## 1 Introduction  
Axial turbines are a main component of turbomachinery used in different industries, such as aviation, power generation, marine propulsion, etc., due to their high power output, small dimensions and high efficiencies. These systems have been in a continuous process of evolution, achieving high performances despite harsh operating conditions (very high temperatures, pressures, and mechanical loads). This evolution was possible due to advances in different fields, such as fluid mechanics, materials and heat transfer. The use of numerical design, Computer Aided Design (CAD) methods and Computational Fluid Dynamics (CFD) led to the introduction of evermore complex geometries and systems (such as cooling systems). A less studied drawback of axial turbines is the rapid decrease in performance at partial loads. Since turbines are designed for a set of nominal inlet parameters and power requirements, when operating at partial regimes (i.e., different inlet temperatures, pressures and mass flows according to the working line of the respective engine) the performance drops significantly. This is caused by a change in flow characteristics in turbine channels, which are not suited for the fixed geometries of the vanes and blades and are designed for nominal regimes. A method to address this decrease in performance is the use of adaptive turbine geometry. Through changing the turbine geometry, depending on the inlet conditions, the flow through the turbine can be controlled to better extract the available energy of the hot gases at the respective regime. The use of adaptive geometry is not a new idea, with a patent obtained as early as 1966 by [PERSON] and [PERSON] [1] for a variable stator turbine. However, due to the extreme environment at which the turbine operates, high temperatures and pressures, a variable geometry turbine could not be used for modern engines without affecting engine reliability. With the aim of controlling the flow through the turbine at partial regimes, in order to improve the performance without affecting engine reliability, an active flow control system has been proposed and characterized in previous works [2; 3]. Instead of using variable geometries, the method consists of the injection of a fluid in specific sections of vanes in order to modify the flow sections, accelerate the flow through the channels and increase the power output. Previous studies showed that power generation can be increased by as much as 30%, depending on the injection system configuration, without increasing the total mass flow through the turbine [2]. The studies have focused on determining the influence of different parameters on the influence of the injection system. It was also showed that the system can be applied to different turbine sizes and for a large operating interval [3]. A similar injection method was researched by numerous authors with a similar aim, flow control in turbine channels. The main difference with the aforementioned studies is that the aim is to decrease certain losses not to control the flow to directly influence power generation. In [4; 5; 6; 7; 8; 9; 10], the authors introduced an injection method in order to accelerate the flow on the suction side of the blade in order to reduce or eliminate the flow detachment at different Reynolds numbers. The results showed that through injecting a fluid in these regions the flow detachment process can be delayed. The authors also studied the use of unsteady jets as a method of controlling flow detachments. The results showed that through using transient flows similar results can be obtained if the correct frequencies are achieved. Similar studies were conducted in [11; 12; 13; 14; 15; 16; 17]. A different approach but with the same goal, that of reducing the losses caused by the appearance of detachments on the suction side of the vanes, was undertaken by [PERSON] and [PERSON] [18]. The authors performed a numerical study in which they used an injection system in the trailing edge area of the vane for a turbine operating at partial regimes.