Xavier Gloerfelt

This study presents the development of a tone noise model dedicated to an open-fan engine. The model is intended for implementation in microphone array techniques to better characterize the dominant sources in wind tunnel experiments and to segregate rotor and stator contributions. It is based on Goldstein’s formulation written in the frequency domain. A decomposition into angular modes through equivalent fixed phase-shifted sources is proposed. The predicted sound field takes into account different contributions investigated in this study: thickness noise, steady and unsteady loading noise (from rotor and stator) in advancing flight configurations, and near-field effects. The unsteady loading harmonics were obtained from unsteady aerodynamic computations. Initial predictions were compared with reference solutions from a time-domain solver at multiple operating points. A drastic reduction in the number of sources through compactness was investigated, with compactness forms adjusted to ensure acceptable discrepancies with previous reliable solutions. The selected compact source-mode propagation model was then used as a steering function in standard array processing tools. Finally, a preliminary validation of the array processing using a deconvolution algorithm and a numerically based cross-spectral matrix with correlated sources is presented.

High-fidelity numerical simulations based on wall-resolved large-eddy simulations (LESs) are used to investigate the vortex shedding dynamics in a linear turbine cascade. The profile geometry is the well-documented LS59 highly loaded rotor blade. The simulation campaign covered several outlet Mach numbers (subsonic and transonic) and several experimental configurations to shed light on the relations between vortex shedding frequency, the laminar or turbulent states of boundary layers, and the resulting cascade losses. A first major result concerned experiments for transonic outlet Mach number. LES without inlet turbulence and LES without tripping the suction-side boundary layer are unable to match the experimental flow field. In the untripped case, the recirculation bubble is shorter leading to a vortex shedding Strouhal number of 0.17, whereas in simulations with trip wire or inlet turbulence, the bubble was longer, with a Strouhal of 0.24. A second finding is that the inlet turbulence intensity is able to drive the switching between two regimes for subsonic outlet Mach numbers: the so-called detached vortex shedding (long bubble, St∼0.24) or a “transonic vortex shedding” (short bubble, St∼0.19). The appearance of shock waves and very coherent rolls in the wake for the “transonic” regime can lead to a doubling of the cascade losses due to the drastic pressure drop near the trailing edge. Such a change in the flow regime, due solely to an increase in freestream turbulence, has not been reported earlier.

This article presents a combined numerical and experimental study of the high-subsonic organic vapor flow in a linear turbine cascade. The profile geometry is the well-documented LS59 highly loaded rotor blade and the working fluid is Novec649, a dense gas used in organic Rankine cycles. Large eddy simulations are carried out with and without the roughness introduced by the additive manufacturing process. The results for the rough blade are in fair agreement with experiments, while the smooth surface induces a change in the vortex shedding regime. A detached shedding, characterized by a long recirculation downstream of the trailing edge and a base pressure plateau, is obtained in the experiments and by discretizing the roughness in the simulation. By contrast, a transonic vortex shedding is established when the surface is smooth: intense vortices roll up immediately after the trailing edge, yielding a short bubble and a lattice of shock waves. A strong pressure drop is observed at the trailing edge, resulting in high profile losses. In both cases, the boundary layer is turbulent ahead of the separation, but its thickness is significantly greater in the rough configuration, which may be the reason for the change of regime.

The dominant mode instability in hypersonic boundary-layer transition is the so-called second-mode instability, which has a peculiar nature strongly coupled with thermoacoustic phenomena. In linear stability theory, the unstable wave is associated with one of the two eigenvalues that originate from the acoustic branches, referred to as slow and fast modes. Interestingly, the unstable mode (slow or fast) reaches its maximum amplification as the other mode (fast or slow) attains a minimum. The phase velocity of the two modes is then very close, and this phenomenon is called synchronization. The aim of the present study is to unravel the physical mechanism that explains the second-mode growth. To that aim, second-order nonlinear equations are written for the disturbances given by linear stability. In this framework, entropy, kinetic energy and temperature energy budgets are obtained up to second order. The budgets are scrutinized for various Mach numbers and for adiabatic and cold-wall thermal conditions. Perturbation entropy budgets clearly show the process is a reversible one. An energy exchange between kinetic energy and temperature energy of the weakly nonlinear modes is driven by pressure–dilatation terms. As underlined in previous studies, the unstable mode experiences an alternate heating and cooling near the wall, which is shown to be a rather nonlinear process. The change in fluctuating thermal energy in the form of a dilatational wave is sustained by pumping disturbance kinetic energy through the pressure–dilatation term, the direction of the conversion being driven by the relative phase between pressure and dilatation. This process is similar for the slow and fast modes, the unstable mode being amplified and the other being damped. No change in the process has been noted at the location of the synchronization, suggesting that the modes have the same nature but evolve independently.