## 1 Introduction  
Aerodynamic and structural design of an impeller are important to the performance of a compressor unit [1]. The design work of a new impeller is mainly focused on the designing of flow passage [2]. Meridional plane design is one of the important parts of the flow passage design. The geometrical profiles of impeller hub and shroud have significant effects on the overall performance of a compressor. This is because the fluid flowing between these two curves not only determines the efficiency of the impeller but also strongly affects the performance of diffuser or volute in downstream [3]. Much progress had been made in last decades [4]. One of the most outstanding works was from [PERSON] [5], who applied the inverse design methods to the flow passage design in turbomachinery. With recent improvement, the advanced optimization methods have been introduced into the design of meridional profiles. [PERSON] [6] and [PERSON] [7] put forward a method to define the meridional channel by a string of Bezier points. This method based on Bernstein-Bezier polynomial patches had already been a guideline of the parameterization of the meridional plane profile. [PERSON] [8] described a kind of three-dimensional inverse method, by which an imposition of mean swirl was defined as optimization specification throughout the meridional section of the turbomachinery. [PERSON] [9] explored an evolutionary optimization algorithm to optimize meridional geometry, by which the secondary flows across the impeller could been reduced greatly. A numerical method coupled with the optimization design methodology, which was consisted of reaction surface method (RSM), statistical approach and genetic algorithm, was developed to obtain optimized hub and shroud line by [PERSON] [10]. Meanwhile, [PERSON] [11] used an evolutionary algorithm with the help of a Bezier curve to make efficiency higher without the reducing of the pressure ratio. As some extra mechanical constraints, such as the maximum stress and stress distribution, had to be considered in the aerodynamic design, the multidisciplinary and global optimization design methods were presented in resent literature. A software using a through-flow computation with a breeder genetic algorithm had been programmed to acquire the optimization of meridional plane [12]. [PERSON] [13] presented a multidisciplinary and multi-objective optimization system based on an artificial neural network to improve the performance of the impeller while the mechanical stresses were kept within the limitation.  
A traditional meridional profile was usually described by several arc lines, and widely adopted in the most of meridional shape design. It was generally believed that for the shroud line and the hub-line on the meridional plane, the arcs and the smoothed connection among these arcs were beneficial to aerodynamic performance. However, during the process of the manufacturing of a compressor unit, it would take most of time to produce this kind of 3D complex impeller with high cost by a 5-axis machine. In order to save time and cost, welding technology is gradually being used in manufacturing of impellers. It is due to the narrowed shrouded structure that the work of welding blades on the disk is very hard. So, a simplified meridional profile of an impeller is needed urgently to substitute the traditional meridional profile. But, although much improvements on impeller design, such as blade profiles, incidence angle and stagger angle, etc., had been greatly achieved, there was not enough attention on how to simplify the impeller structure to adapt to the welding manufacture.  
Therefore, in this paper, a simplified geometrical configuration of the meridional contours is presented, which can simplify the structure of the impeller and be beneficial to the welding manufacture with a little negative effect on the impeller performance.