Thermal energy recovery is being investigated by leading aerospace companies as a means to improve the efficiency of next-generation propulsion systems. The organic Rankine cycle (ORC) system, due to the flexibility of the concept, is arguably the best technology for waste heat recovery and, thus, a promising solution to develop recuperated engines. In such systems, heat exchangers are arguably the most critical components, as their design must balance thermal performance with constraints on weight and volume. Consequently, integrating the optimization of heat exchangers into the overall system design may lead to substantial performance enhancement compared to more traditional iterative design methods. The objective of this study was the development of a systematic methodology for optimizing airborne thermal systems, with a focus on addressing the computational challenges of integrated design. Three design strategies are compared: (i) optimization of the sole cycle parameters while performing heat exchanger sizing for values of the geometrical characteristics defined a priori based on a preliminary investigation of the design space of these components, (ii) concurrent optimization of both the thermodynamic cycle and of the most critical heat exchanger, e.g., the condenser, and, (iii) use of a data-driven surrogate model of the condenser to predict the optimal heat exchanger geometry as a function of any feasible thermodynamic conditions to reduce the number of optimization variables of the integrated design problem. The surrogate model is constructed based on datasets of Pareto-optimal HX designs in the objective space defined by heat exchanger weight and pressure drops. The three design strategies are applied to two case studies featuring supercritical ORC systems utilizing cyclopentane as the working fluid: a combined cycle auxiliary power unit (CC-APU) and a combined cycle turboshaft (CC-TS) engine. Findings indicate that integrated optimization yields performance gains that vary depending on the heat exchanger topology, application, and thermodynamic cycle. For instance, CC-APU designs obtained with the integrated design optimization method are up to 15% lighter than designs obtained with the optimization of the thermodynamic cycle parameters alone, for the same net power output. Microchannel condenser designs with offset strip fins allow for obtaining a better performance than louvered fin-based designs if a low-pressure drop is targeted, whereas louvered fins are advantageous if a higher pressure drop is allowed. The design strategy employing the surrogate model considerably reduces the computational cost, without significantly affecting accuracy: the relative deviation between the Pareto front obtained with the surrogate model and that obtained with the integrated optimization strategy ranges between 1% and 2.9%. These values are comparable to the uncertainty of the predictions of the heat exchanger model. The reduction in computational time required to generate the Pareto fronts associated with the two case studies is up to 200%.

The use of an electrically driven vapor compression cycle (VCC) for the environmental control system (ECS) of next-generation aircraft could substantially reduce fuel consumption. The renovated interest in this technology is due to the advent of new refrigerants featuring low global warming potential and the latest developments in high-speed centrifugal compressors and ultracompact heat exchangers. This paper documents the development of an integrated design optimization method for aircraft ECS, whereby the system-level design is performed along with the preliminary design of its main components. The methodology is used to perform the multipoint and multi-objective design optimization of a bleedless air cycle machine (ACM), i.e., the state-of-the-art ECS installed onboard the Boeing 787, and an electrically driven VCC system for a single-aisle, short-haul aircraft. The performance of the two optimal architectures is compared, showing that the VCC system is characterized by lower weight and electric power consumption than the bleedless ACM but features a higher drag penalty. Overall, the optimal VCC system leads to an 18% reduction in fuel weight penalty with respect to the bleedless ACM for the prescribed application.

The Environmental Control System (ECS) is the main utilizer of non-propulsive power among the aircraft subsystems. Onboard helicopters, the ECS is based on the Vapour Compression Cycle (VCC) concept, and the standard refrigerant is R-134a. The objective of this study is to evaluate the impact of replacing the conventional scroll compressor with a high-speed centrifugal compressor operating with a low-GWP refrigerant as the prime mover of the VCC system. The case study is the ECS of a large helicopter and the sizing operating condition is that of the helicopter on the ground on a hot and humid day. The working fluids identified as potential alternatives to R-134a are the haloolefins R-1233zd(E), R-1234ze(Z), R-1224yd(Z) and R-1336mzz(Z). An integrated design optimization method has been employed to simultaneously account for the design of the VCC system, its main components, and the selection of the working fluid. The model of the VCC system has been coded with the acausal Modelica language. The design of the high-speed compressor has been performed with an in-house program validated with experimental data. The objectives of the optimization are the maximization of the Coefficient of Performance (COP) and the minimization of the system weight. The results show that the use of haloolefins in place of R-134a allows the design of lighter and more efficient VCC systems. In particular, the refrigerant R-1234ze(Z) enables the identification of an optimal design point featuring a 12% increase in COP and a 26% reduction in weight.

