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Numerical Study on Particle–Gas Interaction Close to the Substrates in Thermal Spray Processes with High-Kinetic and Low-Pressure Conditions

  • Georg Mauer
Peer Reviewed
  • 11 Downloads

Abstract

In thermal spray processes, the interaction between the gas jet and the particulate feedstock can affect the coating build-up mechanisms considerably. In particular under high-kinetic and low-pressure conditions, small particles are subjected to rapid deflection and velocity changes close to the substrate. In this work, numerical studies were carried out to investigate the interaction between gas and particles in the substrate boundary layers (BL). Typical conditions for suspension plasma spraying (SPS), plasma spray-physical vapor deposition (PS-PVD), and aerosol deposition (AD) were taken as a basis. Particular importance was attached to the consideration of rarefaction and compressibility effects on the drag force. Typical Stokes numbers for the different thermal spray processes were calculated and compared. Possible effects on the resulting coating build-up mechanisms and microstructure formation are discussed. The results show that just for larger particles in the SPS process the laminar flow attached to the particles begins to separate so that the drag coefficients have to be corrected. Furthermore, slip effects occur in all the investigated processes and must be considered. The comparison of calculated Stokes numbers with critical values shows that there is a disposition to form columnar microstructures or stacking effects depending on the particle size for PS-PVD and SPS, but not for AD.

Keywords

aerosol deposition LPPS PVD/CVD modeling particle plume interaction processing suspension spraying 

List of Symbols

c

Sonic speed (m s−1)

C

Coefficient (–)

d

Diameter (m)

f

Correction factor (–)

F

Force (N)

kB

Boltzmann constant (1.381 × 10−23 J K−1)

Kn

Knudsen number (–)

m

Mass (kg)

Ma

Mach number (–)

p

Pressure (Pa)

Pr

Prandtl number (–)

r

Radial coordinate (m)

R

Specific gas constant (J kg−1 K−1)

Re

Reynolds number (–)

St

Stokes number (–)

t

Time (s)

T

Temperature (K)

v

Velocity (m s−1)

z

Axial coordinate (m)

α

Fitting parameter (–)

β

Fitting parameter (–)

γ

Specific heat capacity ratio (–)

δ

Fitting parameter (–)

κ

Curvature (m−1)

λ

Mean free path length (m)

µ

Dynamic viscosity (Pa s)

ρ

Density (kg m−3)

τ

Characteristic time (s)

Subscripts

Crit

Critical

D

Drag

E

External

g

Gas

jet

Jet

Kn

Related to Knudsen number

M

Molecular

p

Particle

PG

Pressure gradient

Re

Related to Reynolds number

rel

Relative

sub

Substrate

Ambient, not influenced by the substrate

Symbols

\(\dot{}\)

First derivation with respect to time

\(\ddot{}\)

