ABSTRACT. Dense gases are characterised by molecules featuring large numbers of active degrees of freedom (quantified by the cv/R ratio). The isentropes in such gases have the distinct property of following rather closely the isotherms (the two become identical in the limit of cv/R going to infinity). Near the liquid-vapour critical point, this makes the isentropes very shallow and possibly concave (in the pressure-specific volume diagram). Whilst shallow isentropes are desirable when designing expanders (i.e. a large specific-volume increase may be achieved for virtually no pressure drop), could such extreme compressibility effects modify turbulence in a profound manner? This paper discusses two particularly interesting aspects: (i) shock-refraction properties (i.e. the way a shock can redistribute the energy of incoming perturbations), (ii) enstrophy production in homogeneous turbulence. A linear interaction analysis (LIA) is conducted on the shock configuration for which the incoming perturbation is decomposed into linear modes of the compressible Euler equations. The transmission coefficients relative to each eigen modes are solved analytically and results are compared against fully non-linear compressible direct numerical simulation reproducing the weak perturbation of an isolated two-dimensional compression shock wave. The linear analysis is found to be capable of predicting the shock-induced redistribution of the energy of the incoming perturbation between the different eigen modes. Non-ideal gas effects are observed both analytically and numerically with especially an unusual selective response for some particular choice of incoming Mach number. A two-dimensional isotropic turbulence configuration is then numerically investigated for the case of an inviscid compressible dense-gas flow close to the liquid-vapour critical point. Strong non-ideal-gas effects on enstrophy production are observed with the formation of eddy shocklets. In both cases non-convex isentropes close to the liquid-vapour critical point are extremely influential in letting both the shock and the turbulence redistribute any supply of turbulence kinetic energy in ways which are simply not observable in ideal gases. This will hopefully spark enthusiasm amongst turbulence modellers (and their end users?).

ABSTRACT. The accurate modelling and simulation of two-phase flows is a key issue for many engineering applications such as condensing steam within turbines and nozzles, sprays in combustion, fluid mixing systems. Currently, the majority of two-phase models for homogeneous condensation are calibrated on the large amount of experimental data available for water and steam at low reduced pressures. However, the direct application of such models to non-ideal thermodynamic conditions, i.e. in regions where the vapour thermo-physical behaviour departs from that of a perfect gas, is rather questionable and worth of being investigated for application in the proximity of the critical point.

Recently, an increasing number of researches have proposed the use of the method of moments to describe the droplet spectra of the second (discrete) phase. The great advantage of this approach is the unrestricted applicability to any fluid and the relatively low computational cost as compared with the well-established lagrangian and eulerian-eulerian methods.

This work carried out a numerical investigation of quasi-1D condensing flows in supersonic nozzles at high reduced pressures. Two different set of conservation laws, referred to as mixture and continuum phase, were considered and supplemented by transport relations for the dispersed phase formulated through the method of moments. Both models were integrated in time using a segregated approach allowing for metastable conditions by the use of cubic equations of state of increasing complexity.

Numerical calculations were performed on several nozzle test cases for which experimental observations are made available [1]. The results show significant deviations between the numerical models and the experiments while augmenting the inlet total pressure of the nozzle, suggesting that classical models amply validated at low reduced pressures need to be corrected when condensing in non-ideal thermodynamic regions.

References

1. Gyarmathy, G. (2005). Nucleation of steam in high-pressure nozzle experiments. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 219(6), 511–521. doi:10.1243/095765005x31388

Rémi Abgrall (University of Zurich, Institute of Mathematics)

Tulin Kaman (University of Zurich, Institute of Mathematics)

ABSTRACT. The aim of this work is the development of a fully explicit scheme in the framework of time dependent hyperbolic problems with strong interacting discontinuities to retain high order accuracy in the context of compressible multiphase flows. A new methodology is presented to compute compressible two-fluid problems based on the five equation model given in Kapila et al. (Physics of Fluids 2001), which takes the formal limit (see Murrone and Guillard, J. Comp. Physics 2005) of the Baer and Nunziato model (Int. J. of Multiphase flow 1986) when the relaxation parameters tend simultaneously to infinity. We present a predictor-corrector scheme, following the concept of residual distribution in Ricchiuto and Abgrall (J. Comp. Physics 2010). The advantage of this formalism is that the time step is dictated by a CFL- like condition, contrarily to the original Baer- and Nunziato-like system, and, moreover, the system is much smaller. The drawback is that the PDE is written in a non- conservation form. Testing the predictor-corrector scheme on second order accuracy, the study considers one prediction and one correction step, adopting for the space discretization a residual based distribution scheme. This formulation allows seeing the component of the discretization as an error between two different approximations. In particular, the residual is computed considering a Lax Friedrich's scheme (Ricchiuto et al., J. Comp. Physics 2010). In order to construct a stable and non-oscillating approximation of the discontinuities, the residual, maintaining the consistency requirement, is distributed to each node belonging to a cell via a limiter. The last is designed similarly to a positive stream-wise invariant with a filtering term, using instead of the residual its eigenforms. We compare this scheme to a hybrid one, where we couple the presented explicit residual distribution with a classical Glimm’s scheme (J. Sci. Stat. Comp. 1982). In particular, we take advantage of Glimm's ability to approximate the front of shocks, while retaining the advantages of the explicit residual distribution in the other areas. The switch from one scheme to the other is performed by means of a shock detector, capturing large momentum jumps. This numerical methodology can be easily extended to unstructured meshes. With respect to other contributions in that area, we investigate a method that provides for mesh convergence the exact solutions, where the studied non-conservative system is associated to consistent jump relations. Test cases on a stiffened gas for a two phase compressible flow in one dimension for a Riemann problem have verified that the approximation converges to its exact solution. The results have been compared with the pure Glimm’s scheme and the expected exact solution, finding a good overlap and proving the method to be robust.

