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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., Flight Performance and Propulsion

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., Flight Performance and Propulsion

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., Flight Performance and Propulsion

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]., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

This work assessed the accuracy of the SU2 flow solver in predicting the isentropic expansion of Siloxane MM through the converging-diverging nozzle test section of the Organic Rankine Cycle Hybrid Integrated Device (ORCHID) [9]. The expansion is modeled using compressible Euler equations, and assuming adiabatic flow, while the fluid thermodynamic properties are estimated using the Peng-Robinson equation of state. The boundary conditions for the experiment and simulations correspond to a stagnation temperature and pressure of T¯0=253.7∘C and P¯0=18.36bar. At these inlet conditions the compressibility factor of the fluid is Z0= 0.58. The back pressure was equal to P¯b=2.21bar. The Mach number along the centreline, and static pressure along the nozzle surface were used as the system response quantities for the validation exercise. The studied SU2 model provides valid predictions for Mach number and static pressure. The largest deviation observed in the Mach number comparison between the simulation and experiment is in the uniform flow region of the nozzle and is equal to EMach= 0.045. Regarding the pressure trend, the largest discrepancy occurs in the kernel region and is equal to Epressure= 9 kPa. At the same time, the simulated Mach number and static pressure reach a maximum absolute uncertainty of ± 0.015 and of ± 20 kPa, respectively. For both quantities, these values are reached in the region close to the throat. All the uncertainties calculated for the simulated pressure profile were larger than those of the experiments. The static pressure is particularly sensitive to the geometrical uncertainties of the nozzle profile, especially inside the kernel region. A proper characterisation of the nozzle geometry was therefore required to perform a meaningful validation of the fluid dynamic solver. The developed infrastructure can be used in the future for the validation of SU2 in different operating conditions and flow cases., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion, Facility Aerodynamics Laboratory

We present a diffuse interface method for a pressure-based Baer-Nunziato type model for compressible two-phase flows, which allows the use of generic equations of state to describe each phase. The model is made dimensionless by means of a special pressure scaling that recovers the correct scaling of the discrete governing equations in the zero Mach limit, and overcomes the difficulties related to the lack of a clear notion of reference speed of sound in non-equilibrium two-phase flows. The model is equipped with pressure and velocity relaxation terms to impose the mechanical equilibrium between phases after their independent evolution. Two different finite volume schemes are presented. First, a 1D semi-implicit staggered scheme is introduced to show the capability of the model to work with the Peng-Robinson EOS when each phase evolves close to the saturation curve. Then, a preliminary 2D explicit scheme, which does not include the relaxation terms, is presented as a first step toward the development of an unstructured 2D scheme for compressible two-phase flows at all Mach numbers. The validity of the preliminary 2D monolithic implementation of the hyperbolic operator is illustrated through the simulation of a shock-bubble interaction with air and helium. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Non-ideal compressible flows exhibit physical behaviors that are quantitatively and qualitatively different than those of a perfect or ideal gas. As such, the classical gas dynamic relationships that can be found on fluid-mechanics textbooks cannot be directly applied to characterize this type of flows. NiceProp is a tool for interactively learning the fundamentals of non-ideal compressible fluid dynamics and the design implications for fluid machinery components. The software is written in Python and features a highly modular structure to ease code readability and to facilitate its further development. The target audience of the software is represented by students, researchers and industry professionals interested to get started or deepen the comprehension of non-ideal compressible flow phenomena., Flight Performance and Propulsion

Currently, most of the adjoint-based design systems documented in the open literature assume that the fluid behaves as an ideal gas, are restricted to the optimization of a single row of blades, or are not suited to impose geometric constraints. In response to these limitations, this paper presents a gradient-based shape optimization framework for the aerodynamic design of turbomachinery blades operating under nonideal thermodynamic conditions. The proposed design system supports the optimization of multiple blade rows, and it integrates a computer-aided design (CAD)-based parametrization with a Reynolds-averaged Navier–Stokes (RANS) flow solver and its discrete adjoint counterpart. The capabilities of the method were demonstrated by performing the design optimization of a single-stage axial turbine that employs isobutane (R600a) as working fluid. Notably, the aerodynamic optimization respected the minimum thickness constraint at the trailing edge of the stator and rotor blades and reduced the entropy generation within the turbine by 36%, relative to the baseline, which corresponds to a total-to-total isentropic efficiency increase of about 4 percentage points. The analysis of the flow field revealed that the performance improvement was achieved due to the reduction of the wake intensity downstream of the blades and the elimination of a shock-induced separation bubble at the suction side of the stator cascade., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

