Abstract
In this study, some important intrinsic dynamics have been captured after analyzing the relationships between the dynamic pressure at an outlet of centrifugal compressor and fractal characteristics, which is one of powerful descriptions in entropy to measure the disorder or complexity in the nonlinear dynamic system. In particular, the fractal dynamics of dynamic pressure of the flow is studied, as the centrifugal compressor is in surge state, resulting in the dynamic pressure of flow and becoming a serious disorder and complex. First, the dynamic pressure at outlet of a centrifugal compressor with 800 kW is tested and then obtained by controlling the opening of the anti-surge valve at the outlet, and both the stable state and surge are initially tested and analyzed. Subsequently, the fractal dynamics is introduced to study the intrinsic dynamics of dynamic pressure under various working conditions, in order to identify surge, which is one typical flow instability in centrifugal compressor. Following fractal dynamics, the Hurst exponent, autocorrelation functions, and variance in measure theories of entropy are studied to obtain the mono-fractal characteristics of the centrifugal compressor. Further, the multi-fractal spectrums are investigated in some detail, and their physical meanings are consequently explained. At last, the statistical reliability of multi-fractal spectrum by modifying the original data has been studied. The results show that a distinct relationship between the dynamic pressure and fractal characteristics exists, including mono-fractal and multi-fractal, and such fractal dynamics are intrinsic. As the centrifugal compressor is working under normal condition, its autocorrelation function curve demonstrates apparent stochastic characteristics, and its Hurst exponent and variance are lower. However, its autocorrelation function curve demonstrates an apparent heavy tail distribution, and its Hurst exponent and variance are higher, as it is working in an unstable condition, namely, surge. In addition, the results show that the multi-fractal spectrum parameters are closely related to the dynamic pressure. With the state of centrifugal compressor being changed from stable to unstable states, some multi-fractal spectrum parameters Δα, Δf(α), αmax, and f(αmin) become larger, but αmin in the multi-fractal spectrum show the opposite trend, and consistent properties are graphically shown for the randomly shuffled data. As a conclusion, the proposed method, as one measure method for entropy, can be used to feasibly identify the incipient surge of a centrifugal compressor and design its surge controller.
Highlights
As one type of flow instability, surge will occur if the flow of the centrifugal compressor is reduced to a critical value [1]
The dynamic pressure of flow becomes a serious disorder and complex as the centrifugal compressor is in transition from stable state to surge, and the routine methods are difficult to capture and describe the complex characteristics
Autocorrelation, Hurst exponent, and variance are used to describe the mono-fractal characteristics of the dynamic export pressure
Summary
As one type of flow instability, surge will occur if the flow of the centrifugal compressor is reduced to a critical value [1]. Most of the researches still focus on the theoretical study or the numerical model, and the surge active control method, such as neural network, which would not appear to be a very practical method [7] As studied in this field, it is found that flow pressures from inlet, outlet, and impeller behave as nonlinear dynamics as the centrifugal compressor is working in the surge state. Fractal dimensionality and largest Lyapunov exponent, as the measures of the entropy and state functions, have been intensively and exhaustively used in the last 30 years in the study of nonlinear dynamics [9,10,11] Based on such motivation, fractal dynamics are used to describe the characteristic of the flow pressure for the centrifugal compressor. Some results are obtained, and the feasibility of the method to identify surge is accurately verified, and the results will provide an effective way to predict the surge
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