Second derivation with respect to time

Corrected

References

  1. 1.
    H. Kaßner, R. Siegert, D. Hathiramani, R. Vaßen, and D. Stöver, Application of Suspension Plasma Spraying (SPS) for Manufacture of Ceramic Coatings, J. Therm. Spray Technol., 2008, 17(1), p 115-123CrossRefGoogle Scholar
  2. 2.
    R. Vaßen, H. Kaßner, G. Mauer, and D. Stöver, Suspension Plasma Spraying: Process Characteristics and Applications, J. Therm. Spray Technol., 2010, 19(1–2), p 219-225CrossRefGoogle Scholar
  3. 3.
    S. Rezanka, G. Mauer, and R. Vaßen, Improved Thermal Cycling Durability of Thermal Barrier Coatings Manufactured by PS-PVD, J. Therm. Spray Technol., 2014, 23(1–2), p 182-189CrossRefGoogle Scholar
  4. 4.
    N. Curry, K. VanEvery, T. Snyder, J. Susnjar, and S. Bjorklund, Performance Testing of Suspension Plasma Sprayed Thermal Barrier Coatings Produced with Varied Suspension Parameters, Coatings, 2015, 5(3), p 338-356 ((in English))CrossRefGoogle Scholar
  5. 5.
    N. Curry, K. VanEvery, T. Snyder, and N. Markocsan, Thermal Conductivity Analysis and Lifetime Testing of Suspension Plasma-Sprayed Thermal Barrier Coatings, Coatings, 2014, 4(3), p 630-650CrossRefGoogle Scholar
  6. 6.
    B. Bernard, L. Bianchi, A. Malié, A. Joulia, and B. Rémy, Columnar Suspension Plasma Sprayed Coating Microstructural Control for Thermal Barrier Coating Application, J. Eur. Ceram. Soc., 2016, 36(4), p 1081-1089CrossRefGoogle Scholar
  7. 7.
    W. Fan, Y. Bai, J.R. Li, Y. Gao, H.Y. Chen, Y.X. Kang, W.J. Shi, and B.Q. Li, Microstructural Design and Properties of Supersonic Suspension Plasma Sprayed Thermal Barrier Coatings, J. Alloys Compd., 2017, 699, p 763-774CrossRefGoogle Scholar
  8. 8.
    B. Bernard, A. Quet, L. Bianchi, A. Joulia, A. Malié, V. Schick, and B. Rémy, Thermal Insulation Properties of YSZ Coatings: Suspension Plasma Spraying (SPS) versus Electron Beam Physical Vapor Deposition (EB-PVD) and Atmospheric Plasma Spraying (APS), Surf. Coat. Technol., 2017, 318, p 122-128CrossRefGoogle Scholar
  9. 9.
    D. Zhou, O. Guillon, and R. Vaßen, Development of YSZ Thermal Barrier Coatings Using Axial Suspension Plasma Spraying, Coatings, 2017, 7(8), p 120CrossRefGoogle Scholar
  10. 10.
    A. Ganvir, S. Joshi, N. Markocsan, and R. Vassen, Tailoring Columnar Microstructure Of Axial Suspension Plasma Sprayed TBCs for Superior Thermal Shock Performance, Mater. Des., 2018, 144, p 192-208CrossRefGoogle Scholar
  11. 11.
    D. Hanft, J. Exner, M. Schubert, T. Stöcker, P. Fuierer, and R. Moos, An Overview of the Aerosol Deposition Method: Process Fundamentals and New Trends in Materials Applications, J. Ceram. Sci. Technol., 2015, 6(3), p 147-182Google Scholar
  12. 12.
    B. Selvan, K. Ramachandran, B.C. Pillai, and D. Subhakar, Numerical Modelling of Ar-N2 Plasma Jet Impinging on a Flat Substrate, J. Therm. Spray Technol., 2011, 20(3), p 534-548CrossRefGoogle Scholar
  13. 13.
    K. Pourang, C. Moreau, and A. Dolatabadi, Effect of Substrate and Its Shape on in-Flight Particle Characteristics in Suspension Plasma Spraying, J. Therm. Spray Technol., 2016, 25(1–2), p 44-54CrossRefGoogle Scholar
  14. 14.
    K. VanEvery, M.J.M. Krane, R.W. Trice, H. Wang, W. Porter, M. Besser, D. Sordelet, J. Ilavsky, and J. Almer, Column Formation in Suspension Plasma-Sprayed Coatings and Resultant Thermal Properties, J. Therm. Spray Technol., 2011, 20(4), p 817-828CrossRefGoogle Scholar
  15. 15.
    P. Sokołowski, S. Kozerski, L. Pawłowski, and A. Ambroziak, The key Process Parameters Influencing Formation of Columnar Microstructure in Suspension Plasma Sprayed Zirconia Coatings, Surf. Coat. Technol., 2014, 260, p 97-106CrossRefGoogle Scholar
  16. 16.
    P. Sokołowski, L. Pawłowski, D. Dietrich, T. Lampke, and D. Jech, Advanced Microscopic Study of Suspension Plasma-Sprayed Zirconia Coatings with Different Microstructures, J. Therm. Spray Technol., 2016, 25(1–2), p 94-104CrossRefGoogle Scholar
  17. 17.
    O. Racek, The Effect of HVOF Particle-Substrate Interactions on Local Variations in the Coating Microstructure and the Corrosion Resistance, J. Therm. Spray Technol., 2010, 19(5), p 841-851CrossRefGoogle Scholar
  18. 18.
