The blade solidity, namely the blade chordtopitch ratio, largely affects the fluiddynamic performance of turbomachinery. For turbomachines operating with air or steam, the optimal value of the solidity which maximizes the efficiency is estimated with empirical correlations such as the ones proposed by Zweifel (1945) and Traupel (1966). However, if the turbomachine operates with unconventional fluids, the accuracy of these correlations becomes questionable. Examples of such working fluids are the nonideal (dense) vapors of organic compounds (e.g., hydrocarbons, siloxanes) used to operate organic Rankine cycle (ORC) power systems. This study investigates the effect of both the working fluid and the flow compressibility on the optimum pitchtochord ratio of turbine stages. A first principle model for the profile losses is developed for this purpose. Charts providing the optimal pitchtochord ratio for unconventional turbine stages are then provided. Numerical simulations of the flow over a turbine stator cascade have been conducted to validate the model results and evaluate the influence of both working fluid, flow compressibility, and solidity value on the loss breakdown. The results show that the optimal solidity of turbine cascades value significantly increases with the flow compressibility. Therefore, models providing the optimal solidity based on the estimate of passage loss only are not suited for unconventional turbines. @en

In this work, we present an investigation about the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations (DNS) of transitional, zero-pressure gradient boundary layer flows are performed for two fluids characterized by different complexity of the fluid molecules, namely, “air” and siloxane MM. Different sets of thermodynamic free-stream boundary conditions are selected to evaluate the influence of the fluid state on both the frictional loss and the dissipation mechanisms. The thermophysical properties of siloxane MM are calculated with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field, irreversible heat transfer, and turbulent dissipation differs significantly depending on both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS results is then compared against the one obtained using a reduced-order model (ROM), which solves the two-dimensional boundary layer flow equations for an arbitrary fluid [M. Pini and C. De Servi, “Entropy generation in laminar boundary layers of non-ideal fluid flows,” in 2nd International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (Springer, 2020), pp. 104-117]. Results from both the DNS and the ROM show that low values of the overall dissipation are observed in the case of fluids made of simple molecules, e.g., air, and if the fluid is at a thermodynamic state in the proximity of that of the vapor-liquid critical point.

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The blade solidity, namely the blade chord-to-pitch ratio, largely affects the fluid-dynamic performance of turbomachinery and its cost. For turbomachines operating with air or steam, the optimal value of the solidity which maximizes the efficiency is estimated with empirical correlations such as the ones proposed by Zweifel (1945) and Traupel (1966). However, if the turbomachine operates with unconventional fluids, the accuracy of these correlations is questionable. Examples of such fluids are the organic compounds (e.g., hydrocarbons, siloxanes) used in organic Rankine cycle (ORC) power systems. This study concerns an investigation on how the working fluid, its thermodynamic state, and flow compressibility influence the optimum pitch-to-chord ratio of turbine stages. A first principle reduced-order model (ROM) for the computation of profile losses was developed for this purpose. The ROM results are compared with those obtained from numerical simulations of the flow over two axial turbine cascade geometries. The influence of both the working fluid, the flow compressibility, and the solidity value on both the boundary layer state at the blade trailing edge and the base pressure are evaluated. Models to compute mixing and passage losses in the compressible regime as a function of the axial solidity are proposed and discussed. Results show that the value of the optimal solidity of turbine cascades significantly increases with the flow compressibility, and mildly increases if the fluid is in the dense vapor state. Moreover, the optimal solidity value is strongly affected by the mixing process occurring downstream of the blade trailing edge. Therefore, currently available models for its estimation, which are solely based on the minimization of the profile losses, are inaccurate.

