Non-ideal Compressible Fluid Dynamics Research Articles

Efficient implementation of complex equations of state in a high-order framework

In the last decades, the interest in non-ideal compressible fluid dynamics (NICFD) flows and high-order accurate numerical methods, such as discontinuous Galerkin (dG), has quickly grown. In fact, advanced simulation capabilities are of paramount importance to develop new sustainable technologies with higher efficiency and low environmental impact, and to decrease the use of expensive experimental facilities. Nowadays however, the coupling of accurate Computational Fluid Dynamics (CFD) solvers with sophisticated thermodynamic models has been investigated mainly in the finite volume (FV) framework. Moreover, the solution of complex equations of state (EoS) has a too high computational cost for real-life use in industry, which is often overcome with the look-up table (LuT) interpolation approach. LuTs seem to be more suitable for FV solvers rather than high-order or finite element ones, since the interpolation error introduced may deteriorate the higher accuracy provided by these numerical methods. The novelty of this work lies in the assessment of an efficient implementation for real gas simulations in a high-order solver, by resorting to structured LuTs and automatic differentiation (AD). The proposed implementation is assessed with the computation of the inviscid and turbulent flow around a NACA0012. This approach guarantees an overhead of the computational cost around 17% with respect to an ideal gas solver with manually derived jacobian matrix.

Nonideal Compressible Fluid Dynamics of Dense Vapors and Supercritical Fluids

The gas dynamics of single-phase nonreacting fluids whose thermodynamic states are close to vapor-liquid saturation, close to the vapor-liquid critical point, or in supercritical conditions differs quantitatively and qualitatively from the textbook gas dynamics of dilute, ideal gases. Due to nonideal fluid thermodynamic properties, unconventional gas dynamic effects are possible, including nonclassical rarefaction shock waves and the nonmonotonic variation of the Mach number along steady isentropic expansions. This review provides a comprehensive theoretical framework of the fundamentals of nonideal compressible fluid dynamics (NICFD). The relation between nonideal gas dynamics and the complexity of the fluid molecules is clarified. The theoretical, numerical, and experimental tools currently employed to investigate NICFD flows and related applications are reviewed, followed by an overview of industrial processes involving NICFD, ranging from organic Rankine and supercritical CO2 cycle power systems to supercritical processes. The future challenges facing researchers in the field are briefly outlined.

Investigation of non-ideal effects in compressible boundary layers of dense vapors through direct numerical simulations

In this work, we present an investigation about the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations (DNS) of transitional, zero-pressure gradient boundary layer flows are performed for two fluids characterized by different complexity of the fluid molecules, namely, “air” and siloxane MM. Different sets of thermodynamic free-stream boundary conditions are selected to evaluate the influence of the fluid state on both the frictional loss and the dissipation mechanisms. The thermophysical properties of siloxane MM are calculated with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field, irreversible heat transfer, and turbulent dissipation differs significantly depending on both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS results is then compared against the one obtained using a reduced-order model (ROM), which solves the two-dimensional boundary layer flow equations for an arbitrary fluid [M. Pini and C. De Servi, “Entropy generation in laminar boundary layers of non-ideal fluid flows,” in 2nd International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (Springer, 2020), pp. 104–117]. Results from both the DNS and the ROM show that low values of the overall dissipation are observed in the case of fluids made of simple molecules, e.g., air, and if the fluid is at a thermodynamic state in the proximity of that of the vapor–liquid critical point.

Experimental Investigation Techniques for Non-Ideal Compressible Fluid Dynamics

The rising number of applications of the organic Rankine cycle (ORC) or supercritical CO2 (sCO2) power systems have shaped a new branch of fluid mechanics called non-ideal compressible fluid dynamics (NICFD). This field of fluid mechanics is concerned with flows of vapors or gases, which are characterized by substantial deviations from the perfect gas model. In extreme cases, even non-classical gas dynamic phenomena could occur. Although these non-ideal compressible flows are the subject of sophisticated numerical simulation studies today, there is also a growing need for experimental data for validating purposes. In the last couple of years, new experimental test rigs designed for investigating non-ideal compressible fluid dynamics have been developed and commissioned. Classical practical measurement techniques are currently being re-developed and applied to non-ideal compressible flows. Despite its substantial relevance, information about these measurement techniques and their differences from conventional methods in the open literature is scarce. The present review article is an attempt to reduce that gap. After briefly discussing the thermodynamics and fluid dynamics of non-ideal compressible flows, the currently available test rigs and their utilized measurement techniques are reviewed. This review discusses schlieren optical investigations, pneumatic and laser-optical methods, and hot-wire anemometry for non-ideal compressible flows.

