Shock-Boundary Layer Interactions in Supersonic Turbine Cascades

Abstract

The physics of shock-boundary layer interactions in a supersonic turbine cascade is investigated through a wall-resolved large eddy simulation. Special attention is given to the characterization of the low-frequency dynamics of the separation bubbles using flow visualization, spectral analysis, space-time cross correlations, and flow modal decomposition. The mean flowfield shows different shock structures formed on both sides of the airfoil. On the suction side, an oblique shock impinges on the turbulent boundary layer, whereas a Mach reflection interacts with the pressure side boundary layer. Instantaneous flow visualizations illustrate elongated streamwise structures on the incoming boundary layers and their interactions with the shocks and separation bubbles. The passage of high-speed (low-speed) streaks through the recirculation bubbles leads to the downstream (upstream) motion of the separation point on both suction and pressure sides, resulting in spanwise modulation of the bubbles. Space-time cross-correlations reveal that the near-wall streaks drive the suction side separation bubble motion, which in turn promotes the oscillations of the reattachment shock and shear layer flapping. Space-time correlations also indicate the existence of a π phase jump in the pressure fluctuations along the separation bubble on the suction side.After this phase jump, a downstream propagating pressure disturbance is observed, while prior to this point, the pressure disturbances dominantly propagate in the upstream direction. Finally, the organized motions in the shock-boundary layer interactions and their corresponding characteristic frequencies are identified using proper orthogonal decomposition. I. INTRODUCTIONSupersonic fluid machinery offers size and cost reduction in high-speed propulsion and power generation systems [1, 2] and for compact hydrocarbon cracking [3]. The detailed analysis of supersonic turbines is challenging predominantly due to the shock-boundary layer interactions (SBLIs) which arise when the detached oblique shock waves forming at the stator/rotor leading edges impinge on the boundary layers of the neighboring airfoils. The shocks impose intense adverse pressure gradients on the boundary layers that may cause flow separation. This, in turn, leads to the formation of separation and reattachment shocks that *

Comparison of Shock-Boundary Layer Interactions in Adiabatic and Isothermal Supersonic Turbine Cascades

“…Here, an unsteady actuation with a random spanwise treatment is assumed and the amplitude of the disturbances are chosen experimentally in order to guarantee a bypass transition with minimal flow disturbance. More details of the numerical procedure can be found in [5].…”

“…The ratio of specific heats is chosen as 𝛾 = 1.31, the Prandlt number is 𝑃𝑟 = 0.747 and the ratio of the Sutherland constant over inlet temperature is set as 𝑆 𝜇 /𝑇 ∞ = 0.07182. These conditions are chosen based on previous studies [4,5,18]. Therefore, the grid has approximately 68, 000, 000 points.…”

“…They can also be a source of flow unsteadiness, where multiple frequencies are excited due to motion of the incident and reflected shock waves, breathing of the separation bubble, besides the incoming turbulent boundary layer. Typically, the shock wave motion leads to strong pressure fluctuations that can compromise the system's structural integrity [2][3][4][5].…”