Investigations into the plasma spray process

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<ul><li><p>Surface and Coatings Technology, 37(1989)349-358 349</p><p>INVESTIGATIONS INTO THE PLASMA SPRAY PROCESS*</p><p>R. C. DYKHUIZENFluid and Thermal Sciences Department, 1513, Sandia National Laboratories,Albuquerque, NM 87185 - 5800 (U.S.A.)M. F. SMITH</p><p>Metallurgy Department, 1833, Sandia National Laboratories, Albuquerque,NM 87185 - 5800 (U.S.A.)(Received August 24, 1988)</p><p>Summary</p><p>We have previously described a simple analytical model which wasdeveloped to examine momentum and thermal transfer from the plasma jetto the particles in a low pressure plasma spray deposition process. Thismodel correctly predicted the experimentally observed maximum in particleacceleration at intermediate chamber pressures. The calculated results werein good agreement with experimentally measured particle velocities. In thepresent study, this model has been used to investigate the effects of particlesize and mass density on particle velocity. The model has also been used toexplore the effect of variations in selected process parameters on the thermalresponse of the particles. The analytical and experimental results for particlevelocity are again in good agreement, with substantially lower accelerationrates and lower peak velocities for larger, more massive particles. The resultsof the thermal calculations indicate that particle melting is influenced bymany parameters. Better particle melting is achieved at higher chamberpressures. Detailed thermal data which would verify the thermal model arenot yet available; however, the predictions of the thermal model appear tobe in qualitative agreement with empirically developed spray conditions forgood particle melting. The model indicates that difficulties in meltingrefractory materials at very low chamber pressures are related to decreasedplasma temperatures and plasma densities at low chamber pressures.</p><p>1. Introduction</p><p>For nearly 30 years, plasma spray technology has been used to deposita wide range of materials for many different applications. Over the past15 years, demand for high quality coatings of reactive materials has led to</p><p>*Paper presented at NTSC 88, the National Thermal Spray Conference, Cincinnati,OH, U.S.A., October 23 - 27, 1988.</p><p>0257-8972/89/83.50 Elsevier Sequoia/Printed in The Netherlands</p></li><li><p>350</p><p>the development of plasma spraying in vacuum chambers at reduced pres-sures. Despite this long and successful history, the physics of the plasmaspray process is poorly understood. Process parameters are still optimized byempirical methods. The progress of a combined analytical and experimentalstudy designed to investigate the controlling parameters of the plasma sprayprocess is discussed in this paper. Our experimental set-up and preliminaryanalytical results were described in a previous paper [11. These resultscompared favorably with experimental data especially at low chamberpressure levels and short distances from the gun. This current paper presentsimprovements to the analytical model which make possible better com-parisons with experimental results, and give more information on the heattransfer between the plasma gas and the spray particles.</p><p>2. Analytical model</p><p>An analytical model of the plasma gas flow, particle velocity and tem-perature has been developed in order to interpret an understand experi-mental results. The model incorporates many simplifying assumptions thatpermit rapid model development and short computational times. However,it is hoped that enough physics is incorporated so that reasonably accurateresults are obtained, and all trends with spray parameters are properlyrepresented.</p><p>All of the gases are assumed to be perfect gases with constant specificheats, and no corrections are made for the partial ionization of the gases.The gas flow is assumed to vary in only one dimension (that being the direc-tion of the flow) inside the plasma spray gun. Outside the gun, correlationsare used to track only the center-line velocity and temperature as the jetinteracts with the ambient chamber atmosphere.</p><p>Experimentally measured inlet pressure, temperature and flow rate ofthe arc gas are treated as input conditions for the analytical model. Themeasured power input (taken as the power delivered to the spray gun minusthe power lost to the cooling water) is then added to the arc gas flow. Weassume a constant cross-sectional flow area during the heating process.Although this is not quite true for the typical spray gun geometry, it sim-plifies the calculation so that a Rayleigh line calculation for compressiblegas flows [21 can be used to model the heat addition process. There is alimit to the amount of energy that the arc gas can absorb. The gas cannot beaccelerated to speeds in excess of sonic velocity by the addition. Thereforeany additional power that remains after this amount of heat addition isassumed lost. If this lost power turns out to be a large percentage of thetotal power delivered to the arc gas, then one is alerted to possible experi-mental measuring errors or modeling errors.