A Three-Zone Modeling Approach for Centrifugal Compressor Slip Factor Prediction

Abstract

Accurate estimation of slip factor is of paramount importance to ensure centrifugal compressor work input is adequately predicted during the preliminary design process. However, variations in the flow field at impeller exit in both the pitchwise and spanwise directions complicate the evaluation procedure considerably. With the increasing implementation of engine downsizing technologies in the automotive sector, achieving a wide operating range has become a factor of prime importance for centrifugal compressors used in automotive turbocharging applications. As a result of the design features required to achieve this aim, modern impeller geometries have been shown to exhibit an approximately parabolic variation in slip factor across their respective operating maps. By comparison, traditional slip correlations typically exhibit a constant, or at best monotonic, relationship between slip factor and impeller exit flow coefficient. It is this lack of modeling fidelity which the current work seeks to address. In order to tackle these shortcomings, it is proposed that the impeller exit flow should be considered as being made up of three distinct regions: a region of recirculation next to the shroud providing aerodynamic blockage to the stage active flow, and a pitchwise subdivision of the active flow region into jet and wake components. It is illustrated that this hybrid approach in considering both spanwise and pitchwise stratification of the flow permits a better representation of slip factor to be achieved across the operating map. The factors influencing the relative extent of each of these three distinct regions of flow are numerous, requiring detailed investigations to successfully understand their sources and to characterize their extent. A combination of 3D computational fluid dynamics (CFD) data and gas stand test data for six automotive turbocharger compressor stages was employed to achieve this aim. Through application of the extensive interstage static pressure data gathered during gas stand testing at Queen's University Belfast, the results from the 3D CFD models were validated, thus permitting a more in-depth evaluation of the flow field in terms of locations and parameters that could not easily be measured under gas stand test conditions. Building on previous knowledge gained about the variation in shroud side recirculation with geometry and operating condition, the characteristic jet/wake flow structure emanating from the active flow region of the impeller was represented in terms of area and mass flow components. This knowledge allowed individual slip factor values for the jet and wake to be calculated and combined to give an accurate passage average value which exhibited the distinctive nonlinear variation in slip across the operating map which is frequently absent from existing modeling methods. Fundamental considerations of the flow phenomena in each region provided explanation of the results and permitted a modeling approach to be derived to replicate the trends observed in both the experimental data and the CFD simulations.

Investigation of Slip Models for High-Speed Centrifugal Compressors

“…Qiu et al [28] used the traditional geometric parameters to estimate the effect of the relative eddy, but they also incorporated the impeller exit flow coefficient and trailing edge curvature to account for the variation of slip at different operating conditions. Stuart et al [29] extended Qiu et al's model to a multizone technique. Stuart et al used a recirculation model [30] to designate the impeller exit flow as the jet, wake, and recirculation zones to calculate the area of the "active flow region" which the relative eddy occupies.…”

A New Approach to Modeling Slip and Work Input for Centrifugal Compressors

“…(18), The relative error distributions in total temperature rise ratio corresponding to Eqs. (17) and (18) are shown in Figs. 8(b) and 8(c), respectively, with the error distribution for Wiesner's model shown again for reference in Fig.…”

“…The appropriate perfect flow guidance parameters are then provided to Eq. (11), (17), or (18) from the perfect flow guidance operating point to calculate the slip factor. The slip factor and appropriate loss models are used to calculate the actual operating condition.…”

“…Since the publication of Wiesner's model, efforts to develop a reliable method for the prediction of slip factor have continued. Proposals have included experimental curve fits [13,15], potential flow solutions [4,6,16], and multizone techniques [17,18]. The single relative eddy model was proposed by von Backstr€ om [14], which was derived by applying the relative eddy to the impeller as a whole rather than to each passage.…”

“…Qiu et al [9] addressed the variation of slip with flow conditions by incorporating the impeller exit flow coefficient into a relative eddy approach. Stuart et al [18] expanded Qiu's approach to a multizone technique in an effort to improve the off-design utility of the model.…”