This article presents a data-driven method to evaluate thermodynamic properties of pure fluids and mixtures of fixed composition in the ideal- and nonideal thermodynamic states. Thermodynamic consistency is ensured by computing the fluid properties on the basis of the entropy potential and its first- and second- order derivatives, calculated with a physics-informed neural network. The computational performance of the method was investigated by implementing the resulting data-driven model in the open-source SU2 CFD software and by performing RANS simulations of the nonideal compressible flows through an organic Rankine cycle turbine cascade. Compared to using a multiparameter equation of state through a thermodynamic library coupled with SU2, the method was found to be 60 % more computationally efficient while maintaining high accuracy.

High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation-propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-Annulus computational fluid dynamics (CFD) can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flowrate. This approach, however, leads to suboptimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flowrate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely, those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.

Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas-lubricated bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and avoiding contamination of the working fluid. In certain operating conditions, however, the lubricant of the gas bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point, whereby nonideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of nonideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the nondimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of nonideal thermodynamic effects on nondimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

A supersonic inlet turbine can extract substantial energy from the highly fluctuating and transonic flow delivered by a rotating detonation combustor (RDC). However, a transition duct is necessary to achieve the supersonic inlet conditions required by the turbine. In this work, the supersonic transition duct is designed with the method of characteristics (MOC). A generalized implementation of the MOC is proposed for the generation of annular ducts with asymmetric and rotated hub and shroud walls. The model is extended to deal with ideal and non-ideal flows, namely flows characterized by non-ideal thermodynamic effects, and its accuracy has been verified through comparison with results obtained with computational fluid dynamics (CFD) simulations. In addition, boundary layer flow equations are combined with the MOC to predict viscous losses on the endwalls and to adjust duct geometry by accounting for the boundary layer thickness. Furthermore, it is essential to predict the effects of the large unsteadiness generated by the detonation combustor for an efficient operation of the turbine. The maximum incidence angle at the turbine inlet is predicted with a one-dimensional annular duct model. Supersonic duct flow behavior to unsteady inlet conditions is characterized through two-dimensional inviscid axisymmetric unsteady CFD simulations. The accuracy of the reduced order models is finally verified with a three-dimensional unsteady viscous simulation assuming inlet flow conditions representative of RDC operation.

The ORCHID turbine is a laboratory single-stage 10 kW high-speed (∼100 krpm) radial-inflow turbine for high-temperature/high-efficiency organic Rankine cycle (ORC) systems, designed at the Aerospace Propulsion and Power laboratory of Delft University of Technology. It will be installed within a test section of the organic Rankine cycle hybrid integrated device (ORCHID) facility, the setup for fundamental and applied studies on ORC technology currently in operation in the same lab. Experimental data from future measurement campaigns will be employed to validate design and performance prediction tools and to develop best practices for operating these unconventional machines, whose most notable features are the ultrahigh expansion ratio (>40), highly supersonic flow in the stator (Ma > 2), and the large flow deflection within the impeller channels (>90). This article presents the mechanical design and the rotordynamic assessment of the ORCHID turbine rotor, and best practices for the numerical evaluation of the rotordynamic characteristics and stability of high-speed ORC turbine rotors. The emphasis is on three main aspects: i) the modeling and quantification of the damping characteristics of a squeeze film damper (SFD) cartridge for the selected turbocharger ball bearings supporting the turbine shaft; ii) the characterization of the stiffness and damping coefficients of a custom designed pocket gas seal, performed using 3D RANS simulations; iii) the analysis of linear elastic rotordynamic simulations using a finite beam element model of the turbine rotor. Results of the rotordynamic simulations show that the rotor would operate in the sub-critical regime with respect to the first bending mode. The influence of model parameters such as the rotor eccentricity and the orbit radius was included in the analysis by conducting a parametric study of the SFD fluid forces. The Campbell diagrams show that shaft bending frequencies are significantly affected by changes in the SFD dynamic response depending on the rotational speed. The influence of the stiffness of rolling bearing elements and of the destabilizing forces due to the impeller and gas seal cross-coupled stiffness was also evaluated. The rigidity of the rolling elements slightly affects the shaft bending mode, while large values of the destabilizing forces cause a rotordynamic instability of the first rigid mode.

