Skip to main content
SpringerLink
Log in

Predicting the Effects of Powder Feeding Rates on Particle Impact Conditions and Cold Spray Deposited Coatings

  • Peer Reviewed
  • Published:
Journal of Thermal Spray Technology Aims and scope Submit manuscript

Abstract

As the industrial application of the cold spray technology grows, the need to optimize both the cost and the quality of the process grows with it. Parameter selection techniques available today require the use of a coupled system of equations to be solved to involve the losses due to particle loading in the gas stream. Such analyses cause a significant increase in the computational time in comparison with calculations with isentropic flow assumptions. In cold spray operations, engineers and operators may, therefore, neglect the effects of particle loading to simplify the multiparameter optimization process. In this study, two-way coupled (particle–fluid) quasi-one-dimensional fluid dynamics simulations are used to test the particle loading effects under many potential cold spray scenarios. Output of the simulations is statistically analyzed to build regression models that estimate the changes in particle impact velocity and temperature due to particle loading. This approach eases particle loading optimization for more complete analysis on deposition cost and time. The model was validated both numerically and experimentally. Further numerical analyses were completed to test the particle loading capacity and limitations of a nozzle with a commonly used throat size. Additional experimentation helped document the physical limitations to high-rate deposition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Notes

  1. Particle loading is the ratio of the mass flow rate of particles to the mass flow rate of gas in the cold spray nozzle multiphase flow.

Abbreviations

\(A\) (m2):

Cross-sectional area of flow

\(A^{*}\) (m2):

Flow cross-sectional area at nozzle throat

\(C\) :

Fitting constant

\(c_{{{\text{p}}_{\text{p}} }}\) [J/(kg °K)]:

Particle heat capacity

\(d_{\text{e}}\) (m):

Nozzle exit diameter

\(d_{ \hbox{min} }\) (μm):

Minimum particle diameter

\(d_{ \hbox{max} }\) (μm):

Maximum particle diameter

\(\overline{d}_{\text{freq}}\) :

Frequency-based size distribution parameter

\(\overline{d}_{\text{vol}}\) :

Frequency-based size distribution parameter

\({\text{DE}}\) (%):

Deposition efficiency

\(d_{\text{p}}\) (m):

Particle diameter

\(e\) (J/kg):

Internal energy

\(\eta\) :

Ratio of impact velocity to critical velocity

\({\text{ER}}\) :

Expansion ratio

\(f_{\text{CD}}\) :

Log-normal cumulative distribution function

\(F_{\text{D}}\) (N):

Particle drag force

\(F_{\text{p}}\) (N):

Total particle drag force

\(\gamma\) :

Specific heat ratio

\(h_{\text{p}}\) [W/(m2 °K)]:

Heat transfer coefficient

\(k_{\text{g}}\) [W/(m2 °K)]:

Gas thermal conductivity

\(k_{\text{p}}\) [W/(m2 °K)]:

Particle thermal conductivity

\(L_{\text{ex}}\) (m):

Expansion region length

\(L_{\text{shock}}\) (m):

Shock location from the substrate

\({\text{Ma}}\) :

Mach number

\({\text{Ma}}_{\text{e}}\) :

Mach number at nozzle exit

\({\text{Ma}}_{\text{s}}\) :

Mach number downstream of shock

\({\text{MMD}}\) (m):

Mass mean diameter

\(m_{\text{p}}\) (kg):

Particle mass

\(\dot{m}_{\text{g}}\) (kg/s):

Gas flow rate

\(\dot{m}_{\text{p}}\) [kg/(m s)]:

Particle flow rate

\(\mu\) (kg/s):

Gas viscosity

\(N_{\text{p}}\) :

Number of particles

\(Nu\) :

Nusselt number

\(\omega\) (%):

Particle loading rate \((100 \times \dot{m}_{\text{p}} /\dot{m}_{\text{g}} )\)

\(\omega_{\text{c}}\) (%):

Corrected particle loading rate

\(\dot{Q}_{p}\) (W):

Particle heat transfer rate

\(P_{\text{g}}\) (Pa):

Gas pressure

\(Pr\) :

Prandtl number

\(P_{0}\) (Pa):

Total gas pressure

\(R\) [J/(kg °K)]:

Specific gas constant

\(\rho_{\text{g}}\) (kg/m3):

Gas density

\(\rho_{\text{p}}\) (kg/m3):

Particle density

\({\text{SoD}}\) (m):

Standoff distance

\(\sigma_{\text{ult}}\) (Pa):

Particle ultimate tensile strength

\(\overline{\sigma }_{\text{freq}}\) :

