Supersonic expansions of a molecularly complex vapor occurring within the non-ideal thermodynamic region in the close proximity of liquid-vapor saturation curve were characterized experimentally for the first time. Results for two planar converging-diverging nozzles in the adapted regime and at different inlet conditions, from highly non-ideal to dilute gas state, are reported. Measurements of upstream total pressure and temperature are performed in the plenum ahead of the nozzle, while static pressure and supersonic Mach number measurements are carried out along the nozzle centerline. The investigated expansions are of interest for both fundamental research on non-ideal compressible flows and industrial applications, especially in the energy field. Siloxane MDM (octamethyltrisiloxane, C 8 H 24 O 2 Si 3), a high molecular complexity organic compound, is used. Local pressure ratio P∕P T and Mach number M measurements display a dependence on the inlet total state, a typical non-ideal feature different from dilute gas conditions.
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
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Steady oblique shock waves are observed for the first time in non-ideal supersonic flows of single-phase organic vapors. A diamond-shaped airfoil with semi-aperture 7.5 • at the leading edge and 10 • at the trailing edge is placed within a uniform supersonic stream (Mach number M = 1.5) of siloxane fluid MDM (octamethyltrisiloxane, C 8 H 24 O 2 Si 3). Oblique shock waves are observed at varying stagnation conditions in the pre-shock state, for a set of flow deviation angles obtained by changing the attitude of the model with respect to the wind tunnel axis. Stagnation temperatures and pressures reduced by critical values range from 0.928 to 0.979 and from 0.200 to 0.615, respectively. Oblique shock waves are characterized through independent measurements of pressure, temperature and Mach number. Stagnation pressure and temperature are measured in the wind-tunnel settling chamber, while the pre-shock, post-shock and post-expansion static pressures are measured at selected locations close to the airfoil. Direct measurement of the flow Mach number is provided by schlieren visualizations. Experimental results agree with the shock wave theory for two-dimensional steady flows, complemented with state-of-the-art thermodynamic models, and deviate from their well-known, dilute-gas predictions. In particular, measurements show the non-ideal dependence of the pressure ratio across the shock on stagnation conditions in addition to the well-known dependence on the pre-shock Mach number, specific heat ratio and flow deviation angle typical of dilute gas conditions.
Extensive experimental results characterizing the supersonic expansion of an organic vapor in non-ideal conditions are reported in this paper for the first time. The collected data also allowed the assessment of the accuracy of Computational Fluid Dynamic (CFD) tools employed to predict the non-ideal behavior of such flows, including the consistency of thermodynamic models adopted. The investigation has been carried out on the converging-diverging nozzle test section of the Test Rig for Organic VApors (TROVA), at the Laboratory of Compressible fluid-dynamics for Renewable Energy Application (CREA) of Politecnico di Milano. Supersonic nozzle flow was chosen as the simplest one of significance for organic Rankine cycle (ORC) turbine channels. The working fluid under scrutiny is Siloxane MDM, a widely employed compound for high temperature ORCs. MDM vapor expands through the TROVA nozzle at moderate non-ideal conditions in the close proximity of the vapor saturation curve. This is the region where ORC expanders typically operate, thus proving the relevance of the investigation for the ORC community. Indeed, detailed experimental data representative of typical ORC expansions were lacking in the open literature up to date. Two different nozzle geometries, featuring exit Mach number of 2.0 and 1.5 respectively, were tested, exploring a wide range of thermodynamic inlet conditions and diverse levels of non-ideality, from moderate non-ideal state, indicated by a compressibility factor Z = Pv/RT â\u89\u830.80, to dilute gas conditions, Z â\u89¥ 0.97. Maximum operating total pressure and temperature are Pt â\u89\u835 bar and TT â\u89\u83250°C. The nozzle flow is characterized in terms of total pressure, total temperature, static pressure at discrete locations along the nozzle axis, and schlieren imaging. In contrast to the well known case of polytropic ideal gas, the vapor expansion through the nozzle is found to be dependent on the inlet conditions, thus proving the non-ideal character of the flow. This influence is found to be consistent with the one predicted by the quasi-1D theory coupled with simple non-ideal gas models. Experimental data at the nozzle centerline are compared with those resulting from a two-dimensional viscous CFD calculation carried out using the SU2 software suite and the improved Peng Robinson Stryjek Vera (iPRSV) thermodynamic model. A very good accordance is found, demonstrating the high accuracy of the applied tools
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