The radial-inflow turbine (RIT) is a widely adopted turbo-expander in power and propulsion systems of low-to-medium power capacity due to its high efficiency and compactness. Compared to conventional radial turbines for gas turbines and air cycle machines, the design of expanders for high-tem-perature organic Rankine cycle power systems involves additional chal-lenges, as these machines operate with very high expansion or volumetric flow ratio and partly or entirely in the nonideal compressible fluid dynamic regime. This study examines the impact of the working fluid, of the volumetric flow ratio, and of the nonideal thermodynamic effects on the design guidelines for RIT. To this purpose, a reduced-order modeling framework for turbine fluid-dynamic design encompassing a loss model based on first principles is developed and verified against results from uRANS. Results highlighted that at the geometrical scale of interest the impact of the working fluid molecular complexity on the efficiency is marginal. Moreover, it is shown that the average isentropic pressure-volume exponent [Entity In Abstract]) can be used to predict the magnitude of nonideal thermodynamic effects on the stage efficiency, whose variation depends on the value of the volumetric flow ratio and of the work and flow coefficients. Design guidelines that can be used for preliminary turbine design in system-level calculations are presented in graphical form, and illustrate the relation between the optimal set of stage duty coefficients, i.e., the work and flow coefficients that maximize the efficiency, the stage efficiency, the volumetric flow ratio, and the similarity parameter [Entity In Abstract] .

The successful implementation of an airborne propulsion system based on hydrogen-powered fuel cell technology highly depends on the development of an efficient, lightweight and compact air supply compressor. Meeting these requirements by designing the compressor using conventional single-point preliminary design methods can be challenging, due to the very wide range of corrected mass flow rate and pressure ratio values that the air supply compressor must be able to accommodate. The article presents a multi-point design methodology for the preliminary design of centrifugal compressors of air supply systems. The method is implemented in an in-house code, called TurboSim, and allows to perform single- and multi-objective constrained optimization of vaneless centrifugal compressors. Furthermore, an automatic design point selection method is also available. The accuracy of the compressor lumped-parameter model is validated against experimental data obtained on a high-pressure-ratio single-stage vaneless centrifugal compressor from the literature. Subsequently, the design methodology is applied to optimize the compressor of the air supply system of an actual fuel cell powertrain. The results, compared to those obtained with a more conventional single-point design method, show that the multi-point method provides compressor designs that feature superior performance and that better comply with the specified constraints at the target operating points.

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.

High-speed supersonic radial compressors are a critical enabling technology for meeting the requirements of future aviation-propulsion and thermal-management systems. These turbomachines must be designed to be both efficient and robust on the widest possible operating range. Flow instabilities in the form of rotating stall and surge are therefore phenomena that must be accurately predicted early in the design process. Unsteady full-annulus computational fluid dynamics can be used to get accurate information about the onset of instabilities, but at the expense of costly simulations. As a result, the design of new compressors continues to rely on existing correlations for the prediction of the critical mass flow rate. This approach, however, leads to sub-optimal compressor designs. This article provides a review of the numerical methodologies that can be used for the accurate prediction of the critical mass flow rate in high-speed centrifugal compressors. Methods of different fidelity level and computational cost are described. Two particularly promising models, namely those proposed by Spakovszky and Sun, are subsequently examined in more detail. Exemplary applications of these two models are finally discussed.

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.

Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas lubricated bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the gas bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Modeling non-ideal compressible flows in the context of computational fluid-dynamics (CFD) requires the calculation of thermodynamic state properties at each step of the iterative solution process. To this purpose, the use of a built-in fundamental equation of state (EoS) in entropic form, i.e., s= s(e, ρ), can be particularly cost-effective, as all state properties can be explicitly calculated from the conservative variables of the flow solver. This approach can be especially advantageous for massively parallel computations, in which look-up table (LuT) methods can become prohibitively expensive in terms of memory usage. The goal of this research is to: i) develop a fundamental relation based on the entropy potential; ii) create a data-driven model of entropy and its first and second-order derivatives, expressed as a function of density and internal energy; iii) test the performance of the data-driven thermodynamic model on a CFD case study. Notably, two Multi-Layer Perceptron (MLP) models are trained on a synthetic dataset comprising 500k thermodynamic state points, obtained by means of the Span-Wagner EoS. The thermodynamic properties are calculated by differentiating the fundamental equation, thus ensuring thermodynamic consistency. Conversely, thermodynamic stability is properly enforced during the regression process. Albeit the method is applicable to the development of equation of state models for arbitrary fluids and thermodynamic conditions, the present work only considers siloxane MM in the single phase region. The MLP model is implemented in the open-source SU2 software [8] and is used for the numerical simulation of non-ideal compressible flows in a planar converging-diverging nozzle. Finally, the accuracy and the computational performance of the data-driven thermodynamic model are assessed by comparing the resulting flow field, the wall time and the memory requirements with those obtained with direct calls to a cubic EoS, and with a LuT method.

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].