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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., 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

Small satellites with increased capabilities in terms of power and propulsion are being demanded for future missions. This paper addresses an alternative bi-modal solution which consists of a solar thermal propulsion system coupled with a micro-Organic Rankine Cycle system, to co-generate thrust and electrical power. Current literature on bi-modal systems is limited to static power conversion systems such as thermionic conversion processes. Therefore, this paper expands the research of bi-modal systems to dynamic power conversion systems and latent heat storage systems. The paper documents the design process, key design parameters, and feasibility of this system for a Geostationary Transfer Orbit to Lunar Orbit insertion mission. The results of a single-objective optimisation show the system is most suitable on-board small satellites with a gross mass above 300 kg. The propellant accounts for 50% of the total system mass. The final design uses Silicon as the latent heat energy storage system due to its high specific energy of more than 250 Wh/kg. Additionally, the enthalpy method is used to describe the dynamic behaviour of the phase change material and results show the insulation thermal conductivity has the largest effect, up to 17%, on the receiver's maximum achievable steady-state temperature., Space Systems Egineering, Flight Performance and Propulsion, Space Engineering

Turbomachinery design is increasingly carried out by means of automated workflows based on high-fidelity physical models and optimization algorithms. The parametrization of the blade geometry is an essential aspect of such workflows because it defines the design space in which an optimal solution can be found. Currently, parametrization methods used for this purpose are often tailored to one particular type of turbomachinery blade, do not provide shape derivatives required for gradient-based optimization, or are not suited to re-parametrize a baseline blade geometry defined by a set of scattered point coordinates in a systematic way. This paper thus presents a general blade parametrization method for axial, radial, and mixed flow blades based on typical turbomachinery design variables and NURBS curves and surfaces. The shape derivatives are computed by means of the complex-step method, allowing the integration of the parametrization into gradient-based shape optimization workflows. In addition, the method enables the re-parametrization of a blade geometry defined by a cloud of points by solving a two-step optimization problem. The capabilities of the method are demonstrated by replicating eight blade geometries in two and three dimensions with an accuracy comparable to the tolerances of current manufacturing technologies., Flight Performance and Propulsion

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., 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

Turbomachinery blades characterized by highly-loaded, slender profiles and operating under unsteady flow may suffer from aeroelastic shortcomings, like forced response and flutter. One of the ways to mitigate these aeroelastic effects is to redesign the blade profiles, so as to increase aero-damping and decrease aero-forcing. Design optimization based on high-fidelity aeroelastic analysis methods is a formidable task due to the inherent computational cost. This work presents an adjoint-based aeroelastic shape-optimization framework based on reduced order methods for flow analysis and forced response computation. The flow analysis is carried out through a multi-frequency fullyturbulent harmonic balance method, while the forced response is computed by means of the energy method. The capability of the design framework is demonstrated by optimizing two candidate cascades, namely, i) a transonic compressor cascade and, ii) a supersonic impulse turbine rotor operating with toluene as working fluid, initially designed by means of the method of waves. The outcomes of the optimization show significant improvements in terms of forced-response in both cases as a consequence of aero-damping enhancement., 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 presents a fully turbulent two-phase discrete adjoint method for metastable condensing flows targeted to turbomachinery applications. The method is based on a duality preserving algorithm and implemented in the open-source CFD tool SU2. The optimization framework is applied to the shape optimization of two canonical steam turbine cascades, commonly referred to as White cascade and Dykas cascade. The optimization were carried out by minimizing either the liquid volume fraction downstream of the cascade or the total entropy generation due viscous effects and heat transfer. In the first case, the amount of condensate turned out to be reduced by as much as 24%, but without reduction of the generated entropy, while the opposite resulted in the second case. The outcomes demonstrate the capability and computational efficiency of adjoint-based automated design for the shape optimization of turbomachinery operating with phase change flow., 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

