Experimental observation of oblique shock waves in steady non-ideal flows

Abstract

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.

Numerical Investigation of High-Speed Turbulent Boundary Layers of Dense Gases

“…Although a number of numerical studies have investigated in the past dense gas dynamics, most of them are based on simplified models neglecting viscous effects (potential flow or Euler equations) or relying on the Reynolds-Averaged Navier-Stokes equations supplemented with a standard turbulence model (i.e., without any specific calibration or compressibility correction for dense gases). On the other hand, experimental investigations of dense gas flows are particularly difficult and costly, and only very recently some local experimental measurements of pressure and temperature at selected stations in a dense-gas nozzle have been made available (Spinelli et al 2018), as well as Schlieren photographs (Zocca et al 2019). Unfortunately, to the authors' best knowledge, no velocity or Reynolds-stress measurements of turbulent dense gas flows have been obtained yet, and the fine details of transitional and turbulent dense gas flows remain largely unknown.…”

Direct velocity measurements in high-temperature non-ideal vapor flows

“…However, the pressure field can be measured for isentropic flows as the total pressure is conserved and the static pressure is measured through wall pressure taps. This is for instance the case of nozzle flows and uniform flows before/past oblique shocks and expansion fans, where the non-ideal pressure field was successfully measured by the authors in previous experimental campaigns (Spinelli et al 2018;Zocca et al 2019). As it is well known, the velocity field can be inferred from pressure and temperature field, by resorting to the thermodynamic model of the fluid.…”

“…The schlieren technique (Spinelli et al 2016(Spinelli et al , 2017Zocca et al 2018Zocca et al , 2019 is of relatively simple application in hightemperature non-ideal flows, but it is essentially qualitative, even though it can be exploited to measure the local Mach number, from Mach lines, and shock wave/expansion fan geometry (position, slope) (Cammi et al 2021). However, this method can be used only in supersonic flows and with limited accuracy; moreover, to retrieve the velocity field from the Mach number one requires the application of the thermodynamic model, and thus the knowledge of at least two thermodynamic properties at the measuring point.…”

A Review of Some Recent Advancements in Non-Ideal Compressible Fluid Dynamics

“…The experimental verification of the occurrence of non-ideal shock waves can be devised in test rigs working with fluids of high or even moderate molecular complexity. In [50,49], steady oblique shock waves were observed for the first time in non-ideal supersonic flows of single-phase organic vapors. Oblique shock waves were observed and characterized experimentally at varying stagnation conditions in the pre-shock state, for a set of different flow deviation angles.…”