Chemical and Petroleum Engineering, Vol. 42, Nos. 5–6, 2006
COMPRESSORS, PUMPS, AND PIPELINE FITTINGS METHODS OF ROTATING STALL AND SURGE DETECTION IN CENTRIFUGAL COMPRESSORS
Ya. Z. Guzel’baev, A. L. Khavkin, and I. G. Khisameev
Systems for prevention of surging of centrifugal compressors and methods of rotating stall detection and early surge diagnosis using statistical processing of sensor signals of various parameters, i.e., the method of calculation of the correlation function of the signal and the method of calculation of signal dispersion, are discussed. The results of routine tests of air and high-speed air centrifugal compressors and their detachable flow parts are adduced.
The presently available systems for prevention of surging of centrifugal compressors (CC) can be divided roughly into two groups. 1. Systems preventing surge, which are often called antisurge control systems. In this case, the surge boundary is plotted on the gas-dynamic curve of the compressor and to its right (10–15% toward the flow rate increase) is drawn the antisurge control line. If the working point of the compressor curve lies to the left of the control line, the bypass (or dump) valve slightly opens up, which prevents surging of the compressor. The surge boundary is determined experimentally in the course of surge tests or by calculation. As an example, in Fig. 1 are shown the surge boundary line for the supercharger N133-21-01 (curve 1) determined in the course of the surge tests and the antisurge control line (curve 2). 2. Systems responding to incipient surge (surge signal indicators). In these systems, use is made of the distinguishing features of the behavior of the signals from the sensor, which characterize the compressor operation conditions (flow rate, supercharging pressure, current strength of the main electric drive, etc.), and a discrete signal is generated for forced opening of the bypass valve and/or for stopping of the compressor. A surge signal indicator can be installed in addition to the antisurge control system, and if this system fails either due to variation in the parameters of the gas being compressed or due to inadmissible increase in the thickness of the deposit layer in the flow part, the surge signal indicator prevents operation of the compressor in inadmissible surge conditions. Let us examine the second group of surge prevention systems. Research carried out by developers of surge prevention systems for centrifugal compressors was focused on detection of distinguishing features of incipient surge, which is characterized by fluctuations of the (discharge) pressure and the rate of gas flow through the compressor, the delivery temperature, the current strength of the electric drive, etc. Many patents have been granted on this subject in Russia and abroad. For example, an antisurge device based on fixing of the moment of concurrent drop in the delivery pressure and the rate of gas flow through the compressor has been patented [1]. In a series of experiments performed in the 1960s [2, 3], it was found that rotating stall appears in the centrifugal compressor in the region of the working points of the compressor characteristics (curve) near the surge boundary. Theoretical and experimental studies of rotating stall that precedes surge were carried out in [4, 6]. NIIturbokompressor im. V. B. Shneppa ZAO, Kazan. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 6, pp. 30–33, June, 2006. 320
0009-2355/06/0506-0320 ©2006 Springer Science+Business Media, Inc.
ps, MPa 2.2
1
2
1.8 I
II
III
1.4
40
50
60
Q, m3/min
70
Fig. 1. Surge boundary line for the N133-21-01 supercharger: I) surge area; II) danger area; and III) steady operation area.
However, experimental studies of incipient surge were associated with difficulties in acquiring and installing sensors, selecting devices, and recording instruments of the desired precision and speed. And the goal of the studies of rotating stall having extremely weak signals was to create unique, miniature measuring devices that could be installed in the flow part and even on the rotating wheel. The problem of detection of rotating stall in industrial centrifugal compressors under the conditions of their operation appeared virtually unresolvable, so these operations were conducted only in laboratories and on test benches. It has been proved experimentally that from the moment of its appearance the rotating stall bears a relatively regular pattern. At the same time, the components of the signals received from the measuring instruments, which characterize strictly rotating stall phenomenon, are suppressed by intrinsic noises of the sensors and converters, and by external disturbances, which are both electrical and gas-dynamic in nature (for example, the vane frequency, rotation speed variation with time, etc.). It is well known [7–10] that the solutions to the aforementioned problems in radar and optical systems are based on the probability theory where use is made of statistical methods of signal detection in the background of noises and disturbances bearing a random or a pseudorandom character. By analogy with this, there are several methods for detection of rotating stall and early diagnosis of surge in centrifugal compressors using statistical processing of sensor signals of various parameters, which have generally accepted standard selection points and characterize the compressor operation conditions. Method of Calculation of Correlation Function of the Signal. One of the first works in this domain that must be mentioned is [11] where the diagnostics of rotating stall detection is constructed on the basis of analysis of the features of the unsteady processes that precede the surge through calculation of the correlation function of the signal from the pressure pickup: 1 R xx ( m ) = N −m
N −1
∑ xn + m xn .