ABSTRACT. The use of dense gases as working media in turbomachinery, referred to as Organic Rankine Cycle (ORC) turbines, is proposed as a method of recovery of variable energy sources such as waste heat from industrial processes. Whereas a traditional Rankine Cycle operates with steam as the working fluid, ORC turbines use an organic fluid such as hydrocarbons, silicon oils or other organic refrigerants. Proposed heat sources for ORC turbines typically include variable energy sources such as solar thermal collectors or waste heat from industrial processes. As a result, to improve the feasibility of this technology, the resistance to variable input conditions must be taken into account at an early stage of the development process. Robust design has been developed to improve the product quality and reliability in industrial Engineering. The numerical optimization under uncertainties is called Robust Optimization (RO) and it overcomes the limitation of deterministic optimization that neglects the effect of uncertainties in design variables and/or design parameters. The robustness is determined by a measure of insensitivity of the design with respect to variations of the design parameters, like geometrical tolerances or fluctuations of the operating conditions. To measure the robustness of a new design, statistics such as mean and variance (or standard deviation) of a response are calculated in the RO process. In this work an accurate design methodology for 2D supersonic ORC expanders based on a method of characteristics (MOC) generalized to complex equations of state, is used to create a baseline injector shape. Subsequently, this is optimized through a RO loop. The stochastic optimizer is based on a Bayesian Kriging model of the system response to the uncertain parameters, used to approximate statistics (mean and variance) of the uncertain system output, coupled to a multi-objective non-dominated sorting genetic algorithm (NSGA). We search for an optimal shape that maximizes the mean and minimizes the variance of the expander isentropic efficiency. The isentropic efficiency is evaluated by means of RANS (Reynolds Average Navier-Stokes) simulations of the injector. The fluid thermodynamic behavior is modelled by means of the well-known Peng-Robinson-Stryjek-Vera equation of state. The blade shape is parametrized by means of Bezier curves and the design variables are Bezier control points. In order to speed-up the RO process, an additional Kriging model is built to approximate the multi-objective fitness function and an adaptive infill strategy for the individuals is proposed in order to improve the surrogate accuracy at each generation of the NSGA. The robustly optimized ORC expander shape is finally compared, in terms of isentropic efficiency and power output, to the MOC baseline shape and to an injector designed by means of a standard deterministic optimizer.

ABSTRACT. This paper illustrates an innovative approach for improving the prediction of a piston expander for exhaust heat recovery. While nearly 30 percent of the fuel energy is lost as waste heat in the form of hot exhaust gases, exhaust heat recovery promises one of the biggest fuel economy potential regarding the technologies available in the next decade. Applied to heavy commercial vehicles (HCVs), buses or off road vehicles, a bottoming Rankine Cycle (RC) on exhaust heat shows a great potential in recovering the exhaust gases energy, even for part loads. Nowadays it seems to be clear that the heavy duty industry will implement RC on their long haul trucks in the 2020s as an answer to future stringent regulation and the still increasing customers request for operating cost reduction. A 2 to 5% fuel economy is achievable on such vehicles. An experimental and numerical characterization of a piston expander is presented here for assessing the prediction of the proposed physical model. Experimental measurements are characterized and their variability is propagated through the numerical code by means of state-of-art uncertainty quantification techniques. Several sources of uncertainties are taken into account at the same time, thus yielding various indications concerning the most predominant parameters, and their influence on several outputs of interest. Numerical results are validated with respect to the experimental measurements, by comparing numerical and experimental error bars. Additional analysis are then performed by using both ANOVA techniques and surrogate modelling.

Christophe Corre (Laboratoire de Mécanique des Fluides et d'Acoustique)

Matteo Menghetti (Laboratoire de Mécanique des Fluides et d'Acoustique)

ABSTRACT. A study of turbulence in BZT dense gas flows is performed using DNS. It is shown that for a realistic intensity, the turbulence in dense gas flows behaves in a highly compressible manner when the average thermodynamic state lies within the inversion region. A close similarity is observed in the evolution of the TKE when the initial turbulent Mach number and the Taylor Reynolds number are matched regardless of the Equation of State (EoS) considered. A large turbulent Mach number is yet more easily attained in dense gas flows lying in the inversion region because of the low speed of sound associated with it. In this case the turbulence shows a highly compressible evolution with periodic exchanges between the internal and kinetic energies. In order to assess the capabilities of currently available Large Eddy Simulation (LES) subgrid-scale models, a-posteriori tests are performed using the dynamic Smagorinsky model. Coherently with the hypothesis it relies on, the model perfectly captures the evolution of the TKE when the turbulent Mach number is low enough. When using the perfect gas EoS at a higher turbulent Mach number the agreement is reasonable. Yet, when the average thermodynamic state lies within the inversion region and when using the Martin&Hou EoS, the model is not able to capture the correct evolution of the TKE. The results presented in this study call for a specific research effort directed towards the assessment and possibly the development of advanced subgrid-scale models for LES of turbulent dense gas flows.

