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Estimating the speed of sound for the dense vapor phase of D6 (dodecamethylcyclohexasiloxane, C12H36O6Si6) is particularly relevant to the study of nonideal compressible fluid dynamics (NICFD), the gas dynamics of fluids whose properties depart significantly from those related by the ideal gas model. If molecular complexity is sufficiently large, dense vapor flows may exhibit so-called nonclassical gasdynamic effects, and D6 is a candidate for experimental studies aimed at proving for the first time the existence of these exotic phenomena. More in general, speed of sound measurements in the dense vapor phase are important for NICFD applications: for example, complex organic compounds are employed as working fluids in organic Rankine cycle power plants and the correct prediction of the dense-vapor speed of sound is of paramount importance for the design of the supersonic turbines equipping these systems. This type of measurements is challenging and thus rare, especially in the case of complex organic molecules, given the high temperature at which they must be performed, close to the temperature at which the molecule thermally decomposes. Therefore, a new prismatic resonator (the OVAR, organic vapor acoustic resonator) has been conceived, designed, and realized. It is suitable for speed of sound measurements in the vapor phase of organic compounds at temperatures up to approximately 670 K and pressures up to about 1.5 MPa. The speed of sound of D6 (97.4% pure) has been measured along eight isotherms between 555 and 645 K and from nearly saturated density to densities close to ideal gas conditions (compressibility factor Z ≈ 0.95). The estimated relative uncertainty of these sound speed measurements is 0.14%. In addition, corresponding density values have been obtained with an estimated uncertainty between 0.2 kg·m-3 and 1.2 kg·m-3

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.

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 at cruise conditions, as compared to the conventional air cycle machine. 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 computational fluid dynamics and ROMs, and by finite element analysis. 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.

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.

This work assesses the feasibility of the planar PIV technique to study the characteristics of a siloxane vapor D4. Titanium dioxide (TiO2) seeding particles were used to track the motion around a rotating disk in a low speed flow. Vector fields of natural convection (NC) and a superposition of NC and rotating flow were selected as exemplary cases. The particles were capable of tracing the flow since the calculated Stokes number St is 6.5×10-5. The quality of the experimental data is assessed by means of particle seeding density and particle image Signal to Noise ratio (S/N). The final results are deemed acceptable for an accurate assessment of the flow field. Rejected outliers are below 2.3% and the relative uncertainties corresponding to the average velocity fields are below 1%.

The nonlinear propagation of finite amplitude waves in the non-ideal compressible fluid dynamic (NICFD) region of high-molecular weight fluids, and in particular in cases where non-classical gas dynamic phenomena like the formation of rarefaction shock waves may be expected, is of great scientific interest. Almost all the theoretical developments so far are based on the assumption that the waves propagate in a fluid kept in homogeneous conditions. Experimental activities performed with the Flexible Asymmetric Shock Tube (FAST) operated in the laboratories of the Propulsion and Power group at the Delft University of Technology have shown that obtaining such conditions is particularly challenging, especially keeping the tube at constant temperature. Stemming from this observation, this study is a part of a theoretical and numerical investigations aimed at assessing the influence of temperature gradients at the boundary on wave propagation in so-called Bethe-Zel’dovich Thompson (BZT) fluids. The full-wave Westervelt Equation is solved numerically using the Finite Difference Time Domain (FDTD) method. The steepening of the wave front is used as an indicator of shock formation. The effect of varying temperature, and the corresponding variation of the fundamental derivative of gas dynamics on the distortion of rarefaction waves is analyzed by observing the simulated behaviour of the wave as it propagates from a region of negative values of the fundamental derivative of gas dynamics to a region of positive values.

Flows of fluids made of complex organic molecules exhibit unconventional fluid dynamic behavior in the vapor phase if their thermodynamic state is close to that of the vapor-liquid critical point. If the molecule is sufficiently complex, this thermodynamic domain is characterized by negative values of the fundamental derivative of gasdynamics Γ, the fluid is called Bethe-Zel'dovich-Thompson (BZT) fluid, and atypical phenomena, such as rarefaction shockwaves, are theoretically admissible. The nature of the steepening of nonlinear waves in dense vapor flows of organic fluids evolving in this thermodynamic region can be significantly affected by the presence of temperature gradients in the flow. This study investigates the evolution of finite-amplitude acoustic waves in these conditions. The steepening of the wavefront is analyzed using the wavefront expansion technique, and the deformation of the wavefront is simulated numerically by solving the Westervelt equation. The results of simulations of wave propagation in dense vapors indicate that, though Γ governs the nature of steepening waves, local gradients in sound speed and density can alter the rate of steepening and can enhance or delay shock formation in the medium, a result relevant also to the envisaged experiments aimed at proving the existence of nonclassical gasdynamics phenomena in BZT vapors.

