6533b827fe1ef96bd1286e9c

RESEARCH PRODUCT

Analytical description of solid particles kinematics due to a fluid flow and application to the depiction of characteristic kinematics in cold spraying

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Abstract In several multiphase flow applications such as fluidization, thermal spraying, atomization manufacturing and so on, the Newton's law is widely enacted to formulate the particle/fluid kinematic interaction and then to compute particles kinematics. This paper provides analytical solutions of the Newton's law in its time-dependent formulation or simplified formulation, the latter being a reduction of the time dependent problem into a spatial description of the particle motion. It was found that the velocity solution is strictly similar in both cases so that the simplified formulation is viable. The W_ 1 branch of the Lambert's function yields the analytical particle residence time and the particle velocity which enable to characterize particle kinematics and capabilities of cold spraying. Typical particles residence time is of about 10 − 7 –10 − 6  s and a typical characteristic duration is of about 10 − 4 –10 − 3  s to produce a deposit layer. This explains the high productivity rate of cold spraying among innovative additive manufacturing processes. Theoretical limitations of cold spraying are depicted using analytical solutions. Variances of particles velocity are mapped depending on both particle nature and Mach number used in cold spraying. According to analytical laws, the particle velocity using air propellant gas is limited to 600 m/s–1000 m/s for the situation of low particle density-diameter combination (ρ p⁎ D p ) experienced in cold spraying. Helium increases this kinematic limitation up to 1000 m/s–1600 m/s. Such analytical depictions characterize and facilitate a theoretical selection of process parameters including suitable particle features depending on gas nature and kinematic capabilities of cold spraying.