n =0
In this work, for detection of stall generation conditions, a procedure for analyzing the short-term autocorrelation function has been proposed: record of the stochastic process is divided into realization of the process (duration 60 sec) and further into 648 intervals, for each of which the correlation function is calculated. As the stall detection condition are used the maximum value of the autocorrelation function in the stall frequency range and the type of the function close to cosine curve. Method of Signal Dispersion Calculation. Beginning in 1996, almost all centrifugal compressors made by Kazankompressormash were submitted to surge tests in air and later in a real gas at the operation site with recording of the signals preceding the surge on a specially built portable system [12]. 321
Basic theoretical research has revealed that the best rotating stall and surge detection results are obtained by calculation of the dispersion of the signal and its mean mathematical expectation. The initial data were processed in the following order. The whole area of experimental points was divided into j sections, in each of which were 20 values of the quantity being measured. This number of points was chosen so that the recording time did not exceed 0.2 sec and ensured the required precision. The mean values of the signal x and its dispersion σx2 were calculated from the obtained 20 values of the measured quantity: 1 x= N −1
N
∑ xi ;
1 = N −1
σ 2x
i =1
N
∑ ( xi − x ) 2 . i =1
Since two parameters, namely, the compressor (supercharging) pressure pc and the pressure differential on the diaphragm ∆pd, were recorded in the course of the experiments, to the xi value was assigned the pc i value in the first calculation and ∆pd i value in the second. Since the dispersion was calculated from 20 points, the time of the end of the section in real time scale was assigned to the obtained value. Introducing a certain threshold value (setpoint) into the surge detection system, one can determine from the dispersion level the rotating stall and initiation of the surge. The surge initiation condition is σ 2red ≥ σ 2thresh, where σ 2red = k
σ 2x ( x )2
is the reduced dispersion (variation coefficient) of the signal, σ 2thresh is a certain fixed threshold value, and k is a normalizing factor. The dispersion and the average value of the signal were calculated by the equations
σ 2x =
1 N
x=
N
∑ ( xi − x ) 2 ;
(1)
i =1
1 N
N
∑ xi ,
(2)
i =1
where N is the number of signal counts on which the calculation is based, (N – 1)∆t is the time aperture, ∆t is the time between signal counts, and xi the value of the signal at the moment of the last count t0 – (N – 1)∆t. Use of the normalizing factor in Eqs. (1) and (2) instead of the standard factor for calculation of signal dispersion does not change the mathematical significance, but makes formalization of the algorithm in real time scale much easier when it is realized in the microprocessor controllers of the automation systems. For appraisal of this algorithm, its mathematical modeling was done by detection of surge based on real signals from the sensor of pressure differential on the diaphragm, the current strength of the main electrical motor, and the supercharging (delivery) pressure of the centrifugal compressor of various designs and specifications. The records of the signals were obtained during surge tests of the compressors with the help of a set of equipment made especially for these purposes. The mathematical treatment was carried out with the aid of Mathcad mathematical software package. The reliability of the appraisal data was ensured by using real signals from the sensors of various types of compressor for testing the 322
∆p, kPa 100 Setpoint
Algorithm marker
50 ∆p σred 0 3
4
5
6
t, sec
7
Fig. 2. Stall of the supercharger to surge (aperture 20 counts and signal discretization time 10 msec).
∆p, kPa 100 σred
Iem
40
Setpoint 50
∆p
20
Setpoint
5·∆p
σred
0 Surge marker
4
5
6
0
7
4 Algorithm 5 marker
a
6
t, sec
7
b
Fig. 3. Surge of the centrifugal compressor: a) aperture 20 counts, signal sampling time 10 msec; surge detection by ∆p signal; b) Iem is the current strength of the electric motor, aperture 20 counts, signal discretization time 10 msec; surge detection by Iem signal.
