Paradigmatic compressible one-dimensional flows provide insights regarding the loss mechanisms of fluid machinery components typical of power and propulsion systems, like turbomachines and heat exchangers. Their performance also depends on the working fluid, thus, on both molecular complexity and thermodynamic state. Four typical flow configurations have been investigated, namely, Rayleigh and Fanno flows, mixing of two co-flowing streams, and flow injection into a mainstream. It was found that the Grüneisen parameter allows the quantitative characterization of the influence of molecular complexity on losses. Moreover, the influence of dense vapor effects has been evaluated and assessed in terms of other fluid parameters. The analysis allowed the quantification of how, in Rayleigh flows, the energy transferred as heat is converted into kinetic and internal energy of the fluid, and, in Fanno flows, entropy is generated due to friction. In Rayleigh flow, the fluid at the inlet of the channel must have more energy for the flow to choke, depending on the molecular complexity. Similarly, in Fanno flows and for a given value of the compressibility factor, molecular complexity determines the choking point in the channel, and the higher its value the further downstream is the location. Moreover, for both Fanno and Rayleigh flows, if the flow is subsonic and dense vapor effects are relevant, the Mach number varies non-monotonically along the channel. Finally, it was proven that the amount of entropy generated in mixing flows increases with both the fluid molecular complexity and with the thermodynamic non-ideality of the fluid states.

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The recent growth of private options in launch vehicles has substantially raised price competition in the space launch market. This has increased the need to deliver reliable launch vehicles at reduced engine development cost and has led to increased industrial interest in reduced order models. Large-scale liquid rocket engines require high-speed turbopumps to inject cryogenic propellants into the combustion chamber. These pumps can experience cavitation instabilities even when operating near design conditions. Of particular concern is rotating cavitation (RC), which is characterized by an asymmetric cavity rotating at the pump inlet, which can cause severe vibration, breaking of the pump, and loss of the mission. Despite much work in the field, there are limited guidelines to avoid RC during design and its occurrence is often assessed through costly experimental testing. This paper presents a source term based model for stability assessment of rocket engine turbopumps. The approach utilizes mass and momentum source terms to model cavities and hydrodynamic blockage in inviscid, single-phase numerical calculations, reducing the computational cost of the calculations by an order of magnitude compared to traditional numerical methods. Comparison of the results from the model with experiments and high-fidelity calculations indicates agreement of the head coefficient and cavity blockage within 0.26% and 5%, respectively. The computations capture RC in a two-dimensional (2D) inducer at the expected flow coefficient and cavitation number. The mechanism of formation and propagation of the instability is correctly reproduced.@en

The purpose of this paper is to present optimization method of an inducer blade shape to improve its suction performance and clarify the relationship between pump performance and design parameters. In order to conduct the optimization process a response surface based optimization framework was established. Baseline was designed in previous research [1]. The inducers were 3Dprinted in ABS plastic and their wetted and cavitating characteristics were measured. It was confirmed that the optimized inducer can maintain its wetted performance at lower cavitation numbers. A response surface is a mathematical model that approximates the relationship between the input parameters and the objective function from a finite number of learning points within the design space. The design space was defined by four parameters: sweep angle, sweep radius, incidence angle and blade solidity at the tip that controlled the blade shape. The performance of each design was evaluated with a CFD simulation established in a commercial solver. The optimization goal was to minimize the critical cavitation number that corresponds to a 5% drop of pressure increase through the pump due to cavitation. A starting point of the optimization was the industrial pump designed by a Japanese company Teral [1]. The results of the numerical optimization show that the critical cavitation number was decreased by 17.6% with respect to the baseline design. In the experimental results, an average improvement of 15.4% was achieved.

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Carbon capture and storage could significantly reduce carbon dioxide (CO2) emissions. One of the major limitations of this technology is the energy penalty for the compression of CO₂ to supercritical conditions. To reduce the power requirements, supercritical carbon dioxide compressors must operate near saturation where phase change effects are important. Nonequilibrium condensation can occur at the leading edge of the compressor, causing performance and stability issues. The characterization of the fluid at these conditions is vital to enable advanced compressor designs at enhanced efficiency levels but the analysis is challenging due to the lack of data on metastable fluid properties. In this paper, we assess the behavior and nucleation characteristics of high-pressure subcooled CO2 during the expansion in a de Laval nozzle. The assessment is conducted with numerical calculations and corroborated by experimental measurements. The Wilson line is determined via optical measurements in the range of 41-82 bar. The state of the metastable fluid is characterized through pressure and density measurements, with the latter obtained in a first-of-its-kind laser interferometry setup. The inlet conditions of the nozzle are moved close to the critical point to allow for reduced margins to condensation. The analysis suggests that direct extrapolation using the Span and Wagner equation of state (S-W EOS) model yields results within 2% of the experimental data. The results are applied to define inlet conditions for a supercritical carbon dioxide compressor. Full-scale compressor experiments demonstrate that the reduced inlet temperature can decrease the shaft power input by 16%.

