MODELING OF HEAT FLOW AND SOLIDIFICATION DURING … · Trans. Indian Inst. Met. Vol.57, No. 3, June...

Trans. Indian Inst. Met.

Vol.57, No. 3, June 2004, pp. 283-296TP 1894

NOMENCLATURE

Symbol Description Units

Ad Surface area of droplet m2

CD Coefficient of drag -

CL Specific heat capacity perunit mass of liquid J kg-1 K-1

CS Specific heat capacity perunit mass of solid J kg-1 K-1

Cpd Specific heat per unitmass of droplet J kg-1 K-1

CLS Specific heat per unit massof solid-liquid mixture J kg-1 K-1

d Diameter of droplet m

fs Solid fraction -

fR Solid fraction generatedduring recalescence -

g Acceleration due to gravity m s-2

MODELING OF HEAT FLOW AND SOLIDIFICATIONDURING SPRAY DEPOSITION PROCESS

P.Shukla, R.K.Mandal and S.N.OjhaDepartment of Metallurgical Engineering, Banaras Hindu University, Varanasi- 221 005, India

E-mail address: [email protected]

(Received 28 October 2002 ; in revised form 7 June 2004)

ABSTRACT

The solidification behavior of droplets as well as spray-deposit of Al-4.5 wt% Cu alloy is simulated bymodeling based on heat flow analysis. The model incorporates droplet dynamics and their thermal states duringatomization process. The resultant spray enthalpy is used to analyze heat flow during solidification of the spraydeposit. The effect of process variables like atomization pressure, melt superheat and nozzle to substratedistance on the solid fraction and enthalpy of the spray is analyzed. The results of modeling are compared withthe experimentally determined thermal profile of the spray deposit. The results indicate that the cooling ratefor a wide size range of droplets varies from 103-105 Ks-1 in contrast to a slow cooling rate of 1 to 10 Ks-

1 of the spray deposit. Empirical correlation between cooling rate of the spray deposit and the grain size hasbeen established. It is inferred that cooling rate is not the sole determining factor in controlling grain size ofthe deposit during spray deposition process.

h Convective heat transfercoefficient at droplet gas-interface W m-2 K-1

htop Heat transfer coefficient atdeposition surface W m-2 K-1

hbot Heat transfer coefficient atsubstrate-deposit interface W m-2 K-1

Hd Enthalpy of droplet perunit mass J kg-1

Hd Hf - (CL-CS)(TL-Td) J kg-1

Hf Latent heat of fusion perunit mass J kg-1

H Enthalpy in the deposit perunit mass J kg-1

HSPRAY Spray enthalpy per unit mass J kg-1

k Average thermal conductivityof the alloy W m-1 K-1

kg Thermal conductivity of gas W m-1 K-1

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TRANS. INDIAN INST. MET., VOL. 57, NO. 3, JUNE 2004

