Performance prediction of axial-flow compressors with variable geometry using a modified stage-stacking method
LIU Huan1,2, ZHANG Shijie1,2
1. School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100190, China; 2. Key Laboratory of Advanced Energy and Power, Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China
Abstract：[Objective] The stage-stacking method, which is based on stage characteristic curves and uses a sequential calculation scheme, is a valuable tool for predicting the performance of multistage axial-flow compressors. A slight variation in mass flow can cause considerable changes in the pressure ratio because the compressor operates at high speed, and constant speed lines exhibit near-vertical orientation. To avoid this issue, a traditional approach is to convert the mass flow rate boundary into pressure ratio boundary conditions. This undoubtedly increases the complexity of calculations. Furthermore, practical monitoring parameters and boundary conditions linked with other components in an entire gas turbine system are state variables, namely, pressure and temperature, rather than the mass flow rate. Consequently, if we adopt the mass flow rate boundary condition, an initial value must be assumed, and the result may be obtained through an intricate iterative process. Thus, the calculation frequently becomes highly inefficient. Targeting the complexities and inefficiencies inherent in the traditional approach, a modified stage-stacking method is developed. The modified stage-stacking method, similar to the traditional approach, is based on two generalized stage performance curves, namely, pressure coefficient and efficiency curves. Each stage is considered as an independent control volume, delineated by its physical boundary. This method uses thermodynamic parameters—static temperature, static pressure, and axial velocity—along meridional streamline at a mean radius of all stage inlets and outlets as unknown variables. When conservation of mass, momentum, and energy is applied to each stage, a nonlinear system with 3n governing equations is obtained for a compressor of n stages. These equations involve 3n variables with the inlet total pressure, the total temperature, and the outlet total pressure as boundary conditions. Thus, the group of equations can be simultaneously solved. The Newton-Raphson method is used as the iterative numerical solver for the nonlinear algebraic equation set. The thermodynamic properties are determined by functions from the Multiflash library. Furthermore, while assuming a linear mathematical correlation between the variable stator vane and the inlet guide vane (IGV), the impact of the variable geometry of a modern heavy-duty gas turbine compressor on the performance is investigated. In addition, to analyze the effect of air bleeding on compressor performance, the bleeding quantity is deducted from the pertinent continuity equation. According to this approach, a model is developed to predict the performance of a multistage axial-flow compressor featuring variable geometry. To validate the accuracy of the model, four representative compressors for fixed geometry, variable geometry, and interstage bleeding with distinct parameters are selected as research subjects. Compared with field data, the results are in good agreement with an average relative error of only 1.593 % for fixed geometry compressors. For variable geometry compressors, excellent agreement is observed between the predicted results and field data, with a maximum relative error of 3.856 % at high constant speed lines. For low constant speed lines, despite the largest relative error of 10.834 %, the absolute error remains small and within an acceptable range. Of great importance is the strong conformity between the trends of compressor performance with speed variation and IGV adjustments obtained from this model and field data, providing a substantial indication of the result accuracy. If a suitable IGV schedule is chosen, the relative error can be as low as 0.450 %. In addition, the model can accurately estimate the geometric and thermodynamic parameters with limited design parameters, with root mean square errors of 0.022 and 0.918, respectively. These results show that the modified stage-stacking method can not only precisely calculate the overall performance of axial-flow compressors and assess the impact of the variable geometry on compressor performance but also obtain the geometric and thermodynamic parameters of each stage of such compressors. This method serves as a valuable framework for developing steady-state and dynamic compressor models.
刘欢, 张士杰. 基于改进叠加法的变几何轴流压气机性能预测[J]. 清华大学学报（自然科学版）, 2024, 64(5): 869-878.
LIU Huan, ZHANG Shijie. Performance prediction of axial-flow compressors with variable geometry using a modified stage-stacking method. Journal of Tsinghua University(Science and Technology), 2024, 64(5): 869-878.
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2024, Vol. 64 
