EVALUATION AND PREDICTION OF THE EFFECTIVENESS OF SLOT-TYPE CASING TREATMENTS IN A LARGE-SCALE AXIAL COMPRESSOR BY AN INTEGRAL METHOD

A novel integral method is proposed to quickly assess the effectiveness on stability improvement with end-wall casing treatments (CT). The chief advantage claimed for this method is the possibility of using merely one operating point to evaluate various casing treatment configuration instead of calculating the whole performance curves, which would result in a reduced amount of costly and time-consuming experiments. This integral approach is proposed on a basis of the hypothesis that the spike stall precursors can be triggered by forward spillage of the rotor tip leakage flow, and the onset condition of such a spillage is determined by axial momentum balance within the rotor tip region. The cumulative axial momentum for the tip region is captured by setting a series of control volumes at the rotor tip region. This curve resembles a bell, which is named as “bell-shaped curve” are critical to reveal the rotor stability. The peak of this curve indicates the timeand spatialaveraged interface position between the main flow and tip leakage flow. A more downstream peak denotes a farther distance of the interface to leading edge. The effectiveness of various CT can thus be quickly assessed by comparing their corresponding bellshaped curves at the mass flow rate for smooth casing near stall. Three slot-type configurations are evaluated by this method. The impact of the slots on peak efficiency is also investigated by entropy production analysis. According to the analysis, a refined configuration that generates less efficiency penalty while maintaining satisfied stall margin improvement (SMI) is proposed. Its effectiveness is firstly comfirmed by bell-shaped curves and then validated by experiments, which suggest that the bell-shaped curves can be a useful tool on preliminary design phase for casing treatment. INTRODUCTION The stability limit of compressor has been a challenging problem in the advent of the aircraft engine. Casing treatments (CT) are claimed as a practical means to avoid such a failure. During the past decades, experimental and numerical efforts have been successively dedicated to understand the mechanisms of CT [1]. These give some ideas of the CT design and emphasize the need for feedback between the practical design and stall mechanisms. Due to the complexity of the compressor stall, the mechanisms for CT are still not fully understood and conclusions are controversial [2]. An obvious example can be that the most effective locations for the circumferential grooves are around the rotor leading edge according to a few studies [3, 4], but other researchers report that middle and rear chord are the effective locations for stall margin improvement [5, 6]. Slot type casing treatment provides another example. Gonis et al. [7] presented that the shape of the slots determines its effectiveness on stall margin enhancement while Djeghri et al. [8] claimed that the slot shape has minor effect on both peak efficiency and stall margin. The efficiency variation due to CT is even more irregular. It is usually considered that CTs arise extra loss especially for the slot-type ones. However, it is recently reported that several CT are designed without detriment to efficiency. These then one can hardly tell the performance of a CT configuration before real testing it. Hence, at the preliminary design stage, extensive experiments and simulations are in demand to establish a database for CT design, which is fairly costly and time-consuming. To reduce the duration and expense of the CT predesign, a novel approach is proposed previously by authors [9]. Instead of calculating the whole performance curves, the cumulative axial momentum distributions for rotor tip region at the same mass flow for smooth casing (SC) near stall are conducted to identify their efficacies. It markedly reduces the time and difficulty for tracking down the individual stall points for each CT configurations. This approach has been validated to be capable to assess the effectiveness for different groove-type casing treatments on low-speed