Frequency-based size distribution fitting constant

\(\overline{\sigma }_{\text{vol}}\) :

Volume-based size distribution fitting constant

\(u_{\text{c}}\) (m/s):

Critical velocity

\(u_{\text{e}}\) (m/s):

Erosion velocity

\(u_{\text{g}}\) (m/s):

Gas velocity

\(u_{\text{p}}\) (m/s):

Particle velocity

\(u_{\text{pi}}\) (m/s):

Particle impact velocity

\(u_{{{\text{p}}_{\text{ave}} }}\) (m/s):

Size-weighted average particle velocity

\(T_{0}\) (°K):

Total gas pressure

\(T_{\text{g}}\) (°K):

Gas temperature

\(T_{\text{p}}\) (°K):

Particle temperature

\(T_{\text{pi}}\) (°K):

Particle impact temperature

\(T_{\text{r}}\) (°K):

Particle room temperature

t (s):

Time

x (m):

Axial distance

References

  1. V. Champagne, The Cold Spray Materials Deposition Process: Fundamentals and Applications, Woodhead Publishing Limited, Cambridge, 2007

    Book  Google Scholar 

  2. A. Papyrin, V. Kosarev, S. Klinkov, A. Alkimov, and V. Fomin, Cold Spray Technology, Elsevier, Amsterdam, 2007

    Google Scholar 

  3. J. Villafuerte, Modern Cold Spray: Materials, Process, and Applications, Springer, Cham, 2015

    Book  Google Scholar 

  4. E. Irissou, F. Ilinca, W. Wong, J.G. Legoux, S. Yue, Investigation on the Effect of Helium-to-Nitrogen Ratio as Propellent Gas Mixture on the Processing of Titanium Coating using Cold Gas Dynamic Spray, International Thermal Spray Conference, B.R. Marple, A. Agarwal, M.M. Hyland, Y.C. Lau, C.J. Li, R.S. Lima, and A. McDonal Eds., September 27-29, 2011 (Hamburg, Germany), DVS

  5. O.C. Ozdemir, C.A. Widener, D. Helfritch, and F. Delfanian, Estimating the Effect of Helium and Nitrogen Mixing on Deposition Efficiency in Cold Spray, J. Therm. Spray Technol., 2016, 25(4), p 660-671

    Article  Google Scholar 

  6. H. Assadi, F. Gartner, T. Stoltenhoff, and H. Kreye, Bonding Mechanism in Cold Gas Spraying, Acta Mater., 2003, 51, p 4379-4394

    Article  Google Scholar 

  7. T. Schmidt, H. Assadi, F. Gartner, H. Richter, T. Stoltenhoff, H. Kreye, and T. Klassen, From Particle Acceleration to Impact and Bonding in Cold Spraying, J. Therm. Spray Technol., 2009, 18(5-6), p 794-808

    Article  Google Scholar 

  8. M.R. Rokni, C.A. Widener, and V.R. Champagne, Microstructural Stability of Ultrafine Grained Cold Sprayed 6061 Aluminum Alloy, Appl. Surf. Sci., 2014, 290, p 482-489

    Article  Google Scholar 

  9. F.Z. Shaikh, H.D. Blair, R.J. Tabaczynski, and T.Y. Pan, Gas-Dynamic Cold Spraying Lining for Aluminum Engine Block Cylinders, ed., U.S.P.a.T. Office, Ed., 2002

  10. M. Faccoli, G. Cornacchia, D. Maestrini, G.P. Marconi, and R. Roberti, Cold Spray Repair of Martensitic Stainless Steel Components, J. Therm. Spray Technol., 2014, 23(8), p 1270-1280

    Article  Google Scholar 

  11. M. Fukumoto, M. Mashiko, M. Yamada, and E. Yamaguchi, Deposition Behavior of Copper Fine Particles onto Flat Substrate Surface in Cold Spraying, J. Therm. Spray Technol., 2009, 19(1-2), p 89-94

    Article  Google Scholar 

  12. J.M. Hoey, M.J. Robinson, and R.A. Sailer, Micro Cold Spray Printed Top Metallization Layer for Solar Cells, 2014 IEEE 40th Photovoltaic Specialist Converence (Denver, CO), Institute of Electrical and Electronics Engineers Inc., 2014

  13. D.Y. Kim, J.J. Park, J.G. Lee, D. Kim, S.J. Tark, S. Ahn, J.H. Yun, J. Gwak, K.H. Yoon, S. Chandra, and S.S. Yoon, Cold Spray Deposition of Copper Electrodes on Silicon and Glass Substrates, J. Therm. Spray Technol., 2013, 22(7), p 1092-1102