Designing high-performance and aerospace-grade heat exchangers requires detailed characterization of the as-manufactured geometry, including cross-sectional area and surface texture, to reduce uncertainties in performance prediction and issues regarding subsequent system integration. This paper presents experimental testing and analysis of microchannels fabricated using the laser powder directed energy deposition (LP-DED) additive manufacturing (AM) process. Research has shown that as-built surfaces result in differential pressure higher than what is predicted with current correlations and surface enhancements may be required for heat exchangers built using AM to meet the desired pressure drop specifications. Various surface enhancement techniques including abrasive flow machining (AFM), chemical milling (CM), and chemical mechanical polishing (CMP), were applied to the internal surfaces of the channels to tailor flow dynamics and induce variations in pressure drop. Based on experimental flow testing, channels processed with surface enhancements provide a tenfold reduction in differential pressure compared to the as-built channels. After testing, the samples were destructively sectioned to obtain geometric and detailed surface texture information. This characterization helped to inform a new prediction method for determining hydraulic diameter and equivalent sand grain roughness, thus reducing the uncertainty of predicted friction factors. The new correlation allows to estimate friction factor and pressure drop with a deviation from the experimental data that is within 20% of their value. The identification of the mechanisms at the basis of the formation of surface texture allowed to categorize distinct aspects related to friction factor ranges: roughness peaks, peak smoothing/reduction, minimized roughness, and combined waviness and valley reduction.

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 Environmental Control System (ECS) of passenger aircraft is the main consumer of non-propulsive power aboard. A computationally efficient and accurate thermal model of the fuselage is needed for future sustainable aircraft to address ECS preliminary sizing and control design, as the ECS should be re-designed to exploit possible synergies with other thermal management systems on board. Differently from previous works, the present aircraft thermal model is extensively documented and released open-source. Moreover, it is completely based on first principles and the acausal modeling paradigm. It results that the model is scalable, easily extendable, and allows for the estimation of the aircraft thermal loads given limited information about its configuration and flight mission. The predictive capabilities of the model have been assessed by comparing the thermodynamic state estimated at the pack discharge for three ECS operating points of an Airbus A320 with data provided by the manufacturer. The maximum deviation is limited to 2.4 K and 4.5 kPa. The validated thermal model has been used to compute the operating envelope of the A320 ECS, showing that the air supply requirements vary substantially with ambient conditions and flight phases. This calls for a multi-point design strategy when assessing novel ECS configurations.

The gas dynamics of single-phase nonreacting fluids whose thermodynamic states are close to vapor-liquid saturation, close to the vapor-liquid critical point, or in supercritical conditions differs quantitatively and qualitatively from the textbook gas dynamics of dilute, ideal gases. Due to nonideal fluid thermodynamic properties, unconventional gas dynamic effects are possible, including nonclassical rarefaction shock waves and the nonmonotonic variation of the Mach number along steady isentropic expansions. This review provides a comprehensive theoretical framework of the fundamentals of nonideal compressible fluid dynamics (NICFD). The relation between nonideal gas dynamics and the complexity of the fluid molecules is clarified. The theoretical, numerical, and experimental tools currently employed to investigate NICFD flows and related applications are reviewed, followed by an overview of industrial processes involving NICFD, ranging from organic Rankine and supercritical CO2 cycle power systems to supercritical processes. The future challenges facing researchers in the field are briefly outlined.