</p><p>The next step in the model calculation is to add the powder-carryinggas flow to the arc gas flow. Since the powder gas injection ports are atapproximately right angles to the flow, this flow carries in no axial mo-mentum. Mixing of the two gas streams is assumed to occur instantly; and</p></li><li><p>351</p><p>momentum, energy and mass conservation equations are used to predict theresulting flow conditions. The addition of the powder injection gas results ina flow which is slightly supersonic owing to the reduction in the tempera-ture. The pressure of the gas flow is also reduced owing to the requiredacceleration of the powder gas flow.</p><p>Up to this point the spray chamber pressure level does not affect thegas flow calculation. However, as the gas exits from the spray gun, it isassumed to expand isentropically to the chamber pressure. This results in anacceleration of the gas flow if the chamber pressure is lower than the gaspressure and a deceleration if the chamber pressure is higher. Since the Machnumber of the gas prior to this isentropic process is typically very close tounity, any deceleration or acceleration results in an increasl in the flow areaof the plasma jet. No attempt was made to match the calcUlated gas expan-sion to the actual geometry at the expansion end of the spray gun. The twoarea ratios would match only coincidentally (a properly expanded nozzle)at only one chamber pressure. The experimental results presented here fora variety of chamber pressures were from a single gun with an exit areaexpansion ratio of approximately two. This modeling approximation affectsour results in many ways. First, it makes the model easy to implementbecause it avoids the multidimensional calculational problems associatedwith underexpansion, overexpansion and separation in nozzle flows. How-ever, the model may be missing some important physics resulting from theseprocesses. It cannot predict the shock diamonds which form because ofmultidimensional effects. These diamonds are visible at low chamber pres-sures. Also, the model cannot represent differences between nozzle geome-tries with different expansion regions. Nevertheless, reasonable agreementbetween the theoretical and experimental data justify the simplifying as-sumptions made.</p><p>After the isentropic expansion, the model uses a correlation [3] for thecenter-line velocity decay of the jet. Only the center-line gas velocity iscalculated. This allows comparison with experimental data for particlevelocities along the center-line. The jet gas velocity is reduced as it penetratesthe chamber atmosphere owing to the entrainment of ambient gas. The jetcenter-line thermodynamic temperature is also reduced owing to the entrain-ment. Witze [3] suggests use of the Kleinstein [41correlation to determinethe reduction of the jet total enthalpy caused by entrainment of the ambientatmosphere. This, however, proved to be unacceptable in this application.This correlation resulted in the jet temperature reduction occurring soonerand at a faster rate than the jet velocity reduction. This is not physicallyreasonable since it is assumed that the entrainment of the ambient atmo-sphere is the major factor for both. In extreme cases, use of the Kleinsteincorrelation resulted in negative absolute static temperatures for the jet.This was due to the large reduction in the total temperature without anyaccompanying reduction in the kinetic energy of the jet.</p><p>To achieve more consistent modeling of the jet static temperature,the following model was developed. First, it is assumed that the center-line</p></li><li><p>352</p><p>of the jet can be envisioned as a one-dimensional flow of variable area.The mass, momentum and energy balances can be easily written. In thesebalances, it is assumed that changes in the mass and total energy occuronly as a result of entrainment of ambient fluid. It is also assumed that themomentum of this flow remains unchanged and that no pressure gradientexists. The following equation is then derived for the local total enthalpy.</p><p>V / V\H= H+ (]~~~~)J~I0 (1)</p><p>v~ \ V~JIn the above, H3 is the total enthalpy of the jet, H0 is the enthalpy of</p><p>the ambient fluid, V~is the jet exit velocity and V is the local velocity. Useof the Witze [3] correlation for the local velocity then enables the local totalenthalpy to be determined. The jet temperature is obtained by subtractingthe kinetic energy from the total enthalpy, and the local jet density isobtained from the jet temperature. The ambient fluid temperature is as-sumed to be constant (at 600 K), independent of both the ambient pressureand the axial location.</p><p>The results of the plasma jet center-line temperature and velocitycenter-line calculations are used to evaluate the drag and heat transfer ona single particle assumed to travel along the center-line of the plasma jet.The representative particle is modeled to be spherical, and its volume isconsidered constant throughout the heating process. The mass flux of theparticles is low enough not to affect appreciably the momentum or energyof the gas flow.