The present paper demonstrates the time-domain implementation of arbitrary-order non-reflecting boundary conditions for a 3d non-linear time-accurate RANS solver for turbomachinery applications. The conditions are based on the 2d circumferential mode decomposition of the linearized Euler equations. The exact linearized conditions are non-local since they involve space-time Fourier/Laplace transforms. Time-local conditions of arbitrary order are obtained by approximation of the inverse Laplace transform Bessel function convolution kernel by sums of exponential functions. Likewise, this corresponds to a rational function approximation of the exact non-reflecting boundary kernel in the frequency-domain. The boundary conditions are validated against two numerical test cases. The first test case mimics Tyler-Sofrin modes present in turbomachinery applications by prescribing 2d acoustic modes in a uniform flow. The second test case is concerned with the potential contamination of blade flutter analyses by spurious reflections on artificial boundaries. For the benchmark problem Standard Configuration 10, blade flutter with non-zero inter-blade phase angle, acoustic resonance generates spinning waves susceptible to reflection. Contrasting the results of non-reflecting boundary conditions of varying order of accuracy shows that low order conditions can fail for challenging cases, which emphasizes the need for an accurate non-reflecting boundary treatment.