Josette Bellan (Jet Propulsion Laboratory, California Institute of Technology)

ABSTRACT. Direct Numerical Simulation (DNS) is performed of a round fluid jet entering a high-pressure chamber. The chemical compositions and temperatures of the jet and that of the fluid in the chamber are initially prescribed. The governing equations consist of the conservation equations for mass, momentum, species and energy, and are complemented by a real-gas equation of state, as in Masi et al. 2013 who studied temporal mixing layers. The fluxes of species and heat are written in the framework of fluctuation-dissipation theory and include Soret and Dufour effects. For more than two species, the full mass diffusion and thermal diffusion matrices are computed using high-pressure mixing rules which utilize as building blocks the corresponding pairwise diffusion coefficients (see Harstad and Bellan 2004a, 2004b). The mixture viscosity and thermal conductivity are computed using standard mixing rules and corresponding states theory, as in Reid et al. 1987. The jet is sufficiently smaller than the chamber to be considered a free jet, permitting the use of non-reflecting transverse boundary conditions. The inflow and outflow boundary conditions are prescribed. The study focusses on qualitatively reproducing experimental observations made at Reynolds numbers not attainable in DNS (e.g. Oschwald and Schik 1999, Falgout et al. 2015, Falgout et al. 2016, Manin et al. 2015, etc.), particularly the differences observed according to the composition of the injected fluid.

Falgout, Z., Rahm, M., Wang, Z. and Linne, M., Evidence for supercritical mixing layers in the ECN Spray A, Proc. Comb. Inst., 35, 1579-1586, 2015 Falgout, Z., Rahm, M., Sedarsky, D. and Linne, M., Gas/fuel jet interfaces under high pressures and temperatures, Fuel, 168, 14-21, 2016 Harstad, K. and Bellan, J., High-Pressure Binary Mass-Diffusion Coefficients for Combustion Applications, Ind. & Eng. Chem. Res., 43(2), 645-654, 2004a Harstad, K. and Bellan, J., Mixing rules for multicomponent mixture mass diffusion coefficients and thermal diffusion factors, Journal of Chemical Physics, 120(12), 5664-5673, 2004b Manin, J., Pickett, L. M. and Crua, C., Microscopic observation of miscible mixing in sprays at elevated temperatures and pressures, paper 93 presented at the ILASS meeting, Rayleigh, NC., May 2015 Masi, E., Bellan, J., Harstad, K. and Okong’o N., Multi-species turbulent mixing under supercritical-pressure conditions: modeling, Direct Numerical Simulation and analysis revealing species spinodal decomposition, J. Fluid Mech., 721, 578-626, 2013 Oschwald, M. and A. Schik, A., Supercritical nitrogen free jet investigated by spontaneous Raman scattering, Exp. Fluids, 27, 497-506, 1999 Reid, R. C., Prausnitz, J. M. and Polling, B. E., The Properties of Gases and Liquids, 4th edn. McGraw-Hill, 1987

Pietro Molesini (Politecnico di Milano)

Giacomo Persico (politecnico di Milano)

Alberto Guardone (politecnico di Milano)

ABSTRACT. The dynamic response of pressure probes for unsteady flow measurements in turbomachinery is studied for fluids operating in non-ideal thermodynamic conditions. In the last decade the scientific community witnessed a significant growth of the interest towards turbomachinery systems based on Organic Rankine Cycles (ORC). Such devices exploit key features of fluids characterized by high molecular complexity. Under certain conditions of pressure and temperature, typically in the close proximity of the saturation curve and the critical point, the behaviour of these fluids is known to significantly depart from the one of the ideal gas model. The application of advanced and accurate Equations of State (EoS) is crucial for the reliable analysis of ORC turbines, not only for modeling issues or theoretical studies, but also for the design and the application of proper measurement techniques for non-ideal compressible flows. Among the most relevant instrumentations currently applied for the experimental analysis of the flow in turbomachinery, aerodynamic pressure probes stand out for their capability to measure both flow properties and pressure field, thus allowing to estimate the performance of the stationary cascades. With the aim to measure the time-resolved flow and pressure field downstream of turbomachinery rotors, where significant unsteady flows are found, the concept of fast-response aerodynamic pressure probe was intensively developed in the last decade and has been recently demonstrated as a reliable and extremely relevant technique for the experimental analysis of the flow downstream of turbine stages. To extend the application of such a measurement device to ORC turbines, a shortcoming in the available analytical and experimental data calls for a careful investigation of the physics related to such devices in the limit of non-ideal flows. In particular, the evolution of the flow inside the line-cavity system connecting the pressure tap on the probe head with the sub-surface mounted pressure sensor is expected to be highly effected by non-ideal fluid effects. To this end, the step response of a fast-reponse pressure probe, initially designed for unsteady measurements in air turbines/compressors, is investigated numerically in order to assess the expected time response when dealing with a flow in a non-ideal fluid regime. Numerical simulation are carried out exploiting the Non-Ideal Compressible Fluid-Dynamics (NICFD) solver embedded in SU2. SU2 is an open-source collection of software tools for performing Partial Differential Equation analysis originally conceived at Stanford university and currently developed by an joint international team of researchers from different countries. At first, the analysis is carried out assuming ideal gas thermodynamic behavior, to validate the computational framework against experimental dynamic calibration in the low-pressure shock tube of Politecnico di Milano. Then, the Peng-Robinson EoS is applied to accurately represent the expected thermodynamic behaviour of the organic fluid with an ORC turbine. The step-reponse of the probe predicted using the two classes of EoS is then compared to assess the impact of non-ideal effects on the dynamic system in terms of settling time, characteristic frequencies and fluid-dynamic damping.

