Centrifugal compressor is of great importance in industries. High efficiency, high stage pressure ratio, wide operation range, easy to manufacture and easy to maintain make it prevalent in aerospace, automobile and power generation industries. The possibility in improving its efficiency has been pursued all the way along its path of development. Nowadays, energy-saving has been a key competitiveness for any power-consuming product. Dyson V2 centrifugal compressor is powered by a high speed electric motor, and provides suction power to the upstream cyclone separator to separate the dust particles from the air. It is highly desirable that the efficiency can be improved such that less electricity would be consumed. As the first step to improve its efficiency, it is essential to gain some knowledge on the flow phenomena involved, in essence, efficiency is the direct reflection of the quality of the flow field. The flow is viscous, highly unsteady, swirling and transitional inside Dyson V2 centrifugal compressor, strong interaction exists between different flow features, the compound effects of strong curvature, centrifugal force and Coriolis force make it very difficult to obtain an acceptable prediction. Theoretical approach is usually too ideal to take into account different flow features, experimental approach is too costly and generally time-consuming. With the rapid development of CFD techniques and the availability of high performance computers, computational approach is becoming one of the most popular tools during design and development phases.In this work, computational approach has been employed to investigate the performance and the flow behaviour inside the Dyson V2 centrifugal compressor. Validation studies are first conducted to examine the capability of Star CCM+ solver, good agreements are obtained with the experimental data. After that, the flow field inside the Dyson V2 centrifugal compressor is analysed using steady simulation, which is relatively easy to conduct and feasible during the design phase. Different flow phenomena, including tip leakage flow, separation bubble, “jet-wake structure" and corner separation are observed. Vortex roll-up process is identified, it is initialized near the impeller blade leading edge due to tip leakage flow, and grows in the axial part of the impeller, finally, it decays in the radial part of the impeller due to centrifugal force. A loss localization method is employed to identify the sources of significant loss generation, it is found that tip leakage flow is the most significant source of loss, it is initialized near the blade leading edge through vortex roll-up, and very difficult to control. The endwall loss and blade surface loss associated with boundary layer are significant near the impeller outlet and blade suction-side due to the high flow speed, corner separation induced loss in diffuser is also significant. Later, the effects of unsteadiness are investigated through unsteady simulation, it is shown that unsteadiness can help weaken or suppress flow separation and lead to reduced blockage and local loss generation. The impeller-diffuser interaction tends to slow down the high speed flow near the impeller blade suction-side and migrate the high speed flow from suction-side to pressure-side.In literature, riblets have been extensively tested, although the physical mechanisms are not fully understood, it is definitely sure that riblets with proper size can help reduce the turbulent skin friction drag. In this work, riblets have been proposed to reduce the impeller hub endwall loss. However, riblets are of very small size, fully resolved simulation is extremely time-consuming and costly. Curve fitting is applied to correlate the available experimental data on riblets, an expression has been obtained to relate the wall shear stress reduction to non-dimensional spacing and yaw-angle. The riblets are designed and optimized based on the wall shear stress computed from steady simulation, the design value for wall shear stress reduction is around 4%. At the end, the riblets performance is assessed with unsteady simulation, it is confirmed that the riblets design based on steady simulation could perform very well, even under the effects of unsteadiness, a wall shear stress reduction around 4% could be achieved.