  Microstructure evolution in metal additive manufacturing (AM) is a complex
multi-physics and multi-scale problem. Understanding the impact of AM process
conditions on the microstructure evolution and the resulting mechanical
properties of the printed part is an active area of research. At the meltpool
scale, the thermo-fluidic governing equations have been extensively modeled in
the literature to understand the meltpool conditions and the thermal gradients
in its vicinity. In many phenomena governed by partial differential equations,
dimensional analysis and identification of important dimensionless numbers can
provide significant insights into the process dynamics. In this context, a
novel strategy using dimensional analysis and the method of linear least
squares regression to numerically investigate the thermo-fluidic governing
equations of the Laser Powder Bed Fusion AM process is presented in this work.
First, the governing equations are solved using the Finite Element Method, and
the model predictions are validated by comparing with experimentally estimated
cooling rates, and with numerical results from the literature. Then, through
dimensional analysis, an important dimensionless quantity - interpreted as a
measure of heat absorbed by the powdered material and the meltpool, is
identified. This dimensionless measure of heat absorbed, along with classical
dimensionless quantities such as Peclet, Marangoni, and Stefan numbers, is used
to investigate advective transport in the meltpool for different alloys.
Further, the framework is used to study the variations of thermal gradients and
the solidification cooling rate. Important correlations linking meltpool
morphology and microstructure evolution related variables with classical
dimensionless numbers are the key contribution of this work.
