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.

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.

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.

By means of this corrigendum, the authors would like to include relevant information regarding the validation of the meanline turbine model employed in the original article. The improvement regarding the validation of the model was made possible thanks to the contribution of Prof. Jürg Schiffmann. The additional results documented here provide more confidence on the reliability of the model when it applied to mini-ORC turbines. Therefore, we kindly ask the Editor to add his name to the authors list. The following paragraph extends the one that discusses the meanline validation located in Section 2. The turbine preliminary design is performed by means of a meanline code, which is based on the loss models listed in Ref. [1]. These models have been developed for conventional turbomachinery operating with fluids in the ideal gas state, featuring subsonic flows and large Reynolds numbers. The meanline code has been validated with the results of literature test cases presenting these characteristics [2]. It has been also compared against an experimentally validated turbine model for mORC machines operating in the subsonic regime [3]. Table 1 shows the information of the machine geometry for which results of the two codes were compared, while Fig. 1 presents the meridional channel of the turbine. Table 2 shows the corresponding operating conditions. The results of the total-to-static efficiency computation are presented in Fig. 2. It can be observed that the efficiency trend obtained with zTurbo is similar to that computed with the validated EPFL code. The comparison between the two models suggests a deviation lower than 2.5% for all the tested operating conditions. This deviation occurs because each model uses a different set of loss correlations. These correlations are described in Refs. [1,3].

The conventional design of organic Rankine cycle (ORC) power systems starts with the selection of the working fluid and the subsequent optimization of the corresponding thermodynamic cycle. More recently, systematic methods have been proposed integrating the selection of the working fluid into the optimization of the thermodynamic cycle. However, in both cases, the turbine is designed subsequently. This procedure can lead to a suboptimal design, especially in the case of mini- and small-scale ORC systems, since the preselected combination of working fluid and operating conditions may lead to infeasible turbine designs. The resulting iterative design procedure may end in conservative solutions after multiple trial-and-error attempts due to the strong interdependence of the many design variables and constraints involved. In this work, we therefore present a new design and optimization method integrating working fluid selection, thermodynamic cycle design, and preliminary turbine design. To this purpose, our recent 1-stage continuous-molecular targeting (CoMT)-computer-aided molecular design (CAMD) method for the integrated design of the ORC process and working fluid is expanded by a turbine meanline design procedure. Thereby, the search space of the optimization is bounded to regions where the design of the turbine is feasible. The resulting method has been tested for the design of a small-scale high-temperature ORC unit adopting a radial-inflow turbo-expander. The results confirm the potential of the proposed method over the conventional iterative design practice for the design of small-scale ORC turbogenerators.

The realization of commercial mini organic Rankine cycle (ORC) power systems (tens of kW of power output) is currently pursued by means of various research and development activities. The application driving most of the efforts is the waste heat recovery from long-haul truck engines. Obtaining an efficient mini radial inflow turbine, arguably the most suitable type of expander for this application, is particularly challenging, given the small mass flow rate, and the occurrence of nonideal compressible fluid dynamic effects in the stator. Available design methods are currently based on guidelines and loss models developed mainly for turbochargers. The preliminary geometry is subsequently adapted by means of computational fluid-dynamic calculations with codes that are not validated in case of nonideal compressible flows of organic fluids. An experimental 10 kW mini-ORC radial inflow turbine will be realized and tested in the Propulsion and Power Laboratory of the Delft University of Technology, with the aim of providing measurement datasets for the validation of computational fluid dynamics (CFD) tools and the calibration of empirical loss models. The fluid dynamic design and characterization of this machine is reported here. Notably, the turbine is designed using a meanline model in which fluid-dynamic losses are estimated using semi-empirical correlations for conventional radial turbines. The resulting impeller geometry is then optimized using steady-state three-dimensional computational fluid dynamic models and surrogate-based optimization. Finally, a loss breakdown is performed and the results are compared against those obtained by three-dimensional unsteady fluid-dynamic calculations. The outcomes of the study indicate that the optimal layout of mini-ORC turbines significantly differs from that of radial-inflow turbines (RIT) utilized in more traditional applications, confirming the need for experimental campaigns to support the conception of new design practices.

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.

