Coupled Coating Formation Simulation in Thermal Spray Processes using CFD and FEM

Transcription

1 Vol. 3 (2) June 2011 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM J. Prehm C, L. Xin, K. Möhwald, Fr.-W. Bach Institute of Materials Science, Leibniz University Hannover GERMANY Received: 10/11/2010 Revised 24/12/2010 Acceted 23/06/2011 Abstract This aer deals with the simulation of coating formation in Thermal Sray rocesses. That means that imingement and flattening of molten metal- or ceramic articles with a diameter of about 50 microns on a rough surface have to be regarded. In this work, this is accomlished use of the Volume of Fluid method. The disadvantage here is that only the ure flattening rocess can be considered. In order to imlicate the shrinking of the articles due to cooling down after solidification, which is resonsible for the occurrence of ores and thermal stresses, a Finite Element calculation is done subsequent to the CFDcalculation. After the FEM calculation has finished, the newly generated, shrinked article shae has to be re-imorted into the CFD grid. Keywords: Thermal Sraying, atmosheric lasma sraying, simulation, coating formation, Volume of Fluid method, article sreading, ore formation 1. Introduction The aim of this work is to simulate coating formation in the field of thermal sray rocesses. Here, mainly the atmosheric lasma sray rocess is regarded. In atmosheric lasma sraying (APS), the sraying articles are alied onto the substrate, in order to rovide a coating. This is done by use of a lasma beam. To realize this lasma beam, an arc between the cathode and anode is generated in the so-called lasma torch. In the hottest zone of the lasma cone, temeratures of about K occur. The coating material in form of owder is injected into this lasma beam, where it is raidly heated, molten and accelerated. Deending on the chosen rocess arameters, the owder articles iminge at a certain seed and temerature on the substrate. Most of the revious simulations concerning this kind of coating formation can be divided into two categories: The first category covers simulations with which the imact and the sreading of molten articles on the substrate were calculated with the "Volume of fluid" (VOF) method [6]. One disadvantage here is, that the number of article imacts is limited in these cases a few dozen, because of the extremely high comutation time. The mean influence of arameters e.g. article and substrate temerature, article size as well as imact velocity and angle were examined in various ublications [4, 13]. Meanwhile rough substrates are also taken into account [9], while in earlier simulations merely the imact onto flat substrates was investigated. In the second category C Corresonding Author: Jens Prehm rehm@iw.uni-hannover.de All rights reserved. ISSR Journals PII: S (11)3289-X 89

2 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM stochastic models were used in order to simulate coating formation. Here, neither the imact of single articles nor their solidification were comuted. Instead of this, the form of the imacted articles was given on the basis of micrograhs of coatings or revious simulations of article imacts [3, 10]. With such statistical techniques several hundred articles can be included into the modelling of the coating formation. All the above mentioned models are not caable to comute orosities. If necessary they must be integrated into the model, later. Aart from simulations which regard only the coating structure, also rocedures exist, which try to recalculate the mechanical behaviour of the thermal srayed coating. For this, the Finite Element Method (FEM) is used. The inut data for such simulations is normally gathered from micrograhs or measurements. Since orosity is a characteristic roerty of thermal srayed coatings, the ore formation lays a central role within the simulation of the coating formation [15]. Therefore, this article describes a method which allows to comute both, the flattening (with hel of CFD) rocess and the subsequent cooling down rocess (with hel of FEM), which is resonsible for the shrinkage of the articles. 2. Aroach 2.1. CFD Modelling The Volume of Fluid Model At first, the imact, the sreading and the solidification of a molten article on the substrate are comuted with CFD. Here, the volume of fluid algorithm (VOF) is used, which determines the free surface of the article in the comutational grid, time-resolved. In our calculations we use a two hase VOF-Model. The rimary hase is the surrounding gas (air), while the secondary hase consists of the molten article. For the volume fraction of a article in a cell of the comutational grid, the following can be obtained: α = 0 : the cell contains no fluid (article fraction) α =1 : the cell filled with fluid 0< α < 1 : the cell contains an interface between article and gas The transort equation of this volume fraction is calculated via the following conservation equation: 1 ρ r ( αρ ) + αρν ( ) = 0 t (1) The volume fraction of the rimary hase - i.e. the gas - follows as: α +α =1 g (2) In order to discretize equation (1) an imlicit scheme is used [5]: n+ 1 n+ 1 n n α ρ αρ n+ 1 n+ 1 n+ 1 V U f, f Δt f + ( ρ α ) = 0 (3) 90