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

Small satellites with increased capabilities in terms of power and propulsion are being demanded for future missions. This paper proposes a possible solution which is the design of a novel integrated solar thermal system that co-generates propulsion and power on-board mini satellites. The system consists of a solar thermal propulsion system (STP) coupled with a micro-Organic Rankine Cycle (ORC) system to harness the waste heat from the STP receiver to provide electrical power and mitigate the need for solar panels. STP provides an alternative to conventional propulsion systems for missions requiring velocity changes of between 800 m/s and 2500 m/s. Additional advantages include higher specific impulses than chemical propulsion systems, throttability, re-start capabilities, and faster transfer times than electrical propulsion systems. The faster transfer times are especially useful for missions that travel across high radiation regions such as the Van Allen Belt. This unique configuration shares resources such as the concentrator and receiver to potentially extend the power and propulsion capabilities while adhering to the strict mass and volume constraints of small satellites. However, there is currently no literature available on the design process of the proposed bi-modal system. This paper therefore presents an integrated solar thermal design strategy for a Geostationary Transfer Orbit to Lunar orbit insertion mission. The design methodology is described in detail to assist with future evaluations of integrated solar thermal systems for other applications and missions. The system is designed to provide a velocity increment of 1.6 km/s. Five mini-satellite sizes were investigated with a gross wet mass of 100 kg, 200 kg, 300 kg, 400 kg, and 500 kg respectively. Each satellite requires to produce an electrical power of 1 W/kg. The STP system uses water as the propellant due to its safety and performance attributes. Toluene has been selected as the working fluid f, 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., Space Systems Egineering, Flight Performance and Propulsion, Space Engineering

This paper documents a numerical study on entropy generation in zero-pressure gradient, laminar boundary layers of adiabatic non-ideal compressible fluid flows. The entropy generation is expressed in terms of dissipation coefficient $$C:\mathrm {d}$$ and its dependency on free-stream Mach number, fluid molecular complexity, and flow non-ideality is investigated systematically by means of a boundary layer code extended to treat fluids modeled with arbitrary equations of state. The results of the study show that the trend of dissipation coefficient follows that of an incompressible flow for complex fluid molecules like siloxanes in all thermodynamic and flow conditions. For simpler fluids like CO$$:2$$ the trend becomes inversely proportional to the free-stream Mach number and the $$C:\mathrm {d}$$ value can significantly reduce in the non-ideal flow regime, where strong thermo-physical property gradients occur near the wall., 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 fully turbulent discrete ad joint method for three-dimensional multistage turbomachinery design. The method is based on a duality preserving algorithm and is implemented in the open-source computational fluid dynamics tool SU2. The SU2 Reynolds-averaged Navier–Stokes solver is first extended to treat three dimensional steady turbomachinery flow using a conservative formulation of the mixing-plane coupled to non reflective boundary conditions. The numerical features of the flow solver are automatically inherited by the discrete ad joint solver, ensuring the same convergence rate of the primal solver. The flow solver is then validated against experimental data available for three turbine configurations, namely, a one-and-half axial turbine stage, a transonic radial turbine coupled to a downstream diffuser, and a supersonic mini–organic Rankine cycle radial turbine operating with a fluid made by a heavy molecule. Finally the ad joint-based optimization framework is applied to the concurrent shape optimization of three rows of the axial turbine, demonstrating the advantages deriving from adopting multi row automated design methods in the context of turbomachinery design., 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 possibility of taking into account unsteady flow effects if performing turbomachinery shape optimization is attractive to accurately address inherently time dependent design problems. The harmonic balance method is an efficient solution for computational fluid dynamics problems of turbomachinery characterized by quasi-periodic flows. If applied in combination with adjoint methods, it enables the possibility to deal with unsteady fluid-dynamic design in a cost effective manner, opening the way towards multi-disciplinary applications. This paper presents the development of a novel fully-turbulent discrete adjoint based on the time domain harmonic balance method and its application to the constrained fluid dynamic optimization of an axial turbine stage. As opposed to previous works, the proposed method does not require any assumption on the turbulent eddy viscosity and on the set of input frequencies. The results show that the method provides accurate gradients, if compared with second order finite differences, and significant deviation with respect to the sensitivity computed with the constant eddy viscosity approximation. The application of the method to the fluid-dynamic shape optimization of the exemplary stage leads to improve the total-to-static efficiency of 0.8%. The efficiency increase is found to be higher than that obtained by means of a steady state optimization method., Aerodynamics, Flight Performance and Propulsion