# Detailed Design and Aerodynamic Performance Analysis of a Radial-Inflow Turbine
## 1 Introduction  
Compact air cycle machines (ACM) have been widely employed in many industrial applications, such as environment conditioning systems (ECS) and air cycle refrigeration. The coefficient of performance (COP) of the cooling cycles changes dramatically by efficiency and pressure ratio of the ACM [1; 2]. The radial-inflow (RI) turbine is an indispensable member of the ACM, which is regularly used in compact air cooling systems because of its reliability, simplicity and robust construction, fast response, various working fluids (such as organic working fluids), low emission and low manufacturing cost [3; 4; 5]. Thus, the performance of the RI turbine is essential for these types of systems. The aerodynamic design of the radial-inflow turbines is efficiently accomplished in well-known steps. First, a preliminary design is performed to calculate the basic stage component dimensions. An effective preliminary design provides important advantages in terms of quality and productivity for RI turbines and costs about 50% of the engineering time in the design process of a radial-inflow turbine [6]. [PERSON] [7] explains that the second step in the design of radial inflow turbine is the detailed design of the rotor and nozzle blades, according to the geometry dimensions obtained by the preliminary design (first step). In this step, the nozzle blade profile and the pressure and suction sides of the rotor blades are accurately determined. These detailed geometries can be ready for manufacturing. [PERSON] [8] and [PERSON] [9] presented an analytical method to compute the geometrical dimensions of an RI turbine for maximum efficiency based on specific velocity. [PERSON] considered boundary layer loss (profile loss) in nozzle and rotor and tip clearance loss in the design process. He studied the variations in turbine efficiency related to the rotor tip-radius ratio, the exit flow angle at nozzle and the ratio of nozzle blade height to rotor-inlet diameter. [PERSON] [9] provided a computer program to design RI turbines based on power, mass flow rate, inlet temperature and pressure. The design variables included a stator-exit angle, rotor-exit-tip to rotor-inlet radius ratio, rotor-exit-hub to tipradius ratio and distribution of rotor-exit tangential velocity. The program was able to compute the basic dimensions of the turbine stage, temperature and pressure at inlet and outlet sections of each component. [PERSON] [10] developed an advanced program to design a small, cooled radial turbine, which operated at high inlet turbine temperature. This program was able to determine the rotor blade camber line in addition to the capabilities of the program developed by [PERSON]. [PERSON] [11] presented a non-dimensional approach based on non-dimensional power to minimize Mach number at the rotor inlet and outlet so that the passage losses are reduced. The non-dimensional turbine design can then be transformed to the dimensional design by applying inlet stagnation conditions (total temperature and pressure) and mass flow rate. [PERSON] et al. [12] also provided an automated mean-line (1D) approach to the preliminary design of RI turbines. Authors used a brute-force search algorithm to select dimensions based on non-dimensional performance and geometry characteristics. [PERSON] et al. [13] employed an optimization algorithm during preliminary design to remove selective open parameters such as rotor axial length. They also presented a detailed approach for nozzleless volute design. However, all aforementioned works did not describe an approach to achieve the second step in radial-inflow design. Although commercial software such as ANSYS-Vista RTD and RITAL do not provide any information about the rotor detailed design, stator geometry, stator profile and volute dimensional specifications, designers usually use them for the preliminary design [7; 14; 15].