A Numerical Study of Supersonic Rectangular Jet Impingement and Applications to Cold Spray Technology

Particle-laden supersonic jets impinging on a flat surface are of interest to cold gas-dynamic spray technology. Solid particles are propelled to a high velocity through a convergent-divergent nozzle, and upon impact on a substrate surface, they undergo plastic deformation and adhere to the surface. For given particle and substrate materials, particle velocity and temperature at impact are the primary parameters that determine the success of particle deposition. Depending on the particle diameter and density, interactions of particles with the turbulent supersonic jet and the compressed gas region near the substrate surface can have significant effects on particle velocity and temperature. Unlike previous numerical simulations of cold spray, in this dissertation we track solid particles in the instantaneous turbulent fluctuating flow field from the nozzle exit to the substrate surface. Thus, we capture the effects of particle-turbulence interactions on particle velocity and temperature at impact.

The flow field is obtained by direct numerical simulations of a supersonic rectangular particle-laden air jet impinging on a flat substrate. An Eulerian-Lagrangian approach with two-way coupling between solid particles and gas phase is used. Unsteady three-dimensional Navier-Stokes equations are solved using a six-order compact scheme with a tenth-order compact filter combined with WENO dissipation, almost everywhere except in a region around the bow shock where a fifth-order WENO scheme is used. A fourth-order low-storage Runge-Kutta scheme is used for time integration of gas dynamics equations simultaneously with solid particles equations of motion and energy equation for particle temperature. Particles are tracked in instantaneous turbulent jet flow rather than in a mean flow that is commonly used in the previous studies. Supersonic jets for air and helium at Mach number 2.5 and 2.8, respectively, are simulated for two cases for the standoff distance between the nozzle exit and the substrate. Flow structures, mean flow properties, particles impact velocity and particles deposition efficiency on a flat substrate surface are presented. Different grid resolutions are tested using 2, 4 and 8 million points. Good agreement between DNS results and experimental data is obtained for the pressure distribution on the wall and the maximum Mach number profile in wall jet. Probability density functions for particle velocity and temperature at impact are presented. Deposition efficiency for aluminum and copper particles of diameter in the range 1 micron to 40 microns is calculated.

Instantaneous flow fields for the two standoff distances considered exhibit different flow characteristics. For large standoff distance, the jet is unsteady and flaps both for air (Mach number 2.5) and for helium (Mach number 2.8), in the direction normal to the large cross-section of the jet. Linear stability analysis of the mean jet profile validates the oscillation frequency observed in the present numerical study. Available experimental data also validate oscillation frequency. After impingement, the flow re-expands from the compressed gas region into a supersonic wall jet. The pressure on the wall in the expansion region is locally lower than ambient pressure. Strong bow shock only occurs for small standoff distance. For large standoff distance multiple/oblique shocks are observed due to the flapping of the jet.

The one-dimensional model based on isentropic flow calculations produces reliable results for particle velocity and temperature. It is found that the low efficiency in the low-pressure cold spray (LPCS) compared to high-pressure cold spray (HPCS) is mainly due to low temperature of the particles at the exit of the nozzle. Three-dimensional simulations show that small particles are readily influenced by the large-scale turbulent structures developing on jet shear layers, and they drift sideways. However, large particles are less influenced by the turbulent flow. Particles velocity and temperature are affected by the compressed gas layer and remain fairly constant in the jet region. With a small increase in the particles initial temperature, the deposition efficiency in LPCS can be maximized. There is an optimum particle diameter range for maximum deposition efficiency.