# Mechanisms of Sweep on the Performance of Transonic Centrifugal Compressor Impellers
## 1 Introduction  
Centrifugal compressors are widely applied in the oil and gas industries [1; 2], gas turbine engines, and [3; 4; 5] turbochargers [6; 7]. In the aviation industry, transonic centrifugal compressors with a high pressure ratio are required for reduction of manufacturing costs and engine weight. In the automotive industry, the tendency towards downsizing and emissions control in internal combustion engines favors the use of turbochargers with centrifugal compressors of both high pressure ratio and efficiency. One of the prime elements for performance improvement of centrifugal compressors is the impeller. For impellers with tip gaps, the greatest source of loss generation comes from the tip leakage flow [8]. When a shock wave occurs under transonic inlet conditions, the interaction of the shock wave, the boundary layer and tip leakage vortex will further deteriorate the complex flowfield as well as the performance of transonic impellers [9]. Sweep is a degree of freedom of the blade stacking style. When the shroud section of the blade extends upstream in the chord line direction (or axial direction), it is defined as forward sweep. The opposite is regarded as aft sweep. Because the tip geometry changes with the sweep feature, impacts on the tip leakage flow and the shock structure are expected. It is therefore considered a potential way to improve the performance of modern turbomachinery. In axial turbomachines, swept blade design has been studied for over half a century. Its application has been widely spread from compressors to turbines and from rotors to stators [10], especially applied to blade ends to improve the endwall flowfields [11]. For compressor rotors, a detailed survey [12] suggested that forward swept blades improved the efficiency and extended the stall-free operating range by reducing the near-wall and tip clearance losses, as well as controlling the secondary flows and radial migration of high-loss fluid. More recently, [PERSON] et al. [13] optimized the sweep feature, the camber line and the chord length of a transonic axial compressor rotor. The best result in terms of efficiency and stall margin appeared to be aft-swept in combination with an S-shaped camber line and an increased chord length. For compressor fans, [PERSON] [14] concluded that the application of forward sweep in fans with the controlled vortex design concept not only reduces the near-tip loss via moderation of the already intensified radial migration of low-momentum flow, but also decreases the friction loss away from the endwalls by shortening the already elongated flow path. Different designs of forward sweep and aft sweep in a fan with the controlled vortex design concept were examined later by [PERSON] and [PERSON] [15]. The enlarging forward sweep angle appeared to improve the performance especially in low mass flow operating conditions. With regard to transonic axial compressors with shocks, the sweep feature also has a significant effect on the shock structure. [PERSON] et al. [16] concluded that the passage shock would move relatively downstream in the forward sweep design, and vice versa for the aft sweep case. The forward sweep was found to improve both the efficiency and the stall margin. Similar trend of the shock front movement and the efficiency increment was captured in the Rotor 37 case [17; 18]. [PERSON] and [PERSON] [19] applied sweep to a transonic fan, where the stall margin was significantly extended due to the optimized shock structure. URANS and LES methods were recently applied by [PERSON] and [PERSON] [20] to investigate the near-stall flow mechanism of a transonic fan. It is shown that a compound sweep design enabled the passage shock to stay near the leading edge rather than to detach from the blade, which resulted in a much more stable flow structure near the tip region. Among all swept axial cases, it is generally found that the stall margin will be improved by forward sweep and vice versa.