Compressible flows of fluids whose thermophysical properties are related by complex equations are quantitatively and can be qualitatively different from high-speed flows of ideal gases. Nonideal compressible fluid dynamics (NICFD) is concerned with these fluid flows, which are relevant in many processes and power and propulsion systems. Typically, NICFD effects occur if the fluid is an organic compound and its vapor state is close to the vapor–liquid critical point, at high-reduced temperature and pressure (even supercritical). Current design and analysis of devices operating in the nonideal compressible regime demand for validated simulation software, characterized in terms of uncertainty. Moreover, experiments are needed to further validate related theory. Experimental data are limited as generating and measuring these flows is challenging given their high pressure or temperature or both. In addition, flows of organic compounds can be flammable, can thermally decompose, and sealing may demand for special materials. Recently, more research has been devoted to the measurement of these flows using both intrusive and less intrusive techniques relying on optical access and lasers. The transparency and refractive properties of these dense vapors pose additional problems. The ORCHID (organic Rankine cycle hybrid integrated device) at the Aerospace Propulsion and Power Laboratory of Delft University of Technology is a closed-loop facility, used to generate a continuous nonideal supersonic flow of siloxane MM with the vapor at 4bar and 220 °C at the inlet of the test section. Within this work, we have employed particle image velocimetry for the first time to obtain the velocity field in a de Laval nozzle in such flows. Measured velocity fields (expanded uncertainty within 1.1% of the maximum velocity) have been compared with those resulting from a CFD simulation. The comparison between experimental and simulated data is satisfactory, with deviation ranging from 0.1 to 10 % from the throat to the outlet, respectively. This discrepancy is attributed to hardware limitations, which will be overcome in the future experiments. The feasibility of PIV with uncontrolled but fixed seeding density to measure high-speed vapors of organic vapors has been demonstrated, and future experimental campaigns will target flows for which nonideal effects are more pronounced, other paradigmatic configurations, and improvements to the measurement techniques.

This paper presents a preliminary study about a combined-cycle engine based on a turboshaft engine and an organic-Rankine-cycle (ORC) bottoming unit to be used onboard an aircraft with a turboelectric propulsion system. The aim is to analyse whether benefits with respect to mission fuel consumption can be derived by employing such a combined-cycle
engine when compared to a simple-cycle turboshaft engine. For this purpose, a multidisciplinary optimization framework is developed, incorporating models for the engine, ORC system, ORC turbine, heat exchangers, and mission analysis. This framework is coupled with an optimizer to identify the optimal combined-cycle engine design for minimum mission fuel consumption. The results suggest that fuel savings of around 1.5% are possible with the optimized system if compared to the aircraft employing turboshaft engines. Heat exchanger volume is identified as the most constraining parameter when it comes to combined-cycle performance. The analysis of the results suggests as aspects which might lead to further improvements the evaluation of other ORC architectures, working fluids and heat exchanger topologies.

A novel test setup called the asymmetric shock tube for experiments on nonideal rarefaction waves (ASTER) has been commissioned at Delft University of Technology. The ASTER, which works according to the principle of Ludwieg tubes, is designed to generate and measure the speed of small and finite amplitude waves propagating in the dense vapors of fluids formed by complex organic molecules, therefore in the nonideal compressible fluid dynamics regime. The ultimate goal of the associated research is to prove the existence of nonclassical gasdynamics. The setup consists of a high-pressure charge tube and a vacuum tank separated by a glass disk equipped with a breaking mechanism for rarefaction waves experiments. When the glass disk is broken, an expansion wave propagates into the tube in the direction opposite to the fluid flow. The propagation speed of this wave is measured using a time-of-flight method with the help of four fast-response pressure sensors placed equidistantly in the middle of the tube. The charge tube can withstand pressures and temperatures of up to 15 bar and 400∘C. Preliminary rarefaction experiments were successfully conducted using dodecamethylcyclohexasiloxane, D₆, as the working fluid and at pressures and temperatures of up to 9.4 bar and 372∘C, respectively. The results of an experiment featuring the initial state for which a theoretical model predicts the nonclassical acceleration of rarefaction waves show that the propagation is qualitatively different from that put into evidence by experiments for which the propagation is classic. Upcoming setup improvements and experimental campaigns are planned with the objective of experimentally verifying the existence of nonclassical gasdynamics. Graphical abstract: (Figure presented.)

The aircraft Environmental Control System (ECS) is the main consumer of non-propulsive energy, accounting for 3% of the total energy consumption among all the aircraft subsystems. The ECS efficiency can be improved by recurring to an electrically-driven Vapour Compression Cycle (VCC) system for cabin cooling. This work documents the detailed design and the commissioning of a novel experimental test rig, called Inverse organic Rankine cycle Integrated System (IRIS). The setup has been conceived for testing the performance of VCC systems and some of their components for aircraft ECS applications in different operating conditions, and for validating the numerical models developed for systems and components simulations. The facility implements a single-stage compression refrigeration cycle with two test sections: a volumetric compressor testing setup and an air-cooled condenser test bed. The evaporator is heated by a glycol-water mixture, warmed up in an independent loop. The design working fluid is R-1233zd(E). The successful commissioning of the facility is documented by discussing the data recorded during steady-state operation at the design operating point, together with the operation of the setup during start-up and shut-down procedures. The system cooling capacity is equal to 17.88 ± 0.8 kW, which is slightly higher than the design value of 15.5 kW. The difference has a positive effect on the system efficiency, which is 4% higher than the one calculated at design.

