Investigation of non-ideal gas flows around a circular cylinder Camille Matar a , Paola Cinnella a , Xavier Gloerfelt b , Felix Reinker c , Stefan aus der Wiesche c a Sorbonne Universit´e, Institut Jean Le Rond d’Alembert, Paris, France b Arts et M´etiers Institute of Technology, Laboratoire DynFluid, Paris, France c FH M¨ unster, Department of Mechanical Engineering, Steinfurt, Germany Abstract The aerodynamic performance of a cylinder Pitot probe for velocity measurements in compressible non-ideal gas flows, such as those encountered in Organic Rankine Cycle (ORC) turbines, is investigated by means of Computational Fluid Dynamics. Numerical simulations are performed at subsonic and transonic conditions, and freestream Reynolds numbers are in the cylinder critical regime. The working fluid is the organic vapor Novec™649. Air flow simulations at similar inlet conditions are reported for comparison. Steady and unsteady RANS solutions are computed with the Spalart-Allmaras turbulence model. The results are assessed against experimental measurements collected in a wind tunnel. URANS is in good agreement with experimental data for all considered conditions, and delivers reasonably accurate estimations of the cylinder back pressure. Using a dense gas leads to a lower minimum pressure coefficient compared to air, alongside a reduced maximum Mach number due to the non-ideal speed of sound behaviour. In the experimentally studied range of compressibility factors and Mach numbers, discrepancies observed with respect to air flow are mostly an effect of the different isentropic exponents. In the transonic regime, shock waves causing boundary layer separation are weakened in the dense gas, but back pressure is also decreased, contributing to rising form drag. Keywords: Non-ideal gas, transonic, cylinder, Pitot probe, RANS 1. Introduction In recent years, the study of dense-gas dynamics has received increased attention, due to manifold applications in Engineering. One of the most important ones is the design of improved turbine expanders for Organic Rankine Cycle (ORC) power plants [1, 2]. On the one hand, such components work in the transonic to supersonic flow regimes, due to high pressure ratios and generally low speed of sound of the working fluid. This may lead to strong compressibility effects resulting in process efficiency losses. On the other hand, the flow can be optimized to reduce these losses, as well as the choice of working fluid. Dense- gas are molecularly complex and the energy associated with the rotation, vibration or collision between molecules cannot be neglected, unlike air even at typical Rankine cycle machine operating conditions. This in turn increases their density to typically one order of magnitude higher than that of a calorically and thermally perfect gas (PFG). Dense-gas dynamics can be described by using the fundamental derivative of gas dynamics [3]: Γ:“ v 3 2c 2 B 2 p Bv 2     s “ 1 ` ρ c Bc Bρ     s (1) which indicates how the speed of sound c “ a pBp{Bρq s varies with density ρ “ 1{v through isentropic processes, where v is the specific volume, p is the pressure and s is the entropy. Close to the saturation curve, a region where Γ ă 1 may exist, which implies that the rate of change of speed of sound with respect to density, pBc{Bρq s , is negative. Therefore, c drops through compressions and grows through expansions. This in turn lowers the local Mach number, hence reducing the probability of shock wave formation, as well as their strength. It is clear that ORC machines can benefit from this behaviour [4]. Note that for a PFG, expression (1) reduces to Γ “pγ ` 1q{2, where γ “ c p {c v is the specific heat capacity ratio. This implies that Preprint submitted to Energy November 8, 2022