Speed of Sound Measurements in Dense Siloxane D6 Vapor at Temperatures up to 645 K by Means of a New Prismatic Acoustic Resonator.

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.

Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics

ABSTRACT Recently, there is an increased interest in supercritical CO2 and organic Rankine cycles (ORC) for their ability to achieve higher thermodynamic efficiency. However, the non-ideal gas thermodynamic in these cycles may affect the flow properties critically, necessitating the research of non-ideal compressible fluid dynamics (NICFD). Thus, simulation tools that can accurately predict fluid flows with NICFD are significant. This study presents a new approximation Riemann solver in OpenFOAM for NICFD. The new solver uses a real-gas (look-up table based) approximate Riemann flux calculator (modified from HLLC ALE flux calculator) through adding a new thermodynamic library tightly coupled with the OpenFOAM®. To validate the solver, three cases are presented, including a NASA transonic nozzle operating with air, to confirm the ability to correctly simulate the transonic flow phenomena and the shock waves; the VKI 2D cascade operated with MDM to assess the ability in simulating non-ideal gas flows typically to industrial applications; and the dense gas flow (MD4M) passing a backward ramp to illustrate the ability of the flux calculator and look-up table mechanism that can work well in the non-ideal region of fluid properties. This study can benefit future engineering applications of computational fluid mechanics of NICFD and the OpenFOAM community.

Accuracy assessment of the Non-Ideal Computational Fluid Dynamics model for siloxane MDM from the open-source SU2 suite

Abstract The first-ever accuracy assessment of a computational model for Non-Ideal Compressible-Fluid Dynamics (NICFD) flows is presented. The assessment relies on a comparison between numerical predictions, from the open-source suite SU2, and pressure and Mach number measurements of compressible fluid flows in the non-ideal regime. Namely, measurements regard supersonic flows of siloxane MDM (Octamethyltrisiloxane, C 8 H24O 2 Si 3 ) vapor expanding along isentropes in the close proximity of the liquid–vapor saturation curve. The model accuracy assessment takes advantage of an Uncertainty Quantification (UQ) analysis, to compute the variability of the numerical solution with respect the uncertainties affecting the test-rig operating conditions. This allows for an uncertainty-based assessment of the accuracy of numerical predictions. The test set is representative of typical operating conditions of Organic Rankine Cycle systems and it includes compressible flows expanding through a converging–diverging nozzle in mildly-to-highly non-ideal conditions. All the considered flows are well represented by the computational model. Therefore, the reliability of the numerical implementation and the predictiveness of the NICFD model are confirmed.

A look-up table method based on unstructured grids and its application to non-ideal compressible fluid dynamic simulations

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.

Experimental assessment of the open-source SU2 CFD suite for ORC applications

The first-ever experimental assessment of a Computational Fluid Dynamics (CFD) software for Non-Ideal Compressible-Fluid Dynamics (NICFD) flows of interest for ORC applications is presented here. Numerical results using SU2, the open-source suite for multi-physics simulation and design recently extended to deal with complex thermodynamic models of organic fluids, are compared here to experimental results from the Test-Rig for Organic VApours (TROVA) of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREA), Politecnico di Milano. Experimental results regard supersonic expanding flows of siloxane fluid MDM (Octamethyltrisiloxane, C8H24O2Si3) in non-ideal conditions representative of ORC applications. Three different geometries are considered for the assessment of the CFD solver. The first is a converging-diverging nozzle, representative of ORC supersonic stators, in which the fluid is accelerated to supersonic speed from highly non-ideal conditions, with inlet compressibility factor Z = Pv/(RT), computed using reference Equations Of State (EOS) for MDM fluid, as low as Z ~ 0.81. The second geometry is a diamond-shaped airfoil at a neutral angle of attack. The airfoil is plunged into a supersonic flow at Mach 1.5 and Z ~ 0.9, in mildly non-ideal conditions. Oblique shock waves are observed at the airfoil leading edge and interact with the wind-tunnel walls and the rarefaction fan from the airfoil. This test case is useful to understand the physics of oblique shock-wall and shock-shock interactions in turbine cascades operating in off-design conditions. The third geometry is a supersonic backward facing step, in which the formation of an oblique shock is observed experimentally at the reattachment point past the step. The Mach number is around 1.1 and the compressibility factor Z ~ 0.89. This geometry is representative of the trailing edge of turbine blades and it is useful to study the formation of fish-tail shock waves. These NICFD flows are fairly well captured by the CFD solver, thus confirming the validity of both the thermodynamic models and of the CFD implementation, using both the Euler equations for inviscid flows with negligible thermal conductivity and the full Reynolds-averaged compressible Navier-Stokes equations, for non-ideal compressible turbulent flows. In the considered shocked flows, grid adaptation is found to be key to capture the relevant flow features using a reasonable amount of grid points.