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.

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.

Speed of sound measurements are currently of the utmost importance for the development of thermodynamic models of fluids. A need for accurate thermodynamic models was identified for siloxanes, because of their use as working fluid in organic Rankine cycle power systems and because of the scientific interest in non ideal and non classical gas dynamics. The initiative of designing and realizing a novel acoustic resonator capable of performing speed of sound measurements in dense vapors at temperatures up to 400 ∘ C stemmed from these considerations. Preliminary and unique experimental results are presented for siloxane D 6 (dodecamethylcyclohexasiloxane) for two isotherms at 346 ∘ C and 348 ∘ C and at pressures ranging form 5.5 bar to 6 bar. These measurements demonstrate for the first time the possibility of measuring the speed of sound of dense organic vapor at very high temperature. An initial comparison with speed of sound estimations provided by current thermodynamic models shows that the calculated values are approximately 6 % higher.

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.

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.

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 fully-turbulent 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.

The electric hybridization of heavy-duty road vehicles is a promising alternative to reduce the environmental impact of freight and passengers transportation. Employing a micro gas turbine as a prime mover offers several advantages: high power density, fuel flexibility, ultra-low emissions (without the need of exhaust after-treatment), low vibrations and noise, simplicity and lower maintenance cost. State-of-the-art micro gas turbines feature an efficiency of 30%, which can be increased to 40% by employing a mini organic Rankine cycle system as a bottoming power plant. Such a combined-cycle powertrain could achieve considerably higher efficiency with next-gen micro gas turbines and mini ORC systems, especially with an R&D push of the automotive sector. This paper presents the analysis of a hybrid electric heavy-duty vehicle with a prime mover based on this concept. The assessment was performed in two steps: (i) preliminary design of the combined cycle power plant, and (ii) estimation of the vehicle fuel economy and of the emissions over a representative driving cycle. The best combined cycle system stemming from the design exercise features an estimated peak efficiency of 44%, and a nominal power output of about 150 kW. This corresponds to the power demand at cruise condition of a long-haul truck (weight approx. 36 ton). A series configuration with Lithium-Ion batteries was selected for the hybrid powertrain, for it decouples the prime mover dynamics from the power demand. The benchmark is a vehicle featuring a next generation diesel engine, with a peak efficiency equal to 50%. The results show that the fuel economy can be largely improved by increasing the size of the battery in the hybrid powertrain. Furthermore, employing natural gas in the prime mover of the hybrid vehicle leads to ultra-low emissions that are well below the limits set by European and north American regulations, without the need of exhaust gas aftertreatment. Additionally, the CO2 emissions of the hybrid powertrain are considerably lower than that of the benchmark. The work documented here thus demonstrates the potential of this hybrid powertrain concept, especially in terms of exhaust emissions, as a promising transition technology towards the full electrification of the powertrain.

Shape optimization in unsteady flow problems enables the consideration of dynamic effects on design. The ability to treat unsteady effects is attractive, as it can provide performance gains when compared to steady-state design methods for a variety of applications in which time-varying flows are of paramount importance. This is the case, for example, in turbomachinery or rotorcraft design. Given the high computational cost involved in time-accurate design problems, adjoint-based shape optimization is a promising option. However, efficient sensitivity analysis should also be accompanied by a significant decrease in computational cost for the primal flow solution, as well. Reduced-order models, like those based on the harmonic balance concept, in combination with the calculation of gradients via adjoint methods, are proposed for the efficient solution of a certain class of aerodynamics optimization problems. The harmonic balance method is applicable if the flow is characterized by discrete finite dominant flow frequencies that do not need to be integer multiples of a fundamental harmonic. A fully-turbulent harmonic balance discrete adjoint formulation based on a duality-preserving approach is proposed. The method is implemented by leveraging algorithmic differentiation and is applied to two test cases: the constrained shape optimization of both a pitching airfoil and a turbine cascade. A key advantage of the current approach is the accurate computation of gradients as compared to second order finite differences without any approximation in the linearization of the turbulent viscosity. The shape optimization results show significant improvements for the selected time-dependent objective functions, demonstrating that design problems involving almost-periodic unsteady flows can be tackled with manageable computational effort.