ko Partition coefficient -

md Mass of droplet kg

Pr Prandtl number -

Re Reynolds number -

Td Temperature of droplet K

Tg Temperature of gas K

TL Liquidus temperature K

TR Recalescence arresttemperature K

TS Solidus temperature K

TE Eutectic temperature K

TM Melting point of puresolvent K

TN Nucleation temperature K

Tgas Temperature of atomizinggas K

Tsub Temperature of substrate K

T· Cooling rate ofdroplet/preform K s-1

Vg Velocity of gas m s-1

Vd Velocity of droplet m s-1

x Distance solidified alonggrowth axis m

y Distance in the preform m

Y Height of depositionsurface m

Y· Deposition rate per unitarea kgs-1m-2

Wetting angle degree

Density of spray deposit kg m-3

g Density of gas kg m-3

d Density of melt kg m-3

1. INTRODUCTION

Spray deposition (SD) has emerged as a viablealternative to the casting and powder metallurgyroutes of processing monolithic as well as compositematerials 1-5. Its potential for producing near-netshape products has already been demonstrated in thepast for different applications 6-7. Spray depositioninvolves atomization of a molten material by highvelocity gas jets into a spray of micron-sized dropletswhich are subsequently propelled and deposited ontoa substrate to produce preforms of desired shapesthrough maneuvering of the substrate. Owing to theheat transfer by forced convection between thedroplets and the gas, rapid solidification effects arerealized 8. This has been demonstrated based on themicrostructural refinement and chemical homogeneitythat are achieved in the spray deposits. For a givennozzle assembly, the atomization gas pressure, meltsuperheat and the nozzle to substrate distance arethe process variables which influence the thermalstate of the spray during flight and on the depositionsurface. The former governs the nature ofundercooling that a droplet experiences and the latterlargely controls the microstructural characteristicsof the preform. Hence there is a need forunderstanding the nature of microstructural evolutionduring SD process. In the past, several attemptshave been made for modeling the various stepsinvolved in SD9-13 but an integrated andcomprehensive model combining the process ofatomization, droplet dynamics and thermal state ofthe deposition surface is limited in literature10. Inthe present work, an attempt has been made todevelop an integrated approach by combining theoutcome of the droplet dynamics with that of heattransfer on the substrate. This includes (a)experimental measurement of gas velocity betweenthe substrate and nozzle exit (b) computing thevelocity and temperature profile of different sizeddroplets as a function of flight distance and (c)determining the spray enthalpy at the depositionsurface and the temperature profile of the deposit.Further, a comparison between the computed andmeasured temperature profile of the deposit has beencarried out. The experiment conducted as part ofthis investigation has served two objectives. Theseinclude (a) supplementing the computed data basedon model and (b) comparing the predicted behavior

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SHUKLA, et al., : MODELING OF HEAT FLOW AND SOLIDIFICATION DURING SPRAY DEPOSITIONPROCESS

with respect to microstructural characterisations ofthe preform vis-àvis those obtained by experiment.The results facilitate an insight into the microstructuralevolution during SD process.

2. EXPERIMENTAL DETAILS

2.1 Gas Flow Measurement

An indigenously designed convergent-divergent spraynozzle with a throat area of 20.5 mm2 and an exitto throat-area ratio of 3:1 was used to atomize themelt. A metallic flow tube having a concentricallyaligned ceramic insertion is used to deliver the meltin the gas stream to promote atomization. The axialvelocity of the gas was measured using a Pitot tubealigned below the nozzle exit. The static andstagnation ends of the Pitot tube were connected toa mercury manometer. The Pitot tube was traversedaxially downward and the deflection in the mercurycolumn was recorded at regular intervals of 5.0 mmat reservoir pressures of 0.8, 1.0 and 1.2 MPa.These measurements have provided data to calculatethe gas velocity at a particular gas pressure andaxial distance.

2.2 Atomization and Spray Deposition

The atomization of the melt was carried out innitrogen environment at reservoir pressures of 0.8,1.0 and 1.2 MPa. The droplets were allowed tosolidify during flight. The powder particles werecollected at the bottom of the atomization chamberand sieved into various size fraction following ASTMstandard B 214 procedure14. The sieve analysis dataprovided the median particle diameters in the sizerange of 60-70 m and these were used in the analysisof the heat flux calculations on the deposition surface.In another experiment, a mild steel substrate wasintroduced at distances of 0.35 and 0.45 m along thespray axis. Two Chromel-Alumel thermocouples,centered along the axis of the spray and insertedthrough a fine hole in the substrate were used tomeasure the temperature profile within the depositas shown schematically in Fig. 1. The hot junctionsof the thermocouples were positioned at a height of2.0 mm and 10.0 mm from the surface of thesubstrate. The output of the thermocouples wasrecorded during and after deposition using a Data

Acquisition System having a response time of 1.0sec.

2.3 Microstructural Examination

The specimens for microstructural examination weremachined from various locations of the spray deposit.These were polished using standard metallographicprocedure and etched with Keller’s reagent consistingof 1.0 % HF. 1.5 % HCl, 2.5 % HNO3 in water.The microstructural examination was carried out usinga Leitz optical metallograph. The size and sizedistribution of the grains were studied usingquantitative metallographic procedure by using aVIDS Image Analyzer.

3. FORMULATION OF THE MODEL

The consideration of heat transfer process associatedwith spray deposition involves two distinct but closelyrelated steps. These include (1) atomization includingflight of droplets till impingement and (2) depositionof the aggregate of undercooled droplets onto thesubstrate. The complexity of the atomization processand our limited understanding about the variousphenomena involved preclude any analytical solutionof the problem. Most of our understanding about thephysical phenomena involved in spray forming and

Fig. 1 : Schematic diagram of the spray deposition set-up.