Active subspaces for the optimal meanline design of unconventional turbomachinery

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.

1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power

Proceedings of the NICFD 2016 SeminarOctober 19th and 20th, Villa Monastero, Varenna, ItalyPrefaceThis volume contains the papers presented at NICFD 2016: 1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power held on the 19th and 20th of October, 2016, at Villa Monastero, Varenna, Italy. The conference website is nicfd2016.polimi.it.NICFD 2016 promoted the exchange of scientific knowledge and fostered the interaction among researchers and professionals in the field of non-ideal compressible-fluid dynamics, with special emphasis on topics related to propulsion and power applications. The conference themes range from theoretical foundations to advanced numerical and experimental practices and applied technologies. Key themes are: experiments; fundamentals; numerical methods; optimization and UQ; critical and supercritical flows; turbulence and mixing; multi-component fluid flows; applications in ORC power systems; applications in supercritical CO2 power systems; steam turbines; cryogenic flows; condensing flows in nozzles; cavitating flows; super/trans-critical fluids in space propulsion.Four keynote lectures reviewed the state-of-the-art and illustrated future studies and applications: Non-Ideal Compressible Fluid Dynamics: A Challenge for Theory by Prof. Alfred Kluwick, TU Wien, Austria; Cavitation Instabilities in Turbopump Inducers by Prof. Seung Jin Song, Seoul National University, Korea; Industrial applications of turbomachinery operating on non-ideal fluids by Dr. Douglas Hofer, GE Global Research, USA; Wall bounded turbulence in flows with strong property gradients by Prof. Rene Pecnik, Delft University of Technology, The Netherlands.The proceedings gather 27 papers reporting on cutting-edge research activities in NICFD for propulsion and power. The review paper by Prof. Alfred Kluwick opens the collection and provides the perspective on past discoveries, the context of present activities and the roadmap of future challenges in this new, exciting scientific field.We would like to thank all the participants to NICFD 2016 and the members of the Scientific Committee, for providing guidance during the organisation of the conference and for managing the revision of the papers. We thank all reviewers for their invaluable help to attain the high scientific quality of the contributions collected here.The conference was supported in part by the European Research Council under ERC Consolidator Grant N.617603, NSHOCK Project (crealab.polimi.it)Varenna, October 2016Prof. Alberto Guardone, Politecnico di Milano, ChairmanProf. Piero Colonna, Delft University of Technology, Co-chairDr. Andrew Wheeler, Cambridge University, Co-chairGiorgia Cammi, Politecnico di Milano, Program ManagerDavide Vimercati, Politecnico di Milano, Submission ManagerInvited keynote lecturesNon-Ideal Compressible Fluid Dynamics: A Challenge for Theoryby Prof. Alfred Kluwick, Wien Technical University, Austria: The possibility that rarefaction as well as compression shocks may form in single phase vapours was envisaged first by H. A. Bethe (1942), The theory of shock waves for an arbitrary equation of state, Technical Report No. 545, Office of Scientific Research and Development. However, calculations based on the Van der Waals equation of state indicated that the former type of shock is possible only if the ratio of specific heat at constant volume cv to universal gas constant R is larger than about 17.5 which he considered too large to be satisfied by real fluids. This conclusion was contested by P. A. Thompson, (1971) A Fundamental Derivative in Gas Dynamics, Physics of Fluids 14 pp. 1843–1849, who showed that the type of shock capable of forming in arbitrary fluids is determined by the sign of the thermodynamic quantity Γ = v3/(2a2)(∂2P/∂v2)s, which he referred to as the fundamental derivative of gasdynamics. Here v, p, s and a denote specific volume, pressure, entropy and the speed of sound. Thompson and co-workers also showed that the