Images of compressible flows can be post-processed with digital imaging techniques to obtain accurate quantitative information about variables characterizing the flow. For example, the local flow Mach number can be obtained from the angle of Mach lines visualized with the schlieren method. These techniques were recently applied to supersonic flows of dense organic vapors, with the objective of obtaining accurate data to validate theory and CFD codes. Non-ideal compressible fluid dynamics (NICFD) is concerned with these flows, for which therefore the thermodynamic properties of the fluid can be modeled only with equations that are more complex than the ideal gas relations. NICFD flows are relevant, e.g., for applications in the power and chemical industry. However, currently employed image post-processing techniques used to obtain the local Mach number or shock wave angle from schlieren images, like the Hough transform, suffer from few drawbacks, namely a long computational time to obtain the relevant quantities and improvable accuracy. The investigation reported here concerns the application of known digital image processing methods to schlieren images, in this case Gabor filters and Radon transforms, to obtain the local Mach number and the shockwave angle of flows in NICFD conditions. The selected test case is the supersonic expansion of the dense vapor of hexamethyldisiloxane flowing through the nozzle test section of the ORCHID facility in operation at the Propulsion and Power laboratory of Delft University of Technology. The investigated digital image processing techniques provide values of the local Mach number with comparable uncertainty (within 5%) as the Hough transform approach. Moreover, Mach line orientations are computed for the whole field of view, together with Mach line wavelength. It was also proven that these methods are suitable for discerning Mach line orientation even in the case of very complex flow fields, with coexisting Mach waves and shock waves.

In evaporators, the distribution of the liquid and vapor phases among the channels is a convoluted problem, depending on a wide range of parameters. However, maldistribution causes important losses of performance. Due to their complexity, the accurate modeling of such two-phase flows is difficult to handle. Hence, experimental studies are still of great importance to help the understanding of maldistribution behaviors inside evaporators. Most of the experimental investigations of two-phase flow distribution are measuring the liquid and vapor quantities in the channels through a phase separation process, increasing the test duration and complexity. As a consequence, the number of parameters investigated is usually limited. Therefore, a new inline instrumentation method would allow for a more complete study by simplifying the measurement process. In the present work, an isothermal air/water mixture was used as fluid. The distribution of the two phases in eight channels of 10-mm I.D. connected to a simplified header was investigated. The inlet mass flow rates considered ranged from 0 to 0.025 kg/s for the water, and from 0 to 0.022 kg/s for the air. Consequently, qualities x up to 0.7 and void fractions ® up to 0.9 were reached. All the tests were carried at a pressure condition of 7 bar to reach a liquid to vapor density ratio similar to what is encountered for traditional refrigerant. Finally, to allow a continuous measurement process, the mass flow rates in each of the 10-mm I.D. channel were measured using a flowmeter calibrated on a separate line. Since no void fraction meter was coupled, a new iterative methodology, based on the Venturi pressure drops measurement solely, was developed and is proposed here. It proved to successfully predict the vapor and liquid phase flow rates in each channel.

This research evaluates Laser Powder Directed Energy Deposition (LP-DED) for producing fine feature internal microchannels. This study is focused on enhancing and characterising the surfaces of microchannels produced using techniques such as abrasive flow machining, chemical milling, chemical mechanical polishing, electrochemical machining, and thermal energy method to modify internal surfaces of microchannels made from NASA HR-1 Fe-Ni-Cr alloy. Flow testing for discharge coefficient measurement is conducted on processed microchannel samples, followed by characterisation through optical microscopy, Scanning Electron Microscopy (SEM), and Computed Tomography. Findings reveal variations in surfaces due to powder adherence, melt pool undulations, and polishing mechanisms. The study emphasises the significance of removing material equivalent to the mean powder diameter to reduce surface roughness and impact the discharge coefficient. The research proposes a ratio for planarising roughness and waviness peak height and density, offering insights for tailored surface adjustments in specific applications requiring reduced flow resistance. Highlights Internal microchannels with thin-walls were fabricated using the laser powder directed energy deposition process. Various surface enhancements and polishing processes were developed to modify the surface texture of the LP-DED channels. Flow testing was conducted to determine the discharge coefficient. Post-test characterisation was completed to obtain cross sectional area, perimeter, surface texture, and general surface condition to analyse results. Ratio of roughness and waviness peak and density (Spk/Spd and Wp/WPc) is proposed as a relevant surface characterisation parameter. Tailored surface modifications for specific end-use applications.