This paper documents a thermo-fluid-dynamic mean-line model for the preliminary design of multistage axial turbines with blade cooling applicable to supercritical CO2 turbines. Given the working fluid and coolant inlet thermodynamic conditions, blade geometry, number of stages and load criterion, the model computes the stage-by-stage design along with the cooling requirement and ultimately provides an estimate of turbine efficiency via a semi-empirical loss model. Different cooling modes are available and can be selected by the user (stand-alone or combination): convective cooling, film cooling, and thermal barrier coating. The model is applied to attain the preliminary aero-thermal design of the 600 MW cooled axial supercritical CO2 turbine of the Allam cycle. Results show that a load coefficient varying from 3 to 1 throughout the machine, and a reaction degree ranging from 0.1 to 0.5 lead to the maximum total-to-static turbine efficiency of about 85%. Consequently, as opposed to uncooled CO2 turbines, a repeated stage configuration is an unsuited design choice for cooled sCO2 machines. Moreover, the study highlights that film cooling is considerably less effective compared to conventional gas turbines, while increasing the number of stages from 5 to 6 and adopting higher rotational speeds leads to an increased efficiency., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

The environmental control system (ECS) is the largest auxiliary power consumer, i.e, around 75% of non-propulsive power, among the aircraft subsystems. The adoption of a novel ECS architecture, based on an electrically-driven vapor compression cycle system, can enable a twofold increase of coefficient of performance (COP), as compared to the conventional air cycle machine (ACM). The core of this technology is a high-speed, miniature centrifugal compressor, consisting of two impellers mounted in back-to-back configuration, and running on gas bearings operating with refrigerant. The fluid dynamic design optimization of the twin-stage compressor, to be installed in the vapor compression cycle test rig under realization at Delft University of Technology, is documented in this paper. First, the scaling analysis for centrifugal compressor is extended to provide guidelines for the design of twin-stage machines. Then, a multi-objective conceptual design optimization is performed by resorting to an in-house reduced-order model (ROM), coupled to a genetic algorithm. The fluid dynamic performance and the structural integrity of the optimal design are assessed by means of a hybrid framework, encompassing CFD and ROMs, and by FEA. The results show that it is possible to design a twin-stage compressor for the target application, featuring an average efficiency higher than 70%, a maximum compression ratio exceeding 9, and an operating range of 0.27 at the design rotational speed, despite the detrimental effects of motor cooling and miniature size., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

The impact of size and working fluid on the efficiency, operating range, and axial thrust on bearings is examined for high-speed, oil-free centrifugal compressors. First, the development and validation of a reduced-order model based on scaling principles is documented. Then, the validated compressor model is used to generate design maps for stages operating with arbitrary fluid molecules, and characterized by different size. The results show that compressors operating with fluids made by heavy and complex molecules provide lower efficiency over the entire design space, if compared to their simple-molecule counterparts. However, compressors for complex-molecule fluids require lower rotational speed, and generate lower axial thrust on bearings, thus making them particularly suitable for small-scale applications. Furthermore, a decreasing value of the size parameter has a detrimental effect on the stage efficiency, as a result of manufacturing constraints. The results computed by the compressor model suggest that the efficiency penalty is more sensitive to variations of clearance gap than to surface finishing. Lastly, the reduced-order model has been used to perform a design exercise, i.e., the multi-objective optimization of the first compressor stage of the heat pump test rig being realized at Delft University of Technology. The key characteristics of the optimal compressor design has been compared to those derived from the design maps, to corroborate their validity. The optimal design has been extensively characterized by means of CFD, providing further evidence that efficient mini-compressors operating with organic fluids, and featuring pressure ratios up to five at off-design, are feasible., Flight Performance and Propulsion

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., Flight Performance and Propulsion

