Integration of axial velocity-density ratio effects in DNS of a high-speed low-pressure turbine Département A&M (Université de Liège)

Abstract

A high-fidelity numerical study used a high-order discontinuous Galerkin method to examine transonic aerodynamics and streamtube contraction effects of the linear SPLEEN low-pressure turbine cascade. Separation, boundary layer development, and aerodynamic losses were investigated at Mach 0.7, 0.9, and 0.95, under low-Reynolds transitional flow conditions without inlet turbulence. The primary objective was to integrate a computationally efficient quasi-3D Axial Velocity Density Ratio (AVDR) model and validate the spanwise domain by comparing periodic and symmetric boundary conditions against a baseline parallel-wall configuration.

The comparison between periodic and symmetric spanwise boundary conditions for the baseline configuration (AVDR = 1.0) shows remarkably small absolute discrepancies across all operating points. The flow does not develop significant spanwise structures, resulting in negligible spanwise velocity components. However, the symmetry condition enforces a rigid zero-normal-velocity constraint, introducing a localized confinement effect. This blockage introduces a subtle near-boundary inflection in both the isentropic Mach number and skin friction distributions, capturing a minor fraction of structural dissipation and yielding global loss coefficients marginally closer to experimental trends. Due to the lack of prescribed inlet turbulent fluctuations, boundary layers remain thin with highly localized, narrow loss peaks.

The integration of streamtube contraction (AVDR = 1.1) heavily alters the blade aerodynamic loading and flow topology. The contraction introduces a continuous favorable axial pressure gradient, resulting in a generally lower isentropic Mach number across the blade. Absolute skin friction values decrease on the pressure side, noticeably mitigating the pressure-side separation bubble. On the suction side, the additional streamwise momentum makes flow separations significantly less frequent and less severe. Shock wave topology changes at higher Mach numbers; the supersonic bubble at Mach 0.9 is flattened and crushed closer to the blade surface, while the M=1 sonic line at Mach 0.95 detaches from the trailing edge and shifts downstream due to altered Prandtl-Meyer expansion fans.

This investigation provided insights into the aerodynamic influence of spanwise boundary conditions and quasi-three-dimensional streamtube contraction on low-pressure turbine cascades. The results demonstrated that the predictive enhancement of the AVDR formulation is strictly contingent upon an exact calibration matching experimental operating points. Future work recommendations focus on exploring higher Reynolds numbers to trigger full three-dimensional flow structures and analyzing localized midspan wake loss profiles.