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the effect of process parameters on size and sizedistribution of powders is based on experimentalresults. The size and size distribution of dropletsproduced during atomization at different atomizationconditions is determined by characterizing thepowders produced during atomization. The axial gasvelocity as a function of distance from the nozzleexit (Cf. section 2.1) is measured and used as aninput in solving the momentum equation to determinethe velocity of droplets of different sizes. The relativevelocity between the atomizing gas and the dropletdetermines the heat transfer coefficient at the droplet-gas interface. This coefficient is used to calculatethe time-temperature history of droplets by applyingenergy conservation equation. The thermal historyof the droplet is used to evaluate the solidificationbehavior of the droplet by invoking solidificationtheory. A five-stage solidification regime comprisingof (1) cooling in the liquid state till nucleation (2)recalescence of the undercooled droplet (3) segregatedsolidification (4) eutectic solidification and finally(5) cooling in the solid state has been considered.Size-dependent undercooling of droplets based onvolume separation of nucleants15-16 existing in themelt has been employed. The above mentionedcomputations are performed initially on droplets ofspecific sizes. Subsequently, the characteristics ofthe spray are determined from the experimentallydetermined size of the droplets in the spray17. Thisincludes the spray enthalpy, which is an input forthe deposition stage and is used to calculate thethermal history of the deposit. A one-dimensionalheat transfer model, using a finite difference methodis employed to calculate the temperature of the depositby establishing a heat balance between the incomingenthalpy of the spray and the heat dissipated fromthe deposit. All the parameters utilized as input inthe model pertain to Al-4.5 wt. % Cu alloy. Thephysical properties of the gas are taken fromHolman18 whereas those of Al-4.5 wt% Cu alloyfrom Swaminathan19 and are given in Appendix I.

3.1 Droplet Dynamics and Thermal State

In spray atomization, the atomizing gas transfers apart of its kinetic energy to disintegrate the melt intodroplets and the remainder is used to accelerate thedroplets towards the deposition surface. It has beenreported17 that only about 3% of the energy of the

atomizing gas is utilized to atomize the melt. As aresult of this, there would be very little change inthe velocity of the atomizing gas due to the energyconsumed for atomization and hence the atomizinggas velocity measured without atomization can beused even for the case where atomization takes place.The solution of the momentum equation providesthe velocity of the droplet. In the present analysis,only a one dimensional flow is considered and hencethe radial component of the gas velocity has beenignored. Applying Newton’s law of motion on adroplet of diameter d in the vertical direction yieldsa generalized equation of the form.20

dtdV

m dd = ( )dgdgDdg VVVVCA −−ρ−

81

gmgm dd

gd ρ

ρ++ (1)

with the initial condition that Vd = 0 at time t = 0.The first term on the right hand side of Eqn. (1)denotes the drag force, the second the gravitationalforce and the third the buoyancy force acting on thedroplet. The drag coefficient CD arises because offlow separation around the droplet and is a functionof the Reynolds number (Re). The expression forCD 21 for a wide range of Reynolds number varyingfrom 0.1 < Re < 4000 is given by

Re21

Re

0.628.0

5.0++=DC (2)

A velocity dependent heat transfer coefficient isobtained by the well-known correlation of Ranz andMarshall22.

( )33.05.0 PrRe6.00.2 +=d

kh g

(3)

A generalized heat balance equation for a dropletduring solidification23 is given by

dtdf

Hdt

dTC

dtdH s

dd

pdd ∆−= (4)

Cpd and Hd are given by

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( ) ssLLpd fCCCC −−= (5)

( )( )sLsLfd TTCCHH −−−∆=∆ (6)

The L.H.S. in eqn. (4) denotes the rate of changeof enthalpy with time while the two terms in R.H.S.denote respectively the change in sensible heat ofthe droplet and the latent heat released as a result ofsolidification.

Assuming a linear crystal growth velocity for lowundercooling24 and a twinned spherical solidificationinterface given by Lee and Ahn12, the governingdifferential equation for heat transfer in a dropletassumes the following form

dtdT

C dpd = ( )dLi

sd TTk

dtdf

H −

( )gdd

TTdh

−ρ

−6

(7)

subject to the initial condition that Td = TL at x=0and t=0. The growth velocity for highly undercooledmelts shows a power law relationship with meltundercooling25.

However, owing to lack of information regardingthe value of Ki for highly undercooled melt, a linearrelationship has been considered which is true forsmall to moderate degree of undercooling of themelt.