The lack of established optimal design guidelines for turbomachinery operating in the nonideal flow regime (e.g., organic Rankine cycle turbines, CO2 compressors, compressors for refrigeration systems) demands for effective and efficient automated design methods. Past research work focused on gradient-free methods applied to computational fluid-dynamic simulations. The application of the adjoint method is a cost-effective alternative as it enables gradient-based optimization irrespective of the number of design variables. This paper presents the application of a fully turbulent unsteady adjoint method for the automated design of multirow turbomachinery partly operating in the nonideal flow regime. The method therefore allows for the solution of constrained unsteady fluid-dynamic optimization problems, in which the thermodynamic properties of the working fluid need to be modeled by means of complex equations of state. The optimal designs computed with unsteady simulations obtained with the harmonic balance method are then compared with optimal design resulting from mixing-plane simulations. The method is applied to the optimization of 1) a two-dimensional turbine cascade subject to time-varying inlet conditions, and 2) a two-dimensional turbine stage of an organic Rankine cycle power system. The results demonstrate the importance of computing fluid properties using accurate thermodynamic models and of using unsteady simulations for shape optimization of these machines., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

Axial turbine stages for gas generator cycle type rocket engines typically employ highly-loaded supersonic stator vanes. Consequently, the flow pattern downstream of the vanes is characterized by shock waves which induce high-frequency excitation on the subsequent rotor. For this reason, the optimal design of the stator is crucial in the context of development of the next generation of high-performance rocket engines, where reusability is a principal design criterion. A thorough comprehension of the loss mechanisms combined with the adoption of automated optimisation techniques can therefore enable new stator designs that may provide large benefits in terms of overall turbine performance and lifespan. The scope of this study stems from these considerations and its objective is twofold, namely i) the shape optimisation of a su- personic stator for rocket engines and ii) the investigation of the loss mechanisms in supersonic axial turbine stator vanes at on- and off-design conditions. The investigation is performed on stator vanes that are under development for the first turbine stage of a gas generator cycle type rocket engine. The stator vanes are therefore optimised in order to reduce the profile losses by exploiting a novel adjoint optimisation framework for turbomachinery implemented in the open-source code SU2. The effect on the resulting flow field and loss sources is finally investigated. Results show that entropy based loss coefficient gains of 6% can be achieved via shape optimisation and that the fluid- dynamic performance of these vanes is less sensitive to changes in pressure ratio compared to the performance provided by the baseline configuration. Eventually, shock-waves remain the primary loss source., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

This paper reports one of the initial NICFD experiments in the nozzle test section of the ORCHID aimed at providing accurate data for the validation of flow solvers, albeit, at this stage of the research, the focus is limited to inviscid phenomena. Notably, a series of schlieren photographs displaying Mach waves in the supersonic flow of the dense vapor of siloxane MM were obtained and are documented here for the commissioning experiment, namely, for inlet conditions corresponding to a stagnation temperature and pressure of T0=252∘C and P0=18.4bara. At these inlet conditions the compressibility factor of the fluid is Z0= 0.58. The digital processing of the schlieren images allowed to estimate multiple angles formed by the Mach waves stemming from the upper and lower nozzle surfaces because of the infinitesimal density perturbations generated by the, albeit small, roughness of the metal surfaces. These values are related to the local Mach number by a simple geometric relation. Moreover, the total expanded uncertainty in the Mach number was computed. This information together with the estimate of the average Mach number was used for a first assessment of the capability of evaluating NICFD effects occurring in a dense organic vapor flow of MM by comparison with the results of CFD simulations. The outcome of the comparison was satisfactory. It can thus be inferred that the nozzle test section has been commissioned and it is ready for experimental campaigns in which its full potential in terms of measurements accuracy, repeatability, and operational flexibility will be exploited., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion, Aerodynamics

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., Flight Performance and Propulsion

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion

The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation (CSE) is revised and extended to account for the effect of flow non-ideality. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that compressibility effects induced by the fluid molecular complexity and the stage volumetric flow ratio produce an offset in the efficiency trends and in the optimal stage layout. Furthermore, flow non-ideality can lead to either an increase or a decrease of stage efficiency up to 3-4% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure-volume exponent. Three-dimensional (3D) RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model. URANS computations provide equivalent trends, except for case study niMM1, featuring a non-monotonic variation of the generalized isentropic exponent. For such turbine stage, the efficiency is predicted to be higher than the one computed with any steady-state model based on the control volume approach., Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Flight Performance and Propulsion