100
∆p, kPa σred Setpoint 1
50
pc
∆p Algorithm marker
0.5
0 0
1
pc, MPa
2
3
a
4
5
0
Setpoint
Surge marker 1
σred 3
5
t, sec
7
b
Fig. 4. Surge of high-speed compressor: a) aperture 20 counts, signal discretization time 10 msec; surge detection by ∆p signal; b) signal discretization time 10 msec; surge detection by pc signal.
323
∆p, kPa 30 ∆p 20 Algorithm marker
σred
10
0
2
3
4
5
Setpoint
6
7
t, sec
8
Fig. 5. Surge in the detachable flow part SPCh-16/76-1.7 (aperture 20 counts, signal discretization time 10 msec, and surge detection by ∆p signal).
algorithm as well as by the potentials of mathematic treatment of the signals by the software of modern microprocessor controllers, which allow one to perform a volume of calculations in real time scale akin to model calculation. Let us examine the results of the routine tests of various types of centrifugal supercharger (compressor). Gas Centrifugal Supercharger. The tests were performed at Ufaorgsintez company. The test conditions were: initial pressure 0.9 MPa (abs.), final pressure 2.1 MPa (abs.), delivery 133 m3/min. The algorithm diagnosed (identified) the surge in the beginning of the first half-wave of the surge test cycle. The false surge signal was not recorded (Fig. 2). Air Centrifugal Compressor. The tests were performed in a test cell. The test conditions were: initial pressure 0.1 MPa (abs.), final pressure 0.9 MPa (abs.), delivery 63 m3/min. The surge was detected in the first half-wave of the test cycle when use was made of the signal of pressure differential on the diaphragm as well as of the signal of current strength of the main electric motor (Fig. 3). High-Speed Air Compressor. 1. The tests were performed in a test cell. The test conditions were: initial pressure 0.1 MPa (abs.), final pressure 0.9 MPa (abs.), delivery 63 m3/min. The algorithm diagnosed the surge in the beginning of the first half-wave of the test cycle (Fig. 4a). 2. The tests were performed in a test cell. The test conditions were: initial pressure 0.1 MPa (abs.), final pressure 0.9 MPa (abs.), delivery 160 m3/min. The distinctive aspect of this example is that the compressor automation system was fitted with a sensor of pressure differential on the diaphragm. However, the pattern of surge fluctuations of the supercharging pressure allows this signal to be used for antisurge protection purposes. From Fig. 4b it will be seen that the algorithm diagnosed the surge even in the first half-wave of the first thump. In this case, no signal appeared in the second half-wave (more gently sloping curve). It can be concluded that quasidynamic variations in the final pressure caused by variations in the resistance of the network or by the operation of the control system will not lead to false signaling. Detachable Flow Part SPCh-16/76-1.7. The tests were performed at the booster compressor station DKS-1 of Yamburggazdobycha company. The algorithm diagnosed the surge in the beginning of the first half-wave of each cycle of surge fluctuations. False signaling in the transient conditions with opening of the fast-response bypass valve made by Mokweld (the Netherlands) was not registered (Fig. 5). Thus, the investigations performed showed that the proposed algorithms detect the surge effectively and speedily if the choice of the signal sources, sampling time (discretization frequency) of the sensor, and the number of dispersion calculation points on which the time aperture depends are correct.
324
a
b
Fig. 6. Surge signaling device based on microprocessor controllers: a) ROMRS1 (ÉMIKON, Russia); b) CompactLogix (Allen-Bradely, USA).
