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Computational fluid-dynamic modelling of two-phase compressible flows of carbon dioxide in supercritical conditions
Compressible two-phase flows of carbon dioxide in supercritical thermodynamic conditions are encountered in many applications, e.g. ejectors for refrigeration and compressors for power production and carbon capture and sequestration to name a few. Alongside the phase change, transonic/supersonic flow regimes and non-ideal effects also add additional complexities in the simulations of such flows. In this work, we investigate cavitating and condensing flows of carbon dioxide via numerical simulations based on the two-fluid concept, applying both a mixture model and a barotropic model. In the mixture model, the phase change is modelled with an extra transport equation for the mass of the dispersed phase and a source term introduced via a penalty formulation. The barotropic model reproduces the pressure–density relation of the mixture along the upstream isentrope. Both the models assume thermodynamic and mechanical equilibrium between phases and exclude meta-stability effects. All results are compared against experimental data taken from literature and the main numerical issues of the models are discussed in detail. The agreement between the simulations and the experiments is remarkable qualitatively and quantitatively, resulting in the range 2%–4% for pressure and below 1% for temperature in terms of weighted mean absolute percentage error for supercritical expansions, even though suggesting a further margin of improvement in the physical modelling, especially for subcritical expansions. Finally, we show that the barotropic model yields comparable predictions of the expansion processes at a lower computational cost and with an improved solver robustness
CHALLENGES IN SCALING sCO2 COMPRESSOR SPEEDLINE TO DIFFERENT INTAKE THERMODYNAMIC CONDITIONS
Compressors operating with carbon dioxide near the critical point experience complex aerothermodynamic phenomena, where deviations from perfect-gas similarity and two-phase flow effects dominate. Existing models inadequately capture the impact of intake thermodynamic conditions on the choked flow rate, leaving a gap in predictive capabilities for these machines. This work addresses this gap by deriving a correlation to predict the choked flow rate as a function of two generalized parameters: the cavitation/condensation parameter and the isentropic pressure-volume coefficient, which describe two-phase and non-ideal effects. A database of 100 speedlines, generated through CFD simulations with varying thermodynamic conditions and fixed peripheral Mach number, was used to train a symbolic regression algorithm based on gene expression programming. This method was chosen to derive an explicit, easy-to-use analytical expression without assuming a priori functional forms. Results showed that the choked flow rate could vary from 90% to 155% of the nominal value depending on thermodynamic conditions, highlighting the dominant role of the two parameters. The derived correlation demonstrated trends consistent with CFD predictions, with an accuracy of ±3 percentage points for most cases. However, an a-posteriori validation against varying peripheral Mach numbers and an alternative impeller geometry revealed significant discrepancies, underscoring the interplay between thermodynamic conditions, geometry, and aerodynamics. This analysis showed that the peripheral Mach number and the geometric features influence choking behavior unpredictably, limiting the correlation's general applicability. While the proposed correlation is not adequate for quantitative scaling across designs, it provides preliminary insights into qualitative trends. For accurate predictions, high-fidelity CFD remains necessary, highlighting the inherent challenges of universal scaling for near-critical operations in sCO2 compressors
3D CFD study of a DeepWind demonstrator at design, off-design and tilted operating conditions
Energy transition, towards increased renewables, demands for reliable, efficient, and innovative technical solutions, at acceptable cost. Wind energy conversion exhibits one of the greatest potential, mainly in off-shore deployment. Vertical-axis wind turbines are characterized by a reduced wave recovery and enhanced power output, which boost the installation of bigger capacity turbines, properly cluster to maximize the farm density. These two requirements entail deeper understanding of the wake physics and detailed description of the machine performance. A careful 3D CFD investigation, supported by experimental validation, is carried out to define the relevant flow mechanism of a lab-model, DeepWind demonstrator, in upright and tilted condition. The results show how the performance is varying along the span, and how it is affected by a skewed flow. The lower part of the machine benefits from combined effect of blade curvatures and rotor inclination. A thorough description of the complex vortical field complements the performance data, and provide useful considerations apt for promoting the design of future vertical-axis wind turbines, for floating off-shore applications. The performance parameters are then computed for a full-size rotor to show how the Reynolds effect play a relevant role in the machine aerodynamics of bigger capacity turbines