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The vast majority of energy conversion systems currently makes use of fossil fuels, whose combustion generates harmful greenhouse gases. Transitioning to renewable energy sources is thus paramount to limiting the environmental impact of human activities on the climate. In this regard, the harvesting of wasted thermal energy constitutes a promising strategy to increase the efficiency of industrial processes and mobile engines. For instance, technologies such as organic Rankine cycle (ORC) systems enable the energy discarded during the conversion processes to the atmosphere to be repurposed and generate CO2-neutral electricity or additional mechanical work. The efficiency of such systems is subordinate to that of each of the components, among which, is the turbine. Designing more efficient ORC turbines inherently leads to a higher thermodynamic cycle efficiency. However, these turbines operate with complex organic compounds, and part of the expansion process often occurs in the dense vapor state, where the thermodynamic properties exhibit significant deviations from the variations predicted by the ideal gas law. As a consequence, available guidelines for the design of turbomachinery operating with air or steam cannot be used, as they would lead to incorrect sizing and wrong performance estimations. The development of generalized guidelines for turbine design is possible only through a thorough investigation of the internal non-ideal compressible flow inside the vane passage, and by accurately discerning all the possible loss sources. The research outlined in this thesis aims at characterizing non-ideal compressible internal flows of dense vapors and developing new guidelines for the design of unconventional turbines operating with organic fluids, such as those operating in organic Rankine cycle power systems. The influence of both the complexity of the fluid molecules and the thermodynamic state on the flow field is evaluated for some paradigmatic one-dimensional flow configurations. For these processes, loss mechanisms and relevant trends in flow variables are both qualitatively and quantitatively estimated. Moreover, a detailed analysis of the viscous dissipation in turbulent wall-bounded flows of dense vapor is performed by resorting to direct numerical simulations (DNS). Results are compared against those from an in-house reduced-order model (ROM) code solving the two-dimensional boundary layer equations. The combined effects of the working fluid, its thermodynamic state, and the flow compressibility on the flow deviation downstream of turbine cascades are then investigated by means of Reynolds Averaged Navier-Stokes (RANS) calculations on a representative geometry. The results obtained from the simulations are compared against those estimated with reduced-order physical models. Finally, an investigation of the influence of both compressibility and fluid molecular complexity on the optimal solidity of axial turbines is performed using RANS calculations. New design guidelines for the selection of optimal solidity in the preliminary design of non-conventional turbomachinery are proposed and discussed. Results show that turbines operating with compounds characterized by a high complexity of the molecular structure are arguably subjected to higher losses in the mixing region, as well as exhibiting larger viscous dissipation at a given Reynolds number. Moreover, the fluid strongly affects the operational range of the turbine, as well as its design.@en

In this work, we investigate the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations of transitional, zero-pressure gradient boundary layers are performed with an in-house solver considering two fluids characterized by different complexity of the fluid molecules, namely air and siloxane MM. Different sets of thermodynamic free stream boundary conditions are selected to evaluate the influence of the fluid state on the frictional loss and dissipation mechanisms. The thermo-physical properties of siloxane MM are obtained with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field and irreversible heat transfer, and the turbulent dissipation are significantly affected by both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS is then compared against the one obtained from a reduced-order boundary layer CFD model [1] which has been extended to treat fluids modeled with arbitrary equations of state [7].

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In this work we examine the flow deviation and its relationship to critical choking, i.e., choking of the meridional component of velocity, in transonic turbine cascades operating with non-ideal compressible flows. To this purpose, a generalized expression of the corrected flow per unit area as a function of both the thermodynamic state and the molecular complexity of the working fluid, the Mach number, and the amount of swirl is derived. The trends of the corrected flow with respect to these quantities are used to infer physical insights on the flow deviation and on the operability of transonic turbine cascades in off-design conditions. Moreover, reduced-order models for the estimation of the flow deviation and the preliminary assessment of the losses have been developed and validated against the results of CFD simulations performed on a representative transonic turbine stator. Results suggest that flows of dense organic vapors exhibit larger deviations than those pertaining to compounds made of simple molecules, e.g., air. Furthermore, transonic turbines expanding dense vapors reach critical choking conditions at lower Mach numbers than the ones operating with simple molecules, and are affected by larger dissipation due to viscous mixing.

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In this work we examine the behavior of non-ideal compressible swirling flows. Based on a first-principle analysis, we derive a generalized expression of the corrected flow per unit area as function of the isentropic exponent, characteristic Mach numbers, and swirl parameter. The calculated trends of the corrected flow with respect to these parameters, validated against results from high-fidelity computations, are used to infer physical insights on the behavior of swirling flows in turbomachinery cascades. The results suggest that fluid flows characterized by low values of the isentropic exponent show swirling behaviors that are substantially different than those exhibited by perfect gases. Ultimately, this can make the design of efficient turbomachines operating close to the critical point particularly challenging.

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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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