Davide Vimercati (Politecnico di Milano)

Alberto Guardone (Politecnico di Milano)

ABSTRACT. The non-monotone dependence of the speed of sound along adiabatic transformation is demonstrated to result in the admissibility of non-ideal increase of the flow Mach number across oblique shock waves, for pre-shock states in the close proximity of the liquid-vapour saturation curve. This non-ideal behaviour is not admissible for dilute, ideal gases and it associated to a less-than-unity value of the fundamental derivative of gasdynamics. Therefore, non-ideal shock waves are expected to be observed also in fluids with relatively low molecular complexity, including methane and ammonia. The simple yet qualitatively sound van der Waals model is used to confirm the present findings and to provide exemplary non-ideal shock waves.

Adam Head (Delft University of Technology)

Ingo Jahn (The University of Queensland)

ABSTRACT. Radial inflow turbines are an arguably relevant architecture for energy extraction from ORC and supercritical CO2 power cycles. The inclusion of a suitable diffuser in a radial turbine system is essential to the efficient operation of the turbine system in order to recover exhaust kinetic energy as static pressure.

In supercritical CO2 Brayton cycles, the high turbine inlet pressure would lead to a sealing challenge if the rotor was supported in the conventional cantilevered arrangement. An alternative to this is a cantilevered layout with the rotor exit facing the bearing system. While such a layout is attractive for the sealing system, it limits the axial space claim of any diffuser.

Previous studies into conical diffuser geometries for supercritical CO2 have shown that in order to achieve optimal static pressure recovery, longer geometries of a shallower cone angle are necessitated when compared to air.

A diffuser with a combined axial-radial arrangement is investigated as a means to package the aforementioned geometric characteristics into a limited space claim for a 100kW radial inflow turbine.

Michael Pfitzner (Universität der Bundeswehr München)

ABSTRACT. In the present contribution, we study high-pressure combustion of oxygen and methane using Large-Eddy Simulation (LES). The work is motivated by liquid rocket propulsion engines (LRE) in which the chamber pressure often exceeds the critical pressure of the injected fluid and the temperature of one or both propellants is smaller or close to the pseudo-critical temperature. The propellants are thus in a trans- or supercritical state in which the thermodynamic and transport properties are highly non-linear functions of temperature and pressure. Real-gas effects have a significant influence on the operation of LREs and numerous experimental and numerical studies contributed to a better understanding of such flows. Many valuable coaxial single-injector experiments were carried out on the Mascotte test bench to study trans- and supercritical combustion of LOx/GH2 as well as of LOx/GCH4. Among them is the work of Singla et al. who investigated methane combustion at different operating conditions.

This configuration is an interesting test case for numerical tools and serves as a reference for our real-gas LES methods for turbulent combustion presented herein. The implementation is based on the open-source software OpenFOAM. The publicly available code has been extended by a real-gas thermodynamics model based on the Peng-Robinson equation of state together with the volume-translation method of Abudour et al. This method significantly improves the accuracy of the density prediction with respect to the uncorrected version at minimal extra computational cost. The real-gas thermodynamics models are incorporated into a flamelet combustion model to allow for simulations at supercritical pressures. Chemical reactions on the subgrid scales are described using a presumed Beta-shape Probability Density Function.

Preliminary results are encouraging. The figure shows an iso-surface of the stoichiometric mixture fraction colored with the temperature. The characteristic flame shape that has been observed in the experiments is well reproduced. In the final paper we will present the real-gas flamelet approach in greater detail. In particular, the validity of the underling assumptions will be addressed and the necessity of solving an additional energy equation will be discussed. The averaged simulation results will then be compared with the available OH* measurements.

Stefan Aus der Wiesche (University of Applied Sciences Muenster)

Franz Joos (Helmut Schmidt University)

ABSTRACT. The calculation of isentropic flow and normal shock waves of real gases are important, especially in the preliminary design of turbo-machinery and test rigs. In an ideal gas, the relations for one-dimensional isentropic flow and normal shock waves are well known and can be found in standard textbooks. However, for fluids exhibiting strong deviations from the ideal gas assumption universal relations do not exist due to complex equations of state. This paper presents a analytical method for the prediction of isentropic real gas flows and normal shock waves, based on the Redlich-Kwong (RK) equation of state. Explicit expressions based on a series expansion for describing isentropic flow of Novec 649 are compared to Refprop data and ideal gas equations. For moderate pressures the RK method is in very good agreement with the Refprop data, while the ideal gas equations fail to predict the real gas behaviour. The same observations are made for normal shock calculations, where both real gas methods yield very close results. Especially the predicted stagnation pressure losses across a shock wave are in excellent agreement.

