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.

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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.

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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.@en

Fast and accurate computation of thermo-physical properties is essential in computationally expensive simulations involving fluid flows that significantly depart from the ideal gas or ideal liquid behavior. A look-up table algorithm based on unstructured grids is proposed and applied to non-ideal compressible fluid dynamics simulations. The algorithm grants the possibility of a fully automated generation of the tabulated thermodynamic region for any boundary and to use mesh refinement. Results show that the proposed algorithm leads to a computational cost reduction up to one order of magnitude, while retaining the same accuracy level compared to simulations based on more complex equation of state. Furthermore, a comparison of the LuT algorithm with a uniformly spaced quadrilateral tabulation method resulted in similar performance and accuracy.

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The transition towards a more affordable, reliable, and sustainable energy provision paradigm is one of the main 21st century challenges that humanity must overcome to protect the planet from the harmful effect caused by climate change. The concentration of CO2 in the atmosphere has been dramatically increasing since the pre-industrial era. If the increase of green-house gasses emissions continues unabated, this will bring dramatic consequences for planet Earth, compromising eventually the existence of many species, including the human race. To avoid a climate change catastrophe, the share of primary energy coming from renewable energy resources must increase from around 15% in 2015 to 65% in 2050. This energy transition can not rely solely on few successful technologies (i.e., solar photovoltaic, and wind energy), but it must count on a larger variety of technical solutions that are suitable for a wider range of renewable sources and diversity of circumstances. For instance, renewable thermal energy sources for power generation (i.e., geothermal reservoir, biomass fuel, and concentrated solar radiation), can provide a large portion of the world electricity demand in the future. However, the exploitation of a good portion of these sources strongly depends on the market success of technologies such as the Organic Rankine Cycle (ORC) power system. One of the key aspects to make ORC systems economically competitive, especially at the smaller sizes (⇡ 1 − 50 kW), is the realization of highly efficient turbomachinery components. The fluid-dynamic design of ORC turbomachinery significantly differs from the design of traditional machines (i.e., steam and gas turbines), and this is mainly due to the different thermo-physical properties and gas dynamic behavior of the organic working fluids. This means that design methods devised for standard steam and gas turbomachinery can not be used for turbomachinery operating in the Non-ideal compressible fluid dynamics (NICFD) region. Furthermore, no experimental campaigns have ever been carried out to create a body of empirical knowledge to support the design highly efficient ORC turbomachinery. As a consequence, the entire design process of ORC turbomachinery relies only on the use of advanced CFD software. The current trend is to couple CFD tools with numerical optimization techniques in order to automatically obtain optimal flow passage geometries. In particular, adjoint-based methods have clearly demonstrated to be the only optimization technique capable of tackling the multi-stage turbomachinery design problem, in which thousands of design variable must be concurrently optimized. Therefore, the research documented in this PhD dissertation aimed at extending the adjoint method in order to perform the fully-turbulent fluid-dynamic shape optimization of 3D multi-stage ORC turbomachinery. This document contains an extensive introduction, three main chapters, each documenting a building block towards the accomplishment of the main goal of this PhD project, and a final concluding chapter that summarizes all the research outcomes of this work and proposes future steps for research in this field. The first part of the thesis describes the extension of the RANS equations, the convective numerical schemes, and the viscous numerical schemes to the use of complex thermo-physical laws, so to simulate turbulent flows of components working in the NICFD thermodynamic region. The second part documents the derivation of the adjoint solver in order to resolve shape-optimization design problems for 2D single row of ORC turbomachinery. Finally, the last part reports the extension of the adjoint method to 3D multi-stage turbomachinery design. @en

The stator vane of high-temperature Organic Rankine Cycle radial-inflow turbines operates under severe expansion ratios and the associated fluid-dynamic losses account for nearly two-third of the total losses generated inside the machine. The efficiency of the machine can strongly benefit from specialized high-fidelity design methods able to provide shapes attenuating shock wave formation. Shape optimization is certainly a viable option to deal with supersonic ORC stator design, but it is computationally expensive and often case specific. In this work, a robust method to approach the problem in a more systematic manner is documented. The methodology involves an optimization procedure encompassing the method of characteristics extended to non-ideal fluid flow for profiling the diverging part of the nozzle. The subsonic section and semi-bladed suction side are retrieved using a simple conformal geometrical transformation. The method is applied to the design a supersonic ORC stator working with Toluene vapors, for which two blade shapes were already available. The comparison of fluid-dynamic performance clearly indicates that the MoC-Based method is able to provide the best results with the lowest computational effort, and is suitable to be used to draw general design guidelines@en

The capabilities of the open-source SU2 software suite for the numerical simulation of viscous flows over unstructured grid are extended to non-ideal compressible-fluid dynamics (NICFD). A built-in thermodynamic library is incorporated to account for the non-ideal thermodynamic characteristics of fluid flows evolving in the close proximity of the liquid-vapour saturation curve and critical point. The numerical methods, namely the Approximate Riemann Solvers (ARS), viscous fluxes and boundary conditions are generalised to non-ideal fluid properties. Quantities of interest for turbomachinery cascades, as loss coefficients and flow angles, can be automatically determined and used for design optimization. A variety of test cases are carried out to assess the performance of the solver. At first, numerical methods are verified against analytical solution of reference NICFD test cases, including steady shock reflection and unsteady shock tube. Then, non-ideal gas effects in planar nozzles and past turbine cascades, typically encountered in Organic Rankine Cycle applications, are investigated and debated. The obtained results demonstrate that SU2 is highly suited for the analysis and the automatic design of internal flow devices operating in the non-ideal compressible-fluid regime.

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High temperature Organic Rankine Cycles power systems of low power capacity, i.e. 3-50 kW_e, are receiving recognition for distributed and mobile energy generation applications. For this type of power plants, it is customary to adopt a radial-turbine as prime mover, essentially for their ability to cope with very large volumetric flow ratio with limited fluid-dynamic penalty. To date, the design of such turbines is based on design guidelines and loss models developed mainly for turbo-chargers, subsequently adapted by means of non-validated computational fluid-dynamic calculations. In the attempt to provide data sets for CFD validation and calibration of loss models, a mini-ORC radial inflow turbine delivering 10kW of mechanical power will be realized and tested in the Propulsion and Power Laboratory of TU-Delft. The fluid dynamic design and characterization of the machine is detailed in this paper. According to available models, the results indicate that the optimal layout of mini-ORC turbines can substantially differ from that of radial-inflow turbines utilized in more traditional applications, strengthening the need of experimental campaigns to support the conception of new design practices.

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