    Article  Google Scholar 

  14. F. Raletz, M. Vardelle, and G. Ezo’o, Critical Particle Velocity Under Cold Spray Conditions, Surf. Coat. Technol., 2006, 201, p 1942-1947

    Article  Google Scholar 

  15. K. Binder, J. Gottschalk, M. Kollenda, M. Gartner, and T. Klassen, Influence of Impact Angle and Gas Temperature on Mechanical Properties of Titanium Cold Spray Deposits, J. Therm. Spray Technol., 2010, 20(1-2), p 234-242

    Article  Google Scholar 

  16. D.K. Christoullis, S. Guetta, V. Guipont, and M. Jeandin, The Influence of the Substrate on the Deposition of Cold-Sprayed Titanium: An Experimental and Numerical Study, J. Therm. Spray Technol., 2010, 20(3), p 523-533

    Article  Google Scholar 

  17. T. Marrocco, D.G. McCartney, P.H. Shipway, and A.J. Sturgeon, Production of Titanium Deposits by Cold Gas Dynamic Spray: Numerical Modeling and Experimental Characterization, J. Therm. Spray Technol., 2006, 15(2), p 263-272

    Article  Google Scholar 

  18. M.R. Rokni, C.A. Widener, O.C. Ozdemir, and G.A. Crawford, Microstructure and Mechanical Properties of Cold Sprayed 6061 Al in As-Sprayed and Heat Treated Condition, Surf. Coat. Technol., 2017, 309, p 641-650

    Article  Google Scholar 

  19. H. Assadi, H. Kreye, F. Gartner, and T. Klassen, Cold Spraying—A Materials Perspective, Acta Mater., 2016, 116(1), p 382-407

    Article  Google Scholar 

  20. R. Drehmann, T. Grund, T. Lampke, B. Wielage, K. Manygoats, T. Schucknecht, and D. Rafaja, Splat Formation and Adhesion Mechanisms of Cold Gas-Sprayed Al Coatings on Al2O3 Substrates, J. Therm. Spray Technol., 2013, 23(1-2), p 68-75

    Article  Google Scholar 

  21. M. Gardon, A. Latorre, M. Torrell, S. Dosta, J. Fernandez, and J.M. Guilemany, Cold Gas Spray Titanium Coatings onto a Biocompatible Polymer, Mater. Lett., 2013, 106, p 97-99

    Article  Google Scholar 

  22. R. Lupoi and W. O’Neill, Deposition of metallic coatings on polymer surfaces using cold spray, Surf. Coat. Technol., 2010, 205, p 2167-2173

    Article  Google Scholar 

  23. A. Ganesan, J. Affi, M. Yamada, and M. Fukumoto, Bonding Behavior Studies of Cold Sprayed Copper Coating on the PVC Polymer Substrate, Surf. Coat. Technol., 2012, 207, p 262-269

    Article  Google Scholar 

  24. M. Winnicki, A. Malachowska, T. Piwowarczyk, M. Rutkowska-Gorczyca, and A. Ambroziak, The Bond Strength of Al + Al2O3 Cermet Coatings Deposited by Low-Pressure Cold Spraying, Arch. Civ. Mech. Eng., 2016, 16(4), p 743-752

    Article  Google Scholar 

  25. H. Assadi, T. Schmidt, H. Richter, J.-O. Kliemann, K. Binder, F. Gartner, T. Klassen, and H. Kreye, On Parameter Selection in Cold Spraying, J. Therm. Spray Technol., 2011, 20(6), p 1161-1176

    Article  Google Scholar 

  26. J.D. Anderson, Modern Compressible Flow with Historical Perspective, McGraw-Hill Inc., New York, 2012

    Google Scholar 

  27. R.C. Dykhuizen and M.F. Smith, Gas Dynamic Principles of Cold Spray, J. Therm. Spray Technol., 1998, 7(2), p 205-212

    Article  Google Scholar 

  28. M. Grujicic, J.R. Saylor, D.E. Beasley, W.S. DeRosset, and D. Helfritch, Computational Analysis of the Interfacial Bonding between Feed-Powder Particles and the Substrate in the Cold-Gas Dynamic-Spray Process, Appl. Surf. Sci., 2003, 219, p 211-227

    Article  Google Scholar 

  29. M. Grujicic, C.L. Zhao, C. Tong, W.S. DeRosset, and D. Helfritch, Analysis of the Impact Velocity of Powder Particles in the Cold-Gas Dynamic-Spray Process, Mater. Sci. Eng., A, 2004, 368, p 222-230