3 A single momentum equation is solved throughout the domain, and the resulting velocity field is shared among the hases. The momentum equation, shown below, is deendent on the volume fractions of all hases through the roerties ρ and μ. The VOF model treats energy, E, and temerature, T, as mass-averaged variables: E = ( α ρ E + α ρ E )/ ( α ρ + α ρ ) g g g g g (4) where E q for each hase is based on the secific heat of that hase and the shared temerature. The roerties ρ eff and λ eff (effective density and effective thermal conductivity) are shared by the hases. The density is calculated as: ρ = α ρ + (1 α ) ρ, (5) eff g g whereas the effective thermal conductivity is obtained by: λ = α λ + (1 α ) λ eff g g The energy equation is: r ( ρ eff E) + ( ν( ρ eff E + )) = λeff T t (6) (7) As indicated above, a solidification model is imlemented in the VOF method [11, 12] Geometry and hysical roerties of the model At Thermal Sray rocesses the surface, that is to be coated, is roughened by use of grid blasting. That means that corundum articles with defined size fractions are blasted to the substrate. In order to consider this aroach in the simulations, an algorithm which can take into account the deformation of the surface due to the imact of the shot during grid blasting was develoed. In this model the form, the diameter, the deth of enetration and the quantity of the shot can be varied. Moreover a secific attenuation factor is integrated in the model. By hel of Laser Scanning Microscoe analysis, witch has a sacial resolution of about 1 nm, it is ossible to measure the roughness of grid blasted surfaces saceresolved. Hence the simulated surface toologies can be attuned to reality. The so measured roughness eaks are about 30 μm. Fig. 1 shows a simulated surface toology of the substrate. The basic material of this substrate is steel (1.0037), while for the sraying articles a ceramic is used. Here alumina goes into action, because it is a widely used coating material in the fields of corrosion rotection and thermal barrier coatings. In the following calculations the steel substrate has an initial temerature of about 400 K, while the temerature of the alumina articles is about 2400 K. This means, that the melting temerature of alumina (aroximately 2323 K) is exceeded and that the individual alumina articles are molten, so that they can be treated as a fluid in the CFD simulation. As temerature deendent roerties of liquid alumina the following variables were used: density, secific heat, conductivity, surface tension and as a very imortant issue concerning the flattening rocess, the viscosity. Moreover the latent heat is integrated into 91

4 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM the model. The temerature deendent surface tension of liquid alumina is taken from the following formula [17]: 5 σ ( T) = ( T T m ) (8) This formula is based on surface tension measurements in the temerature range of 2190 K to 2500 K. The surrounding gas is treated as air with the temerature deendent roerties of an ideal gas. In order to obtain initial values for the article diameter, the velocity and the temerature, measurements were done. Velocity and diameter are measured with hel of a newly develoed article diagnostics system, the article shae imaging (PSI) [7, 16] and moreover by use of article image velocimetry [2], while the surface temerature measurements are obtained by sectroscoic methods [8]. Figure 1. Simulation of a grid blasted substrate Comutational grid and boundary conditions An examle of the comutational grid can be found in Fig. 2. The blue colored surfaces indicate the outlets. They are defined as ressure-outlets at oerating ressure with a total backflow temerature of about 700 K. At the dark red colored surface a wall boundary is used, which reresents the surface. In the case of the first flattening article, only the steel surface has to be considered. Afterwards one has to distinguish, whether the wall consists of the steel substrate or of a formally solidified alumina article. The cylindrical zones in the grid indicate the initial ositions of the articles, just before iminging. This kind of geometry was chosen, in order to minimize the number of cells in the grid. With hel of samle calculations it could be ensured that such a grid geometry delivers retty good aroximations, because the gas flow shows no significant influence. By use of this kind of grid geometry the total number of cells could be decreased from aroximately 5 million cells to about 2 million cells, which significantly reduces the calculation time. The comutational grid, used in the simulations was made out of tetra elements. These elements have an average size from about 1 micron u to about 3 microns, deending on the osition in the grid. The regions, where the flattening and solidification of the articles takes lace, are meshed with smaller element sizes, while in regions, where no significant velocity and ressure changes are exected, the element size is increased u 92