The versatility of the algorithm is confirmed by the stability of its operation in all routine tests in spite of the fact that various types of compressor were chosen for the tests, the frequency of surge fluctuations varied in a wide range, and the sources of the signal were various types of sensor. The investigations carried out have helped determine the optimum signal discretization (sampling) frequency and the number of dispersion calculation points. The investigations showed that diminution of the time aperture of dispersion calculation relative to the optimum value impairs the effectiveness of the surge detection algorithm and increases the probability of false signaling caused by noise and disturbance. Increase of calculation aperture will impair the speed of action of the algorithm and reduce sensitivity. Note that for reliable action of the algorithms it is necessary to perform the dispersion calculation for the whole aperture in each step of sampling of the signal from the sensor, i.e., it is necessary to carry out continuous processing of the signal in real time scale. Advantages of units for detection of surge in centrifugal compressors based on analysis of probability characteristics: • high reliability and efficiency of surge detection; • noise and disturbance tolerance; • absence of false surge signaling; and • potential for practical realization in real time scale in modern industrial programmable controllers of automation systems. Based on the approved methods of surge detection using probability characteristics of the operation conditions of centrifugal compressors, procedures for surge detection and systems for their implementation, which are protected by a number of Russian Federation patents, have been developed. These procedures are based on the calculation of dispersion of signals from the sensors in real time scale, analysis of the degree of instability of the process (by comparing the normative parameters of the dispersion with the established values), and transmission of the respective signals to the compressor control system. In order to introduce these methods to the centrifugal compressor control systems, special software has been developed that allows optimization of the procedure of calculation in real time scale of the statistical functions required for surge detection. Applied programs have been developed for practical implementation of these procedures on the basis of both domestic and foreign industrial microprocessor controllers. At present, almost all centrifugal compressor automation systems (AS) made by Kazankompressormash are fitted with surge signaling devices. These signaling devices are either integrated into the PLC controller as a special program block in the applied program and as a high-speed analog signal input module or are a separate small microprocessor controller. Signaling devices based on the controller ROMRS1 (Fig. 6a) have been successfully pressed into service in the AS of the air and gas compressors AÉROKOM AA-250/9.4, GTs1-119/1.35-14.3, AÉROKOM 112/1.5-19G, 2GTs2-23/21-37, 3GTs2-38/9.5-28, 2GTs2-18/13-33, and others made by Kazankompressormash and V. B. Shnepp NIIturbokompressor as well as of the compressors Neva-É and Neva-P (ChKD, Czech Republic).
325
The signaling device based on the CompactLogix controller (Fig. 6b) has been used in the AS of a 5TsD-208/30-45M compressor (Kazankompressormash). The surge detection system integrated into the AS with a ControlLogix controller as the base (i.e., without a separate signaling device) has been used for 2GTs-2-41/58-79, 4GTs1-200/3.5M1, and 5GTs1-300/0.1-1.2 compressors (Kazankompressormash).
REFERENCES 1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 11. 12.
326
S. I. Fedosova, N. A. Krylova, and Ya. Z. Guzel’baev, Antisurge Devise of Compressor, Russian Federation Patent No. 1125410 (1983). R. A. Izmailov, “Unsteady processes in centrifugal compressor,” Kompress. Tekh. Pnevmat., No. 5 (2000). K. P. Seleznev and Yu. V. Patrin, “Transient phenomena in centrifugal compressor stage,” Kompress. Kholod. Mashinostr., No. 5, TsINTIkhimneftemash (Central Research Institute of Scientific and Technical Information, and Techno-Economic Research in Chemical and Petroleum Machine Building), Moscow (1966). E. M. Greitzer, “Surge and rotating stall in axial flow compressions, Part I: Theoretical compressor model,” Trans. ASME, 1976. Ser. A, J. Engine for Power, 1998. P. Meherwan and P. E. Boyce, “Rotating stall of centrifugal compressors,” Part I, Diesel and Gas Turbine Worldwide, No. 8 (1988). A. H. Stenning, “Rotating stall and surge,” Trans. ASME, Ser. J, 102, No. 1 (1980). V. N. Tikhonov, Statistical Radio Engineering [in Russian], Sovetskoe Radio, Moscow (1966). O’Neil, An Introduction to Statistical Optics [Russian translation], Inostrannaya Literatura, Moscow (1966). N. S. Shestov, Detection of Optical Signals in Random Noise Background [in Russian], Sovetskoe Radio, Moscow (1965). Yu. V. Prokhorov and Yu. A. Rozanov, Probability Theory [in Russian], Nauka, Moscow (1967). R. A. Izmailov et al., “Surge diagnosis in centrifugal compressor by analysis of unsteady processes,” Proekt. Issled. Kompress. Mashin, Collec. Res. Papers, No. 4, Kazan (1999). Ya. Z. Guzel’baev and A. L. Khavkin, “Special system for surge studies,” Proekt. Issled. Kompress. Mashin, Collec. Res. Papers, No. 3, Kazan (1997).