The droplet temperature is obtained inserting theexpression for crystal growth velocity into eqn. (7).The temperature profile during recalescence isobtained by

+++−= tAxA

xAxAk

TTi

Nd 43

22

31

231

(8)

where the constants are defined as

:3

:2

32231

dC

HkA

dC

HkA

pd

di

pd

di ∆−=

∆=

( )dC

TThkA

dCh

Adpd

Lgasi

dpd ρ

−−=

ρ−

=6

:6

43 (9)

The details of the solution are given by Shukla et al16.Recalescence arrest temperature TR is obtained by

setting 0=dt

dTd i.e. when the rate of release of

latent heat slows down and equals the heat dissipatedinto the quenching medium. After the end ofrecalescence, further solidification of the dropletinvolves solute segregation. The fraction of solidgenerated during this mode by solidification can bepredicted by Scheil’s equation.

( )( )ok

dM

RMrs TT

TTff

−

−−

−−=1

1

11 (10)

It must be emphasized that Schiel’s equation26

assumes no diffusion in the solid state and completemixing in the liquid phase with equilibrium at theliquid-solid interface. The temperature profile duringthe eutectic solidification and in the solid state isobtained by solving Eqn. (7) with relevant conditions.

3.2 Heat Flow During Deposition

The modeling of heat transfer during the depositionstage follows the solution of droplet heat transferand their solidification behavior. The thermalcondition of the mass median particle diameter isassumed to represent the thermal condition of theentire spray17 and the total spray enthalpy iscalculated based on this. On the basis of thisassumption and with the mass flow rate of the meltknown, the incoming spray enthalpy is calculated.The equation governing the heat transfer in thepreform using an enthalpy formulation27 is given as

∂∂

∂∂

=∂∂

ρyT

yk

H(11)

where at time t = 0 and y = 0, T = Tspraycorresponding to the deposition distance. The averagethermal conductivity (k) is the mean of thermalconductivity of liquid and solid melt. Enthalpy hasbeen used in the above formulation to take intoaccount the change in heat content as a result ofsolidification. The computational domain in the ydirection (growth direction) is of length Ydep and isthe deposit height formed during the deposition

288


period. In a chosen computational time interval (sayt), the increment in height is y = t ( Ydep/tdep). Atthe end of each time increment, the temperature ofthe instantaneous topmost surface is put equal toTspray corresponding to the current deposition distance.At the bottom surface of the deposit, a heat fluxbalance yields

[ ]subbot TThyT

k −=∂∂

(12)

At the top surface of the growing deposit, the heatbalance is given by

(13)

In eqns. (11-13), H is the net enthalpy input at thetop surface of the deposit and is equal to thedifference between the enthalpies of the incomingspray and the topmost layer of the deposit and Y

• is

the deposition rate per unit area. In the absence ofmeasured values of heat transfer coefficient, in thepresent investigation a value of 1100 W m-2 K-1 hasbeen used for hbot during the deposition stage. Aconvective heat transfer coefficient (htop) value of200 W m-2 K-1 during the deposition stage and 100W m-2 K-1 during natural cooling in the post-deposition stage has been used. The spray impingingon the substrate imparts a high value of heat transfercoefficient (hbot) because of the intimate contactbetween the deposit and the substrate during thedeposition process. Similar values have been reportedby other investigators17. The gas velocity at thedeposition surface falls to a value close to around 50ms-1. At this value of gas velocity, the forcedconvective heat transfer at the top surface (htop) hasbeen reported to be around 200 W m-2 K-1 by Estradaand Duszczyk28 while a lower value is reported whenthe gas is turned off because then the cooling occursby natural convection. These values arecommensurate with those reported by otherinvestigators17. Enthalpy and temperature are relatedby the following relationships.

H =

( )ESSf TTCH −+∆+ for T > TL (14)

H = ( ) ( ) ( )SLssss TTCfTTCf −−+− 1

( ) ( )ESSfs TTCHf −+∆−+ 1

for TS < T < TL (15)

H = CS(T – TE) for T < TS (16)

In eqns. (14-16), the reference temperature forenthalpy measurement is TE, the eutectic temperature.The enthalpy term consists of the sensible heat ofthe solid till T = TS, the heat of fusion Hf, sensibleheat of the solid-liquid between TL & TS and thesensible heat of the liquid above TL.

