The choice of key geometric parameters in the numerical optimization of centrifugal compressor impellers

The article deals with the choice of key geometric parameters and the range of their variation in solving the optimization problem of centrifugal compressor impellers using computational fluid dynamics. The study was carried out using Numeca Fine / Turbo package. The influence of more than 10 geometric parameters on the efficiency and the head of the impeller was considered. The influence degree evaluation of investigated optimization parameters was provide by changing the parameters value in a preset range and analyzing their impact on the efficiency and head of the impeller. As a result, the main geometric parameters of optimization, which should be considered first, were identified. Other parameters may not be considered within the optimization problem, and can be assigned to the standard values. In addition, recommendations on optimal ranges of parameter values were given.


Introduction
Modern optimization algorithms together with mathematical models realized in packages of computational gas dynamics allow to automate the process of searching for optimal solutions [4,5]. The structure of the gas flow in the impellers of centrifugal compressors has a complex nature [6,7], therefore numerical optimization of the flow makes it possible to obtain the most efficient impeller at low costs in comparison with field experiments.
However, when solving optimization problems, the question arises of the rationality and validity of the calculation models, criteria, parameters and optimization algorithms used [8]. Also, the efficiency of selecting the main optimization parameters and parametrization of the geometric model of the object under study is important.
The aim of work is to determine the main and minor geometric parameters of optimization of the impeller of the Central Committee, as well as to estimate the rational ranges of variation of the parameters considered.
The object of investigation is a high-pressure impeller of the first stage of an industrial air centrifugal compressor.

Methods
The computational part is performed using three-dimensional modeling of viscous flow using CFD methods in the Numeca Fine / Turbo software package. Information on the main aspects of the calculation in the complex used is given in [9]. An optimal calculation model has been chosen for the parameters of the grid model and the computational domain that provide the optimal relationship between the accuracy, the rate of convergence of the problem, and the time spent in calculating [10] for selected turbulence models Shear Stress Transport (SST) [11] and Spalart-Allmaras (SA ) [12].
The calculated region and shape of the impeller blades are shown in Fig. 1. The sample regions were not taken into account. Consequently, the values of efficiency on the graphs are polytropic hydraulic.    [13]; b) in a small area of the best coefficients combination from (a); out of the range, which is recommended in literature [13] For the given impeller, a design with combinations of coefficients greater than the recommended ones does not give acceptable efficiency.

Meridian rounding of the cover and main disk
The geometrical variation of the line of the covering disk is shown in Fig. 3. Table 1 shows the values of the dimensional r and the relative radius (referred to the diameter of the impeller D2).  The complex rounding of the covering disk, formed by a combination of several radii, straight lines and Bezier curves, is shown in Figure 4. The variants of the rounding of the main disk are considered: the radius disk (Figure 5a) and the complex one (Figure 5c). Accordingly, Figures 5b and 5d show the calculated values of the hydraulic polytropic efficiency. Table 2 shows the values of the dimensional and relative radii for the radius transition of the meridional line of the main disk.

The meridional shape of the covering disk within the interblade channel
The variation of the meridian shape of the covering disk is shown in Fig. 6a, b. The results of the calculation are shown in Fig. 6c, d, e for 15 variants of the curved shape of the covering disk. The paper [14] compared the RC with the same load distribution on the blades with different meridional form, i.e. for different b = f (r).

Complex of parameters of the input edge in the meridional section
The parameters of the input edge -diameter D1, angle of inclination to the axis of rotation φ and edge radius R, determining the position and shape of the leading edge in the meridian plane (Fig. 7a, b, c) are considered separately. Variants with random combinations of these parameters are also calculated (Figure 7d), for which the calculation results are shown in

Input and output edges in radial section
The main variants of the input and output edges of the impeller blades are considered ( Figure 8).

Evaluation and selection of optimization parameters
The influence of the bushing diameter, the diameter of the entrance to the RC D0, the number of blades is considered.
As a result, all the parameters considered are summarized in Table 3. The contribution of the parameter was estimated both by the effect on the efficiency of the work of the impeller, and by the effect on the head. The value of the efficiency of the initial version of the impeller is 93.7%.

Conclusions
It should be noted that, in addition to the analysis of geometric parameters, the selection of parameters of the calculation model, such as: the computational domain, grid parameters, boundary conditions, solver settings, etc., is of great importance in solving the optimization problem [15][16][17][18][19][20].