Estimates of turbulence modeling uncertainties in NACA65 cascade flow predictions by Bayesian model-scenario averaging

Abstract

Purpose The Reynolds-averaged Navier–Stokes (RANS) equations represent the computational workhorse for engineering design, despite their numerous flaws. Improving and quantifying the uncertainties associated with RANS models is particularly critical in view of the analysis and optimization of complex turbomachinery flows. Design/methodology/approach First, an efficient strategy is introduced for calibrating turbulence model coefficients from high-fidelity data. The results are highly sensitive to the flow configuration (called a calibration scenario) used to inform the coefficients. Second, the bias introduced by the choice of a specific turbulence model is reduced by constructing a mixture model by means of Bayesian model-scenario averaging (BMSA). The BMSA model makes predictions of flows not included in the calibration scenarios as a probability-weighted average of a set of competing turbulence models, each supplemented with multiple sets of closure coefficients inferred from alternative calibration scenarios. Findings Different choices for the scenario probabilities are assessed for the prediction of the NACA65 V103 cascade at off-design conditions. In all cases, BMSA improves the solution accuracy with respect to the baseline turbulence models, and the estimated uncertainty intervals encompass reasonably well the reference data. The BMSA results were found to be little sensitive to the user-defined scenario-weighting criterion, both in terms of average prediction and of estimated confidence intervals. Originality/value A delicate step in the BMSA is the selection of suitable scenario-weighting criteria, i.e. suitable prior probability mass functions (PMFs) for the calibration scenarios. The role of such PMFs is to assign higher probability to calibration scenarios more likely to provide an accurate estimate of model coefficients for the new flow. In this paper, three mixture models are constructed, based on alternative choices of the scenario probabilities. The authors then compare the capabilities of three different criteria.

Space-dependent turbulence model aggregation using machine learning

“…Ratio of total Reynolds stresses to normal Reynolds stresses linear compressor cascade, widely studied in the literature [52,53,54,55,56] and already used as a test case in our previous works [18,19]. The cascade is representative of the mid-span section of a stator blade in a highly loaded axial compressor [52].…”

“…More recently, [10] explored a Bayesian framework, namely, Bayesian Model-Scenario Averaging (BMSA), to calibrate and combine the predictions obtained from a set of competing baseline LEVM models calibrated on various data sets (scenarios). BMSA has been successfully applied to provide stochastic predictions for a variety of flows, including 3D wings [17] and compressor cascades [18,19].…”