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. Jurg 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 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.

The capture of CO2 from power plant flue gases provides an opportunity to mitigate emissions that are harmful to the global climate. While the process of CO2 capture using an aqueous amine solution is well-known from experience in other technical sectors (e.g., acid gas removal in the gas processing industry), its operation combined with a power plant still needs investigation because in this case, the interaction with power plants that are increasingly operated dynamically poses control challenges. This article presents the dynamic modeling of CO2 capture plants followed by a detailed validation using transient measurements recorded from the pilot plant operated at the Maasvlakte power station in the Netherlands. The model predictions are in good agreement with the experimental data related to the transient changes of the main process variables such as flow rate, CO2 concentrations, temperatures, and solvent loading. The validated model was used to study the effects of fast power plant transients on the capture plant operation. A relevant result of this work is that an integrated CO2 capture plant might enable more dynamic operation of retrofitted fossil fuel power plants because the large amount of steam needed by the capture process can be diverted rapidly to and from the power plant.

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.

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.

Supersonic stator vanes account for two-thirds of the fluid-dynamic losses in high temperature mini-Organic Rankine Cycle (ORC) turbines. As a result, the overall performance of the turbo-expander mainly depends on the design of the stator. Currently, there is no established correlation for the optimal design of such cascades. This work concerns an investigation about the accuracy of the only design method currently available for the design of supersonic stators operating with fluids made of complex molecules. A physics-based analytical model and a CFD-based model were developed to estimate the optimal post-expansion ratio and to compare their results with the Deych’s model. The analysis shows that the Deych’s method fails to accurately predict the optimum value of the post-expansion ratio. The study covers also the assessment of the optimum post-expansion ratio in relation to the solidity, the design flow angle and the total-to-static expansion ratio. The outcome demonstrates that there exists a unique optimum post-expansion ratio for a set of primary stator design parameters. In summary, vanes operating with a substance made of complex molecule as the working fluid, which is typical of high-temperature ORC turbines, feature a unique theoretical value of the optimum post-expansion ratio for a given total-to-static expansion ratio. New correlations are required to predict this value.

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.

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds ( Re ) and the Stuart ( N ) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field ( Re H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number ( Re H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.

This work is focused on the design optimization of a pre-combustion CO2 capture plant comprising a sweet high-temperature water–gas shift process and an integrated H2S and CO2 removal process using a mixture of dimethylethers of polyethylene glycol as physical solvent. The steady-state model of the commercial-scale plant has been derived from pilot plant models, which have been extensively validated against experimental data obtained from the pre-combustion CO2 capture facility realized at the Buggenum IGCC power station in the Netherlands. A two-phase optimization-based design approach suited to the use of process simulator environments has been adopted. In the first phase, global design decisions at plant level are evaluated, targeting the minimization of the energy consumption due to CO2 capture. These are the extent of CO conversion in the water–gas shift unit and the percentage of CO2 capture in the removal unit. An optimization of both global design variables is presented considering (i) a wide range of carbon capture targets, (ii) deactivation of catalyst activity throughout the catalyst life and (iii) different operational limits of the steam/CO ratio in the water–gas shift unit. Experimental data from the pilot plant has been used to determine the rate of catalyst deactivation and the operational limits of steam/CO ratio. The second phase of the design procedure targets the local decision variables at unit level. Two studies are presented focusing on: (1) the design of the solvent regeneration and CO2 compression section, and (2) the impact of the solvent temperature on the energy consumption and equipment cost of the removal unit. The design optimization revealed that the specific energy consumption of the pre-combustion capture unit can be reduced by 10% when operating at a minimum molar steam/CO ratio of 1.5 in comparison to the current vendor suggestion of 2.65. These energy savings come at the cost of a lower optimal carbon capture rate, namely 78% instead of 87.5% as reported in the preliminary design.

We present a new flux-conserving treatment of non-conformal mesh block interfaces for the numerical solution of conservation laws by high order finite-volume schemes. An auxiliary mesh is used at the interface to establish a connectivity between non-conformal blocks. The method does not involve any flux interpolation and conservation is therefore guaranteed by construction, without enforcing additional constraints. Additionally, several gradient reconstructions across the interface have been adapted and their order of accuracy is studied analytically and numerically. Applications to two and three dimensional fluid dynamic problems are considered, and the verification of the method is provided by comparing solutions obtained on single-block grids with no interfaces. Also the accuracy and numerical stability of the interface treatment is demonstrated empirically for a variety of test cases, such as a cylinder in supersonic cross-flow, low Mach-number vortex shedding, and a transonic turbine stage. The exemplary flow simulation problems are solved using explicit and implicit time integration schemes. The obtained results successfully demonstrate the effectiveness of the proposed method for stationary non-conformal blocks domains, as well as for mesh blocks in relative motion.

