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In many aeronautics and marine applications, the unsteady forces generated by propulsion rotors due to turbulence ingestion are a significant source of noise and create serious concerns. The understanding of rotor turbulence ingestion and the rotor noise generation mechanisms is vital to achieve an optimal design or apply noise control strategy. The current study is the first attempt to numerically investigate an underwater rotor ingesting grid-generated turbulence by large eddy simulation combined with the Ffowcs-Williams and Hawkings equation. The flow characteristics of two directly simulated turbulence grids with a mesh spacing of 4 and 6 in. are investigated and proved to be adequate for the rotor turbulence ingestion study. The simulated unsteady force spectra of the rotor show better agreement with the experimental results in terms of amplitudes and frequency ranges of the first haystack and broadband components compared to previous theoretical and numerical studies. The unsteady forces and noise of the rotor downstream of the 4-in. grid are slightly higher than those downstream of the 6-in. grid. A far-field noise prediction approach based on the time derivatives of the rotor axial and radial unsteady forces are investigated and validated. The far-field noise spectra and the rotor noise directivities predicted by the time derivative approach agree well with the Ffowcs-Williams and Hawkings equation in the main frequency range of underwater rotor noise. The noise directivities are found to be dominated by axial force related dipole sources. [ABSTRACT FROM AUTHOR]