ABSTRACT. This paper discusses the shape-optimization of non-conventional centrifugal turbine nozzles for Organic Rankine Cycle (ORC) applications. The optimal aerodynamic design is supported by the use of a non-intrusive, gradient-free technique specifically developed for shape optimization of turbomachinery profiles. The method is constructed as a combination of a geometrical parametrization technique based on B-Splines, a high-fidelity and experimentally validated Computational Fluid Dynamic (CFD) solver, and a surrogate-based evolutionary strategy. The non-ideal gas behaviour featuring the flow of organic fluids in the cascades of interest is introduced via a look-up-table approach, which is rigorously applied throughout the whole optimization process thanks to the non-intrusive character of the evolutionary strategy. Two transonic centrifugal nozzles are considered, featuring very different loading and radial extension. The use of a systematic and automatic design method to such a non-conventional configuration highlights the character of centrifugal cascades, which require a specific and non-trivial definition of the shape, especially in the rear part, to avoid the onset of shock waves. It is shown that the optimization acts in similar way for the two cascades, identifying an optimal curvature of the blade that both provides a relevant increase of cascade performance and a reduction of downstream gradients.

Harald Kunte (Leibniz Universitaet Hannover)

Joerg Seume (Leibniz Universitaet Hannover)

ABSTRACT. The aerothermodynamic design of supersonic axial, single stage impulse turbine for an Ethanol-based waste recovery system for commercial trucks is described as is the mechanical design of seals, bearings, and the electrical design of the generator. The test data presented show a remarkably good agreement between the CFD-based design computations and the test data.

Vitale Salvatore (Delft University of Technology)

Piero Colonna (Delft University of Technology)

Giulio Gori (Politecnico di Milano)

Alberto Guardone (Politecnico di Milano)

Tom Economon (Stanford University)

Juan J. Alonso (Stanford University)

Francisco Palacios (The Boeing Company)

ABSTRACT. 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 ther- modynamic 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 prop- erties. Non-reflecting boundary conditions are furthermore implemented to enhance the fidelity of turbomachinery simulations. A variety of test cases are carried out to assess the performance of the solver. At first, numer- ical methods are verified against analytical solution of reference NICFD test cases, including steady shock reflection in two spatial dimensions. Then, non-ideal gas effects 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.

ABSTRACT. Calculation of tail probabilities remains very challenging even with the most recent and performing uncertainty quantification techniques. To tackle this problem, this work aims at proposing an efficient method basing on Monte Carlo method, importance sampling and interpolation methods making use of Adjoint states. Several approaches are proposed in literature for using adjoint evaluations for accelerating Monte Carlo convergence. Generally, they rely on the building of a linear approximation in order to compute the small probability that the objective function exceeds a certain critical value, usually representing the probability that a system fails or suffers catastrophic losses. The adjoint calculation is then used to calculate the sensitivity gradient, which can be used to approximate the objective function as a linear function of the random variables describing the sources of uncertainty. The information provided by this linear approximation permits to reduce the variance of the Monte Carlo method using control variate and importance sampling. The method proposed here is based on a continuous update of the interpolation function via the gradient computation, which is then used with the importance sampling technique. The advantages of such an approach is to improve and retain the good convergence properties of MC methods when treating a very high number of dimension, by further accelerating the convergence by using the interpolation on functional evaluations and gradients. The interest of this kind of approach for predicting non-classical gasdynamics phenomena is then demonstrated with several examples, such as the computation of a rarefaction shock wave (RSW) in a dense-gas shock tube. In this case, since a RSW is relatively weak and that the prediction of its occurrence and intensity are highly sensitive to uncertainties on the initial flow conditions and on the fluid thermodynamic model, the objective is to obtain a reliable estimate for the RSW probability of occurrence.

Andrea Rurale (Politecnico di Milano)

Andrea Spinelli (Politecnico di Milano)

Alberto Guardone (Politecnico di Milano)

ABSTRACT. Supercritical carbon dioxide (sCO2) is currently being considered as working fluid in several industrial and energy applications thanks to its relative low critical pressure and temperature. Despite its widely usage, a comprehensive understanding of the fundamental properties of carbon dioxide flows in supercritical conditionsis not available. Preliminary theoretical and numerical studies using accurate equations of state [1] and non-ideal flow solvers [2], are yet to be complemented with experimental data. Different experimental activities have been recently carried out to investigate sCO2 flows in specificallyconditions. For instance, Lettieri and collaborators assessed the condensation effects in sCO2 compressors and defined a criterion to establish whether the fluid might condense [3]. At KAIST, professor Lee’s research team is developing an experimental facility to accurately take into account non-ideal gas effects during sCO2 compressor design and performance analysis. Finally, the university of Seville and Altran have designed pressurized sCO2 wind tunnel to improve to design of blade cascade of turbo-machinery [5]. The design of a novel sCO2 wind tunnel is under-way at CREA (Compressible-fluid dynamics for Renewable Energy Application) Lab at Politecnico di Milano. Fundamental studies of supersonic sCO2 flows will be carried out in the close proximity of the critical point and the liquid-vapor saturation curve, where sCO2 compressors are designed to operate. Moreover, the test-rig will be used as a calibration tunnel for non-ideal flows pressure probes and optical measurement techniques, including Schlieren and Laser Doppler Velocimetry (LDV). The present work outlines the preliminary design of the plant and the technical specifications of the relevant components. To reach supersonic speeds, the test section consists in a convergent-divergent nozzle followed by a rectangular-section chamber for flow visualization. Three possible configurations are initially taken into account to drive the fluid through the nozzle: an open-loop, a Joule-Brayton cycle and a Rankine cycle. A preliminary analysis of mass flows indicates that the last configuration is the most suitable for the operating conditions of interest. Then, the main components of the plant, namely the pump, the heater, the chiller and the heat exchangers are designed and a preliminary cost analysis is also carried out.