Complete thermodynamic models were developed for the estimation of thermodynamic properties of biphenyl (C12H10, CAS number 92-52-4), diphenyl ether (C12H10O, CAS number 101-84-8), and of their mixtures. These compounds are used as heat transfer fluids, both in the liquid and in the vapor phase, especially in the eutectic formulation (commercially known mainly as Therminol® VP-1 and Dowtherm® A). In particular, these fluids are adopted as thermal energy carriers in concentrated solar power plants using parabolic troughs linear concentrators. The developed models are based on the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) and on the improved PRSV (iPRSV) technical equations of state (EoS), complemented by the Wong–Sandler mixing rules. The models’ performance is discussed and their predictions compared with experimental data. It is proven that, from an engineering viewpoint, sufficiently accurate predictions can be obtained with both models. The model based on the PC-SAFT EoS is overall more accurate, but its mathematical complexity could play a significant role if computation time is an issue. On the other hand, the iPRSV-based model could be the solution of choice for applications requiring maximum computational efficiency such as, e.g., the process-level simulation of parabolic troughs solar collectors.

Widespread adoption of renewable energy technologies will arguably benefit from the availability of economically viable distributed thermal power conversion systems. For this reason, considerable efforts have been dedicated in recent years to R&D over mini-organic Rankine cycle (ORC) power plants, thus with a power capacity approximately in the 3–50 kW range. The application of these systems for waste heat recovery from diesel engines of long-haul trucks stands out because of the possibility of achieving economy of production. Many technical challenges need to be solved, as the system must be sufficiently efficient, light, and compact. The design paradigm is therefore completely different from that of conventional stationary ORC power plants of much larger capacity. A high speed turbine is arguably the expander of choice, if high conversion efficiency is targeted, thus high maximum cycle temperature. Given the lack of knowledge on the design of these turbines, which depends on a large number of constraints, a novel optimal design method integrating the preliminary design of the thermodynamic cycle and that of the turbine has been developed. The method is applicable to radial inflow, axial and radial outflow turbines, and to superheated and supercritical cycle configurations. After a limited number of working fluids are selected, the feasible design space is explored by means of thermodynamic cycle design calculations integrated with a simplified turbine design procedure, whereby the isentropic expansion efficiency is prescribed. Starting from the resulting design space, optimal preliminary designs are obtained by combining cycle calculations with a 1D mean-line code, subject to constraints. The application of the procedure is illustrated for a test case: the design of turbines to be tested in a new experimental setup named organic rankine cycle hybrid integrated device (ORCHID) which is being constructed at the Delft University of Technology, Delft, The Netherlands. The first turbine selected for further design and construction employs siloxane MM (hexamethyldisiloxane, C6H18OSi2), supercritical cycle, and the radial inflow configuration. The main preliminary design specifications are power output equal to 11.6 kW, turbine inlet temperature equal to 300 °C, maximum cycle pressure equal to 19.9 bar, expansion ratio equal to 72, rotational speed equal to 90 krpm, inlet diameter equal to 75 mm, minimum blade height equal to 2 mm, degree of reaction equal to 0.44, and estimated total-to-static efficiency equal to 77.3%. Results of the design calculations are affected by considerable uncertainty related to the loss correlations employed for the preliminary turbine design, as they have not been validated yet for this highly unconventional supersonic and transonic mini turbine. Future work will be dedicated to the extension of the method to encompass the preliminary design of heat exchangers and the off-design operation of the system.

This paper presents a feasibility study on a waste heat recovery system for heavy-duty truck engines based on organic Rankine cycle (ORC) technology. The elements of novelty of the work are: i) the proposed plant configuration, and ii) the feasibility study that encompasses the whole preliminary design workflow of the system, namely, from the thermodynamic cycle optimization and the components preliminary sizing, to dynamic modelling and the design of a PI-based control system. The conceived ORC turbogenerator employs hexamethyldisiloxane (MM) as working fluid and achieves a maximum rated mechanical power of approximately 5 kW at the design point, corresponding to a truck cruise speed and a Diesel engine power output of 85 km h-1 and 100 kW respectively. Regarding the dynamic performance, the higher response time of the ORC unit compared to that of the Diesel engine makes the adoption of an advanced control system necessary. In particular, the simulation of a PI-based control system shows that it becomes impossible to prevent the thermal decomposition of the working fluid when the engine operates continuously at high power levels. This case study demonstrates the importance for automotive ORC applications of performing the investigation of dynamic performance and control design already in the early design phase.