5 to three times. Fig. 3 shows a cross section of the grid. Here the cell size distribution can be seen. Figure 2. Examle of a comutational grid for CFD calculations In the calculations the PISO algorithm was used for ressure-velocity couling. On the basis of ast exerience it could be shown, that a fixed time stam of 5.0 e -10 s is the most suitable solution, in order to obtain stable results. In Fig. 4 the velocity field of a flattening article onto already solidified articles is shown. Fig. 4a illustrates the initial osition of the article at the start of the calculation. The initial velocity magnitude was 150 m/s in negative vertical direction. In Fig. 4b the flattening rocess has almost finished. The flow time at this oint is 0.5 μs. These calculations were carried out with the commercial CFD software Fluent. Figure 3. Cross section of a comutational grid, showing the cell size distribution 2.2. Couling of CFD and FEM As to be seen in Fig. 4, with use of CFD the flattening rocess of the articles can be successfully calculated. The effects that occur due to cooling down of the article, e.g. the shrinking of the articles and the constitution of micro ores, cannot be treated with CFD. On the other hand, exerimental investigations of the coating roerties indicate, that these effects have a significant influence. In order to accomlish the couling of CFD and FEM, the stes, figured out in Fig. 5 have to be realized. Beyond the arameters that directly result of the CFD-calculation, the most imortant task is to carry out a contact definition 93

6 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM between article and substrate or rather between two colliding articles. This contact definition is deendent on: 1. the contact time 2. the temerature difference between article and bedrock 3. the distance between article and bedrock The so called contact time is the minimal time frame, which is needed that diffusion rocesses with the substrate material can take lace. Figure 4. Velocity fields of a flattening article Figure 5. Schematic of the couling rocedure These above-mentioned arameters have to be obtained out of the CFD-calculation. For this reason, the CFD-model was modified. A new rimary zone in the fluid regime of 94

7 the grid was created (see Fig. 6). This zone, which is ositioned at the bottom layer of the grid, is the only area, where contact between the article and the bedrock is ossible. This newly created zone is analyzed after every time ste and the arameters: volume fraction of the article, temerature and flow time are written to a file, so that they can be rocessed afterwards. Fig. 7 shows a front view of the substrate with contact areas at different contact times. In the red colored areas, the conditions for the secific contact definitions are met. The contact time in Fig. 7a is e -8 s, while the contact time in Fig. 7b was chosen as 5.0 e -8 s. Which value is the most realistic one, must be comared with exeriment. Figure 6. Possible contact zone Once the contact areas are defined, the FEM-calculation can be set u. First of all, the shae of the flattened article has to be extracted out of the CFD grid. In order to transfer this shae into a Finite Element volume mesh, the commercial meshing tool Hyermesh was used. During the FEM-calculations, the heat transfer in the substrate in thickness direction is not modeled. In order to justify this, the thermal diffusion distance was estimated. The thermal diffusion distance can be defined as: s : = α t (9) d th c 6 7 With tyical values of α th = 1e m²/s and tc = 1e s, the thermal diffusion distance 7 can be estimated to = 3e m. Due to the fact, that this value is significantly smaller than sd the average cell height of about one micron, the heat transfer was neglected. After the FEM-calculation has finished, the newly generated shrinked article shae has to be re-imorted into the CFD grid, where it is now art of the surface with the thermal roerties of alumina. 95

8 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM 3. Results Figure 7. Contact definition at different contact times, a) 1.0 e -8 s; b) 5.0 e -8 s The FEM calculations were done with the FEM software Abaqus. As a result, one can see in Fig. 8 the shrinking of a article due to cooling down. The maximum dislacement due to cooling down is about 1 micron. Since the average height of a flattened article is about the same dimension, this result demonstrates the imortance of FEM calculations at coating formation simulations. Moreover the curling u of the article edges can be observed, Fig. 8. Most of the bottom side of the flattened article is bonded to the substrate, so that it cannot contract. On the other hand, the uer surface shrinks, which causes the edges to curl u. The curling u of the edges is u to one micron in the vertical direction. Hence this effect has a significant influence to the formation of micro ores. In the field of Thermal sraying, curling u is a well known effect. In [14] this effect is investigated at single molten metal dros. In addition to the exeriment an analytical model of curlu angle is resented. Figure 8. Particle shrinking and curling-u due to cooling down The constitution of micro ores is an interlay between the shrinking effects as described above and the fact that the mold filling during sreading is not comletely guaranteed. Fig. 9 shows such micro ores witch are formed throughout the rocess of sreading and cooling down. 96

9 Figure 9. Pores at the background of a article A verification of the simulation can best be determined by use of cross sections, obtained from real coatings. The steel secimen was coated using a trile-cathode lasma torch [1]. The sray owder was alumina having a article size of 22 μm to 45 μm. In Fig. 10, a comarison of exeriment and simulation is illustrated. The diverse colours indicate different articles. Both, the ore content and size as well as the article shaes are in good qualitative agreement. 4. Conclusion Figure 10. Comarison of exeriment and simulation The goal of the simulations, shown in this aer, is to imrove coating formation simulations in the field of Thermal Sraying with resect to shrinking effects and the occurrence of micro ores due to cooling down. Here, a couled CFD and FEM calculation is resented. With use 97