The preliminary fluid dynamic design of turbomachinery operating with non-standard working fluids and unusual operating conditions and specifications can be very challenging because of the lack of know-how and guidelines. Examples are the design of turbomachinery for small-capacity organic Rankine cycle and supercritical CO₂ cycle power plants, whereby the efficiency of turbomachinery components has also a strong influence on the net conversion efficiency of the system. These machines operate with the fluid in thermodynamic states which, for part of the process, largely deviate from those obeying to the ideal gas law. This in turn implies the presence of so-called non-ideal compressible fluid dynamics effects. Active subspaces, a model reduction technique, is at the basis of the methodology presented here, which is aimed at the optimal meanline design of unconventional turbomachinery. The resulting surrogate model depends on a very small set of non-physical variables, called active variables. The procedure integrates into a single constrained optimization framework the selection of the working fluid, the thermodynamic cycle calculation and the preliminary sizing of the turbomachinery component. As a demonstration of the advantages of the proposed approach, the design of a 10kW mini organic Rankine cycle turbine with a turbine inlet temperature of 240°C is illustrated. In this case, approximately the same maximum efficiency is estimated for three dissimilar turbines operating with different working fluids and rather different thermodynamic cycles. The use of active subspaces allows the seamless evaluation of the sensitivity of results to input parameters, both those related to the machine and the working fluid. The novel design procedure is compared in terms of computational efficiency to a conventional approach based on the coupling of a genetic algorithm directly with a meanline code. Results show that the calculation based on the use of surrogate models is more than two orders of magnitude faster. The surrogate can be used to solve any design problem within the specified boundaries of the design envelope. Results are affected by uncertainty on the estimation of losses and of non-ideal compressible fluid dynamics effects, which, in turn, do not affect the applicability of the method, which will become quantitatively accurate once this information will be available. Work to this end is underway in various laboratories.

Mini ORC power systems with the capability to deliver 3-50 kWe are receiving increased recognition for applications such as heat recovery from automotive engines, or distributed power generation from geothermal reservoirs and solar irradiation. Efficient and reliable expanders are the enabling components of such power systems, and all the related developments are currently at the research stage [1]. In the open literature experimental gas dynamic data is limited concerning the fluids and the flow conditions of interest for ORC expanders [2]. Therefore, CFD tools used for the fluid dynamic design of these components cannot be validated against reliable test cases. To bridge this gap, new experimental facilities are currently being built, such as the ORCHID setup [3]. The availability of proper experimental datasets is not, however, the sole requirement for validating a CFD code. Another precondition, equivalently important, is to define an appropriate validation methodology. This paper introduces the first steps towards the validation of a CFD solver for non-ideal compressible flows. Notably, a numerical procedure based on uncertainty quantification analysis has been conceived to assess the accuracy of the thermophysical sub-model of the code, i.e. the equation of state (EoS). Due to the lack of suitable experimental data, a synthetic dataset is generated and used to investigate the validity of the procedure. The associated validation exercise confirms the applicability of the proposed procedure, but also points out that the adopted validation metrics should be complemented with additional statistical indicators.

Organic Rankine Cycle (ORC) power systems are receiving increased recognition for the conversion of thermal energy when the source potential and/or its temperature are comparatively low. Mini-ORC units in the power output range of 350 kWe are actively studied for applications involving heat recovery from automotive engines and the exploitation of solar energy. Efficient expanders are the enabling components of such systems, and all the related developments are at the early research stage. Notably, no experimental gasdynamic data are available in the open literature concerning the fluids and flow conditions of interest for mini-ORC expanders. Therefore, all the performance estimation and the fluid dynamic design methodologies adopted in the field rely on non-validated tools. In order to bridge this gap, a new experimental facility capable of continuous operation is being designed and built at Delft University of Technology, the Netherlands. The Organic Rankine Cycle Hybrid Integrated Device (ORCHID) is a research facility resembling a state-of-Theart high-Temperature ORC system. It is flexible enough to treat different working fluids and operating conditions with the added benefit of two interchangeable Test Sections (TS's). The first TS is a supersonic nozzle with optical access whose purpose is to perform gas dynamic experiments on dense organic flows in order to validate numerical codes. The second TS is a test-bench for mini-ORC expanders of any configuration up to a power output of 100 kWe. This paper presents the preliminary design of the ORCHID setup, discussing how the required operational flexibility was attained. The envisaged experiments of the two TS's are also described.