    Article  Google Scholar 

  30. D. Helfritch, V. Champagne, A Model Study of Powder Particle Size Effects in Cold Spray Deposition, ed., U.S.A.R. Laboratory, Ed., 2008

  31. B. Jodoin, Cold Spray Nozzle Mach Number Limitation, J. Therm. Spray Technol., 2002, 11(4), p 496-507

    Article  Google Scholar 

  32. B. Jodoin, F. Raletz, and M. Vardelle, Cold Spray Modeling and Validation Using an Optical Diagnostic Method, Surf. Coat. Technol., 2006, 200, p 4424-4432

    Article  Google Scholar 

  33. M.C. Meyer, S. Yin, K.A. McDonnell, O. Stier, and R. Lupoi, Feed Rate Effect on Particulate Acceleration in Cold Spray Under Low Stagnation Pressure Conditions, Surf. Coat. Technol., 2016, 304, p 237-245

    Article  Google Scholar 

  34. K. Taylor, B. Jodoin, and J. Karov, Particle Loading Effect in Cold Spray, J. Therm. Spray Technol., 2005, 15(2), p 273-279

    Article  Google Scholar 

  35. J.D.J. Anderson, Computational Fluid Dynamics: The Basics with Applications, McGraw-Hill Inc., New York, 1995

    Google Scholar 

  36. R.B. Bird, W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, 2nd ed., Wiley, Hoboken, 2002, p 27, 276, 439

  37. J.F. Wendt, Computational Fluid Dynamics: An Introduction, 3rd ed., Springer, Berlin, 2009

    Book  Google Scholar 

  38. H. Schlichting, Boundary Layer Theory, 7 ed., F.J. Cerra, Ed., McGraw-Hill Book Company, Inc., New York, 1987, p 596-667

  39. A. Bejan, Heat Transfer, Wiley, Hoboken, 1993

    Google Scholar 

  40. D.J. Carlson and R.F. Hogland, Particle Drag and Heat Transfer in Rocket Nozzles, AIAA J., 1964, 2(11), p 1980-1984

    Article  Google Scholar 

  41. Y.A. Cengel and M.A. Boles, Thermodynamics: An Engineering Approach, 5th ed., McGraw-Hill College, New York, 2006

    Google Scholar 

  42. F.M. White, Fluid Mechanics, 7th ed., McGraw-Hill, New York, 2011, p 608-681

    Google Scholar 

  43. A. Moridi, S.M. Hassani-Gangaraj, and M. Guagliano, A Hybrid Approach to Determine Critical and Erosion Velocities in the Cold Spray Process, Appl. Surf. Sci., 2013, 273, p 617-624

    Article  Google Scholar 

  44. T. Schmidt, F. Gartner, H. Assadi, and H. Kreye, Development of a Generalized Parameter Window for Cold Spray Deposition, Acta Mater., 2006, 54, p 729-742

    Article  Google Scholar 

  45. J.R. Davis, Concise Metals Engineering Data Book, ASM International, Ohio, 1997

    Google Scholar 

  46. CSM Evolution: Product Manual, 1st ed., Tecnar Automation Ltd., 2013

  47. Standard Guide for Metallographic Preparation of Thermal Sprayed Coatings, E1920-03, ASTM International, 2014

  48. M.J.R. Williams, Multiphase Flow Research, Nova Science Publishers Inc., New York, 2009

    Google Scholar 

  49. R. Boyer, G.C. Welsch, and E.W. Collings, Materials Properties Handbook: Titanium Alloys, ASM International, Ohio, 1994

    Google Scholar 

Download references

Acknowledgments

This work was supported by the U.S. Army Research Laboratory under the Contract Nos. W911NF-15-2-0034 and W15QKN-16-C-0094. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the U.S. Government.

Author information

Authors and Affiliations

  1. Northeastern University, Boston, MA, USA

    Ozan C. Ozdemir

  2. South Dakota School of Mines and Technology, Rapid City, SD, USA

    Christian A. Widener & Michael J. Carter

  3. VRC Metal Systems, Rapid City, SD, USA

    Kyle W. Johnson

Authors
  1. Ozan C. Ozdemir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian A. Widener
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael J. Carter
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kyle W. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ozan C. Ozdemir.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ozdemir, O.C., Widener, C.A., Carter, M.J. et al. Predicting the Effects of Powder Feeding Rates on Particle Impact Conditions and Cold Spray Deposited Coatings. J Therm Spray Tech 26, 1598–1615 (2017). https://doi.org/10.1007/s11666-017-0611-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11666-017-0611-0

Keywords

Search

Navigation