Purpose This paper aims to investigate global pressure fluctuations in compressible transitional flows in a low-pressure turbine cascade because of variations in the free-stream turbulence and its interaction with the boundary layers. Design/methodology/approach Transition process resolving numerical simulations are performed with different types of inflow turbulence. The unsteady three-dimensional fully compressible Navier–Stokes equations are solved using a sixth-order compact difference and a tenth-order filtering method. First, simulations of both K-regime and bypass transitions are conducted for a flat plate boundary layer to validate the use of the filter in computing different transition routes. Second, computations of the cascade flows are conducted. Cases of no free-stream turbulence, isotropic free-stream turbulence of 5 per cent and wakes from an upstream cylinder are compared. For wakes, variations in wake trajectory depending on the cylinder blade relative position are also taken into account. Findings The different transition routes are successfully reproduced by the present method even with strong filtering. When feedback phenomena occur near the trailing edge, high-frequency oscillations dominate in the flow field. Low-frequency oscillations become dominant when the blade boundary layer becomes turbulent. Thus, the effects of the free-stream turbulence and its interaction with the boundary layer appear as changes in the global pressure fluctuation. Originality/value The free-stream turbulence qualitatively affects global pressure fluctuations, which become a medium to convey boundary-layer information away from the cascade.

This study focuses on the calibration of Spalart--Allmaras turbulence model parameters using the Bayesian inference approach to reproduce experimental measurements of corner flow separation in linear compressor cascade. The quantity of interest selected for the calibration process is the pitchwise distribution of Mach number in the wake of the linear compressor cascade. The model parameters are assumed to be random variables obeying uniform prior probability distributions. Sensitivity analysis is used to rank the importance and select the most influential turbulence model parameters for the calibration process. The sensitivity ranking indicates that two model parameters cb1 and kappa are the most influential random variables resulting in a two--parameter Bayesian calibration process. The likelihood distribution is specified in the form of the Gauss distribution to include the experimental uncertainty. The likelihood distribution is used together with prior distribution to compute posterior probabilities of selected model parameters. The polynomial chaos expansion is employed as a surrogate model to reduce the cost of posterior calculation. Numerical simulations with calibrated turbulence parameters show a significant increase in the accuracy of Mach number profile prediction for separated flows in linear compressor cascade. Numerical simulations also demonstrate that the calibrated set of model coefficients produce accurate predictions of the total pressure and Mach number profiles for the range of incidence angles that were not part of the calibration process.

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Compressor performance prediction is still one of the significant interests in the turbomachinery research field. The two critical parameters for compressor design are adiabatic efficiency and stability margin. The Spalart-Allmaras (SA) turbulence model and modified SA models are widely used in that design process. However, the prediction accuracy is not always satisfactory. In most cases, the SA model predicts larger stall mass flow, and the RC-QCR SA model underestimates efficiency. This study proposes a new combination of the modified SA model (R-H-QCR model). R-H-QCR stands for Rotation-Helicity-Quadratic constitutive relation. The model increases or decreases turbulent viscosity based on flow rotation, energy backscatter, and anisotropy of turbulence flow field. The Bayesian inference framework calibrates the model parameters to predict accurately both efficiency and stability in the 3.5 stage compressor. The R-H-QCR, RC-QCR, and default SA models are evaluated in the multi-stage compressor. For the performance prediction, the R-H-QCR model predicts a better stability margin than the SA model and better efficiency than the RC-QCR model. In addition, the spanwise distribution of normalized total pressure is well captured by the R-H-QCR model, indicating that the R-H-QCR model improves flow field prediction.

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