A novel test setup called the asymmetric shock tube for experiments on nonideal rarefaction waves (ASTER) has been commissioned at Delft University of Technology. The ASTER, which works according to the principle of Ludwieg tubes, is designed to generate and measure the speed of small and finite amplitude waves propagating in the dense vapors of fluids formed by complex organic molecules, therefore in the nonideal compressible fluid dynamics regime. The ultimate goal of the associated research is to prove the existence of nonclassical gasdynamics. The setup consists of a high-pressure charge tube and a vacuum tank separated by a glass disk equipped with a breaking mechanism for rarefaction waves experiments. When the glass disk is broken, an expansion wave propagates into the tube in the direction opposite to the fluid flow. The propagation speed of this wave is measured using a time-of-flight method with the help of four fast-response pressure sensors placed equidistantly in the middle of the tube. The charge tube can withstand pressures and temperatures of up to 15 bar and 400∘C. Preliminary rarefaction experiments were successfully conducted using dodecamethylcyclohexasiloxane, D₆, as the working fluid and at pressures and temperatures of up to 9.4 bar and 372∘C, respectively. The results of an experiment featuring the initial state for which a theoretical model predicts the nonclassical acceleration of rarefaction waves show that the propagation is qualitatively different from that put into evidence by experiments for which the propagation is classic. Upcoming setup improvements and experimental campaigns are planned with the objective of experimentally verifying the existence of nonclassical gasdynamics. Graphical abstract: (Figure presented.)

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The study of compressible fluid dynamics has traditionally focused on flows of gases whose thermodynamic properties are related according to the ideal-gas law. In this context, for a long time, it has been demonstrated that shock waves in gases are exclusively of the compressive type, characterized by a discontinuity across which the fluid pressure rapidly increases. However, in the 1940s, world-renowned scientists such as Bethe and Zel’dovich put forth the theoretical possibility of the formation of rarefaction shock waves (RSWs) if the fluid is a high molecular complexity compound and its thermodynamic state is that of a dense vapour. Across such a RSW, the flow experiences an abrupt drop in pressure. The theoretical concept of RSWs became more known and gained widespread acceptance when further investigations were conducted in the 1970s by Thompson and his colleagues. They introduced the fundamental derivative of gasdynamics Γ, the caloric fluid property that determines the nature of shock waves that can occur in a flow depending on the molecular complexity of the fluid and its thermodynamic state. To acknowledge the significant contributions of the aforementioned scientists to this field of fluid mechanics, fluids that possess the unique characteristic of theoretically admitting RSWs due to the occurrence of thermodynamic states featuring Γ < 0 in the dense-vapour phase are referred to as BZT fluids. The branch of fluid dynamics dealing with fluid flows that might display characteristics that are radically different or even opposite to those of classical gas dynamics is aptly called nonclassical gasdynamics. Despite extensive theoretical knowledge of nonclassical gas dynamics, which includes rarefaction shock waves (RSWs), there is still a lack of compelling experimental evidence supporting their existence. The motivation for the research documented in this dissertation is two-fold: firstly, it is crucial to conduct experiments that can provide empirical validation of nonclassical gas dynamics, with a specific focus on observing RSWs, which have proven elusive in previous attempts. Secondly, performing accurate measurements of fluid properties in the dense-vapour thermodynamic regime has the potential to improve the thermodynamic models of BZT fluids or fluids made of complex organic molecules in general. This in turn can contribute to a more accurate characterisation of flows in practical applications that involve these fluids, such as turbine flows in Organic Rankine Cycle (ORC) systems or compressors in high temperature heat pumps. This research work aimed to provide conclusive experimental evidence for the existence of nonclassical expansion shock waves in the flows of a candidate BZT fluid, siloxane D6. For this purpose, two novel test facilities namely the Asymmetric Shock Tube for Experiments on Rarefaction Waves (ASTER) and the Organic Vapour Acoustic Resonator (OVAR) have been conceived, developed, designed, built and commissioned at TU Delft. Relevant theoretical studies were performed to complement the experimental observation of nonclassical effects. Novel measurements of fluid properties in the nonclassical gasdynamic region of the candidate BZT fluid were executed, the outcomes of which are useful for the improvement and the optimisation of thermodynamic models for this fluid. @en

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

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This paper describes the design, functioning, and preliminary experiments in the Asymmetric Shock Tube for Experiments on Rarefaction Waves (ASTER), a Ludwieg-type shock tube designed and realised to measure waves propagating in dense vapour flows of organic fluids. The setup is designed to operate at pressures and temperatures of up to 15 bar and 400^∘ C. The high and low-pressure sections of the tube are separated by a glass-disk barrier to ensure quasi-instantaneous opening. When the glass disk is broken, a rarefaction wave propagates into the tube. The wave speed is measured using a time-of-flight method with the help of four pressure transducers placed at known distances from each other. Leakage rates of 2.2 × 10^{- 4} mbar · l · s^{- 1} at vacuum and 5 × 10^{- 4} mbar · l · s^{- 1} at superatmospheric pressures were measured, which is considered sufficient for the conceived experiments. Preliminary rarefaction experiments in the dense vapours of dodecamethylcyclohexasiloxane, D₆, were successfully performed at various thermodynamic conditions. Also, a method for the estimation of sound speeds from the pressure sensor recordings is proposed. Results are found to be within 2.5% of the values predicted by the state-of-the-art thermodynamic model for D₆.

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

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

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

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