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Six turbulence models frequently used in compressor aerodynamics were employed in the detailed numerical investigations of a low-speed large-scale axial compressor rotor, for which the tip flows were measured in detail with stereoscopic particle image velocimetry, to assess the predictive capabilities of the turbulence models for large-scale vortices in the tip region of the rotor. The six turbulence models include: the mixing-length model, the SpalartAllmaras model, the standard k " model, the shear-stress transport k ! model, the v 2 f model, and the Reynolds stress model. Their results were carefully discussed and compared with the measurements both on velocity fields and turbulence stresses. It was found that the Reynolds stress model is superior to the others in the prediction of the tip-leakage vortex at the design condition, whereas the standard k " model shows the best results in the prediction of the corner vortex at the near-stall condition. Although the simulation could predict the large-scale tip vortices well in the mean flowfield, the computed flow mechanism has large discrepancy with the reality. Nomenclature A = compressor axial direction H = distance from the hub to the tip in the radial direction p = static pressure R = compressor radial direction T = compressor tangential direction u, v, w = mean velocity components in the x, y, and z directions X = distance from the rotor suction surface in the x direction x, y, z = Cartesian coordinates Y = distance from the rotor hub in the y direction y = nondimensional turbulence wall function = kinematic viscosity = fluid density ! = vorticity Subscript c = the center of the tip-leakage vortex Superscripts = time average 0 = fluctuating quantity

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The stimulated Raman adiabatic passage shows an efficient technique that accurately transfers population between two discrete quantum states with the same parity in three-level quantum systems based on adiabatic evolution. This technique has widely theoretical and experimental applications in many fields of physics, chemistry, and beyond. Here, we present a general approach to robust stimulated Raman shortcut-to-adiabatic passage with invariant-based optimal control. By controlling the dynamical process, we inversely design a family of Hamiltonians with non-divergent Rabi frequencies that can realize fast and accurate population transfer from the first to the third level, while the systematic errors are largely suppressed in general. Furthermore, a detailed trade-off relation between the population of the intermediate state and the amplitudes of Rabi frequencies in the transfer process is illustrated. These results provide an optimal route toward manipulating the evolution of three-level quantum systems in future quantum information processing.

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