4. RESULTS AND DISCUSSION

4.1 Droplet Velocity and Thermal State

The measured gas velocity showed an exponentialdecay with distance with a velocity decay profilerepresented by an equation of the form

−

+= Czz

g

o

BeAV (17)

where the constants A, B, zo and C are 15.88, 376.06,0.0326 and 0.080 respectively in appropriate unitsfor a reservoir pressure of 1.0 MPa. The gas velocitymeasurements were repeated three times and theerror was within ±2 %. The mass flow rate of thegas through the atomizer was measured by arotameter connected on-line and calibrated for aninlet gas pressure of 1.20 MPa in a mass flow raterange of 0.61-6.1 kg min-1 of nitrogen gas.

The variation in velocity of different-sized dropletsas a function of flight distance computed usingeqn. (1) is presented in Fig. 2. A comparison of thevelocity profiles of a wide size range of droplets inthe spray shows that a 20 m droplet attains amaximum velocity of 230 m s-1 in less than 0.1 mcompared to a maximum velocity of 100 m s-1 of a160 m size droplet attained at a flight distance of0.15 m. Other intermediate size droplets show asimilar behaviour. Larger size droplets, due to theirlarge inertia, are observed to accelerate and decelerateslowly at greater flight distance compared to smallsize droplets. The temperature profiles of differentsize droplets as a function of flight distance are

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presented in Fig. (3). These are obtained byemploying Eqn. 7 with appropriate modificationscorresponding to the solidification conditionmentioned in Section 3.0. Prior to solidification, thedroplets in the spray are subjected to differentundercooling depending upon their size. The presentwork, based on the analysis of nucleant free fractionof droplets in gas atomization process, facilitates topredict the size dependent undercooling of droplets.Considering droplet size limits of 10 and 180 mfor homogeneous and heterogeneous nucleationcondition respectively, the expression for sizedependent nucleation potency of droplets can beobtained as f( ) = a + bd–1.16 The undercoolingachieved by two widely different size droplets of 20and 160 m is 175 and 10 K respectively. Fig. 3shows the five distinct stages of cooling andsolidification for the 20 m droplet where completesolidification takes place at a flight distance of about

0.15 m. The droplet of 160 m remains in a mushystate till a much larger distance. Droplets ofintermediate sizes show similar behaviour.

4.2 Spray Characteristics

The spray characteristics represent the aggregateeffect of droplets comprising the spray under differentatomizing conditions. The sieve analysis of theatomized powders at atomization pressures of 0.8,1.0 and 1.2 MPa yielded the mass median particlediameters of 74, 64 and 60 m respectively. Thetemperature of these particle sizes at the desireddeposition distance was used to calculate the sprayenthalpy. The spray characteristics at depositiondistances of 0.35 and 0.45 m are shown in Table 1.A lower spray temperature and consequently highersolid fraction at larger deposition distance is observed.The effect of gas pressure on the spray enthalpy atvarious deposition distances is presented in Fig. (4)while the effect of superheat on the incoming sprayenthalpy is presented in Fig. (5). These figures areused to calculate the enthalpy of the incoming sprayat different deposition distances and degree ofsuperheat and is used as an input in Eqn. (11). It isseen that the spray enthalpy decreases with anincrease in the deposition distance owing to the factthat a longer flight time of the droplet to travellarger deposition distance facilitates heat removaland consequently a decrease in the incoming sprayenthalpy. The relationship between atomization gaspressure and incoming spray enthalpy howeverdepends on two opposing tendencies. A higheratomization pressure leads to an increase in the gas

Fig. 2 : Variation in gas and droplet velocity for a widesize range of droplets (Gas exit velocity=384 ms-1

Fig. 3 : Temperature profile of two widely different sizeddroplets during cooling from a melt superheat of100 K.

Fig. 4 : Effect of gas pressure on the spray enthalpy atdifferent deposition distances.

290


exit velocity and reduces the size of droplets due tomore efficient atomization29. Hence the sprayenthalpy is determined by the relative magnitude ofthese opposing effects.

The variation in spray enthalpy with melt superheat(Fig.5) shows that the spray enthalpy at a particulardeposition distance increases with melt superheat.At a deposition distance of 0.35 m, the spray enthalpyfraction increases from 0.60 to about 0.80 as themelt superheat is increased from 100 K to 200 K.The magnitude of this change is significant whencompared with the effect of atomising gas pressureon incoming spray enthalpy (Fig.4) where there is amarginal change in spray enthalpy owing to changinggas pressure. It is thus inferred that at a givendeposition distance, the melt superheat has asignificantly greater influence on the incoming sprayenthalpy than atomization gas pressure. This haspractical utility from an engineering point of view.It is easier to vary melt superheat than to increasegas pressure because of the associated problem ofexcessive pipeline pressure. Since the shape andmicrostructure of the preform depends upon the liquid

content impinging on the top surface of the preform,a judicious choice of melt superheat and atomizationgas pressure can produce preforms of optimum shapeand the desired microstructure of the spray-deposit.

