Gazdynamic characteristics of the centrifugal compressor calculation

Gas-dynamic characteristics of the compressor make it possible to evaluate its energy and economic properties, to predict the values of capacity, the generated gas pressure and the power consumption during the compressor operation. For more in-depth consideration of the compressor, it is desirable to have the characteristics of its individual stages. The element-by-element analysis of the characteristics of each stage makes it possible to improve the coordination of the operation of the individual elements with each other and thereby improve the gas-dynamic characteristics of the compressor. The loss factor  and the static pressure recovery factor can be used as the values characterizing the properties of the individual elements of the stage. Coefficients  and  are suitable for evaluating the energy properties of any element of the stage. To assess the effect of the element in question on the economy of the stage, it is necessary to establish what proportion of the work required for compression is the "loss" of energy in a given element, i.e. find the reduction in efficiency stage   due to dissipation of energy into heat in this element. Calculation of performance of the centrifugal compressor is performed from the inlet to the outlet using the equations of state, of process, of continuity and conservation of energy. The initial data are geometric parameters of the compressor, the composition and the initial parameters of compressed gas, the rotational speed of the rotor. The basis of the elementwise calculation of gas-dynamic characteristics is the gas-dynamic characteristics of the stage elements. The calculation can be performed using the characteristics of the stage elements taken from the own bank of experimental data or using the generalized characteristics of the stage elements. To obtain generalized characteristics of the impeller, blade and no-blade diffusers, reverse guide vanes, experimental data were used, published in the works of Galerkin, Den, Rees, Seleznev and others, as well as experimental data obtained by the author. The generalized characteristics are obtained in the form of analytical dependences of the loss coefficients on the angles of attack or flow angles by approximation of experimental data. These dependences were used to analyze the gas-dynamic characteristics of a centrifugal compressor, which made it possible to develop recommendations for their improvement.


Introduction
Gasdynamic characteristics of the compressor make it possible to evaluate its energy and economic properties, to predict the values of capacity, the generated gas pressure, the power consumption during the compressor operation. For more in-depth consideration of the compressor, it is desirable to have the characteristics of its individual stages. The element-by-element analysis of the characteristics of each stage makes it possible to improve the coordination of the operation of the individual elements with each other and thereby improve the gas-dynamic characteristics of the compressor.
The values characterizing the properties of the individual elements of the stage can be the loss factor and the static pressure recovery factor. Coefficients and are suitable for evaluating the energy properties of any element of the stage. To assess the effect of the element in question on the economy of the stage, it is necessary to establish what proportion of the work required for compression is the "loss" of energy in a given element, i.e. find the reduction in efficiency stage due to dissipation of energy into heat in the element under consideration. The elementwise analysis of the compressor's work can be a powerful tool for improving its flowing part. The creation of software for elementwise calculation of gasdynamic characteristics of a centrifugal compressor is undoubtedly an actuation one.

Gasdynamic characteristics calculation method
Calculation of the gasdynamic characteristics of the compressor is carried out in series from the inlet to the outlet, using the equations of state, process, continuity and conservation of energy [1,2].
The initial data are the geometric parameters of the compressor, the composition and initial parameters of the compressible gas, the rotor speed. The number of calculated compressor operating conditions by flow rate is usually not more than 10.
Initial calculation data. The initial data are: 1) geometric parameters ( Fig. 1): d0small diameter at the impeller inlet; D0large diameter at the impeller inlet; D1diameter at the impeller blade inlet; D2diameter at the impeller blade outlet; D3diameter at the diffuser inlet; D4diameter at the diffuser outlet; Розділ 1. Холодильна техніка _______________________________________________________________________________________________________________ 5 D5diameter at the return channel inlet; b1width at the impeller blade inlet; b2width at the impeller blade outlet; b3width at the diffuser inlet; b4width at the diffuser outlet; b5width at the return channel inlet; 1 b angle at the impeller blade inlet; 2 b angle at the impeller blade outlet; 3 b angle at the diffuser inlet; 4 b angle at the diffuser outlet; 5 b angle at the return channel inlet; 6 b angle at the return channel outlet; 1 3 5 ,, z z zquantity of blades of impeller, diffuser and return channel respectively.

2) gas parameters:
Rgas constant, J / (kg K); kadiabatic index; p cisobaric specific heat, J / (kg K); zcoefficient of compressibility; , in in pTpressure and temperature of gas at the compressor inlet; 3) gasdynamic characteristics of the elements stage: loss factor of the impeller; 1 iangle of attack at the impeller blade inlet;   6. Total pressure at the impeller inlet 7. Total temperature at the impeller inlet 8. Total density at the impeller inlet 9. Static density at the impeller inlet 13. Radial velocity at the impeller inlet 19. Radial velocity at the impeller outlet

Obtainment of the gasdynamic characteristics of the stage elements
The basis of the elementwise calculation of gasdynamic characteristics is the gasdynamic characteristics of the stage elements. The calculation can be performed using the characteristics of the stage elements taken from the own bank of experimental data or using the generalized characteristics of the stage elements.
For convenience of calculation automation, the experimental data [2,3,4,5,6,7] were approximated using the program «UniAprox2.04» and the analytical form of the generalized characteristics was obtained.
The results of approximation for the loss factors of the stage elements are represented below.
Dependence of the loss factor on the angle of attack of the impeller are represented on figure 2.

Results
For example, an elementwise analysis of the compressor 16GTS2-340 / 60-85M is performed. The most effective operating condition is the 4th. Figure 8 shows the data that allows you to determine how aligned the operating condition of the compressor stages are.
The loss factors of the elements of the 1st stage of the compressor are close to the minimum, but for the elements of the second stage, it is possible to reduce the values of the loss factors (increase in the efficiency). To do this, it is needed to reduce the angle of attack at the entrance to the impeller by 3-4 0 , increase the angle of the flow to 20 0 , reduce the angle of attack at the entrance to the vane diffuser by 4-5 0 . The correction of the size of the flow part, which ensures the required changes in the flow parameters, can be performed in various ways, for example by changing the width of the channels.

Conclusions
Elementwise analysis makes it possible to improve the coordination of the work of individual elements of the stages of a centrifugal compressor with each other and, consequently, to increase its efficiency.