10 Couled Coating Formation Simulation in Thermal Sray Processes using CFD and FEM of CFD, the flattening and the solidification of the articles is simulated, while the Finite Element Method is used in order to simulate the shrinking effects. Due to the fact that the time between two successive article imacts at the same lace is statistically greater than the solidification time of the first article, the searate treatment of the two rocesses is ossible. It could be shown, that this rocedure has a significant influence on the resulting coating roerties, hence the micro ores are of the same dimension as the height of the flattened articles. In future work, we lan to exand the model and to scale it u, so that it will be ossible to simulate macroscoic coatings. This results in the fact that the simulations can be comared with real coatings in a better way. Acknowledgement The authors gratefully acknowledge the German Research Foundation (DFG) for the financial suort within the roject bundle Homogenization of Coating Proerties in Atmosheric Plasma Sraying (PAK 193), and esecially for the suort of the subroject Simulation of the structure of coatings, which are srayed by use of 3-cathode lasma sraying (BA 851/92-1). Nomenclature α Cell based volume fraction of the article σ Surface tension α Cell based volume fraction of the gas g α th Thermal diffusity ρ Particle density t Contact time c r ν Cell based velocity vector of the article s Thermal diffusion distance d f Cell based number of faces P Pressure U f Volume flux through the face E Energy Δt Time ste λ Thermal conductivity α Face value of the volume fraction T Temerature, f V Cell volume T m Melting temerature E Energy σ Surface tension λ Thermal conductivity α th Thermal diffusity T Temerature t c Contact time T Melting temerature m s d Thermal diffusion distance References [1] Bach, F.W., Möhwald, K., Laarmann, A. and Wenz, T. (editors) Modern Surface Technology, chater Trilex II - Develoment of an Economical High-erformance Plasma Sray System, ages WILEY, [2] Bach, F.W., Möhwald, K., Rothardt, T., Prehm, J., Engl, L., Hartz, K. and Drößler, B. Particle image velocimetry in thermal sraying. Materials Science and Engineering A, 383(1): , [3] Beauvais, S., Guiont, V., N Guyen, F., Jeandin, M., Jeulin, A., Robisson, D. and Saenger, R., Study of the orosity in lasma-srayed alumina through an innovative 3-dimensional simulation of the coating build-u. Proc. International Thermal Sray Conference, [4] Bussmann, M., Chandra, S. and Mostaghimi, J., Numerical results of off-angle thermal sray article imact. Proc. UTSC, Düsseldorf, Germany, ages , [5] Fluent_Inc. Fluent 6.3 user s guide. 98

11 htt://my.fit.edu/itresources/manuals/fluent6.3/hel/html/ug/main_re.htm. [6] Hirt C.W. and Nichols, B.D. Volume of fluid (vof) method for the dynamics of free boundaries. Journal of Comutational Physics, 39: , [7] Landes, K., Diagnostics in lasma sraying techniques. Surface and Coatings Technology, 201(5): , [8] Mauer, G., Vaßen, R. and Stöver, D., Comarison and alications of dv-2000 and accurasray-g3 diagnostic systems. Journal of Thermal Sray Technology, 16(3): , [9] Raessi, M., Mostaghimi, J. and Bussmann, M., Imact and solidification of drolets onto rough substrates. Proc. International Thermal Sray Conference, [10] Steinke T. and Bäker, M., Simulation of thermal srayed coatings, Proc. International Thermal Sray Conference, [11] Voller V.R. and Prakash, C., A fixed-grid numerical modeling methodology for convectiondiffusion mushy region hase-change roblems. Int. J. Heat Mass Transfer, 30(8): , [12] Voller, V.R. and Swaminathan, C.R. Generalized source-based method for solidification hase change. Numer. Heat Transfer B, 19(2): , [13] Wan, Y.P., Prasad, V., Wang, X.G., Samath, S. and Fincke, J.R., Model and owder article heating, melting, resolidification, and evaoration in lasma sraying rocesses. Journal of Heat Transfer - Transactions of the ASME, 121: , [14] Xue, M., Chandra, S., and Mostaghimi, J. Investigation of slat curling u in thermal sray coatings. Journal of Thermal Sray Technology, 15: , [15] Xue, M., Mostaghimi, J. and Chandra, S. Prediction of coating microstructure. Proc. International Thermal Sray Conference, [16] Zimmermann, S. and Landes, K. A article image shae imaging (si) investigation of articles in a lasma jet. Materials Science and Engineering A, 383(1): , [17] Paradis, P.F. and Ishikawa, T. Surface Tension and Viscosity Measurements of Liquid and Undercooled Alumina by Containerless Techniques. Jaanese Journal of Alied Physics, 44(7A): ,