This paper documents the extension of several widespread flux schemes, used in finite-volume Navier–Stokes solvers, for the simulation of flows whose fluid properties must be estimated with complex thermophysical models. Exact Jacobian matrices for the convective fluxes are derived with no assumption on the fluid equations of state model for Liou's AUSM+, Toro et al.'s HLLC, and Kurganov and Tadmor's central scheme. The Jacobians of the diffusive fluxes are expressed using the formulation proposed by Pulliam and Steger, resulting in additional terms due to the viscosity and thermal conductivity variations. An efficient look-up table approach is thoroughly studied and proposed as an alternative to the direct solution of the equation of state model for the fluid thermophysical property evaluation. The newly introduced schemes are validated and tested in terms of accuracy and convergence rate on a series of one- and two-dimensional test cases. The results indicate that the Jacobian must be based on the same flux formulation as the one used on the right-hand side of the implicit equation to achieve numerically converged solutions.

Complete thermodynamic models are developed for the perfluorocarbons PP80 (perfluoro-2-methyl-3-ethylpentane, C 8 F 18 , CASRN: 354-97-2) and PP90 (perfluoro-2,4-dimethyl-3-ethylpentane, C 9 F 20 , CASRN: 50285-18-2). These perfluorocarbons can be used as working fluids in energy conversion applications, like organic Rankine cycle (ORC) power systems operating at medium and high temperatures. Other areas of use of PP80 and PP90 are in the electronic industry for component testing, in the chemical industry as a hazardous reaction suppressant and as tracers in the oil and gas industry. The improved equation of state of Peng–Robinson modified by Stryjek–Vera (iPRSV) is adopted, supplemented with a third order polynomial for the ideal gas isobaric heat capacity as a function of temperature. Vapor–liquid pressures for both fluids were measured in a temperature range spanning 358–508 K. The vapor–pressure temperature range for the fitting of the equation of state is extended down to 270 K by extrapolation of the Wagner–Ambrose equation that is used for the correlation of the aforementioned measured data. Ideal gas isobaric heat capacities data are estimated with the Joback method. The obtained thermodynamic models are arguably sufficiently accurate for preliminary engineering calculations, for example for the thermodynamic design of ORC power systems.

The non-classical gas dynamics of binary mixtures of organic fluids in the vapour phase is investigated for the first time. A predictive thermodynamic model is used to compute the relevant mixture properties, including its critical point coordinates and the local value of the fundamental derivative of gas dynamics $\Gamma $. The considered model is the improved Peng–Robinson Stryjek–Vera cubic equation of state, complemented by the Wong–Sandler mixing rules. A finite thermodynamic region is found where the nonlinearity parameter $\Gamma $ is negative and therefore non-classical gas dynamics phenomena are admissible. A non-monotone dependence of $\Gamma $ on the mixture composition is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the minimum value of $\Gamma $ in the mixture being always larger than that of its more complex component. The observed dependence indicates that non-ideal mixing has a strong influence on the gas dynamics behaviour, either classical or non-classical, of the mixture. Numerical experiments of the supersonic expansion of a mixture flow around a sharp corner show the transition from the classical configuration, exhibiting an isentropic rarefaction fan centred at the expansion corner, to non-classical ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is changed.

A technical equation of state (EoS), according to the perturbed chain statistical associating fluid theory (PC-SAFT), is developed for solvent blends composed of polyethylene glycol dimethylethers (PEGDMEs/glymes), that is, CH3O[CH2CH2O]nCH3 with n = 3, ..., 9. These solvent blends are employed in industry under the commercial names Selexol or Genosorb, primarily for the physical absorption of H2S and CO2 from acid gases. The molecular parameters for the EoSs of the pure fluids comprising the solvent, notably for the n = 3 and 4 members of the homologous series, are obtained by fitting the PC-SAFT EoS to published vapor pressure and liquid density data. Because of the limited availability of experimental data for the glymes with n ≥ 5, PC-SAFT is used as a predictive tool to determine the molecular parameters for the n = 5, ..., 9 members of the homologous series. To exploit the extrapolative capabilities of PC-SAFT, the n = 1 and 2 members of the homologous series are included in this study. The mixture ...