    P.L. Fauchais, J.V.R. Heberlein, and M.I. Boulos, Thermal Spray Fundamentals: From Powder to Part, Springer, Berlin, 2014CrossRefGoogle Scholar
  19. 19.
    F. Bahbou, P. Nylén, Relationship between surface topography parameters and adhesion strength for plasma spraying, Thermal Spray 2005: Thermal Spray Connects: Explore Its Surfacing Potential!, ed. by E. Lugscheider, May 2–4, 2005 (Basel, Switzerland), DVS-German Welding Society, pp. 1027–1031Google Scholar
  20. 20.
    P. Fauchais, M. Vardelle, A. Vardelle, and S. Goutier, What Do We Know, What are the Current Limitations of Suspension Plasma Spraying?, J. Therm. Spray Technol., 2015, 24(7), p 1120-1129CrossRefGoogle Scholar
  21. 21.
    R.C. Seshadri, G. Dwivedi, V. Viswanathan, and S. Sampath, Characterizing Suspension Plasma Spray Coating Formation Dynamics Through Curvature Measurements, J. Therm. Spray Technol., 2016, 25(8), p 1666-1683CrossRefGoogle Scholar
  22. 22.
    Y. Zhao, Z. Yu, M.-P. Planche, A. Lasalle, A. Allimant, G. Montavon, and H. Liao, Influence of Substrate Properties on the Formation of Suspension Plasma Sprayed Coatings, J. Therm. Spray Technol., 2018, 27(1–2), p 73-83CrossRefGoogle Scholar
  23. 23.
    M. Gupta, N. Markocsan, X.-H. Li, and L. Östergren, Influence of Bondcoat Spray Process on Lifetime of Suspension Plasma-Sprayed Thermal Barrier Coatings, J. Therm. Spray Technol., 2018, 27(1–2), p 84-97CrossRefGoogle Scholar
  24. 24.
    B. Bernard, A. Quet, L. Bianchi, V. Schick, A. Joulia, A. Malié, and B. Rémy, Effect of Suspension Plasma-Sprayed YSZ Columnar Microstructure and Bond Coat Surface Preparation on Thermal Barrier Coating Properties, J. Therm. Spray Technol., 2017, 26(2–3), p 1025-1037CrossRefGoogle Scholar
  25. 25.
    A. Farrokhpanah, T.W. Coyle, and J. Mostaghimi, Numerical Study of Suspension Plasma Spraying, J. Therm. Spray Technol., 2017, 26(1–2), p 12-36CrossRefGoogle Scholar
  26. 26.
    J. Oberste-Berghaus, S. Bouaricha, J.-G. Legoux, C. Moreau, Injection conditions and in-flight particle states in suspension plasma spraying of alumina and zirconia nano-ceramics, Thermal Spray 2005: Thermal Spray Connects: Explore Its Surfacing Potential!, ed. by E. Lugscheider, May 2–4, 2005 (Basel, Switzerland), DVS-German Welding Society, pp. 512–518Google Scholar
  27. 27.
    P. Wang, W. He, G. Mauer, R. Mücke, and R. Vaßen, Monte Carlo Simulation of Column Growth in Plasma Spray Physical Vapor Deposition Process, Surf. Coat. Technol., 2018, 335, p 188-197CrossRefGoogle Scholar
  28. 28.
    M. Parmar, A. Haselbacher, and S. Balachandar, Generalized Basset–Boussinesq–Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow, Phys. Rev. Lett., 2011, 106(8), p 084501CrossRefGoogle Scholar
  29. 29.
    L. von Schiller, N. Naumann, Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung, VDI Zeitschrift (1857–1968), 77(12), 318–320 (1933)Google Scholar
  30. 30.
    E. Loth, Compressibility and Rarefaction Effects on Drag of a Spherical Particle, AIAA J., 2008, 46(9), p 2219-2228CrossRefGoogle Scholar
  31. 31.
    G.A. Bird, Definition of Mean Free Path for Real Gases, Phys. Fluids, 1983, 26(11), p 3222-3223CrossRefGoogle Scholar
  32. 32.
    X. Chen and E. Pfender, Effect of the Knudsen Number on Heat Transfer to a Particle Immersed into a Thermal Plasma, Plasma Chem. Plasma Process., 1983, 3(1), p 97-113CrossRefGoogle Scholar
  33. 33.
    X. Chen and X. Chen, Drag on a Metallic or Nonmetallic Particle Exposed to a Rarefied Plasma Flow, Plasma Chem. Plasma Process., 1989, 9(3), p 387-408CrossRefGoogle Scholar
  34. 34.
    X. Chen and P. He, Heat Transfer from a Rarefied Plasma Flow to a Metallic or Nonmetallic Particle, Plasma Chem. Plasma Process., 1986, 6(4), p 313-333CrossRefGoogle Scholar
  35. 35.
    Y.P. Chyou and E. Pfender, Behavior of Particulates in Thermal Plasma Flows, Plasma Chem. Plasma Process., 1989, 9(1), p 45-71CrossRefGoogle Scholar
  36. 36.
    D.J. Rader, Momentum Slip Correction Factor for Small Particles in Nine Common Gases, J. Aerosol Sci., 1990, 21(2), p 161-168CrossRefGoogle Scholar
  37. 37.
    J.H. Kim, G.W. Mulholland, S.R. Kukuck, and D.Y.H. Pui, Slip Correction Measurements of Certified PSL Nanoparticles Using a Nanometer Differential Mobility Analyzer (Nano-DMA) for Knudsen Number From 0.5 to 83, J. Res. Natl. Inst. Stand. Technol., 2005, 110(1), p 31-54CrossRefGoogle Scholar
