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

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

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.

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

Radial-Inflow Turbines are considered the most suited expanders for waste heat recovery via high-temperature mini-organic Rankine Cycle (ORC) turbogenerators thanks to high compactness, large expansion ratio handled by a single stage, and comparatively low weight. Reaching high efficiency in these machines is however a formidable challenge, as they are bounded to operate with expansion ratios exceeding 40. Although scarcely investigated in the published literature, the size of the stator-rotor radial gap is a key design parameter as it has a large influence on fluid-dynamic performance, manufacturing, and mechanical integrity. In addition, the working conditions of the turbine are such that the stator operates with highly supersonic flows in the non-ideal thermodynamic regime, making the flow pattern in stator-rotor radial gap, which can be regarded as an area-decreasing channel, very complex. Under these conditions, the radial gap size could impact the stage efficiency up to few percentage points. The paper presents a study aimed at investigating the impact of variable radial gap on the fluid-dynamic performance of radial-inflow turbines for high-temperature mini-ORC power systems. The reference turbine is a supersonic machine for laboratory experiments under realization at Delft University of Technology, referred to as ORCHID turbine. First, a theoretical analysis is carried out to identify the relevant non-dimensional parameters governing the flow physics in the gap. Then, the effect of the radial gap size on the fluid-dynamic performance of the ORCHID turbine is assessed by means of RANS and uRANS computations. The results show that the change in radial gap size leads to a redistribution of expansion ratio between vaned and vaneless part of stationary component via a substantial change of the stator trailing edge flow structures, which, in turn strongly affects stator loss and stage efficiency, leading to 8% points reduction.