There is a growing interest in organic Rankine cycle turbogenerators because of their ability to efficiently utilize external heat sources at low-to-medium temperature in the small-to-medium power range. High-temperature organic Rankine cycle turbines typically operate at very high pressure ratio and expand the organic working fluid in the dense-vapour thermodynamic region, thus requiring computational fluid dynamics solvers coupled with accurate thermodynamic models for their performance assessment and design. In this article we present a steady-state three-dimensional viscous computational fluid dynamics study of the Tri-O-Gen organic Rankine cycle radial turbine, including the radial nozzle, the rotor and the diffuser. The turbine operates with toluene as the working fluid, whose accurate thermophysical properties are obtained with a look-up table approach. Based on the three-dimensional simulation results, together with a two-dimensional fluid dynamic optimisation procedure documented elsewhere, an improved nozzle geometry is designed, manufactured and experimentally tested. Measurements show it delivers 5 kWe or 4% more net power output, as well as improved off-design performance.

This document describes the results of an investigation on the variation of the so-called fundamental derivative of gas dynamics, Γ, in the vapor–liquid critical region of well-measured substances, namely methane, carbon dioxide and water, for which accurate, scaled fundamental equations are available. The results demonstrate that for a pure fluid in the single-phase thermodynamic regime, Γ diverges to +∞ independent of the direction of approach of the vapor–liquid critical point. Furthermore, in the two-phase thermodynamic regime, Γ diverges to −∞ independent of the direction of approach of the vapor–liquid critical point. These two qualitative results, as well as the value of the exponent giving the power-law dependence of Γ along the critical isochore as a function of |T − TC|/T (T is the temperature and “C” indicates its critical point value), namely ≈−0.89, are similar for all pure, non-ionized fluids belonging to the class of 3-dimensional Ising-like systems, i.e., systems governed by short-range forces.

Organic Rankine cycle (ORC) turbogenerators are the most viable option to convert sustainable energy sources in the low-to-medium power output range (from tens of kWe to several MWe). The design of efficient ORC turbines is particularly challenging due to their inherent unsteady nature (high expansion ratios and low speed of sound of organic compounds) and to the fact that the expansion encompasses thermodynamic states in the dense vapor region, where the ideal gas assumption does not hold. This work investigates the unsteady nonideal fluid dynamics and performance of a high expansion ratio ORC turbine by means of detailed Reynolds-averaged Navier–Stokes (RANS) simulations. The complex shock interactions resulting from the supersonic flow (M ≈ 2.8 at the vanes exit) are related to the blade loading, which can fluctuate up to 60% of the time-averaged value. A detailed loss analysis shows that shock-induced boundary layer separation on the suction side of the rotor blades is responsible for most of the losses in the rotor, and that further significant contributions are given by the boundary layer in the diverging part of the stator and by trailing edge losses. Efficiency loss due to unsteady interactions is quantified in 1.4% in absolute percentage points at design rotational speed. Thermophysical properties are found to feature large variations due to temperature even after the strong expansion in the nozzle vanes, thus supporting the use of accurate fluid models in the whole turbine stage.

There is a high potential for civil applications of Unmanned Aerial Vehicles (UAV) in areas such as goods transport, telecommunication, remote monitoring and sensing, surveillance, search and rescue, and disaster management. Developments in areas such as telecommunication, control and information technology offer opportunities for long range remotely or automatically piloted missions. This requires efficient and light-weight small propulsion systems. The potential of turboprop propulsion for civil UAVs using micro turbine technology has been explored and compared with existing concepts, such as piston engine driven propellers. Different propulsion concepts have been analyzed and the application areas where advanced turboprops would be superior to other systems such as reciprocating engines and electric motors, identified. However, turboprop engines of the small power capacity required for the aircraft concepts and missions considered are not currently available with competitive performance. A conceptual design study of a micro turboprop engine has been performed by downscaling an existing reference engine. Scale effects on efficiency have been taken into account, as well as effects of technological progress. Engine cycle optimization has been carried out and the effects of turbine inlet temperature, compressor pressure ratio, engine size, and component efficiency have been investigated. An aerodynamic and flight performance model of a baseline UAV has been developed in order to predict mission performance. This model has been coupled to a turboprop model to evaluate system performance with different engine configurations for the selected mission. The outcome of the study provides information about the technological improvements in terms of cycle efficiency required to make the micro-turboprop a competitive solution. The Propulsion and Power group of Delft University of Technology will pursue these R&D goals in an attempt to contribute to the development of civil UAV technology.