Numerical analysis of a centrifugal compressor operating with supercritical CO2

Abstract

This study investigates the performance of a centrifugal compressor stage operating with supercritical CO2. The candidate geometry comprises a channel diffuser and is based on main dimensions of a test-loop compressor operated by Sandia National Laboratories. A non-dimensional performance curve is derived through three-dimensional RANS calculations performed with an in-house compressible CFD solver and is compared to experimental data as well as a meanline analysis that is conducted applying a single-zone modelling approach, including internal and external loss models. Within the CFD simulations, real gas thermophysical properties of carbon dioxide are assessed through an accurate and efficient tabulation procedure, the Spline-Based Table Look-Up Method (SBTL), which is optimised for the density-based solver architecture. The conducted RANS calculations show an ideal head rise of up to 41 % through the channel diffuser compared to an ideal head assessment considering the impeller. The applied meanline methodology pro∗Address all correspondence to this author. vides good agreement with the impeller performance characteristics derived from RANS calculations over the entire investigated flow range. Except for flow coefficients exceeding values of φ ≈ 0.043, where an abrupt decrease of the ideal head recovery is identified in the CFD assessments, which is not resembled by the meanline diffuser model, also satisfactory agreement of the meanline stage performance characteristics with the CFD results is obtained. Hence, applicability of the corresponding meanline loss models for sCO2 compressor analysis is indicated. INTRODUCTION Closed power cycles utilising supercritical carbon dioxide as the working fluid exhibit several advantages compared to conventional power cycles. These power systems are predominantly designed as Brayton cycles where the compression is conducted at thermodynamic states that are lying close to the vapour-liquid critical point of CO2 and are therefore characterised by a high fluid density. Hence, compression work is reduced significantly. Furthermore, high fluid density enables compact component de1 DOI: 10.17185/duepublico/73966 sign and ultimately paves the way for a small physical footprint of the overall plant. Supercritical power systems can also be coupled to a variety of heat sources, allowing for a broad range of applications. Despite increased research efforts, there are still enduring challenges which need to be overcome until sCO2 cycles can be commercialised. Key issues concern reliable process control, the design of compact and effective heat exchangers as well as the realisation of satisfactory turbomachinery performance characteristics. Predominantly, centrifugal compressors are applied in sCO2 Brayton cycles and, in particular, the main compressor of a recompression layout is expected to be a radial configuration for a broad range of system scales due to its lower volume flow and wider range to facilitate variations in gas properties [8]. Design and analysis methods are sophisticated for centrifugal compressors operating with fluids obeying the ideal gas law. However, because of the scarcity of reference data, the validity of respective methods is still uncertain when these are applied to compressors operating with real fluids. In particular, fluid states near the critical point are characterised by highly non-linear and rapidly changing property behaviour. Adressing these issues, predictive CFD simulations, accounting for thermophysical real gas properties with a high degree of accuracy, allow for an insight into the dynamic development of flow field and are therefore an important tool to improve the aerothermal design and analysis of sCO2 turbomachinery. The majority of numerical studies of sCO2 compressors in the literature refer to a main compressor geometry operated in a compression test-loop by Sandia National Laboratories (SNL). The compressor has undergone extensive testing and until today provides one of the very few cases for which experimental reference data as well as the respective compressor geometry is at least partially documented in the form of main dimensions. In one of the first studies related to the SNL compressor, Pecnik et al. [26] performed 3D RANS calculations of a main compressor impeller resembling the SNL main compressor design. A computed speed line indicated higher head generation compared to the experimental data used for validation purposes. Deviations were attributed to the simplified geometry not considering the vaned diffuser and the impeller clearance. Analysis of the flow field showed thermodynamic states of the flow domain lying within the vapour-liquid region. These were identified at the impeller blade tip suction side and the trailing edge, as a result of flow acceleration and the decrease of static conditions. In following studies of the research group, the complete stage geometry, comprising the vaned diffuser and tip clearance, was modeled. A significant reduction in head generation was observed for a single operating point compared to the previous study, giving better agreement with the referenced experimental data [31]. Performance map calculations conducted for three rotational speeds in [32] showed that the shares of fluid zones located close to the impeller leading edges with state conditions in the two-phase region increase for higher rotational speeds, whereas a reversed dependency was observed regarding the regions close to the trailing edges. Baltadjiev et al. [6] introduced a time scale ratio relating liquid droplet formation time to the residence time of flow under subcritical conditions in order to quantify the possibility of condensation within a low-flow-coefficient sCO2 compressor stage. For all investigated operating conditions away from the critical point, the time scale ratio was much smaller than one, suggesting improbability of condensation. Nevertheless, the authors pointed out that a time scale ratio of 1 could be reached for operating points that are more closely located to the critical point, due to an increased subcritical expansion and asymptotically vanishing surface tension. 3D RANS simulations of the SNL compressor were also conducted by Ameli et al. [1; 3], who focused on the effects of lookup table resolution of the applied bilinear interpolation routine on performance and flow field predictions. It was shown that higher table resolutions resulted in a better agreement with experimental data regarding efficiency, whereas the assessment of pressure ratio proved to be rather insensitive. Especially, the resolution of near-critical properties was stressed, as the authors stated that 0.5 % error in the lookup table can have a significant impact on the performance prediction at close-critical operating conditions. The authors also showed that higher table resolutions resulted in an increased assessment of flow regions within the two-phase region because of lower values of speed of sound. In a preliminary study prior to this work [19], the performance as well as the flow field of an impeller geometry resembling the main dimensions of the SNL main compressor were investigated. Reasonable performance metrics were derived for two compressor inlet states lying in the supercritical and gas phase region, respectively. A high degree of machine similitude was observed for compressor operation at these inlet states through a non-dimensional performance curve representation. Similar to the observations from the authors referenced before, the flow field highlighted fluid zones inside the vapour-liquid region near the blade leading edge suction sides due to flow acceleration. These were quantified by their volumetric share for different flow coefficients. Contrary to previously cited authors, who all used bilinear interpolation techniques to account for the thermophysical properties of CO2, property table interpolation was conducted through the Spline-Based-Table-Lookup Method (SBTL) [20; 21]. The method indicated low computational overhead compared to an ideal gas reference calculation while providing accuracies within the deviation of the underlying state equation, being the SpanWagner equation of state [35]. Building on the previous work [19], this study extends the compressor performance testing to also account for the channel type diffuser that was not modeled before. This is believed to improve the comparability with the experimental results as a vaned