required condition for the existence of rarefaction shocks, that Γ takes on negative values, is indeed satisfied for several fluorocarbon vapours. This finding spawned a burst of theoretical studies elaborating on the unusual and often counterintuitive behaviour of flows with rarefaction shocks present. This produced results not only of a theoretical nature but results also suggesting the practical importance of Non-Ideal Compressible Fluid Dynamics (NICFD) in general. The present talk addresses some of the challenges encountered in connection with the theoretical treatment of the associated flow behaviour. Weakly nonlinear acoustic waves of small but finite amplitude serve as a starting point. Here mixed rather than strictly positive nonlinearity generates a wealth of phenomena not possible in perfect gases. Examples of steady flows where these nonclassical effects play a decisive role (and which may be useful also for future experimental work) are quasi 1D nozzle flows and transonic 2D flows past corners. The investigation of dissipative effects reveals completely different mechanisms for the regularisation of shock discontinuities in unconfined and confined flows. As a final example of nonclassical phenomena in NICFD the problem of laminar boundary layers with constant pressure gradient will be considered. In contrast to the classical Howarth problem solutions do not necessarily terminate in the form of a Goldstein singularity but may be continued beyond the point of zero wall shear. The local flow behaviour then is governed by an equation of Fisher type which describes the transition from strictly steady to unsteady periodic flow exhibiting early signs of the onset of turbulence.Cavitation Instabilities in Turbopump Inducersby Prof. Seung Jin Song, Seoul National University, Korea: Turbopumps deliver liquid fuel and oxidizer into the main combustion chamber in liquid rocket engines and are usually composed of radial pumps driven by axial turbines. Turbopumps operate under extreme environments characterized by high speeds, high pressures, cryogenic temperatures, and steep temperature gradients. Therefore, turbopumps are the critical devices which determine the success of liquid rocket systems. To prevent cavitation in the pumps, turbopumps deploy inducers, and, yet, the inducers themselves undergo cavitation. This cavitation can have thermodynamic, hydrodynamic, and even rotordynamic consequences. This talk will present such issues which arise in turbopump development efforts.Industrial applications of turbomachinery operating on non-ideal fluidsby Dr. Douglas Hofer, General Electric Global Research, USA: 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.Wall bounded turbulence in flows with strong property gradientsby Prof. Rene Pecnik, Technical University of Delft, The Netherlands: 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.Scientific Committee of NICFD 2016Prof. Paola Cinnella, Arts et Métiers ParisTech ENSAM, FranceDr. Pietro Congedo, INRIA Bordeaux, FranceDr. Douglas Hofer, GE Global Research, USADr. Christos Markides, Imperial College London, United KingdomDr. Rene Pecnik, TU Delft, The NetherlandsDr. Steffen Schmidt, Technische Universiteit Munich, GermanyProf. Toru Shimada, JAXA, JapanDr. Andrea Spinelli, Politecnico di Milano, ItalyDr. Emile Touber, Imperial College London, United KingdomDr. Teemu Turunen-Saaresti, Lappeenranta University of Technology, FinlandProf. Rosaria Vetrano, Von Karman Institute, BelgiumReview StatementsEach paper accepted for publication underwent two rounds of review by two anonymous reviewers. The review process of each paper was managed by two members of the Scientific Committee. The first round of reviews took place before the conference. During the conference, each delegate had access to a web portal to input her/his review for each presented paper, in either an anonymous or named way. The second round of reviews took place after the conference and considered the opinion of the two anonymous reviewers as well as the delegates’. Final acceptance was decided by the two managing members of the Scientific Committee together with the Conference Chairman.