  38. 38.
    E. Cunningham, On the Velocity of Steady Fall of Spherical Particles through Fluid Medium, Proc. R. Soc. Lond. Ser. A, 1910, 83, p 357-365CrossRefGoogle Scholar
  39. 39.
    C. Delbos, J. Fazilleau, V. Rat, J.F. Coudert, P. Fauchais, and B. Pateyron, Phenomena Involved in Suspension Plasma Spraying Part 2: Zirconia Particle Treatment and Coating Formation, Plasma Chem. Plasma Process., 2006, 26(4), p 393-414CrossRefGoogle Scholar
  40. 40.
    C.G. Phillips and S.R. Kaye, The Influence of the Viscous Boundary Layer on the Critical Stokes Number for Particle Impaction Near a Stagnation Point, J. Aerosol Sci., 1999, 30(9), p 709-718CrossRefGoogle Scholar
  41. 41.
    E. Pohlhausen, Der Wärmeaustausch zwischen festen Körpern und Flüssigkeiten mit kleiner reibung und kleiner Wärmeleitung, ZAMM J. Appl. Math. Mech./Zeitschrift für Angewandte Mathematik und Mechanik, 1(2), 115–121 (1921) (in German)Google Scholar
  42. 42.
    H. Schlichting and K. Gersten, Grenzschichttheorie, Springer, Berlin, 2006Google Scholar
  43. 43.
    G. Mauer and R. Vaßen, Conditions for Nucleation and Growth in the Substrate Boundary Layer at Plasma Spray-Physical Vapor Deposition (PS-PVD), Surf. Coat. Technol., 2018,  https://doi.org/10.1016/j.surfcoat.2018.06.086 CrossRefGoogle Scholar
  44. 44.
    C.D. Donaldson and R.S. Snedeker, A Study of Free Jet Impingement. Part 1. Mean Properties of Free and Impinging Jets, J. Fluid Mech., 2006, 45(2), p 281-319CrossRefGoogle Scholar
  45. 45.
    A. Mahdavi and A. McDonald, Analytical Study of The Heat Transfer Coefficient of the Impinging Air Jet During Cold Spraying, Int. J. Therm. Sci., 2018, 130, p 289-297CrossRefGoogle Scholar
  46. 46.
    W. He, G. Mauer, M. Gindrat, R. Wäger, and R. Vaßen, Investigations on the Nature of Ceramic Deposits in Plasma Spray-Physical Vapor Deposition, J. Therm. Spray Technol., 2017, 26(1), p 83-92CrossRefGoogle Scholar
  47. 47.
    S. Gordon, B.J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications—Analysis. NASA-Reference Publication, 1311 part 1, NASA Lewis Research Center, 1994Google Scholar
  48. 48.
    S. Gordon, B.J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications—User’s Manual and Program Description. NASA-Reference Publication 1311, part 2, NASA Lewis Research Center, 1996Google Scholar
  49. 49.
    M. Vardelle, A. Vardelle, P. Fauchais, and M.I. Boulos, Plasma-Particle Momentum and Heat Transfer: Modelling and Measurements, AIChE J., 1983, 29(2), p 238-243CrossRefGoogle Scholar
  50. 50.
    G. Mauer, A. Hospach, N. Zotov, and R. Vaßen, Process Conditions and Microstructures of Ceramic Coatings by Gas Phase Deposition Based on Plasma Spraying, J. Therm. Spray Technol., 2013, 22(2–3), p 83-89CrossRefGoogle Scholar
  51. 51.
    G. Mauer, Plasma Characteristics and Plasma-Feedstock Interaction Under PS-PVD Process Conditions, Plasma Chem. Plasma Process., 2014, 34(5), p 1171-1186CrossRefGoogle Scholar
  52. 52.
    M. Jadidi, M. Mousavi, S. Moghtadernejad, and A. Dolatabadi, A Three-Dimensional Analysis of the Suspension Plasma Spray Impinging on a Flat Substrate, J. Therm. Spray Technol., 2015, 24(1–2), p 11-23Google Scholar
  53. 53.
    M. Jadidi, A.Z. Yeganeh, and A. Dolatabadi, Numerical Study of Suspension HVOF Spray and Particle Behavior Near Flat and Cylindrical Substrates, J. Therm. Spray Technol., 2018, 27(1–2), p 59-72CrossRefGoogle Scholar
  54. 54.
    W. He, G. Mauer, M. Gindrat, R. Wäger, and R. Vaßen, Investigations on the Nature of Ceramic Deposits in Plasma Spray-Physical Vapor Deposition, J. Therm. Spray Technol., 2016, 26(1–2), p 83-92Google Scholar
  55. 55.
    G. Mauer and R. Vaßen, Plasma Spray-PVD: Plasma Characteristics and Impact on Coating Properties, J. Phys. Conf. Ser., 2012, 406, p 012005CrossRefGoogle Scholar
  56. 56.
    F.M. White, Viscous Fluid Flow, 2nd ed., McGraw-Hill, New York, 1991Google Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.Institute of Energy and Climate Research: IEK-1Forschungszentrum Jülich GmbHJülichGermany

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