The influence of turbulence inflow generation on direct numerical simulations (DNS) of high-speed turbulent boundary layers at Mach numbers of 2 and 5.84 is investigated. Two main classes of inflow conditions are considered, based on the recycling/rescaling (RR) and the digital filtering (DF) approach, along with suitably modified versions. A series of DNS using very long streamwise domains is first carried out to provide reliable data for the subsequent investigation. A set of diagnostic parameters is then selected to verify achievement of an equilibrium state, and correlation laws for those quantities are obtained based on benchmark cases. Simulations using shorter domains, with extent comparable with that used in the current literature, are then carried out and compared with the benchmark data. Significant deviations from equilibrium conditions are found, to a different extent for the various flow properties, and depending on the inflow turbulence seeding. We find that the RR method yields superior performance in the evaluation of the inner-scaled wall pressure fluctuations and the turbulent shear stress. DF methods instead yield quicker adjustment and better accuracy in the prediction of wall friction and of the streamwise Reynolds stress in supersonic cases. Unrealistically high values of the wall pressure variance are obtained by the baseline DF method, while the proposed DF alternatives recover a closer agreement with respect to the benchmark. The hypersonic test case highlights that similar distribution of wall friction and heat transfer are obtained by both RR and DF baseline methods.
Graphical abstract
The combustion noise in aero-engines is known to originate from two different sources. First, the unsteady heat release in the combustion chamber generates the direct combustion noise. Second, hot and cold spots of air generated by the combustion process are convected and accelerated by the turbine stages and give rise to the so-called indirect combustion noise. The present work targets, by using a numerical approach, the generation mechanism of indirect combustion noise for a simplified geometry of a turbine stator passage. Periodic temperature fluctuations are imposed at the inlet, permitting to simulate hot and cold packets of air coming from the unsteady combustion. Three-dimensional Large Eddy Simulation (LES) calculations are conducted for transonic operating conditions to evaluate the blade acoustic response to the forced temperature perturbations at the inlet plane. Transonic conditions are characterized by trailing edge expansion waves and shocks. It is notably shown that their movement can be excited if disturbances with a particular frequency are injected in the domain.
We derive a scaling law for the characteristic frequencies of wall pressure fluctuations in swept shock wave/turbulent boundary layer interactions in the presence of cylindrical symmetry, based on analysis of a direct numerical simulations database. Direct numerical simulations in large domains show evidence of spanwise rippling of the separation line, with typical wavelength proportional to separation bubble size. Pressure disturbances around the separation line are shown to be convected at a phase speed proportional to the cross-flow velocity. This information is leveraged to derive a simple model for low-frequency unsteadiness, which extends previous two-dimensional models (Piponniau et al., J. Fluid Mech., vol. 629, 2009, pp. 87–108), and which correctly predicts growth of the typical frequency with the sweep angle. Inferences regarding the typical frequencies in more general swept shock wave/turbulent boundary layer interactions are also discussed.
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