Experimental observation of supersonic non-ideal compressible-fluid flows

The branch of fluid mechanics devoted to the study of compressible flows whose behaviour deviates from the one predicted by the ideal-gas model is termed Non-Ideal Compressible-Fluid Dynamics (NICFD). Departure from ideal behaviour is typically observed in fluids made of complex molecules, operating in thermodynamic conditions close to the liquid-vapour saturation curve and critical point. Differently from the ideal-gas case, non-ideal flow dynamics is strongly influenced by the process conditions, and peculiar flow patterns such as rarefaction shock waves, shock waves with either upstream or downstream sonic states, and split shocks are physically admissible. Complex thermodynamic models were devised and applied to the theoretical analysis and numerical simulation of non-ideal flows. However, only few experimental data in the NICFD regime were available up to date. In the present thesis, experimental benchmark tests are devised and measurements are performed to provide assessment to NICFD theory, thermodynamic models and numerical simulation tools. Experiments are carried out in the Test Rig for Organic VApors (TROVA), the blow-down wind tunnel of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREALab) of Politecnico di Milano, while numerical simulations are performed using the open-source NICFD solver SU2. Two main flow configurations are considered, namely adapted flows in planar converging-diverging nozzles and uniform supersonic flows with oblique shock waves and expansion fans. An experimental campaign is carried out to study the NICFD flow of siloxane vapour MDM (octamethyltrisiloxane, C8H24O2Si3) in a planar converging-diverging nozzle. The nozzle is designed using the method of characteristics, complemented with state-of-the-art Equations of State (EoS) dealing with non-ideal flow behaviour. Operation of the nozzle is characterised through pressure and temperature measurements, schlieren visualizations, and numerical simulations. Numerical simulations and theoretical predictions based on the isentropic hypothesis for nozzle expansions agree well with experimental data. Consistently with NICFD theory, reservoir conditions are found to significantly influence both the pressure ratio and the Mach number distribution along the nozzle axis. Numerical simulations and the NICFD theory are then extensively applied to the study of supersonic expansions in converging-diverging nozzles, both in the ideal and NICF regimes. Two different topics related to the design and operation of converging-diverging nozzles are addressed. First, a design solution aimed at fixing the location of the minimum-area section of the nozzle is discussed. The geometry of planar converging-diverging nozzles operating with air and MDM is modified by the introduction of a small recessed step at the geometrical throat. The recessed step triggers boundary layer separation and fixes the location of the minimum-area section of the nozzle. Experiments and numerical simulations are applied to the analysis of the adapted flow. A complex perturbation wave pattern originates at the step location, and propagates up to the exhaust section of the nozzle through multiple reflections at the nozzle walls and interactions at the nozzle symmetry axis. Pressure measurements performed along the nozzle axis show that the perturbation introduced by the step influences the flow only locally. For the nozzle operating with MDM in the NICFD regime, the configuration of the perturbation wave pattern in the throat region is found to depend on reservoir conditions. Second, a key parameter for the design and performance analysis of supersonic nozzles is investigated, namely the discharged massflow rate. A closed-form expression for this parameter is derived analytically. The massflow rate is found to be dependent on the radius of curvature of the nozzle profile at the throat section, on the molecular complexity of the working fluid, and on process conditions. A numerical verification of the dependence of the discharged massflow rate on relevant design parameters is performed, both in the ideal and non-ideal flow regimes. The dependence of the massflow rate on the fluid properties and on process conditions is confirmed. Moreover, the discharged massflow rate is found to be affected by the overall shape of the converging portion, and not only by the local curvature of the nozzle profile at the throat section. This is true even in the case of smooth convergents. A second experimental campaign is carried out to characterize oblique shock waves and expansion fans occurring in the NICFD regime. A diamond-shaped airfoil with semi-aperture 7.5° at leading edge and 10° at the trailing edge is placed in a uniform supersonic stream of MDM, which in test conditions is a single-phase vapour lying in the NICFD region. Two oblique shocks at the airfoil leading-edge and centered expansion fans at the shoulder are observed. Oblique shock waves and expansion fans are studied at varying upstream stagnation conditions, for six deviation angles in the range 6.5°-10° obtained by changing the attitude of the model with respect to the wind tunnel axis. Experimental results are assessed against the inviscid shock-expansion theory for two-dimensional steady flows, complemented with state-of-the-art EoS. All the geometrical configurations and operating conditions explored in wind-tunnel tests are reproduced numerically. In the inviscid core of the flow, where measurements are performed, numerical results agree fairly well with experimental data. A significant dependence of the pre-shock, post-shock and post-expansion states on the corresponding upstream flow conditions is found, and the speed of sound is seen to decrease across shock waves and increase upon expansion fans, consistently with the NICFD theory applied to the tested thermodynamic conditions.