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In this paper we present and validate a shape optimization framework for the design of splitter blades that extends the operative range under cavitation while maintaining the wetted performance of rocket engine turbopumps. For a target turbopump applicatio n, the optimization framework allows for independent changes to the blade angle distributions across the span and to the pitchwise position of the splitter blades while preserving the thickness distributions. The optimization is conducted with a surrogate - based gradient method. The geometry is optimized at a fixed cavitation number corresponding to a 5% head coefficient drop - off, while constraints are imposed on the wet pump performance. It is found that this approach, coupled with the surrogate - based opti mization process , reduces the computational cost of the optimization process by minimizing the number of multiphase calculations. The numerical results suggest that the optimized splitter blades successfully increase the pump operative range by 2.2% and i ncrease the head coefficient by 5.3% compared to the baseline case with non - optimized splitters. These results are corroborated by experiments conducted in a closed - loop water test facility . Several pump geometries are tested through rapid prototyping usin g additive manufacturing. The experimental data validate the optimization framework, demonstrating a 4.7% increase of pump operative range and a 7.6% increase in head coefficient. The calculations are used to gain insight in the physical mechanisms for the performance improvement. The analysis of the results indicates that the improved performance is due to the optimized position and shape of the splitter blades which increase the pump slip factor . The paper breaks new ground in defining an efficient design methodology for the improvement of cavitating performance in rocket turbopumps @en

The recent growth of private options in launch vehicles has substantially raised price competition in the space launch market. This has increased the need to deliver reliable launch vehicles at reduced engine development cost, and has led to increased industrial interest in reduced order models. Large - scale liquid rocket engines require high - speed turbopumps to inject cryogenic propellants into the combustion chamber. These pumps can experience cavitation instabilities even when operating near design conditions. Of particular concern is rotating cavitation, which is characterized by an asymmetric cavity rotati ng a t the pump inlet , which can cause severe vibration, breaking of the pump and loss of the mission. Despite much work in the field, there are limited guidelines to avoid rotating cavitation during design and its occurrence is often assessed through costl y experimental testing. This paper presents a source term based model for stability assessment of rocket engine turbopumps. The approach utilizes mass and momentum source terms to model cavities and hydrodynamic blockage in inviscid, single - phase numerica l calculations, reducing the computational cost of the calculations by an order of magnitude compared to traditional numerical methods. Comparison of the results from the model with experiments and high - fidelity calculations indicates agreement of the head coefficient and cavity blockage within 0.26% and 5% respectively. The computations capture rotating cavitation in a 2D inducer at the expected flow coefficient and cavitation number. The mechanism of formation and propagation of the instability is correct ly reproduced . @en

This paper presents a numeric al framework for characterizing fuel injection in modern combustors. The approach utilizes scaling analysis to describe the dro plet evaporation in non - dimensional and fluid - independent terms. The results of the model are validated against published experimental data of isolated droplets evaporating at subcritical and near - critical conditions. The model is incorporated in a spray c alculation framework and extended to the supercritical regime to assess the impact of different fluid - properties and evaporation models on temperature and fuel vapor distributions. The results suggest that in a non - convective environment the transient and quasi - steady evaporation rates vary exponentially with Lewis number. Furthermore, the results show fluid - independent behavior of the droplet evaporation, indicating that a single - component fluid can potentially be used as a modeling surrogate for jet fuel . The first - principles analysis demonstrates that classical evaporation models overestimate transient evaporation and underestimate quasi - steady evaporation, with discrepancies up to 70% at supercritica l conditions. This is due to limitations in fuel - prope rty description and the lack of non - isothermal droplet characterization at near - critical conditions. The temperature profiles are typically under - predicted and fuel vapor concentrations are over - predicted in standard spray calculations with subcritical eva poration models. As such the proposed framework breaks new ground in modeling of supercritical fuel injection. The improved quality in the predicted fuel concentration and temperature distribution can enable more accurate assessment of flame position, impr oving the estimation of combustion stability margins and NOx emissions. The model can be incorporated in commercial codes to guide the design of combustors operating at supercritical conditions. @en

On a ten - year timescale, Carbon Capture and Storage could significantly reduce carbon dioxide (CO 2 ) emissions. One of the major limitations of this technology is the energy penalty for the compression of CO 2 to supercritical conditions, which can re quire up to 15 % of the plant’s gross power output. To reduce the power requirements supercritical carbon dioxide compressors must operate at reduced temperatures and near saturation where phase change effects are important. Non - equilibrium condensation can occur in the high - speed flow at the leading edge of the compressor, causing performance and stability issues. The characterization of the fluid at these conditions is vital to enable advanced compressor designs at enhanced efficiency levels but the analysis is challenging due to the lack of data on the metastable fluid properties. In this paper we assess the metastable behavior and nucleation characteristics of high - pressure subcooled carbon dioxide during the expansion in a Laval nozzle. The assessment is cond ucted with numerical calculations, supported and corroborated by experimental measurements. The Wilson line is determined via optical measurements in the range of 41 and 82 bar and near the critical point. The state of the metastable fluid is fully charact erized through pressure and density measurements, with the latter obtained in a first of its kind laser interferometry set up. In a systematic analysis the inlet conditions of the nozzle are moved close to the critical point to allow for large gradients in fluid properties and reduced margin to condensation. The results of calculations using a direct extrapolation of the Span and Wagner equation of state model are compared with the experimental measurements. The analysis suggests that the direct extrapolati on using the Span and Wagner model yields results within 2% of the experimental @en