Rémi Abgrall (University of Zurich)

Pietro Marco Congedo (INRIA)

ABSTRACT. Cavitation is characterized by vapor bubbles creation in the liquid phase as a consequence of a pressure drop. This phenomenon can be reproduced by means of several two-phase models. An equation of state is commonly used in order to define the thermophysical properties of the two fluids and to close the model. The aim of this work is to study how the uncertain parameters of the equation of state (EOS) can influence the prediction of the cavitation structures.

These uncertainties are propagated through a two-phase numerical solver for evaluating the impact on the predictive character of the numerical solution.

The variability of the mixture velocity and the mixture pressure are analyzed.

Paola Cinnella (Laboratoire DynFluid - Arts et Métiers ParisTech)

Xavier Gloerfelt (Laboratoire DynFluid - Arts et Métiers ParisTech)

Francesco Grasso (Laboratoire DynFluid - Arts et Métiers ParisTech)

ABSTRACT. The influence of dense gas effects on compressible turbulence is investigated by means of direct numerical simulations of the decay of compressible homogeneous isotropic turbulence (CHIT) and of supersonic turbulent flows through a plane channel (TCF). For both configurations, a parametric study on the Mach and Reynolds numbers is carried out. The dense gas considered in these parametric studies is PP11, a heavy fluorocarbon. The results are systematically compared to those obtained for a diatomic perfect gas (air). Additional DNS of the CHIT and TCF configurations are carried out, for fixed Mach and Reynolds numbers, also for a refrigerant (R245fa) and a siloxane (D5), in the aim of quantifying the influence of the fluid complexity on turbulence evolution. In our computations, the thermodynamic behaviour of the dense gases is modelled by means of advanced equations of state, i.e., the Martin-Hou equation for PP11 and the technical Span-Wagner equation of state for the other fluids. In all cases, the Chung-Lee-Starling law, that takes into account correction terms for dense gases near the critical region, is used to model the fluid transport properties (dynamic viscosity and thermal conductivity). For CHIT cases, turbulent Mach numbers up to 1 are analysed using mesh resolutions up to 768^3. The differences in both large- and small-scale dynamics are evaluated and a detailed topological study of the flow is carried out, as well as a statistical analysis of the turbulent structures found. Afterwards, wall-bounded dense-gas turbulence is studied for the TCF configuration. Bulk Mach numbers up to 3 and bulk Reynolds numbers up to 12000 are investigated. The computational grids are chosen in order to ensure a good spatial resolution in all directions, i.e., in wall values, dx=10-15, dyw=0.6-0.8 and dz=4-7, resulting in mesh up to 5*10^8 grid points. Average profiles of the thermodynamic quantities are found to exhibit significant differences with respect to perfect-gas solutions at the same Mach and Reynolds number. Precisely, friction heating effects are considerably smaller, due to the much weaker coupling between thermal and kinetic fields. Velocity profiles for dense gas flows are much less sensitive to the Mach number and collapse in the logarithmic region, unlike the case of air. The characteristic size of the observed turbulent structures is closer to that observed in incompressible turbulence. Moreover, the different behavior of viscosity and thermal conductivity leads to important variations of the local Prandtl and Reynolds numbers. A detailed analysis of the energy spectra, level of turbulence anisotropy, thermodynamic correlations across the channel, turbulent kinetic energy budgets and topological structures will also be presented.

Fabio Cozzi (Politecnico di Milano - Energy Department)

Giorgia Cammi (Politecnico di Milano - Energy Department)

Marta Zocca (Politecnico di Milano - Department of Aerospace Science and Technology)

Paolo Gaetani (Politecnico di Milano - Energy Department)

Vincenzo Dossena (Politecnico di Milano - Energy Department)

Alberto Guardone (Politecnico di Milano - Department of Aerospace Science and Technology)

