This paper presents a fully turbulent two-phase discrete adjoint method for metastable condensing flows targeted to turbomachinery applications. The method is based on a duality preserving algorithm and implemented in the open-source CFD tool SU2. The optimization framework is applied to the shape optimization of two canonical steam turbine cascades, commonly referred to as White cascade and Dykas cascade. The optimization were carried out by minimizing either the liquid volume fraction downstream of the cascade or the total entropy generation due viscous effects and heat transfer. In the first case, the amount of condensate turned out to be reduced by as much as 24%, but without reduction of the generated entropy, while the opposite resulted in the second case. The outcomes demonstrate the capability and computational efficiency of adjoint-based automated design for the shape optimization of turbomachinery operating with phase change flow.@en

Metastable condensation is the phase transition from vapor to liquid that occurs in a fluid subjected to rapid temperature variations. Under these conditions, the nucleation process is triggered when the fluid is in a supersaturated thermodynamic state. The dispersed phase forming during the process of condensation is not in stable thermodynamic equilibrium with the surrounding vapor. As a consequence, models suitable for condensing flows under large temperature gradients, which are relevant to many scientific studies and industrial applications, are rather complex as they must correctly treat metastable thermodynamic states. Applications of metastable condensation flowmodels include improved climate models [1], biomedical treatments [2], heat transfer enhancement for industrial purposes [3], natural gas separation [4], power conversion [5] and many others. The scope of the research documented in this dissertation is the numerical investigation of metastable condensing flows in turbomachinery for propulsion and power applications. The flow inside turbomachinery components is highly compressible, with absolute temperature gradients that can reach values of the order of 1e6 K/s[6], in the case of supersonic expansions. In such extreme conditions, metastable phenomena impact severely on the component performance in terms of both thermodynamic and fluid dynamic losses and lifetime. The number of technologies for propulsion and power characterised by the presence of condensing mixtures in turbomachinery is increasing. Considerable research and development efforts are currently concerned with components of next-generation thermal power and refrigeration systems, in which the flow undergoes metastable condensation. The characterization of metastable condensing flows and the development of advanced fluid dynamic design tools capable of treating these complex flow phenomena are fundamental steps towards the commercial application fo such promising technologies. @en

An investigation on non-equilibrium condensing steam flow is conducted to attain a semi-analytical model for the prediction of the Wilson point up to the critical point. The database for the analysis includes experimental observations in various nozzles and conditions (ranging from 20 to 150 bar) taken from the literature as well as additional data at lower and higher reduced pressures, generated by means of a calibrated quasi-1D model based on the method of moments. The simplified model is based on a reformulation of the Wilson point in terms of activation time, defined as the temporal interval between the instant at which the flow is at saturation conditions and the inception stable of condensation. This allows to incorporate the dependency of the Wilson point on the cooling rate and dew-point temperature, which are found the key parameters affecting the delay of condensation. The accuracy of the approach is proved by predicting the degree of subcooling on four different test cases, with deviations against experiments in the range of 1−10%. As demonstrated, the same approach can be exploited to design nozzles free of condensation.@en

High-pressure non-equilibrium condensing flows are investigated in this paper through a quasi-1D Euler model coupled to the method of moments for the physical characterization of the dispersed phase. Two different numerical approaches, namely the so-called (a) the mixture and (b) continuum phase model, are compared in terms of computational efficiency and accuracy. The results are verified against experimental data of high-speed condensing steam measured at high pressure (100.7 bar). The analysis demonstrates that Model (b) markedly outperforms the mixture model in terms of computational cost, while retaining comparable accuracy. However, both models, in their original formulation, lead to considerable deviations in the nucleation onset prediction as well as an overestimation of the average droplet radius. A further investigation is then conducted to figure out the main physical parameters affecting the condensation process, i.e. the surface tension, the growth rate and the nucleation rate. It is eventually inferred that applying proper correction to these three quantities allows to obtain best fit with the experimental data. A final calculation is carried out to show the dependence of these three correcting factors from the thermodynamic conditions of the mixture.

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This preliminary study considers a combined cycle configu­ration for aeroengines, whereby thermal energy from the exhaust of the gas turbine is partly recovered in order to obtain additional mechanical power. The waste heat recovery system is based on a closed thermodynamic bottoming cycle with supercritical car­ bon dioxide (scCO2) as working fluid, allowing to achieve a very high power density. As first step of the investigation a thermo­dynamic cycle analysis of the combined-cycle engine (CCE) is carried out. Results are compared to those of the intercooled­recuperative engine (IRE) configuration for the same operating conditions and calculated under the same modeling assumptions. The estimated nominal SFC of the proposed CCE configuration is approximately 20% lower compared to that of a conventional turbofan, and 6% lower than that of the IRE, if pressure drops in the heat exchangers are neglected. Such large gain justified further analysis, by including the preliminary sizing of main components. Once the sizing of heat exchangers is factored in, the thermodynamic benefit of the CCE is offset by the penalty due to the weight of the additional equip­ment. This is mainly caused by i) the space constraints of the turbofan nacelle, which strongly limit the recoverable thermal power, and ii) the lack of proper het exchanger technology for such a highly unconventional application. These issues, and the many other that need consideration, will be addressed in an upcoming research project encompassing a much wider scope involving new aircraft and propulsion system @en

This work proposes and assesses two numerical models for solving high-speed condensing flows in metastable conditions. Each model involves a set of governing equations (mass, momentum, and energy) for the mixture or the continuum phase, i.e. the vapor, and two additional transport equations to characterize the dispersed phase. Such relations are formulated through the so-called method of moments that allows to represent the wetness fraction and the number of droplets of the liquid. The transport relations are discretized in space by means of a new coupled up-wind scheme. A segregated implicit time integration strategy is exploited to hasten the convergence of the full system to steady-state. The performance and accuracy of both models are thoroughly investigated on a reference quasi-1D problem and confronted against experimental data and more advanced two-phase flow models. Results show that experimental observations are adequately predicted, especially concerning the droplets dimension. It is additionally inferred that the new upwind flux is beneficial to improve robustness of the underlying numerical methods. Finally, it is demonstrated that the continuum phase model outperforms the mixture one in terms of numerical stability and computational cost, thereby making it very promising for the extension to multi-dimensional problems.

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