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.

The aircraft Environmental Control System (ECS) is the primary consumer of non-propulsive power at cruise conditions, hence, its performance optimization is crucial for the reduction of specific fuel consumption. A novel integrated system design optimization method is presented: thermodynamic cycle, component sizing and working fluid are taken into account simultaneously. This method was applied to the ECS of large rotorcraft based on a Vapour Compression Cycle system electrically driven by a high-speed centrifugal compressor. Steady-state and lumped parameter system component models have been developed using the Modelica acausal modelling language. The optimization design framework consists of an in-house code, featuring a Python-Modelica interface. The study case refers to a critical operating condition: the helicopter is on the ground during a hot and humid day. The working fluid is R-134a. The multi-objective optimization targets the maximization of the system efficiency and the minimization of system weight. The results show that more efficient systems can be designed only with heavier components. The design feasibility of high-speed centrifugal compressors is demonstrated. The advantage of an integrated system design optimization framework for complex energy systems is proved, allowing for the analysis of the impact of both component design and working fluid on system performance.

Waste heat recovery (WHR) from aeroengines via compact organic Rankine cycle (ORC) units may increase the fuel efficiency of air transportation. Heat exchangers are arguably the key components of ORC systems for aeronautical applications and their design must be optimized to guarantee the best trade-off between fluid pressure drop, weight and induced aircraft drag. At present, no heat exchangers design guidelines are available for waste heat recovery systems aboard aircraft. This study, thus, contributes to defining a proper design methodology for ORC systems of such applications. The chosen test case is a supercritical ORC system with cyclopentane as the working fluid, which recovers waste heat from the auxiliary power unit of an aircraft. The exhaust gas temperature and mass flow rate of the power unit are known and kept constant in the analysis, and so are the ambient conditions, which define the cold sink of the ORC turbogenerator. Three design strategies targeting minimum mass and maximum net power output of the ORC unit have been assessed. In the first one, the multi-objective optimization is performed by prescribing a priori the geometry and frontal area of the heat exchangers. Thus, only the cycle parameters are optimized. The second method tackles, instead, the simultaneous optimization of the geometric parameters of the condenser and the cycle parameters. It was found that the integrated design allows for system mass reduction by 10 - 12% for a given ORC power output, highlighting the importance of performing the simultaneous optimization of the thermodynamic process and the heat exchanger geometry. Finally, the third method addresses the same optimal design problem by leveraging a reduced-order model of the condenser to predict the optimal design space of this component. The generated Pareto front obtained with this method is very similar to that found by optimizing simultaneously the complete condenser geometry and the cycle parameters. The mean deviation is about 2%. With just one heat exchanger surrogate model, the Pareto front was generated in one fourth of the computational time. This is due to the lower number of optimization variables and the faster objective function evaluation.

The use of mixtures as working fluids of organic Rankine cycle (ORC) waste heat recovery (WHR) power plants has been proposed in the past to improve the matching between the temperature profile of the hot and the cold streams of condensers and evaporators, thus to possibly increase the energy conversion efficiency of the system. The goal of this study is to assess the benefits in terms of efficiency, environmental (GWP) and operational safety (flammability) that can be obtained by selecting optimal binary mixtures as working fluids of air-cooled ORC bottoming power plants of medium-capacity industrial gas turbines. Furthermore, two thermodynamic cycle configurations are analyzed, namely the simple recuperated cycle and the so-called split-cycle configurations. The benchmark case is a combined cycle power plant formed by an industrial gas turbine and an air-cooled recuperated ORC power unit with cyclopentane as the working fluid. The results of this study indicate that binary mixtures provide the designer with a wider choice of optimal working fluids, however, in the case of the recuperated-cycle configuration, no improvement in terms of combined cycle efficiency over the benchmark case can be achieved. The split-cycle configuration leads to an increase of combined cycle efficiency of the order of 1.5%, both in case of pure and blended working fluids. Furthermore, for this cycle configuration the use of Novec 649 as working fluid is advantageous because it is environmentally and operationally safe, and it does not involve any penalty in terms of combined cycle efficiency if compared to the benchmark case. Additionally, the use of this fluid would lead to a more compact turbine, as the corresponding thermodynamic cycle would determine a turbine volume flow ratio that is half of the value of the benchmark case and a specific enthalpy difference over the expansion that is one fifth.

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.