Analytical investigation into the powder distribution and laser beam-powder flow interaction in laser direct energy deposition with a continuous coaxial nozzle

•Powder distribution formulae are established considering the divergence angles of the powder jet.•Laser attenuation formulae are derived considering powder distribution modes.•Powder temperature formulae with different trajectories are analyzed and derived.•Proposed formulae are validated and used to analyze interaction between laser beam and powder flow in LDED process.