</p><p>The particle is initiated with zero axial momentum at the axial locationof the powder injection ports. The relative velocity between the plasma andthe particle results in a drag force [51that accelerates the particle. The dragcalculation includes non-continuum effects, which significantly influence thedrag on small particles. As the plasma jet slows down, owing to the entrain-ment of the ambient gas, it eventually has a lower velocity than the particle.Then the drag force slows the particle down. This process occurs at largerdistances from the gun as the pressure is lowered.</p><p>The thermal model assumes a high Biot number, so a single temperatureis used to represent the thermal state of the particle. A recovery factor [61of unity is used to account for the viscous dissipation and stagnation tem-perature rise of the plasma gas flow. The thermal energy transfer model alsotakes into account non-continuum effects [7]. The particle temperature isfixed at its melting temperature (once this is reached) until the particleabsorbs enough energy to melt completely.</p><p>The current model does not include thermal radiation heat transfer.Moreover, the only effect of ionelectron recombination on the heat transferprocess is its effect on the thermal conductivity of the gas. The gas is as-sumed always to be in thermodynamic equilibrium, and higher temperaturestherefore cause higher fractions of the gas to be ionized. This results in ahigher conductivity coefficient. Owing to the nature of the arc-generated</p></li><li><p>353</p><p>plasma, a larger than equilibrium amount of the plasma gas may be ionizedin the actual plasma spray jet.</p><p>Many properties are required for the thermal model. The gas viscosityand conductivity are treated as functions of temperature [8], and theeffective mixture values are obtained from gas mixture correlations [9]. TheWilke method is used for the viscosity, and the Browkaw method is used forthe conductivity of gas mixtures. The particle heat capacity is also treated asa function of temperature [10] while it is in the solid state. Latent heat ofmelting is included in the calculations. The temperature variation of theparticle heat capacity in the molten state was not available.</p><p>3. Results</p><p>The following results have been obtained with the analytical modeldescribed in this paper. Comparisons with experimental data are providedwhen the data are available. Figure 1 shows the plasma velocity predictionsfor the conditions in Table 1. Figure 2 shows the plasma temperature. Theinitial changes in these figures depict the assumed isentropic expansionregion. This is followed by the constant potential core region. The later</p><p>TABLE 1Experimental parameters</p><p>Input gas pressure 160 kPaInput gas flow rate 45 x 106 mol s~1Input gas composition 72% Ar, 28% HeGross power 31.2 kWNet power 15.2 kWGun flow area 27.8 X 10~ m2</p><p>4000 -~-~</p><p> 600 Torr</p><p>~.- 3000 ( \ 300 Torr/ \ 50</p><p>Distance from Powder Inlection Ports (cm)Fig. 1. Computed plasma gas velocity profiles.</p></li><li><p>354</p><p>:::: ~3000 -</p><p>0 ~0 10 20 30 40</p><p>Distance from Powder Injection Ports (cm)Fig. 2. Computed plasma gas temperature profiles.</p><p>/ ~ 68~At2O3</p><p>&gt; / /_._~ 200 59 cm T~gsto~ ~l</p><p>Distance from Powder Injection Ports (cm)Fig. 3. Comparison of computed and experimental particle velocities for 50 Torr spraychamber pressure.</p><p>changes reflect the slow-down and cool-down caused by chamber gas entrain-ment. These gas conditions are then used to calculate the particle response.</p><p>The model best predicts the particle velocity obtained when sprayinginto a very low pressure chamber. Figure 3 shows a comparison of thevelocity profile for different sized particles sprayed into a chamber main-tained at 50 Torr. The model properly accounts for the different sizes anddensities of the particles that were used. As expected, the lighter and lessdense particles approach the gas velocity most rapidly.</p><p>Figure 4 showG a comparison of the experimental and predicted velo-city profiles for a single-size particle sprayed at the three chamber pressurelevels. As reported earlier [11, the model predicts the proper trends, withlarger initial particle accelerations at an intermediate pressure. However,this plot shows that the differences between the predicted and measuredvelocity profiles become greater as the chamber pressure is increased. This isthought to be due to the increased interactions of the jet with the ambientatmosphere at the higher pressures. Since that is the weakest point of themodel (see next section), the errors of approximation are more pronounced</p></li><li><p>355</p><p>600 600 Torr</p><p>0102030600 </p><p>300 Ton-</p><p>50 Torr</p><p>49 wn frJ203</p><p>0 I I0 10 20 30</p><p>Distance from Powder Injection Ports (cm)Fig. 4. Comparison of computed and experimental A1203 particle velocities for variousspray chamber pressures.</p><p>at the higher pressures. The assumption that the temperature of the chamberatmosphere is independent of the chamber pressure level needs to be inves-tigated experimentally. Use of different chamber temperature levels at eac...</p></li></ul>

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