ABSTRACT. Many industrial turbomachinery applications involve fluids that are not amenable to ideal gas assumptions.   The classical application is steam turbines where both pressures above ~20 bar and condensing liquid in the low pressure turbine leads to significant departures from the ideal gas relationships.  In aviation engines and industrial gas turbines the high temperatures result in dissociation effects that render the ideal gas assumptions invalid.   The processing of hydrocarbons frequently involves the intersection of non-ideal fluids and turbomachinery with applications ranging from gas compression to multiphase pumping.   The emergence of closed loop power cycles using supercritical CO2 as a working fluid brings another set of challenges for the industry to understand including operation of turbomachinery very near the critical point and potential for liquid and solid condensation.   This talk will touch on each of these areas and provide an overview of industrial practice and open questions where further research is needed.

ABSTRACT. Turbulent fluid flows with large gradients of thermo-physical properties can occur in a wide range of engineering applications, such as in flows with strong heat transfer at the wall, high-speed flows and in application with dense gases. The mean velocity, near-wall turbulent structures and mixing of scalar fields are greatly affected by near wall gradients in fluid properties. In order to study these effects, we will use direct numerical simulations with different constitutive relations for density and viscosity as a function of temperature, to mimic a wide range of fluid behaviours and to develop a generalised framework for studying scaling laws and turbulence modulations in variable property flows. The first part of the presentation will be on mean velocity scaling. Based on observations we will discuss a velocity scaling that is solely based on the semi-local Reynolds number. This scaling is able to collapse velocity profiles irrespective of near-wall density and viscosity gradients. In the second part we will outline how near-wall density and viscosity gradients alter the Reynolds stress generation mechanism and inter-component energy transfer among turbulent stresses. In the last part of the presentation we will discuss how these effects alter heat transfer in turbulent pipe flows with fluids close to the vapour liquid critical point. In addition to that, we will also refer to recent advances in turbulence research for dense gases made by other researchers.

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.

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.

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. 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

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.

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.

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.

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.

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.

ABSTRACT. On a ten-year timescale, Carbon Capture and Storage (CCS) could significantly reduce carbon dioxide (CO2) emissions. One of the major limitations of this technology is the energy penalty for the compression of CO2 to supercritical conditions, which can require up to 20% of the plant’s gross power output. To reduce the power requirements supercritical carbon dioxide compressors must operate at reduced temperatures and near saturation where phase change effects are important. Non-equilibrium condensation can occur in the high-speed flow at the leading edge of the compressor, causing performance and stability issues. The characterization of the fluid at such conditions is vital to enable advanced compressor designs at enhanced efficiency levels but the analysis is challenging due to the lack of data on the metastable fluid properties. In this paper we assess the metastable behavior and nucleation characteristics of high-pressure subcooled carbon dioxide during the expansion in a Laval nozzle. The assessment is conducted with numerical calculations, supported and corroborated by experimental measurements. The objectives are (i) to determine the amount of subcooling that occurs in the fast adiabatic expansions of saturated carbon dioxide before nucleation establishes phase equilibrium, (ii) to characterize the state of the metastable phase and to assess the feasibility of direct properties extrapolation, and (iii) to quantify the influence of the expansion rate on the time scales that characterize condensation. The Wilson lines are determined via optical measurements in the range of 41 and 82 bar and near the critical point. The state of the metastable fluid is fully characterized through pressure and density measurements, with the latter obtained in a first of its kind laser interferometry set up. In a systematic analysis the inlet conditions of the nozzle are moved close to the critical point to allow for large gradients in fluid properties and reduced margin to condensation. The results of calculations using a cubic spline base extrapolation and direct extrapolation of the Span and Wagner and a Peng and Robinson equation of state are compared with the experimental measurements. The analysis suggests that the cubic spline extrapolation method can represent the metastable properties within 5% of the measured values, while direct extrapolation using the Span and Wagner model yields results within 1.5%.

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.

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.