4.3 Cooling Rate of the Spray-Deposit

A comparison of the measured and calculatedtemperature profiles at a nozzle to substrate distanceof 0.35 m (exp. 1) and 0.45 m (exp. 2) is depictedin Fig. (6) and Fig. (7) respectively. Thethermocouples Tc1 and Tc2 record the temperaturein the preform at 2.0 mm and 10.0 mm respectivelyfrom the substrate surface. The deposition time is19.0 s in exp. 1 and 34.0 s in exp. 2. Thethermocouple Tc1 attains a stable profile earlier thanTc2 because it is embedded earlier in the growingpreform. Tc1 in expt.1 records temperature close to580 oC while Tc2 records about 615 oC during thedeposition period. There is difference between themeasured and calculated values of the temperatureduring the initial stage of deposition and also in thepost deposition stage. During the initial stage of thedeposition, the thermocouples are the first to becovered by the spray because of their protrusionover the substrate and a cap of solidified alloy isformed. Therefore the temperature rise recorded iskinky. The perform gradually builds to a height tofinally embed the thermocouples and thereafter themeasured and calculated values coincide. Terminationof deposition is manifested by a sharp change in theslopes of the two curves. The temperature profile inthe post deposition regime does not exhibit anexponential decay profile as reported by otherinvestigators30. This difference could be due to theuse of a water-cooled copper substrate andconsequently a higher value of heat transfercoefficient in their investigations compared to a mild

Fig. 5 : Effect of melt superheat on the spray enthalpy atdifferent deposition distances.

Table 1THE SPRAY CHARACTERISTICS AT DEPOSITION DISTANCES OF 0.35 AND 0.45 m.

Deposition Spray Solid Fraction Spray EnthalpyDistance (m) Temperature (fS) (kJ kg-1)

(oC)

0.35 632 0.62 212

0.45 600 0.84 104

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Fig. 6 : Computed and measured temperature at adeposition distance of 0.35 m.

Fig. 7 : Computed and measured temperature at adeposition distance of 0.45 m.

steel substrate without a cooling arrangement usedin the present case.

On the basis of the computed temperature profiles,the cooling rate at a distance of 2.0 mm, 10.0 mmand the deposition surface in exp. 1 and exp. 2 arecalculated and are shown in Fig. 8 and Fig. 9respectively. It is worthwhile to note that at a distanceof 2.0 mm from the bottom of the deposit, an initialcooling rate of 2.5 K s-1 is experienced due to theinitial rapid heat loss to a cold substrate. As thedeposit height builds up, the incoming heat flux isnot readily dissipated, leading to a gradual decreasein the cooling rate. The cooling rate shows a sharpincrease at the termination of deposition and attainsa peak value of about 5 K s-1 which then decreasesand levels out at about 3 K s-1. The deposition surfaceexperiences heating during the deposition process.The cooling/heating rate is calculated on the basis of

Fig. 8 : Variation in cooling rate with time in the preformat a deposition distance of 0.35 m

Fig. 9 : Variation in cooling rate with time in the preformat a deposition distance of 0.45 m.

difference in temperature between the present andpast values at a given location. The present value oftemperature at the deposition surface is close to theaverage spray temperature while the past valueincludes the effect of heat dissipation. The differencein these values is initially large but graduallydecreases as the heat dissipation through the substratedecreases with time. The heating rate changes tocooling rate when the deposition process is terminatedand then a peak cooling rate of8 K s-1 is achieved. The cooling rate then decreasesin a similar fashion to a constant value of about3 K s-1. The larger drop in the cooling rate of thedeposition surface as compared to the location closerto the bottom surface is due to the sudden removalof incoming heat source at the top surface while thebottom still continues to receive heat from the over

292


lying preform material. The cooling rate profile at10.0 mm from the bottom is also shown on the samegraph. The lower cooling rate at this location,compared to the bottom surface is because of itsproximity to the continuous heat source at the top.Interestingly, the nominal difference in the coolingrates experienced by the different surfaces gives aninsight into the nature of evolution of microstructuresin spray deposited materials which is dealt in thefollowing section. The computed cooling rate curvefor exp. 2 is of a similar nature. The cooling rateat the bottom surface in this case is lesser due to thereduced heat transfer rate at the bottom surfaceresulting from the smaller temperature gradient acrossthe preform-substrate interface as a result of lowerspray temperature.

