Optimization of a centrifugal compressor impeller using CFD: the choice of simulation model parameters
Abstract. Nowadays the optimization using computational fluid dynamics (CFD) plays an important role in the design process of turbomachines. However, for the successful and productive optimization it is necessary to define a simulation model correctly and rationally. The article deals with the choice of a grid and computational domain parameters for optimization of centrifugal compressor impellers using computational fluid dynamics. Searching and applying optimal parameters of the grid model, the computational domain and solver settings allows engineers to carry out a highaccuracy modelling and to use computational capability effectively. The presented research was conducted using Numeca Fine/Turbo package with SpalartAllmaras and Shear Stress Transport turbulence models. Two radial impellers was investigated: the highpressure at ѱ_{T}=0.71 and the lowpressure at ѱ_{T}=0.43. The following parameters of the computational model were considered: the location of inlet and outlet boundaries, type of mesh topology, size of mesh and mesh parameter y^{+}. Results of the investigation demonstrate that the choice of optimal parameters leads to the significant reduction of the computational time. Optimal parameters in comparison with nonoptimal but visually similar parameters can reduce the calculation time up to 4 times. Besides, it is established that some parameters have a major impact on the result of modelling.
Introduction
The design quality of the flowpath is one of the basic factors that determine the overall efficiency of centrifugal compressors. Automatic optimization techniques are used for the aerodynamic and mechanical design of turbomachine components. The optimization algorithm based on a sequence of 3D simulations for a large number of stage shape variations, which are generated to improve output parameters, as efficiency, pressure ratio, head etc. There are many approaches to optimization, which are good for optimal solution search [1]. Therefore, proper problem definition, the selection of the main parameters and criteria for optimization allows designers to significantly improve the performance of the final product [2].
Most computational fluid dynamic software packages include the fullcycle optimization algorithm with geometrical model parameterization, geometry and mesh regenerating tools. This allows CFD users to easily use geometric CFD optimization software to automatically generate design variants. These software packages often include a builtin optimization algorithm (in most cases it is genetic algorithm) or have the ability to use thirdparty code, as IOSO. Thus, technical aspects is well understood at the moment, and it is not problem to realize a sequence of calculations.
Despite the many advantages, their use is usually limited to simple applications in industrial practice, because of their high computational cost. During optimization computing systems work through many variants of a flowpath to achieve the desired result. If a powerful cluster with hundreds of cores carries out the calculations [3], the efficiency of optimization will not drop. This will increase only the workload of computing machine and the cost of electricity. In the case of lowpower computing systems, performance of the works and the manufacture of products will be reduced. For this reason, one of the main problem that an iteration of optimization takes long time to compute. Therefore, one of the methods of increasing the optimization effectiveness is to decrease the time per one iteration while keeping the adequacy of calculation results. In this way, efficiency of the optimization mostly depends on the accuracy of the simulation model [4].

The aim of study and the object of research
The aim of the study is to investigate the influence of the computational domain and mesh model parameters on the integral parameters of the impeller and the rate of obtaining a converging solution. The best combination of these parameters will be used for future multiobjective optimization.
In this study, computation models of two radial impellers of the centrifugal compressor with cylindrical blades have been used:
The first one is a lowpressure impeller (IMP1) with the meancamber curve of the blade formed by a circular arc. The flow rate coefficient F=0.06; the Euler work coefficient ψ_{T}=0.43; the impeller exit diameter is 0.82m; blade outlet angle β_{bl2}=32°; the number of blades z=13.
The second one is a highpressure impeller (IMP2) impeller with the meancamber curve of the blade formed by an sshaped curve. The flow rate coefficient F=0.064; the Euler work coefficient ψ_{T}=0.71; the impeller exit diameter is 0.4m; blade outlet angle β_{bl2}=75°; the number of blades z=24.
Mesh model generation and subsequent computations were carried out using Numeca Fine/Turbo. The Fine/Turbo is a specialized CFD suite for rotating machinery with incompressible and compressible fluids that proved oneself as the fastest, accurate and convenient tool [5].
The computational domain and variations of the inlet and outlet boundary are shown in figure 1. The following boundary conditions were applied: steady conditions, air ideal gas as fluid, total pressure and temperature as inlet boundary condition, mass flow as outlet boundary condition. The following two turbulence models were compared: SpalartAllmaras and Shear Stress Transport. Furthermore, the regions of labyrinth seals were not included in the computational model to speed up the calculations. The values of the polytropic efficiency presented below was corrected for estimated losses of the disk friction and leakage through labyrinth seals.