The Bayesian uncertainty quantification technique has become well-established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accura...

Discrete roughness-induced transition in Mach flow controlled by two-dimensional wall blowing is studied using direct numerical simulation. Spectral analysis and flow freezing operations reveal that the main source of unsteadiness in the case without blowing is the separated shear layer/counter-rotating vortex system: the shear layer is bent by the vortex pair, and this interaction induces disturbance growth at the shear layer. With the existence of weak wall blowing, the transition is delayed. Flow visualization demonstrates that upstream-positioned blowing achieves this by lifting the inflow boundary layer and decreasing the roughness Reynolds number. In contrast, downstream-positioned blowing takes effect by weakening the counter-rotating vortex pair and inhibiting the interaction. Vorticity transportation analysis suggests that this result is accomplished by increasing dissipation for streamwise vorticity and converting some of it into spanwise vorticity. In cases with strong wall blowing, the control effect is reversed, as wall blowing with enough strength can induce unsteadiness and promote transition. In upstream-positioned strong blowing cases, a new unstable mode is observed in spectral results throughout the near-roughness region, and further analysis indicates that this mode originating from the separation zone upstream of the blowing is the key factor for transition. With regard to downstream-positioned strong blowing cases, a very low-frequency mode is generated from the separation bubble between the roughness element and the blowing, but it only provides an initial disturbance for the transition process. The transition that occurs downstream is due to the distortion of the boundary layer in the wake.

The classical four-equation γ-Re transition model has presented excellent accuracy in low-speed boundary layer transition prediction. However, once the incoming flow reaches hypersonic speed, the original model is no longer applicable due to the compressibility problem and the appearance of multiple instability modes. Recently, there has been widespread interest in data-driven modeling for quantifying uncertainty or improving model prediction accuracy. In this paper, a data-driven framework based on field inversion and machine learning is performed to extend the prediction capability of the original γ-Re transition model for the hypersonic boundary layer transition.First, the iterative regularized ensemble Kalman filter method is applied to obtain the spatial distribution of the perturbation correction term β for the switching function F_onset1, and the effectiveness of this method is initially verified in the hypersonic flat plate case. Then, the random forest algorithm is adopted to construct a mapping from the average flow features to β. The generalizability of the well-trained learning model is fully validated in the blunt cone cases with different unit Reynolds numbers, free-stream flow temperature, and bluntness. The simulation results indicate that the performance of the original γ-Re transition model in the hypersonic boundary layer transition prediction is significantly improved, and the boundary layer transition onset location and the length of transition zone can be correctly obtained. In addition, the machine learning model investigates the importance of the input features and confirms that the effective length scale plays a significant role in the numerical simulation of the hypersonic boundary layer transition.

Shock wave-boundary layer interactions (SWBLIs) have a tremendous influence on the performance of hypersonic vehicles. For the numerical simulation of such engineering flows, Reynolds averaged Navier-Stokes (RANS) still occupies an irreplaceable role. However, parameters of turbulence models in RANS have substantial uncertainties, which impact the reliability of simulation results. Thus, the aim of the present study is to conduct an uncertainty analysis on parameters in the shear-stress transport (SST) turbulence model for the simulation of SWBLIs. In the current work, uncertainty quantification was performed first. A surrogate model was constructed by the non-intrusive polynomial chaos (NIPC) method to propagate uncertainties from model parameters to the quantities of interests (QoIs) and quantify them. In the subsequent sensitivity analysis, the key parameters were identified for such flow by calculating the Sobol index of each parameter for various QoIs. The results indicate that uncertainties of model parameters led to non-negligible uncertainties in those QoIs, particularly in skin friction and wall heat flux. The parameters α₁, σ_ω1, β₁ were identified as primary contributors through the sensitivity analysis. Moreover, the specific effects of the three parameters on the flow prediction were analyzed by changing the parameters’ values separately.