4.4 Microstructural Features

The microstructures of the spray formed alloy at adeposition distance of 0.35 m are shown inFig. 10 (a,b,c). The height of the spray deposit was3.5 cm. These microstructures invariably showequiaxed grain morphology of the primary -phaseat different locations in the spray deposit. Eventhough the spray deposited alloy shows considerableuniformity in grain size, small variation in grainsize is observed at different locations in the depositin the transverse direction. The bottom section ofthe deposit reveals maximum grains in the size rangeof 12 to 40 m with a mean grain size of 25 m.At this location, a mixed grain size distributionconsisting of smaller grains coexisting with largerones is observed. Absence of splat boundaries at thebottom surface indicates that either the spraycontained sufficient amount of liquid to check theimmediate freezing of droplets or the heat transfercoefficient at the deposit-substrate interface wassufficiently low, resulting in reduced heat loss. Thegrain size increases with increasing distance towardthe middle section of the spray deposit. In the middlesection of the deposit, the grain size distributionbecomes more uniform with majority of grains lyingbetween 25 to 35 m with a mean grain size of 30

m. The grain size continues to increase even abovethe middle section upto 30 mm from the bottom. Asmall decrease in grain size is observed in the topportion on the preform. In the top section, the meangrain size is observed to be 28 m. As in the bottom

Fig. 10 : Micrographs showing equiaxed grain morphologyin spray deposited alloy (a) bottom (b) middle and(c) top section. The deposition distance is 0.35 m.

section, both smaller and larger grains are also visiblein the top portion of the deposit. A mixed type ofgrain size distribution at the bottom and top portionsof the deposit and a uniform distribution at the middleseems to evolve due to two different types ofsolidification conditions at these locations. As theresults of modeling in Figs.(6&7) indicate, a liquidpool builds up on the deposition surface during

293


deposition. The spray on the deposition surface afterthe deposition has progressed for some time, impingeson a pool of liquid under relatively steady condition.The spray impinges on this liquid pool, whichstabilizes its impact and provides sufficient freezingtime and consequently uniform and larger grains. Incontrast, at the top and bottom regions, unsteadydeposition conditions prevail due to abrupt terminationand commencement of deposition. As a result of thisand the smaller freezing time at these locations, amixed grain microstructure with a smaller mean grainsize is produced. Alternatively, it has been reported30

that smaller particles which are in a fully solidifiedstate at the time of impingement may act as anucleation site for the surrounding melt. The solidifiedparticles undergo annealing and their boundaries arenot discernible in the final microstructure. Becauseof the high temperature annealing, microstructuralcoarsening would further influence the grain size ofthe deposit. The occurrence of a mixed grainmicrostructure could be the result of finer grainformed during annealing surrounded by larger grainsformed by the nucleation caused by the solidifiedparticle. The solidified particles act as efficientnucleation sites on locations which have a low liquidcontent to check their re-melting. The bottom andtop surface of the deposit are locations of low liquidcontent on the deposition surface. A considerablegrain refinement is noticed at different locations inthe deposit at a deposition distance of 0.45 m. Theheight of the deposit in this case is 30 mm. Themean grain size increases from 12 m in the bottomsection to 15 m in the middle. A mixed type ofgrain size distribution is more pronounced in thebottom section. As in the previous case, the meangrain size decreases to 10 m in the top portion ofthe deposit. In the present investigation the averagecomputed cooling rate at different locations withinthe preform is shown in Fig. 11. The average coolingrate is calculated with the help of the followingexpression

f

Savg t

TTT

−= max&

(18)

where Tmax is the maximum temperature attained ata location during the deposition process. The coolingrates calculated using Eqn. (18) are the averagecooling rates at a particular location throughout the

deposition and post-deposition regime. The averagecooling rate is used to gain an understanding aboutthe variation in the grain size within the deposit.The average cooling rate has a high value(~ 15 oC s-1) at the bottom of the deposit(y = 0 mm). This is due to the initial chilling effectof the substrate. The cooling rate drastically falls toa value of around 2.5 oC s-1 at about 1.0 mm fromthe substrate. Thereafter, it gradually increases withincreasing deposit height, attaining a value of5 oC s-1 at the top of the deposit in exp. 1 and7 oC s-1 in exp. 2. The average cooling rate at aparticular location is higher in exp. 2 because of thelower freezing time. The cooling rate increases withdeposit height because the contribution of the increasein Tmax with deposit height is larger than thecorresponding change in tf.

