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Off-design Performance Prediction in Multistage Centrifugal Compressors
Limitations of Similitude Method
Compressor Type: API617 Multistage Barrel, 7 Stages (7 x 520 mm); 100% Speed = 10168 RPM
Design Case (Natural Gas) Simulation:
Fig. 1a Design case (natural gas) performance obtained with multi-stage stacking algorithm
Fig. 1b Design case (natural gas) performance map simulation (similitude method)
Off-design Case Map (Nitrogen), Stage-Stacking Algorithm vs. Similitude Method:
Fig. 2a Off-design simulation obtained with similitude method
Fig. 2b Off-design simulation obtained with multi stage stacking algorithm
Analysis of the Deviation for Off-design Case @ Surge Flow - Speed Curve 8133 RPM
Tab.1 Original Performance (Stage Stacking Algorithm):
Tab.2 Similitude -based Performance:
Change of Surge Initiating Stage vs. Gases (@Equal Mach No.):
Tab.3 Stage Stacking Algorithm Comparative Results (CTrend / SIZER module calculations)
Discussion (N2 case):
Tab.3 above shows which compressor stage number is initiating surge at given peripheral Mach numbers. In multistage configuration the stage that initiates surge, similarly choke, has bearing on the final shape of the overall compressor map. Note that the initiating stage may change when the density/properties of the gas vary for a fixed Mach number. For the present example, at Peripheral Mach No. Mu=~0.57, the slope of surge line for design case is correlated to stage No. SR= 2 while for N2 case SR=1 (i.e., no change of slope yet with increasing speeds). Since the performance map (non dimensional) characterization of the similitude method is based on design case as reference map (Fig. 1), a deviation in surge line prediction between N2 case maps of Fig. 2a and 2b becomes noticeable at speeds 7100~7300 rpm. Also at Mu=~0.62 the slope of surge line for design case is correlated with stage No. SR=7 while for N2 case, SR=3; this results in further distortion in predicted surge limit line at higher speeds.
Because the similitude method inherently assumes that the compressor behaves as a single-stage machine, the multi-stage stacking effects due to compressibility which are exemplified above are not captured in the definition of the overall map. The significance of the deviations/errors resulting (~10% on surge flow for the case at hand 8133 RPM) is dependent upon (a) the number of stages stacked thermodynamically in a compressor section, (b) the density of the off-design gas and (c) the operating speeds being predicted. The higher these numbers are, the more prominent the risk of inaccurate performance prediction with similitude method.