ABSTRACT. The early experimental results on the characterization of expanding flows of siloxane vapor MDM (C8H24O2Si3, octamethyltrisiloxane) are presented. The measurements were performed on the Test-Rig for Organic Vapours (TROVA) at the CREA Laboratory of Politecnico di Milano. The TROVA test-rig was built [1] in order to investigate the non-ideal compressible-fluid behavior of typical expanding flows occurring within organic Rankine cycles (ORC) turbine passages. The test rig implements a batch subcritical or supercritical Rankine cycle where a planar converging-diverging nozzle replaces the turbine and represents a test section of significance. Investigations related to both fields of non-ideal compressible-fluid dynamics fundamentals and turbomachinery are allowed [2]. Moreover, future researches are planned using linear blade cascade as test section. The nozzle can be operated with different working fluids and operating conditions aiming at measuring independently the pressure, the temperature and the velocity field and thus providing data to verify the thermo-fluid dynamic models adopted to predict the behavior of these flows. The limiting values of pressure and temperature are 50 bar and 400 °C respectively. The early measurements are performed along the nozzle axis, where an isentropic process is expected to occur. In particular, the results reported here refer to the nozzle operated in adapted conditions using the siloxane vapor MDM as working fluid in a thermodynamic region where mild non-ideal compressible-fluid effects are present. Both total temperature and total pressure of the nozzle are measured upstream of the test section, while static pressure are measured along the nozzle axis. Schlieren visualizations are also carried out in order to complement the pressure measurement with information about the 2D density gradient field. The Laser Doppler Velocimetry technique is planned to be used in the future for velocity measurements. The measured flow field has also been interpreted by resorting to the quasi-one-dimensional theory and two dimensional CFD viscous calculation. In both cases state-of-the-art thermodynamic models were applied.

1] A. Spinelli, M. Pini, V. Dossena, P. Gaetani, F. Casella, 2013. “Design, Simulation, and Construction of a Test Rig for Organic Vapours”. ASME Journal of Engineering for Gas Turbines and Power, Vol. 135, 042303. [2] A. Guardone, A. Spinelli, V. Dossena, 2013. “Influence of Molecular Complexity on Nozzle Design for an Organic Vapor Wind Tunnel”. ASME Journal of Engineering for Gas Turbines and Power, Vol. 135, 042307. [3] A. Spinelli, V. Dossena, P. Gaetani, C. Osnaghi, D. Colombo, “Design of a Test Rig for Organic Vapours”. In Proceedings of ASME Turbo Expo 2010, June 14-18, 2010, Glasgow – UK – GT2010-22959.

Kouichi Ishizaka (Mitsubishi Heavy Industries Ltd.)

Junichi Okamoto (Mitsubishi Heavy Industries Ltd.)

Yasuhide Watanabe (JAXA)

ABSTRACT. The LE-7A engine is the first-stage engine of the Japanese-made H-IIA launch vehicle. This engine has been developed by improving and reducing the price of the LE-7 engine used in the H-II launch vehicle. In the qualification combustion tests, the original designed LE-7A (LE-7A-OR) engine experienced two major problems, a large side load in the transient state of engine start and stop and melt on nozzle generative cooling tubes. The reason for the troubles of the LE-7A-OR engine was investigated by conducting experimental and numerical studies. In actual engine conditions, the main hot gas stream is a heated steam. Furthermore, the main stream temperature in the nozzle changes from approximately 3500 K at the throat to 500 K at the exit. In such a case, the specific heat ratio changes depending on the temperature. A similarity of the Mach number should be considered when conducting a model flow test with a similar flow condition of the Mach number between an actual engine combustion test and a model flow test. High-speed flow tests were conducted using CO2 gas heated up to 673 K as a working fluid and a 1:12 sub-scaled model nozzle of the LE-7A-OR engine configuration. The problems of the side force and the conducted form of the shock waves generated in the nozzle of the LE-7A-OR engine during engine start and stop were reproduced by the model tests of experimental and numerical investigations. This study presented that the model flow test using heated CO2 gas is useful and effective in verifying the numerical analysis and the design verification before actual engine combustion tests.

Paul Sapin (Imperial College London)

Christoph Barfuss (Technische Universität München)

Drazen Fabris (Santa Clara University)

Christos N. Markides (Imperial College London)

ABSTRACT. The efficiency of expanders is of prime importance in determining the overall performance of a variety of thermodynamic power systems, with reciprocating-piston expanders favoured at intermediate-scales of application (typically 10-100 kW). Once the mechanical losses in reciprocating machines are minimized (e.g. through careful valve design and operation), losses due to the unsteady thermal-energy exchange between the working fluid and the solid walls of the containing device can become the dominant loss mechanism. In this work, gas-spring devices are investigated numerically in order to focus explicitly on the thermodynamic losses that arise due to this unsteady heat transfer. The specific aim of the study is to investigate the behaviour of real gases in gas springs and compare this to that of ideal gases in order to attain a better understanding of the impact of real-gas effects on the thermally induced losses in reciprocating expanders and compressors. A CFD-model of a gas spring is developed in OpenFOAM. Three different fluid models are compared: an ideal-gas model with constant thermodynamic and transport properties; an ideal-gas model with temperature-dependent properties; and a real-gas model using the Peng-Robinson equation-of-state with temperature and pressure-dependent properties. Results indicate that, for simple, mono- and diatomic gases, like helium or nitrogen, there is a negligible difference in the pressure and temperature oscillations over a cycle between the ideal and real-gas models. However, when considering heavier (organic) molecules, such as propane, the ideal-gas model tends to overestimate the temperature and pressure compared to the real-gas model, especially if the temperature dependency of the thermodynamic properties is not taken into account. In fact, the ideal-gas model predicts higher pressures by as much as 25% compared to the real-gas model. Additionally, the ideal-gas models (both alternatives) underestimate the thermally induced loss compared to the real-gas model for heavier gases. This discrepancy is most pronounced at rotational speeds where the losses are highest. The real-gas model predicts a peak loss of 8.9% of the compression work, while the ideal-gas model predicts a peak loss of 5.7%. These differences in the work loss are due to the fact that the gas behaves less ideal during expansion than during compression, with the compressibility factor being lower during compression. This behaviour cannot be captured with the ideal-gas law. It is concluded that real-gas effects must be taken into account in order to predict accurately the thermally induced loss mechanism when using heavy fluid molecules in such devices.