On sCO2 compressor performance maps at variable intake thermodynamic conditions
Unconventional aero-thermodynamic phenomena affect the performance of compressors that operate with carbon dioxide (CO2) close to its thermodynamic critical point. As a consequence, whether compressor performance maps based on conventional scaling parameters, such as flow coefficient and peripheral Mach number, still posses general features remains an open question. In this work, we show that additional dimensionless parameters are needed to ensure full similarity conditions when intake thermodynamic conditions vary. Thanks to a combination of three-dimensional turbulent flow simulations, analytical developments and physical flow considerations, three main phenomena are shown to affect compressor operation when changing the upstream total state: (i) non-ideal effects that can modify the fluid compressibility from liquid-like to gas-like and vice versa, (ii) the extent of the two-phase region within the blade channel, (iii) the resulting compressibility of the two-phase mixture. Three dimensionless parameters are introduced to separately account for these effects and their relationship is highlighted. The influence of these parameters on compressor performance maps is widely discussed, shedding light on the way they act in the modification of the ideal similarity based only on the flow coefficient and the peripheral Mach number. As a general result, two additional dimensionless parameters are needed to guarantee similarity conditions in presence of non-ideal flows of CO2 subject to phase change. These findings are expected to be relevant for the plant regulation in off-design conditions and for planning experimental campaigns at different thermodynamic conditions
Turbulence Measurements Downstream of a Combustor Simulator Designed for Studies on the Combustor–Turbine Interaction †
Turbulence intensity impacts the performance of turbine stages and it is an important inlet boundary condition for CFD computations; the knowledge of its value at the turbine inlet is then of paramount importance. In combustor–turbine interaction experimental studies, combustor simulators replace real combustors and allow for the introduction of flow perturbation at the turbine inlet. Therefore, the turbulence intensity of a combustor simulator used in a wide experimental campaign at Politecnico di Milano is characterized using a hot-wire probe in a blow-down wind tunnel, and the results are compared to URANS CFD computations. This combustor simulator can generate a combination of a swirl profile with a steady/unsteady temperature disturbance. In the cold unsteady disturbance case, hot-wire measurements are phase-averaged at the frequency of the injected perturbation. The combustor simulator turbulence intensity is measured at two different axial positions to understand its evolution
THE ROLE OF ENDWALL SHAPE OPTIMIZATION IN THE DESIGN OF SUPERSONIC TURBINES FOR ROTATING DETONATION ENGINES
Rotating detonation engines (RDE) are characterized by a thermodynamic cycle with an efficiency gain up to 15% at medium pressure ratios with respect to systems based on the conventional Joule-Bryton cycle. Multiple turbine designs can be considered and this paper deals with the supersonic inlet configuration. After having reviewed the main design steps of an exemplary RDE supersonic turbine, the paper focuses on the considerable effects that endwall losses have on the performance of supersonic-inlet turbines and on the reasons why endwall contouring is strongly recommended for an efficient design. Parametric analyses, carried out by a novel in-house mean-line code validated against CFD, reveal that endwall friction losses contribute significantly to the overall stage loss. Endwall boundary layers also reduce the effective area, which can be critical for the self-starting capability of the supersonic channel. Therefore, a variable blade height geometry is necessary to extend the design space and guarantee a higher efficiency with respect to a constant-span configuration. The in-house CFD-based evolutionary shape optimization code was adapted to search for the optimal endwall shape for these unconventional machines. The optimal shape reduces shock losses and deviation angles and provides a significant gain in efficiency and work extraction. Finally, a novel technique is proposed to design the three-dimensional shape of the rotor based on the method of characteristics and tailored on the flow delivered by the stator
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