto the surface tension force was observed. Itcan also be seen that the solidification starts10.0 ms after the spread has taken place.Figure 4 also shows the velocity profile of Al-33Cu/air system. It can be noted from the figurethat air adjacent to Al-33Cu, is dragged in thedirection of spread and a re-circulating flow inthe air can be observed.

Droplet spreads radially after impingementon the substrate along the surface of thesubstrate as shown in the phase profile (Figure3) and velocity profile (Figure 4). Thinsolidification layers were developed at theedge of the droplet 10 ms after the impact; thesolidification layers progressed to the most ofthe contact surface as the droplet spreadedat 20 ms; and full solidification finished at 76ms. The phase contour and velocity vectorresults are shown in Figures 3 and 4,respectively. On impact, the high impactvelocity generates a high pressure regionunder the droplet; forced the liquid to flow overthe contact surface while the effect of surfacetension was comparatively less; the maximumflow velocity was achieved at the edge whereall the momentum was transferred to the radialdirection and the cross-section area wassmall. The velocity at the edge was found tobe 5.59 ms-1 after 1.0 ms which is higher thanthe impact velocity of 3.13 ms-1. With thespreading and solidification progressed, the

flow of liquid metal reduced and the effect ofsurface tension became significant, whichgenerated high pressure regions at the edgesand finally reversed the flow back towards thecentre as shown in the 8.0 ms time frame plot

Figure 3: Phase Profile of ImpingingAl-33Cu Droplet on the Substrate

Figure 4: Velocity Profile of theAl-33Cu/Air System

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in Figure 4. This resulted into the formation ofbump at the edge of the splat.

The simulated evolution of droplet shape(Figure 3) has been reported earlier (Fukaiet al., 2000). The bump near the edge hasbeen observed even when there is no cooling(Sikalo and Ganic, 2006). The physicalreasons for the bump formation are not fullyunderstood although surface tension and theexistence of the bump because of themaximum cooling near the edge (Figure 5)(Fukai et al., 2000) could be suggested as twoof the reasons.

The thermal contour in Figure 5 showsconvective cooling at the top surface, whereAl-33Cu is cooler than the inner region.

Similarly conductive cooling of Al-33Cu nearthe substrate can be seen along with heatingup of the substrate as shown in thetemperature profile plotted (Figure 5). Figure6 shows the liquid fraction within Al-33Cusystem.

Figure 5: Temperature Profile ofImpinging Al-33Cu Droplet on the

Substrate

Figure 6: Liquid Fraction Profile ofAl-33Cu/Air System

Estimation of Solidification FrontSpeedFrom the liquid fraction profile the position ofthe solidification front can be tracked. It canbe observed that the front is almost parallel tothe substrate and therefore the heat transfermust be predominated by the substratecooling.

When a solidification layer grows, the lowerpart of the liquid splat loses momentum as itsolidifies to become a part of solidified layer.Solidification may take place during spreading,

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but the solidified layer growth velocity is slowcompared to when solidification starts aftercomplete spread. Therefore, a splat retainsradial momentum during spreading andreaches its maximum diameter whilesolidifying.

Solidification front speed was estimatedbased on the liquid fraction profile at 10different locations. Figure 7 shows the differentlocations in the splat along the radial direction.The simulated front speed of solidification ofthe splat was determined from variation ofliquid fraction profile with time. The ratio ofsolidified thickness to elapsed time gives thefront speed of the splat solidification. The splatsolidification is almost unidirectional, it startsfrom the interface of the substrate and the effectof convection is negligible as compared to theconduction. The front speed was not found tobe fixed across the cross section. It is mainlydue to variation in thickness of splat (Kumaret al., 2010).

VALIDATION OF THE MODELThe experimental validation was carried outfor a droplet of diameters 5.39 mm and havinga superheat of 150 K (initial temperature = 973

Figure 7: Profile of Deformed DropletLocation for Determination of Cooling

Rate at Different Positions

Figure 8: Lamellar Eutectic Microstructure of 5.39 mm Diameter Droplet

K). The solidified droplets were sectioned atdifferent locations (Figure 7) and the sectionedpieces were metallographically prepared tocharacterize the microstructure.Microstructures of 5.39 mm droplet depositedover substrate are shown in the Figure 8.

For validation, solidification front velocitiesin droplet having diameter of 5.39 mm werecalculated using the model developed in thepresent work. These values were plugged inthe Jackson-Hunt relationship (2V = 88 µm3/s) (Jones, 1982) for calculation of ë from thosevelocities. Figure 9 shows the experimentalvalues obtained for various sections which areshown in Figures 7 and 8 superimposed on

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those the ones calculated from this model. Avery good correlation can be seen in the plotbetween experimental and simulated valueswithin standard errors of experimentalmeasurements.

CONCLUSIONThe droplet impingement and solidificationmodel was simulated for droplet of diameter5.39 mm, initial droplet temperatures of 973K, and impingement velocities of 3.13 ms-1.The simulation carried out for droplet (diameter= 5.39 mm, impinging velocity = 3.13 ms-1,initial temperature = 973 K) suggests thefollowing.

• The spread of the droplet occurred within ashort time frame of 5.0 ms and nodisintegration and observed that thesolidification starts 10.0 ms after the spreadhas taken place.

• On impact, the maximum flow velocity wasachieved at the edge where all the

momentum was transferred to the radialdirection and the cross-section area wassmall. The velocity at the edge was foundto be 5.59 ms-1 after 1.0 ms which is higherthan the impact velocity which was 3.13ms-1. As the spreading and solidificationprogressed, the flow of liquid metal reducedand the effect of surface tension becamesignificant, which generated high pressureregions at the edges and finally reversedthe flow back towards the centre. Thisresulted into the formation of bump at theedge of the splat.

• The prediction of the model on dropletspreading matched well with theexperimental findings and so did theprediction of the interlamellar spacings atdifferent locations of the splat.

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Figure 9: Interlamellar Spacing versusGrowth Velocity

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solidification of impinging molten metal …€¦ · · 2017-10-19486 int. j. mech. eng. &...

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