Attempts have been made to establish an empiricalrelationship between an average cooling rate andgrain size.10,13,31-32 Empirical correlations for coolingrate and secondary dendrite arm spacing are reportedin literature10 to be of the form

nTADAS −= & (19)

where DAS denotes the dendrite arm spacing, T& isthe cooling rate and A and n are constants. For7075-Al alloys, reported values of A and n as 45 m(K s-1)-n and 0.25 respectively10. For other alloys, asimilar relationship is reported with different valuesof the constant. Although the physical significanceof such a relationship is not clear, nevertheless this

Fig. 11 : Computed average cooling rate across the depositat deposition distances of 0.35m and 0.45 m.

294


relationship is useful for the prediction of the scaleof microstructure based on thermal measurements.

Grain size measurements were made by theseinvestivators at the same locations and a correlationbetween the average cooling rate and the grain sizeestablished. In the case of spray formed alloys, thegrain size is taken as the primary dendrite spacing.In the present investigation, the values of A and nare calculated to be 36.28 and 0.265 respectivelyfor a deposition distance of 0.35 m by using themeasured grain size and calculated cooling rate inEqn. (19). However when these values are used toestimate the grain size variation at a depositiondistance of 0.45 m, there is appreciable error. Forexample, using the estimated values of A and n, amean grain size of 15 m would be obtained undera cooling rate of 28 K s-1. Such large values ofcooling rate are not encountered during spraydeposition as observed from the thermal profile ofthe deposit. If the data for cooling rate and grainsize obtained at a deposition distance of 0.45 m isfitted into a power law relation (Eqn. 19), the valuesof A and n obtained are 56.2 and 0.81 respectively.It is therefore inferred that cooling rate is not thesole determining factor in controlling grain size. Inexpt. 1, where a sufficient liquid pool exists at thetop, it is proposed that re-melting of dendrites leadsto a reduction in the available nucleation sites. At alarger deposition distance of 0.45 m, grain coarseningis reduced as a result of insufficient liquid.33

5. CONCLUSIONS

The following conclusions are drawn from the presentinvestigation:

(1) The cooling rate of the spray deposit variesfrom 1-10 Ks-1.

(2) The maximum temperature recorded at a locationof 10.0 mm is 580 oC and 615 oC at a depositiondistance of 0.35 and 0.45 m respectivelyindicating that a larger spray enthalpy at asmaller deposition distance leads to a highertemperature of the preform.

(3) The melt superheat largely determines theincoming spray enthalpy compared to atomizationgas pressure.

(4) The microstructure of the spray deposit showsequi-axed grain morphology of the primaryphase. The microstructure of the spray depositdoes not appear to be governed solely by thecooling rate associated with the spray depositionprocess.

ACKNOWLEDGEMENT

One of the authors (Prashant Shukla) wishes to thankthe Council for Scientific and Industrial Research(CSIR), India for the financial assistance providedunder the CSIR Research Grant No. 9/13/963/2000under which this work was carried out.

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APPENDIX I

Thermo-physical properties of Al-4.5 wt % Cu alloy

Heat of fusion ( Hf) 3.48 103 J kg-1

Density ( d) 2800 kg m-3

Specific heat of liquid (CL) 982 J kg-1 K-1

Specific heat of solid (Cs) 900 J kg-1 K-1

Surface energy ( SL) 1.31 10-2 J m-2

Thermal conductivity of liquid (kl) 97.8 W m-1 K-1

Thermal conductivity of solid (ks) 211.4 W m-1 K-1

Melting temperature of Al (TM) 934 K

Liquidus temperature (TL) 919 K

Solidus Temperature (TS) 833 K

Eutectic temperature (TE) 821 K

Equilibrium partition coefficient (ko) 0.14

Thermo-physical properties of N2 gas

Specific heat (Cpg) 1.04 J kg-1 K-1

Thermal conductivity (kg) 2.6 10-2 W m-1 K-1

Density ( g) 1.16 kg m-3

Kinematic viscosity (µg) 1.78 10-5 N s m-2

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