SU2: the Open-Source Software for Non-ideal Compressible Flows

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 thermodynamic 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 properties. Quantities of interest for turbomachinery cascades, as loss coefficients and flow angles, can be automatically determined and used for design optimization.A variety of test cases are carried out to assess the performance of the solver. At first, numerical methods are verified against analytical solution of reference NICFD test cases, including steady shock reflection and unsteady shock tube. Then, non-ideal gas effects in planar nozzles and 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.

Non-Ideal Compressible-Fluid Dynamics of Fast-Response Pressure Probes for Unsteady Flow Measurements in Turbomachinery

The dynamic response of pressure probes for unsteady flow measurements in turbomachinery is investigated numerically for fluids operating in non-ideal thermodynamic conditions, which are relevant for e.g. Organic Rankine Cycles (ORC) and super-critical CO2 applications. The step response of a fast-response pressure probe is investigated numerically in order to assess the expected time response when operating in the non-ideal fluid regime. Numerical simulations are carried out exploiting the Non-Ideal Compressible Fluid-Dynamics (NICFD) solver embedded in the open-source fluid dynamics code SU2. The computational framework is assessed against available experimental data for air in dilute conditions. Then, polytropic ideal gas (PIG), i.e. constant specific heats, and Peng-Robinson Stryjek-Vera (PRSV) models are applied to simulate the flow field within the probe operating with siloxane fluid octamethyltrisiloxane (MDM). The step responses are found to depend mainly on the speed of sound of the working fluid, indicating that molecular complexity plays a major role in determining the promptness of the measurement devices. According to the PRSV model, non-ideal effects can increase the step response time with respect to the acoustic theory predictions. The fundamental derivative of gas-dynamic is confirmed to be the driving parameter for evaluating non-ideal thermodynamic effects related to the dynamic calibration of fast-response aerodynamic pressure probes.

Non-Ideal Compressible Fluid Dynamics: A Challenge for Theory

The possibility that compression as well as rarefaction shocks may form in single phase vapours was envisaged first by Bethe (1942). However calculations based on the Van der Waals equation of state indicated that the latter type of shock is possible only if the specific heat at constant volume cv divided by the universal gas constant R is larger than about 17.5 which he considered too large to be satisfied by real fluids. This conclusion was contested by Thompson (1971) who showed that the type of shock capable of forming in arbitrary fluids is determined by the sign of the thermodynamic quantityto which he referred to as fundamental derivative of gas dynamics. Here v, p, s and c denote the specific volume, the pressure, the entropy and the speed of sound. Thompson and co-workers also showed that the required condition for the existence of rarefaction shocks, that Γ may take on negative values, is indeed satisfied for a number of hydrocarbon and fluorocarbon vapours. This finding spawned a burst of theoretical studies elaborating on the unusual and often counterintuitive behaviour of shocks with rarefaction shocks present. These produced both results of theoretical character but also results suggesting the practical importance of Non-Ideal Compressible Fluid Dynamics in general. The present paper addresses some of the challenges encountered in connection with the theoretical treatment of the associated flow behaviour. Weakly nonlinear acoustic waves of finite amplitude serve as a starting point. Here mixed rather than strictly positive nonlinearity generates a wealth of phenomena not possible in perfect gases. Examples of steady flows where these non-classical effects play a decisive role (and which may be useful also for future experimental work) are quasi one-dimensional nozzle flows and transonic two-dimensional flows past corners. The study of viscous effects concentrates on laminar flows of boundary layer type. Here non-classical phenomena are caused by the uncommon smallness of the Eckert number but also by the unconventional Mach number dependence on p in the external inviscid flow region.

Preliminary characterization of an expanding flow of siloxane vapor MDM

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 VApors (TROVA) at the CREA Laboratory of Politecnico di Milano. The TROVA test-rig was built 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 Rankine cycle where a planar converging-diverging nozzle replaces the turbine and represents a test section. Investigations related to both fields of non-ideal compressible-fluid dynamics fundamentals and turbomachinery are allowed. 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 thermodynamic regions where mild to medium 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.

The flexible asymmetric shock tube (FAST): a Ludwieg tube facility for wave propagation measurements in high-temperature vapours of organic fluids

This paper describes the commissioning of the flexible asymmetric shock tube (FAST), a novel Ludwieg tube-type facility designed and built at Delft University of Technology, together with the results of preliminary experiments. The FAST is conceived to measure the velocity of waves propagating in dense vapours of organic fluids, in the so-called non-ideal compressible fluid dynamics (NICFD) regime, and can operate at pressures and temperatures as high as 21 bar and 400 ?C, respectively. The set-up is equipped with a special fast-opening valve, separating the high-pressure charge tube from the low-pressure plenum. When the valve is opened, a wave propagates into the charge tube. The wave speed is measured using a time-of-flight technique employing four pressure transducers placed at known distances from each other. The first tests led to the following results: (1) the leakage rate of 5×10?4mbarl s?1 for subatmospheric and 5×10?2mbarl s?1 for a superatmospheric pressure is compatible with the purpose of the conceived experiments, (2) the process start-up time of the valve has been found to be between 2.1 and 9.0 ms, (3) preliminary rarefaction wave experiments in the dense vapour of siloxane D6 (dodecamethylcyclohexasiloxane, an organic fluid) were successfully accomplished up to temperatures of 300?C, and (4) a method for the estimation of the speed of sound from wave propagation experiments is proposed. Results are found to be within 2.1 % of accurate model predictions for various gases. The method is then applied to estimate the speed of sound of D6 in the NICFD regime.