Alireza Ameli (Lappeenranta University of Technology)

Ali Afzalifar (Lappeenranta University of Technology)

ABSTRACT. Carbon dioxide (CO2) is very promising alternative for a working fluid of future energy conversion and refrigeration cycles. CO2 has low global warming potential compared to refrigerants and supercritical CO2 Brayton cycle ought to have better efficiency than today’s counter parts. However, there are several issues concerning behavior of supercritical CO2 in aforementioned applications. One of these issues is a condensation of a supercritical fluid.

Non-equilibrium condensation of carbon dioxide in a converging-diverging nozzle was investigated in this article. An external real gas properties table was implemented in the flow solver to estimate the fluid properties in supercritical, metastable and saturation regions. An in-house FORTRAN code and CFX Expression Language files were coupled with flow solver to model the non-equilibrium condensation simulation of carbon dioxide in vicinity of the critical point. Metastable region of carbon dioxide has not been measured experimentally and it was handled by extrapolating the gas properties onto the liquid region.

Numerical results were compared with the experimental measurements. By investigation the Mach number inside the nozzle, it can be seen that although the maximum of phase change is occurred at the outlet boundary condition, but the flow becomes supersonic in upstream region near the throat where speed of sound is minimum in that region.

Antti Uusitalo (Lappeenranta University of Technology)

Juha Honkatukia (Lappeenranta University of Technology)

ABSTRACT. Organic Rankine Cycle is a mature technology for many application e.g. biomass power plants, waste heat recovery and geothermal power. Recently more attention is paid on an ORC utilizing the high temperature heat with relatively small power. One of the attracting application of such ORCs would be utilization of the waste heat of the exhaust gas of the engines in mobile applications.

In this paper, the experimental results of an ORC process utilizing high temperature exhaust gas heat and using siloxane MDM as a working fluid are presented and discussed. Also a design procedure of the ORC process is described and discussed. The analysis of major components of the process, namely evaporator, recuperator, pump and turbogenerator is done. The turbine type utilized in the turbogenerator is a radial inflow turbine and the turbogenerator consist of the turbine, the electric motor and the pump.

Based on the results, it was identified that the studied system is capable efficiently recover the waste heat of the exhaust gases and it has the potential of using high molecular weight and high critical temperature fluids as the working fluids in high-temperature small-scale ORC applications. The turbine power was found to be sensitive for the turbine outlet pressure and pressure losses in the recuperator and condenser.

Francisco Dura Galiana (University of Southampton)

Carlos de Miranda Ventura (University of Cambridge)

ABSTRACT. This paper describes a number of recent investigations into the effect of dense gas dynamics on ORC transonic turbine performance. We describe a combination of experimental, analytical and computational studies which are used to determine how, in-particular, trailing-edge loss changes with choice of working fluid. A Ludwieg tube transient wind-tunnel is used to simulate a supersonic base flow which mimics an ORC turbine vane trailing-edge flow. Experimental measurements of wake profiles and trailing-edge base pressure with different working fluids are used to validate high-order CFD simulations. In order to capture the correct mixing in the base region, Large-Eddy Simulations (LES) are performed and verified against the experimental data by comparing the LES with different spatial and temporal resolutions. RANS and Detached-Eddy Simulation (DES) are also compared with experimental data. The effect of different modelling methods and working fluid on mixed-out loss is then determined.

Abdulnaser I Sayma (City University London)

Christos N Markides (Imperial College London)

ABSTRACT. A significant improvement in the economy-of-scale of small-scale organic Rankine cycle (ORC) systems can arise from the appropriate design of components that can be manufactured in large volumes and implemented flexibly into a wide range of systems and potential applications. This, in turn, requires accurate predictions of component performance that can capture variations in the cycle conditions, parameters or changes to the working fluid. In this paper previous work investigating a modified similitude theory used to predict the performance of subsonic ORC turbines is extended to analyse the supersonic flow of organic fluids within 2D converging-diverging nozzles. Two nozzles are developed using a minimum length method of characteristics design model coupled to REFPROP. These are designed for R245fa and Toluene as working fluids with nozzle exit Mach numbers of 1.4 and 1.7 respectively. First, the nozzle performance is confirmed using CFD simulations, and then further CFD simulations are performed to evaluate the performance of the same nozzles over a range of different inlet conditions and with different working fluids. The CFD simulations are compared to predictions made using the original and modified similitude theories, and also to predictions made by conserving the Prandtl-Meyer function for the different operating conditions. The results indicate that whilst the modified similitude model does not accurately predict nozzle performance, conserving the Prandtl-Meyer function allows to predict the nozzle outlet Mach number to within 2% providing there is not a significant change in the polytropic index. Finally, the effect of working fluid replacement on the ORC system is discussed, and preliminary results demonstrate the possibility of matching a particular turbine to a heat source through optimal working fluid selection.