A scaling analysis of turbulent transport in laser surface alloying process

Abstract

A systematic procedure for scaling analysis of three-dimensional transient turbulent momentum, heat, and mass transfer in a typical laser surfacealloying process is presented. With suitable choices of nondimensional parameters, the governing equations coupled with appropriate boundary conditions are first scaled, and the relative significance of various terms appearing in them are accordingly analyzed. The analysis is then utilized to predict the orders of magnitude of some important quantities, such as the velocity scale at the top surface, thermal boundary layer thickness, temperature rise in the pool, turbulent kinetic energy, and its dissipation rate at the top surface. The scaling predictions are also assessed by comparison with numerical and experimental results, and an excellent agreement is observed in order-of-magnitude sense. Using the scaling predictions, the influence of various processing parameters on the system variables can be well recognized, which enables us to develop a deeper insight into the physical problem of interest. Moreover, some of the quantities predicted from the scaling analysis can be utilized for optimized selection of appropriate grid size for full numerical simulation of the process.